7

The list of topics you want to study corresponds rather to abstract algebra than group theory. You did not say why you are interested specifically in group theory, but I believe that acquaintance with various algebraic structures in addition to groups would be beneficial for any person learning mathematics beyond school mathematics. Therefore, abstract ...


5

To repeat my comments: I can recommend Fraleigh's classic introduction. It is easy to read for beginners, with many exercises, from easy to difficult, on which self-learners could check themselves. John B. Fraleigh A First Course in Abstract Algebra, 7th Edition. Pearson, 2002.           Because it's been around so ...


4

Math With Bad Drawing has some images that approach an info-graph (and in general is just a great website for math education), for example: https://mathwithbaddrawings.com/2015/07/01/infinity-plus-one-please-check-your-intuitions-at-the-front-desk/ There are some good geometry ones, especially around old compass and straight-edge constructions but that ...


3

I'll echo @XanderHenderson in the comments that Hungerford's Abstract Algebra: An Introduction is a really nice textbook. It's what I had as an undergraduate, and I'm currently re-reading it for maybe the third time. It's one of my favorite, well-written, clear texts. Note that he's committed to a pedagogy that starts from the most familiar/concrete and ...


3

I liked this Discrete Mathematics: An Open Introduction, by Oscar Levin, for generating functions, so I'm guessing it will be good for recurrence relations.


3

"Kids usually struggle with every one of these concepts, let alone all of them together. It is difficult to get the whole picture and all the moving parts. So this place (proof) seems like a good place to show all of this in action." I'm afraid there is no "complete picture" of all the facets of logic and proof that you mention, interrelating in one ...


1

Better yet, I very much liked generatingfunctionology by Herbert Wilf; it is the go-to text for what you are seeking. It addresses generating functions, and considerable help for understanding recurrence relations. (And it's free from the author, and downloadable as a pdf.!) In addition, you'll find extensive information at Ronald L. Graham, Donald E. ...


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