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I am bored

as i took the last bite from my corn muffin i realized that this was no corn muffin! its a chocolate whole wheat muffin i rushed home to tell my grandpa and he sad..................................blahblahbla

this bag is awesome

notch is cool cus he made cool minecraft therfore im cool because i found dirt and hey whats that?

i remember my grandpas first advise stay alive he told ZzzzzzzzzzzzzzzzzzzzzzzzZZZZZZZZZZZZZZZZZzzzzzzzzzzzzzzz oh hi there i forgot you were still there any ways

Hi.

(Insert Moby ****, Tale of Two Cities, and Pride and Prejudice here.)

o-o

Quote from CreepsInMyMind

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of quantity, structure, space, and change.^[2] Mathematicians seek outpatterns^[3][4] and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorousdeduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions.
Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapesand motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared inGreek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.^[5]
Galileo Galilei (1564–1642) said, 'The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth'.^[6] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences".^[7] Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions".^[8] David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."^[9] Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality".^[10]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.<sup>[11]


Etymology

The word "mathematics" comes from the Greek μάθημα (máthēma), which means in ancient Greek what one learns, what one gets to know, hence also study and science, and in modern Greek just lesson.
The word máthēma comes from μανθάνω (manthano) in ancient Greek and from μαθαίνω (mathaino) in modern Greek, both of which mean to learn.
The word "mathematics" in Greek came to have the narrower and more technical meaning "mathematical study", even in Classical times.[12] Its adjective is μαθηματικός (mathēmatikós), meaning related to learning or studious, which likewise further came to mean mathematical. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), Latin: ars mathematica, meant the mathematical art. In Latin, and in English until around 1700, the term "mathematics" more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This has resulted in several mistranslations: a particularly notorious one is Saint Augustine's warning that Christians should beware of "mathematici" meaning astrologers, which is sometimes mistranslated as a condemnation of mathematicians.
The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica(Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle (384-322BC), and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek.[13] In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.


The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[14] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[15]Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Since numeracy pre-dated writing, further steps were needed for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]</sup>

^{Mayan numerals}

^{The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[16] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.[17]
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviewsdatabase since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and theirproofs."[18]}

How interesting.... I see now the detailed history of mathematics and numbers and its evolution throughout the generations of research.

Interesting... I read it all! How informative!

Boredom is such an interesting topic. I never knew that boredom is more complex than just being bored!

The Complete Damage Formula for Diamond & Pearl

By X-Act and Peterko, updated by Kaphotics.

1. Introduction
2. The Damage Formula and How to Use It
3. The Base Power and Its Modifiers
[alphalist=A]

4. Moves having a Variable Base Power
5. Items that affect Base Power
6. User Abilities that affect Base Power
7. Foe Abilities that affect Base Power
[/alphalist]

8. The Attack and Special Attack stats and their Modifiers
[alphalist=A]

9. The Stat Modifier Multipliers
10. Abilities that change the Attack or Special Attack stat
11. Items that change the Attack or Special Attack stat
[/alphalist]

12. The Defense and Special Defense stats and their Modifiers
13. The First Modifier to the Damage Formula
14. The Second Modifier to the Damage Formula
15. The Third Modifier to the Damage Formula
16. Exceptional Cases

Introduction

The Damage Formula is one of the two most important calculations in a Pokemon game (the other one being the Stats Formula). Here, we provide the damage formula for Diamond, Pearl, and Platinum (DPP). Note that this formula is not the same as that for the games preceding DPP, so don't use it to calculate damage for other games.
I need to immediately thank Peterko for all the testing data he has provided for me. This guide wouldn't have seen the light of day without all his efforts. He literally triggered the damage formula thousands of times (not an exaggeration) during the game so that I could come up with such a detailed description of it. I cannot thank him enough for his efforts. Thank you Peterko... you are one of the best testers I've ever seen!
Section 1: The Damage Formula and How to Use It

Here is the damage formula for DPP:
Damage Formula = (((((((Level × 2 ÷ 5) + 2) × BasePower × [Sp]Atk ÷ 50) ÷ [Sp]Def) × Mod1) + 2) ×
CH × Mod2 × R ÷ 100) × STAB × Type1 × Type2 × Mod3)
where: Level The user's current level. BasePower The move's Base Power (after performing all necessary modifiers to it... see Section 2). [Sp]Atk The user's Attack or Special Attack stat (after performing all necessary modifiers to it... see Section 3). If the move used is physical, the Attack stat is utilized; otherwise, the Special Attack stat is used. [Sp]Def The foe's Defense or Special Defense stat (after performing all necessary modifiers to it... see Section 4). If the move used is physical, the Defense stat is utilized; otherwise, the Special Defense stat is used. Mod1 The first modifier to the damage formula. See Section 5 for more details. CH 3 if the move is a critical hit and the user has the Sniper ability, 2 if the move is a critical hit and the user's ability is not Sniper, and 1 otherwise. Mod2 The second modifier to the damage formula. See Section 6 for more details. R (100 - Rand), where Rand is a random whole number between 0 and 15 inclusive with uniform probability. This produces a whole number between 85 and 100 inclusive, with uniform probability. STAB 2 if the move is of the same type as that of the user and the user has the Adaptability ability, 1.5 if the move is of the same type as that of the user and the user's ability is not Adaptability, and 1 otherwise. This is known as Same Type Attack Bonus (hence STAB). Type1 2 if the move is super effective against the first type of the foe, 0.5 if the move is not very effective against the first type of the foe, 0 if the move type does not affect the first type of the foe, and 1 otherwise. Type2 2 if the move is super effective against the second type of the foe, 0.5 if the move is not very effective against the second type of the foe, 0 if the move type does not affect the type of the foe, and 1 otherwise (or if the foe has only one type). Mod3 The third modifier to the damage formula. See Section 7 for more details.
It should be immediately mentioned that after successfully performing an operator (an operator being +, -, × or ÷), you need to "round down" the number to the nearest whole number before performing the next one. In simple terms, this means to remove all the numbers to the right of the decimal point every time the answer is a decimal before proceeding with the next arithmetic operation.
If the damage formula's damage is 0 and the foe is not immune to the move used, the damage dealt will be 1 instead. This will happen if, say, a Level 2 Bidoof uses Tackle against a Level 100 Aggron. To paraphrase, unless the move does not affect the foe, the minimum amount of damage done is 1.
The way the formula is written above is such that you can actually ignore all the brackets and proceed from left to right (ignoring the BODMAS rules, so to speak) and still come up with the correct answer.
Let's provide an example here. For the sake of simplicity, we shall assume that Mod1, Mod2, and Mod3 are all 1 in this example.
Say we want to calculate the minimum and maximum damage that a Level 47 Staraptor with 140 Attack stat will deal with the move Aerial Ace against a Roserade with 77 Defense stat.

1. We start with the Level of Staraptor, 47, and multiply it by 2, getting 94.
2. Next, we divide 94 by 5, getting 18.8, which is rounded down to 18.
3. Next, we add 2 to 18, getting 20.
4. Next, we multiply 20 by 60 (the move power of Aerial Ace), getting 1200.
5. Next, we multiply 1200 by 140 (the Attack stat of Staraptor), getting 168000.
6. Next, we divide 168000 by 50, getting 3360.
7. Next, we divide 3360 by 77 (the Defense stat of Roserade), getting 43.636363..., which is rounded down to 43.
8. Next, we multiply 43 by 1 (Mod1 is 1 here), getting 43.***
9. Next, we add 2 to 43, getting 45.
10. Next, we multiply 45 by 1 (assuming that we didn't get a critical hit here), getting 45.***
11. Next, we multiply 45 by 1 (Mod2 is 1 here), getting 45.***
12. Next, we multiply 45 by 85 (the minimum number that the random number can be), getting 3825.
13. Next, we divide 3825 by 100, getting 38.25, which is rounded down to 38.
14. Next, we multiply 38 by 1.5 (since Aerial Ace is Flying-type, like one of Staraptor's types is), getting 57.
15. Next, we multiply 57 by 2 (since Aerial Ace is Flying-type, which is super effective against Roserade's first type, Grass), getting 114.
16. Next, we multiply 114 by 1 (since Aerial Ace is Flying-type, which is neutral against Roserade's second type, Poison), getting 114.***
17. Finally, we multiply 114 by 1 (Mod3 is 1 here), getting 114.***

So Staraptor's minimum damage would be 114.
For the maximum damage, we do exactly the same steps, except that we multiply by 100 instead of by 85 in Step 12. We get 134 as the maximum damage if we do that. Try it out. (If you do not get 134, make sure that you have actually rounded down your answer at EVERY step in the calculation.)
Note: The steps marked *** can be omitted, since multiplying by 1 does not change the answer.
Section 2: The Base Power and its Modifiers

The Base Power of the move might be considered to be simple, but in fact it can change by many things during the battle that can affect it.
So many, in fact, that it can be summarised by the following formula:
BasePower = HH × BP × IT × CHG × MS × WS × UA × FA
where HH 1.5 if the move has been boosted by the move Helping Hand by the partner, and 1 otherwise. BP The Base Power of the move. This is usually found easily, like 80 for Energy Ball, 60 for Aerial Ace, etc. Some moves have a variable BP, a list of which is given in Section 2A. IT The item multiplier. The list of items that affect Base Power, together with their effects, is given in Section 2B. CHG 2 if the Pokemon's last move was Charge and this move's type is Electric and 1 otherwise. MS 0.5 if one of the Pokemon in play used the move Mud Sport and this move's type is Electric, and 1 otherwise. WS 0.5 if one of the Pokemon in play used the move Water Sport and this move's type is Fire, and 1 otherwise. UA The user ability multiplier. A list of user abilities that affect Base Power, together with their effects, is given in Section 2C. FA The foe ability multiplier. A list of foe abilities that affect Base Power, together with their effects, is given in Section 2D.
The Base Power is calculated from left to right, and is rounded down before the next multiplication is performed. The order of the multiplications is as written in the formula above... changing the order might result in the incorrect Base Power.
Section 2A - Moves having a Variable Base Power

