book-recommendations

[gray crystal]

:(

[gray gazelle]

could anyone recommend me a game theory book to self-study from?

[night knot]

A Course in Game Theory by Osborne and Rubenstein is what I'm personally using

[radiant night]

Do you like Serge Lang?

[willow pecan]

Lang bad

[gray gazelle]

thanks

got it

[remote ginkgo]

Maschler solan

Though it dumbs stuff down a lot

The treatment is rather warped compared to what von neumann did

[vocal panther]

I have a bit of a list of books I'm looking for:

• A book with precalculus-ish content but more theoretical and more proof-based
• An intro to calculus book with more content attuned to mathematicians
• Another intro calculus book more focused on people interested in engineering
• A textbook for real-world everyday mathematics (difficulty at about ~algebra 2/precalculus level)

I'm working on a project to look into changing high school mathematics curriculum in my area to make it more applicable to all fields instead of solely for calculus

Idk if these requests are too broad and too much but any and all recommendations are helpful

[willow pecan]

For the first one, Lang's Basic Mathematics seems to cover that

For the third, that seems to be what Stewart is

What do you consider everyday mathematics to be

[vocal panther]

Well sort of taxes things and whatnot

[willow pecan]

I feel like that mostly falls into precalculus and then presenting it with examples and stuff?

For 2, either Spivak or Apostol

[vocal panther]

alright oki doki

[vocal panther]

thank you so so much

[earnest schooner]

I just learned about integrals and derivatives

Where should I go from here and what books would I need to self study ?

Would I go into Calc 3, DE linear algebra? Cause idk

[karmic thorn]

Any of the routes work, although linear algebra before calc 3 might be a good idea.

[earnest schooner]

What topics are covered in linear algebra ?

[karmic thorn]

A first course in linear algebra will talk about systems of linear equations, matrices, computations you can perform with matrices, eigenvalues, eigenvectors

[earnest schooner]

I will look into some books surrounding it, do you have any off the top of your head ?

[karmic thorn]

For such a first course, there's Strang's Introduction to Linear Algebra or Lay's Linear Algebra and its Applications

[earnest schooner]

Pdfs anywhere or a physical book?

[karmic thorn]

You can find both 👀

[sage python]

Do you want proofs or computations Atomless?

[earnest schooner]

And thats sufficient for the entire course?

[sage python]

Also I hard recommend LA before Calc 3 or ODEs

[earnest schooner]

Idk. I just did Calc 2

[sage python]

People who do it the other way think about things wrong

[earnest schooner]

I finished all the math for my degree but I enjoyed it and want to study here and there about it

[sage python]

Gotcha, so basically you can do "proof-based math"

Think in calculus, big theme is the fundamental theorem of calculus, right?

[earnest schooner]

Yeah I got that

Basically anything about integrals and derivatives I got down

Some DE as well

[sage python]

Your calc 2 class probably stated that like, oh okay you can take a continuous function f, and then define F(x) = \int_0^x f(t) dt

Then F'(x) = f(x)

[earnest schooner]

Yeah looks familiar

[sage python]

And then the other version that if f has an antiderivative F, then \int_a^b f(t) dt = F(b) - F(a)

Now you mostly used this to find integrals

In a proof-based calculus class you'd be super careful about all your definitions

What's the definition of a real number, a limit, a continuous function

[earnest schooner]

Would these be covered within linear algebra specifically

[sage python]

And you can actually show that the fundamental theorem of calculus is true

Well, I'm more describing the difference between proof-based and non-proof-based math in a setting you're familiar with

You used FTC to compute integrals

[earnest schooner]

Yeah

Just the application, not the theory as to why it's true

[sage python]

But in principle you could spend less time computing integrals and more time establishing definitions and proving the theorems that other people use to compute

[earnest schooner]

What are the prerequisites for stuff like that

[sage python]

In principle you can take any topic and learn it with proofs. I think linear algebra can be a starting point for proof-based math in general

You could also do Spivak Calculus, which proves what you've done

Or you could find another starting point altogether. Depends less on the subject and more on the book

If you wanna learn a new topic and see the proofs

I suggest either linear algebra or discrete math

[earnest schooner]

There Is a lot to think about here haha

I think to keep it simple LA would be nice

[still umbra]

A lot of higher level math tends to be very proof based

[earnest schooner]

Builds a foundation for me and then I can get into more complex and focused areas of my interest

[sage python]

Look up "Linear Algebra Done Wrong" by Treil

Or "Linear Algebra" by Friedberg-Insel-Spence

Those are nowadays my two main linear algebra recs that have a proofsy angle. Hoffman-Kunze prob assumes more "mathematical maturity" than you've got if you're starting intro to proofs, and tbh it's veeeery old school

[earnest schooner]

Haha I appreciate the insight and reccomendations. I will probably start with one of those two

Thank you for the input bro, appreciate it !!

[sage python]

np fam

[cobalt arch]

Is there a graduate book for combinatorics that actually builds up from combinatorial set theory?

I would prefer a book that actually begins from first principles, although in the context of combinatorics and not set theory (however if the latter is the case then it is ok)

Whoever answers, ping me

[gaunt bobcat]

I’m gonna start calculus pretty soon which one should I buy? And what are the main differences

[novel obsidian]

Don't buy Stewart

Don't buy any books

You will break the bank fast, instead just (don't) pirate spivak or just use Khan or Paul's online notes or something

[gaunt bobcat]

I found them used for a good price, but if u recommend it I guess I’ll try those sources first

[gray gazelle]

Does there exist a linear algebra problem book similar to Polya-Szego or Kaczor-Nowak (lots of non-trivial problems)?

[half mountain]

Probably there might be a book by halmos

[marble grotto]

There's also a book called miniatures in linear algebra which is quite cool

[gray gazelle]

i'm looking for an (advanced) undergraduate abstract algebra book, but one that starts from the basics. (for the first abstract algebra course, but taken after theoretical linear algebra course), any recommendations?

[hollow peak]

Basically any intro abstract algebra text meets that criteria

I personally use a mix of Knapp's "Basic Algebra" and Dummit and Foote

[frosty girder]

Langs algebra

[hollow peak]

people here love artin

also Jacobson is great too

[frosty girder]

i did read a little artin, and i liked it quite a bit

[hollow peak]

artin is in particular good if you want to refresh your linear algebra, but beyond that it is a very well written book

[gray gazelle]

any thoughts on brešar's undergraduate algebra?

https://www.amazon.com/Undergraduate-Algebra-Approach-Springer-Mathematics/dp/3030140520

[hollow peak]

Haven't heard of that before

[gray gazelle]

its concept seems nice to me

[hollow peak]

It looks good to me!

I recommend doing some perusing of the pdf versions from lbgn before you buy of course

[gray gazelle]

of course yes i'll take a look

i'll probably take artin or bresar

thank you for help

[hollow peak]

👍 👍 👍

[gray gazelle]

Are dictionaries useful in mathematics?

https://www.booktopia.com.au/the-concise-oxford-dictionary-of-mathematics-richard-earl/book/9780198845355.html

For example ^

clear, jargon-free definitions
Hmm…

Can’t be useful without jargon…

I am curious what jargon free definitions look like in that book because it seems like there is some advanced stuff

[cobalt arch]

Constructively

[glad prairie]

That looks like a really cool book

[icy knot]

Out of curiosity, how many calculus books do you own?
I have several. Thomas Calculus and Analytic Geometry 2nd edition, published in 1956. I also have the same title but the author was Murray Protter , published in 1960 , I have Ron Larson’s 9th edition of Multivariable Calculus and Div, Curl, and all that by Shey. For Analysis I have Understanding Analysis by Abbott. I was tempted to get another book for real analysis, but that might be overkill. For Linear Algebra I have Serg Lang’s book and for a more applied view I have Coding the Matrix. Was wondering if it was worth getting another book from an abstract point of view, because if I’m honest I didn’t really get it when I took the class for my math degree—the proof based version. I’m set on getting the Charles Pinter book for Abstract Algebra, but the Topics in Algebra by Herstein looks intriguing. Also plan to buy Concrete Math by Knuth. For Complex Analysis which I asked about a few days ago, I think I will go with Matthias Beck’s book. Thanks for the suggestions.

