Textbook:
Journey through Genius: Great Theorem of Mathematics by William Dunham
More Great Theorems A Supplemetary Text

Weekly Syllabus - Math 460 - Fall 2016

Week: Calender Date
Topic
Reading Assignments
Th Aug 25 Introduction to the Math Seminar ...
Th Sept 1 Hippocrates Quadrature of the Lune Dunham Ch 1
Writing Proofs in Math 460
Th Sept 8 Euclid's Proof of the Pythagorean Theorem
Saccheri-Legendre Theorem
Dunham Ch 2
Three Famous Problems - Part I
The Saccheri-Legendre Theorem
Th Sept 15 Euclid and the Infinitude of Primes Dunham Ch 3
Three Famous Problems - Part II
Th Sept 22 Archimedes' Determination of Circular Area Dunham Ch 4
Th Sept 29 Heron's Formula for Triangular Area Dunham Ch 5
Th Oct 6 Cardano and the Solution of the Cubic Dunham Ch
Th Oct 13 A Gem from Isaac Newton Dunham Ch 7
Th Oct 20 The Bernoulli's and the Harmonic Series Dunham Ch 8
Th Oct 27 The Extraordinary Sums of Leonard Euler Dunham Ch 9
The Euclid-Euler Theorem
Paper Topics Due
Th Nov 3 A Sample of Euler's Number Theory Dunham Ch 10 pp. 223 - 235
On the Density of Primes
Th Nov 10 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 17 The Non-Denumerabililty of the Continuum Dunham Ch 11
Liouville's Inequality and Proof that ... is transcendental
Th Dec 1 Cantor and the Transfinite Realm Dunham Ch 12
The Schroder-Bernstein Theorem
Th Dec 8 Mathematics of the 20th Century L. Becerra & R. Barnes: The Evolution of Mathematical Certainty
Papers Due
Wed Dec 14
8:00 - 11:00 AM
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.