Here is a list of moves having variable Base Power. This Base Power is equal to BP in the Base Power formula. Move name Base Power Assurance 100 if the foe was hurt that turn, 50 otherwise. Avalanche 120 if the targeted Pokemon did damage to the user, 60 otherwise. Brine 130 if the targeted Pokemon's current HP is less than or equal to half of its maximum HP, rounded down, 65 otherwise. Crush Grip*** 1 + (120 × Foe's Current HP ÷ Foe's Max HP), rounded down. Eruption*** 150 × User's Current HP ÷ User's Max HP, rounded down. Facade 140 if the user is paralyzed, poisoned, or burned, 70 otherwise. Flail 200 if CP is between 0 and 1, 150 if CP is between 2 and 5, 100 if CP is between 6 and 12, 80 if CP is between 13 and 21, 40 if CP is between 22 and 42, and 20 if CP is between 43 and 64, where CP = User's Current HP × 64 ÷ User's Total HP, rounded down. Fling*** Check the move's page for more details. Frustration 102 - (User's Happiness × 2 ÷ 5), rounded down. If BP is 0, it becomes 1. Fury Cutter 10 if Fury Cutter was not already used or it missed when it was last used, otherwise, BP is double the BP of the last used Fury Cutter. If BP is greater than 160, it becomes 160. Grass Knot 20 if W is between 0 and 10, 40 if W is between 10.1 and 25, 60 if W is between 25.1 and 50, 80 if W is between 50.1 and 100, 100 if W is between 100.1 and 200, and 120 otherwise, where W is the weight of the foe in kilograms. Gyro Ball 1 + (25 × Foe's Speed ÷ User's Speed), rounded down. If BP is greater than 150, it becomes 150. Ice Ball If Defense Curl was used by the user in any of the previous turns, then 60 for the first turn that Ice Ball is used, followed by 120, 240, 480 and 960 for the second, third, fourth and fifth turns respectively. If Defense Curl was not used by the user in any of the previous turns, then 30 for the first turn that Ice Ball is used, then 60, 120, 240, and 480 for the second, third, fourth and fifth turns respectively. If Ice Ball fails, BP restarts from 60 or 30 in its next usage. Hidden Power Check the move's page for more details. Low Kick 20 if W is between 0 and 10, 40 if W is between 10.1 and 25, 60 if W is between 25.1 and 50, 80 if W is between 50.1 and 100, 100 if W is between 100.1 and 200, and 120 otherwise, where W is the weight of the foe in kilograms. Magnitude 10 if R is between 0 and 4 (Magnitude 4), 30 if R is between 5 and 14 (Magnitude 5), 50 if R is between 15 and 34 (Magnitude 6), 70 if R is between 35 and 64 (Magnitude 7), 90 if R is between 65 and 84 (Magnitude 8), 110 if R is between 85 and 94 (Magnitude 9), and 150 if R is between 95 and 99 (Magnitude 10), where R is a random whole number between 0 and 99 with uniform probability. Natural Gift Check the move's page for more details Nature Power Becomes Earthquake if the location is on a road or in the desert, Tri Attack if the location is inside a building (this is the default choice in battles), Seed Bomb if the location is on grass or tall grass, Rock Slide if the location is in a cave or on a mountain, Blizzard if the location is on snow, and Hydro Pump if the location is on a pond or in the sea. Payback 100 if the targeted Pokemon moves before the user, 50 otherwise. Present*** 40 if R is between 0 and 102, 80 if R is between 103 and 179, 120 if R is between 179 and 204, and 0 and the foe is healed by 80 HP otherwise, where R is a random whole number between 0 and 255 inclusive, with uniform probability. Punishment 60 + (20 × Sum of positive stat modifiers of the foe). If BP is greater than 200, it becomes 200. Pursuit 80 if the foe switches out during that turn, 40 otherwise. Return User's Happiness × 2 ÷ 5, rounded down. If BP is 0, it becomes 1. Revenge 120 if the targeted Pokemon did damage to the user, 60 otherwise. Reversal 200 if CP is between 0 and 1, 150 if CP is between 2 and 5, 100 if CP is between 6 and 12, 80 if CP is between 13 and 21, 40 if CP is between 22 and 42, and 20 if CP is between 43 and 64, where CP = User's Current HP × 64 ÷ User's Total HP, rounded down. Rollout If Defense Curl was used by the user in any of the previous turns, then 60 for the first turn that Rollout is used, followed by 120, 240, 480 and 960 for the second, third, fourth and fifth turns, respectively. If Defense Curl was not used by the user in any of the previous turns, then 30 for the first turn that Rollout is used, then 60, 120, 240, and 480 for the second, third, fourth and fifth turns, respectively. If Rollout fails, BP restarts from 60 or 30 in its next usage. SmellingSalt 120 if the foe is paralyzed (and is healed from paralysis afterwards), 60 otherwise. Spit Up 100 if one Stockpile was used, 200 if two Stockpiles were used, 300 if three Stockpiles were used, 0 otherwise. Stomp 130 if the foe used the move Minimize, 65 otherwise. Triple Kick 10 in the first kick, 20 in the second kick, 30 in the third kick. Trump Card 40 if P is at least 4, 50 if P is 3, 60 if P is 2, 80 if P is 1, and 200 if P is 0, where P is the PP of Trump Card after being used. Wake-Up Slap 120 if the foe is asleep (and is healed from sleep afterwards), 60 otherwise. Water Spout*** 150 × User's Current HP ÷ User's Max HP, rounded down. Weather Ball 100 if the weather is Sunny Day, Rain Dance, Sandstorm, Hail, or Fog, 50 otherwise. Wring Out 1 + (120 × Foe's Current HP ÷ Foe’s Max HP), rounded down.
*** - Exact BP not confirmed.
Section 2B - Items that affect Base Power

The following items equipped to the user provide the following boost to the IT multiplier: Item name IT multiplier Muscle Band 1.1 if the move used is physical, 1 otherwise. Wise Glasses 1.1 if the move used is special, 1 otherwise. Type-boosting items, plates and incenses 1.2 if the move used is of the same type as the type that the item, plate or incense boosts, 1 otherwise. Adamant Orb 1.2 if the user is Dialga and the move used is Steel- or Dragon-type, 1 otherwise. Lustrous Orb 1.2 if the user is Palkia and the move used is Water- or Dragon-type, 1 otherwise. Griseous Orb 1.2 if the user is Giratina and the move used is Ghost- or Dragon-type, 1 otherwise. Any other item 1.
Section 2C - User Abilities that affect Base Power

The following abilities provide the following numbers to the UA multiplier if the user has one of them: User ability UA multiplier Rivalry 1.25 if the user is of the same gender as the targeted Pokemon, 0.75 if the user is of the opposite gender of the targeted Pokemon, 1 otherwise. Reckless 1.2 if the user uses a recoil move, 1 otherwise. Iron Fist 1.2 if the user uses a punching move, 1 otherwise. Blaze 1.5 if the user uses a Fire move and its current HP is less than 1/3 of its maximum HP (rounded down), 1 otherwise. Overgrow 1.5 if the user uses a Grass move and its current HP is less than 1/3 of its maximum HP (rounded down), 1 otherwise. Torrent 1.5 if the user uses a Water move and its current HP is less than 1/3 of its maximum HP (rounded down), 1 otherwise. Swarm 1.5 if the user uses a Bug move and its current HP is less than 1/3 of its maximum HP (rounded down), 1 otherwise. Technician 1.5 if the user uses a move with BP at most 60, 1 otherwise. All other user abilities 1.
Section 2D - Foe Abilities that affect Base Power

The following abilities provide the following numbers to the FA multiplier if the foe has one of them: Foe ability FA multiplier Thick Fat 0.5 if the user is using an Ice or Fire move, 1 otherwise. Heatproof 0.5 if the user is using a Fire move, 1 otherwise. Dry Skin 1.25 if the user is using a Fire move, 1 otherwise. All other foe abilities 1.
Section 3 - The Attack and Special Attack stats and their Modifiers

The Attack and Special Attack stats can also be changed throughout the match by various things.
[Sp]Atk = Stat × SM × AM × IM
where: Stat The normal Attack or Special Attack stat. SM The stat modifier multiplier. See Section 3A for more information. AM The ability modifier. See Section 3B for a list of abilities that change the attacking stats. IM The item modifier. See Section 3C for a list of items that change the attacking stats.
As we said for the calculation of the Base Power, the above multiplication is also performed from left to right, rounding down before performing the next one.
Section 3A - The Stat Modifier Multipliers

Each stat (excluding HP) has a stat modifier which is a whole number between -6 and 6 inclusive. This stat modifier starts from 0 and is changed by various moves like Swords Dance and Defense Curl. Some attacks can also change either the user’s stat modifier or that of the foe as a secondary effect, like Overheat and Shadow Ball.
The effect of SM is the following: Stat Modifier SM multiplier Decimal Approximate -6 2/8 0.25 -5 2/7 0.2857 -4 2/6 0.3333 -3 2/5 0.4 -2 2/4 0.5 -1 2/3 0.6667 0 2/2 1 +1 3/2 1.5 +2 4/2 2 +3 5/2 2.5 +4 6/2 3 +5 7/2 3.5 +6 8/2 4
A few points: Critical Hits If the Stat Modifier for Attack or Special Attack is less than zero, SM is made equal to 1 if the attack hits for a critical hit. Also, if the Stat Modifier for Defense or Special Defense is greater than zero, SM is made equal to 1 if the attack hits for a critical hit. Unaware If the user has the ability Unaware, SM for Defense or Special Defense of the foe is made equal to 1. If the foe has the ability Unaware, SM for Attack or Special Attack of the user is made equal to 1. Simple If any Pokemon has the ability Simple, SM conforms to a different chart, as shown below. Stat Modifier SM multiplier Decimal Approximate -3 to -6 2/8 0.25 -2 2/6 0.3333 -1 2/4 0.5 0 2/2 1 +1 4/2 2 +2 6/2 3 +3 to +6 8/2 4
Section 3B - Abilities that change the Attack or Special Attack stat

