Proofs and fundamentals [electronic resource] : a first course in abstract mathematics / Ethan D. Bloch.
This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses suc...
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| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York :
Springer,
©2011.
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| Edition: | 2nd ed. |
| Series: | Undergraduate texts in mathematics.
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| Subjects: |
| Summary: | This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis. This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. Reviews of the first edition: This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course. --Zentralblatt Math 'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization ... There are large exercise sets throughout the book ... the exercises are well integrated with the text and vary appropriately from easy to hard ... Perhaps the book's greatest strength is the author's zeal and skill for helping students write mathematics better. --MAA Online. |
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| Physical Description: | 1 online resource (xxiv, 359 pages). |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781441971272 1441971270 1441971262 9781441971265 |
| Source of Description, Etc. Note: | Source of description: Print version record. |