This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises, many of which are small research problems requiring substantial study or outside reading. Some problems call for new proofs for theorems already covered or for inductive explorations and proofs of theorems found in later chapters.

Elementary Number Theory: An Algebraic Approach (Dover Books on Mathematics)

Science & Math

Ethan D. Bolker

Mathematics

Dover Publications

This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises.

Elementary Number Theory: An Algebraic Approach

W. A. Benjamin Advanced Bk Program

<p>Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them common sense and common knowledge not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world this text helps students use it thoughtfully and wisely. This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully and critically about numerical information in everyday contexts.</p>

Common Sense Mathematics: Second Edition (AMS/MAA Textbooks)

Maura B. Mast

American Mathematical Society

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Books by Ethan D. Bolker