Here is a list of abilities that modify the Attack or Special Attack stat of the user, which affect the AM multiplier:
Abilities that affect the Attack stat: Ability name AM multiplier Pure Power 2. Huge Power 2. Flower Gift 1.5 if Sunny Day is in effect, AM = 1 otherwise. Guts 1.5 if the user is paralyzed, poisoned, burned, or asleep, AM = 1 otherwise. Hustle 1.5 (and physical moves have 80% accuracy). Slow Start 0.5 if the user has been in the battlefield for less than 5 turns, AM = 1 otherwise. Other abilities 1.
If there are two simultaneous boosts in the Attack stat, first apply the attacking Pokemon's ability boost, then the allies ability boost.
Abilities that affect the Special Attack stat: Ability name AM multiplier Plus 1.5 if the partner has ability Minus, 1 otherwise. Minus 1.5 if the partner has ability Plus, 1 otherwise. Solar Power 1.5 if Sunny Day is in effect (and loses 1/8 of HP per turn), 1 otherwise. Other abilities 1.
Section 3C - Items that change the Attack or Special Attack stat

Here is a list of items that modify the Attack or Special Attack stat of the user, which affect the IM multiplier:
Items that affect the Attack stat: Item name IM multiplier Choice Band 1.5 (the user can't use any other move). Light Ball 2 if the user is Pikachu, 1 otherwise. Thick Club 2 if the user is Cubone or Marowak, 1 otherwise. Other items 1.
Items that affect the Special Attack stat: Item name IM multiplier Choice Specs 1.5 (the user can't use any other move). Light Ball 2 if the user is Pikachu, 1 otherwise. Soul Dew 1.5 if the user is Latios or Latias, 1 otherwise. Deepseatooth 2 if the user is Clamperl, 1 otherwise. Other items 1.
Section 4 - The Defense and Special Defense stats and their Modifiers

Various changes can also be performed to the Defense and Special Defense stats of the foe during a match.
In this case, there aren't many things that can change the Defense or Special Defense stats:
[Sp]Def = Stat × SM × Mod × SX
where: Stat The normal Defense or Special Defense stat. SM The stat modifier multiplier. See Section 3A for more information. SX 0.5 if the move used by the user is Selfdestruct or Explosion, otherwise 1. Mod A modifier depending on a few factors. These are as follows:
Defense modifiers:
Name Modifier Metal Powder 1.5 if the foe is Ditto, is holding the item Metal Powder and has not used the move Transform. Marvel Scale 1.5 if the foe has the ability Marvel Scale and is paralysed, poisoned, burned, asleep, or frozen.
Special Defense modifiers:
Name Modifier Sandstorm 1.5 if Sandstorm is in effect and the foe is of Rock-type. Soul Dew 1.5 if the foe is Latios or Latias and is holding the item Soul Dew. Metal Powder 1.5 if the foe is Ditto, is holding the item Metal Powder and has not used the move Transform. Deepseascale 2 if the foe is Clamperl and is holding the item Deepseascale. Flower Gift 1.5 if one of the foes has the ability Flower Gift and Sunny Day is in effect.
Otherwise, Mod = 1.
Again, remember to multiply from left to right and round down after each multiplication.
If there are two simultaneous boosts in Mod, first apply the ability boost, then the item boost, and finally the Sandstorm boost.
If the Defense or Special Defense stat is equal to zero after all these modifiers, it becomes 1 instead.
Section 5 - The First Modifier to the Damage Formula

This section will explain the function of Mod1, the first modifier to the damage formula.
Mod1 = BRN × RL × TVT × SR × FF
where: BRN The Burn modifier RL The Reflect/Light Screen modifier TVT The 2v2 modifier SR The Sunny Day/Rain Dance modifier FF The Flash Fire modifier
BRN is 0.5 if the move performed is physical, the user is affected by the burn special condition and the user's ability is not Guts, and 1 otherwise.
RL is:

• 0.5 if the move performed is physical, the foe has setup a Reflect and the game is 1vs1.
• 0.5 if the move performed is special, the foe has setup a Light Screen and the game is 1vs1.
• 2/3 if the move performed is physical, the foe has setup a Reflect and the game is 2v2.
• 2/3 if the move performed is special, the foe has setup a Light Screen and the game is 2v2.
• 1 otherwise.

Also, if the move is a critical hit, RL is made equal to 1 no matter what.
TVT is 0.75 if the game is 2v2 and the move used hits more than one Pokemon, and 1 otherwise. Note: These moves don't always hit for 75% damage. Research on what conditions trigger the 75% damage is being carried out.
SR is:

• 1.5 if Sunny Day is in effect and the move is of Fire-type.
• 1.5 if Rain Dance is in effect and the move is of Water-type.
• 0.5 if Sunny Day is in effect and the move is of Water-type.
• 0.5 if Rain Dance is in effect and the move is of Fire-type.
• 1 otherwise.

FF is 1.5 if the user has the ability Flash Fire, was previously attacked by a move that is of Fire-type, and is using a Fire move, 1 otherwise.
Yet again, it must be emphasized that the order of the multiplication must be as written above.
Section 6 - The Second Modifier to the Damage Formula

This section explains what affects Mod2, the second modifier of the damage formula.
Mod2 is

• 1.3 if the user is holding the item Life Orb.
• 1, 1.1, 1.2, 1.3, ..., 2 if the user is holding the item Metronome and has used the same move once, twice, three times, four times, ... etc. consecutively.
• 1.5 if the user is attacking with the move Me First.
• 1 otherwise.

In the case when the Pokemon is using Me First and is also holding the item Life Orb or Metronome, the item boost multiplier is done first, followed by the Me First (x1.5) multiplier.
Section 7 - The Third Modifier to the Damage Formula

Finally, we come to the third and final modifier to the damage formula, Mod3.
Mod3 = SRF × EB × TL × TRB
where: SRF The Solid Rock/Filter modifier EB The Expert Belt modifier TL The Tinted Lens modifier TRB The type-resisting Berry modifier
SRF is 0.75 if the foe's ability is Solid Rock or Filter and the move used is super effective against it, and 1 otherwise.
EB is 1.2 if the user is holding the item Expert Belt and the move used is super effective against the foe, and 1 otherwise.
TL is 2 if the user's ability is Tinted Lens and the move used is not very effective against the foe, and 1 otherwise.
TRB is:

• 0.5 if the foe is holding one of the type resisting Berries and the move used is super effective and of the same type as the type that the Berry knocks down.
• 0.5 if the foe is holding Chilan Berry and the move used is Normal-type.
• 1 otherwise.

Remember once again that the multiplication must be carried out in the order listed above.
Section 8 - Exceptional Cases

The eighth and final section will concern moves that do not follow the damage formula to the rule.

1. Doom Desire and Future Sight use a slightly different variation of the damage formula for the calculation of the damage dealt two turns after they are used. They use the Special Defense stat of the foe that was targeted when the move was used. Type1 and Type2 are also both equal to 1 irrespective of the type of the Pokemon that is being dealt damage.
2. When Spit Up is used, the variable R in the damage formula (i.e. the random number between 85 and 100) is always taken to be 100.
3. Pain Split does not even do damage. The user's remaining HP and that of the foe are averaged and rounded down, and then both are set to this value.
4. There are certain moves that do not use the usual damage formula to determine the damage done to the foe. Here is a list of them, and how to determine the damage dealt by each: Bide Damage is equal to twice the damage received during the last two turns to the last Pokemon attacking the user. Counter Damage is equal to twice the damage received from the last Pokemon attacking the user during that turn, if the move used was physical. Dragon Rage Damage is always 40. Endeavor Damage is equal to the foe's remaining HP minus the user's remaining HP. It fails if this number is not positive. Fissure, Guillotine, Horn Drill and Sheer Cold Damage is equal to the foe's maximum HP (even if the foe is behind a substitute, in which case this amount of damage is dealt to the substitute instead). Metal Burst Damage is equal to 1.5 times the damage received from the last Pokemon attacking the user during that turn. Fails if that Pokemon is your partner. Mirror Coat Damage is equal to twice the damage received from the last Pokemon attacking the user during that turn, if the move used was special. Night Shade Damage is equal to the user's Level. Psywave Damage is equal to (R + 5) × Level ÷ 10, rounded down, where R is a random whole number between 0 and 10 inclusive with uniform probability, and Level is the user's Level. Seismic Toss Damage is equal to the user's Level. SonicBoom Damage is always 20. Super Fang Damage is equal to half the foe's remaining HP, rounded down. (If this damage is 0, it becomes 1 instead.)

So, I was walking in a street. There were more people there. I ate a hamburger. End of story.

Brush cyl 22 6 4

command not found: Fail


derped farlands

(Insert Every Episode Ever Made and Every Episode To Be Made of Grey's Anatomy Here)

Beat that sucka.

Future Nyan and DJ Pon-3 walking down the street...

AND THERE WAS A BEAR CHASING THEM INTO AN AVATAR!!!!

They realized that was my avatar. I lock them inside.

This post is a derp.

A B C D E F G H I K oops forgot J L M N O P Q S R T U V W Y X Z now I know my ABQ's next time wont you eat your pet Emu?

haha,now here's mine!



The modern world is an electrified world. The light bulb, in particular, profoundly changed human existence by illuminating the night and making it hospitable to a wide range of human activity. The electric light, one of the everyday conveniences that most affects our lives, was invented in 1879 by Thomas Alva Edison. He was neither the first nor the only person trying to invent an incandescent light bulb. THE STORY
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HOW IT WORKS
DID YOU KNOW? Invention: electric light bulb in 1879
Definition: noun / electric light bulb / incandescent lamp Function: An electric lamp in which a filament is heated to incandescence by an electric current. Today's incandescent light bulbs use filaments made of tungsten rather than carbon of the 1880's. Patent: 223,898 (US) issued January 27, 1880 Inventor: Thomas Alva Edison
Criteria: First practical. Modern prototype. Entrepreneur. Birth: February 11, 1847 in Milan, Ohio Death: October 18, 1931 in West Orange, New Jersey Nationality: American


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The world's oldest light bulb has been burning for 109 years - so little wonder it has a fan club with thousands of members and its own website.

