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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries. This book accomplishes the vast majority of what it was written to do. Solow develops, with careful detail and numerous examples, all of the proof techniques typically introduced in a proof-writing class.
Starting with the basic idea of logically manipulating both sides of the proposition in an attempt to connect them, he works up to more subtle and more powerful techniques involving uniqueness, methods of induction, and proof by contrapositive.
The last hundred pages or so are devoted to examples from particular subjects, including linear and abstract algebra, analysis, and set theory. Throughout the book, the author presents many ubiquitous mathematical definitions. An introduction to such a wide range of mathematics early in the curriculum will provide up-and-coming math majors with a more accurate idea of their future studies, helping to dispel the freshman fear that all mathematics is like Calculus II.
The explanation of proof by contradiction and the description of induction are wonderful. They are extremely intuitive and provide the reader with a satisfying understanding of how these tools function. Not everything is so intuitive though. Some of the proofs feel a bit contrived, the logic a bit obscure.
This gap may be indicative of the maturity that comes with mathematical experience. The language that Solow creates to describe general proof methods at times becomes hard to read. Some of the sentences seem as though they should have been spoken rather than read; maybe some italics are needed to set off longer phrases e.
Definitions are sometimes used in exercises before the chapters in which they are introduced. This mix-up is just confusing for an experienced reader, but could really be a problem for a beginner, particularly when the purpose of the book is to teach precise logical argumentation. This book is a very solid, detailed introduction to mathematical proof-writing.
It would function well as the main text if the focus of the class was writing proofs, and it would serve excellently as a supplement to classes that offer proof-writing as a side goal: a course in discrete mathematics, an introductory class in set theory, or a basic course in topology.
William Porter is an undergraduate mathematics-physics double major at a small liberal arts college. He enjoys ballroom dancing, cooking, and T. He thinks that Rachmaninoff writes amazing music and rain is the best weather. His favorite Big Bang Theory character is Sheldon. Skip to main content. Search form Search. Login Join Give Shops.
Halmos - Lester R. Ford Awards Merten M. Daniel Solow. Publication Date:. Number of Pages:. BLL Rating:. The Truth of It All. The Forward-Backward Method 3. On Definitions and Mathematical Terminology. Quantifiers I: The Construction Method.
Quantifiers III: Specialization. Quantifiers IV: Nested Quantifiers. Nots of Nots Lead to Knots. The Contradiction Method. The Contrapositive Method. The Uniqueness Methods Solutions to Selected Exercises. Transition to Advanced Mathematics. Log in to post comments.
How to Read and Do Proofs : An Introduction to Mathematical Thought Processes
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How to Read and Do Proofs
How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, 6th Edition