A *Bridge to Abstract Mathematics* will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions, rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs.

The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises; Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound; in the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.

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This book is a complete guide to mathematical proof. Through plentiful examples and exercises, the mathematical novice will learn how to prove theorems and explore some fascinating areas of abstract mathematics. This book is ideal preparation for a university course in pure mathematics, and a valuable resource for educators.

Ralph W. Oberste-Vorth earned his Ph.D. in mathematics from Cornell University. In 2002, he became the Chariman of the Department of Mathematics at Marshall University. In 2011, he accepted a position as the Chairman of the Department of Mathematics and Computer Science at Indiana State University.

Aristides Mouzakitis received his BA and MA in mathematics from Hunter College. In Greece, he has worked as a teacher in secondary education and as an English-Greek translator of popular mathematics books and articles. In 2009, he earned his doctorate in mathematics education from the University of Exeter in England.

Bonita Lawrence is currently a Professor of Mathematics at Marshall University. She received her baccalaureate degree in Mathematics Education from Cameron University in 1979. After ten years of teaching, she returned to school and earned her Master's degree in Mathematics at Auburn University and went on to receive her Ph.D. in Mathematics at University of Texas at Arlington.

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**Book Description **Mathematical Association of America, United States, 2013. Hardback. Book Condition: New. Language: English . Brand New Book. Mathematics is a science that concerns theorems that must be proved within a system of axioms and definitions. With this book, the mathematical novice will learn how to prove theorems and explore the universe of abstract mathematics. The introductory chapters familiarise the reader with some fundamental ideas, including the axiomatic method, symbolic logic and mathematical language. This leads to a discussion of the nature of proof, along with various methods for proving statements. The subsequent chapters present some foundational topics in pure mathematics, including detailed introductions to set theory, number systems and calculus. Through these fascinating topics, supplemented by plenty of examples and exercises, the reader will hone their proof skills. This complete guide to proof is ideal preparation for a university course in pure mathematics, and a valuable resource for educators. Bookseller Inventory # AAZ9780883857793

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**Book Description **Mathematical Association of America, United States, 2013. Hardback. Book Condition: New. Language: English . Brand New Book. Mathematics is a science that concerns theorems that must be proved within a system of axioms and definitions. With this book, the mathematical novice will learn how to prove theorems and explore the universe of abstract mathematics. The introductory chapters familiarise the reader with some fundamental ideas, including the axiomatic method, symbolic logic and mathematical language. This leads to a discussion of the nature of proof, along with various methods for proving statements. The subsequent chapters present some foundational topics in pure mathematics, including detailed introductions to set theory, number systems and calculus. Through these fascinating topics, supplemented by plenty of examples and exercises, the reader will hone their proof skills. This complete guide to proof is ideal preparation for a university course in pure mathematics, and a valuable resource for educators. Bookseller Inventory # AAZ9780883857793

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**Book Description **Mathematical Association of America, 2012. Book Condition: New. 2012. Hardcover. A complete guide to mathematical proof, with plentiful exercises and examples. Ideal for educators, and as preparation for students. Series: Mathematical Association of America Textbooks. Num Pages: 249 pages, illustrations. BIC Classification: PBC. Category: (U) Tertiary Education (US: College). Dimension: 261 x 180 x 20. Weight in Grams: 598. Series: Mathematical Association of America Textbooks. 249 pages. A complete guide to mathematical proof, with plentiful exercises and examples. Ideal for educators, and as preparation for students. Cateogry: (U) Tertiary Education (US: College). BIC Classification: PBC. Dimension: 261 x 180 x 20. Weight: 598. . . . . . . Bookseller Inventory # V9780883857793

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**Book Description **Mathematical Association of America. Book Condition: New. 2012. Hardcover. A complete guide to mathematical proof, with plentiful exercises and examples. Ideal for educators, and as preparation for students. Series: Mathematical Association of America Textbooks. Num Pages: 249 pages, illustrations. BIC Classification: PBC. Category: (U) Tertiary Education (US: College). Dimension: 261 x 180 x 20. Weight in Grams: 598. Series: Mathematical Association of America Textbooks. 249 pages. A complete guide to mathematical proof, with plentiful exercises and examples. Ideal for educators, and as preparation for students. Cateogry: (U) Tertiary Education (US: College). BIC Classification: PBC. Dimension: 261 x 180 x 20. Weight: 598. . . . . . Books ship from the US and Ireland. Bookseller Inventory # V9780883857793

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