Number Theory Through Inquiry (Maa Textbooks) (Mathematical Association of America Textbooks) | 
 enlarge | Authors: David C. Marshall, Edward Odell, Michael Starbird
Publisher: Mathematical Assn of Amer
Category: Book
List Price: $51.00
Buy New: $41.71
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Rating:  1 reviews
Sales Rank: 80590
Media: Hardcover
Pages: 150
Number Of Items: 1
Shipping Weight (lbs): 0.7
Dimensions (in): 9.1 x 6 x 0.5
ISBN: 0883857510
Dewey Decimal Number: 512
EAN: 9780883857519
Publication Date: December 6, 2007
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Shipping: International shipping available
Condition: Brand New. Delivery is usually 5 - 8 working days from order, International is by Royal Mail Airmail
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Product Description
Number Theory Through Inquiry; is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy ;Number Theory Through Inquiry.; Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and theydevelop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas. They develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.
Book Description
This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book is designed to develop students' mathematical thinking skills, particularly theorem-proving skills, whilst helping them understand some of the wonderfully rich ideas in the mathematical study of numbers.
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| Customer Reviews:
Can be used as a text, would require significant instructor supplements November 3, 2008
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
If you were to use this book as a text in a number theory course, you first must have made the decision to teach it in a nonstandard manner. The approach used in the presentation of number theory is not the traditional listing of the fundamental theorems with their proofs. Concepts are stated as theorems but in no case is a proof offered.
There are several groups of specific exercises such as
Illustrate the division algorithm m = nq + r for m = 25, n = 7; m = 277, n = 4; m = 33, n = 22; m = 33, n = 45.
Questions such as
Do every two integers have at least one common divisor?
What other numbers can you show to be irrational? Make and prove the most general conjecture you can.
Which natural numbers can be written as the sum of two squares of natural numbers? State and prove the most general theorem possible about which natural numbers can be written as the sum of two squares of natural numbers, and prove it.
At several points in the text, there are exercises called "Blank paper exercises" which have the following structure.
After not looking at the material in this chapter for a day or two, take a blank piece of paper and outline the development of that material in as much detail as you can without referring to the text or to notes. Places where you get stuck or can't remember highlight areas that may call for further study.
The coverage is generally what is found in an introductory course in number theory. However, the lack of proofs means that either the students must derive them on their own, look them up in another reference or have the instructor provide them. While this does not preclude the use of this book, it will require extra effort on the part of the student and/or the instructor.
Published in Journal of Recreational Mathematics, reprinted with permission
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