Publication year: 2020
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this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise.This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts.
Subject: Mathematics and Statistics, Abstract mathematics textbook, Abstract mathematics game, Abstract mathematics problems, Hackenbush game, Nim game, Fundamental theorem of arithmetic, Primitives mathematics, Higher mathematics transition, Transition to higher mathematics, Math statement proof, Mathematical induction, Parallel postulate, Axiom of choice, Fundamental theorem of equivalence relations, Generalized continuum hypothesis, Hungarian approach mathematics, Mathematical Logic and Foundations, Algebra, Analysis, History of Mathematical Sciences