A first course in abstract algebra

What Hacker News says

1. hdjjhhvvhgaNov 2021
   Sure. I feel that many contemporary undergraduate/college textbooks are actually fine in this regard (like Topics in Contemporary Math by Bello, Britton, and Kaul). As for the rest, some of my favorites:

   - Warner, Pure Mathematcis for Beginners

   - Devlin, Introduction to Mathematical Thinking

   - Stewart, Concepts of Modern Mathematics

   - Herrmann, Sally, Number, Shape, and Symmetry

   - Baylis, What is Mathematical Analysis?

   - Feil, Krone, Essential Discrete Math for Computer Science

   - Rotman, A First Course in Abstract Algebra with Applications

   - Banjamin, Chartrand, Zhang, The Fascinating World of Graph Theory

   - Zou, Mult-Variable Calculus: A First Step

   - Hubbard, The World According to Wavelets

   - Sayama, Introduction to the Modeling and Analysis of Complex Systems

   - Darst, Introduction to Linear Programming: Applications and Extensions

   - Sourin, Making Images with Mathematics

   - Gallian, Contemporary Abstract Algebra

   And many others. Of course, all such lists are completely arbitrary. Once I get familiar with a certain topic, elaborate explanations seem redundant and I feel like shouting, "Get to the point already!" - whereas the same explanations can be extremely helpful for a beginner.

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2. magnioApr 2021
   > Dummit/Foote, Abstract algebra

   > In fact, overall I would use this book as a reference instead of a primary text, because the idea of reading it through from start to finish scares me.

   That tome scared me too. If you want to self-study abstract algebra, either Fraleigh's "A First Course in Abstract Algebra" or Paulsen's "Abstract Algebra: An Interactive Approach" is a better choice IMHO. Both are more accessible, come with detailed explanations, and the Paulsen book is even accompanied by SageMath code snippets for you to run.

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3. irchansApr 2020
   Maybe "A first course in Abstract Algebra" by Fraleigh available on Kindle for less than $10. https://www.amazon.com/dp/0201763907

   (It's not focused on Monoids. It also covers groups, rings, and fields from a mathematical point of view. It's written for an undergraduate math major with no prior experience in these areas.)

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4. nandemoAug 2019
   My favourite abstract algebra textbook is Fraleigh's A First Course in Abstract Algebra. Unlike the article here, which just dumps you a bunch of definitions, the book introduces each structure with proper motivation. It's not a CS approach though.

   https://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/... (the 1-star reviews apply to the Kindle version, not the contents. Just get the paperback and you'll be fine)

   If you want a CS approach I suggest learning basic Haskell then tackling the fantastic Typeclassopedia. The downside is you'll be missing on structures/theorems that are super useful in math but not that useful in programming.

   https://wiki.haskell.org/Typeclassopedia

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5. mirceamApr 2019
   Not a mathematician, but have spent some time self-learning math. I have not gone through the following books entirely, however I've used them when needed to learn or clarify a concept:

   > Group Theory - I would look for a good abstract algebra book that also covers groups, such as A First Course in Abstract Algebra, Fraleigh or Basic Algebra, Knapp. Another popular recommendation is Abstract Algebra, Dummit and Foote.

   > Topology I think you should first look at a real analysis course and understand metric space topology for Euclidean spaces. If you have taken calculus, you can try and go through Baby Rudin. For topology specifically you can look into Munkres or Introduction to Topological Manifolds, J Lee.

   > Measure Theory T. Tao has a good book on this topic.

   > Differential Geometry Introduction to Smooth Manifolds by J Lee

   > Probability Probability Theory, Achim Klenke

   > Game Theory Game Theory by Maschler, Solan & Zamir

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6. mleventalJan 2019
   goofy suggestion. those are both either grad or senior undergrad books depending on where you are. much better suggestion is

   A Book of Abstract Algebra by Pinter (really gentle)

   or

   A First Course in Abstract Algebra by Fraleigh

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