book-recommendations

[gray gazelle]

has anyone read loomis and sternberg?

[foggy relic]

is stein-shakarchi complex analysis good?

[gray gazelle]

Yes it’s very good.

(You may or not may not be able to get it for a discounted price off the internet)

[foggy relic]

how much real analysis should i know prior

[heady ember]

Just google the pdf

[foggy relic]

I've used libgen many times before.

[gray gazelle]

That’s what I was saying in a discreet way mr dummy dum dum

[heady ember]

[warm glen]

it's on my reading list

i heard rudin sucks for multivariable

but i wonder if i should bother with such a tough book (loomis/sternberg) or if i can consider myself "knowledgeable" enough in multivariable analysis after reading something like shifrin

[normal sandal]

Recommendations for a readable (fun?) intro combi book?

context: looking for something to read whole taking a break from analysis

[sage python]

I wouldn't use Stein-Shakarchi for complex analysis. Toy contour shit is annoying

And iirc he doesn't give the best way of viewing stuff imo

[gray gazelle]

Why would a physicist want to understand it

Rudin's Real and Complex Analysis should have this

[sterile remnant]

What's a functional analysis book that you'd recommend to a physicist?

[fading goblet]

I would recommend to study books by J. T. Oden which called Applied Functional Analysis, which actually more geared toward engineers, but in general an accessible books..

[fading goblet]

What kind of background do you have? Have you get exposed to bit of Analysis, such as Introduction to Real Analysis by Bartle?

If I assume you have, I think it is good to get the next book by Bartle, The Element of Integration and Lebesgue Measure, which quite accessible (for me, at least).

Otherwise, I would recommend you to check books by H. Shima and T. Nakayama, "Higher Mathematics for Physics and Engineering," which geared toward non-mathematicians reader to approach Analysis in general.. They touch Tensor Analysis in the last part of the books, but if you feel the Tensor part have not enough material in it, you always know where to go
cough Hassani, Mathematical Physics cough
🤣

[gray gazelle]

Hi, any calculus textbooks with good and generally hard exercises, where you really get something out of?

[lime sapphire]

spivak

[gray gazelle]

Do you have insight on how well Apostol Calculus does compared to Spivak’s?

In terms exercises

[lime sapphire]

not really but from whats been said, apostol exercises are a bit dry

[gray gazelle]

apostols exercises are more computational than spivaks, which almost all ask for proofs

[night knot]

Apostol has a mix of proof exercises and computational exercises

Not as proof heavy as Spivak though

[gray gazelle]

I loved spivak, one of my favorite books ever

[dense gust]

guys what books would you recommend for Algebra which covers the main topics and little bit of algebra 2 not the whole thing, if available could you also recommend any workbook to practice few sums, Thanks.

[fossil arch]

Why do you think they're better than Rudin?

[sage python]

Mainly a better treatment of multivariable calculus/differential forms/Lebesgue integration

Also one gripe with Rudin is that he doesn't really think about subspaces the right way

Like, e.g. to me you speak of "compact metric spaces"

And if a subset of a metric space is compact, you're calling it compact because it is a compact metric space in the subspace topology

[brittle latch]

anyone got opinions or experiences with Aluffi vs. Artin for algebra

[foggy relic]

Right what would you recommend then

[foggy relic]

I read a good chunk of Aluffi, read aluffi if you're intersted in categories, artin otherwise

[lime sapphire]

Whats it called?

[night prism]

Analysis in Euclidean Space

[crimson leaf]

So right now I'm working through this proofing book called a Transition to Advanced Mathematics on my own then I plan on doing one of these three Analysis by Terence Tao, A first course in abstract algebra by Fraleigh, and Topology by Munkres. I am having a hard time deciding which one to start though, I've been told they're each good books but I'm not sure how they each are to work through so if anyone could give insight that'd be great

[fervent lava]

I think tao only have 2 undergrad analysis book and a measure theory book.

People in here have typically said that analysis before topology.

I think your missing linear algbera in there unless Fraleigh covers it.

So it depends which one your more excited to start with.

