Extending the Frontiers of Mathematics: Inquiries into proof and argumentation | 
 enlarge | Author: Edward B. Burger
Publisher: Key College
Category: Book
Buy New: $67.52
New (10) Used (6) from $34.21
Rating:  1 reviews
Sales Rank: 972094
Media: Paperback
Edition: 1
Pages: 128
Number Of Items: 1
Shipping Weight (lbs): 0.7
Dimensions (in): 8.9 x 6 x 0.6
ISBN: 1597570427
Dewey Decimal Number: 511.36
EAN: 9781597570428
Publication Date: March 28, 2007
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Shipping: International shipping available
Condition: Book is brand new, and has never been opened. Thousands of satisfied customers!
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Product Description
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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| Customer Reviews:
Incomplete and Misleading March 6, 2008
Shai (Starkville, MS USA)
2 out of 2 found this review helpful
This book makes a point of presenting arguments in clearly understood, often nonmathematical terms. Considering the type of course this book will accompany is generally a course for math majors, this is not well-advised, as students will likely be unprepared for higher level math courses where such a casual approach is not taken.
One of the key features of this book is the presentation of theorems as ambiguous statements, and it is left to the reader to determine their veracity. The vast majority of theorems are presented in this way, requiring the reader to "prove and extend" or "disprove and salvage" the statements. This would be a fine approach if there were some kind of answer key with the correct, complete theorems given. But there is not. So students are left with a lot of ambiguous statements, the proofs of which often depend on applying results of earlier, ambiguous statements. This is a very bad approach for a foundational math course, as students generally will not know whether their work is correct or incorrect, and consequently, whether the foundational theorems presented are correct, incomplete, or outright false. I find myself frequently consulting other sources just to determine if what I'm being told in the book is reliable.
This book is also very expensive considering its length (barely over 100 pages) and binding (paperback).
In summation, this book fails as an introduction for math majors for lack of depth, and it fails as an introduction for nonmajors for lack of clarity. The book is also filled with really, awfully bad puns.
I absolutely do not recommend it.
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