[willow pecan]

I own 0 calculus books

[gray gazelle]

I have 2 anal books though

Real anal- baby rudin and bartle

[gray gazelle]

Can you try reading Vinberg's course in algebra?

[slim peak]

You helped me to notice the following : I have plenty of Linear and General Algebra books, but absolutely none of Calculus wtf

[gray gazelle]

What is concrete math btw?

[modern stone]

Is Pinter’s book on AA good for a beginner?

[remote ginkgo]

yeah

[brittle breach]

what's a good book on Galois theory

I prefer less wordy books unless it's just that good

[gusty smelt]

For field Galois theory I liked Lang’s section on it

I know ppl also like df but it’s wordy so probably not wh@t you are looking for

[gray gazelle]

@brittle breachfor the future you can use the word terse which means less wordy, and will make it easier to look up books

[sage python]

Or perhaps concise... I think you'll see terse when people complain about its lack of wordiness and concise when they praise it 😛

[brittle breach]

yeah, concise and clear is more what I'm looking for

[sudden kindle]

Dummit and Foote chapter 13 + 14

[icy knot]

It is Concrete Mathematics, it’s a math book for Computer Science. Summations, recurrence relations, number theory, discrete probability, binomial coefficients, generating functions, etc.

[calm crane]

i personally found galois theory to be a topic that you only truely understand "why galois theory" when you actually do number theory

otherwise it feels like ah so group fields subgroup intermediate extension cute i guess

[gray gazelle]

wait, it isnt just that?

[calm crane]

wellllll

thats the core idea i suppose

but the implications and what you can do with that is

a lot

but i really only appreciated like what you can really do with it when learning algebraic number theory

(specifically say splitting of primes and eventually kummer/cft but at that point galois fees quite comfy)

[icy knot]

Is this a good introductory book for algebra? It’s part of the Graduate text series for AMS, but some of the reviews seem to think it’s accessible for beginners. I’m a senior math major, so I’m trying to stay in my lane when it comes to advanced topics.

[cobalt arch]

Anyone?

No one

Not a single soul

[sudden kindle]

This is why I want a alg nt theory book that also introduces abstract algebra

Maybe I should say specifically galois theory

[cobalt arch]

Why?

[sudden kindle]

But even ring theory u could motivate with alg nt

[sudden kindle]

Yeah!

[sudden kindle]

Because you're actually using Galois theory in a natural context

What is the most natural field by you can think of? Q
What are the finite extentions of Q? Number fields.

[cobalt arch]

I see

What is the fundamental problem that Galois theory tries to solve, I guess the earliest motivation must have been the unsolvability of polynomials with degree greater than 4

But

Beyond that

[calm crane]

it is important not primarily because of its historical use (there was another proof and the topological proof is way more powerful anyways) but because of what future implications it had - so learning it without some bigger picture is somewhat a struggle
i guess this applies to many "topics" as well - without sufficient "big picture" motivation it feels like you're wandering pointlessly and examining an interesting connection to death

i suppose this is where examples are somewhat useful but really for topics like this they feel quite meh

[calm crane]

^ agree with this sentiment, i would like a book that does abstract algebra and number theory in a nice way together

but personally im not sure what a good order would be either

[calm crane]

tho over here it is also nice to learn about ramification over local fields - the situation over there is a lot nicer

[forest sleet]

I don't do combinatorics but Stanley Enumerative Combinatorics is I think pretty standard for graduate combinatorics

idk if that's what you're looking for though

[cobalt arch]

I am looking more so for something along the lines of first principles thinking when it comes to how the concepts in combinatorics are generated from set theoretical machinery.

What this means is

I don't want just the combinatorial machinery

But the underlying set theory

And how this machinery arises from it

[sage python]

The underlying set theory isn't that substantial

Like the set theory definition of a graph takes seconds

At least for the combo I've seen it doesn't take much to formalize

[atomic hound]

Please,mathy people, what would be a good book for person the does not know anything about probability?

[empty mortar]

im using grimmet and stirzaker for baby probability but if you're looking for a serious one idk (with like measure theory)

[hearty steppe]

Grimmet and Stirzaker? Gona check that out

Probability and random processes https://g.co/kgs/83s5pP

This?

Oh this is interesting. This is a good probability intro book for maths

[misty wyvern]

Grimmet and Stirzaker is my favorite ugrad book for prob. For grad I like Kallenberg.

Be careful, grad probability isn't just a different level of rigor, you need measure theory.

And functional analysis.

[jaunty acorn]

should i read spivak's calculus book or tom apostol?

[gray gazelle]

Apostols book covers integrals first rather than derivatives

Which is unorthodox

If you're doing it in tandem with a class I'm pretty sure they're gonna start with derivatives

@jaunty acorn

[jaunty acorn]

yup thats true

I can just skip the integral section and go for the derivatives first

[gray gazelle]

That would be complicating things

Then just go for spivak

@jaunty acorn is this a proof based course?

[jaunty acorn]

no its for my maths general

[gray gazelle]

Then maybe Stewart's?

[jaunty acorn]

my professors flamed when i talked about stewart he said that his books are too dry

[gray gazelle]

Oh man

Honestly that's the only not proof based iirc

[jaunty acorn]

but can you tell me which one is better in terms of self study and also has good problems (quality>quantity)

[gray gazelle]

I'm gonna be honest with you

I never read apostol's

Only spivak

And spivak's book is an intro to real analysis more than a calculs book

[jaunty acorn]

ngl book is too much costly and not everyone loves pdf

[gray gazelle]

Also

Spivak's has solutions to All the problems

[jaunty acorn]

well then spivak

sounds more appropriate for me who has lots of problems in solving 😆

[gray gazelle]

You must be mathematicly 'mature' in a way

Do you know how to write proofs?

[jaunty acorn]

just the basics

[gray gazelle]

Well be ready to do proof exercises

[jaunty acorn]

"shaking"

[gray gazelle]

@jaunty acorn you have professor Leonard too

And Paul's online math notes

[jaunty acorn]

he is a saviour

[jaunty acorn]

don't have it do you have any link to it?

[gray gazelle]

And again if you feel like you don't understand something

You can ask here

People will help you

@jaunty acorn

https://tutorial.math.lamar.edu/classes/calci/calci.aspx

[jaunty acorn]

ofc the people in here are cool

[atomic hound]

could be a introdutory book

i gonna check them out

[vocal hatch]

hey folks, I'm looking for an introductory book/lecture series on numerical analysis. Can anyone recommend something?

[karmic thorn]

Richard Burden's Numerical Analysis is nice.

[subtle siren]

IDK if I would consider Grimm and Stir as 'baby probability.' But it's a good source nonetheless

[subtle siren]

For pure math I would probably agree, although I think G&S is 'too comprehensive'

I would recommend probabilitycourse.com instead for seriously basic probability

[vocal hatch]

thanks!

[fathom blaze]

what books u recomend a self learner (Topology) and what are the prequisites to even study it ?

[lavish gorge]

Do you know real analysis?

[fathom blaze]

not profoundly

we went through limits. functions and series

multivariable calculus . def eqtns

[surreal phoenix]

Does topology really even use analysis

isn't it the other way around

Only reference to analysis I've seen brought up is the epsilon delta definition of continuity, and that was just to compare it to the topology definition

[lavish gorge]

Analysis motivates topology

[surreal phoenix]

If you know your set theory, functions, and some degree of real analysis to help understand some of the more concrete examples, I think you'll be fine

that may be so, but I wouldn't call analysis a prereq

[lavish gorge]

You should know metric spaces and compactness before you go into topology

I tried learning general topology before analysis and it was horrible

[iron granite]

I read some metric space stuff from Pugh's Analysis and I don't see how it's related to topology.