[crimson leaf]

I've been working through Lang since end of last semester but I take LA next semester

[night prism]

Is that Roman’s lecture series?

[crimson leaf]

No it's a book by Smith, Eggen, and St.Andre

[viscid grove]

What are some good books on rigorous probability theory

Ones like Durrett

Possibly with solutions for at least some problems

[supple knot]

Guys just gotted back in maths (lol i have been back in maths 3 times last month) for just starting, ehst is a good book for quick arithmethic?

[gray gazelle]

Uh... what? Why would someone make a book about that... and why would you want to learn it.
It's not what mathematicians do, we are not living calculators

[hallow oriole]

the second question's unfair, maybe he just wants to do it for fun

that said

no one ever would make a book about that

(if you want a quick method for mental arithmetic look up the trachtenberg method)

[orchid musk]

so i'm trying to figure out if given a map from R3 to R3 , (for example f:[x,y,z] -> [g(x,y,z), h(x,y,z), q(x,y,z)]) where each coordinate of the output is a rational function, is cyclic, as in iterated upon enough times to return the original coordinate [x,y,z]. I'm specifically looking at the case over finite fields and the map is from projective space to projective space, but the core idea is the same. any recommended sources to read up on would be appreciated!

[lime sapphire]

Interesting

[daring reef]

What are some texts other than Hatcher that have a good section on homology (without requiring significant homotopy theory as a prerequisite)? Am currently using hatcher to learn the homology needed for a project, but I would like a second book to reference

(also something that isn't from an abstract homological algebra/category theoretic viewpoint)

[viscid grove]

Has anyone seen J yeh's real analysis?

If so is that book good for self studying?

[fading goblet]

Hei, @stark turtle, is it okay to go here?

[wicked trout]

Is there a book about synthetic math which is related to other fields besides geometry ?

[stark turtle]

Yes !

So um basically what are you looking for ?

In Zworski's semiclassical analysis he talks about propagation of semiclassical singularities (wave front sets and stuff), but I haven't seen quantum chaos so far. Not that I know what it looks like 😅

There's a chapter on Quantum ergodicity but I've got no idea what's in it 🤔

[fading goblet]

At first, naively, I wanted to seek what I called "the culmination of every concept I like," which involved, not surprisingly, Fourier Analysis, Hamiltonian Dynamics, and Differential Geometry..🤣

Yet, I was really young and naive.. I just want to go there but do not have enough preparation.. It also can't be helped that I come from Physics which didn't really focused on doing proof, so I kinda thrown the idea at first because I felt really overwhelmed, thought that I need to learn about Functional Analysis so on and so forth..

Later on, because my further study, where I work with Dynamical Systems in general, involving Bifurcation Theory and helping my friend in doing Hamiltonian Chaos (numerically), I kinda looking for doing something of "Dynamical Systems that applicable to Physics"

Don't get me wrong, it is applicable to Physics, but it kinda in implicit way.. It doesn't come up explicitly like in Population Dynamics or Epidemiology where I could find equilibrium point and solve for the stability, looking for bifurcation point..

Later, because I come up with scattering phenomena, solitons, and Hamiltonian Dynamics of PDEs. I come up with notion of Semiclassical Analysis and I thought, "welp, why don't give it a second chance,"

Yet, I kinda wanted to seek a topic which both interest my Math and Physics side.. And later, I come up with a friend in the progress in of its PhD and talk to me that Quantum Chaos quite hot nowadays because it could give an explanation about Information Theory of Black Holes using Maximal Lyapunov Exponents..

So, I kinda, "yep, challenge accepted, I think I could done something here,"

But, I kinda stuck again, because there is so many things to learn yet my focused quite split in a bad way.

[fading goblet]

Long story short, I kinda wanted to seek notion of stability and bifurcation that come up in both classical mechanics and quantum mechanics..

Or, if it's about Hamiltonian Systems, I wanted to know about when I could have Hamiltonian Chaos or when Quasi-Periodic Solutions come up in both regimes, or in even simplyfing terms, I want to look for Integrable Systems..

And at first, I thought Semiclassical Analysis and Quantum Chaos might help me understand those..

