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Posts with #VisualAlgebra

#VisualAlgebra

Public posts on X that use #VisualAlgebra.

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  1. Matt Macauley@VisualAlgebra
    This week, I recorded 4 new #VisualAlgebra YouTube videos on group actions. I heavily use the following concepts: 1. G-sets 2. Action graphs 3. Group switchboards 4. Fixed point tables. Interested? I'll give you a preview here. Please share! 🧵👇1/16
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    85641319.9K
  2. Matt Macauley@VisualAlgebra
    I just made two new #VisualAlgebra videos, and each of them has some fun group theory puzzles. Lecture 2.7: Dicyclic and diquaternion groups Lecture 2.8: Semidihedral and semiabelian groups Come learn about these fun relatively unknown groups! URL in the replies. 👇
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    118562636.9K
  3. Matt Macauley@VisualAlgebra
    I made two new #VisualAlgebra videos about semidirect products, that are done even before I introduce the concept of a normal subgroup. Lecture 2.9: Semidirect products, intuitively Lecture 2.10: Examples of semidirect products
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    36853723.4K
  4. Matt Macauley@VisualAlgebra
    💥 Some personal news 💥 #VisualAlgebra is finally DONE! I just sent off an 820-page pdf to the editor. Almost exactly 7 years after I started. The zip file that contains the 100+ plain text LaTeX files and nothing else is a whopping 5.4 MB. Now onward to Volume 2!
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  5. Matt Macauley@VisualAlgebra
    I haven't posted a #VisualAlgebra thread in a while. I've made a bunch of never-before-seen visuals on algebraic number theory, and I'm really excited to share them with you! 1/n🧵👇
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  6. Matt Macauley@VisualAlgebra
    #Week1 of #GraduateVisualAlgebra in the books! As promised in my ugrad #VisualAlgebra meta-thread ( I'll post summaries for each day -- LOTS of never-before-seen materials! We'll return to Felix & his topological 🍼 later in the class. 1/8 Wed 🧵👇
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    Matt Macauley @VisualAlgebra
    Now that my #VisualAlgebra class is in the books, I want to post a long "meta thread" of all 16 weekly threads, with daily summaries. Here's my entire class, including lectures, HW, & exams, in one convenient place. And stayed tuned for some surprise announcements below!👇🧵
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  7. Matt Macauley@VisualAlgebra
    Now that my #VisualAlgebra class is in the books, I want to post a long "meta thread" of all 16 weekly threads, with daily summaries. Here's my entire class, including lectures, HW, & exams, in one convenient place. And stayed tuned for some surprise announcements below!👇🧵
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    665441
  8. Matt Macauley@VisualAlgebra
    I want to share some fun unique problems from my Graduate #VisualAlgebra Final Exam yesterday. This first one involves quotients of the Gaussian integers. Note how one quotient has order 10, and the other has order 13. What does this tell us about irreducibility? 1/10
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  9. Matt Macauley@VisualAlgebra
    New #VisualAlgebra video! Lecture 3.2: Subgroup lattices There are LOTS of fun pictures in here. I'm obviously biased, but I really think that this will be greatly beneficial to anyone taking or teaching abstract algebra. Check it out, and please share! 1/2 👇(URL below)
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  10. Matt Macauley@VisualAlgebra
    We finally finished up "Chapter 2: Examples of Groups" today, in #Week6 of #VisualAlgebra. We also held a fun CONTEST, which I'll describe below! Last week, I showed the following 3 Cayley diagrams, and asked: which one is *not* a (nontrivial) direct product? 1/14 Mon 🧵👇
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    11056
  11. Matt Macauley@VisualAlgebra
    @VisualAlgebra
    And many of these are deeply insightful for holistically understanding groups, rings, and fields. #VisualAlgebra isn't "instead" of the classic material, it's IN ADDITION to. Here's one last question from my exam; I like this style and have hundreds just like this. 9/10
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  12. Matt Macauley@VisualAlgebra
    🚨🚨 #MathTwitter Announcement! 🚨🚨 As I'm going through and finalizing chapters in my #VisualAlgebra book, I'm recording a new set of YouTube videos in tandem. This will be more than twice as long as my existing #VisualGroupTheory playlist, with MUCH more content. 1/3 👇
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    33522420.4K
  13. Matt Macauley@VisualAlgebra
