Journey through Genius: Great Theorem of Mathematics by William Dunham

Weekly Syllabus - Math 460 - Fall 2017

Week: Calender Date
Reading Assignments
Th Aug 24 Introduction to the Math Seminar ...
Th Aug 31 Hippocrates Quadrature of the Lune Dunham Ch 1
Writing Proofs in Math 460
Two Other Quadrable Lunes
Th Sept 7 Euclid's Proof of the Pythagorean Theorem
Saccheri-Legendre Theorem
Dunham Ch 2
Three Famous Problems - Part I
The Saccheri-Legendre Theorem
Th Sept 14 Euclid and the Infinitude of Primes Dunham Ch 3
Three Famous Problems - Part II
On the Scarcity of Primes
Th Sept 21 Archimedes' Determination of Circular Area Dunham Ch 4
Archimedes' Determination of pi
Th Sept 28 Heron's Formula for Triangular Area Dunham Ch 5
Th Oct 5 Cardano and the Solution of the Cubic Dunham Ch 6
x4+y4=z4 has no non-trivial integer solution
Th Oct 12 A Gem from Isaac Newton Dunham Ch 7
The Leibniz-Gregory Series
Th Oct 19 The Bernoulli's and the Harmonic Series Dunham Ch 8
On the Density of Primes
Th Oct 26 The Extraordinary Sums of Leonard Euler Dunham Ch 9
The Euclid-Euler Theorem
Paper Topics Due
Th Nov 2 A Sample of Euler's Number Theory Dunham Ch 10 pp. 223 - 235
Euler's Formula
Th Nov 9 Mathematics of the 19th Century Dunham Ch 10 pp. 235 - 244; Ch 11 pp 245-251
Judith Grabiner: Who Gave you the Epsilon? Cauchy and the Origins of Rigorous Calculus
Gauss and the Regular Heptadecagon
Cauchy's Proof of the IVT
Th Nov 16 The Non-Denumerabililty of the Continuum Dunham Ch 11
Liouville's Inequality and Proof that ... is transcendental
Th Nov 30 Cantor and the Transfinite Realm Dunham Ch 12
The Schroder-Bernstein Theorem
Th Dec 7 Mathematics of the 20th Century L. Becerra & R. Barnes: The Evolution of Mathematical Certainty
Papers Due
During Exam Week Final Presentations Critiques on Papers Due

" This,therefore is mathematics: she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes the oblivion and ignorance which are ours by birth "

Proclus 5th Century C.E.