Is there an abstract algebra book that emphasizes the applications to "real world" problems?

Update: By real world, I mean mostly related to physics or other sciences. But references to coding theory or cryptography are also welcome.

  • $\begingroup$ Depends what you mean by "real word" problems. If you allow coding theory, or cryptography, then there are a lot of books. $\endgroup$ – Dietrich Burde Oct 7 '14 at 13:35
  • $\begingroup$ @DietrichBurde That is not exactly what I had in mind, but please, tell me some references that include the topics you mentioned. $\endgroup$ – Dal Oct 8 '14 at 20:33
  • $\begingroup$ Adventures in Group Theory (Rubik's Cube, Merlin's Machine, and Other Mathematical Toys) by David Joyner. $\endgroup$ – Alexander Konovalov Oct 9 '14 at 11:38

$\textbf{1)-}$ Applications of Abstract Algebra with MAPLE by Richard Klima, N.P. Sigmon, E. Stitzinger.

This book will give you so much cryptography using abstract algebra that you will be busy on maple for a few months. It is interesting and great book if you want to use MAPLE.

$\textbf{2)-}$ Applied Abstract Algebra by Lidl and Pilz.

Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. After discussing Lattices and Boolean algebra, they move on to Finite fields and thus come coding theory and cryptography. No computers are needed to read this wonderful text. You must take a look on this one if looking to go in cryptography. Now not just cryptography, this is the only book I have seen which applies algebra in Fields you can't even imagine. Just look at the context of Chapter $7$ of this book, then you will know what I am talking about. Here it is ..enter image description here

$\textbf{3)-}$ Topics in Applied Abstract Algebra by S.R. Nagpaul & S.K. Jain here

4) Group Theory and Physics by Sternberg here. Wonderful book If you are a Physicist

$\textbf{5)-}$ There is one more, Group Theory in Physics: An Introduction by Cornwell, I am not sure as I haven't read it , but my physicist friends have appreciated it a lot here It uses a lot of abstract algebra.

$\textbf{6)}$ Last but not the least is , (if you are a Chemist), Group Theory and Chemistry by David Bishop. My roommate use to study it. He was chemistry major. I looked at Index and wow, Chemistry is empty without algebra...!!!


Check out Contemporary Abstract Algebra by J.A Galian


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