And here I am, quite in the corner, didn't know how to move on with my topics..🤣

Seems overambitious for commoner like me..🤣

[stark turtle]

Oh okay, I think I kinda see what situation you're in 😆
I was talking with one of the researchers in the research team I'm beginning to integrate (I'm at the end of my master's degree and will be doing a PhD starting from September), and he said to me "I feel like Zworski was very careful and motivated for the first half of his book. Then he kinda gave up on giving explanations for the second half" 😂
I feel it describes quite well the "interesting, not-so-classic"-part of Zworski's book (that is to say, everything past the """basic""" symbols and pseudo-differential theory). Concerning those parts, which I'm driving in recently, I really have to rewrite them with my own words otherwise I couldn't quite understand it with my end-of-master-knowledge. I guess it's comprehensible by many researchers, but even my future PhD teacher told me that the proof of the theorem we were talking about today wasn't obvious to him.

So yeah, basically Zworski is a really nice reference to have an introduction to semiclassical analysis, but if you want to drive into the latter half, be prepared to write the proofs with your own words 😆

I don't know about chaos, but I feel like the whole point of Zworski's book (and in fact of semiclassical analysis, If I grasped the notion well) is to see how to approach quantum evolutions with classical theory. And to give actual formulas, that is to say asymptotic developments depending on the semiclassical parameter h (basically Planck's constant, which you make into a variable because why not eh ?)

Like, the central theorem of my master's degree internship is really "oh look at that quantum evolution. Well in fact you can approach it with this nice classical Hamiltonian system 😌 "

Oh, and if you want to look into integrable systems, I could ask my teacher who taught me a class about resonances and Hamiltonian systems and integrable systems last semester if you want 🙂

[fading goblet]

Hmm... What things do you recommend to brush up before studying Zworski's book? Do you recommend brush up most thing in Lebesgue Integrals and Functional Analysis?
😄

[fading goblet]

Ahhh.. This motivates me even more to studying Zworski's book.
Truly what I looking for..

I should plan my study as soon as possible and keep the pace so I could be ready when my PhD come up to me..😄

[fading goblet]

Woah, is that possible? Thank you very much.. I appreciate it a lot..😃

I actually kinda have a bits here and there with Hamiltonian Systems, which I got from quite variety of books (we say something like Arnold book, Goldstein, even to Verhulst book, I would need to integrate this knowledge as soon as I can), but sometimes I felt that I don't really confident with my theoretical skills..😅

[stark turtle]

I'll respond tomorrow, it's getting late here so I'm going to bed ^^

[forest sleet]

Yeah you need at least grad real analysis. If you're only interested in quantum ergodic theorem, the lecture notes I linked a while ago are easier to read since they do a slightly simpler case

[fading goblet]

Looks like it's time to hit Royden books again for nice exposure of Grad Real Analysis..😆

[compact crypt]

https://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198572220

what are your opinions in this book?

it seems to have a lot of content and solutions

but some people say that it is not for beginners

would you recommend doing durrett first?

[blazing canopy]

Neither book is for beginners. Grimmett and Stirzaker covers more material and has a massive amount of exercises. Durrett has a more measure-theoretic focus.

[compact crypt]

I have done analysis and know what measure is

would it not be enough?

[compact crypt]

is grimmett and stirzaker less 'rigorous' btw?

[blazing canopy]

It does not focus on rigor in the same way as Durrett, because it turns out that the measure theoretic foundations of probability aren't fully necessary to really do a lot of the actual work in most of the standard topics. You should be fine if you've taken analysis.

[compact crypt]

okay thnx

[sage python]

Honestly someone should write a real analysis book that does probability and ergodic theory

Ah nice

[rich sequoia]

What do you think about teaching baby rudin to a child

[dapper root]

Bad

[gray jungle]

really bad

[smoky zephyr]

teaching analysis to anyone that young sounds terrible

[tardy walrus]

Nah children suck. Do it.

