A Transition to Advanced Mathematics [Hardcover]

Douglas Smith (Author), Maurice Eggen (Author), Richard St. Andre (Author)

Book Description

ISBN-10: 0534399002 | ISBN-13: 978-0534399009 | Publication Date: June 14, 2005 | Edition: 6

TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses.

Editorial Reviews

About the Author

Douglas Smith is Professor of Mathematics at the University of North Carolina at Wilmington. Dr. Smith's fields of interest include Combinatorics / Design Theory (Team Tournaments, Latin Squares, and applications), Mathematical Logic, Set Theory, and Collegiate Mathematics Education.

Maurice Eggen is Professor of Computer Science at Trinity University. Dr. Eggen's research areas include Parallel and Distributed Processing, Numerical Methods, Algorithm Design, and Functional Programming.

Richard St. Andre is Associate Dean of the College of Science and Technology at Central Michigan University. Dr. St. Andre's teaching interests are quite diverse with a particular interest in lower division service courses in both mathematics and computer science. --This text refers to an out of print or unavailable edition of this title.

Product Details

• Hardcover: 384 pages
• Publisher: Brooks Cole; 6 edition (June 14, 2005)
• Language: English
• ISBN-10: 0534399002
• ISBN-13: 978-0534399009
• Product Dimensions: 9.2 x 7.4 x 0.8 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.1 out of 5 stars  See all reviews (37 customer reviews)
• Amazon Best Sellers Rank: #229,792 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

12 of 13 people found the following review helpful:

4.0 out of 5 stars Underrated Mathematics Text, July 10, 2007

By 

Leicester Dedlock (Ames, IA United States) - See all my reviews

This review is from: A Transition to Advanced Mathematics (Hardcover)

I've honestly never understood the negativity thrown towards this book.

This book introduces basic proof-writing techniques, naive set theory, cardinality, functions, and also includes a very brief introduction to abstract algebra and real analysis. I thought that the section on proofs was quite well done even though there are better textbooks which cover this topic more extensively with more examples. The examples are generally simple and are pulled almost exclusively from number theory, but they provide understanding. The set theory chapter is not very rigorous, but it meets the goals of the type of student who would take such a class. A more rigorous (i.e. axiomatic) introduction to set theory would require an entire semester, and the goal of this book is simply to provide students with just enough tools to prepare themselves for classes like Abstract/Modern Algebra, Real Analysis, and Set Theory, but not much more. Also, I consider the proofs to be generally well-written although there are occasional mistakes.

The chapters introducing abstract algebra and real analysis don't provide much information, but only serve to give students a taste of the fields. I felt that they should have either been omitted (since you won't learn much) or they should have been introduced with more rigor and explanation.

Some people have complained that the exercises were too hard. I felt that the opposite was true. All of the problems are either trivial or of medium difficulty. I think that the problem was that the proofs presented in the text were even easier. The proofs are generally well-written, but it would have been nice to see more challenging proofs to give the student a better idea of how to work the more challenging homework problems.

It's not the best or the worst text that you can find on this subject. At minimum, it's at least underrated (though overpriced).

16 of 20 people found the following review helpful:

4.0 out of 5 stars Read Carefully and Think!, January 25, 2006

By 

Erik Wallace "Erik Wallace" - See all my reviews
(REAL NAME)   

This review is from: A Transition to Advanced Mathematics (Hardcover)

Firstly, I must clarify: other reviewers have said that the book claims 1 + 2 does not equal 3. They are not reading carefully enough. I have the 5th edition, and this is exactly what it says (on page 18 for the 5th edition).

"The sentence 'x1 is equal to x2 + x3' is an open sentence with three variables. If we denote this sentence by P(x1,x2,x3), then P(7,3,4) is true since 7 = 3 + 4, while P(1,2,3) is false."

Now to translate for them, in the case of P(1,2,3)
x1 = 1, x2 = 2 and x3 = 3. Thus the sentence says 1 = 2 + 3 which is false, not 1 + 2 = 3 as other reviewers have claimed. What is confusing is the order and the abstract expression. In the order given P(3,1,2) would say 3 = 1 + 2.

Now as for my rating, I do not claim that the book is ideal. But, it does fill a gap in math education, and there are not many other books like it. A good replacement would be an introduction to logic, or to set theory, but this book contains both. I hope we will see more books like this in the future, and if we do then we may eventually find one worth bragging about.

Currently, though, there is no such book that I know of, and believe me I have seen a lot of books. In the meantime this book can serve as a valuable reference. So, as per my title: read carefully and think! If you do that, then the contents of this book should be crystal clear to you.

6 of 7 people found the following review helpful:

4.0 out of 5 stars Not a Bad Textbook, November 9, 2006

By 

Alethio Grapher (Denver, CO USA) - See all my reviews

Amazon Verified Purchase

This review is from: A Transition to Advanced Mathematics (Hardcover)

We've been using this in our Introduction to Mathematical Proofs class (an upper-level undergraduate math class). I was a little nervous after seeing so many bad reviews here, but it's been a fine textbook. It's easy to learn the material from the book, and the question/problem sets are useful too. I don't have any other books of this type to compare it to, of course, but the layout of the text and material is clear, with definitions and properties given as needed.