#math textbooks

[algebraic-dumbass]

hey! I'm a 4th year math undergrad in the States and I am astounded by your knowledge of algebra. it's my favorite branch of math and I know a lot more than my peers but not nearly as much as you. where did you learn? any textbook recommendations?

keep up the great mathematics and posts!

haha, well, I don't know that much algebra to be honest (me using a fancy word in a joke means i have heard of it before, not that I actually know how to work with it!)

But yknow I could give out some resources, so here they are (so far I have mostly learned from classes but yknow i'm at that point where i'm starting to need to transition from listening to someone ramble to reading someone's ramblings and then rambling myself)

For basic linear algebra I didn't learn through a textbook, but I have heard good things about Sheldon Axler's Linear Algebra Done Right and it seems similar to what the classes I had did (besides the whole hating on determinants part, though I kinda get it).

For some introductory group theory, I also had a class on it, but the lecture notes are wonderful. I would happily give the link to them here but since they're specifically the lecture notes of the class from my uni I would be kinda doxxing myself. Also they're in French. I will give out some of the references my prof gave in the bibliography of the lecture notes (I have not read them, pardon me if they're actually terrible and shot your dog): FInite Groups, an Introduction by Serre (pdf link), Linear Representations of Finite Groups also by Serre (pdf link), Algebra by Serge Lang (pdf link). Since our prof is a number theorist he sometimes went on number theory tangents and for that there's Serre's A Course in Arithmetic (pdf link). I'm starting to think our prof likes how Serre writes.

For pure category theory and homological algebra I have read part of these lecture notes. I think a good book for category theory is Emily Riehl's Category Theory in Context (pdf link). For homological algebra, a famous book that I have read some parts of is Weibel's An Introduction to Homological Algebra (pdf link). Warning: all pdfs I found of it on the internet all have some typographygore going on. If anyone knows of a good pdf please tell me.

For commutative algebra, A Term of Commutative Algebra by Altman and Kleinman (pdf link). I haven't read all of it (I intend to read more as I need more CA) but the parts of it I read are good. It also has solutions to the exercises which is neat.

For algebraic geometry (admittedly not fully algebra), I am currently reading Ravi Vakil's The Rising Sea, and I intend on getting a physical copy when it gets published because I like it. It tries to have few prerequisites, so for instance it has chapters on category theory and sheaf theory (though I don't claim it is the best place to learn category theory).

For algebraic topology (even less fully algebra, but yknow), I have learned singular cohomology and some other stuff using Hatcher. I know some people despise the book (and I get where they're coming from). For "basic" algebraic topology i.e. the fundamental group and singular homology I have learned through a class and by reading Topologie Algébrique by Félix and Tanré (pdf link). The book is very good but only in French AFAIK.

For (basic) homotopy theory (does it count as algebra? not fully but what you gonna do this is my post) I have read the first part of Bruno Vallette's lecture notes. I don't know if they're that good. Now I'm reading a bit of obstruction theory from Davis and Kirk's Lecture Notes in Algebraic Topology (pdf link) and I like it a lot! The only frustrating part is when you want to learn one specific thing and find they left it as a "Project", but apart from that I like how they write. It also has exercises within the text which I appreciate.

For pure sheaf theory, a friend recommended me Torsten Wedhorn's Manifolds, Sheaves and Cohomology, specifically chapter 3 (which is, you guessed it, the chapter on sheaves). I only read chapter 3, and I think it was alright (maybe a bit dry). I also gave up at the inverse image sheaf because I can only tolerate so much pure sheaf theory. I will come back to it when I need it. The whole book itself actually does differential geometry, but using the language of modern geometry i.e. locally ringed spaces. I have no idea how good it is at that or how good this POV is in general, read at your own risk.

Also please note I have not fully read through any of these references, but I don't think you're supposed to read every math book you ever touch cover to cover.

thanks for the kind comments, and I hope at least one of the things above may be helpful to you!

[shapefrog27]

I hate it when the math textbook is like "convince yourself." No, I'm sorry that is the whole reason you exist, it is to convince me. You could have written two sentences about why, but no you chose violence.

[alchemy-and-royalty]

What book made me cry? math textbook I don’t cry over books :D

[then-ponder]

Hey I’m looking to create a “Library” of math specific textbooks. But math books - especially foundational math textbooks - are incredibly hard to find. For whatever reasons it’s impossible to find more than the mit book on sets and I haven’t found any books on logic in any field math or otherwise that was designed for the discussion of logic.

If you know of a math textbook please send me an ask or a reblog and I will review put it in my post about textbook recommendations. I’m specifically looking for pure math books. While the book can be written from a non-math perspective ie philosophers writing about logic, it must focus on the math.

[theplaguedogs]

[fandomhopper23]

Throcky. diagnosing fractures since when he started skateboarding.

Also 'equipped with a dick'? I'm dying.

Throckmorton

[physics-dirtbag]

I am selling some stuff (books, textbooks, clothes) on Mercari to help fund my impending move to Chicago! I am happy to negotiate on price, talk about doing a bundle for a discount or about a swap!

