Experimental introduction to number theory - Providence : American Mathematical Society, 2018 - xii, 313 p. : ill. ; 26 cm. - Pure and applied undergraduate texts ; 31 .

Includes bibliographical references and index.

This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems.

9781470430979

Number theory

Instructional exposition

Elementary number theory

Diophantine equations

Probabilistic theory

Metric theory of algorithms

Diophantine approximation

Finite fields and commutative rings

Polynomials

Dynamical systems and ergodic theory

Rational maps

Non-Archimedean dynamical systems

Arithmetic

512.7 / HUT