Introduction to Mathematical Structures and Proofs (Undergraduate Texts in Mathematics) 2nd Edition by Larry J. Gerstein (PDF)

Description

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 rigor—and the flexible thinking—required 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). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a delightful book. It is well written, clear and even funny in places. Dr. Gerstein has done an excellent job of making his subject appealing. The only flaws I can find are a few misprints of Teeorem numbers when referring to topics covered elsewhere in the text, an error certainly not worth the subtraction of even half a star.Dr. Gersten begins by discussing logic, then set theory. He then teaches topics in Functions, finite and infinite sets, combinatorics and number theory as a way to teach the art of writing clear proofs. Toward the last half of the book, there is more emphasis on the mathematics than teaching how to write proofs, but the real purpose is to lead the reader onto the path to becoming a mathematician. He succeeds beautifully.The competition for the undergraduate’s purchase would probably be Hammack’s Book of Proof, another excellent text. Hammack takes a different approach, using the construction of proofs as a way to introduce the student to mathematical concepts. This book is briefer and written at a more basic level than Gerstein’s book. If you are self-assured in math, proceed directly to Gersteins book. However, why deny yourself the pleasure of reading either of these books? They give different looks at their subjects, and I doubt that many will regret buying and reading both books, starting with Hammack. I certainly don’t.

⭐This book had a huge amount of material covering a wide range of topics. The treatments of the diverse areas are well integrated. The exercises are difficult but manageable based on the discussion. I would recommend it to others who, like me, have a background in an application of math (physics in my case) but have never surveyed math rigorously.Few or no errors found despite painstaking study.The chapter on number theory seemed overly ambitious and I had to skip over the last part of it.

⭐It’s a good book for a hard subject, it’s a very readable textbook and the author’s wit adds a personality to the text. The only fault is that there aren’t a lot of practice problems for some sections, and only the odd answers have solutions in the back of the book.

⭐We are using this book in my Foundations of Math class, which deals a lot with graph and set theory, as well as proofs. The professor chose the book after listening to the author speak at a conference, and I’d say it was a good choice. The book reads very easily, and the problems do well at not being overly complex, while still being challenging enough to conduce learning.

⭐That’s all – 5 stars

⭐Dr. Gerstein is now a friend of mine. I highly recommend this textbook in the Field of Logic and Mathematics.

⭐Un libro excepcional, tanto por los ejemplos elegidos para introducir los conceptos fundamentales, como por el mantenimiento del rigor, aunque exento de una excesiva aridez formal. Muy recomendable para lectores interesados en adquirir una buena base para poder abordar, con la preparación suficiente, temas más complejos de análisis matemático.

⭐

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