Game Theory Explains How Cooperation Evolved When the manuscript crossed his desk, Joshua Plotkin, a theoretical biologist at the University of Pennsylvania, was immediately intrigued. The physicist Freeman Dyson and the computer scientist William Press, both highly accomplished in their fields, had found a new solution to a famous, decades-old game theory scenario called the prisoner’s dilemma, in which players must decide whether to cheat or cooperate with a partner. The prisoner’s dilemma has long been used to help explain how cooperation might endure in nature. Press and Dyson’s new solution to the problem, however, threw that rosy perspective into question. Plotkin found the duo’s math remarkable in its elegance. Candace diCarlo Joshua Plotkin has applied the prisoner’s dilemma to evolving populations. Press and Dyson’s paper looked at a classic game theory scenario — a pair of players engaged in repeated confrontation. The work is entirely theoretical at this point. Tit for Tat Vervet monkeys are known for their alarm calls.

Purplemath calculus.org - THE CALCULUS PAGE . 21 GIFs That Explain Mathematical Concepts “Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.” Danica McKellar As we usher in the start of a new school year, it’s time to hit the ground running in your classes! Math can be pretty tough, but since it is the language in which scientists interpret the Universe, there’s really no getting around learning it. Check out these gifs that will help you visualize some tricky aspects of math, so you can dominate your exams this year. Ellipse: Via: giphy Solving Pascal triangles: Via: Hersfold via Wikimedia Commons Use FOIL to easily multiply binomials: Via: mathcaptain Here’s how you solve logarithms: Via: imgur Use this trick so you don’t get mixed up when doing matrix transpositions: Via: Wikimedia Commons What the Pythagorean Theorem is really trying to show you: Via: giphy Exterior angles of polygons will ALWAYS add up to 360 degrees: Via: math.stackexchange Via: imgur Via: Wikimedia Commons Via: reddit

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The On-Line Encyclopedia of Integer Sequences® (OEIS®) Devlin's Angle Exponential and Logarithmic functions Exponential functions Definition Take a > 0 and not equal to 1 . Then, the function defined by f : R -> R : x -> ax is called an exponential function with base a. Graph and properties Let f(x) = an exponential function with a > 1. From the graphs we see that The domain is R The range is the set of strictly positive real numbers The function is continuous in its domain The function is increasing if a > 1 and decreasing if 0 < a < 1 The x-axis is a horizontal asymptote Examples: y = 3x ; y = 0.5x ; y = 100.2x-1 Logarithmic functions Definition and basic properties Take a > 0 and not equal to 1 . are either increasing or decreasing, the inverse functions are defined. loga(x) log10(x) is written as log(x) So, From this we see that the domain of the logarithmic function is the set of strictly positive real numbers, and the range is R. log2(8) = 3 ; log3(sqrt(3)) = 0.5 ; log(0.01) = -2 From the definition it follows immediately that Example: log(102x+1) = 2x+1 Graph log2(x) ; log(2x+4) ; log0.5(x) Thus,

Statlect, the digital textbook Graphing Calculator Untitled Graph Create AccountorSign In powered by powered by functions $$π Create AccountorSign In to save your graphs! + New Blank Graph Examples Lines: Slope Intercept Form example Lines: Point Slope Form example Lines: Two Point Form example Parabolas: Standard Form example Parabolas: Vertex Form example Parabolas: Standard Form + Tangent example Trigonometry: Period and Amplitude example Trigonometry: Phase example Trigonometry: Wave Interference example Trigonometry: Unit Circle example Conic Sections: Circle example Conic Sections: Parabola and Focus example Conic Sections: Ellipse with Foci example Conic Sections: Hyperbola example Polar: Rose example Polar: Logarithmic Spiral example Polar: Limacon example Polar: Conic Sections example Parametric: Introduction example Parametric: Cycloid example Transformations: Translating a Function example Transformations: Scaling a Function example Transformations: Inverse of a Function example Statistics: Linear Regression example Statistics: Anscomb's Quartet example

MATH1200 Calculus The author of this page, Kevin Hutchinson would welcome any comments or suggestions for its improvement. Lecturer Lecturer: Dr Kevin Hutchinson Office: Room 8, Mathematics Department, Second Floor, Science Lecture Theatre Building Phone: 716 2577 e-mail: kevin.hutchinson@ucd.ie Office Hours: Tuesday 4-5 pm, Thursday 3-4 pm, or by appointment. Syllabus The syllabus for this course is entirely determined by the classnotes and assigned homework. For an outline of the course syllabus, aims and objectives, click here. Texts The primary `text' for this course is the classnotes provided below. Homeworks Calculus homework will be assigned throughout the year, once every fortnight during term. Here is the first homework for the current year (2004/5): Homework 1 (2004) Here is the third homework for the current year (2004/5): Homework 3 (2004) Here is the fifth homework for the current year (2004/5): Homework 5 (2004) Here is the seventh homework for the current year (2004/5): Homework 7 (2004)

17 Equations That Changed The World

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