[rich sequoia]

analysis is just addition and multiplication of reals

and messing about with numbers

children's education isn't rigourous

[white laurel]

It would be like teaching a monkey how to speak English fluently

[smoky zephyr]

this guy really just said that analysis is just rigorous arithmetic

[daring reef]

What are some texts other than Hatcher that have a good section on homology (without requiring significant homotopy theory as a prerequisite)? Am currently using hatcher to learn the homology needed for a project, but I would like a second book to reference

[cursive orbit]

well baby rudin is for babies

after all, it's in the name

[grand thistle]

which of these three do you guys recommend?

1. baby rudin + spivak calc on manifolds
2. browder analysis
3. schroder analysis

(for self studying)

for reference, i think i would be pretty comfortable with proofs since i'm currently working through aluffi's algebra: chapter 0 and i'm going to be going through at least 4 chapters of it before i begin analysis

[cursive orbit]

first is definitely not for the faint of heart

[grand thistle]

yup i know

[smoky zephyr]

1. is ew

[grand thistle]

im kind of leaning towards browder rn

but i also already have a copy of rudin so idk

i mean browder literally says he based the book on option 1

i think i'll go with browder

i don't really like switching books in the middle of things anyway

[sage python]

I mean Browder is good too for sure

[glad prairie]

Dami's shilling immediately begins to take its grasp on the server

[grand thistle]

yes

[sage python]

It's because my suggestions are good

[foggy relic]

how are the problems in schroder dami? I don't know enough analysis to determine exercise quality on first glance

[sage python]

I haven't checked them out too deeply

Honestly I only found Schroder in the last... Week

Actually I had heard of it years ago but forgot about it until last week

Looked at it a bit and was like oh shit

[fervent lava]

Option 1 is what I am doing.

spivak calc on manifolds to me covers stuff that I am very interested that most multivariable analysis book skip over.

[foggy relic]

dosent pugh have a chapter on multivariable analysis?

[fervent lava]

Yeah

[grand thistle]

oh really? what are those things because i'm interested in learning multi well as well

im going to be learning multivariable analysis without ever having done calc 3, so im thinking spivak com might be too hard

[sage python]

Eh it's fine

You'll miss some topics though

Like Lagrange multipliers

Browder seems to basically be Rudin + slightly better measure theory + Spivak CoM

[cursive orbit]

I thought spivak had lagrange multipliers as an exercise

although I might be remembering wrong

[grand thistle]

are they important?

[sage python]

Schroder I give a slight edge to but but enough if you were already working through something else and happy with it

[grand thistle]

i don't wanna miss something i should know

[gray gazelle]

no

[sage python]

I'd say they're good to know. It's an optimization thing, so matters more in stuff like stats and applications, though I like to think of the spectral theorem in that way. But in principle can be learned elsewhere or skipped

[gray gazelle]

lagrange multiplies are a gimmick lmao

[sage python]

LM was more an example, basically I wondered how comprehensive Spivak was relative to a full on calc 3 class. But it doesn't assume it, just that it focuses fully on building to Stokes' thm

[fervent lava]

He does.

I looked over it once

[sage python]

Ah okay

Makes sense iirc it follows from implicit function theorem?

[cursive orbit]

yep

[mellow bison]

What’s a good book for Euclidean geometry, like something geared for olympiads and has a lot of theorems and stuff

[night prism]

It’s wild how a concept can seem so nebulous from a given source, but then another is able to explain it in a way that makes it practically effortless to absorb

[gray gazelle]

I do miss them already

[sage python]

So

Within math I've only seen Lagrange multipliers used to give a nice proof of the spectral theorem

[gray gazelle]

I mean that I miss using them

[hoary flint]

any books for theoric basic math

[fervent lava]

Maybe serge lang basic mathematics. It’s proof based.

[hybrid chasm]

Lmao

I vow to teach my future children category theory before they turn 5

[gray gazelle]

for someone who's done LA and analysis out of axler & rudin, would you recommend calculus on manifolds or analysis on manifolds?

and like what is the difference

[iron moth]

Hi

I need more books than just the big fat notebooks and I'm in grade 5

[lime sapphire]

Books won't do you much good in grade five

[lime sapphire]

Keep practicing on khan academy

[unreal elm]

I dont

they were tedious af

[sterile remnant]

Is it necessary to have knowledge in differential geometry of curves and surfaces to learn about differential geometry (on manifolds)?

