book-recommendations

[rigid trail]

I really like "type theory and formal proof" by nederpelt and geuvers

I skimmed through it and am now going through it from the start slowly

[undone finch]

I have this one and have been working through it.
But I don't think it's the computability/proof theory I'm looking for.
Maybe my understanding is bad though. lol.

[rigid trail]

Wdym by computability

[undone finch]

https://en.wikipedia.org/wiki/Computability_theory

[rigid trail]

There is strong normalization in typed lambda calculuses

So if you can represent a computation with valid types, it will terminate

Type theory and recursion theory are pretty closely related

[dim pendant]

If you learn calculus then a good way to get a feel of mathematics is to spend a week going through "Elliptic Tales", it's a book that introduces an aspect of Langland's assuming only basic differential calculus, and building up the algebra, projective geometry, analysis, etc.

Even if you don't necessarily want to spend your life doing math, by studying the book you'll get first hand experience putting together a beautiful piece of math

[oblique current]

i love explaining so yes, i want to become a teacher of math in a future, thats why i was asking for books about it

[oblique current]

i will give it a try, thanks

[dim pendant]

In uni you will take a handful of advanced math courses, likely not more than analysis I and abstract algebra I. When that time comes, just know that they will be good for you, like veggies.

[oblique current]

I was talking with my teacher about that, sounds interesting, like, the history of the math

[dim pendant]

It's sort of a mixture of how to teach math, a review of stuff, history, and a bit of advanced math

Most schools will require a strong 4 year degree or longer, and you will be asked to take probably abstract algebra or real analysis I in that degree

my high school algebra 1 teacher had to struggle through abstract algebra to get his degree but it's just one semester

[oblique current]

Yeah, i see that, in here, is 3 to 4 years aprox

[dim pendant]

Anyway, hope you like the stuff you've been recommended c:

[oblique current]

Yess, tysm c:

[trim kayak]

Hey everyone. I have basic knowledge of Algebra, Geometry, Trig, and Stats but want to learn more. I really like all 4 of these but I'm not sure if should learn more advanced topics within these subjects or learn something new like Calculus or Linear Algebra.

What would you suggest I do? Should I learn more about these as an intro before moving to something more advanced?

Could you also recommend some preferred textbooks that you suggest I use for learning and practicing problems?

Thanks!! 🙂

[marsh ingot]

Sources for Poisson integral?

Nevermind, I got ones on harmonic analysis

[remote sparrow]

for treatments of structural proof theory, you can look at takeuti's Proof Theory or troelstra and schwichtenberg's Basic Proof Theory. for a text that has much more focus on ordinal analysis, see pohlers' Proof Theory: The First Step into Impredicativity. of course, proof theory encompasses more than structural proof theory or ordinal analysis, so you'll have to be more specific about what you want.

for computability, you can look at bridges' Computability: A Mathematical Sketchbook, odifreddi's Classical Recursion Theory, roger's Theory of Recursive Functions and Effective Computability, and soare's Turing Computability: Theory and Applications (soare also has an older book, Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets, which has more details about certain topics). cutland's Computability: An Introduction to Recursive Function Theory and weber's Computability Theory are also good even if they are not graduate introductions.

[trim kayak]

Any recommendations for calculus or trig books? I'm looking for intro to calc to start out and more advanced trig.

Are any calc books, other than Stewart, just as good? I'm going to check a used bookstore and I may not find Stewart's books. Thanks!!

[remote sparrow]

thomas and larson are reputable authors

https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/B005WNPGW2

if you don't see stewart at your used bookstore, you can also just buy used copies from amazon

https://www.amazon.com/Calculus-Early-Transcendentals-Seventh-Stewart/dp/0538498714

https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552

[trim kayak]

That's true. Thought I would check a local store first. If not, I can order on Amazon.

Would you suggest Stewart's Early Transcendentals text over just a regular edition instead?

[undone finch]

@remote sparrow Thank you incredibly much.

[stiff grail]

hai

books on odes ez?
like the ones "cal made easy by thomspon:

thanks

[remote sparrow]

early transcendentals is by far more common than the "regular" edition at u.s. universities as far as i know. the main difference with early transcendentals is that exponentials, logarithms, and trigonometric functions are introduced early. late transcendentals introduces the exponential and log functions after they can be formally defined.

[earnest wolf]

where to learn "cool haskell"?
not just the syntax, but the core ideas it lies upon

I can ofc just choose a random category theory book, but that might take forever to digest

[shy silo]

I'll ask again, any recommendations for analytic number theory?

[trim kayak]

@remote sparrow Should I learn more about Trig and Stats since I do know a little about them or should I move on to something else such as Calc?

[remote sparrow]

just do calculus

[trim kayak]

Hmm okay. Thanks!

[earnest wolf]

https://mathematics.gg/books/number-theory

check the second one

why isn't there Abbott on https://mathematics.gg/books/real-analysis

[heady ember]

Make a review yourself.

Learn from Thanos

[earnest wolf]

thru a PR to the repo?

[shy silo]

I tried apostol

I wasn't liking it

💀

I already knew the stuff pre analytic, so I tried skipping there

the group part in his group killed me, iirc he uses non standard nomenclature

[heady ember]

PR? Dm modmail probably

[shy silo]

Guess I'll have to read it since the other book is just elementary and I already had introductory number theory

[jovial parrot]

Is there Rudin

Wow I saw that cat picture on snap

lol Rudin is the first one

Baseeeeed

[earnest wolf]

||the closest I was ever to snap is here||

[jovial parrot]

Dang

[jovial parrot]

Where do you find these

Like

I went to the website

And it’s not there

These aren’t linked

Links you can’t navigate to

That’s a lot of fucking books

Before submitting a review we must have read the entire book huh?

[trail hemlock]

amukh hv u heard of real analysis by N.L Carothers

its really nice

[jovial parrot]

I Havnt what’s it about

[trail hemlock]

😐

wdym whats it about

but hoestly i wish i had read this instead of rudin

its so good bruh

[earnest wolf]

https://mathematics.gg/books

notice that adding a slash to the end breaks the site lol

[rose hazel]

github pages treats books/ as a directory, so it looks for an index.html in that directory. while books is treated as a file, its pretty easy to fix, so i dunno why they havent

[remote sparrow]

did you hear about carothers from this server or somewhere else

[earnest wolf]

i mean, it isn't github pages' problem per se
it's jekyll's

i have a personal static website hosted on github pages, but its """backend""" is on hugo – and it's a bit more smart abt it

[trail hemlock]

from google

cant remember exactly what, but i stumbled across a post shilling carothers so i checked it out

really really nice imo

[rose hazel]

yeah what i meant is its not configured correctly, i am not a big fan of jekyll tbh.

[trail hemlock]

why, is it popular here?

[earnest wolf]

drop is a big fan of it

I bet it was him whom google asked in the first place

[trail hemlock]

loll

[remote sparrow]

i found out about carothers from tai danae bradley's blog

[earnest wolf]

jokes aside, but drop really knows a lot of cool books

[trim kayak]

When buying a math textbook, would everyone prefer the newer or newest edition even if slightly more expensive than the previous edition?

[remote sparrow]

it just depends on the book

[trim kayak]

I'm debating about which Stewart Calc book to purchase. I'm looking at the two links you sent me earlier. Paperback of the 7th edition is only $3.77 but the cover looks different and old. The 8th edition is $24.25 for a hardcover in good condition. Seems like the 8th would be better but I'm just not sure.

[remote sparrow]

paperback? i wouldn't get a paperback

the hardcovers are pretty decent

[trim kayak]

Hardcover lasts longer but no paperback? I have several paperback texts from over the years.

Hmm ok

[remote sparrow]

i'm not 100% against paperbacks

but stewart's calc book is fine to get as a hardback

like i own many paperbacks

paperbacks are easier to open, but i think a hardcover is worth it in this case since it'll last a lot longer

[trim kayak]

Okay. Maybe I'll get hardback of the 8th edition. Can I assume there are solutions in the back?

[remote sparrow]

i don't like POD hardcovers though, like the ones from springer

[trim kayak]

Ohh. I don't have any of those

[molten gulch]

what's POD?

[trim kayak]

Print on Demand

[remote sparrow]

i think there might be answers in the back? there might also be a student solutions manual for sale

but stewart is so popular and the questions are mostly similar across editions, so you're bound to find answers on the web

also, many routine computational problems can be solved with computer algebra systems like wolframalpha or symbolab

[trim kayak]

Oh okay. Good to know. I'm checking other sites to see if there is anything cheaper. Nothing yet.

Do you have Stewart's texts too?

[remote sparrow]

i have the 6th edition that i bought a while ago

[trim kayak]

Oh that's cool. There are sites for hardcover 8th edition for almost $500! Thats nuts!!

[remote sparrow]

https://www.bookfinder.com/

you can use this site to look for deals

[trim kayak]

Oohh. Never seen this one. Thanks!!

Are these pretty reliable sites? There are quite a few I've never heard of. I found the 8th edition for $10.58 from BooksRun.

Oh nevermind its a rental.

[echo tendon]

Im looking for a linear programming / optimization textbook thats concise and cohesive

[heady ember]

Will he drop off one day?

