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Synopsis
In the real world of research mathematics, mathematicians do not know in advance if their assertions are true or false. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation requires students to develop a mature process that will serve them throughout their professional careers, either inside or outside of mathematics. Its inquiry-based approach to the foundations of mathematics promotes exploring proofs and other advanced mathematical ideas through these features:
- Puzzles and patterns introduce the pedagogy. These precursors to proofs generate creativity and imagination that the author builds on later
- Prove and extend or disprove and salvage, a consistent format of the text, provides a framework for approaching problems and creating mathematical proofs
- Mathematical challenges are presented which build upon each other, motivate analytical skills, and foster interesting discussion
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Review
From the reviews:
"Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation ... offers an attractive and very plausible approach. The level of sophistication seems just about right for first or second-year college students. ... Although most students who might use this book would have studied calculus, the text is useful for a broader group because only one or two modules require any knowledge of calculus. This is a carefully conceived and well-thought-out approach to the ‘introduction to proof’ course, and it’s worth a careful look." (William J. Satzer, MathDL, July, 2007)
"This book is by Burger (William College) will serve ... courses better than many competitors. Though sufficient accessible to reach the weakest students, he nevertheless avoids the trap of exercises that request purely hygienic proofs -- formal verifications’ of statements no sentient person could doubt. ... Summing Up: Both books: Recommended. Upper-division undergraduates through faculty." (D. V. Feldman, CHOICE, Vol. 45 (3), November, 2007)
"About this title" may belong to another edition of this title.
- PublisherKey College
- Publication date2007
- ISBN 10 1597570427
- ISBN 13 9781597570428
- BindingPaperback
- LanguageEnglish
- Number of pages128
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