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A Transition to Proof

Neil R. Nicholson
Publisher: 
CRC
Publication Date: 
2019
Number of Pages: 
462
Format: 
Hardcover
Series: 
Textbooks in Mathematics
Price: 
99.95
ISBN: 
9780429259838
Category: 
Textbook
[Reviewed by
Tom Schulte
, on
08/24/2019
]
Generally, I find works promising to guide the reader in constructing proofs and approaching advanced mathematics reside at either end of a spectrum. At one end, at least an advanced undergraduate is the target, at the other, the material is too lacking in rigor for serious merit. Here, easily two-thirds of the material on symbolic logic and writing proofs has value to the high school student planning to major in mathematics as well as correct any bad habits in the aforementioned advanced undergraduate.
 
The focus is not on the calculus sequence but rather developing tools and techniques for pure mathematics subjects such as set theory and topology. First, the foundational language and techniques of proofs are established in the first few chapters on symbolic logic and set theory through detailed and patient exposition. For instance, induction is developed over thirty pages. Then, the reader moves seamlessly into applying the acquired skills in later chapters on cardinality and (an author favorite) introductory topology. Thus, transition occurs.
 
Other key features of this book include selected solutions and hints. Also, there are numerous called out “tips” exemplified and detailed such as:
 
Unnecessary variables congest a proof
and
 
Do not use symbols to start sentences.
These are compiled and expanded into an appendix ready for review and reference before submitting a key assignment or authoring a paper.

 

Tom Schulte is the Web Coordinator for the Louisiana-Mississippi Section of the MAA.

See the publisher's web page.

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