Will my puns drop off one day? No, of course not.
||You can't drop beyond the global minimum ||

[ruby plaza]

I want to master algebra. Specifically the topics mentioned below:
Algebra: Sets, operations on sets. Prime numbers, factorization of integers and divisibility.
Rational and irrational numbers. Permutations and combinations, basic probability. Binomial
Theorem. Logarithms. Polynomials: Remainder Theorem, Theory of quadratic equations and
expressions, relations between roots and coefficients. Arithmetic and geometric progressions.
Inequalities involving arithmetic, geometric and harmonic means. Complex numbers. Matrices
and determinants.
Is there any book i can refer to prepare these topics at an Olympiad level. What other resources can i utilize?

[trail hemlock]

I think you are looking for AoPS Intermediate Algebra

it covers all of this, and a lot more

[wraith sandal]

is lee's topological manifolds a great intro to point set topology?

[trail hemlock]

yes

well

lee situates a lot of topology around more interesting topics

as a strict pointset text, i would go with munkres

i personally used Conway's A Course in Point-Set Topology but munkres is objectively better

[wraith sandal]

but what if i am interested to study further topics such as differental geometry and algebraic topology, would lee be better for me than munkres?

[trail hemlock]

yeah probably

i cant say for sure, i havent read munkres, but lee is apart of a series so it would def be easier to segue into his later books

[wraith sandal]

okay thx

[trail hemlock]

this might also be helpful

[heady ember]

You don't need the whole of Munkres

[trail hemlock]

munkres got me yawning fr

[heady ember]

You could read Hatcher's point set notes or something

[trail hemlock]

iirc the university of toronto has some nice notes as well

[ruby plaza]

thanks for the suggestion. Can i approach it as a beginner or do i need to have some background in these topics?

[trail hemlock]

well aops intermediate algebra is written assuming familiarity with Algebra 1

but you dont need any background on the topics you mentioned, no

basic algebra skills should suffice

perhaps from Knapp's book this part is a joke btw

[subtle violet]

as an analyst i think doing the first 4 chapters of lee ITM were pretty useless for me ngl

[wraith sandal]

that is helpful thanks

[trail hemlock]

i ended up doing the problems from the first few chapters and skipping it bcz i read conway's book lol

[heady ember]

What topology resource would you give your suremark to?

[old elk]

I have the Munkres one, but I still feel it's too much for me to handle.

[subtle violet]

idk i haven’t done any more topology since then, but i have a book sitting on my shelf called “introduction to topology and modern analysis” that james recommended

by someone named simmons

[heady ember]

I see

[subtle violet]

so i’ll probably take a peek at that at some point

[old elk]

I feel that Morris is good

[trail hemlock]

Willard is good too

[subtle violet]

i just remember attempting to read a book on malliavin calculus and it cursorily defined (what turns out to be something called) the compact-open topology and i was like, lee didn’t mention this shit

[trail hemlock]

lee basically mentioned like 2 topology things and then rants abt more interesting shit for the rest of the book

hes such a silly guy 😭

[trail hemlock]

(i see this as a good thing)

[old elk]

Does it say that the topology in lee variety is

bad?

[subtle violet]

yea if you’re into manifolds

[trail hemlock]

i think they are cool

[subtle violet]

does what say

[trail hemlock]

im on the latter chapters of lee, hoping to start rotman soon

chat how cooked am i

[old elk]

Did you just say that lee's manifold topology book is a bad thing?****

my english :c

[old elk]

You should jump to differential geometry, right?

[subtle violet]

tbh i do suppose topology is like the least interesting aspect of manifolds, like you can kind of glean what a manifold is intuitively but it’s just there to provide needed formalism

whereas with like function spaces in analysis they might not even be metric spaces and you need topology to even talk about them at all

[trail hemlock]

yeah im gonna do spivak

ive heard the writing is super clean

[subtle violet]

i dont think its bad tbh, but i just feel like it wasn’t that useful for me since i ended up studying things in a different direction from what lee does

[old elk]

How do you read a book so fast?

[subtle violet]

uh

sometimes you don’t

but if you’re well-prepared sometimes it’s easy

like i spent a whole year working through own textbook and then i flew through the next book in a couple weekends

though the second book was way shorter

[old elk]

Sometimes it happens, that's why choosing a book to learn is really complicated, although there are youtube courses hehe, maybe an indu explaining

It should be noted that sometimes I feel frustrated in not being able to learn well from a book, maybe it's my habits and my agility and taking notes of a whole book, I'm really stupid.

That sounds like a hobby for you hahah

[hazy cloud]

Can anyone recommend some books on the cohomology of arithmetic groups. I know there is one by Harder and the first 2-3 chapters look manageable, but uh... is there like a "... for dummies" version of that?

A more concrete goal would be to get the proof of Eichler-Shimura and the theory surrounding it for GL_2

[trim kayak]

Is anyone here reading and studying math just for fun? 😀

I'm excited to start reading through Stewart's Calc textbook. I took Calc years ago but want to study and learn it again just for fun. I hope that's not too weird. 🥸🤓

[fresh skiff]

Why Stewart's calculus and why not other resources like spivak (maybe it will be much fun if you try some other source with another level of difficulty)

[pliant wadi]

any notes/resources to read more about hilbert spaces?

[pliant wadi]

I am using Brezis' book, any supplementary material?

[foggy quest]

functional analysis section of https://link.springer.com/book/10.1007/978-3-031-33859-5

[spice nova]

Are there any magazines or similar news feeds that would help with finding a topic/question for an undergrad thesis? My focus of study has been analysis and stochastics, though I'd be interested in doing something algebra-related.

I'm going through journals i found online but it's slow and I'm not sure they're useful.

[gray gazelle]

wtf

i got some weird error message from the discussion channel

i kicked my self out by accident

[molten gulch]

you enabled the studying role

you can undo it with ,iamnot studying

[gray gazelle]

lmao okay

based tho

to kick of the distractions

[fresh skiff]

is there a reference where i can study double sequences?
There is a section in abbott but its not enough
I am finding a reference where i can find statements like

sup sup a{i,j} = sup sup a{i,j} for real sequeces and in this case we can intercahnge limits

etc

[trim kayak]

Oh I don't know. A few people here suggested Stewart's textbooks.

[fresh skiff]

oh, is it your first encounter with calculus?

[trim kayak]

No, I have taken Calc classes before but it was years ago. I just want to learn it again for some strange reason.

[fresh skiff]

maybe pauls notes will be useful if you wanna have a quick view

[trim kayak]

Oohh I'll check that out too, thanks. I want to go through an entire Calc text too.

[fresh skiff]

yeah then take a look at stewarts book or maybe on other books as well

the one you find easier, pick it and read it

[pliant wadi]

Hey thanks! I'll check that out.

[undone finch]

Any recommendations on a hyper geometric geometry text preferably from the perspective of incident geometry, but then it builds up to other, modern approaches?

Alternatively, a general Incident Geometry text might work too, but not sure if that's a thing.
I'm imagining something like a "General Incident Geometry", probably using methods from topology and order/lattice theory to develop the material

[gray gazelle]

,iamnot studying

[hasty eagle]

Removed the studying! role from you.

[vital bane]

by spending lots of time everyday on it

[vital bane]

Spivak

Can anyone suggest a differential equations course, preferably something like MIT OCW or anything similar like a youtube lecture series covering these topics?

Not necessarily a book

I found this https://ocw.mit.edu/courses/18-034-honors-differential-equations-spring-2009/

But I'm not sure if this is very suitable for learning those specific topics (within a time constraint)

[vital bane]

btw I don't really want a mathematically rigorous proof based course on ODEs

I just wanna be able to learn and use these facts, I will go through some other resources to learn rigorous ODEs when I have time

[solar oar]

Hello! i i wish to find a good book for prealgebra, If there is any recomendation i would appreciate it.

[trail hemlock]

aops prealgebra is good

https://artofproblemsolving.com/store/book/prealgebra

[fresh skiff]

Spivak calculus?

[fresh skiff]

I think usually it's a second course in ODEs, which requires measure theory

[remote sparrow]

#book-recommendations message

[zinc thistle]

what are good resources to get a good grasp on point set topology? something beyond the level of munkres

[graceful moon]

I’m not really sure there is much more to point set topology, it’s really more of a toolbox for doing other stuff

I guess something like Lees topological manifolds could be worth a look?

[hazy cloud]

It's kind of a dead field outside of logic, you introduce what you must and then move to a subject you want to apply your toolkit at

[gray jungle]

dugunji topology book is quite good, lots of topics

[vital bane]

do you know any recorded lectures that follow these books?

[cobalt arch]

Maybe Kelley's General Topology is a good choice for what you are looking for. Kelley almost titled it "What Every Young Analyst Should Know". I think it is the bare minimum or the basis for graduate general topology. You can expand from there to more sophisticated material.

[vale marsh]

Are there any good number theory books that goes over the Hardy-Littlewood Circle Method?

[heady ember]

Just revive it yourself

[hazy cloud]

The world has enough cardinal invariants 😔

[heady ember]

Spread the church to mars

Problem solved (maybe)

[undone finch]

Do you mean general topology or specifically point set topology?

[foggy quest]

Introduction to Differential Equations here is good: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/.

[heady ember]

We found Taylor's alt

[fresh skiff]

Oh cool. Yeah that could be a good way. For myself, i didn't study calculus from some specific book. I used a lot of online resources, studied particular topics from random books etc.
Now i will revise my calculus using spivak and Paul's notes.

[near jewel]

Use what calculus in a good university use. And follow the course, if you want to deepen.

[fresh skiff]

Yeah.

[copper warren]

Would naive set theory by halmos be a good primer for the topic? If Im not mistaken it doesn't have any problems, what can I do about that?

[gray gazelle]

It has exercises (not many) dispersed throughout the text

[copper warren]

Oh that’s great, is it a good book though?

