TTC Math - Theory Collection


480p - An Introduction to Number Theory (2008 ) x265
01 - Number Theory and Mathematical Research
02 - Natural Numbers and Their Personalities
03 - Triangular Numbers and Their Progressions
04 - Geometric Progressions, Exponential Growth
05 - Recurrence Sequences
06 - The Binet Formula and the Towers of Hanoi
07 - The Classical Theory of Prime Numbers
08 - Euler's Product Formula and Divisibility
09 - The Prime Number Theorem and Riemann
10 - Division Algorithm and Modular Arithmetic
11 - Cryptography and Fermat's Little Theorem
14 - Fermat's Last Theorem
15 - Factorization and Algebraic Number Theory
16 - Pythagorean Triples
17 - An Introduction to Algebraic Geometry
18 - The Complex Structure of Elliptic Curves
19 - The Abundance of Irrational Numbers
20 - Transcending the Algebraic Numbers
21 - Diophantine Approximation
22 - Writing Real Numbers as Continued Fractions
23 - Applications Involving Continued Fractions
24 - A Journey's End and the Journey Ahead


480p - Great Thinkers, Great Theorems (2010) x265
00. Professor Bio
01. Theorems as Masterpieces
02. Mathematics before Euclid
03. The Greatest Mathematics Book of All
04. Euclid's Elements—Triangles and Polygons
05. Number Theory in Euclid
06. The Life and Works of Archimedes
07. Archimedes' Determination of Circular Area
08. Heron's Formula for Triangular Area
09. Al-Khwarizmi and Islamic Mathematics
10. A Horatio Algebra Story
11. To the Cubic and Beyond
12. The Heroic Century
13. The Legacy of Newton
14. Newton's Infinite Series
15. Newton's Proof of Heron's Formula
16. The Legacy of Leibniz
17. The Bernoullis and the Calculus Wars
18. Euler, the Master
19. Euler's Extraordinary Sum
20. Euler and the Partitioning of Numbers
21. Gauss—the Prince of Mathematicians
22. The 19th Century—Rigor and Liberation
23. Cantor and the Infinite
24. Beyond the Infinite
Great Thinkers, Great Theorems (2010).pdf


480p - Prove It - The Art of Mathematical Argument (2012) x265
01-What Are Proofs, and How Do I Do Them
02-The Root of Proof—A Brief Look at Geometry
03-The Building Blocks—Introduction to Logic
04-More Blocks—Negations and Implications
05-Existence and Uniqueness—Quantifiers
06-The Simplest Road—Direct Proofs
07-Let’s Go Backward—Proofs by Contradiction
08-Let’s Go Both Ways—If-and-Only-If Proofs
09-The Language of Mathematics—Set Theory
10-Bigger and Bigger Sets—Infinite Sets
11-Mathematical Induction
12-Deeper and Deeper—More Induction
13-Strong Induction and the Fibonacci Numbers
14-I Exist Therefore I Am—Existence Proofs
15-I Am One of a Kind—Uniqueness Proofs
16-Let Me Count the Ways—Enumeration Proofs
17-Not True! Counterexamples and Paradoxes
18-When 1 = 2—False Proofs
19-A Picture Says It All—Visual Proofs
20-The Queen of Mathematics—Number Theory
21-Primal Studies—More Number Theory
22-Fun with Triangular and Square Numbers
23-Perfect Numbers and Mersenne Primes
24-Let’s Wrap It Up—The Number e
Prove It - The Art of Mathematical Argument.pdf
Velleman-How to Prove it.pdf