A Friendly Introduction to Abstract Algebra

by Ryota Matsuura

A Friendly Introduction to Abstract Algebra offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics. The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own. Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.

387 pages, Paperback

Published July 5, 2022

Reviews

[Blerta · Rating 5 out of 5]

MY FAVORITE MATH CLASS THIS SEMESTER

Literally just about every theorem has the proof written right underneath it and there’s always like 2-3 examples then using each theorem, it is legit a friendly introduction

[Lucille Nguyen · Rating 4 out of 5]

What it says on the tin: a largely self-contained and accessible introduction to abstract algebra. Calls the structure "commutative group" instead of "Abelian group" which is probably good for an introduction but continuing the practice on to the later chapters probably isn't a good way to get students familiar with the terminology of mathematics. Pretty comprehensive for a little introduction and covers quite a bit of ground in its pages.

[Liam Gallagher · Rating 5 out of 5]

Pretty awesome