Schedule of topics: MA 3513, Spring 2017

Date       Chapter       Description 
Jan 9 1.1, 1.2 Pythagorean Theorem, Pythagorean triples
Jan 11 1.2, 1.3 Method to generate Pythagorean triples, rational points on the circle
Jan 13 1.3, 1.4 more rational points on circle, "Book" proof of Pythagorean Theorem

Jan 16 Martin Luther King Day! (no class)
Jan 18 1.5, 1.6 ErdÅ‘s, irrational numbers, Hilbert's distance idea
Jan 20 2.1, 2.2 Euclid and proofs, regular polyhedra

Jan 23 2.2 regular polyhedra, angle deficits (Descartes and Euler)
Jan 25 2.3 ruler and compass constructions
Jan 27 2.3 ruler and compass lemmas, doubling cube/ssquaring circle

Jan 30 2.3, 2.4 constructible n-gons, conic sections
Feb 1 2.4, 2.5 more on conics, toric/spiric sections, epicycles
Feb 3 3.2 polygonal numbers

Feb 6 3.2 calculating polygonal numbers (with several methods)
Feb 8 3.2 prime numbers, perfect numbers
Feb 10 3.2 perfect numbers, Mersenne primes

Feb 13 Exam 1
Feb 15 3.3 the Euclidean algorith, consequences
Feb 17 twin primes, Zhang; Fermat's Last Theorem, Wiles

Feb 20 3.4 Pell's equation, approximating sqrt(2)
Feb 22 3.4, 3.5 anthyphairesis, Diophantine chord and tangent method
Feb 24 3.5, 4.1 more Diophantine; Zeno's paradox

Feb 27 4.2 the Theory of Proportions and Dedekind cuts
Mar 1 4.3 the Method of Exhaustion on the circle
Mar 3 4.3 the Method of Exhaustion on a pyramid

Mar 6 5.1, 5.2 from Greece to Asia; modular arithmetic
Mar 8 5.2 Sun Zi, inverses mod m
Mar 10 5.2, 5.3 the Chinese Remainder Theorem, work of Aryabhatta

Mar 13 Spring Break! (no class)
Mar 15 Spring Break! (no class)
Mar 17 Spring Break! (no class)

Mar 20 5.4 Pell's Equation in India
Mar 22 5.5 the Cyclic Process for solving Pell-like equations
Mar 24 5.5 Cyclic Process examples

Mar 27 Exam 2
Mar 29 6.1 polynomial basics
Mar 31 6.1 Al-Khwarizmi and the development of algebra

Apr 3 Mary Ellen Rudin and the non-shellable ball
Apr 5 6.2 Gaussian eliminiation in China
Apr 7 6.3 the quadratic equation for the Babylonians

Apr 10 induction review
Apr 12 6.4, 6.5 quadratic irrationals, history of cubic equation
Apr 14 Religious holiday! (no class)

Apr 17 6.5, 6.6 the cubic equation, trisecting the angle
Apr 19 6.6, 6.7 n-secting the angle, the quartic equation
Apr 21 6.7 there is no quintic equation

Apr 24 7.1, 7.2 analytic geometry
Apr 26 Euclian Algorithm for polynomials, motivation for rings

May 1 Final exam   (12:00 - 3:00pm)