[surreal phoenix]

You won't, if you haven't done topology

or at least know what a topological space is

[karmic thorn]

Analysis is not a hard prereq for pointset but it largely motivates the subject and a lot of examples/intuition.

[stray veldt]

a big part of e.g. munkres deals with the question of when a topological space is really a metric space

[odd spade]

I would say taking real analysis is at least v good practice for a topology class

[stray veldt]

i also think that some idea of analysis (metric spaces) and/or mathematical maturity is good (if not required) for (point-set) topology, otherwise it can easily feel very unmotivated and abstract
to answer the original question: munkres is "the standard" intro topology book, but i also like "introduction to topological manifolds" (despite it's title, this is a standard topology book, with a slight view towards differential geometry) and i heard that "topology without tears" is a decent first pass (probably the easiest you can get and available freely); if you are category theory brained (read: view towards algebraic topology) you might also check the newer book "topology: a categorical approach" which looks nice

@fathom blaze

[lavish gorge]

IMO general topology should come after convergence in function spaces

And after metric space theory

[median salmon]

Can someone recommend a good book for combinatorics?

[mystic orbit]

Would anyone recommend the art of problem solving Vol 1 for sharpening your mathematical intuition and problem solving skills?

I want to get into contest math and I'm not sure if I should start with college stuff or high school stuff

[willow pecan]

Contest math does not require college level math

It generally doesn't even involve calculus much

[mystic orbit]

I'm talking about contests like the Putnam or something

Do you need to have experience with high school contest math to compete there?

[willow pecan]

Oh

It helps, especially with the discrete math questions

But it isn't necessary

[mystic orbit]

Then ig could at least start with AoPS just because it's a classic

And then from there go to more advanced stuff

Do you know if the books get any harder tho?

Coz I've been looking at the problems of the first chapter and they seem totally docile

[rare pulsar]

I vaguely remember having AoPS and then dropping it because I was too old anyways

There's a lot of competition math problem books out there, but tbh I think you would be better served just grinding whatever the math olympiad bros release every year or so, if I knew about them ahead of time

[rare pulsar]

Depending on how math mature you are, just learn to write proofs

Also learn TeX, if you want to do some of the lengthier problems.

Good books on proof are pretty well known, and after you do that I think at the very least you should have a vague understanding of what those questions are even saying.

[mystic orbit]

I see

[rare pulsar]

Also, one more plug for the non-existent "visual probability theory but for all probability theory" book

[uncut zealot]

Does anyone know a good resource for how to actually, like, compute the galois group of a polynomial (i.e. of its splitting field over the field on which the polynomial is defined)? For my background, I learned galois theory using the book by Ian Stewart, but it basically avoided the whole computational aspect as much as possible and I'm kind of curious to get into the details of that.

[sudden kindle]

I did bunch of these exercises from dummit and foote that had u compute the galois group of a polynomial

After doing a bunch of these exercises, I concluded that computing galois groups of polynomials is a lot like computing integrals of functions in calculus class. Its a bunch of tricks and techniques that work is special cases but no general method.

If you asked me to compute the galois group of an innocent looking polynomial now, I probably couldn't do it because I lost the skill due to it being so long since I did those type of exercises

But yeah maybe look at dummit and foote and try to do some of the exercises

[velvet briar]

Yeah it's usually just probing to get group properties, then finding the group these properties match

[gray gazelle]

Anyone reccommend any books/papers on knot theory for a beginner (who's not very good at point-set topology)?

[dapper root]

There literally is a formula for solving them up to degree 4 that’s outlined in D&F tho

At least over Q

[gray gazelle]

they do knots in dummit and foote? :o

i don't remember that part of my pdf

[dapper root]

Sorry this is in response to PTY

I figured it’s clear from context that that was what I was responding to

[gray gazelle]

no worried i'm just pulling your leg

[dapper root]

My legs don’t stretch much

They’re plastic

[gray gazelle]

clearly if you read all of D&F your legs must have withered away from all the sitting

i opened it back up and i forgot how truly huge it is

[dapper root]

No it’s cuz I’m a lawnchair

[gray gazelle]

not in a bad way neither, its a great reference for that reason

[dapper root]

With a monkey’s head

[gray gazelle]

oh fair

[sudden kindle]

Yeah and them there's more tricks like reducing mod p

I dubbed those 'mod p tricks' in my hw solutions

[dapper root]

Lol

[sage python]

There's also a formula for integrating all polynomials. Lebesgue: 1, Galois: 0

[gray gazelle]

pwned

too bad galois wasn't old enough to shoot lebesgue in the face

[dapper root]

Get shot in the face?

[gray gazelle]

yeah lebesgue was born 50 years after and galois was an angry man

or at the very least passionate

[distant falcon]

Does anyone know of a website or any books which have a lot of practice problems for combinatorics and NT (contest math level)? If you have worksheets regarding the same then could you kindly DM me the pics? If it helps, I am currently preparing for a national level contest.

[karmic thorn]

AoPS?

[distant falcon]

I can't see any topic specific worksheets or problem sets on the site.

[karmic thorn]

Hmmm

I don't know much about contest math specific resources, but a lot of elementary NT recs are in a pinned message.

Here

[distant falcon]

Thx a lot!

Any links for combinatorics?

[karmic thorn]

You could also try asking on the olympiad server in #old-network

[distant falcon]

Sure, thx!

[karmic thorn]

I don't know much about contest math oriented books, but Miklos Bona's A Walk Through Combinatorics is a good undergrad level introduction

[distant falcon]

Does it include a lot of practice problems?

[karmic thorn]

Yes

It also has solutions and hints to a lot of exercises

Makes it handy for self-study if you don't fall for the temptation to give up early

[distant falcon]

Thx a lot! I was looking for just that type of book.

[karmic thorn]

[sage kelp]

Any book or lecture notes to learn about the cardinality of sets?

[fervent lava]

https://www.people.vcu.edu/~rhammack/BookOfProof2/Cardinality.pdf

[sage kelp]

Thanks @fervent lava

[late spear]

do u guys know a book for socializing and making friends? not particulary focused for business ppl, but like just for normal teenagers

[late spear]

the latter

[gray gazelle]

wendler improve your social skills

it teaches you from the fundamentals

made by a person with aspergers

[distant falcon]

Does anyone know a good book to learn geometry, from the basics? It would be helpful if it is contest math- oriented.

[gray gazelle]

Kiselev's 2 volumes on Geometry are good for basics. You can also use Coxeter's "Geometry Revisited" as a reference.

[distant falcon]

Thx @gray gazelle

[molten rose]

Euclidean geometry in Mathematical Olympiads by Evan Chen and
A Beautiful Journey Through Olympiad Geometry by Stefan Lozanovski are also pretty great

[humble bluff]

not actually

only need basic analysis

which is most of the time not needed as well

but everything in set theory is needed

[icy knot]

I’m such an indecisive buyer, but I finally purchased A Book of Abstract Algebra by Charles Pinter, Analytic Function Theory by Einar Hille, and An Introduction to the Theory of Computation by Michael Sipser. I wanted a physical copy of an enumerative combinatorics/discrete math book, but then I remembered that I have the pdf of Brualdi’s book, Rosen’s book, and Concrete Math by Donald Knuth.

[gray gazelle]

Can anyone suggest a good book for in depth algebra ? I am not interested in any kind of Competition per se just for maths

[frosty girder]

Hall and knights Higher algebra is pretty good

[dark bear]

Can anyone suggest a book that will be helpful for Geometry?

Or at least Geometry A?

[rigid zinc]

Anyone has a good statistics book to recommend?

[peak dragon]

i love Sipser's book, i like the writing style and the exposition of the topic, its fun to read

[gray gazelle]

I'm working through Greub's book on Multilinear Algebra and some exercises require stuff about dual spaces and honestly I never even learned much about them. I need a crash course haha!
Web resources or books appreciated

does anyone have any spicy romace recomneded?

[queen flare]

Anyone know any good books for introing differential equations and/or linear algebra?

[gray gazelle]

@gray gazelle uhmm yh........

