Visual group theory
by Nathan C. Carter · first published 2009
71% recommend29% neutral
Why HN recommends it
Approachable, conversational introduction to group theory that is heavy on pictures and examples, treating groups as groups of actions rather than abstractly; suits self-learners and anyone who finds dry algebra hard.
Summarised by Claude from recommending comments
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…a pure definition–theorem–proof kind of structure. But many other areas of pure mathematics at the undergraduate level and above are presented in a similar fashion. (I recommend Nathan Carter’s book Visual Group Theory for a lovely counter-example to the prevailing trend, which starts with the concrete, and is very accessible. http://web.bentley.edu/empl/c/ncarter/vgt/)
on “Why do many math books have so much detail and so little enlightenment? (2010)” ↗…fancier parts of an undergraduate group theory course (Sylow theorems, etc.) are accessible to high school students who go through the work. I wouldn’t hesitate to recommend Nathan Carter’s lovely book Visual Group Theory to any bright 15 year old. But for a (say) 10-year-old, just learning about the symmetries of shapes and tilings is plenty of useful and interesting math.
on “A Coloring Book about Group Theory” ↗If you like pictures, another couple nice books are Nathan Carter’s Visual Group Theory and Marty Weissman’s Illustrated Theory of Numbers, both of which should be accessible to motivated high school students. http://web.bentley.edu/empl/c/ncarter/vgt/ http://illustratedtheoryofnumbers.com
on “Ask HN: Recommend a maths book for a teenager?” ↗…undergraduate technical education. To learn group theory, ring theory, etc., you want to start with a nice stable of explicit concrete examples, explored deeply (I would recommend Nathan Carter’s book Visual Group Theory as a start for someone with a high school math or undergraduate engineering background). Otherwise the theorems and proofs are just symbol twiddling and pattern-matching to some assignment handed down…
on “The Exterior Algebra and Central Notions in Mathematics (2015) [pdf]” ↗…needs 2 generators, so you can’t keep performing a single flip/operation on your mattress and get all viable positions out of it. For folks trying to learn group theory, I recommend Nathan Carter’s book Visual Group Theory, an approachable introduction written in conversational style, full of great pictures (unlike most group theory textbooks, which are abstract and symbol-heavy). http://web.bentley.edu/empl/c/ncarter/vgt/…
on “An insomniac's guide to the group theory of mattress flipping (2005)” ↗A wonderful book that doesn't suffer the discussed flaw is Visual Group Theory by Nathan Carter, discussed on HN earlier. It provides ample motivation and examples before diving into the theorems. https://news.ycombinator.com/item?id=11745486
on “Why do many math books have so much detail and so little enlightenment? (2010)” ↗Visual Group Theory by Nathan Carter is a great introduction. There's a free preview online with the first few chapters, and you can find the whole thing for free through the usual channels.
on “Twice as happy customers means half the marketing spend” ↗Just one suggestion, but https://www.euclidea.xyz/ is a great place to start. Visual Group Theory sounds appropriate too: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/0...
on “A most unexpected answer to a counting puzzle [video]” ↗…mathematics, to give you some perspective on it all? Something I wish I'd known when I did my degree, Norman Wildberger has a great course: https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL55C7C8378... Visual Group Theory, by Nathan Carter is a book you can get something from no matter your level of maths, imho. If you know some linear algebra, Gilbert Strang's course on YouTube may be interesting - https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
on “Ask HN: How to Study Mathematics?” ↗> taught in an incredibly abstract manner And that’s a shame, because a lot of group theory originated in concrete, tangible problems. Check out the book Visual Group Theory by Nathan Carter, discussed (a bit) here: https://news.ycombinator.com/item?id=11745486 https://news.ycombinator.com/item?id=16345844
on “Rotations with quaternions” ↗…equipped than most. Another intro book I thought of was Peter Eccle's introduction to mathematical reasoning. Might be worth looking at. If you want a nice leisurely introduction to groups Nathan Carter's Visual group theory is nice. I got a lot of use out of the princeton encyclopedias of math. Dont expect for them to really teach you anything, but the articles are nice for seeing whats out there. Definitely try to learn…
on “A Programmer’s Introduction to Mathematics” ↗…into abstract definitions and expecting them to symbol-twiddle their way to solutions of unmotivated problems. For anyone wanting to learn about e.g. group theory, let me recommend Nathan Carter’s book Visual Group Theory http://web.bentley.edu/empl/c/ncarter/vgt/
on “Why won’t anyone teach me math?” ↗For group theory, I love Nathan Carter's Visual Group Theory -- very example and picture based. Rather than treating groups abstractly from the beginning, it treats them as "groups of actions" which in my opinion is the best way to view the subject. For a more…
on “Ask HN: Does this math education idea make sense?” ↗…you learn the same way everyone else does, you'll have an easier time talking to others and finding materials on the internet. I know some very innovative books which I highly recommend, for example Visual Group Theory by Nathan Carter: https://bookstore.ams.org/clrm-32/ But the innovation is pedagogical, in what Carter chooses to emphasize and how he presents everything. At the book's core, Carter agrees with everyone…
on “The case against geometric algebra” ↗Visual Group Theory by Nathan Carter is another one I have been enjoying.
on “Immersive Linear Algebra – textbook with fully interactive figures (2015)” ↗