[aliciafranklyn]

Year 7 is when it starts to get into more complex concepts compared to primary school, where maths is often taught with little structure. So, choose a year 7 textbook for maths to help kids boost their grades and confidence.📚

[yourfaveisanavatar]

every single maths textbook ever is a spiral leitner send post

every math textbook is a spiral leitner!

[fishnchip3011]

alex this is what u get for crushing on a boy in stem

[kokokoula]

dino information

a/n: quick idea i had, and at this point i have completely given up on trying to write things properly. i just want sleep :,)

you and tsukishima are deciding on something to watch for movie night, and somewhere during the decision making he comments on how you can never sit through a documentary.

"i won't fall asleep, i promise!" you are so sure about it that you even wrap your pinkie around his to make a point. it's a shame that less than an hour into the film, he finds you resting heavily against his shoulder, breathing soft and slow.

"(name)?" kei turns to check on you, moving your hair out of your face and tucking it behind your ears. you shift a bit, but are otherwise completely knocked out. he grins triumphantly and reaches for his phone to get a picture of you. he will say it's for proof when you wake up tomorrow, but it'll still be there in his camera roll even long after the bet is forgotten.

tsukishima has to give you credit for trying though. he had noticed you nodding off earlier, but you caught yourself before you drifted off to sleep. it was amusing, and he still appreciated that you made an effort. not that he will spare you from his teasing.

kei grabs the remote and switches off the tv. he has watched the documentary before anyways, and it will be much more comfortable for you to sleep on the bed than against him. without waking you up, he carries you back in his arms to your shared room.

---

"what are you reading, tsukki?" you ask as you join him on the bed and take your spot beside him.

"paleontology." he replies, putting an arm around your shoulders instinctively without looking away from his book.

"read to me." you suggest as you lay your head on his lap. he raises an eyebrow at you.

"do i need to remind you that you can't even sit through a documentary?"

"i know that, but it's different this time. it's narrated by you." he brings the book into your line of sight so that you can't see him blushing. shit, and you said it so casually too. he clears his throat.

"fine, but if you fall asleep, i won't do it ever again." he starts from where he left off. sure enough, this time you did listen, and eagerly in fact, asking him questions and making notes here and there.

while you learn new dinosaur facts, kei learns again how much he is loved by you.

[exnihilo-etc]

hey mathblr i just wanted to let you know that i love you and literally all my creative content is math focused but i just happen to be kinda dogshit at math and only know high school level maths and even then just barely so thx for having me and being so nice

[imperfect-autodidact]

After 8 minutes of utter anger and 6 minutes of reflection I realised something:

My problem isn’t the counting.

It is word problems.

Like I had a meltdown with all those dice, cards, digits and lists of letters, but it all disappeared when I encountered the problem with mathematical symbols. Very easy proof, I haven’t lost any calories while writing it. Nice, right?

Fuck word problems, I’m going to make some tea and add whiskey in it to wind down

[lilacandladybugs]

hey mathblr does anyone know why math textbooks explain things using the most convoluted language known to man. im out here rewriting passages in my own words so my brain doesnt explode cant they just talk normally. who writes this stuff

[then-ponder]

Math professors would get a lot more out of their books if they would just put key words - words that they take the time to define - in the index.

Like what the fuck does consistent mean? I know what it means, but your index lists it 300 pages from where you first use it.

[physicsgoblin]

Physics and Mathematics Resources (plus some Chemistry):

I will update this because I know I have more recommend textbooks somewhere in my files, I'm just too tired to look right now. Latest update: 5/13/25

Physics:

The Science Spot--Mostly lesson plans for teaching kids

The Physics Classroom Tutorial--Has interactive online activities and models. Some videos and also some chemistry stuff.

HyperPhysics--Quite possibly the best resource I've ever seen because it shows how all concepts are linked together. The site isn't loading for me but it says it's up. There is a downloadable version on the Internet Archive (though it doesn't look as nice and clean). EDIT: I found a GitHub that lets you clone and download the html so you can click through it offline and it works! If people are interested I can make a tutorial, it was very easy.

PhET--A ton of demonstrations and tutorials. Also has some for mathematics and chemistry.

Paradigms Physics Notes--this was the curriculum that was used in my junior and senior classes. A lot of stuff here. If you are interest about teaching physics using this method, you can read more here.

Quantum Mathamatica Add-on--Useful for calculations.

The Hypertextbook--uhh lots here. Problems, solutions, explanations, etc.

oPhysics--interactive physics software.

MiniPhysics--more demonstrations and interactive software.

Michel van Biezen--really clear work-throughs of many subjects (algebra, calculus, chemistry, physics). He actually has a tumblr but has been active in like a decade @ilectureonline

Mathematics:

Paul's Online Math Notes--Got my whole class through junior and senior year

Calculator Soup--a lot of different kinds of calculators

3Blue1Brown--Very interesting youtube channel that shows a lot of calculus and linear algebraic principals visually or in intuitive ways.

Mathologer--more interesting advanced mathematical concepts.

General:

OpenStax--Free textbooks, legally