[glossy mirage]

does anyone have any books about vector space and subspace?

[smoky zephyr]

any intro linear algebra book lol

[rich sequoia]

do your nation's olympiads, or competition problems on aops

[slow roost]

Technically no. Everything can be developed on manifolds for your first time. But it's likely to seem less motivated and more difficult without that experience

[sterile remnant]

So would a book like Loring Tu's Intro to Manifolds be ok as a first exposure to differential geometry?

[slow roost]

yup

[sterile remnant]

thank you!

[mellow bison]

Anyone?

[gray jungle]

recently been reading no longer human by osamu dazai and im loving it

its a novel that tries to show certain aspecrs of danzai life
but not directly
and its written beautifully and sheds light perfectly on various themes such as suicide ,anxiety depression and so forth

i am still in early parts of it but so far its been a pleasure to read and you can judge if yourself if you chose to read it.

[brisk sluice]

Anyone know anything about Enumerative geomtry?

[loud cradle]

I've read the first half to two thirds of Sedgewick, and bits and pieces of Graham et al..

they're quite different in focus. sedgewick's goal is to teach you specific algorithms, example implementations (in Java), and elementary analysis of their running times and memory usage. graham's is a math book focused on stuff that is useful for algorithm analysis

graham would be overkill initially IMO, but useful if you want to delve into algorithm analysis in the future

sedgewick is a great book for learning algorithms and data structures, and doesn't assume that you are a particularly proficient programmer, although it assumes you know basic ideas like if/else, loops, etc

btw, there's an excellent (and free) two-part coursera course taught by sedgewick and based on his book

your background should be perfect for sedgewick then. owning the book is definitely a good idea even if you take the course, since as you would expect, the lectures can't go into as much depth as the book. but do take the course if you have time - the lectures are good but the assignments (six or seven substantial programs that must be implemented and submitted for a grade, and have to pass all their tests including running time constraints) are really excellent

it's a really good book IMO, i don't think you will be disappointed. for context I worked as a software engineer for 25+ years before retiring last year

[novel solar]

Good book for conic sections and analytical geometry

[karmic thorn]

Any recommendations for well-written math textbooks geared towards high school students? I don't have any specific topic in mind, just looking for books that exposit topics not covered at school but are interesting (while offering a better glimpse into what mathematics after school is like), and are also not just about math contests.

Silverman's A Friendly Introduction to Number Theory seems to be a book in that spirit.

[novel solar]

Why not math contest books that are well written?

[karmic thorn]

I may be off the mark, but they seem to suffer from the problem of focussing on a very narrow range of topics and unusually challenging problems that require a bigger bag of tools than what one acquires at school. That way, it doesn't seem to be a very honest representative of what math at, say, undergrad level looks like.

I do like old school stuff like Fomin's Mathematical Circles and would be fine with some equivalent textbooks.

[novel solar]

Have you seen yaglom's challenging mathematical problem with elementary solutions

[karmic thorn]

I'll take a look.

[flint forge]

Jacob Luries Higher Topos theory

[stray veldt]

Proofs from the Book by Aigner and Ziegler

also maybe unironically napkin

[karmic thorn]

[karmic thorn]

[stray veldt]

also "yearning for the impossible" by stillwell

[karmic thorn]

Will take a look

[grand thistle]

can anyone give a source that gives a (very concise) introduction to odes? All of the traditional textbooks seem to be over 400 pages each and i really don't want to spend that much time on them, i wanna just have the bare basics needed to learn other things. I'm basically looking for something that is like the hatcher topology notes to odes. I've found one that seems like what i'm looking for here.

[gray gazelle]

Best math resources?

[gray gazelle]

https://m.youtube.com/watch?v=5UqNZZx8e_A
10 min youtube vid

[hollow shore]

Anneli Lax (New Mathematical Library) series seems to fit the bill

[grand thistle]

i'm not looking for videos, i'm looking for lecture notes or a very short book

also i don't think that 10 minute video covers enough to be a first course in odes..

