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New and Noteworthy Titles on our Bookshelf
May 2023
Irrationality and Transcendence in Number Theory
By David Angell. Chapman and Hall/CRC, 2021, 224 pp.
The early Greeks believed that the ratio of lengths of line segments would always be a rational number. When this was found to be false by the Pythagorean school, the study of irrational numbers began. Irrationality and Transcendence in Number Theory touches on the impact and ideas of irrational numbers from their discovery to current work relying on the work of Alan Baker and Kurt Mahler.
Written as a textbook for advanced undergraduates or early grad students, it is recommended that the reader have a background in basic number theory, including modular arithmetic, calculus, linear algebra, and group theory. In each case, appendices are included that can be used to remind or guide the reader through this content, if necessary. Topics covered include, but are not limited to irrationality, transcendence, Diophantine equations, continued fractions, and automata theory.
The author strives to provide additional insight into proofs by discussing the spirit and motivation for various arguments before presenting the actual proof. For example, this is done when introducing Hermite’s method for proving irrationality, beginning with a discussion of why is irrational for , prior to giving the formal proof. Written in an approachable manner, this book would be an excellent text or resource for anyone teaching or learning about irrational and transcendental numbers.

The Art of Mathematics – Take Two
Tea Time in Cambridge
By Béla Bollobás. Cambridge University Press, 2022, 348 pp.
Courtesy of Cambridge University Press through PLSclear.
There is nothing quite like the thrill of solving a mathematical problem. Whether it’s finally overcoming the roadblock in a proof or working out a brainteaser, many of us chase that feeling. If that describes you, don’t hesitate to check out The Art of Mathematics – Take Two.
A successor to The Art of Mathematics: Coffee Time in Memphis, this book collects 128 mathematical problems, written at all levels. Questions cover a wide range of topics including analysis, graph theory, and linear algebra. Some questions are easy to state and their solutions are accessible for calculus students. Others require a more mature mathematical background and can serve as an introduction to a new field of mathematics. At the back of the book there are hints and detailed solutions to each question. Where appropriate, historical context of a question or solution is provided. Many of the problems have historical ties to Cambridge mathematicians or physicists, such as John Edensor Littlewood and Paul Dirac.
This book would be a great source of problems to talk about at a departmental tea or for a problem-solving seminar. The problems don’t need to be answered in any order and the reader is encouraged to flip through the questions until they find one that sticks with them. With so many interesting problems and topics, you are bound to have plenty to choose from!