[brittle breach]

Finite dim vector spaces Halmos

[gray gazelle]

I'll check it out thanks

[loud cradle]

The book by Simmons is pretty nice for ODEs. https://www.amazon.com/Differential-Applications-Historical-International-Mathematics/dp/0070575401

[queen flare]

thanks

[primal spear]

can someone recommend a book that covers vector operators in curvilinear coordinates, or just curvilinear coordinates in general?

[foggy relic]

its not contest focused though

for contests, aops intro to combinatorics is good

it introduces combinations from scratch and covers most of the combinatorics topics that are found in the entry competitions

[cobalt arch]

So do you have any one preference when considering my requirements?

[queen flare]

Would you recommend the 2nd or 3rd edition?

[gray gazelle]

So I am wanting to learn about Algebraic inequalities but cant seem to find a book for beginners like all of them use of difficult words so they go over my head so it would be helpful if u could suggest me an easy book to start with. Thank You

[loud cradle]

I think I have the 2nd edition, but I'm not sure as I recently moved and most of my books are still in boxes. I doubt it makes much difference - if you want to save money you could get a used copy of an older edition and I'm sure it will still be good.

[smoky zephyr]

what’s a book that helps me understand all the stuff in calculus 3, rather than it just like, teaching it all to me

if that makes any sense at all

[smoky zephyr]

are you serious or did you just send that sticker to send that sticker

[empty mortar]

Idk I mean calculus in general lol

If you’re only talking calc 3, idk

[smoky zephyr]

i’m done with calculus 3, i just don’t understand a lot of stuff in it

[empty mortar]

What parts? Someone could probably give you a better recommendation if you specify I.e is it like stokes theorem or something that’s confusing

If it’s vectors, have you tried linear algebra? I had a little linear algebra before calc 3 and it helped

[smoky zephyr]

probably just the line integral and surface integral stuff

i know how to do all the stuff i was asked, i just don’t understand how it all works

[broken meadow]

hmm

more analysis, differential geometry and stuff

[smoky zephyr]

wait what

i have to say, i was kind of expecting an analysis response

[loud cradle]

You could try Hubbard and Hubbard, "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach", http://matrixeditions.com/5thUnifiedApproach.html

[south salmon]

spivak

[hollow dome]

Our saviou

R

[smoky zephyr]

ok thanks

[shell flax]

best number theory book

for introduction

[gray gazelle]

Check the pins

[halcyon hornet]

Although I have not read it, Burton's Elementary Number Theory is pretty famous.

[gray gazelle]

can anyone recommend a good book for an introduction to chaos theory?

[gray gazelle]

I see that you're a fan of good will hunting

[primal spear]

taylor's classical mechanics has an introduction from a physics perspective

[gray gazelle]

"classical mechanics" by john taylor

isnt that like 900 pages?

[gray gazelle]

yep

[gray gazelle]

khan academy has a pretty good collection of calc 3 videos and they're actually made by grant sanderson (3b1b guy)

[gray gazelle]

i'm not that good at physics, but i'll check it out anyway. thank you!

"mah boi's wicked smah"

[craggy dome]

Does anyone have any recommendations for an introductory book about tilings? Perhaps on a graduate level?

[finite saffron]

bruh

[mystic orbit]

I thought "the art of problem solving" was hard

It's just standard high school shit

It feels like sat prep more than anything

Is there something similar but more challenging?

Some book specifically geared to cultivate problem solving skills?

[true veldt]

Art of problem solving has pretty hard problems in it

Oops just realized the channel I'm in

Well there are other problem books too that I remember picking from for math contests and generally just puzzles for my friends

Let's see

[mystic orbit]

Really?

I've only been checking out problems with a needle for the first 4 chapters (which are supposedly hard)

And they seemed pretty docile

[brittle breach]

For That I am currently reading chapter 9 of Rudin.
And an intro manifold book

[frosty girder]

what would be the pre reqs for an intro to manifold book

[brittle breach]

I am guessing chapter 9 of Rudin
A good feel for inverse and implicit function theorem

Lin alg and topology

[gray gazelle]

@brittle breachcan i ask what you used for LA ?

book that is

[analog pollen]

Think its wise to do a full course in analysis before

[brittle breach]

fundamentals of linear algebra Carroll

[gray gazelle]

thanks

[past ice]

So if I recall correctly, the book has "exercises" that are embedded in the text and "problems" at the end of each chapter. The exercises are supposed to be straightforward. But also you might be at the stage where the book really is too easy for you. You might want to check out Zeitz's The Art and Craft of Problem Solving, which I think is just a better and more broadly useful book in general.

[shy compass]

anyone know any good problem sets (or textbooks with problem sets) for complex analysis?

[foggy fiber]

Not sure if this is what you're looking for, but had this in my bookmarks randomly lol: https://fac.ksu.edu.sa/sites/default/files/2016_complex_analysis_problems_solutions.pdf

[primal spear]

nah it's about 600

[misty wyvern]

Does anyone have a book they want to stan? Grad level but not too dense so it can serve as bedside reading.

Just looking to learn something new without having to stretch my noggin too hard.

[dapper root]

Matsumura

Except that’s dense

[karmic thorn]

Mathematical Logic, Ebbinghaus

[misty wyvern]

The next poster is going to recommend Wiles because they're an epic gamer.

[tulip blade]

If youre interested in math and computational complexity i think the book mathematics and computation by avi wigderson is fantastic

[misty wyvern]

That's more of a survey but yes, it's very good.

[tulip blade]

Its more of a big survey of complexity. I think it is more suitable for bedside reading

[misty wyvern]

Actually it's not even a survey, it's just Wigderson flexing how much better he is than the rest of us.

[restive falcon]

what are some good intro abstract algebra books which focus on theory

[willow pecan]

Dummitt and Foote maybe?

[restive falcon]

thanks

[willow pecan]

#book-recommendations message

Here's a comprehensive discussion

[misty wyvern]

what are some good intro abstract algebra books which focus on theory

Rudin

[restive falcon]

I'll try knapp

ok this looks like it has a lot to do

[remote nova]

If you want a shorter text you can try this one.

Looking back at it, it appears as thought it expects maturity or prior experience with the material but even so it's still very readable and you should be able to work through it.

[vocal panther]

"Proofs: A Long-Form Mathematics Textbook" by Jay Cummings

a visual proof on why it is a good book

(also the content is really good at helping me get a good understanding of the basics of higher math, would recommend)

[late plinth]

Anyone got fun numerical linear algebra/analysis book? Learned a decent amount from uni courses but would like to learn more

[south salmon]

idk as much about fun as being more in-depth, but I think the trefethen numerical linear algebra book is quite good

@late plinth

[late plinth]

Will check out

[south salmon]

Then for numerical PDEs/ODEs, I recommend Leveque @late plinth

[late plinth]

Will also check out? For the numerical pde/ode do u think I need to take pde class before delving in?

Only taken up to diff eq lol

For diff eq stuff

[south salmon]

It’s not necessary to have a substantial understanding, but I’d recommend knowing enough about boundary value problems to understand what it is you are solving

so maybe what might be covered at the tail end of an intro diffeqs course

[late plinth]

Ah doesn’t sound too bad then

[south salmon]

I think LeVeque goes through different classes of PDEs as well, so you should familiarize yourself with those as well

I think all you’d really ever need is Part 1 of Evans PDEs (chapter 1-4)

[smoky zephyr]

kirby since you’re already here, what do you think is needed to read evans pdes

[south salmon]

linear algebra, analysis, and a moderate grasp on ODEs methods

ofc mvc too

evans PDEs is typically a grad textbook so..

