Number Theory Through Inquiry

by Marshall, David C.; Odell, Edward; Starbird, Michael

• ISBN13: 9780883857519
• ISBN10: 0883857510
• Format: Hardcover
• Copyright: 2007-12-06
• Publisher: Mathematical Assn of Amer

Summary

This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first 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 independent study, or for a course designed as an introduction to abstract mathematics. 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, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.

Author Biography

David Marshall was born in Anaheim, California and spent most of his early life in and around Orange County. After receiving a bachelor's degree in mathematics from California State University at Fullerton he left the Golden State to attend graduate school at the University of Arizona. David received his Ph.D. in mathematics in 2000 specializing in the field of algebraic number theory. He held postdoctoral positions at McMaster University in Hamilton, Ontario and The University of Texas at Austin before becoming an Assistant Professor at Monmouth University in West Long Branch, New Jersey. David has been an active member of the MAA and AMS for over 10 years and currently serves as the Program Editor for the MAA's New Jersey section. Edward Odell was born in White Plains, New York. He attended the State University of New York at Binghamton as an undergraduate and received his Ph.D. from MIT in 1975. After teaching 2 years at Yale University he joined the faculty of The University of Texas at Austin where he has been since 1977, currently as the John T. Stuart III Centennial Professor of mathematics. He is an internationally recognized researcher in his area, the geometry of Banach spaces and is a much sought after speaker. Odell was an invited speaker at the 1994 International Congress of Mathematics in Zurich. He has given series lectures at various venues in Spain and recently at the Chern Institute in Tianjin, China. He is the co-author of Analysis and Logic and co-editor of two books in the Springer Lecture series. Michael Starbird received his B.A. degree from Pomona College and his Ph.D. from the University of Wisconsin, Madison. He is a distinguished Teaching Professor of mathematics at The University of Texas at Austin and is a member of UT's Academy of Distinguished Teachers. He has won many teaching awards, including the 2007 Mathematical Association of America Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. He has written two books with co-author Edward B. Burger; The Heart of Mathematics: An invitation to effective thinking and Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas. Starbird has produced four video courses for the Teaching Company: Change and Motion: Calculus Made Clear; Meaning from Data: Statistics Made Clear; What are the Chances? Probability Made Clear; and, with collaborator Edward B. Burger, The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas.

Table of Contents

Introduction

Divide and conquer

Prime time

A modular world

Fermat's Little theorem and Euler's theorem

Public key cryptography

Polynomial congruences and primitive roots

The golden rule: quadratic reciprocity

Pythagorean triples, sums of squares, and Fermat's Last Theorem

Rationals close to irrationals and the Pell equation

The search for primes

Mathematical induction: the domino effect

Index

Table of Contents provided by Publisher. All Rights Reserved.