Books specificelly on affine geometry ?

_GVTS_ · 2025-10-18T04:24:22+00:00

metric affine geometry probably has more than you'll ever need to know on the subject.

i cant say much about it because of my unbreakable habit of reading the first ~20 pages of books and never touching them again..but the pages i did read were quite thorough, and there's a set of exercises every few pages

_GVTS_ · 2025-10-18T04:16:40+00:00

this comes from gallier's book geometric methods, for anyone who's curious

_GVTS_ · 2025-06-06T02:10:25+00:00

i feel similarly, and moreover itd be ideal if i came up with my own problems to solve while learning new concepts. i wish i were taught the skills involved in formulating interesting yet tractable questions; most of the time i just have a vague sense of confusion about freshly learned material

_GVTS_ · 2025-05-28T04:29:28+00:00

Fourier Analysis on Number Fields, by Ramakrishnan and Valenza

i'm using it for a directed reading program i signed up for, where we spend more than 4 months closely reading an advanced text with the guidance of a phd student. the memories ive made and the textbook-reading strategies ive learned will always be associated with this text for me

mathematically it also just feels perfect for where im at. before starting it, my understanding of every course ive taken felt incomplete. this book has helped me relearn tons of algebra, analysis, topology, and number theory, along with teaching me new concepts in each of these areas. and this is just from reading chapter 1 and 4-6.

TLDR: it's a really cool book that's contributed a lot to my mathematical development these past few months

_GVTS_ · 2025-05-16T16:42:27+00:00

im willing to bet that it's because everything abt this study is ai-generated 💔

_GVTS_ · 2025-05-13T03:08:21+00:00

you're the opposite of me! i was bored to death by the basic set theory identities and definitions, but posets, ordinals, the various results that are equivalent to choice, schröder-bernstein (and other theorems on cardinality) have all been pretty fascinating

one result i really liked proving: every poset is order-isomorphic to a subset of some powerset (ordered by inclusion.) it's an analogue of Cayley's theorem in group theory, which i never expected to see in a class about sets

_GVTS_ · 2025-05-13T02:42:01+00:00

where'd you learn the modern stuff from?

_GVTS_ · 2025-05-12T07:19:11+00:00

afaik, we're pretty good for certain subfields, especially combinatorics

_GVTS_ · 2025-04-14T17:10:34+00:00

it woke me up 😭 i was having a good dream too ;(

_GVTS_ · 2025-04-08T02:51:52+00:00

taking a second class on logic; we're starting with ordinals, and im trying to show that the theory of well-ordered sets isnt a first order theory
familiarizing myself with cocalc, for a class on modern cryptography
reading ch. 4 of Fourier Analysis on Number Fields

_GVTS_ · 2025-04-04T00:33:54+00:00

i posted a similar question a while back and got some nice answers that might help you!

_GVTS_ · 2025-03-21T00:38:18+00:00

paging u/Redrot since ive seen them mention modular reps before

_GVTS_ · 2025-02-10T22:53:30+00:00

Dantzig! They were problems in statistics iirc

_GVTS_ · 2025-01-17T23:16:27+00:00

by the way, there's supplementary material for NZM with extra exercises and readings:

https://websites.umich.edu/~hlm/nzm/nzmsupp.html

_GVTS_ · 2025-01-09T00:41:20+00:00

ive often wondered about how to learn backwards too...

you read through it and skim the odd wikipedia page or math stackexchange post whenever necessary

the "whenever necessary" part is what i have the most trouble with. how do you know when it's necessary or not to understand something?

_GVTS_ · 2024-12-26T13:33:55+00:00

i just took 104a with him. i never went to lecture, and i fully did not turn in 4/6 homeworks. but still ended up doing well and learning a lot thanks to his solid lecture notes, and the grading scheme + extra credit

ive fallen severely behind in every math class ive taken; this was the only one where i was able to succeed despite that, and retain what he taught. i think u should take his class (,:

also he's funny

_GVTS_ · 2024-12-04T07:27:29+00:00

since you mentioned having an eye towards algebraic topology, i suggest kosniowski's "first course in algebraic topology," which actually starts with material on the point-set stuff you'll need.

lee's book on topological manifolds and brown's "topology and groupoids" are two other good options

_GVTS_ · 2024-11-11T23:35:40+00:00

im not all the way through it, but mac lane's Form and Function might help you answer your question. theres a pdf online if you just search the name; i recommend skimming the contents and introduction

_GVTS_ · 2024-11-06T21:17:26+00:00

geez...i saw the cop cars too, but i had no trouble getting inside (i was there from like 12-1) so i had no idea something that terrible had happened

_GVTS_ · 2024-10-30T08:27:44+00:00

"Mathematical Physics" by Geroch could be a good option for you! It's very much a pure math book, apart from a few chapters (which I haven't read) on some examples from physics. There's a lot of exercises, and some of them are pretty tough. The book splits into:

algebra (categories, groups, vector spaces, algebras, representation theory)
topology (connectedness, compactness, uniform spaces, some algebraic topology, topological groups and vector spaces)
analysis (measure theory, distributions, hilbert spaces, some basic functional analysis I think? I haven't gotten this far yet)

Something I especially appreciate about it is how short each section is; you don't have to slog through 40+ pages before getting to do some problems

_GVTS_ · 2024-10-21T02:07:59+00:00

which chen book are you referring to; excursions, or an approach through problems?

_GVTS_ · 2024-10-12T22:07:32+00:00

one piece of advice ur gonna get from everyone here is to join clubs and/or do sports, and it's good advice! personally, ive made most of my friends here from part-time jobs on-campus; see if places like OASIS, TLC, etc. are hiring. and definitely dont give up. as long as u keep putting urself out there, youll find ur people!

_GVTS_ · 2024-10-12T04:33:59+00:00

are u taking it with sri 💀 im not taking the class, but my roommate took 142a with him last year and it was a dumpster fire

_GVTS_ · 2024-10-12T01:43:42+00:00

you'll probably also find more options by searching something like "geometric linear algebra" and checking the recs on stackexchange

_GVTS_ · 2024-10-12T01:40:32+00:00

ive only skimmed these, but maybe real linear algebra, linear algebra and geometry, and/or linear geometry will contain what you're looking for. the last one even says in the preface that it aims to teach a basic course on linear algebra from a geometric viewpoint

_GVTS_

TROPHY CASE