Free Abstract Math, Abstract Algebra & Proofs Textbooks

Some consider abstract math “higher” or “pure math.” It’s a new term for me but it seems like abstract math creates the rules that other forms of mathematics follow. One of the authors showcased here on The Free Textbook List explained that abstract math “requires conceptual reasoning about abstract ideas (as well as manipulating symbols), in particular on understanding and constructing proofs. Abstract math is mathematics for its own sake. In doing abstract math, you state theorems and prove them mostly in the context of mathematical ideas rather than applications or ideas from other fields.” (as defined by Charles Wells of

I suspect anyone looking for abstract math textbooks or abstract algebra textbooks will find my little definition quite pedestrian. Hopefully, they will find the free online textbooks and materials of much more use to their studies.

List of Free Abstract Math, Abstract Algebra & Proofs Textbooks

Abstract Algebra Online

Written by: John A. Beachy and William D. Blair

Abstract Algebra Online Textbook based on the earlier works of John A. Beachy and William D. Blair. For advanced undergrads and 1st year graduate students.

Written by: Charles Wells (Case Western Reserve University)

An abstract math professor created an entire website focussed on clear and concise word choices in forming his teachings. The glossary is a true hidden gem.

An Introduction to Proofs and the Mathematical Vernacular

Written by: Martin Day (Virginia Tech)

This text or ‘bridge course’ aids students moving from calculational math, generally after 2 years of calculus, to more theoretical and proof-driven math.

Book of Proof

Written by: Richard Hammack (Virginia Commonwealth University)

The Book of Proof is a free online abstract math textbook written to help students expand from computational mathematics to theoretical mathematics.

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