As EU rules deny householders the right to use traditional filament bulbs, the so-called 'Centennial Light' has been on almost constantly since 1901.

It holds pride of place in Fire Station 6, in Livermore, northern California.

The longest time the Guinness World Record-holding bulb has ever been turned off for is just a week.

Dangling above the fire engines, people come for hundreds and thousands of miles to see the diminutive symbol.

The bulb was designed by Adolphe Chailet, who competed with the likes of the world famous Thomas Edison to make the best bulb.

Despite his amazing design Chailet was never as successful as Edison even though his bulb was proved to survive higher voltages.

Bulb protector Steve Bunn said the secret of the lights success was down to good old fashioned engineering.

He said: 'They certainly don't make them like this anymore, it's a real sign of how some things were better made in the past.

'The man who invented the bulb was Adolphe Chailet and he sounded by all accounts to be a very serious person.

'But when it comes to spark, he did perform an experiment where several competitors, including Edison.

'All the bulbs were subjected to a test of increasing voltage, and exploded, all except for Chailet's which just got brighter.

'That would have been fun to watch.

'The appeal of the light is worldwide, a few weeks ago I received a message from someone living in

Read more: http://www.dailymail.co.uk/news/article-1243138/Still-glowing-strong-109-years-worlds-oldest-lightbulb.html#ixzz1sq7XXUMA

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The Apple (a.k.a. Star Rock) is a 1979 musical science fiction film starring Catherine Mary Stewart and directed by Menahem Golan. It is a discoesque rock opera-styled feature, set in a futuristic 1994, dealing with themes of conformity versus rebellion and infused with Biblical allegories (namely the tale of Adam and Eve). It is one of the few movie musicals that has not yet been a live musical.
The film was a low budget attempt by the young Cannon studio to capitalize on the success of music-oriented films like Saturday Night Fever and Grease. Set in America but filmed in Germany, it was released in West Germany as Star Rock in 1979. The film was critically panned and a box office bomb when given an extremely limited U.S. release in the fall of 1980 under its current title. It may have underperformed in theaters because of the waning popularity of disco music and its rathercampy plotline. However, in later years the film has gone on to enjoy a small cult following.

all acknowledgements go to the wiki i got this from.

The United States is a federal constitutional republic, in which the President of the United States (the head of state and head of government), Congress, and judiciary share powers reserved to the national government, and the federal government shares sovereignty with the state governments.
The executive branch is headed by the President and is independent of the legislature. Legislative power is vested in the two chambers of Congress, the Senate and the House of Representatives. The judicial branch (or judiciary), composed of the Supreme Court and lower federal courts, exercises judicial power (or judiciary). The judiciary's function is to interpret the United States Constitution and federal laws and regulations. This includes resolving disputes between the executive and legislative branches. The federal government's layout is explained in the Constitution. Two political parties, the Democratic Party and the Republican Party, have dominated American politics since the American Civil War, although other parties have also existed.
There are major differences between the political system of the United States and that of most other developed democracies. These include greater power in the upper house of the legislature, a wider scope of power held by the Supreme Court, the separation of powers between the legislature and the executive, and the dominance of only two main parties. Third parties have less political influence in the United States than in other developed country democracies.
The federal entity created by the U.S. Constitution is the dominant feature of the American governmental system. However, most people are also subject to a state government, and all are subject to various units of local government. The latter include counties, municipalities, and special districts.
This multiplicity of jurisdictions reflects the country's history. The federal government was created by the states, which as colonies were established separately and governed themselves independently of the others. Units of local government were created by the colonies to efficiently carry out various state functions. As the country expanded, it admitted new states modeled on the existing ones.

Visual Overview of Electoral System

Contents
[hide]

• 1 Political culture
• 1.1 Colonial origins
• 1.2 American ideology
• 1.3 Suffrage
• 2 State government
• 3 Local government
• 3.1 Mayor-Council
• 3.2 The Commission
• 3.3 Council-Manager
• 3.4 County government
• 3.5 Town and village government
• 4 Campaign finance
• 5 Political parties and elections
• 5.1 Political parties
• 5.2 Elections
• 5.3 Organization of American political parties
• 5.4 General developments
• 5.5 Development of the two-party system in the United States
• 6 Political pressure groups
• 7 Reform
• 8 See also
• 9 References
• 9.1 Further reading
• 10 External links

[edit] Political culture

[edit] Colonial origins

Main articles: Colonial history of the United States and Thirteen Colonies
The American political culture is deeply rooted in the colonial experience and the American Revolution. The colonies were exceptional in the European world for their vibrant political culture, which attracted the most talented and ambitious young men into politics.^[1] First, suffrage was the most widespread in the world, with every man who owned a certain amount of property allowed to vote. While fewer than 1% of British men could vote, a majority of white American men were eligible. While the roots of democracy were apparent, nevertheless deference was typically shown to social elites in colonial elections.^[2] That deference declined sharply with the American Revolution. Second, in each colony a wide range of public and private business was decided by elected bodies, especially the assemblies and county governments.^[3] Topic of public concern and debate included land grants, commercial subsidies, and taxation, as well as oversight of roads, poor relief, taverns, and schools. Americans spent a great deal of time in court, as private lawsuits were very common. Legal affairs were overseen by local judges and juries, with a central role for trained lawyers. This promoted the rapid expansion of the legal profession, and dominant role of lawyers in politics was apparent by the 1770s, as attested by the careers of John Adams and Thomas Jefferson, among many others.^[4] Thirdly, the American colonies were exceptional in world context because of the growth of representation of different interest groups. Unlike Europe, where the royal court, aristocratic families and the established church were in control, the American political culture was open to merchants, landlords, petty farmers, artisans, Anglicans, Presbyterians, Quakers, Germans, Scotch Irish, Yankees, Yorkers, and many other identifiable groups. Over 90% of the representatives elected to the legislature lived in their districts, unlike England where it was common to have a member of Parliament and absentee member of Parliament. Finally, and most dramatically, the Americans were fascinated by and increasingly adopted the political values of Republicanism, which stressed equal rights, the need for virtuous citizens, and the evils of corruption, luxury, and aristocracy.^[5] None of the colonies had political parties of the sort that formed in the 1790s, but each had shifting factions that vied for power.
[edit] American ideology

Republicanism, along with a form of classical liberalism remains the dominant ideology. Central documents include the Declaration of Independence (1776), the Constitution (1787), the Federalist Papers (1788), the Bill of Rights (1791), and Lincoln's "Gettysburg Address" (1863), among others. Among the core tenets of this ideology are the following:^[6]

• Civic duty: citizens have the responsibility to understand and support the government, participate in elections, pay taxes, and perform military service.
• Opposition to Political corruption.
• Democracy: The government is answerable to citizens, who may change the representatives through elections.
• Equality before the law: The laws should attach no special privilege to any citizen. Government officials are subject to the law just as others are.
• Freedom of religion: The government can neither support nor suppress religion.
• Freedom of speech: The government cannot restrict through law or action the personal, non-violent speech of a citizen; a marketplace of ideas.

At the time of the United States' founding, the economy was predominantly one of agriculture and small private businesses, and state governments left welfare issues to private or local initiative. Laissez-faire ideology was largely discredited during the Great Depression. Between the 1930s and 1970s, fiscal policy was characterized by the Keynesian consensus, a time during which modern American liberalism dominated economic policy virtually unchallenged. Since the late 1970s and early 1980s, however, laissez-faire ideology, as explained especially by Milton Friedman, has once more become a powerful force in American politics.^[7] While the American welfare state expanded more than threefold after WWII, it has been at 20% of GDP since the late 1970s.^[8][9] Today, modern American liberalism, and modern American conservatism are engaged in a continuous political battle, characterized by what the Economist describes as "greater divisiveness [and] close, but bitterly fought elections."^[10]
[edit] Suffrage

Main article: Voting rights in the United States
Suffrage is nearly universal for citizens 18 years of age and older. All states and the District of Columbia contribute to the electoral vote for President. However, the District, and other U.S. holdings like Puerto Rico and Guam, lack representation in Congress. These constituencies do not have the right to choose any political figure outside their respective areas. Each commonwealth, territory, or district can only elect a non-voting delegate to serve in the House of Representatives.
Woman's Suffrage
Women’s suffrage became an important issue after the American Civil War. The reason it rose to the forefront is because after the war African American men were granted the right to vote. After that, women wanted to have the right to vote as well. Two major interest groups were formed. The first group was the National Woman Suffrage Association, formed by Susan B. Anthony and Elizabeth Cady Stanton. The main purpose of this group of women was to work for suffrage on the federal level and to push for more governmental changes, such as the granting of property rights to married women.^[11] The second group that was formed was the American Woman Suffrage Association, formed by Lucy Stone. The main goal of this group was to give women the right to vote ^[12] All of these women had one goal; they wanted political equality for women, which would lead to an expansion of economic rights as well. In 1890, the two groups merged to form the National American Woman Suffrage Association (NAWSA). The NAWSA mobilized state by state to obtain the vote. In 1920, the 19th amendment to the U.S. Constitution was passed, saying that the right to vote could not be denied because of gender.^[13]
[edit] State government

See also: State governments of the United States
States governments have the power to make laws for all citizens that are not granted to the federal government or denied to the states in the U.S. Constitution.These include education, family law, contract law, and most crimes. Unlike the federal government, which only has those powers granted to it in the Constitution, a state government has inherent powers allowing it to act unless limited by a provision of the state or national constitution.
Like the federal government, state governments have three branches: executive, legislative, and judicial. The chief executive of a state is its popularly elected governor, who typically holds office for a four-year term (although in some states the term is two years). Except for Nebraska, which has unicameral legislature, all states have a bicameral legislature, with the upper house usually called the Senate and the lower house called the House of Representatives, the House of Delegates, Assembly or something similar. In most states, senators serve four-year terms, and members of the lower house serve two-year terms.
The constitutions of the various states differ in some details but generally follow a pattern similar to that of the federal Constitution, including a statement of the rights of the people and a plan for organizing the government. However, state constitutions are generally more detailed.
[edit] Local government

See also: Urban politics in the United States
There are 89,500 local governments, including 3,033 counties, 19,492 municipalities, 16,500 townships, 13,000 school districts, and 37,000 other special districts that deal with issues like fire protection.^[14] Local governments directly serve the needs of the people, providing everything from police and fire protection to sanitary codes, health regulations, education, public transportation, and housing. Typically local elections are nonpartisan--local activists suspend their party affiliations when campaigning and governing.^[15]
About 28% of the people live in cities of 100,000 or more population. City governments are chartered by states, and their charters detail the objectives and powers of the municipal government. For most big cities, cooperation with both state and federal organizations is essential to meeting the needs of their residents. Types of city governments vary widely across the nation. However, almost all have a central council, elected by the voters, and an executive officer, assisted by various department heads, to manage the city's affairs. Cities in the West and South usually have nonpartisan local politics.
There are three general types of city government: the mayor-council, the commission, and the council-manager. These are the pure forms; many cities have developed a combination of two or three of them.
[edit] Mayor-Council

This is the oldest form of city government in the United States and, until the beginning of the 20th century, was used by nearly all American cities. Its structure is like that of the state and national governments, with an elected mayor as chief of the executive branch and an elected council that represents the various neighborhoods forming the legislative branch. The mayor appoints heads of city departments and other officials, sometimes with the approval of the council. He or she has the power of veto over ordinances (the laws of the city) and often is responsible for preparing the city's budget. The council passes city ordinances, sets the tax rate on property, and apportions money among the various city departments. As cities have grown, council seats have usually come to represent more than a single neighborhood.
[edit] The Commission

This combines both the legislative and executive functions in one group of officials, usually three or more in number, elected city-wide. Each commissioner supervises the work of one or more city departments. Commissioners also set policies and rules by which the city is operated. One is named chairperson of the body and is often called the mayor, although his or her power is equivalent to that of the other commissioners.^[16]
[edit] Council-Manager

The city manager is a response to the increasing complexity of urban problems that need management ability not often possessed by elected public officials. The answer has been to entrust most of the executive powers, including law enforcement and provision of services, to a highly trained and experienced professional city manager.
The city manager plan has been adopted by a large number of cities. Under this plan, a small, elected council makes the city ordinances and sets policy, but hires a paid administrator, also called a city manager, to carry out its decisions. The manager draws up the city budget and supervises most of the departments. Usually, there is no set term; the manager serves as long as the council is satisfied with his or her work.
[edit] County government

The county is a subdivision of the state, sometimes (but not always) containing two or more townships and several villages. New York City is so large that it is divided into five separate boroughs, each a county in its own right. On the other hand, Arlington County, Virginia, the United States' smallest county, located just across the Potomac River from Washington, D.C., is both an urbanized and suburban area, governed by a unitary county administration. In other cities, both the city and county governments have merged, creating a consolidated city–county government.
In most U.S. counties, one town or city is designated as the county seat, and this is where the government offices are located and where the board of commissioners or supervisors meets. In small counties, boards are chosen by the county; in the larger ones, supervisors represent separate districts or townships. The board collects taxes for state and local governments; borrows and appropriates money; fixes the salaries of county employees; supervises elections; builds and maintains highways and bridges; and administers national, state, and county welfare programs. In very small counties, the executive and legislative power may lie entirely with a sole commissioner, who is assisted by boards to supervise taxes and elections. In some New England states, counties do not have any governmental function and are simply a division of land.
[edit] Town and village government

Thousands of municipal jurisdictions are too small to qualify as city governments. These are chartered as towns and villages and deal with local needs such as paving and lighting the streets, ensuring a water supply, providing police and fire protection, and waste management. In many states of the US, the term town does not have any specific meaning; it is simply an informal term applied to populated places (both incorporated and unincorporated municipalities). Moreover, in some states, the term town is equivalent to how civil townships are used in other states.
The government is usually entrusted to an elected board or council, which may be known by a variety of names: town or village council, board of selectmen, board of supervisors, board of commissioners. The board may have a chairperson or president who functions as chief executive officer, or there may be an elected mayor. Governmental employees may include a clerk, treasurer, police and fire officers, and health and welfare officers.
One unique aspect of local government, found mostly in the New England region of the United States, is the town meeting. Once a year, sometimes more often if needed, the registered voters of the town meet in open session to elect officers, debate local issues, and pass laws for operating the government. As a body, they decide on road construction and repair, construction of public buildings and facilities, tax rates, and the town budget. The town meeting, which has existed for more than three centuries in some places, is often cited as the purest form of direct democracy, in which the governmental power is not delegated, but is exercised directly and regularly by all the people.
[edit] Campaign finance

Main article: Campaign finance in the United States
Successful participation, especially in federal elections, requires large amounts of money, especially for television advertising.^[17] This money is very difficult to raise by appeals to a mass base,^[18] although in the 2008 election, candidates from both parties had success with raising money from citizens over the Internet,^[19] as had Howard Dean with his Internet appeals. Both parties generally depend on wealthy donors and organizations - traditionally the Democrats depended on donations from organized labor while the Republicans relied on business donations^{[citation needed]}. This dependency on donors is controversial, and has led to laws limiting spending on political campaigns being enacted (see campaign finance reform). Opponents of campaign finance laws cite the First Amendment's guarantee of free speech, and challenge campaign finance laws because they attempt to circumvent the people's constitutionally guaranteed rights. Even when laws are upheld, the complication of compliance with the First Amendment requires careful and cautious drafting of legislation, leading to laws that are still fairly limited in scope, especially in comparison to those of other countries such as the United Kingdom, France or Canada.
Fundraising plays a large role in getting a candidate elected to public office. Without large sums money, a candidate has no chance of achieving their goal. In 2004 general elections, 95% of House races and 91% of senate races were won by candidates who spent the most on his campaign. (howstuffworks.com) Attempts to limit the influence of money on American political campaigns dates back to the 1860s. Recent, Congress passed legislation requiring candidates to disclose. Sources of campaign contributions and how the money is spent and regulated use of “soft money” contributions. (brookings.edu)^[20] The best and most comprehensive reform is voluntary public financing of all federal elections where candidates have strong incentives to replace private money with public funding. http://www.cleanupwashington.org/cfr/ Elections represent the will of the people rather than the influence of moneyed interests. (publiccitizen.com)^[21]
The 2012 presidential campaign was slow to develop in both candidates and fundraising. EX: By the end of September, the financial positions of Republican contenders in the cycle were worse than those of Democrats at the same point in the 2004 campaign. (opensecrets.org) EXAMPLE: Candidates running for office in Georgia come under one of two sets of laws, federal and state, that govern the raising and spending of campaign finance laws have been frequent targets of reform efforts.
[edit] Political parties and elections

The United States Constitution has never formally addressed the issue of political parties, primarily because the Founding Fathers did not originally intend for American politics to be partisan. In Federalist Papers No. 9 and No. 10, Alexander Hamilton and James Madison, respectively, wrote specifically about the dangers of domestic political factions. In addition, the first President of the United States, George Washington, was not a member of any political party at the time of his election or throughout his tenure as president. Furthermore, he hoped that political parties would not be formed, fearing conflict and stagnation.^[22] Nevertheless, the beginnings of the American two-party system emerged from his immediate circle of advisers, including Hamilton and Madison.
In partisan elections, candidates are nominated by a political party or seek public office as an independent. Each state has significant discretion in deciding how candidates are nominated, and thus eligible to appear on the election ballot. Typically, major party candidates are formally chosen in a party primary or convention, whereas minor party and Independents are required to complete a petitioning process.
[edit] Political parties

Main article: Political parties in the United States
The modern political party system in the United States is a two-party system dominated by the Democratic Party and the Republican Party. These two parties have won every United States presidential election since 1852 and have controlled the United States Congress since at least 1856. Several other third parties from time to time achieve relatively minor representation at the national and state levels.
Among the two major parties, the Democratic Party generally positions itself as left-of-center in American politics and supports an American liberalism platform, while the Republican Party generally positions itself as right-of-center and supports an American conservatism platform.
Political Animals
When most people talk about politics, some think of the animals that have been used to represent each of the parties. The two animals that are used are the donkey and the elephant; the elephant representing the Republican Party and the donkey representing the Democratic Party. A very popular cartoonist, in the early years of U.S. political satire, was Thomas Nast. A German immigrant who grew up in New York State, Nast to use humor to show what was going on in politics. He is well known for many cartoons regarding specific parts of politics that sparked his interest, but he introduced the two animals. Many political figures liked the idea of having an animal represent them. The Democratic Party said they liked the donkey because it represented their party as brave and intelligent. The Republican Party said they liked the elephant because it showed strength and dignity. The elephant cartoon was named, “The Off Year,” presented in November 17, 1877 in the Harper’s Weekly. He decided to use it because he was a strong Republican and wanted to use a strong and powerful animal to support his political views. The donkey cartoon, “A Live Jackass Kicking a Dead Lion”, shown in Harper’s Weekly, in January 15, 1870. The donkey had been used during Andrew Jackson’s campaign. Thomas Nast didn’t create the idea to use the donkey; he just used his artistic skills to amplify the idea.
[edit] Elections

For more details on this topic, see Elections in the United States.
Unlike the United Kingdom and other similar parliamentary systems, Americans vote for a specific candidate instead of directly selecting a particular political party. With a federal government, officials are elected at the federal (national), state and local levels. On a national level, the President, is elected indirectly by the people, through an Electoral College. In modern times, the electors virtually always vote with the popular vote of their state. All members of Congress, and the offices at the state and local levels are directly elected.
Both federal and state laws regulate elections. The United States Constitution defines (to a basic extent) how federal elections are held, in Article One and Article Two and various amendments. State law regulates most aspects of electoral law, including primaries, the eligibility of voters (beyond the basic constitutional definition), the running of each state's electoral college, and the running of state and local elections.
[edit] Organization of American political parties

