Blast Into Math!
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740303308
Table of contents: title: Content; title: Preface; title: 1. To the reader; title: 2. Pure mathematics: the proof of the pudding is in the eating; title: 2.1. A universal language; title: 2.2. Theorems, propositions, and lemmas; title: 2.3. Logic; title: 2.4. Ready? Set? Prove!; title: 2.5. Exercises; title: 2.6. Examples and hints; title: 3. Sets of numbers: mathematical playgrounds; title: 3.1. Set theory; title: 3.2. Numbers; title: 3.3. The least upper bound property; title: 3.4. Proof by induction; title: 3.5. Exercises; title: 3.6. Examples and hints; title: 4. The Euclidean algorithm: a computational recipe; title: 4.1. Division; title: 4.2. Greatest common divisors; title: 4.3. Proof of the Euclidean Algorithm; title: 4.4. Greatest common divisors in disguise; title: 4.5. Exercises; title: 4.6. Examples and hints; title: 5. Prime numbers: indestructible building blocks; title: 5.1. Ingredients in the proof of the Fundamental Theorem of Arithmetic; title: 5.2. Unique prime factorization: the Fundamental Theorem of Arithmetic; title: 5.3. How many primes are there?; title: 5.4. Counting infinity; title: 5.5. Exercises; title: 5.6. Examples and hints; title: 6. Mathematical perspectives: all your base are belong to us; title: 6.1. Number bases: infinitely many mathematical perspectives; title: 6.2. Fractions in bases; title: 6.3. Exercises; title: 6.4. Examples and hints; title: 7. Analytic number theory: ants, ghosts and giants; title: 7.1. Sequences: mathematical ants; title: 7.2. Real numbers and friendly rational numbers; title: 7.3. Series: a tower of mathematical ants; title: 7.4. Decimal expansions; title: 7.5. The Prime Number Theorem; title: 7.6. Exercises; title: 7.7. Examples and hints; title: 8. Afterword; title: 9. Bibliography