[smoky zephyr]

i unfortunately expected this

[south salmon]

but I’ve seen it used in undergraduate settings

[smoky zephyr]

well i’ll be able to read it hopefully later next year

[south salmon]

Yeah, for now, I’d just study linear algebra, mvc, and work your way towards analtsis

so then you can move towards diffeqs, and functional

[smoky zephyr]

yeah i’m already done with mvc and basically done with odes

[south salmon]

the biggest timesuck is going to be getting strong in analysis

[frosty girder]

tfw i havent done either of those and i started with analysis

[smoky zephyr]

i won’t necessarily try to speedrun analysis, but i would at least like to not spend a crazy amount of time on it

[south salmon]

when I refer to analysis, I refer to what analysis is in the states, which is the course placed above calculus and is a course on proofs in the foundations of calculus 1-3 (which then later builds into measure theory; functional analysis, and fourier analysis etc.)

[halcyon hornet]

Shyshu has not done LA?!

[frosty girder]

Nope lol

[frosty girder]

i am doing that only

using apostols book

[halcyon hornet]

Smh still do not know how people do proofs and love them.

[frosty girder]

its fun

[manic cape]

idk there's some kind of satisfaction that comes afterwards

[south salmon]

yeah, it’s not feasible to speedrun the subject, most of the time it will take 2 semesters’ time for it

[smoky zephyr]

how long is that exactly

i don’t remember how long a semester is

[south salmon]

30 weeks

[frosty girder]

the first sem would usually go till like riemann integration or so right?

[smoky zephyr]

this is probably going to sound terrible but i somehow did odes in a month so i bet i can get that done in a few months

[halcyon hornet]

Woah that much for just 1 topic-

[frosty girder]

haha

its not one topic senku

[halcyon hornet]

I am such a huge speedrunner that is the reason why I suck at Mothermatics .

[south salmon]

first semester is limits and strategies, derivatives, riemann integration, etc. this can go deeper into more general topological concepts like metric spaces, compactness, etc. as time permits

[halcyon hornet]

.

[south salmon]

ODEs isn’t analysis

[smoky zephyr]

i didn’t say it was

[south salmon]

Maybe you could, but it’s dangerous to just read a book and feel like you understand it

bc practice problems are key

[frosty girder]

i see yeah

[smoky zephyr]

i always do the practice problems

[frosty girder]

analysis practice problems arent exactly what you are used to ig

[halcyon hornet]

What are they like?

[smoky zephyr]

i’m going to get stumped a lot aren’t i

[south salmon]

and I’m not saying it’s not possible, I just don’t want you to 1. burn out or 2. get too ahead of yourself and feel lost if it doesn’t go well
you’re still in hs, no?

[frosty girder]

yup

that is super common

[smoky zephyr]

yeah i am

i don’t do tons and tons of math anyways so burning out isn’t a concern

[south salmon]

yeah, analysis is just going to be a jump
I presume at least you’re adjusted to proofs from linear algebra?

[smoky zephyr]

no i haven’t done anything with proofs yet

i haven’t even started LA

[halcyon hornet]

Both of those happened to me and I still suck at Math .

[halcyon hornet]

But did not you-

[south salmon]

hm, yeah linear algebra is kind of important, what did you go over for ODEs bc linear algebra is kinda crucial for that

[frosty girder]

one of the simpler exercises u would see early in an analysis course is this
Let $f:S \to T$ be a function. if $A$ and $B$ are arbitrary subsets of S and T, prove that
$f(A \cup B)=f(A) \cup f(B)$ and $f(A \cap B)= f(A) \cap f(B)$

[smoky zephyr]

the linear algebra that was needed for odes was taught in odes for what i used

[halcyon hornet]

What does "-->" represent?

[frosty girder]

give me a sec

[south salmon]

cap is intersect

[hasty eagle]

Shyshu of the Kanga Gang ✓

[late plinth]

Is real anal hard? Ppl at my school be saying it’s like hardest thing ever lol

[frosty girder]

yup, thanks

[frosty girder]

its not exactly that its hard in and of itself

the proofs feel out of the blue

[south salmon]

real analysis is difficult mostly because it’ll be abstract

[frosty girder]

the definitions are rather intuitive i would say

[smoky zephyr]

kirby what book did you use for real analysis

shyshu too

[frosty girder]

it means the function "goes" from the set S to T

[late plinth]

Ah I see, U think I will be fine if I took discrete and combo when I start discrete?

[frosty girder]

i am using Apostol

[mystic orbit]

Not if you're into it

[coral narwhal]

there is no substitute to rudin

[halcyon hornet]

Huh.

[late plinth]

Ah I see, idk too much about analysis cuz I’m smooth Brain applied math and Cs

[south salmon]

For my first/second course? Baby rudin and Tao 1 (these are not good books)
For my third course? Tao 2 (meh)
For my most recent? Folland (and I used Rudin and Stein for reference)

[frosty girder]

Folland is the measure theory book or sth like that right?

[south salmon]

the most recent books were good

yeah

[frosty girder]

Noice

[mystic orbit]

Although, I'm not really sure what you mean by "real"

[frosty girder]

it deals with real functions

[mystic orbit]

Is there a virtual kind?

[frosty girder]

and stuff in the real world

[mystic orbit]

Wait what?

[frosty girder]

no i stuff allowed

[south salmon]

[frosty girder]

it just means no complex stuff allowed

[late plinth]

Is complex anal the just applied af cuz no proof class is prereq to it for my school?

[mystic orbit]

So when you guys say anal

You mean...?

[hollow dome]

Yes we mean it

[south salmon]

a complex analysis course that has no proof class requirement is just a contour integral course

[frosty girder]

complex anal is said to be "trivial" lmao

[frosty girder]

Oof

[frosty girder]

we mean real analysis lmao

[mystic orbit]

Oh

[late plinth]

Well the official name is analysis but ppl taking it just call real anal at my school

https://math.gatech.edu/courses/math/4317

[frosty girder]

we also call it real anal here

leads to some interesting convos

[south salmon]

we just say analysis

[frosty girder]

here as in this server

im not in college yet

[late plinth]

It’s a double entendre for how u feel while taking course lol

[frosty girder]

hs life moment

[frosty girder]

lmaooo

i shouldnt have laughed at that

but i did

[south salmon]

I will say that saying real analysis doesn’t allow complex is a little bit disingenuous

[frosty girder]

true, most real analysis books also introduce complex numbers

[south salmon]

well, they also take complex values functions bc it doesn’t matter much because the functional analysis still works out (you just need to be careful with conjugates)

or complex measures are a thing too

[frosty girder]

im still on the topology chapter , havent made progress in a month thanks to tests

[late plinth]

U said u were in hs right? U must be one smart person lol

[halcyon hornet]

He is very smart.

Now he will disagree to me.

But he is.

[late plinth]

Furthest I got in hs was multi and linear, analysis in hs is insane

[frosty girder]

na lol

[frosty girder]

i havent actually done multi or linear, but i plan to do them both soon

[late plinth]

Ah multi is p ez

And linear u will love cuz it’s also p abstract

[frosty girder]

that i will

[frosty girder]

😌

i did like one chapter out of friedbergs book

and i loved it

and i also did 2 from artins algebra

loved that as well

[late plinth]

Hm don’t know what that I used strang when I took lol

[frosty girder]

friedberg is like pretty popular rec for intro lin alg

[late plinth]

End of strang is p cool w some stuff on game theory and linear programming

[halcyon hornet]

I know you, Shyshu 😌.

[frosty girder]

Ooo

[frosty girder]

from what i have heard, it does seem easy lol

[late plinth]

Also fun stuff like condition number and pseudoinverse which is nice to know if u want to do stuff w numerical methods

[frosty girder]

sounds nice

i will restart with maths from after 9th jan

[late plinth]

Hf

[frosty girder]

🙏

(this is also a hifi emoji if u look at it that way)

[slate gyro]

Lmaooo I love that sticker's name!

shit wrong channel

[frosty girder]

yesss lol

[finite saffron]

where can i get some resources to learn diff eqs? (preferably for free and not pirated)

[gray gazelle]

MIT OCW or Paul's Online Notes

[finite saffron]

wait, paul's covers diff eqs? i thought it was only up to calc 3

[frosty girder]

@finite saffron

[subtle siren]

Pauls' DE notes are fantastic

[gray gazelle]

yeah it does DEs

[paper stratus]

What's the most beginner friendly book for intro to abstract algebra? or resource(it doesn't have to be a book)
hopefully self-contained too and makes very little assumptions

[tulip blade]

This may not be considered math but any good recs for coding theory books?

[willow pecan]

See #book-recommendations message for a discussion for abstract algebra books

[tulip blade]

idk the exact name but search abstract algebra by fraleigh and it should come up. I thought it was pretty good and beginner-friendly. I prefer dummit and foote though.

[night knot]

Information Theory and Coding, Kelbert and Suhov
Introduction to Coding and Information Theory, Steven Roman

[paper stratus]

lmao the course i'll probably take next semester uses dummit and foote as it's #1 text and fraleigh as its #2

any reasons for that preference though?

[still jay]

I recommend Pinter's Introduction to Abstract Algebra. It's quite expository and very well written, especially if you just want a light introduction to algebra.

[slate gyro]

is that the same steven roman who wrote "advanced linear algebra"?

[tulip blade]

Better exercises and I like the way its structured more.

[night knot]

Yep! The one and the same!

[gray gazelle]

any good first-order logic books?

[karmic thorn]

A Friendly Introduction to Mathematical Logic by Leary

Or Mathematical Logic by Ebbinghaus

[paper stratus]

you could also pick up an intro to proofs book

they usually have a FOL section

[gray gazelle]

that's what i thought

i reasoned that a book meant solely for first order logic would be better

[paper stratus]

what's your purpose for learning FOL though?

[gray gazelle]

the book in question was Velleman's how to prove it

uhhh

i got a logic class

[dapper root]

That isn’t really first order logic I think, at least not to any actual depth

Re: intro proof books

[paper stratus]

oh if it's a logic class, then yeah

i thought it was for discrete math purposes

[gray gazelle]

exactly

[gray gazelle]

which do you prefer

[karmic thorn]

Both are good, the former is available for free officially and lives up to its title

The latter is good too but it steps up quicker

Since it's a GTM

[gray gazelle]

GTM ?

[willow pecan]

Graduate text in mathematics

[karmic thorn]

[willow pecan]

The graduate doesn't actually mean anything though

[gray gazelle]

oh arent those very difficult ?

[willow pecan]

Ignore the graduate

[karmic thorn]

I feel GTM texts often say "no formal prereqs" but also step up faster than standard non-GTM textbooks

But yeah

Just check out both

See what suits you better

[gray gazelle]

alright, thanks

[karmic thorn]

[gray gazelle]

https://www.amazon.com/Mathematical-Logic-Graduate-Texts-Mathematics-dp-3030738388/dp/3030738388/ref=dp_ob_title_bk
https://www.amazon.com/Mathematical-Logic-Undergraduate-Texts-Mathematics/dp/0387942580
one is undergrad the other is graduate which do i get ? @karmic thorn

[karmic thorn]

I've seen the former

I'm not sure what the undergrad text cuts down on

You could check out either

[gray gazelle]

alright

[paper stratus]

aren't the prereqs some "mathematical maturity"

[karmic thorn]

Often, yes

[paper stratus]

idk if there's like a canonical definition of "mathematical maturity"

[tulip blade]

That basically means no formal prereq.

[stray veldt]

no formal prereq (but you might will suffer)

(this is a joke, i think ebbinghaus is really approachable)

[paper stratus]

nah it's like a range from 0 - 100

[icy knot]

FYI, Springer is selling books for half off through tomorrow. I purchased John Stilwell’s The Real Numbers. Coupon code is HOLIDAY21.

[hearty steppe]

I felt this when I skimmed thru the beginning of Deistel’s graph theory 😆

[karmic thorn]

Right

[hearty steppe]

https://tenor.com/view/im-not-alone-anymore-frank-sinatra-not-alone-im-not-lonely-anymore-im-not-gonna-be-alone-gif-17824476

[tulip blade]

My fav graph theory book

The book by douglas west is really good too.

[fierce dome]

can you please recommend me some books to be good at high-school mathematics, please?

[paper stratus]

wdym? be more specific

[fierce dome]

geometry, calculus

[paper stratus]

i mean calculus, the standard is probably strang

[fierce dome]

strang?

wdym?

[paper stratus]

gilbert strang calculus

another really good book is

[fossil arch]

Why do people not like Lang’s complex analysis book?

Or is it just too much for a first course

[gray gazelle]

its too easy

[fossil arch]

Cause I was watching a video and I got a peek into it and I saw a nice illustration so I took a look, it covers a lot of stuff it seems. Didn’t read much though but I also saw some stuff with homotopy and that interests me too

[fossil arch]

Like exercise wise?

[gray gazelle]

lol no im just kidding i've never even seen the book

Here’s a good book from Roger Penrose: Cycles of Time

[fossil arch]

nvm I’m skimming through it and it looks so terse and boring

[willow pecan]

Lang is known for writing a lot of books, not for writing good books

[tidal mural]

Guys is there any sat practice beside barrons

[paper stratus]

yeah baby Rudin

jk barrons should be enough

barrons probably has harder questions

[vagrant lodge]

recommendation: the bible

[tidal mural]

Ty

[tidal mural]

Tru

[compact swift]

Kaplan and Princeton review

[south salmon]

suggesting books like rudin to impressionable high schoolers trying to get help

[vagrant lodge]

Holly bible: new testament

[gray gazelle]

Based

I second that

[foggy relic]

$300 books are now $150

jk

[brisk ice]

might be a bit off topic but what would you say the quality of these books are for the price? https://www.humblebundle.com/books/applied-mathematics-mercury-learning-books?hmb_source=&hmb_medium=product_tile&hmb_campaign=mosaic_section_1_layout_index_2_layout_type_threes_tile_index_2_c_appliedmathematicsmercurylearning_bookbundle

Might just pay $1 for the lowest tier and maybe the linear algebra book is good

https://styluspub.presswarehouse.com/browse/book/9781683923763/Linear-Algebra

[brisk ice]

Although I already have 3 books I had acquired through covid which are

[smoky zephyr]

darn i sent a message with that but it didn’t send

[smoky zephyr]

brandon i have 9 LA books in my notes

[brisk ice]

Any of these books good or is there a preference out of them

[brisk ice]

i hAvE a WhOlE bOoK aS mY nOtEs

why do you have 9LA books

[smoky zephyr]

when i tried some LA books at first i got lost in the first few pages

so i got all these just in case

probably unnecessary

but they’re there

[brisk ice]

you got them?

[smoky zephyr]

no lol

i have pdfs in my notes

[brisk ice]

and you paid for them?

[smoky zephyr]

no

[brisk ice]

[smoky zephyr]

i didn’t pirate anything though

lol

literally just look up a pdf of something

[brisk ice]

....

[smoky zephyr]

what is that pirating

[brisk ice]

yes

[foggy relic]

axler

[smoky zephyr]

whatever

[foggy relic]

arr

libgen is a lifesaver

[brisk ice]

I mean I also look up "required text book for course" + pdf

[smoky zephyr]

i just don’t download any actually pirated books

[foggy relic]

why not just download

easier to access

unless you bookmark the pdf link

[brisk ice]

until that link goes down

[brisk ice]

I should add that if it was in the public domain then I guess it wouldn't be considered piracy

[manic cape]

cant wait for alg top classics to be in the public domain

[smoky zephyr]

i don’t care that much anyways, i just don’t download anything for some reason

[empty mortar]

hard cover > online

[smoky zephyr]

free > paid

[brisk ice]

not even if you have some e reader thing?

[empty mortar]

no at least not for me

I can focus with hardcover but i end up going to discord if I have an online text

lol

[manic cape]

then uninstall discord

[empty mortar]

you underestimate my willpower

overestimate*

[brisk ice]

Then neko just goes to the discord website

Might have to call discord to the the site down while neko works

[smoky zephyr]

neko don’t worry i’m sure they’ll do it for you

#chill

[vagrant lodge]

ok

[paper stratus]

axler is pretty good

i think ill use it

he also have yt videos

[tribal kernel]

Every professor I’ve had has had the same opinion of this book: the treatment of determinants is not very good. It’s fine at a basic level for all else. If you want a good linear algebra book that goes over everything you’d need at a basic level, I like Hoffman and Kunz. I also have a copy of “Finite Dimensional Linear Algebra” by Halmos which seems nice. Additionally, the subject is widespread enough that many professors upload their typed linear lecture notes online for free. They intend for others to use it, so it’s not piracy. I’m afraid I haven’t read the other books in your collection.

https://www.math.brown.edu/streil/papers/LADW/LADW.html

I have not read this, but a friend of mine speaks highly of this book. It’s supposed to be lecture notes which are made free online by the professor and is intended as a first course in liberal algebra with rigorous proof techniques and applications to analysis developed.

[fervent lava]

Currently reading it and I like it.

[tribal kernel]

[analog pollen]

libgen is in the public domain tho

everyone can access

[brisk ice]

😉

[remote ginkgo]

i hate the notation in this book

[remote ginkgo]

olver is quite good in general

[mellow bison]

what would you need to know before doing linear algebra

[remote ginkgo]

grade school algebra

maybe the definition of terms like "commutative" "associative"

some basic exposure to plane geometry maybe

(knowing how to compute areas of parallelograms, for example)

[mellow bison]

ohk hm I could actually try learning it then

[mellow bison]

though should I learn calculus first?

[brisk ice]

I think you could learn them both at the same time

assuming I guess it some just basic linear algebra course, I am not sure how the proofy ones go

[smoky zephyr]

you don’t need calculus for linear algebra

[half mountain]

Just read upto ring and ideal and know the definition of field, for linear transformation- read homo- and iso- theorems together...probably u might ace it

[viral moth]

i mean those arent necessary for a basic level of linalg understanding

[violet horizon]

u dont need any of this before linear algebra lmao, though knowing abt linear transformations is hugely helpful

I just precursed learning linear algebra with 3b1b's essence of linalg series and basic vector stuff like knowing cross/dot products, knowing what a determinant is

def know ur basic proof methods depending on if ur instructor(?) is more proof-y/rigorous or computational

[misty wyvern]

to study linear algebra you should be very familiar with algebra, i recommend aluffi

[gray gazelle]

[late plinth]

Just basic algebra

It’s p abstract so u also gotta

Be good at visualizing stuff

[modern stone]

How’s the style and what’s the intended audience of Stewart’s book on calculus?

[gray gazelle]

The style is pretty standard. Intended audience includes Engineering and Physics students.

[modern stone]

What is standard style?

[tawny copper]

Actually false

If It works for you fine, but you don't need to

[surreal phoenix]

What approach does Friedberg take in his LA book? An Axler kinda approach? The more usual determinant approach? Or somewhere in between?

[cobalt arch]

Looking once again for a combinatorics book that begins with first principles, within the context of combinatorics, that is fully rigorous

Should I just read combinatorial set theory?

[cobalt arch]

Self-contained

[cobalt arch]

The carnot machine is more efficient, well it is more efficient than everything so.

[karmic thorn]

The standard approach for a proof-based LA book, determinants are treated as usual and not like Axler.

[surreal phoenix]

Got it, thank you

[odd spade]

What does Axler do with determinants?

[frosty girder]

He doesnt do anything

Lol

He takes a no determinant approach to lin alg

[odd spade]

Oh I see

[mellow bison]

Would this be a good book for a beginner or not

[gray gazelle]

any book that covers inequalities better than spivak's calculus ?

An Introduction to the Theory of Functional Equations and Inequalities BY KUCZMA

[peak heart]

Hello, i'm looking for book(s) (in french if it's possible) to learn stats and probability from 0 (I've high school level). Someone can guide me please

[foggy relic]

for linalg, strang is also pretty good

the writing style is kind of weird though

tbh

[foggy relic]

https://www.maa.org/sites/default/files/pdf/awards/Axler-Ford-1996.pdf

[sage python]

Doing characteristic and minimal polynomials without determinants is kind of stupid if I'm being completely honest

[slender dragon]

Why? I only know it using determinants

[gray gazelle]

i just wish determinants were better motivated

instead of people getting mad about them

cause they're just about the most useful thing around linear algebra

I think the motivation i would give to a student if i were to teach them linalg would be to think of the matrices as a basis of vectors, and to tell them to try to come up with a test for linear independence along the diagonals that's consistent when you shuffle the basis vectors around

its important to know when a set of vectors are linearly independent cause it tells you about the dimension of the space it describes, plus it helps with that understanding of why linear dependence shows that the matrix isn't invertible

[icy knot]

I used Richard Brualdi’s book for the Combinatorics class I just completed. I thought it had a good balance of rigor and computation. At least half of the end of chapter exercises were “Prove this…..Show that…..”

[sudden kindle]

I think one nice way to introduce determinants is by giving the axioms for a determinant function, and justify these axioms by checking its true for the volume-of-a-paralelipiped function

And then also checking the axioms hold for the summation formula definition for determinant, the one with n! terms

You could give that as an exercise

[gray gazelle]

I think building up the 2d case, and showing that every dimension up is a recursion of that helps

[loud cradle]

I think that's the best approach. One step you didn't mention is to show from the axioms that such a function (if it exists) is unique. Then you show existence via the summation formula.

I also don't hate Axler's approach which is to define eigenvalues (including algebraic multiplicity) independently of determinants, and then he defines the determinant as the product of the eigenvalues.

[fervent lava]

Analytic Inequalities by N. Kazarinoff recommend by spivak at the back of his calculus book.

[gray gazelle]

@fervent lava I found Introduction to Inequalities by beckenbach too

Ehh I'll look into them later thanks for the suggestion

[sharp latch]

Ch 7 of Larson’s problem solving through problems, though not super in depth

[analog pollen]

diagonalization without determinants

[gray gazelle]

axler

[gray gazelle]

as long as you have the polynomials its fine, no?

atleast that's how i feel

[violet horizon]

no

no it isnt

it isnt fine

[slender dragon]

Without determinant how do you find the characteristic polynomial? I think you should have to find the minimal polynomial and then use Cayley-Hamilton Theorem

[sage python]

snakeman that doesn't cut it by itself

Because you don't know the algebraic multiplicities of eigenvalues

Axler's strat is to triangularize the matrix

(So if you're over R, complexify)

Then take product of t-diagonal

[dapper root]

This is so dumb

Lmao

[sage python]

This is why I say Axler for that part is a genuinely bad book to use

It teaches you to think about things in moronic ways

[dapper root]

Like even over R

Can we computationally always triangularize a matrix?

Taking a determinant is a piss easy, if computationally inefficient, operation

But writing a program to do it is easy as shit

[sage python]

Something something Gaussian elimination? idk

[dense pewter]

triangularizing a matrix just comes down to finding a char poly and then solving systems of linear equations

one for each eigenvalue

[dapper root]

How do you do that without taking a determinant lol

[dense pewter]

guess and check

[dapper root]

[gray gazelle]

it's actually amazing that you can tell just how far up his ass axler's head is after taking a real linear algebra course

[dense pewter]

hahaha

[sage python]

I think the fact that he does functional analysis may contribute to it

[slender dragon]

Use Determinant or guess and check. What's better?

[sage python]

Like he says the only thing in undergrad math where determinants are crucial is change of variables iirc

[dense pewter]

guess and check

[sage python]

Like

Bruh

[gray gazelle]

nobody, not even professors, know what "undergrad" means

[sage python]

Just because you work in infinite dimensional spaces and don't use determinants

Doesn't mean fucking algebra and diffgeo

Don't exist

[slender dragon]

I like Axler book for Linear Transformations

I read only the first three chapters

[gray gazelle]

you are not allowed to like axler on this server sorry

[sage python]

I mean sure the first part is fine, I just think there are tons of books that have respectable treatments of basics of vector spaces/matrices/linear maps

[slender dragon]

For Eigenvalues, Jordan Form and all of that I used Hoffman

[sage python]

Hoffman-Kunze is kinda what I used and I liked it overall? BUt it's def a bit old school at this rate

If only the typesetting, plus some features of the organization

[slender dragon]

Its notation is awful

[dapper root]

I kind of like old books

[sage python]

Linear Algebra Done Wrong actually seems very good

[dapper root]

But this is an opinion formed by already having a lot of exposure

[slender dragon]

What book do you recommended now?

[sage python]

Friedberg-Insel-Spence is kind of "the standard" nowadays it seems

[slender dragon]

For Linear Algebra

[sage python]

So I prob recommend one of those two?

[dapper root]

I know what the modern terminology should be and stuff, and with that perspective books from the 70s and stuff are pretty nice

[slender dragon]

Is this like Hofmman Kunze ?

[sage python]

It's kind of a modern HK I think

[slender dragon]

I haven't seen Cyclic decomposition in any book

Even in Axler book

[sage python]

Chmonkey: I mean I don't think it's old school in the sense of, an old take on the material

[dapper root]

I mean it’s linear algebra, I don’t think a first course linear algebra course is changing much

I just have found that I like the way they’re written

[slender dragon]

Sometimes the upper case letter are bigger that the summation symboo

Symbol

[sage python]

The main things are that it has a chapter 1 on linear equations which is... idk a lot of what's in there kinda just gets subsumed so it sticks out weirdly

[slender dragon]

And sometimes HK uses like 3 summation symbols

And all seems very awful

[sage python]

And I think he proves things with sums when it's not fully necessary

The main thing though

Is the typesetting

[dapper root]

Yeah I mean this book in particular may have issues

[sage python]

That's the feature of the oldness which is

[dapper root]

But in general I don’t really take issue with older books that people have moved on from just… cause they’re old

And I meme with the typesetting stuff but it really doesn’t bother me

[sage python]

Ooo I remember it had a really hilarious diss somewhere early on

[slender dragon]

I found some new one. It's from 2021. It's called Galois Theory and Advanced Linear Álgebra

[dapper root]

Idk, in a sense I guess I’m too 70s France-pilled so I like Serre and Bourbaki and stuff

Bourbaki not as a learning text, before I catch flak

[sage python]

The fuckin beat down

[gray gazelle]

based

[slender dragon]

After reading a book on Linear Algebra. Do you recommended reading one in Advanced Linear Algebra?

[gray gazelle]

no

[broken meadow]

i wanted to do exactly this so i bought roman

[forest sleet]

abstract algebra would probably be a better use of time than more linear algebra

[gray gazelle]

learn something more useful like cooking or sewing

[slender dragon]

I took a course on Abstract Algebra before Linear Algebra

[broken meadow]

good

take more

(abstract algebra)

[dapper root]

Yes

[broken meadow]

chmonkey when do you think i could be ready to read matsumura

[forest sleet]

no take more analysis

[slender dragon]

I taked Lie Algebras and Commutative Algebra. Then I realized I had to take Linear Algebra

[broken meadow]

i will learn about rings fields modules and stuff in this spring from dummit foote

[dapper root]

Will you learn the tensor product?

[broken meadow]

i think so

[slender dragon]

I love Dummit and Foote. I recommend it a lot

[dapper root]

Besides what you’ll learn, you need to know some basic homological algebra.

[broken meadow]

okey

[dapper root]

I think you can get what you need from like… chapter VIII of Aluffi

Or maybe there’s also an earlier section

[broken meadow]

o okey noted will do

[dapper root]

You don’t need crazy stuff, just a few of the homological lemma a (5 lemma, snake lemma)

[slender dragon]

Do you know what's the advantage of learning Category Theory alongside Abstract Algebra?

[dapper root]

And some idea of how derived functors work (you don’t need a proof, it’s better to just do that later)

Included in there is projective/injective modules

After that, you should be good

[broken meadow]

alr chm sounds good

[dapper root]

Granted, Matsumura has an appendix on homological algebra but

I don’t think relying on an appendix on something you’ve never seen does many favors

[dapper root]

Honestly, at first it’s minimal

I think there’s no harm to phrasing things in a more categorical fashion, and it means you don’t have to do it later

Also I personally dislike “category theory” as like… a term when it’s used like this

To do eg Algebraic Geometry you need to use category theory at a certain point and it’s similar in algebra too

[slender dragon]

Well. I just mean the book of Aluffi. I haven't read it yet

[sage python]

Is the appendix self-contained?

[dapper root]

But it’s not like you’re a “category theorist”

[sage python]

Could you just consider that to be the 0th chapter of the book?

[dapper root]

I forget, I can check but it’s short. It won’t be enough to understand terse proofs involving homology

So yeah with Aluffi, it doesn’t do much until the end

But IMO just having the language established from the start provides an advantage because you don’t have to re-learn stuff later then translate

It’s like, if everything’s new why not just learn it in the language you’d eventually be using anyway?

Besides, I think the sorts of category theory that you use most often is quite easy to pick up after you wrap your head around what’s going on. You don’t have to be doing crazy sounding tensor category symmetric monoidal infinity buzzword category stuff

This is why I don’t like the term because it seems to evoke a different sort of idea in most people’s heads than what’s actually going on

I don’t feel like I know much category theory, because functors and stuff just feel like algebra to me

[slender dragon]

I see

[rugged maple]

linear algebra done right or linear algebra done wrong?

i have an introductory grasp in LA, and I am wondering which one's fit for me

[karmic thorn]

Given that LADR is dissed here on an almost-daily basis, LADW might be more optimal.

[frosty girder]

yeah LADW or Friedberg are a good choice

[sudden kindle]

LADR is good

[crude sable]

there's LADW too

[gray gazelle]

Waiting for LADO

[slim peak]

LOTR is also a good books series

[foggy relic]

how does the content in strang compare to the content in ladw

[main void]

I really loved ladw, i studied it before starting my bachelors in mathematics and it is written very nicely, nice exercises and gives you a nice intuition for almost all important concepts

i found strang a bit more "basic" iirc

that being said i might be confusing strang with another la book...

Does anyone have a nice "mathematical" book on probability theory?
I'm searching for some kind of equivalent to Munkres but in probability, where the exercises aren't just some combinatoric tricks or straightforward computations.

A lot of the books i saw recommended aren't really oriented towards math students which makes them quite boring (for a math student at least)

[foggy relic]

does ladw have all the lin alg required to learn differential geometry?

[frosty girder]

oh yeah that reminds me of a good question
much much lin alg is needed to do diff geo?

[main void]

I guess up to spectral theorem and inner products

[frosty girder]

[main void]

Tbf inner products arent that hard to understand and spectral theorem is quite natural, it aint too hard to understand intuitively and it doesnt rely on too much definitions

Apparently you guys dont like ladr, but its explained quite nicely in there i find

Also, that being said, i havent done much diff geom, mostly diff geometry in R^3 with metric tensors etc, which is nice visually, but there are a lot of computations

[main void]

?

[remote ginkgo]

Kolmogorov

[foggy relic]

another related question, how much analysis/topology is required for diff geo

[main void]

nice ty

[remote ginkgo]

None

Not for classical diff geo

But for abstract diff geo you need differential topology, some algebraic topology, and just general topology stuff

And it would help to have taken a manifold analysis course

[analog pollen]

You need to know proofs

[foggy relic]

im talking abt the actual content

[analog pollen]

You learn proofs in analysis and topology

And afaik the main text used for diff geo is lee, which does require topology @foggy relic

Analysis is not needed

Although i would still learn it cuz it comes in handy for topology

[slender dragon]

Probability Path of Resnick

That's not oriented to math student either (I found it a little sarcastic). But it includes all the proofs and uses measure theory.

[hearty steppe]

This is a book?

[sharp flame]

I guess this is kind of off topic but could someone tell me about some websites where I can practice my math?

[smoky zephyr]

@sharp flame this is better fit in #math-discussion for next time, but depending on what it is, the wolfram alpha problem generator could work