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25 Cards in this Set

  • Front
  • Back
-worked with Littlefield and Ramanujan
-Hardy Weinburg hypothesis- how dominant and recessive characteristics propogate in a large population
-proved infinite # of primes
-Mathmaticians Apology
-goal of founding all mathematics on set theory
- Leech's Lattice Order
- Numbers expressed as sums of fifth powers
- Game of Life
- discovered surreal numbers
- topology and dynamical systems
- Poincare conjecture
- Field's medal
- 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
- 0-10 points for 6 problems
Millennium Problems
- Clay Mathematics Instit.
- one million $ prize, potential of 7 million
- leading mathematics instit. in Germany, in the Black Forest, free of distractions
- 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