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A Primer of Abstract Mathematics (Classroom Resource Materials) Paperback – July, 1998

ISBN-13: 978-0883857083 ISBN-10: 0883857081 Edition: 0th

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Product Details

  • Series: Classroom Resource Materials
  • Paperback: 190 pages
  • Publisher: The Mathematical Association of America (July 1998)
  • Language: English
  • ISBN-10: 0883857081
  • ISBN-13: 978-0883857083
  • Product Dimensions: 6 x 0.4 x 9 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #1,181,050 in Books (See Top 100 in Books)

Editorial Reviews

Book Description

The purpose of this book is to prepare the reader for abstract mathematics. Ash tries to aid intuition by keeping proofs short and as informal as possible, and using concrete examples as illustration. Thus it is an ideal textbook for an audience with limited experience in formalism and abstraction.

Customer Reviews

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Most Helpful Customer Reviews

12 of 12 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on December 29, 2003
Format: Paperback
I would alter the title by dropping the word abstract, as the book could be considered a primer on the mathematics of an undergraduate major. I recently completed teaching a course in fundamentals of logic and arithmetic for elementary education majors and many of the topics we covered are in here. The basics of logic, counting, sets and functions, the content of the first two chapters of this book, were all in the fundamentals class, although obviously not to this level of detail. Factoring, unique factorization, modular arithmetic, and the cardinality of sets, covered in chapters four and five, were also the subjects of several of my lectures. Only the principles of linear algebra and linear operators, the topics of chapters 5 and 6, are in this book but were not in my class.
The coverage here is basic, with a set of problems at the end of each section. Solutions to all of the problems are given at the end of the book, a very commendable thing to have done. All of the topics covered are explained in a routine, yet thorough manner. By that I mean that the explanatory strategy is largely a traditional one, with definitions, theorems, proofs and interspersed examples where appropriate. Diagrams are used, but only rarely.
Solid, but not spectacular, this book covers the fundamentals of mathematics that all students should know before they begin calculus and linear algebra. It can serve as a primer or a refresher, depending on whether you are moving forward or are retracing old ground.
Published in the recreational mathematics e-mail newsletter, reprinted with permission.
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16 of 17 people found the following review helpful By Serban Popovici on January 24, 2004
Format: Paperback
I have used many of Robert Ash's book, including "Information Theory", which was his first published textbook based on notes he used at Columbia University to teach a course by the same name and which were subsequently used by other instructors, and "Basic Probability Theory". His books all have the same characteristic: simple direct introduction to the subject, powerful penetration to the core of the subject matter with no clutter and a deceptively comprehensive coverage in a succint manner. Any time spent with any of his books is well spent. In this instance I can not think of a better introduction to abstract mathematics. As another reviewer noted, the treatment of linear algebra is evidence of Ash's concise and powerful method. Having said this I would strongly reccomend, as Ash himself does, that the reader consult other books to flesh out the treatment, or better still to create and work through his own examples and exercises. Highly recommended!
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1 of 1 people found the following review helpful By Gabi on September 23, 2014
Format: Paperback Verified Purchase
For a mathematician Robert B. Ash is very clear. If you have ever read books written by other math authors, this book is a fresh breeze.
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0 of 2 people found the following review helpful By Andrea V on February 22, 2012
Format: Paperback
This book, as promised was in excellent condition and came in a timely manner. I'm using this book for a discrete mathematics course, and it serves as a very helpful tool in understanding what is going on.
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2 of 7 people found the following review helpful By Charles Ashbacher on December 22, 2003
Format: Paperback
I would alter the title by dropping the word abstract, as the book could be considered a primer on the mathematics of an undergraduate major. I recently completed teaching a course in fundamentals of logic and arithmetic for elementary education majors and many of the topics we covered are in here. The basics of logic, counting, sets and functions, the content of the first two chapters of this book, were all in the fundamentals class, although obviously not to this level of detail. Factoring, unique factorization, modular arithmetic, and the cardinality of sets, covered in chapters four and five, were also the subjects of several of my lectures. Only the principles of linear algebra and linear operators, the topics of chapters 5 and 6, are in this book but were not in my class.
The coverage here is basic, with a set of problems at the end of each section. Solutions to all of the problems are given at the end of the book, a very commendable thing to have done. All of the topics covered are explained in a routine, yet thorough manner. By that I mean that the explanatory strategy is largely a traditional one, with definitions, theorems, proofs and interspersed examples where appropriate. Diagrams are used, but only rarely.
Solid, but not spectacular, this book covers the fundamentals of mathematics that all students should know before they begin calculus and linear algebra. It can serve as a primer or a refresher, depending on whether you are moving forward or are retracing old ground.
Published in the recreational mathematics e-mail newsletter, reprinted with permission.
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