[gray gazelle]

It’s by Halmos, so yes

[timid delta]

I kinda have a big issue rn :'D

I'm a physics student but one relative gifted me for birthday a book on Differential Geometry, the William M. Boothby one... It was very expensive so I want to use it, but my formal math knowledge isn't great, where do I even start?

[graceful moon]

Linear algebra for differential geometry

I’d recommend Hoffman Kunze but there’s a lot of good options out there, Friedberg Insel and Spence is another book people like but I’ve not read that

[timid delta]

Thanks :3

[molten gulch]

we personally have enjoyed FIS of what we've read so far

[gray gazelle]

Hello, are there any books related to stochastic control theory applied to finance ?

[trim kayak]

I ordered a calc textbook that should be delivered very soon. Should I skim the chapter, then go back and read it, take notes, and then practice the problems?

[warm river]

Do you just start reading such a book? Like page for page, writing it down, trying to solve it/write topics in your own terms or how do you approach such a book (for studying/understanding the topics)

[echo nimbus]

The bible

[graceful moon]

Everyone has their own methods,

personally I wouldn’t recommend writing it all out, I do at most just definitions and maybe big theorems. I tend to just read through the chapter, try to understand the definitions, every time I read a new theorem have a think about how I might show it, why we need certain assumptions etc. then I try to do problems and usually need to come back and properly comb through the material again

I would say if it’s your first maths book HK isn’t the most gentle introduction

[warm river]

I never read a math book in that sense. I am interested, since I study CS and i am going to do my Masters in AI. My current Uni doesnt have a lot of math, they dont focus on it very much plus its all in german. My master will be in English and they focus on math, so i am thinking of starting to learn linear algebra, probability etc.

Like i had the topics but i forgot them already

[graceful moon]

Ah yeah in that case Hoffman Kunze might not be too bad if you already knew linear algebra at one point, it’s not a very applied view point though it’s definitely for pure maths

Freidberg Insel and Spence could also be worth a look, I’ve heard it’s essentially just a more modern version of HK

I should really take a look at it myself at some point

[mossy flume]

FIS my beloved

And yes you read a math text by starting at page one and doing a large portion of the exercises

It is hard but math is hard

Also it'll get easier as you go

[warm river]

I thought that already. A good friend of mine, who is doing his Phd in Math, told me its just repetition and his tip for me was to put everything in sentences. Write out the equation in sentences, should help me to understand it easier.

But I will give FIS a try

[molten gulch]

We think the one (extremely minor) issue we have with FIS is them using "onto" and "one-to-one" for "injective" and "surjective" respectively

[mossy flume]

This is such a minor issue that I wouldn't not-recommend the text just based off that

[mossy flume]

Yea come back and use this server #linear-algebra as you get stuck

[warm river]

Awesome FIS starts with Vectors and Matrices, all which i need for my LLM

[mossy flume]

Proof based math is hard at first for sure

[warm river]

That for sure. My friend showed me how one of his class mates proofed that 1 + 1 = 2. First i was like, well its obvious, it has to be 2. But then he showed me his pages and damn, proofing something seems hard for sure

[mossy flume]

I think I know what book you're thinking of with that

And that's not how proofs actually are

[molten gulch]

Oh absolutely lol, hence we said "extremely minor"

we absolutely LOVE the book otherwise

[graceful moon]

That’s a bit of a different thing but yeah proofs can be a bit different to what you’re used to

[warm river]

It was not a book, it was his own proof, which he did in class as a project

It could be stolen out of a book, i dont know that. Dont quote me on that

[molten gulch]

the proof out of the book would be over 300 pages long afaik, if it's the book we're thinking of

[heady ember]

Sounds like bs. The proof that 1+1=2 is trivial: by definition.

[gray gazelle]

it's not trivial, i was there at the inception of numbers and let me tell you, it took a while

[earnest wolf]

now I need to reverse those captions to make everyone else equally angry

[vast leaf]

Currently reading Knot Theory by Vassily Manturov and I highly recommend it

[gray jungle]

I mean maybe OP meant peano axiom construction, which is actually a good way to introduce proofs lol

I quite literally learnt proof based math from first chapters of tao

[rain hound]

~~ if we define N as an inductive type then 1+1 is definitionally equal to 2 ~~

[rain hound]

same

that book is hard for a first proof based course. But it is so worth it

It really gets you thorough in a way that really no other math book I’ve looked at does. (other than foundations haha)

[gray jungle]

yeah

this proposition will never stop being funny

[heady ember]

I'm not familiar with the Piano axioms, but isn't it still immediate by definition?

Hi James btw

[heady ember]

Real men learn ordinals and cardinals for their first proof based course

[gray jungle]

with some axioms it works out yeah

[subtle violet]

i’m more familiar with the Harpsichord axioms myself

[earnest wolf]

proving that reals satisfy Archimedean property is equally funny imo

like, was there any doubt that they could be bounded before proving it?

[willow merlin]

which book

explains the properties of the argument of complex numbers

[tropic nacelle]

https://www.stewartcalculus.com/data/ESSENTIAL CALCULUS Early Transcendentals/upfiles/topics/ess_at_12_cn_stu.pdf
Stewart's Calculus should work

specifically, the end of page 3

[hazy cloud]

No way, his analysis text?

I did too, those few chapters are really damn good at this

[zinc thistle]

Either would be nice to have recommendations for :)

[gray gazelle]

i need help

whats a good book to self study on the topic of Quadratic Equation

[timid delta]

is Serge Lang Linear Algebra any good?

[gray gazelle]

There are books on know theory?

*knot

Sick af

[high garden]

from where should i learn calc ?

[humble spire]

Aops lntro to algebra?

[remote vortex]

What a relief

That said, proving that 0 < 1 is also genuinely something that needs to be done if your starting point is the standard axioms of ordered field.

[earnest wolf]

now prove "0=0"

||how do we know it's the same zero||
||how do we know it's zero||
||how do we know that we know||

[remote vortex]

Philosophically you have an excellent point; mathematically I'd just start from the premise of operating within the general framework of first-order logic with equality.

In which case 0=0 follows from the reflexivity property of equality.

[summer lagoon]

To prove 0=0, you have to prove that the proof that prove 0=0 is good, but then you have to prove that the proof to prove that the proof that 0=0 is true, is true. But then..

[remote vortex]

Yep, pretty much, as observed by Carroll and probably others before him: https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles

[earnest wolf]

I see
so "0=0" is still at the "conjecture" phase

I think I begin to see why mathematicians and scientists try to moderate their incorporation of philosophy into their fields

or mb we just need a better framework of logic that might mimic what our brains do better, that a formal system

[vast leaf]

https://tutorial.math.lamar.edu/ pretty good resource

[vital bane]

He said "Don't laugh!" so don't laugh!!

is this Tao btw?

[molten gulch]

that's tao

[vital bane]

I should check out Tao's measure theory book some time

analysis-I as well

[restive falcon]

same yeah

[trail hemlock]

yes it’s quite good, but there are better choices. i’d go with friedburg insel space

i used lang and in retrospect FIS would have been a better choice

[remote sparrow]

do axler!

[trail hemlock]

wb bass

[daring lake]

I didn't know Tao had one

[sharp goblet]

what's a good resource in proof theory?

[remote sparrow]

why did bro self-react himself so many times

[molten gulch]

what the hell-

[remote sparrow]

@sharp goblet

also look at peter smith's guide and diligentclerk's logic reading list in pins

[sharp goblet]

"takeuti's Proof Theory" mmmh , I will look at this..., I am looking just for a mathematical introduction

#book-recommendations message ??!!

[sharp goblet]

schizophrenia is the key for success, right?

• "yeah , of course"
  you see, he said it is

[vital bane]

[vital bane]

Yea Axler look really good too

[winged bluff]

Does anyone have a recommendation for a mathematically rigorous book that covers the following topics:

Basic concepts/examples in machine learning:  supervised and unsupervised learning, generalisation concept with linear models and neural networks, and model selection;
quick review of eigenvalue decomposition, singular value decomposition, and convex optimization (Lagrangian multiplier theory);
statistical description of data such as normalisation, correlation and independence.
Kernel methods: support vector machines (large margin, dual formulation, quadratic programming, PSD kernels) and representation theory;
Bayesian learning and generalisation.
Modelling and regression (ML and MAP solutions, LASSO models);
statistical learning theory (VC dimension, Covering number, Rademacher complexity, excess risk analysis)
Unsupervised learning (PCA, GMM clustering model and EM algorithm, feature selection, density estimation);
stochastic online learning for big data.

[worldly brook]

ok not as complex, but I'd say statquest illustrated guide to machine learning is pretty good, and covers some of those topics pretty well explained best book I've ever read so far, also lmk if u got other good book recommendations or If u find any book covering that, I'm also in the seek of a book in ML.

[fresh skiff]

To get the attention ofc lmao

[daring lake]

https://www.statlearning.com/

wrong one

i know one but it got lost in my list of pdfs lmao

[spare loom]

Any book recommendations on matrices?

[winged bluff]

Thanks, I'll take a look at this

[winged bluff]

Lmk if you find 🙂

[willow rose]

looking for suggesting books or materials that can help my children get into mathematics? i got a 1, 3, 5, and 10 year old.

[heady ember]

(A pure joke) ||Baby Rudin --- its good even for babies||

[willow rose]

im gonna smoke you to find it funny 🙂

[heady ember]

Free lung cancer

[willow rose]

https://artofproblemsolving.com/store/list/all-products 🙂

[pliant wadi]

there's a fun book called 'What's the name of this book?' has dracula in its name iirc, I have some fond memories with it.

