Journey Into Mathematics: An Introduction to Proofs
Rotman, Joseph, Journey into Mathematics: The World of Proof Prompting readers to do mathematics, not merely read about it, this proactive book has users reading and writing proofs at the outset. Complete proofs are given from the start, and coverage begins with elementary mathematics to allow focus on the writing and reading of proofs without the distraction of absorbing new ideas simultaneously.KEY TOPICS:Contains material that is familiar to calculus readers (i.e., induction, binomial theorem, polygonal, using the Diophantine parametrization of the circle by rational functions to solve trigonometric identities, etc.), and engages readers throughout with interesting expositions using history, etymology, and humorous asides. Material is presented as a 'single story' to aid in the subjects progressive growth and development.For mathematicians.
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algebra angle approximates area(D assume Axiom base step binomial binomial coefficients calculus called coefficients complex numbers compute convergence Corollary cos2 course cube root cubic formula cubic polynomial defined definition denote Diophantus disk equal equation example Exercise false Figure Find the roots follows geometric Getting Close Principle given Greek hence Hint inductive step inequality inscribed irrational l+t2 Lemma logically equivalent mathematical induction Moivre's theorem multiplication notation nth roots parallelogram parametrized perimeter polygon positive integers positive numbers prime problem proof of Theorem propositional calculus prove Pythagorean theorem Pythagorean triple quadratic formula quartic formula radius rational function rational number rational point real numbers right triangle root of f(x roots of unity says sequence side lengths sides of lengths sin2 Small Terms square root subset trigonometry true truth table unit circle values write