See also: Political party strength in U.S. states
American political parties are more loosely organized than those in other countries. The two major parties, in particular, have no formal organization at the national level that controls membership, activities, or policy positions, though some state affiliates do. Thus, for an American to say that he or she is a member of the Democratic or Republican party, is quite different from a Briton's stating that he or she is a member of the Conservative or Labour party. In the United States, one can often become a "member" of a party, merely by stating that fact. In some U.S. states, a voter can register as a member of one or another party and/or vote in the primary election for one or another party. Such participation does not restrict one's choices in any way. It also does not give a person any particular rights or obligations within the party, other than possibly allowing that person to vote in that party's primary elections. A person may choose to attend meetings of one local party committee one day and another party committee the next day. The sole factor that brings one "closer to the action" is the quantity and quality of participation in party activities and the ability to persuade others in attendance to give one responsibility.
Party identification becomes somewhat formalized when a person runs for partisan office. In most states, this means declaring oneself a candidate for the nomination of a particular party and intent to enter that party's primary election for an office. A party committee may choose to endorse one or another of those who is seeking the nomination, but in the end the choice is up to those who choose to vote in the primary, and it is often difficult to tell who is going to do the voting.
The result is that American political parties have weak central organizations and little central ideology, except by consensus. A party really cannot prevent a person who disagrees with the majority of positions of the party or actively works against the party's aims from claiming party membership, so long as the voters who choose to vote in the primary elections elect that person. Once in office, an elected official may change parties simply by declaring such intent.
At the federal level, each of the two major parties has a national committee (See, Democratic National Committee, Republican National Committee) that acts as the hub for much fund-raising and campaign activities, particularly in presidential campaigns. The exact composition of these committees is different for each party, but they are made up primarily of representatives from state parties and affiliated organizations, and others important to the party. However, the national committees do not have the power to direct the activities of members of the party.
Both parties also have separate campaign committees which work to elect candidates at a specific level. The most significant of these are the Hill committees, which work to elect candidates to each house of Congress.
State parties exist in all fifty states, though their structures differ according to state law, as well as party rules at both the national and the state level.
Despite these weak organizations, elections are still usually portrayed as national races between the political parties. In what is known as "presidential coattails", candidates in presidential elections become the de facto leader of their respective party, and thus usually bring out supporters who in turn then vote for his party's candidates for other offices. On the other hand, federal midterm elections (where only Congress and not the president is up for election) are usually regarded as a referendum on the sitting president's performance, with voters either voting in or out the president's party's candidates, which in turn helps the next session of Congress to either pass or block the president's agenda, respectively.^[23][24]
[edit] General developments

See also: History of the United States Republican Party and History of the United States Democratic Party
Most of the Founding Fathers rejected political parties as divisive and disruptive. By the 1790s, however, most joined one of the two new parties, and by the 1830s parties had become accepted as central to the democracy.^[25] By the 1790s, the First Party System was born. Men who held opposing views strengthened their cause by identifying and organizing men of like mind. The followers of Alexander Hamilton, were called "Federalists"; they favored a strong central government that would support the interests of national defense, commerce and industry. The followers of Thomas Jefferson, the Jeffersonians took up the name "Republicans"; they preferred a decentralized agrarian republic in which the federal government had limited power.^[26][27]
By 1828, the First Party System had collapsed. Two new parties emerged from the remnants of the Jeffersonian Democracy, forming the Second Party System with the Whigs, brought to life in opposition to President Andrew Jackson and his new Democratic Party. The forces of Jacksonian Democracy, based among urban workers, Southern poor whites, and western farmers, dominated the era.^[28]
In the 1850s, the issue of slavery took center stage, with disagreement in particular over the question of whether slavery should be permitted in the country's new territories in the West. The Whig Party straddled the issue and sank to its death after the overwhelming electoral defeat by Franklin Pierce in the 1852 presidential election. Ex-Whigs joined the Know Nothings or the newly formed Republican Party. While the Know Nothing party was short-lived, Republicans would survive the intense politics leading up to the Civil War. The primary Republican policy was that slavery be excluded from all the territories. Just six years later, this new party captured the presidency when Abraham Lincoln won the election of 1860. By then, parties were well established as the country's dominant political organizations, and party allegiance had become an important part of most people's consciousness. Party loyalty was passed from fathers to sons, and party activities, including spectacular campaign events, complete with uniformed marching groups and torchlight parades, were a part of the social life of many communities.
By the 1920s, however, this boisterous folksiness had diminished. Municipal reforms, civil service reform, corrupt practices acts, and presidential primaries to replace the power of politicians at national conventions had all helped to clean up politics.
[edit] Development of the two-party system in the United States

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See also: Causes of a two-party system
Since the 1790s, the country has been run by two major parties. Many minor or third political parties appear from time to time. They tend to serve a means to advocate policies that eventually are adopted by the two major political parties. At various times the Socialist Party, the Farmer-Labor Party and the Populist Party for a few years had considerable local strength, and then faded away—although in Minnesota, the Farmer–Labor Party merged into the state's Democratic Party, which is now officially known as the Democratic–Farmer–Labor Party. At present, the Libertarian Party is the most successful third party. New York State has a number of additional third parties, who sometimes run their own candidates for office and sometimes nominate the nominees of the two main parties. In the District of Columbia, the D.C. Statehood Party has served as a strong third party behind the Democratic Party and Republican Party.
Most officials in America are elected from single-member districts and win office by beating out their opponents in a system for determining winners called first-past-the-post; the one who gets the plurality wins, (which is not the same thing as actually getting a majority of votes). This encourages the two-party system; see Duverger's law. In the absence of multi-seat congressional districts, proportional representation is impossible and third parties cannot thrive. Although elections to the Senate elect two senators per constituency (state), staggered terms effectively result in single-seat constituencies for elections to the Senate.
Another critical factor has been ballot access law. Originally, voters went to the polls and publicly stated which candidate they supported. Later on, this developed into a process whereby each political party would create its own ballot and thus the voter would put the party's ballot into the voting box. In the late nineteenth century, states began to adopt the Australian Secret Ballot Method, and it eventually became the national standard. The secret ballot method ensured that the privacy of voters would be protected (hence government jobs could no longer be awarded to loyal voters) and each state would be responsible for creating one official ballot. The fact that state legislatures were dominated by Democrats and Republicans provided these parties an opportunity to pass discriminatory laws against minor political parties, yet such laws did not start to arise until the first Red Scare that hit America after World War I. State legislatures began to enact tough laws that made it harder for minor political parties to run candidates for office by requiring a high number of petition signatures from citizens and decreasing the length of time that such a petition could legally be circulated.
It should also be noted that while more often than not, party members will "toe the line" and support their party's policies, they are free to vote against their own party and vote with the opposition ("cross the aisle") when they please.
"In America the same political labels (Democratic and Republican) cover virtually all public officeholders, and therefore most voters are everywhere mobilized in the name of these two parties," says Nelson W. Polsby, professor of political science, in the book New Federalist Papers: Essays in Defense of the Constitution. "Yet Democrats and Republicans are not everywhere the same. Variations (sometimes subtle, sometimes blatant) in the 50 political cultures of the states yield considerable differences overall in what it means to be, or to vote, Democratic or Republican. These differences suggest that one may be justified in referring to the American two-party system as masking something more like a hundred-party system."
[edit] Political pressure groups

See also: Advocacy group
Special interest groups advocate the cause of their specific constituency. Business organizations will favor low corporate taxes and restrictions of the right to strike, whereas labor unions will support minimum wage legislation and protection for collective bargaining. Other private interest groups, such as churches and ethnic groups, are more concerned about broader issues of policy that can affect their organizations or their beliefs.
One type of private interest group that has grown in number and influence in recent years is the political action committee or PAC. These are independent groups, organized around a single issue or set of issues, which contribute money to political campaigns for U.S. Congress or the presidency. PACs are limited in the amounts they can contribute directly to candidates in federal elections. There are no restrictions, however, on the amounts PACs can spend independently to advocate a point of view or to urge the election of candidates to office. PACs today number in the thousands.
"The number of interest groups has mushroomed, with more and more of them operating offices in Washington, D.C., and representing themselves directly to Congress and federal agencies," says Michael Schudson in his 1998 book The Good Citizen: A History of American Civic Life. "Many organizations that keep an eye on Washington seek financial and moral support from ordinary citizens. Since many of them focus on a narrow set of concerns or even on a single issue, and often a single issue of enormous emotional weight, they compete with the parties for citizens' dollars, time, and passion."
The amount of money spent by these special interests continues to grow, as campaigns become increasingly expensive. Many Americans have the feeling that these wealthy interests, whether corporations, unions or PACs, are so powerful that ordinary citizens can do little to counteract their influences.

"Maths" and "Math" redirect here. For other uses see Mathematics (disambiguation) and Math (disambiguation).





Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study ofquantity, structure, space, and change.^[2] Mathematicians seek out patterns^[3][4] and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures bymathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorousdeduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions.
Through the use of abstraction and logical reasoning, mathematics developed from counting,calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written recordsexist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid'sElements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with newscientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.^[5]
Galileo Galilei (1564–1642) said, 'The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth'.^[6] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences".^[7] Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions".^[8] David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."^[9] Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality".^[10]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and thesocial sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.^[11]

• 1 Etymology
• 2 History
• 3 Inspiration, pure and applied mathematics, and aesthetics
• 4 Notation, language, and rigor
• 5 Fields of mathematics
• 5.1 Foundations and philosophy
• 5.2 Pure mathematics
• 5.2.1 Quantity
• 5.2.2 Structure
• 5.2.3 Space
• 5.2.4 Change
• 5.3 Applied mathematics
• 5.3.1 Statistics and other decision sciences
• 5.3.2 Computational mathematics
• 6 Mathematics as profession
• 7 Mathematics as science
• 8 See also
• 9 Notes
• 10 References
• 11 Further reading
• 12 External links

Etymology

The word "mathematics" comes from the Greek μάθημα (máthēma), which means in ancient Greek what one learns, what one gets to know, hence also study and science, and in modern Greek just lesson.
The word máthēma comes from μανθάνω (manthano) in ancient Greek and from μαθαίνω (mathaino) in modern Greek, both of which mean to learn.
The word "mathematics" in Greek came to have the narrower and more technical meaning "mathematical study", even in Classical times.^[12] Its adjective is μαθηματικός (mathēmatikós), meaning related to learning or studious, which likewise further came to meanmathematical. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), Latin: ars mathematica, meant the mathematical art. In Latin, and in English until around 1700, the term "mathematics" more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This has resulted in several mistranslations: a particularly notorious one is Saint Augustine's warning that Christians should beware of "mathematici" meaning astrologers, which is sometimes mistranslated as a condemnation of mathematicians.
The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle (384-322BC), and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek.^[13] In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.
History

Main article: History of mathematics






The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,^[14] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.^[15] Elementary arithmetic (addition,subtraction, multiplication and division) naturally followed.
Since numeracy pre-dated writing, further steps were needed for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.^{[citation needed]} Numeral systems have been many and diverse, with the first known written numerals created by Egyptians inMiddle Kingdom texts such as the Rhind Mathematical Papyrus.^{[citation needed]}







The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry fortaxation and other financial calculations, for building and construction, and for astronomy.^[16]The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.^[17]
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in theMathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and theirproofs."^[18]
Inspiration, pure and applied mathematics, and aesthetics

Main article: Mathematical beauty






Mathematics arises from many different kinds of problems. At first these were found in commerce,land measurement, architecture and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, thephysicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.^[19] Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics. However pure mathematics topics often turn out to have applications, e.g. number theory in cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics".^[20] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.^[21] Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He identified criteria such as significance, unexpectedness, inevitability, and economy as factors that contribute to a mathematical aesthetic.^[22] Mathematicians often strive to find proofs that are particularly elegant, proofs from "The Book" of God according to Paul Erdős.^[23][24] The popularity ofrecreational mathematics is another sign of the pleasure many find in solving mathematical questions.
Notation, language, and rigor

Main article: Mathematical notation







Most of the mathematical notation in use today was not invented until the 16th century.^[25] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery.^[26] Euler (1707–1783) was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax (which to a limited extent varies from author to author and from discipline to discipline) and encodes information that would be difficult to write in any other way.
Mathematical language can be difficult to understand for beginners. Words such as or and only have more precise meanings than in everyday speech. Moreover, words such as open and field have been given specialized mathematical meanings. Technical terms such as homeomorphism and integrablehave precise meanings in mathematics. Additionally, shorthand phrases such as "iff" for "if and only if" belong to mathematical jargon. There is a reason for special notation and technical vocabulary: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.^[27] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.^[28]
Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.^[29]
Fields of mathematics








See also: Areas of mathematics and Glossary of areas of mathematics

Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
Foundations and philosophy

In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic includes the mathematical study of logic and the applications of formal logic to other areas of mathematics; set theory is the branch of mathematics that studies sets or collections of objects. Category theory, which deals in an abstract way with mathematical structuresand relationships between them, is still in development. The phrase "crisis of foundations" describes the search for a rigorous foundation for mathematics that took place from approximately 1900 to 1930.^[30] Some disagreement about the foundations of mathematics continues to the present day. The crisis of foundations was stimulated by a number of controversies at the time, including thecontroversy over Cantor's set theory and the Brouwer-Hilbert controversy.
Mathematical logic is concerned with setting mathematics within a rigorous axiomatic framework, and studying the implications of such a framework. As such, it is home to Gödel's incompleteness theorems which (informally) imply that any effective formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proven are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Whatever finite collection of number-theoretical axioms is taken as a foundation, Gödel showed how to construct a formal statement that is a true number-theoretical fact, but which does not follow from those axioms. Therefore no formal system is a complete axiomatization of full number theory. Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science^{[citation needed]}, as well as to Category Theory.
Theoretical computer science includes computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most well known model – the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. A famous problem is the "P=NP?" problem, one of the Millennium Prize Problems.^[31] Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy. Mathematical logic Set theory Category theory Theory of computation
Pure mathematics

Quantity

The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. The twin prime conjecture and Goldbach's conjecture are two unsolved problems in number theory.
As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity". Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets. Natural numbers Integers Rational numbers Real numbers Complex numbers
Structure

Many mathematical objects, such as sets of numbers and functions, exhibit internal structure as a consequence of operations orrelations that are defined on the set. Mathematics then studies properties of those sets that can be expressed in terms of that structure; for instance number theory studies properties of the set of integers that can be expressed in terms of arithmetic operations. Moreover, it frequently happens that different such structured sets (or structures) exhibit similar properties, which makes it possible, by a further step of abstraction, to state axioms for a class of structures, and then study at once the whole class of structures satisfying these axioms. Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra. By its great generality, abstract algebra can often be applied to seemingly unrelated problems; for instance a number of ancient problems concerning compass and straightedge constructions were finally solved using Galois theory, which involves field theory and group theory. Another example of an algebraic theory is linear algebra, which is the general study of vector spaces, whose elements called vectors have both quantity and direction, and can be used to model (relations between) points in space. This is one example of the phenomenon that the originally unrelated areas of geometry and algebra have very strong interactions in modern mathematics. Combinatorics studies ways of enumerating the number of objects that fit a given structure. Combinatorics Number theory Group theory Graph theory Order theory
Space

The study of space originates with geometry – in particular, Euclidean geometry. Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions; it combines space and numbers, and encompasses the well-known Pythagorean theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Convex and discrete geometry was developed to solve problems in number theory and functional analysis but now is pursued with an eye on applications in optimization and computer science. Within differential geometry are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus. Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may have been the greatest growth area in 20th century mathematics; it includespoint-set topology, set-theoretic topology, algebraic topology and differential topology. In particular, instances of modern day topology are metrizability theory, axiomatic set theory, homotopy theory, and Morse theory. Topology also includes the now solved Poincaré conjecture. Other results in geometry and topology, including the four color theorem and Kepler conjecture, have been proved only with the help of computers. Geometry Trigonometry Differential geometry Topology Fractal geometry Measure theory
Change

Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and functions of a real variable is known as real analysis, with complex analysis the equivalent field for the complex numbers. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis isquantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied asdifferential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior. Calculus Vector calculus Differential equations Dynamical systems Chaos theory Complex analysis
Applied mathematics

Applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes theprofessional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the formulation, study, and use of mathematical models in science, engineering, and other areas of mathematical practice.
In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake. Thus, the activity of applied mathematics is vitally connected with research in pure mathematics.
Statistics and other decision sciences

Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially withprobability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments;^[32] the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.^[33]
Statistical theory studies decision problems such as minimizing the risk (expected loss) of a statistical action, such as using aprocedure in, for example, parameter estimation, hypothesis testing, and selecting the best. In these traditional areas of mathematical statistics, a statistical-decision problem is formulated by minimizing an objective function, like expected loss or cost, under specific constraints: For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence.^[34] Because of its use of optimization, the mathematical theory of statistics shares concerns with other decision sciences, such as operations research, control theory, and mathematical economics.^[35]
Computational mathematics

Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmicmatrix and graph theory. Other areas of computational mathematics include computer algebra and symbolic computation. Mathematical physics Fluid dynamics Numerical analysis Optimization Probability theory Statistics Cryptography Mathematical finance Game theory Mathematical biology Mathematical chemistry Mathematical economics Control theory
Mathematics as profession

Arguably the most prestigious award in mathematics is the Fields Medal,^[36][37] established in 1936 and now awarded every 4 years. The Fields Medal is often considered a mathematical equivalent to the Nobel Prize.
The Wolf Prize in Mathematics, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize, was introduced in 2003. The Chern Medal was introduced in 2010 to recognize lifetime achievement. These accolades are awarded in recognition of a particular body of work, which may be innovational, or provide a solution to an outstanding problem in an established field.
A famous list of 23 open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems.
Mathematics as science







Gauss referred to mathematics as "the Queen of the Sciences".^[7] In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to sciencemeans a "field of knowledge", and this was the original meaning of "science" in English, also. Of course, mathematics is in this sense a field of knowledge. The specialization restricting the meaning of "science" to natural science follows the rise of Baconian science, which contrasted "natural science" to scholasticism, the Aristotelean method of inquiring from first principles. Of course, the role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."^[10] More recently, Marcus du Sautoy has called mathematics 'the Queen of Science...the main driving force behind scientific discovery'.^[39]
Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.^[40] However, in the 1930s Gödel's incompleteness theoremsconvinced many mathematicians^[who?] that mathematics cannot be reduced to logic alone, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology,hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."^[41] Other thinkers, notably Imre Lakatos, have applied a version offalsificationism to mathematics itself.
An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.^[42] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method.^{[citation needed]}
The opinions of mathematicians on this matter are varied. Many mathematicians^[who?] feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others^[who?] feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science andengineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.^{[citation needed]} See also

Mathematics portal Book: Mathematics Wikipedia books are collections of articles that can be downloaded or ordered in print.
Main article: Lists of mathematics topics

