## Journey into Mathematics: An Introduction to ProofsStudents learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics.Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers. |

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algebra angle approximation area(D assume Axiom base step binomial coefficients complex numbers compute convergence Corollary cosine course cube root cubic formula cubic polynomial defined definition denote Diophantus disk equal example Exercise false Figure Find the roots follows geometric Getting Close Principle given Greek hence Hint inductive step inequality inscribed integer integer ℓ irrational number kℓ Lemma logically equivalent mathematical induction Moivre’s theorem multiplication negative notation nth roots parallelogram parametrized perimeter polygons positive integers positive numbers prime problem proof of Theorem propositional calculus prove Pythagorean theorem Pythagorean triple quadratic 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 small terms square root statements S(n subset trigonometric true truth table unit circle values