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.

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.

With this we wish all the readers a happy voyage on the mathematical journey they are about to undertake into this delightful and beautiful realm of abstract algebra.

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 …

Nov 15, 2018 · This is the idea behind abstract algebra. The present course is the study of a \group," which is a set with an asso-ciative operation, having an identity element, and such that each element …

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 …

Jun 27, 2025 · This textbook is recommended for a upper division undergraduate course on abstract algebra and contains enough materials to cover a two-semester sequence, with particular emphasis …

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.

In one sense the core ideas of algebra are abstracted out and viewed from a much larger lens. For example, the problem of finding analogues of the quadratic formula, around the mid 1500’s, led to …