• Definitions of mathematics
• Mathematics and art
• Mathematics education

Notes

• ^ No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art depends on the artist's imagination (see Euclid).
• ^ "Department of Mathematics and Computer Science: Adelphi University". Academics.adelphi.edu. Retrieved 2011-11-04.
• ^ Steen, L.A. (April 29, 1988). The Science of Patterns Science, 240: 611–616. And summarized at Association for Supervision and Curriculum Development, www.ascd.org.
• ^ Devlin, Keith, Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library) 1996, ISBN 978-0-7167-5047-5
• ^ Eves
• ^ Marcus du Sautoy, A Brief History of Mathematics: 1. Newton and Leibniz, BBC Radio 4, 27/09/2010.
• ^ ^{a b} Waltershausen
• ^ Peirce, p. 97.
• ^ Hilbert, D. (1919-20), Natur und Mathematisches Erkennen: Vorlesungen, gehalten 1919-1920 in Göttingen. Nach der Ausarbeitung von Paul Bernays (Edited and with an English introduction by David E. Rowe), Basel, Birkhäuser (1992).
• ^ ^{a b} Einstein, p. 28. The quote is Einstein's answer to the question: "how can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" He, too, is concerned with The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
• ^ Peterson
• ^ Both senses can be found in Plato. Liddell and Scott, s.voceμαθηματικός
• ^ The Oxford Dictionary of English Etymology, Oxford English Dictionary, sub "mathematics", "mathematic", "mathematics"
• ^ S. Dehaene; G. Dehaene-Lambertz; L. Cohen (Aug 1998). "Abstract representations of numbers in the animal and human brain". Trends in Neuroscience 21 (8): 355–361.doi:10.1016/S0166-2236(98)01263-6. PMID 9720604.
• ^ See, for example, Raymond L. Wilder, Evolution of Mathematical Concepts; an Elementary Study, passim
• ^ Kline 1990, Chapter 1.
• ^ "A History of Greek Mathematics: From Thales to Euclid". Thomas Little Heath (1981).ISBN 0-486-24073-8
• ^ Sevryuk
• ^ Johnson, Gerald W.; Lapidus, Michel L. (2002). The Feynman Integral and Feynman's Operational Calculus. Oxford University Press. ISBN 0821824139.
• ^ Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics 13 (1): 1–14.
• ^ "Mathematics Subject Classification 2010" (PDF). Retrieved 2010-11-09.
• ^ Hardy, G. H. (1940). A Mathematician's Apology. Cambridge University Press.ISBN 0521427061.
• ^ Gold, Bonnie; Simons, Rogers A. (2008). Proof and Other Dilemmas: Mathematics and Philosophy. MAA.
• ^ Aigner, Martin; Ziegler, Günter M. (2001). Proofs from The Book. Springer.ISBN 3540404600.
• ^ Earliest Uses of Various Mathematical Symbols (Contains many further references).
• ^ Kline, p. 140, on Diophantus; p.261, on Vieta.
• ^ See false proof for simple examples of what can go wrong in a formal proof.
• ^ Ivars Peterson, The Mathematical Tourist, Freeman, 1988, ISBN 0-7167-1953-3. p. 4 "A few complain that the computer program can't be verified properly", (in reference to the Haken-Apple proof of the Four Color Theorem).
• ^ Patrick Suppes, Axiomatic Set Theory, Dover, 1972, ISBN 0-486-61630-4. p. 1, "Among the many branches of modern mathematics set theory occupies a unique place: with a few rare exceptions the entities which are studied and analyzed in mathematics may be regarded as certain particular sets or classes of objects."
• ^ Luke Howard Hodgkin & Luke Hodgkin, A History of Mathematics, Oxford University Press, 2005.
• ^ Clay Mathematics Institute, P=NP, claymath.org
• ^ Rao, C.R. (1997) Statistics and Truth: Putting Chance to Work, World Scientific. ISBN 9810231113
• ^ Like other mathematical sciences such as physics and computer science, statistics is an autonomous discipline rather than a branch of applied mathematics. Like research physicists and computer scientists, research statisticians are mathematical scientists. Many statisticians have a degree in mathematics, and some statisticians are also mathematicians.
• ^ Rao, C. R. (1981). "Foreword". In Arthanari, T. S.; Dodge, Yadolah. Wiley Series in Probability and Mathematical Statistics. Wiley. pp. vii–viii. ISBN 0-471-08073-X.MR607328.
• ^ Whittle (1994, pp. 10–11 and 14–18): Whittle, Peter (1994). "Almost home". In Kelly, F. P..Probability, statistics and optimisation: A Tribute to Peter Whittle (previously "A realised path: The Cambridge Statistical Laboratory upto 1993 (revised 2002)" ed.). Chichester: John Wiley. pp. 1–28. ISBN 0471948292.
• ^ "The Fields Medal is now indisputably the best known and most influential award in mathematics." Monastyrsky
• ^ Riehm
• ^ Zeidler, Eberhard (2004). Oxford User's Guide to Mathematics. Oxford, UK: Oxford University Press. p. 1188. ISBN 0198507631.
• ^ Marcus du Sautoy, A Brief History of Mathematics: 10. Nicolas Bourbaki, BBC Radio 4, 01/10/2010.
• ^ Shasha, Dennis Elliot; Lazere, Cathy A. (1998). Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists. Springer. p. 228.
• ^ Popper 1995, p. 56
• ^ Ziman

References

• Courant, Richard and H. Robbins, What Is Mathematics? : An Elementary Approach to Ideas and Methods, Oxford University Press, USA; 2 edition (July 18, 1996). ISBN 0-19-510519-2.
• Einstein, Albert (1923). Sidelights on Relativity (Geometry and Experience). P. Dutton., Co.
• du Sautoy, Marcus, A Brief History of Mathematics, BBC Radio 4(2010).
• Eves, Howard, An Introduction to the History of Mathematics, Sixth Edition, Saunders, 1990, ISBN 0-03-029558-0.
• Kline, Morris, Mathematical Thought from Ancient to Modern Times, Oxford University Press, USA; Paperback edition (March 1, 1990).ISBN 0-19-506135-7.
• Monastyrsky, Michael (2001) (PDF). Some Trends in Modern Mathematics and the Fields Medal. Canadian Mathematical Society. Retrieved 2006-07-28.
• Oxford English Dictionary, second edition, ed. John Simpson and Edmund Weiner, Clarendon Press, 1989, ISBN 0-19-861186-2.
• The Oxford Dictionary of English Etymology, 1983 reprint. ISBN 0-19-861112-9.
• Pappas, Theoni, The Joy Of Mathematics, Wide World Publishing; Revised edition (June 1989). ISBN 0-933174-65-9.
• Peirce, Benjamin (1881). Peirce, Charles Sanders. ed. "Linear associative algebra". American Journal of Mathematics (Johns Hopkins University) 4 (1–4): 97–229. doi:10.2307/2369153. Corrected, expanded, and annotated revision with an 1875 paper by B. Peirce and annotations by his son, C. S. Peirce, of the 1872 lithograph ed. Google Eprint and as an extract, D. Van Nostrand, 1882, Google Eprint..
• Peterson, Ivars, Mathematical Tourist, New and Updated Snapshots of Modern Mathematics, Owl Books, 2001, ISBN 0-8050-7159-8.
• Popper, Karl R. (1995). "On knowledge". In Search of a Better World: Lectures and Essays from Thirty Years. Routledge. ISBN 0-415-13548-6.
• Riehm, Carl (August 2002). "The Early History of the Fields Medal" (PDF). Notices of the AMS (AMS) 49 (7): 778–782.
• Sevryuk, Mikhail B. (January 2006). "Book Reviews" (PDF).Bulletin of the American Mathematical Society 43 (1): 101–109.doi:10.1090/S0273-0979-05-01069-4. Retrieved 2006-06-24.
• Waltershausen, Wolfgang Sartorius von (1856, repr. 1965). Gauss zum Gedächtniss. Sändig Reprint Verlag H. R. Wohlwend.ISBN 3-253-01702-8. ISSN B0000BN5SQ ASIN: B0000BN5SQ.

Further reading

• Benson, Donald C., The Moment of Proof: Mathematical Epiphanies,Oxford University Press, USA; New Ed edition (December 14, 2000).ISBN 0-19-513919-4.
• Boyer, Carl B., A History of Mathematics, Wiley; 2 edition (March 6, 1991). ISBN 0-471-54397-7. — A concise history of mathematics from the Concept of Number to contemporary Mathematics.
• Davis, Philip J. and Hersh, Reuben, The Mathematical Experience. Mariner Books; Reprint edition (January 14, 1999). ISBN 0-395-92968-7.
• Gullberg, Jan, Mathematics — From the Birth of Numbers. W. W. Norton & Company; 1st edition (October 1997). ISBN 0-393-04002-X.
• Hazewinkel, Michiel (ed.), Encyclopaedia of Mathematics. Kluwer Academic Publishers 2000. — A translated and expanded version of a Soviet mathematics encyclopedia, in ten (expensive) volumes, the most complete and authoritative work available. Also in paperback and on CD-ROM, and online.
• Jourdain, Philip E. B., The Nature of Mathematics, in The World of Mathematics, James R. Newman, editor, Dover Publications, 2003,ISBN 0-486-43268-8.

External links
Find more about Mathematics on Wikipedia'ssister projects: Definitions and translations from Wiktionary Images and media from Commons Learning resources from Wikiversity News stories from Wikinews Quotations from Wikiquote Source texts from Wikisource Textbooks from Wikibooks

• Mathematics on In Our Time at the BBC. (listen now)
• Free Mathematics books Free Mathematics books collection.
• Encyclopaedia of Mathematics online encyclopaedia from Springer, Graduate-level reference work with over 8,000 entries, illuminating nearly 50,000 notions in mathematics.
• HyperMath site at Georgia State University
• FreeScience Library The mathematics section of FreeScience library
• Rusin, Dave: The Mathematical Atlas. A guided tour through the various branches of modern mathematics. (Can also be found at NIU.edu.)
• Polyanin, Andrei: EqWorld: The World of Mathematical Equations. An online resource focusing on algebraic, ordinary differential, partial differential (mathematical physics), integral, and other mathematical equations.
• Cain, George: Online Mathematics Textbooks available free online.
• Tricki, Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques.
• Mathematical Structures, list information about classes of mathematical structures.
• Mathematician Biographies. The MacTutor History of Mathematics archive Extensive history and quotes from all famous mathematicians.
• Metamath. A site and a language, that formalize mathematics from its foundations.
• Nrich, a prize-winning site for students from age five from Cambridge University
• Open Problem Garden, a wiki of open problems in mathematics
• Planet Math. An online mathematics encyclopedia under construction, focusing on modern mathematics. Uses the Attribution-ShareAlikelicense, allowing article exchange with Wikipedia. Uses TeX markup.
• Some mathematics applets, at MIT
• Weisstein, Eric et al.: MathWorld: World of Mathematics. An online encyclopedia of mathematics.
• Patrick Jones' Video Tutorials on Mathematics
• Citizendium: Theory (mathematics).
• du Sautoy, Marcus, A Brief History of Mathematics, BBC Radio 4 (2010).
• MathOverflow A Q&A site for research level mathematics
• Math Games a collection of over 250 math games that exercise the mathematical mind.

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