That's a good one

My favourite one as a kid was though certainly

'Murderous Maths' although I am not sure if pre-school kids would find it as amusing

there's a fun website for it too

I feel that as a super young kid, I mostly enjoyed math via games

you can explore conway's book on CGT maybe

find some fun games, something they might engage with

(Stay away from Conway's 'Numbers and games' for now ig XD, the other book, I don't recall the name rn has a lot of fun games)

[willow rose]

that murderous math seems like good material for my 10 year old

[slate rampart]

Murderous Maths carried High School. It has so many topics like binomail coefficients, algebra, trigonometry and probability that you wont learn until later on amd teaches it in a great way for 7-11 year olds

It helped teach daunting topics entertainingly, and I'd personally reccomend

[pliant wadi]

Check this one out

https://en.wikipedia.org/wiki/Winning_Ways_for_Your_Mathematical_Plays

[foggy quest]

https://www.di.ens.fr/~fbach/ltfp_book.pdf

[torn blade]

books for learning the following aspects of point set topology? nothing toooo long please
Basic definitions
Convergence
Continuity
Bases
Subspaces
Product Spaces
Quotient Spaces
Metric Spaces
Connectedness
Compactness
Separation Axioms

[foggy quest]

Folland's real analysis book.

[torn blade]

yeah but i want what (in your opinion) is the best one

[daring fox]

Hey, i want to start self study of Numerical analysis 1 and functional analysis, So i need a good book for them, your recommendations matters alot for me.

[marsh ingot]

Conway, A course in Functional analysis

[cinder pulsar]

oi

eita chat errado

[lunar junco]

any recommendations for discrete math guys? need to learn it for a data structures course and some upcoming electronics courses

[molten gulch]

epp or rosen are good in our experience

[lunar junco]

thanks i did check rosen out since it seems to be the most standard book out there, i'll check out epp asw

[molten gulch]

They both cover about the same amount of material so one alone should be fine

[lunar junco]

also is studying math solely from a book better in any way over doing it using a course online?

or is there no such thing

[lunar junco]

cool

[molten gulch]

You can use videos or such alongside the book, the key is to do as many problems as possible

[lunar junco]

makes sense

[earnest wolf]

Can anyone recommend good lecture notes and/or video lectures on computational complexity theory?

[minor hearth]

have you done computation theory before?

[earnest wolf]

lots of algorithms – yes
other branches of computation theory, like automatas, formal languages and computability – no

[minor hearth]

I'd say study computation theory (i.e. automatas, languages, etc.) first - this could be via Hopcroft or Sipser

After that, Papadimitriou or Arora-Barak might be of interest

[earnest wolf]

all of those are books, right?

[minor hearth]

yeah

[winged bluff]

Zankyu!

[pale scarab]

It's important to build the skill of reading a textbook. As you go further you are just not going to find the material in an online lecture at a detail required for understanding.

I also find many people fool themselves on how active they are when watching a video vs reading a book.

The key is of course to do as many problems as you can.

[remote sparrow]

munkres

gamelin

willard

[torn blade]

thanks!

i did a chat search of topology and saw Lee intro to topological manifolds recommended so i just started that

[tribal crow]

I like Lee

he doesn’t really talk about the separation axioms in depth though

[formal cypress]

I only know the basics from school, but I want to learn for the future because I'm bored... What book should I get?

[marsh ingot]

Calculus, linear algebra, topology,...

[formal cypress]

Thanks!

[molten gulch]

what specifically do you want to do

(excuse the ghost ping please)

[marsh ingot]

No problem

I know he didnt specify what grade or level

[molten gulch]

my point was more that just from them saying "basics from school" just left it a bit nebulous

yeah

[marsh ingot]

Basics from school sounds as middle or high school

[formal cypress]

I live in the Czech Republic. We have a different school system there. Our elementary school is for 9 years. Now I'm a ninth grader and I'm 15. I know about basic algebra or functions, etc.

So nor much

not*

[earnest wolf]

Sipser
I think I found what I need
There is a course by him on MIT OCW, with video lectures and lecture notes

Thanks

[minor hearth]

Yep, he has the lectures as well - one thing I'd mention is that the first chunk (computation theory) goes a lot faster than a first course on it would

Papadimitriou is even faster in that it does everything using Turing Machines and leaves finite automata in the exercises

[trail hemlock]

willard is amazing reference btw thanks for the rec (was a while back)

[gray jungle]

you need to actively interact with it, dont just read it, try to write down arguments yourself and see where you get stuck and why the author did something in a certain way

you might even end up finding better proofs sometimes, some authors can genuinly do a more complicated proof than whats necessary

[gray gazelle]

or probably do the problems and exercises

then when you get something wrong that's where you reread the chapter and etc2

[queen pendant]

hi, I'm thinking of reading kiselev's geometry (both volumes) but when I looked to the exercises, there is a lot of proof so do I need to have a proof knowledge ? and to what level ?

[pliant wadi]

Are there any interesting online resources for PDEs

Books, websites, lecture notes?

Lecture videos, etc; anything of the sort?

Brezis is one ik about ig

Then there's Evans

Anything else?

[remote sparrow]

no

it was a textbook for middle schoolers

doesn't mean it's easy or trivial

i'm just saying generations of russian middle schoolers have used it

[restive falcon]

Is there a good text on pdes from a "pure" mathematical perspective

i.e. not designed to cater to physicists etc

[heady ember]

Evans or Taylor, maybe?

Those are two I see commonly rec'd for PDEs

[restive falcon]

ok evans looks like what i want

[restive falcon]

thanks

[cold elbow]

is there any book/resource with alot of good integral problems (with solutions preferably)

[gray gazelle]

Is there any nice book to start from fundamentals for self-study? (I'm starting over due to weak maths, cuz I think weak fundamentals are creating problems in learning advanced maths for me.) (by fundamentals I mean the middle school)

[empty junco]

how much background do you have

[restive falcon]

measure theory, i can probably learn some functional analysis if necessary

also basic odes

[humble spire]

Try langs high school geo book

I liked that pretty well

[trim kayak]

I ordered a calc textbook and received it a few days ago. Should I skim the chapter, then go back and read it, take notes, and then practice the problems?

[remote sparrow]

if you want

[trim kayak]

Just trying to figure out the best way to learn it. I flipped through the book and it looks tough!!

[remote sparrow]

there are lectures and notes online

[trim kayak]

Yeah I've found quite a few. Not sure if taking my own notes would be helpful too.

[covert vector]

Any recommendations for real analysis books? Preferably with compelling exercises. I've got the necessary calculus background (at least, I like to think so) and I'd like a fun real analysis book to pass the time :v

[molten gulch]

I've seen Abbott, Tao, and Rudin recommended here before

[trail hemlock]

rudin's problemset is the nicest that i have come across

ive also taken a look at real analysis by N.L Carothers, and i think its a really nice book that should be mentioned along with rudin, tao, and abbott

[covert vector]

noted! I've been considering rudin but some of its cons (such as being terse and not particularly fun to get through) have turned me off but maybe I'll just look more so at the exercises

[trail hemlock]

yeah its fairly popular to read another book and do exercises from rudin

although be wary of the fact that an exercise in rudin may be an already proven theorem in your book

[covert vector]

ahh alright

should i pick more than one other book or just one other book (or is it just up to me)

[trail hemlock]

its purely a matter of preference. rudin, tao, abbott, (carothers is my personal addition), are all really good books which have been used by thousands of students, you are not gonna go wrong with any of them

do you like rudin's terse style (or feel that you learn better this way), would you rather read abbott's clean writing and supplament with rudin's more difficullt exercises, do you prefer how tao lays out theorems and explainations, etc

[covert vector]

👍 👍 !! thanks a ton!

[molten gulch]

How hard is rudin, would you say?

(asking as someone with almost no analysis experience)

[trail hemlock]

if you can get through chapter 2 and 3, you are golden

idk if i can say "how hard", its difficult because it asks a lot of the reader

essentially all of the proofs skip nontrivial steps and make the reader really consider some nuanced details/ideas, and this is very time consuming

but a good level of maturity, and above all else a lot of time, as well as the obvious calculus background, are the only true prerequisites

[foggy quest]

Folland's book. Taylor's book: https://link.springer.com/book/10.1007/978-3-031-33859-5

[gray gazelle]

any good books for computational statistics?

[willow merlin]

what would be the equivalent of Abbots intro RA but for Set Theory, I see a lot of the books introduce set theory in the first chapters but I wanted a dedicated pdf I can read for Set theory, if possible... Even if its weird to ask for something that should be already known, but I was interested about index sets and maybe posets?

[oak tide]

Weird question but any manga recommendations

[willow merlin]

I am liking vagabond and 21st century boys, maybe one piece if you are younger

hajime no ippo I like it aswell

[heady ember]

Enderton's Elements of Set Theory, I guess.

[trail hemlock]

baby jech was my intro, its fairly nice

[heady ember]

A more advanced --- graduate --- text is Kunen's Set Theory.

[heady ember]

Baby Jech right? That's misleading.

[trail hemlock]

yeah baby jech

[heady ember]

People normally read this before big Jech, from what I know.

[remote sparrow]

goldrei's Classic Set Theory

[inland bronze]

reccommend me a book

cuz why not

[glacial mica]

im curently self studying stewart calculus what book whould you recomend after compleating stewart calc

[tropic nacelle]

what do you want to learn after?

[glacial mica]

im open to anything but mainly I want to know if I should go to real analysis or multiveriable/diferential equations

[gilded shuttle]

stewart’s book has multivariable

and a bit of differential equations

[final vessel]

h

[vital bane]

I have another question

Why would anyone read big Jech

[heady ember]

Its a door that allows you to access more set theory.

A prerequesite for stuff like Kanamori

[vital bane]

there's more...

[pliant wadi]

Oh I have seen it. Do you maybe have some lecture notes recommendations?

[trim kayak]

Which Stewart's book are you using? I ordered a used copy of Stewart's Early Transcendentals Calculus 8th Edition text and have been looking through it. It seems pretty good!

[glacial mica]

8th edition

[trim kayak]

Early Transcendentals?

[glacial mica]

No just the normal edition

Im at chapter 5 which is intigral appications and its been pretty good so far

[trim kayak]

I'm doing a little review before I start reading through it. I flipped through it a bit. Looks like it gets tough!!

[molten gulch]

early and late transcendentals are both fine, it's just whether functions like e or ln are introduced prior to their formal defintiions

[trim kayak]

I want to learn more about Calc just for fun. Any suggestions for reviewing basic calc and starting to learn the concepts in the calc book? I'm thinking about reading the chapter, taking notes, and then practicing the problems.

Some of the concepts toward the middle and end of the book look pretty tough.

[bleak ember]

how do i read a math book? i bought stephen abbott's understanding analysis and read the first chapter, but its lowkey intimidating

[slender cargo]

Is this your first math book involving proofs? If so, try out one of the many introduction to proof books out there

[bleak ember]

this is! do you have a recommendation for intro to proofs?

[slender cargo]

Paging @remote sparrow

[slender cargo]

Also, have you taken calculus?

[bleak ember]

yes

up to calculus 3

[heady ember]

Abbott is a suitable enough intro to proofs, from what I've heard about it.

Just start reading

active reading

[slender cargo]

Eh.. sure. I think it's fine to take a bit of time to go through an intro to proofs if one feels uncomfortable with proofs.

[slender cargo]

Here's a free resource:
https://richardhammack.github.io/BookOfProof/Main.pdf

I know Velleman's Intro to Proofs is popular. I've heard good things about Jay Cummings Proofs: A Long Form Math book also.

You can also take @heady ember 's suggestion and just move forward with learning proofs from Abbott's book. But yes, you'll have to read actively and take your time

[heady ember]

Yeah of course

Even now I have many days where I don't make much progress at all

But I'm just self-studying for now, so there's no rush.

Well, except my insatiable thirst for power

Just try to have fun!

[remote sparrow]

#book-recommendations message

[trail hemlock]

ill second grass's suggestion, as doing a similar thing has helped me understand what i read a LOT better

[slender wasp]

one option is do Spivak upto chapter 8 (upto the foundations) and then come back to Abbott. And/Or, you can supplement Abbott with 18.100A lecture videos from MIT OCW.

18.100A is intro to proofs + real analysis.

[serene cove]

any maths book for middle schooler ?

[marsh ingot]

Baby Rudin

[tender river]

what kind

[jaunty steppe]

it depends on what kind of math you want to go into detail: i recommend you to learn how to do every type of equations and learn lot of euclidean geometry

[serene cove]

Geometry related

[tender river]

#book-recommendations message

[willow summit]

Does anyone have any book recommendations, or really any resources, for learning to write formal proofs?

I'm an undergraduate doing my first analysis courses, and almost of all of my work thus far has been almost entirely computational

So writing proofs in proper format has never been that much of a priority until now, and I'm realizing I have a really hard time writing it in a way that makes sense

[serene cove]

thanks 🤧

[tender river]

how formal are we talking? most people develop the skills to writing proofs simply through experience, read more proofs, show the ones youve written to your friends or to the context specific channel here, for analysis that would be #real-complex-analysis where you can ask for a review of your work

[willow summit]

That's very fair. I don't know many people irl who can help me with this stuff, most are at my same level if you understand what I mean. I think I'm going to start trying to be more active on here and ask for help on that sort of thing

[hearty steppe]

I just want to double check that Gelfrand is the most approachable book (haven’t looked through it yet) for people who don’t have complete conviction for mathematical rigor but are from a more social sciences oriented background and other fields of study in terms of exploring calculus of variations more intuitively. I found a lot of videos and some notes online but definitely just want to double check here because I don’t really study maths intensely like most of you

Also my autism makes it difficult to just sift through rigor that isn’t really broken down with English… I spent a good few years working through foundational linear algebra/proofs focused texts and tried working through a little bit of some analysis and abstract algebra texts

There’s some challenging books like Folland’s real analysis where the rigor isn’t too bad but it really builds up later… although still a fun read

[fresh skiff]

axler has written his MT book really nicely

just today i realised it

[earnest wolf]

his linear algebra book is also golden

[fresh skiff]

oh yeah

but i haven't studied it

[vast leaf]

Combinatorial set theory with a Gentle Introduction to Forcing is a great book

[vale solar]

highly recommend

[tribal crow]

I happen to have a copy of Munkres in front of me as I write this

[analog lava]

are hatcher's algebraic topology and tu's smooth manifolds enough to begin reading characteristic classes-MS?

[dim sierra]

Yes definitely

[analog lava]

thank you king i love lukas

[remote sparrow]

https://www.rxddit.com/r/PracticalGuideToEvil/comments/1gv1fis/pgte_is_getting_ebook_and_paperback_versions_done/

@glad rampart

[willow merlin]

which book explains cauchy mvt for dummies?

[loud cradle]

spivak's calculus

[heady ember]

Schroder and baby Rudin both have it

[gray gazelle]

Could someone recommend resources (not just books) for Wavelet analysis?

[wraith sandal]

Hello, would I have a hard time studying analysis if I am comfortable proofs but have no knowledge of calculus 2?

[heady ember]

Well, you don't really need to compute stuff in analysis. So, calculus would only be helpful in helping you get prior intuition, if you learnt it well.

Hence, if you actively read and form good intuition, then that shouldn't really be an issue.

But even if you think you are comfortable with proofs, you may still have trouble with analysis --- that's normal.

Smash your head on the brick wall and it will eventually crack and break

~~if you don't break first ~~

[wraith sandal]

Good to know thanks

[wraith sandal]

Yeah, I was kinda worried because I was struggling with Abbott's first theorem in chapter 2 but I think it's because I skipped chapter 1 lol

[heady ember]

Don't skip a chapter unless you aren't interested in it and it isn't needed for future chapters you are interested in.

[gilded shuttle]

this feels like the math equivalent of a physics kid picking up a quantum mechanics book because it’s cool without actually learning the necessary prerequisites

[heady ember]

Yeah

[trail hemlock]

maybe try spivak's calculus, its an intro calc text which also serves as a good intro to analysis book. u can move onto abbott from there

esp if u dont have calc 2 experience, jumping right into analysis is not a great idea

[marsh ingot]

Some sources or book for Poisson kernel? An introduction and properties

Need to undestand how the Poisson kernel make a holomorphic extension

[sleek python]

What kind of maths do you learn with this book

[trail hemlock]

evil math 😱😰😨🙀😧

[willow summit]

I have my final exam for analysis coming up, and I want to get deeper into the subject matter.

[normal crystal]

it's a reprint of Spivak

[willow summit]

But I can't decide if I should go through a text like Spivak's Calculus or Tao's Analysis, in order to get a really strong sense of analysis, or instead go off an do something else I'm interested in like first order logic or topology

[wraith sandal]

I will use that as reference but next semester i will take calc 2

[willow summit]

Would it be that helpful in future math classes to have a very strong sense of analysis? Or do I go for something new and engaging?

[sleek python]

depends

Are you a maths major?

It's always useful to have a very strong sense of analysis even if you're not a maths major, but useful isn't always necessary

[willow summit]

I'm doing a minor in math, but I'd like to do more with it

So I'll be taking many more math classes after this, including real and complex analysis

But I'm also mostly doing it for fun as something enjoyable

[sleek python]

I see, in the case a text that goes in depth would be a good idea

[willow summit]

I'm doing a major in International Relations and minor in Pure Mathematics

Which always throws people for a loop lol

[sleek python]

It'd an interesting combo for sure

[willow summit]

Ok then. In that case I guess I just have to decide between Spivak and Tao

I've looked at both of them and I'm not sure which one I like more

[sleek python]

But if you're interested in studying maths for studying maths then yeah try to go in depth whenever you have the opportunity

I have used neither of those, but they're both often recommended

I do like Tao's style in his blog though, so if his book is written similarly it'd probably be good

[vital bane]

@heady ember

[sleek python]

Tbh you're not obligated to use just one book

[willow summit]

Just go the most in depth

Por que no los dos

[heady ember]

What

[vital bane]

Forcing mentioned

[sleek python]

You can just pick chapters from both and check if the other book says things differently when you struggle

[heady ember]

ok

[willow summit]

True

[vital bane]

you hate forcing now?

finally we have broken grass free from the grasps of set theory

[heady ember]

No but why would you ping me over someone mentioning forcing

That's sullable.

[marble solar]

A good one is John Conways complex variables text on the poisson kernel

[rigid trail]

Can't believe they named a guy after Conway's Game of Life

[remote sparrow]

none

[marble solar]

fun fact: it's a different John conway

[marsh ingot]

Thanks

[marsh ingot]

This one?
https://link.springer.com/book/10.1007/978-1-4612-6313-5

[tawny apex]

What book should i get next after getting calc linear alg and stats

[crimson pagoda]

elements of statistical learning

[mossy flume]

wdym get

like have you worked through the books you have already?

[tawny apex]

buy

[mossy flume]

have you considered working through the books you already have

[tawny apex]

buying in advance
buying it early*

[slate wedge]

What kind of math books/textbooks do you guys recommend? I've always been a math person but I feel like my math classes only scrapped the surface 95% of the time.

[dim sierra]

What classes have you taken

[slate wedge]

Alg1 and Geometry

[dim sierra]

I think Art of Problem Solving’s intro books are good then

https://artofproblemsolving.com/store

[slate wedge]

ty

[normal sun]

yall got online calculus books 😒

[trail hemlock]

https://schtschenok.github.io/calculus-made-easy/
pdf: https://www.gutenberg.org/files/33283/33283-pdf.pdf

[fresh skiff]

I just released, ch4 of Folland (set point topology) doesn't require the knowledge of previous chapters
Except a bit of convergence i guess

Am i right?

[lyric cove]

hey guys can anyone recommend a basic math book?

cause i need to work more in basic math

[wicked sand]

Would you guys recommend Goldstein for learning classical mechanics? I'm wondering if there are more mathematics oriented/rigorous options, even just as supplementary material.

[fast bane]

hey, any recommendation for abstract algebra (undergrad)

[heady ember]

Look in pinned

[fast bane]

i didn't really found any

[heady ember]

[fast bane]

thank u SM

[fringe heart]

I hear a lot of people talk about how amazing math is and how it powers every aspect of our lives, but as someone who lucked their way through math as a kid and doesn't know much at all, I guess I've never appreciated or tried to appreciate it.

Any books which go through things like this, maybe the evolution of math and its uses in our lives? Preferably not too technical but anything works.

[daring lake]

if you got the background ye

it is mathematically rigorous from the start

[wicked sand]

Yeah I should be fine with it, cheers!

[urban light]

What do you mean by basic math? Lang has a book called Basic Mathematics. And there is an algebra book by Gelfand. Gelfand also has a book on coordinates and another on functions/graphs. I haven't looked at any of these personally, but I remember the algebra one looking neat. I don't think any of these books are meant to be "easy," so if you're after a problem drill book these are not it.

If someone is struggling with D&F or Artin they should try Fraleigh or Pinter, imo. Particularly if the reason they are struggling is lack of "mathematical maturity." (The tradeoff, of course, is these books will only take you so far.)

[sage python]

Possibly? My vibe is that at that point it might be better to find some easier intro to proofs type class, like discrete math or elementary number theory

And build your way back up to algebra

[graceful moon]

I feel like ENT is the correct choice because it essentially motivates most of basic algebra

[lyric cove]

i mean like something related to HS math

algebra, geometry, trigonometry

and stuff

[urban light]

Lang's Basic Mathematics and the Gelfand books are supposed to be that level. Lang also has a geometry book, and Gelfand has a trig book. I don't know anyone who actually used them. But the Gelfand books in particular get a lot of praise.

[sharp latch]

Honestly your best bet is probably pop math YouTube channels like numberphile/3b1b/standupmaths. But in terms of books I loved Things to Make and Do in the 4th Dimension by Matt Parker when I was in high school

[urban light]

Ian Stewart has a book called Concepts of Mathematics that I like. It is targeted at laymen.

[eternal tulip]

thoughts on "categories for the working mathematician" by saunders mac lane? https://books.google.ch/books?id=MXboNPdTv7QC
found it in my hs library so i have the physical version aswell which is way easier to read imo

(I have no prior knowledge of category theory)

[timber mesa]

it's the usual recommendation for an intro. to category theory

from what little I've read of it, seems well written

in any case you could complement it with e.g. Riehl for a more current reference

[eternal tulip]

Okay! Thanks :)

[mossy flume]

How much other math have u done?

IMO it is a mistake to look at category theory prior to having a foundation in algebra + analysis loosely speaking

cause without background in different areas, category theory (at least to me) seems like general nonsense

[crimson leaf]

Yeah I would even say without analysis, algebra, and topology it feels like you'd be lacking in any reason to ever want to use categories and any nice/useful examples that come up you probably wouldn't understand

[balmy crown]

Whats peoples opinion on Basic Analysis I: Introduction to Real Analysis, Volume I by Jiri Lebl?

im planning on reading this over the winter break alongside the Real analysis lecture videos from MIT Courseware

[urban light]

For enough. But if, for example, a motivated high school student wanted to learn algebra then I think a book like Fraleigh would be good.

[noble vapor]

conic sections book?

[balmy crown]

Do you prefer Lebl or Abbott?

[slender wasp]

I didn't look at Lebl coz I thought I would be getting the material from the 18.100A video lectures. I just used the ocw lectures with Abbott.

[tender river]

there's aluffis chapter 0 too if youre willing to go that path

[dim ether]

AoPS books are (absurdly) expensive (at least as someone who lives alone; I cannot afford to spend $60-70$ on individual books). Does anyone know if there is a way to buy them used for cheap? (All used copies I have seen go for 45$+)

[quick hornet]

legally, probably not no

with a lot of textbooks there are often "international editions" that are somewhat lower quality materials and are substantially cheaper

but afaik the import of these domestically is... ambiguously legal

in any case i dont know if AOPS has such editions

if they do then youll probably find them on indian marketplaces, but no guarantees they can ship internationally

of course piracy is the other option but we cannot endorse that on this server

$70 is a bargain by textbook standards fwiw, the textbook industry is very pricey

undergraduate-level texts typically go for $100-$200, prices do tend to come down at a graduate level unless the book is out of print though (if its out of print then expect to pay like $500 unless you can Find A Guy At Springer to do you a solid)

[heady ember]

Some books are legally free on the Internet Archive too, so that's worth checking out from time to time, I guess.

lmao texit

[quick hornet]

you can also check out your local library

a regular public library is unlikely to have a diverse catalogue of textbooks but you can put in a special request to the librarian and see what they can do

a university library will almost certainly have AOPS in it

not all university libraries are open to the public though, YMMV

mine allowed anyone to come into the library and read but only students and faculty could check out books, for example

[loud cradle]

some university libraries will let you buy a library card if you're general public (not a student or faculty)

the local university here offers this for $50/year

[quick hornet]

in general, most librarians want to help you so it never hurts to ask

genuinely an incredible community resource

[fresh skiff]

Yes

[fresh skiff]

https://youtu.be/shlcMzQMMjA?si=CznAuyDJlM-VBCzj

[slender wasp]

Nope, the most recent/available one for 18.100A follows Lebl. But, I thought they went well with Abbott. They don't do topology though. I'm not aware of any other lecture videos using Abbott.

[stiff grail]

what workbook should I get to practice intermediate to advance integrals?

[wintry jewel]

Hey, any recommendations to understand linear algebra and geometry intuitively with real world applications and formulations

[tender river]

#book-recommendations message

[vital bane]

"Inside Interesting Integrals" by Paul J Nahin

[uncut nest]

Any book recommendations for higher level probability and statistics?

[stiff grail]

thanks

[fresh skiff]

what is your feedback on point set topology from folland (CH4)

this might be a dumb question, since already a lot of books exists

[balmy crown]

In your opinion how does this compare to Lebl's lecture?

[fresh skiff]

what is this

[balmy crown]

The MIT Courseware lectures on Real Analysis

[silk bluff]

I would recommend some books from B. Hrabal, tho i am not sure if its translated, but cool books!

[normal crystal]

looks like some are
do you have a favorite?

[silk bluff]

well I never read them to the end, but I heard parts of it so I recommend: Postřižiny, Obsluhoval jsem anglického krále

[willow merlin]

which book explains elementary vector calculus?

[molten gulch]

any calculus textbook should cover this (like thomas or stewart), we also like schey's div grad and curl as a supplement

[marsh ingot]

Vector calculus versus vector analysis

[willow merlin]

I didnt know vector analysis was available, any good references ?

for an introduction to the topic

[heady ember]

Assuming you have done intro analysis, the following are two texts for analysis on normed spaces:

1. Henri Cartan Differential Calculus
2. Coleman Rodney Calculus on Normed Vector Spaces
   (recommended by James)

Otherwise, for analysis on R^n, you can use Amann Escher, Folland (not his MT book, but his multivar book), etc

[heady ember]

Oh and Schroder also covers analysis on normed vector spaces (in probably less detail) from scratch --- it teaches proofs and intro analysis from scratch.
Bernd S. Schroder - Mathematical Analysis A Concise Introduction 2007

[oak tide]

appreciate it ill check it out

[timid delta]

Is Serge Lang Undergraduate Analysis textbook any good?

[sage vale]

yo do you guys know any good books for learning geometry?

[molten gulch]

Euclidean, Noneuclidean, differential, algebraic, analytic....which one?

[sage vale]

Euclidean and non-Euclidean

[abstract frost]

are the "Springer Undergraduate Mathematics Series" books worth purchasing? because they're always going for $60+ online

[timber mesa]

that'll depend on the book but there are some good ones

though ig you could say that of just any of Springer's collections

all of their books go around that price at least

[abstract frost]

aw man that sucks :(

[balmy elm]

any texts for cohomology that explore the riemann-hilbert correspondence and relatedd topics without a lot of pre-requisites beyond like fulton and d'n'f?

[remote sparrow]

some softcovers go for $16 periodically

which books do you want

[abstract frost]

i was looking for introduction to linear algebra by serge lang

[remote sparrow]

i think that's a utm

i think there are better linear algebra books than that though

[abstract frost]

wait do all springer books cost a lot?

[remote sparrow]

depends, but $40-80 regular price is on the low end for textbooks (which isn't great either)

i think there should be a holiday sale coming soon

[abstract frost]

on thriftbooks?

[remote sparrow]

on springer

[abstract frost]

i see

[remote sparrow]

#book-recommendations message

other linear algebra books to look at @abstract frost

[abstract frost]

thank you :)

[heady ember]

Just wait till a sale: black friday or something. Alternatively, just sail the seven seas.

[foggy quest]

The pdfs are basically free, so I guess they make their money from hard copy sales

[timber mesa]

well, that and institutional access to their journals

probably the #1 thing soaking up grant money and national R&D budgets lol

[earnest wolf]

so you are saying they are free, but they still sell 'em

[timber mesa]

free if you have institutional access through your uni

well a good chunk of them

[daring lake]

any opinions on Roman?

[graceful moon]

Except when it very occasionally just doesn’t let you? I’m not sure if this is an issue anyone else has but sometimes I’m not automatically logged onto springer through eduroam, and I try to sign in via institutional access and just nothing happens it’s kinda frustrating

[oak flower]

A first proof based calc book that seems to be popular (and I loved) is Understanding Analysis, by Abott

[floral lantern]

Do you want to understand calculus conceptually or rigorously?

If you want to understand it conceptually and why it matters, I think just doing some physics will go along, long way towards that.

If you want to understand the foundations of calculus, you’re looking for real analysis. The typical beginner book for analysis is abbott’s book, but if you find it too proofy or formal, spivak’s proof-based calculus book is meant for first year undergrads to understand calculus rigorously (without working through all the machinery of analysis)

[floral lantern]

Spivak may be more appropiate if you have never done proof based mathematics before

So I would go with that

When you take your linear algebra course, consider studying proof-based abstract linear algebra as well

[snow plover]

Are there any good books on probability and statistics?

[remote sparrow]

blitzstein and hwang is good for probability

wackerly, mendenhall, and scheaffer is good for mathematical statistics

https://link.springer.com/shop/springernature/holiday-sale/en-us/

only 30% off

😭

worse than last year's sale

https://link.springer.com/book/10.1007/3-540-44761-X

wait big jech literally went up in price from last year

and we only have 30% sale...

[dim sierra]

is there a way to view which GTM texts are on sale?

[remote sparrow]

i think you just apply the coupon code at checkout

[earnest wolf]

sorry for interjecting, but which of jechs books is the big jech?

the one u linked above? or is that the baby jech?

[remote sparrow]

the one i linked

little jech is published by crc press

[graceful moon]

Ouch yeah it’s not quite the sale last year, the one book I wanted is still 45 for the soft cover

[willow merlin]

is there a book that can serve as intro to: ladr

[graceful moon]

Something like Nicholsons or Strangs LA book should be more gentle and give you a better grounding

The advantage of strang is that there is accompanying lectures through MIT OCW

[earnest wolf]

I'd say it's self-sufficient?

content-wise
other than that, just some level of mathematical maturity (being comfortable with proofs) is required

[remote sparrow]

LADR can stand by itself, but these are good precursors: #book-recommendations message

how do people figure out when select springer softcovers are $16 btw?

[modern sphinx]

Lang makes... some choices. Some I agree with, some I don't.

One of the big ones is that he does most things in the context of (subsets of) a normed vector space, rather than a metric space. In an exercise, he shows you how to isometrically embed any metric space into a normed vector space, so there's no actual loss, but it may obscure some things.

Relatedly, Lang does things in a lot more generality than most people do. A lot of modern texts focus on R or R^n first, and Lang does do this a bit, but he very quickly ramps up the abstraction, in a way more common in an algebra course.

Lang includes a LOT of material on Fourier analysis, which is a Very Good Thing. Fourier analysis is what analysis was made to do (don't at me). It's good to learn this. Alas, a typical course doesn't have time to cover it. Which gets me to:

Lang is loooooong. 642 pages or so. Way tooo long for a year long course, but he gets to include loads of goodies, which you don't get in a typical textbook (see above point about Fourier analysis, though he also gets to differential forms and Stokes' theorem)

Some folks have told me they think his proofs can be clunky and obscure what's going on. IDK if I agree with them or not; Lang's where I started and I haven't gone back to him in a while. I love the stuff about approximations to the identity and his slick proof of Weierstrass approximation using these ideas, but other stuff (like implicit function theorem) I just don't remember his treatment well.

I'll say, Lang's a number theorist and it shows in some of his examples in that book (e.g. using Fourier analysis to solve the Basel problem)

[next orbit]

Hi guys

Recommendations for study engineering? So I will enter the university in 1 month, and I want to prepare for that, which books should I use for math and psychics (mechatronics engineering)

In a web page I read about using "University physics" by Young and Freeman, for math Thomas's Calculus and Stewart's Calculus

[timid delta]

Thanks, this perspective is very helpful, I think I will use it after all!

[timid delta]

Engineering statics and dynamics

Is like University physics but more Engineering focused and only covers Mechanics in detail

[next orbit]

Cool

[next orbit]

Author?

[timid delta]

I'm sorry lmao, the title is wrong, Mandela effect

Is vector Mechanics for Engineers

Beer, Johnson, Mazurek, Cornwell, Einsenberg

I didn't use this one myself, I went with Taylor (as I study physics) but I checked out and I think is pretty good?

It covers a lot which is important

[next orbit]

It's ok

Thanks u

[young gust]

Has anyone read flatland by Edwin Abbott Abbott?

[gray gazelle]

Any ideas for books for casual math I can use during college? Nothing too intense, but something fairly advanced that school doesn't usually go in detail with. Like maybe calculus from scratch, or something else.

[formal bronze]

Abstract Algebra by Dummit and Foote

[gray gazelle]

The orange cover book?

Abstract Algebra...

[formal bronze]

Yeah I'm pretty sure the cover is orange

[gray gazelle]

Alright, I'd save it for consideration, thanks

[formal bronze]

Or maybe Elementary Number Theory by DM Burton, that's a bit more usable for casual purposes

[gray gazelle]

There r a lot of versions online for the book

7th ed?

It's yellow cover with blue spiral ish art at centre and blue text for title

[formal bronze]

Yeah that's the one I have

Edition shouldn't matter all that much though

[gray gazelle]

Oki, thank you so much friend, really appreciated :)

[steep root]

Lookin for a book that covers linear algebra

[tender river]

https://hefferon.net/linearalgebra/ or https://axler.net/ depending on course syllabus

[steep root]

No course syllabus, im less than a year away from uni

😭

[formal bronze]

Hoffman and Kunze

[fresh skiff]

How much multivariable calculus is need for PDEs (in particular Strauss)

[remote sparrow]

https://bookstore.ams.org/amstext-54/

i'm curious if you want to try this book instead

also aren't you doing measure theory atm? if you finish that you could look at evans

[normal crystal]

why did AMS increase prices and switch to softcover (mostly) with their new books last few years
did their underlying costs really change to that extent🤔

[fresh skiff]

Oh. I haven't heard about this book

Yes I am doing Measure theory and real analysis atm

Let me check this book

[remote sparrow]

it's new; i found out about it from the statistics server

[vital bane]

Starting PDEs without finishing RA and MT?

[remote sparrow]

possible depending on the book

[vital bane]

I don't mean in terms of prerequisities

I meant that in terms of doing too much at once

Don't make the mistakes I've made Afzal

[fresh skiff]

This books covers a variety of topics

Including it's onw prerequisites as well

Interesting

[fresh skiff]

No way
I was making somekind of plan how will I go.
RA + MT → PDE + LA or AA + LA

[vital bane]

I would suggest AA + LA AA is one of the fundamental pillars that everyone must have

[fresh skiff]

Ah i see
I was thinking like Artin (that will cover both LA and AA).
But i would like to study La separately

Btw interestingly this semester I have FA (functional analysis)

[vital bane]

Then you better catch up on MT quick

[vital bane]

I would suggest a separate book like FIS as you can learn far more Linear Algebra (it's extremely applicable in all sorts of fields within and outside of math)

[fresh skiff]

Yeah, so my plan is to spend twice time on analysis than MT, i believe i will cover/review (atleast abbott in reasonable amount of time)

[fresh skiff]

Makes sense

Thank you Neam !

