An Elementary Transition to Abstract Mathematics

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An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role.The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; ...