Excursions in Number Theory, Algebra, and Analysis

Kenneth Ireland [1937–1991] was Professor of Mathematics at the University of New Brunswick, Canada. Before UNB, he held positions at Johns Hopkins, Brandeis, Brown, Bowdoin, and a visiting membership in the Institute for Advanced Study. Known for his broad interests and active involvement in all areas of departmental life, he had a lasting impact on generations of students as a teacher and mentor. His widely acclaimed book with Michael Rosen, A Classical Introduction to Modern Number Theory, appears in the series Graduate Texts in Mathematics.Al Cuoco is a Distinguished Scholar at Education Development Center in Massachusetts. Before EDC, he taught high school mathematics for 24 years to a wide range of students in the Woburn, Massachusetts public schools. At EDC, he works in curriculum development, professional development, and education policy, and for over three decades, he has worked with Glenn Stevens in the PROMYS for Teachers program atBoston University. His mathematical interests and research publications lie in algebraic number theory.

“It was my good luck then to receive an invitation to review Excursions in Number Theory, Algebra, and Analysis. The book is a remarkable tribute to the legacy of Kenneth Ireland. … it is important to acknowledge that anyone wishing to center a course on this text will face significant challenges. Given all that is on offer here, these challenges would seem well worth taking on!” (Paul Pollack, The Mathematical Intelligencer, July 6, 2024)“This book is very well motivated and well organized. As its title indicates, it collects topics from algebra and analysis, answering some questions from number theory. This book can be considered as a text as well, for an undergraduate course ... .” (Mehdi Hassani, zbMATH 1529.11001, 2024)“Rather than being a book that one reads from cover to cover, Excursions is a curated collection problems followed by expository material aimed at providing background material useful for solving these problems. I imagine it would be a great experience to have a course taught out of this book. The second author clearly enjoyed the experience of studying this material under the guidance of the first author and wanted to make that experience available to others.” (John D. Cook, MAA Reviews, June 17, 2023)

• Preface.- 1. Dialing In Problems.- 2. Polygons and Modular Arithmetic.- 3. The Fundamental Theorem of Arithmetic.- 4. The Fundamental Theorem of Algebra.- 5. Irrational, Algebraic and Transcendental Numbers.- 6. Fourier Series and Gauss Sums.- Epilogue.- Notation.- Bibliography.- Index.