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Reddit mentions of Visual Group Theory (MAA Problem Book Series)

Sentiment score: 7
Reddit mentions: 9

We found 9 Reddit mentions of Visual Group Theory (MAA Problem Book Series). Here are the top ones.

Visual Group Theory (MAA Problem Book Series)
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Found 9 comments on Visual Group Theory (MAA Problem Book Series):

u/Pyromane_Wapusk · 14 pointsr/learnmath

There are definitely ways to visualize algebraic concepts and many algebraic concepts crop up in geometry. Unfortunately, many books and classes won't emphasize visual intuition. So algebra may be harder for you. In some ways, you get over it even if it isn't your cup of tea, but there are also resources for transfering visual/geometric intuition onto algebraic concepts.

After reading it for myself, I recommend the books visual group theory by Nathan Carter, and algebra, concrete and abstract by Frederick Goodman. The first focuses a lot on visual intuition for group theory, but a lot concepts in group theory generalize to abstract algebra in general. The second book is a more traditional book, less focus on visual intuition, uses symmetry of geometrical objects and linear algebra for many of the examples.

u/jacobolus · 13 pointsr/math

I highly recommend you read the relevant chapters of Nathan Carter’s book Visual Group Theory (site, amzn).

u/unclesaamm · 7 pointsr/math

Your professors really aren't expecting you to reinvent groundbreaking proofs from scratch, given some basic axioms. It's much more likely that you're missing "hints" - exercises often build off previous proofs done in class, for example.

I appreciated Laura Alcock's writings on this, in helping me overcome my fear of studying math in general:
https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/

https://www.amazon.com/dp/0198723539/ <-- even though you aren't in analysis, the way she writes about approaching math classes in general is helpful

If you really do struggle with the mechanics of proof, you should take some time to harden that skill on its own. I found this to be filled with helpful and gentle exercises, with answers: https://www.amazon.com/dp/0989472108/ref=rdr_ext_sb_ti_sims_2

And one more idea is that it can't hurt for you to supplement what you're learning in class with a more intuitive, chatty text. This book is filled with colorful examples that may help your leap into more abstract territory: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X

u/beanscad · 5 pointsr/learnmath

https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X

I'm not much of a visual person so I didn't learn much from skimming it, but many people stand by it and it's a beautiful exposition (of a topic I also think is beautiful) indeed!

u/gopher9 · 5 pointsr/musictheory

Lewin's book is... interesting. It's a rare kind of music theory book which involves some actual math (with absolutely abhorrent typesetting). But it's actually quite straightforward if you know some basic group theory.

So I recommend to take a look at Visual Group Theory lectures on youtube: https://www.youtube.com/watch?v=UwTQdOop-nU&list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv. By the way, there's also a book with the same name.

u/NeverACliche · 4 pointsr/math

> I'm hoping for something like what Div, Grad, Curl and All That does for Vector Calculus.

Is that a math text? I am not really familiar with it, but from what I heard it sounds more like a physics/engineering text. Does it have any formal proofs in it?

You won't be able to get too far with a proofless(?) Abstract Algebra text if there exists one to begin with. Even Charles Pinter's A Book of Abstract Algebra presupposes some degree of mathematical maturity.

Anyway, try these and see if you like them:


Visual Group Theory by Nathan Carter


Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem by Al Cuoco, Joseph J. Rotman

u/rcochrane · 3 pointsr/math

FWIW I had no fun with mathematics in school and didn't start studying it til I was in my thirties. I'm no genius, but I now teach the subject and still self-study it. You don't need any mysterious talent to get very competent at university-level maths, just to be interested enough in it to put the hours in.

Self-study is hard and frustrating. Be prepared for that. Reading one page can take a day. You can stare at a definition or theorem for hours and not understand it. Looking things up in multiple books can really help with that -- there are some good resources online as well. Also, some things just take a while to "cook" in the brain; keep at it. Take lots and lots of notes, preferably with pictures. Do plenty of exercises. When you're really stumped, post here.

I'll echo what others have said: add to Spivak a couple of other books so you can change it up. A book on group theory and one on linear algebra would be a nice combination -- maybe one on discrete maths, probability or something similar as well if that interests you. For group theory I think this book is fantastic, though it's expensive.

If you really want to make it through Spivak, make a plan. Break the book down into, say, 50-page chunks and make 50 pages your target for each week (I have no idea whether this is too ambitious for you -- try it and see). Track your progress. Celebrate when you hit milestones.

Good luck!

[EDIT: Also, be aware that maths books aren't really designed to be read like novels. Skim a chapter first looking for the highlights and general ideas, then drill into some of the details. Skip things that seem difficult and see if they become important later, then go back (with more motivation) etc.]

u/lamson12 · 2 pointsr/math

Here is an actual blog post that conveys the width of the text box better. Here is a Tufte-inspired LaTeX package that is nice for writing papers and displaying side-notes; it is not necessary for now but will be useful later on. To use it, create a tex file and type the following:

\documentclass{article}
\usepackage{tufte-latex}

\begin{document}
blah blah blah
\end{document}

But don't worry about it too much; for now, just look at the Sample handout to get a sense for what good design looks like.

I mention AoPS because they have good problem-solving books and will deepen your understanding of the material, plus there is an emphasis on proof-writing when solving USA(J)MO and harder problems. Their community and resources tabs have many useful things, including a LaTeX tutorial.

Free intro to proofs books/course notes are a google search away and videos on youtube/etc too. You can also get a free library membership as a community member at a nearby university to check out books. Consider Aluffi's notes, Chartrand, Smith et al, etc.

You can also look into Analysis with intro to proof, a student-friendly approach to abstract algebra, an illustrated theory of numbers, visual group theory, and visual complex analysis to get some motivation. It is difficult to learn math on your own, but it is fulfilling once you get it. Read a proof, try to break it down into your own words, then connect it with what you already know.

Feel free to PM me v2 of your proof :)

u/Oh_How_Absurd · 1 pointr/math

Eh. Not every abstract algebra/group theory textbook even tries to link its topics to the intuitive modes of thinking that evolution had to work with.

https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X

This book might be worth a shot?

..You're probably beyond this level though.