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.
eBook - PDF
Bridge to Abstract Mathematics
- 254 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Bridge to Abstract Mathematics
About this book
Information
Subtopic
Mathematics GeneralIndex
MathematicsTable of contents
- front cover
- copyright page
- title page
- Contents
- Some Notes on Notation
- To the Students
- For the Professors
- I THE AXIOMATIC METHOD
- II SET THEORY
- III NUMBER SYSTEMS
- IV TIME SCALES
- V HINTS
- Bibliography
- Index
- About the Authors
- Back Cover
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Yes, you can access Bridge to Abstract Mathematics by Ralph W. Oberste-Vorth,Aristides Mouzakitis,Bonita A. Lawrence in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.