How to Think about Abstract Algebra

What Hacker News says

1. vmilnerJun 2022
   I’m glad they gave their book award to

   “How to think about Abstract Algebra” by Lara Alcock

   Having dipped into it I’d massively recommend it to anyone about to start a maths degree (or just interested in groups, rings, fields generally).

   thread
2. cg30eNov 2021
   For sure. I'll list some books for introduction to proofs, abstract algebra, real analysis, topology and category theory. These are not comprehensive, just listing books off the top of my head. I'll definitely be leaving off personal favorites other people have. You'll like some better than others. Some of these are beginner books and some are more advanced. A good tutor can help you get through the more advanced books. I tried to list the most beginner friendly book first in the list under each subject. Then the more advanced books later in the list.

   Introduction to Proofs:

   Just pick one of these that speaks to you the most. All three are good.

   Discrete Mathematics with Applications - Epp

   Discrete Mathematics and Its Applications - Rosen

   Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al.

   Abstract Algebra:

   How to Think about Abstract Algebra - Alcock

   Abstract Algebra - Pinter

   Abstract Algebra: A First Course - Saracino

   Algebra - Artin

   Abstract Algebra - Herstein

   Abstract Algebra - Dummit & Foote

   Linear Algebra:

   Maybe an engineering based book first if you haven't seen linear algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh).

   Then:

   Linear Algebra - Friedberg, et al

   Linear Algebra Done Right - Axler

   Linear Algebra - Hoffman & Kunze

   Real Analysis:

   How to Think About Analysis - Alcock

   Understanding Analysis - Abbott

   Tao's Analysis text

   Principles of Mathematical Analysis - Rudin

   Topology:

   Topology - Munkres

   Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson, and John Terilla

   Check out this list:

   http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others.

   Category theory:

   Categories and Toposes: Visualized and Explained - Southwell

   Conceptual Mathematics: A First Introduction to Categories - Lawvere

   Category Theory for Programmers - Milewski (if you like functional programming)

   Programming with Categories - Fong, Milewski, Spivak (if you like functional programming)

   Category Theory in Context - Riehl

   There are a few others by Spivak which you may like.

   If you don't know category theory whatsoever then I like Southwell the best (pair them up with his youtube videos). Eugenia Cheng also has a nice set of lecture videos.

   If you already know math pretty well, then Riehl is a favorite.

   Hope that helps!

   Show morethread
3. iueijasdknAug 2021
   I recommend "How to Think About Abstract Algebra" by Lara Alcock and "A Book of Abstract Algebra" by Charles Pinter.
   thread