Proofs and Ideas

In this textbook, Dr. Sethuraman provides an easy to follow guide to various mathematical topics, such as induction, sets, sequences, and groups, which mathematics students would need to understand in order to perform well in upper level mathematics courses. The book is written in a way so that students should not be intimidated by the content but eases the reader into each complex idea. Also, within a given chapter are worked out examples, as well as many independent practice problems that students could complete on their own to further understanding of topics.

 

Dr. Sethuraman has a way of showing how proofs need not be intimidating. Even from the beginning of the book, he discusses proofs in Chapter 1 in an understandable way. Later in the text, the author included an entire chapter, Chapter 6, to introduce the formal idea of proof and different types of proofs to students before beginning detailed discussions on other proof examples like induction in Chapter 7.  

 

This textbook would be useful for any student who wanted to have some basic background knowledge about important mathematics topics before enrolling in upper-level mathematics courses, especially any proof-based courses such as Abstract Algebra and Real Analysis.

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Ann Wheeler is a Professor of Mathematics Education at Texas Woman's University in Denton, Texas.  Her research interests include the use of technology and children's literature in mathematics.