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25 Cards in this Set
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Hardy

worked with Littlefield and Ramanujan
Hardy Weinburg hypothesis how dominant and recessive characteristics propogate in a large population proved infinite # of primes Mathmaticians Apology 

Bourbaki

goal of founding all mathematics on set theory


Conway

 Leech's Lattice Order
 Numbers expressed as sums of fifth powers  Game of Life  discovered surreal numbers 

Smale

 topology and dynamical systems
 Poincare conjecture  Field's medal 

Wiles

 number theory
 proved Fermat's Last Theorem  3 lectures, was revealed as flawed, he corrected it 

Field's Medal

 once every four years to four people
 like the Nobel prize of math  under 40 crowd  honors expanding the boundries of a certain field 

Putnam Exam

 began in 1927
 undergrads  010 points for 6 problems 

Millennium Problems

 Clay Mathematics Instit.
 one million $ prize, potential of 7 million 

Oberwolfach

 leading mathematics instit. in Germany, in the Black Forest, free of distractions


Gottingen

 used to be the best math place in the world
 alumni include Guass, Riemann, and Hilbert  the Nazis came and messed it up, is no longer really prestegious 

Moore Method

 created by Robert Lee Moore
 give students a list of axioms, students were to develop theorms and proofs  RLM is named after him  "The student is taught the best who is told the least" 

Preditor Prey equations

 explains dynamics of biological systems
 Lotka Volterra  prey have unlimited food supply and reproduce exponentially 

cantor diagonization

used to produce a decimal expansion that is not in the list... thus the cardinality of the continum


Euclid's 5th postulate

 If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines if produced indefinately, meet on that side which are the angles less than two right angles


Playfair's 5th postulate

 given a line l and a point p not on l, there is exactly one line through p parallel to l


Godel proved what about the Continum Hypothesis?

that if it is true, there is no condradiction in math


Cowen proved what about the Continum Hypothesis?

that if it is false, there is no contradction in math


what is the continum hypothesis

no set exists whose cardinality is greater than aleph naught, but less than the continum


what are the three characteristics that axioms have to have?

a) consistancy can't be contradictory
b) completeness everything has to have truth value c) independence no axiom can be proved by another (bc that would be redundant) 

what are the three axioms for groups

a) if (ab)c, then a(bc)
b) e is an identity element (ea=ae=a) (mult=1, add=0) c) there is an inverse of every element that with the first element it produces the identity 

What is an abelian group

 one in which ab = ba
 those square things are not abelian 

absolute geometry

set of theorms that can be proven using only the first four postualtes


Euclidean geometry

 uses all 5 postulates


in absolute geometry, what can you prove about the angles of a triangle

the sum of the angles of a triangle is less than or equal to 180 degrees


in absolute geometry, if one angle sum of a triangle is less than 180, then

the sums of all triangles is less than 180
