This very simple looking abstract concept hides enormous depth. To illustrate this, observe that calculus is just the study of certain classes of functions (continuous, differentiable or integrable) from R to R.

From the links below you can download an EPUB or PDF version of Abstract Algebra: Theory and Applications and the corresponding PreTeXt source which is licensed under the GNU Free …

When we open a textbook of abstract algebra for the first time and peruse the table of contents, we are struck by the unfamiliarity of almost every topic we see listed.

A basic knowledge of set theory, mathe-matical induction, equivalence relations, and matrices is a must. Even more important is the ability to read and understand mathematical proofs. In this chapter we …

When we open a textbook of abstract algebra for the first time and peruse the table of contents, we are struck by the unfamiliarity of almost every topic we see listed. Algebra is a subject we know well, but …

We define a set X as a collection of “similar” objects, e.g., the names of the 2023-2024 Golden State Warriors, the menu items at the cafeteria this evening, or any collection of real numbers.

We will study the groups abstractly and also group the groups in some natural groups of groups (decide which of the words ”group” are technical terms). Here is a possibly new example: let G = {1, −1, i, −i}, …

This is a very gentle one-semester introduction to abstract algebra. After a warmup chapter on integer divisibility, we consider the basic objects of abstract algebra: rings and elds, vector spaces, and groups.

Of great historical importance is the notion of prime and the property discovered by Euclid that characterizes a prime that became a cornerstone of modern algebra.

This text is intended for a one or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields.