| Dewey Class |
511.3 |
| Title |
Introduction to Mathematical Structures and Proofs ([Ebook]) / by Larry J. Gerstein. |
| Author |
Gerstein, Larry J. |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
2nd ed. 2012. |
| Publication |
New York, NY : Springer |
| , 2012. |
| Physical Details |
XIII, 401 pages :133 illus. : online resource. |
| Series |
Undergraduate texts in mathematics 0172-6056 |
| ISBN |
9781461442653 |
| Summary Note |
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigorâand the flexible thinkingârequired to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader.  The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers).  From a review of the first edition: "...Gerstein wantsâvery gentlyâto teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. ...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledgeâ¦. Gersteinâs book states quite plainly that the text is designed for use in a transitions course. Nothing benefits a textbook author more than having his goals clearly in mind, and Gersteinâs book achieves its goals. I would be happy to use it in a transitions course.â âSteven Krantz, American Mathematical Monthly: |
| Contents note |
Preface to the Second Edition -- Preface to the First Edition -- 1. Logic -- 2. Sets -- 3. Functions -- 4. Finite and Infinite Sets -- 5. Combinatorics -- 6. Number Theory -- 7. Complex Numbers -- Hints and Partial Solutions to Selected Odd-Numbered Exercises -- Index. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
http://dx.doi.org/10.1007/978-1-4614-4265-3 |
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