[remote sparrow]

#book-recommendations message

#book-recommendations message

@fresh skiff

[tender river]

oh, if youre self learning in hs then both of these books are also accompanied by some videos that you can check out https://youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw&si=qMqUPoLEkP40nRm9 for axler and https://youtube.com/playlist?list=PLwF3A0R8OzMoMlE1-SaEh8h9VqUlO-r52&si=YltDEgOXug15DnYi for hefferon

[heady ember]

Azfal becoming CatBread#2

Speedrunning to reach PDEs

[remote vortex]

You can really do a lot of FA without much in the way of measure theory, all you're losing is the availability of L^p spaces as a class of examples, the Riesz-Markov-Kakutani theorem, and Landau's theorem on duality between L^p and L^q (but you can still do the l^p vs l^q version)

[heady ember]

Hi Outti

[stable flicker]

Isn't L^p like huge.
And also huge in applications

[steep root]

love bro 🫶

[fresh skiff]

wow these are superb!! Thank You Sour Drop

[fresh skiff]

no

just curious to know, cuz i have seen multi variable as prerequires bunch of times

[heady ember]

Come read

• Henri Cartan Differential Calculus
• Coleman Rodney Calculus on Normed Vector Spaces
  with me

(After I finish Rudin and FIS)

[fresh skiff]

i check both books they are awesome. Cartan looks advanced while coleman seems like with minimum prerequisites

[torn blade]

anyone have a book(s) that cover these topics in multivarcalc & diffeqs?
Arc length formula, surface area of revolution formula
Polar, cylincdrical, spherical coordinates
Sketching graphs in cartesian or some other coordinate system
Partial derivatives, classifying critical points, partial chain rule of parameterised curves
Double integrals, using the Jacobian, integrating with polar coords
Triple integrals, integrating with cylindrical/spherical coords
First order DEs: seperable, linear, transforming to seperable/linear (homogenous ODEs/bernoulli ODEs), exact equations
Second order DEs: homogenous and non-homogenous, applications to mechanics, resonance

[trail hemlock]

i took a course in computational MVC (for hs dont ask ), should I read Cartan?

i already read analysis on manifolds but i need smth to do this summer

[remote sparrow]

stewart calc for multivariable calculus, boyce and diprima for differential equations

[torn blade]

thanks xx

[heady ember]

Computational mvc doesn't teach you the inverse/implicit function theorems right?

You probably need some degree of rigor, either way.

[remote sparrow]

complex analysis maybe

[trail hemlock]

yeah i got tired of my class and read folland's calc book 😭

[heady ember]

Nice

[earnest wolf]

is "distributed algorithms" by Lynch good as a first read?

• is it up to date? [the field is relatively new, so...]
• is the exposition good?
• maybe you can recommend any other books / lecture notes

[trail hemlock]

yeah im gonna do this soon

as soon as finals are over and i finish stein's fourirt analysis

[stiff grail]

any resource to learn feynman trick for integration?

[vocal violet]

recommend me good book to start reading again for college, it been 2 year since high school

my reading/writing level below average how to improve

[remote sparrow]

https://www.amazon.com/Everyones-Author-Andrea-Lunsford/dp/1324045108

https://www.amazon.com/dp/1324060131

also, try reading more books generally

ideally you aren't only reading books that are made to be as easily digestible as possible

[civic silo]

does anyone recommend reading the joy of x

[zenith peak]

Do you have recommendations on where to start with calc and linear algebra I’m in high school

[native cradle]

Mathematical Physiology: I: Cellular Physiology, is this a nice casual read?

I know no biology, must say that

[gray gazelle]

I have the same question

[zenith peak]

Twins

[daring lake]

Calc: Stewart's Calculus
LA: Axler's Linear Algebra Done Right

[open merlin]

You'd probably want something more calculation focused than Axler for LA, I'm guessing

[willow merlin]

which book gives examples of vector spaces with functions inside

like instead of n-tuples, functions or polynomials

I am just curious about the topic, not like I know anything

[tender river]

analysis books

[obtuse spoke]

Is there any higher trig book that I can read (I completed Loney Trig)

[gray gazelle]

Thank you

[gray gazelle]

Letting you know, that your question has been responded to know, best of luck!

[zenith peak]

Thank you so much

[native cradle]

isn't stewart too hand wavey ?

[daring lake]

Well they are in high school, so I wasn't gonna throw Rudin or Spivak for reccs.

Most calc books are around similar to Stewart eitherway like Thomas

[marble solar]

Yeah, I think at the high school level Thomas, Stewart are good recommendations

[sturdy sail]

Any reccomendations for Invariant Theory and GIT?

[torn blade]

not really? what makes u say that

[earnest wolf]

if anyone else misses pbs infinite series – their previous (and amazing!) host started a yt channel

(she actually launched it two years ago but I fount out only now lol)

[median iron]

Ask this in a Computer Science server maybe, I would be interested in knowing the answer too

[earnest wolf]

the CS server is completely dead

even tho #theoretical-cs finally opened, no one there replied either : (

[remote sparrow]

try reddit

[mossy flume]

or cstheory stack exchange

[trim kayak]

Is it good?

[charred vigil]

hi ppl, im trying to self study math, physics and proggraming, buy idk where to start, any introductory book to the theme or one that contains the most information, but everything will be appreciated, thanks

[charred osprey]

Not long before we get #theoretical-phys

/j

[remote sparrow]

*#math-phys

mathematical physics != theoretical physics

[median iron]

The Physics server has a great channel for this to be honest, I think it's the highlight of that entire server

Though I might be biased

[median iron]

Lots of strong, active people, though a lot left or got kicked recently

[native cradle]

Doesn't prove anything

well for the most part

[earnest path]

I just used it for calc 1 and it was fine, I think in-depth proofs would be difficult to follow for most of it's intended audience

It does include Proofs of Theorems as part of the Appendix (F) for those so inclined
(I don't want to argue, but I do feel like it is a decent calculus book)

[loud cradle]

don't mention these sites or link to them, it's against server rules

[gray gazelle]

Just mentioning is against the server rules?

[loud cradle]

yep

[native cradle]

fair

I just feel it could do with a bit more rigor

but that's just me

[remote sparrow]

https://press.uchicago.edu/ucp/books/book/chicago/R/bo195982549.html

@halcyon mesa i stumbled upon this book and the introduction seems interesting

[steel cloud]

I completed Carothers Part 1 metric space, what should I do next? Measure theory? But there are entrance exams for the master so I have to revise the undergraduate stuffs so which problem book is good for it ?

[buoyant halo]

i see you everywhere

are you phd?

how have you read every book under the sun

my university dodesn't even follow textbooks for our courses : (

[earnest wolf]

they probably do, even if they don't say what book(s) in particular

undergrad is very standardized

[earnest wolf]

btw, u don't have to read a book cover to cover all the time (:

personally, I sometimes see what chapters I like and study them deeper, while only skimming the rest, if at all

[shrewd swan]

Is there any good Geometry textbooks, specifically for proofs?

[earnest wolf]

u mean like high-school Euclidean geometry?

or non-euclidian ones?
or differential geometry?

for proofs tho I'd suggest probably a dedicated course? [book/lecture notes/video lectures]

or just study any proof-based subject, not necessarily geometry, that you like — you will pick it up along the way

[torn blade]

any book(s) that cover the following topics in ODEs:
Homogenous first order ODEs
Bernoulli first order ODEs
Second order ODEs in mechanics
Pure and practical resonance (in second order ODEs)

[torn blade]

the 2nd book here sadly doesnt cover these 4

well it does a small amount but not enough for my exams

[native grotto]

is there any books to help me study geometry from 0? i know algebra but didn’t studied geometry, it’s seems harder for me much more

[vast jackal]

yes

Aops Intro to Geometry

or maybe umm Khan Academy if you like it

[vast jackal]

If you're looking for Euclidean Geometry try EGMO by evan chen

[foggy quest]

https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2020/10/diffeq.pdf

[remote sparrow]

i'll be a masters student next spring

[torn blade]

i read books on like most classes i take lol

[glad wren]

Elementary and Advanced Trigonometry by Miller, Kenneth S (skip elementary section and read advanced section)
Advanced Trigonometry by CV Durell

[novel obsidian]

Perhaps James Robinson's "An Introduction to Ordinary Differential Equations" is what you're looking for

[sour haven]

Are there any good pdf books for algebra 1,2 trigonometry geometry(basically everything) because i can't afford books that cost over 80 dollars

Khan academy is bad doesnt explain concepts

In 1.5 half years i give final exams

[frozen pivot]

the cengage elementary geometry for college students is a good geometry textbook

there is an intro to geometry in that textbook as well

[sour haven]

Il look into that rn

What about the others

I wish books were less expensive

[frozen pivot]

i would highly recommend the aops algebra and geometry textbooks as well

they explain the concepts really well and have very challenging problems

they also have a solutions manual which give very detailed solutions

[sour haven]

Can i make it

The final exams have calculus

And these limits

I know until f(x) =y+mx

I dont know trigonometry and geometry

I got those books and im looking around

With hard work i will make it

These exams i give are called panhellenic exams

Which is really hard

[frozen pivot]

you can if you study math textbooks front to back

1.5 years is a short time to learn it all

you will have to spend a lot of time

[vast jackal]

try aops

idk if there's trig

[near jewel]

Always an alternative to borrow a textbook from library (though it might vary on time).

[heady ember]

Just sail the seven seas

[verbal bane]

Heyo guys, I am currently going over AP Calculus AB and I am constantly suffering because the teacher isn't explaining properly and I have never expected such rigorous course from my perspective. Is there some really well written AP Calculus AB Textbook that actually gets straight to the point and explain concepts well enough? Like one of those "The Princeton Review" but with even more questionaries and such.

[trail hemlock]

Larson's Calculus is prob what you are looking for

a lot of editions and versions exist, u can pretty much pick any and be fine

[trail hemlock]

its been 5 months, how is it?

[heady ember]

Yeh you're right

[umbral field]

if it was bad for intro analysis it would be called Neh

[torn blade]

what topics in physics might be of interest to me as a maths student? My uni has no classes i can take on it and i never did it in high school. id like a book that assumes no physics knowledge but also mathematically rigorous enough to not bore me to death. i have experience in vector calculus, linear algebra, diffeqs & more so it doesnt necessarily need to cover these again

[tribal crow]

that background is definitely enough to get going on most of the UG physics curriculum

it's a little hard for me to give an answer, because most subfields of physics could interest a math student imho, depending on the person