Introduction to mathematical structures and proofs /
<p>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. <i>Introduction to Mathematical Structures and Pro...
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| Format: | E-book |
| Język: | English |
| Wydane: |
New York, NY
Springer New York
2012.
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| Wydanie: | 2nd ed. 2012. |
| Seria: | Undergraduate Texts in Mathematics
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| Hasła przedmiotowe: | |
| Dostęp online: | Click here to view the full text content |
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| Streszczenie: | <p>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. <i>Introduction to Mathematical Structures and Proofs</i> 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 rigor-and the flexible thinking-required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. </p><p> </p><p>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).</p><p> </p><p>From a review of the first edition: </p><p>"...Gerstein wants-very gently-to 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 knowledge....</p><p>Gerstein's 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 Gerstein's book achieves its goals. I would be happy to use it in a transitions course." </p>-Steven Krantz, <b>American Mathematical Monthly </b> |
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| Opis fizyczny: | 1 online resource (XIII, 401 pages) 133 illustration, digital. |
| ISBN: | 9781461442653 |
| ISSN: | 0172-6056 |