Prove It The Art Of Mathematical Argument Pdf
[PDF] Prove It - The Art of Mathematical Argument (2012)
ISBN: b2e1ae72a4
Category: Tutorial
Posted on 2018-01-12, by luongquocchinh.
Description
Author: Unknown | Category: Mathematics | Language: English | Page: 1 | ISBN: db2e1ae72a4d45acb27574597319f2f6 |
Description: Mathematical proof is the gold standard of knowledge. Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time. Imagine, then, the thrill of being able to prove something in mathematics. The experience is the closest you can get to glimpsing the abstract order behind all things. Only by doing a proof can you reach the deep insights that mathematics offersâ€"that tell you why something is true, not merely that it is true. Such insights are invaluable for getting a grasp of the key concepts in every branch of mathematics, from algebra to number theory, from geometry to calculus and beyond. Lectures 01 What Are Proofs, and How Do I Do Them? 02 The Root of Proofâ€"A Brief Look at Geometry 03 The Building Blocksâ€"Introduction to Logic 04 More Blocksâ€"Negations and Implications 05 Existence and Uniquenessâ€"Quantifiers 06 The Simplest Roadâ€"Direct Proofs 07 Let’s Go Backwardâ€"Proofs by Contradiction 08 Let’s Go Both Waysâ€"If-and-Only-If Proofs 09 The Language of Mathematicsâ€"Set Theory 10 Bigger and Bigger Setsâ€"Infinite Sets 11 Mathematical Induction 12 Deeper and Deeperâ€"More Induction 13 Strong Induction and the Fibonacci Numbers 14 I Exist Therefore I Amâ€"Existence Proofs 15 I Am One of a Kindâ€"Uniqueness Proofs 16 Let Me Count the Waysâ€"Enumeration Proofs 17 Not True! Counterexamples and Paradoxes 18 When 1 = 2â€"False Proofs 19 A Picture Says It Allâ€"Visual Proofs 20 The Queen of Mathematicsâ€"Number Theory 21 Primal Studiesâ€"More Number Theory 22 Fun with Triangular and Square Numbers 23 Perfect Numbers and Mersenne Primes 24 Let’s Wrap It Upâ€"The Number e
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