Number Theory Through Inquiry
Seiten
2007
Mathematical Association of America (Verlag)
978-0-88385-751-9 (ISBN)
Mathematical Association of America (Verlag)
978-0-88385-751-9 (ISBN)
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An innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals: to help students develop mathematical thinking skills, particularly, theorem-proving skills; and to help students understand some of the wonderfully rich ideas in the mathematical study of numbers.
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.
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.
David C. Marshall is an Assistant Professor of Mathematics at Monmouth University in West Long Branch, New Jersey. Edward Odell is Professor of Mathematics at The University of Texas at Austin. Michael Starbird is Professor of Mathematics and a University Distinguished Teaching Professor at The University of Texas at Austin.
0. Introduction; 1. Divide and conquer; 2. Prime time; 3. A modular world; 4. Fermat's Little theorem and Euler's theorem; 5. Public key cryptography; 6. Polynomial congruences and primitive roots; 7. The golden rule: quadratic reciprocity; 8. Pythagorean triples, sums of squares, and Fermat's Last Theorem; 9. Rationals close to irrationals and the Pell equation; 10. The search for primes; Appendix A. Mathematical induction: the domino effect; Index.
| Erscheint lt. Verlag | 17.4.2008 |
|---|---|
| Reihe/Serie | MAA Textbooks |
| Sprache | englisch |
| Maße | 152 x 231 mm |
| Gewicht | 320 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-88385-751-0 / 0883857510 |
| ISBN-13 | 978-0-88385-751-9 / 9780883857519 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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