Introduction to Mathematical Structures and Proofs (eBook)

Larry Gerstein (Autor)

eBook Download: PDF

2012 | 2nd ed. 2012
XIII, 401 Seiten
Springer New York (Verlag)
978-1-4614-4265-3 (ISBN)

Infos

This updated and revised second edition is designed to help students advance from basic calculus to higher-level linear and abstract algebra and number theory. It introduces an array of fundamental structures and shows how to balance intuition and rigor.

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".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. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.).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.

- Steven Krantz, American Mathematical Monthly

"This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses.The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student."
- S. Gottwald, Zentralblatt

This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors.

Autor

Gerstein's primary areas of research have been in quadratic forms and number theory and he has published extensively in these areas. The author's first edition of "Introduction to Mathematical Structures and Proofs" has sold to date (8/2/2010) over 6000 copies and has gone through 5 printings. Gerstein himself has a transition course at UC, Santa Barbara (Math 8-A transition to higher mathematics) from his book since its first publication date. The first edition also received 2 glowing reviews by Steve Krantz for the American Mathematical Monthly, and S. Gottwald for Zentralblatt.

Inhalt

-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets. - 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index

Produkt-Details

• Erscheint lt. Verlag: 5.6.2012
• Reihe/Serie: Undergraduate Texts in Mathematics
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• Schlagworte: Cantor's theorems • counting principles • fundamental theorem of arithmetic • Mathematical Induction • number-theoretic functions • Proof Techniques • relations and partitions • set constructions • transition course
• ISBN-10: 1-4614-4265-6 / 1461442656
• ISBN-13: 978-1-4614-4265-3 / 9781461442653