Abstract Algebra: Theory and Applications by Thomas W. Judson 2017 edition; hardcover; 434 pages
ISBN 978-1944325-05-3; $25.99 Purchase;
download.

Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract
algebra to college juniors and seniors in a rigorous manner. Its strengths
include a wide range of exercises, both computational and theoretical, plus many nontrivial applications.
The first half of the book presents group theory, through the Sylow theorems,
with enough material for a semester-long course. The second-half is suitable for a second
semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields,
concluding with Galois Theory.

Linear Algebra
by Jim Hefferon
3rd edition (2017); paperback; 508 pages
ISBN 978-1944325-03-9; $21.95 Purchase;
download.

The approach is developmental. Although it covers the requisite material by proving things, it does not assume that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise each student's level of mathematical maturity.

Active Calculus
by Boelkins, Austin, and Schlicker
2016 edition; paperback; 550 pages
ISBN 978-1944325-00-8; $20.95 Purchase;
download.

IActive Calculus is different from most existing texts in at least the following ways: The style of the text requires students to be active learners; there are very few worked examples in the text, with there instead being 3 or 4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas. Each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class. The exercises are few in number and challenging in nature. The book is open source and can be used as a primary or supplemental text.

Introduction to Modern Set Theory
by Judith Roitman
3rd edition; paperback; 220 pages
ISBN 978-0-9898975-1-8; $12.99 Purchase;
download.

Introduction to Modern Set Theory is designed
for a one-semester course in set theory at the advanced undergraduate or beginning graduate level.
Three features are the full integration into the text of the study of models of set theory,
the use of illustrative examples both in the text and in the exercises,
and the integration of consistency results and large cardinals into the text early on.
This book is aimed at two audiences: students who are interested in studying set theory
for its own sake, and students in other areas who may be curious about applications of
set theory to their field. In particular, great care is taken to develop the intuitions
that lie behind modern,
as well as classical, set theory, and to connect set theory with the rest of mathematics.

A First Course in Complex Analysis
by Beck, Marchesi, Pixton, and Sabalka
Edition 1.53; paperback; 216 pages
ISBN 978-1944325-04-6; $11.95 Purchase;
download.

A First Course in Complex Analysis was developed from lecture notes for a one-semester undergraduate course taught by the authors. For many students, complex analysis is the first rigorous analysis (if not mathematics) class they take, and these notes reflect this. The authors try to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated from scratch.

Lecture Notes in Functional Analysis
by William L. Paschke
in production.

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What is an L3C?

A low-profit limited liability company (L3C) is a company that is created for a specific educational or charitable purpose. The purpose of Orthogonal Publishing L3C is to help create and/or disseminate free and/or low-cost open-content educational materials. One of the main ways we do so is by publishing low-cost print editions of high-quality open-content books. Orthogonal Publishing L3C is registered in Michigan, one of only a few states that recognize L3Cs, and is located in Ann Arbor.

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Who does the art on the covers?

The cover art for Abstract Algebra and Modern Set Theory is by Robert A. Chaffer, and is used with his explicit permission. See his online gallery. Dr. Chaffer is Professor Emeritus at Central Michigan University. His academic interests are in abstract algebra, combinatorics, geometry, and computer applications. Since retirement from teaching he has devoted much of his time to applying those interests to creation of art images.

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