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A very smart non-mathematician friend is looking to learn about groups, and I was wondering if people might have suggestions (this is NOT a duplicate of this question, since a textbook is not what I am looking for, at least not at first).

Community
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Igor Rivin
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    Have a look at the Numberphile video series on youtube. They have a lot of videos for non-mathematicians who are interested! – Edward Evans Mar 28 '16 at 13:46
  • @Ed_4434 Thanks! I will check it out... – Igor Rivin Mar 28 '16 at 13:48
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    Your non-mathematician friend might find the book Abel's Proof, by Peter Pesic, worth a look. – Barry Cipra Mar 28 '16 at 13:56
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    Why exactly do they want to learn about groups? If it is for an application (e.g. point group theory in inorganic chemistry) then it might be best to go for a presentation that is interlaced with the application, rather than a standard mathematical presentation. – Ian Mar 28 '16 at 14:00
  • Compared with most advanced mathematics, basic group theory is not very difficult. Your friend might be surprised at how much success she has with a regular undergraduate textbook. The John Fraleigh book is very readable. – MJD Mar 28 '16 at 14:38
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    @Ian My friend is interested on general principles (she is actually a film-maker!) – Igor Rivin Mar 28 '16 at 14:51
  • A book with a lot of group theory which is related to particle physics and that i like a lot is ''Lie Groups in Particle Physics'' by Georgi – tired Mar 28 '16 at 16:21
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    If you round to the nearest hour, people use an Abelian additive group of order $12$ or $24$ every day when working with time. That's secretly everyone's first group. – Todd Wilcox Mar 28 '16 at 18:47
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    @ToddWilcox: unless you count the order-2 group containing yourself and your reflection in a mirror :-) – Steve Jessop Mar 29 '16 at 09:51
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    Take a look at Introduction to Group Theory. It's pretty gentle, and doesn't assume much prior knowledge, except some familiarity with basic algebra notation. – PM 2Ring Mar 29 '16 at 12:01
  • Most textbooks on introductory group theory don't require any particular mathematical prerequisites beyond being comfortable with abstraction and proofs. – anomaly Apr 20 '16 at 14:13

6 Answers6

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Groups and Symmetry: A Guide to Discovering Mathematics, by David W. Farmer.

The highlighted title may convince that it assumes not too much mathematics for the learner. It is very little book, not of the type Definition-Theorem-Proof.

At least (in on-line preview) I don't find a single concrete mathematical statement, but always beautiful pictures and only that.

enter image description here

p Groups
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Try The Fascination of Groups by Budden.

lhf
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I recommend the Marcus du Sautoy's book: Finding Moonshine : Mathematician's Journey Through Symmetry
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He is also the author of The Music of the Primes.

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Two books not yet mentioned that the OP might want to consider are:

Groups in the New Mathematics by Irving Adler (1967)

Groups and Their Graphs by Israel Grossman and Wilhelm Magnus (1964)

Dave L. Renfro
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I recommend Carter's Visual Group Theory. It makes heavy use of pictures and diagrams (hence the name) and I found it very clear.

Deusovi
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I would suggest to read, Simon Singh's Fermat's Last Theorem. http://simonsingh.net/books/fermats-last-theorem/

It starts with the introduction to simple problem, solutions. And entire history as it evolves to solve the problem surrounding group theory. And then into advanced theory.

Guru
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  • Ahhh.. I see "-1" on the answer. Care to explain why? I thought Simon Singh was a good start for a non-mathematician. – Guru Dec 02 '19 at 05:10