    This is SO COOL! 57 pages of #VisualAlgebra written by a 4-time Putnam Fellow and Stanford Professor. I’m telling you, visual learning is the way of the future. I can’t wait to dive into this in more detail later.
    Daniel Litt @littmath
    This, by Ravi Vakil, on depicting homological algebra with puzzle pieces, is insanely cool:
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  14. Daniel Litt✓@littmath
    This, by Ravi Vakil, on depicting homological algebra with puzzle pieces, is insanely cool:
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  15. Matt Macauley@VisualAlgebra
    @VisualAlgebra
    I am finishing up my #VisualAlgebra textbook this summer, and I'm really excited how it's turning out! I will (eventually) be making all of my slides, including LaTeX files & images, freely available. For now, you can view my course materials here: 4/6
    2018
  16. Matt Macauley@VisualAlgebra
    Just finished Chapter 7 of #VisualAlgebra this evening (or a very rough draft of it). Imported it back into the main doc, and hit compile...553 pages! I debating stopping here, but I think I'll write one more chapter, on Galois Theory. Too much rich material to pass up!
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  17. Matt Macauley@VisualAlgebra
    @VisualAlgebra
    If you want to see the entire exam, you can find it here: If you want to see my course materials, such as slides, HW, and all 18 #VisualAlgebra exams I've given, they're all here: Enjoy! 10/10
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  18. Matt Macauley@VisualAlgebra
    @VisualAlgebra
    In #Week5 of #VisualAlgebra, we learned about some "uncommon" groups that we used throughout the semester: dicyclic, diquaternion, semidihedral, semiabelian. We also saw how to construct semidirect products of cyclic groups using Cayley diagrams.
    Matt Macauley @VisualAlgebra
    Can't believe it's already #Week5 in #VisualAlgebra! Today we learned about the dicyclic and diquaternion groups, which aren't widely known (and really hard to motivate w/o visuals), but they are really neat constructions. Definitely tune into this one! 1/14 Mon
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  19. Matt Macauley@VisualAlgebra
    Can't believe it's already #Week5 in #VisualAlgebra! Today we learned about the dicyclic and diquaternion groups, which aren't widely known (and really hard to motivate w/o visuals), but they are really neat constructions. Definitely tune into this one! 1/14 Mon
    2522
  20. Matt Macauley@VisualAlgebra
    @VisualAlgebra
    We started #Week6 of #VisualAlgebra with groups of matrices, the Hamitonians, and a discussion of the classification of finite groups. Then we moved into subgroups & their lattices, cosets, and normal subgroups.
    Matt Macauley @VisualAlgebra
    We finally finished up "Chapter 2: Examples of Groups" today, in #Week6 of #VisualAlgebra. We also held a fun CONTEST, which I'll describe below! Last week, I showed the following 3 Cayley diagrams, and asked: which one is *not* a (nontrivial) direct product? 1/14 Mon 🧵👇
    102
  21. Matt Macauley@VisualAlgebra
    It's Week 4 of #VisualAlgebra, though more like Week 3 b/c of starting Friday, and MLK Day off. Today we discussed abelian groups. It's easy to recognize whether a group is abelian from a Cayley diagram or Cayley table. These are adapted from @nathancarter5's VGT book. 1/6 Mon
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  22. Matt Macauley@VisualAlgebra
    We started #Week7 in #VisualAlgebra yesterday with the tower law. Here are two ways to think about it. One involves cosets as "boxes" in a grid, and the other is in terms of the subgroup lattice: to find the index [H:K], just take the product of the edges b/w them. 1/8 Mon
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  23. Matt Macauley@VisualAlgebra
    Today was the 1st day of my Spring 2022 Abstract Algebra class! This semester, I'll be tweeting class summaries & visual highlights, every MWF in weekly threads, and fun creative HW exercises. Feel free to engage! Can anybody think of a good hashtag? (Also need a book title.)
    Steven Strogatz @stevenstrogatz
    I wish I had taken Abstract Algebra from @mattmacauley when I was in college. Here’s how he teaches it: In contrast, when I asked my teacher what I should think about when I think about groups, he said, “Think about the axioms.”
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  24. Steven Strogatz✓@stevenstrogatz
    I wish I had taken Abstract Algebra from @mattmacauley when I was in college. Here’s how he teaches it: In contrast, when I asked my teacher what I should think about when I think about groups, he said, “Think about the axioms.”
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    351761.1K
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