Description
Each chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness. IBL "Exploration" worksheets appear in many sections, some of which involve numerical investigations. To assist students who may not have experience with programming languages, Python worksheets are available on the book's website. The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects. The topics covered in these explorations are public key cryptography, Lagrange's four-square theorem, units and Pell's Equation, various cases of the solution to Fermat's Last Theorem, and a peek into other deeper mysteries of algebraic number theory.
Students should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the "numberverse."
About the Author
Cam McLeman is Associate Professor of Mathematics at the University of Michigan-Flint.
Erin McNicholas is Professor of Mathematics at Willamette University in Salem, Oregon.
Colin Starr is a Professor of Mathematics at Willamette University in Salem, Oregon.
Book Information
ISBN 9783030989309
Author Cam McLeman
Format Hardback
Page Count 372
Imprint Springer Nature Switzerland AG
Publisher Springer Nature Switzerland AG