[gray gazelle]

Just an intro from the looks

[grand thistle]

yeah, i'm more looking for a source that covers more than just what the subject is about, but has all the theorems and proofs while being concise

[karmic thorn]

[coral narwhal]

I don't think it fits the exact description but maybe somewhere close to it, I learned about this book from 3b1b from the video he has about brachistochrones along with strogatz, the book is called "the mathematical mechanic" by mark levi this uses physical reasoning (usually high school physics ) to solve math problems

[karmic thorn]

Sounds cool! I'll take a look at it.

[west sedge]

Hi, can anyone recommend a lecture playlist/book that covers analysis in an intuitive yet still rigorous way? I need a way to understand analysis and use my imagination, not just logic, because I understand analysis quite well but I cannot do it on my own that well and I believe the intuition is missing, I also need the playlist/book to provide appropriate motivation for the introduction of certain definitions etc.. thank you so much!

I have tried Abbott and Rudin and yet still fail to keep going with the problems, I feel that I cannot think on my own, some proofs I can do on my own that are straight forward yes, otherwise no. Someone here recommended Apostol's book

[livid ermine]

I think if you cannot do abbott after giving it a good go, you should maybe wait a little with analysis and try something else maybe

[west sedge]

I just cant kickoff my problems well, I learned differential geometry, multivariable analysis, and when I touched functional analysis, even though I could understand it and could understand the proofs, I struggled immensely with the problems again, making me believe that I probably should go back to analysis to actually learn how properly start proofs on my own

[gray gazelle]

Understanding Analysis by Steven Abbott is a great one to look at for you

Oh oops didn’t read the post below it, nevermind!

[gray jungle]

i would suggest going back to whatever book you used and try to construct the proofs ( preferably for notable theorems ) yourself , perhaps while noting down your thought process to understand how you approach these problems in hopes to improve on that , however this might be a bit inefficient and a tid bit slow for most people but i found good results doing this, do note that the aim in doing this (for me at least) was not to perfectly be able to come up with proofs but to try to find solutions of my own and how i would personally approach it then later find out if i was correct ,had the wrong approach , was a bit too overkill , had a serious missunderstanding etc.
this is not the method i would use for a 1st time running through a theoretic course as im too focused on understanding the material than being creative about it but certainly viable for a 2nd run through the course, or at least i think it is.

i have struggle with exactly what you mentioned and i started to realize the problem wasnt really the book ,it was my lack of hmm whats the word im looking for

[gray gazelle]

Like when you study a math book @west sedge do you take notes on the proofs that they write on the major theorems at all?

[gray jungle]

my own interaction with the material i suppose?

[gray gazelle]

Because those usually give major hints if not entire solutions to the exercises they give. Like in Abbott’s analysis, his exercises are literally direct applications of the theorems he talked about in each section.

[smoky zephyr]

oh god this is literally me

[west sedge]

Depends on what you mean by that, I spend quite a good chunk of time trying to understand a proof, I succeed in this most of the time, but doing a, lets say, intermediate level problem on my own is difficult for me

I wish I could have the perfect way to describe my struggles but I don't know

[west sedge]

Yeah, and I'm trying to look for a better way of perceiving things in analysis

Because so far in my life, the things I struggled with and told myself I would never be able to do or understand, I ultimately conquered them, however the case with rigorous mathematics is taking way too long and feels like I am so lost

Like what ingredient is missing in the way I tackle problems?

The problen with that question is that no one can enter inside my brain and understand what I mean, but I am still giving it a shot to look for advice

[blazing canopy]

By any chance do you struggle to visualize things in your mind?

[west sedge]

In those topics yeah, maybe I can only visualize the simplest of things, the most obvious examples.

However, I am a physics major and my imagination in physics is very good

I could solve physics problems using my intuition usually immediately, but as a physics major I always loved to know where everything came from

And thats what introduced me to abstract maths

[blazing canopy]

In that case probably the only thing you lack in practice. For the most part, learning how to prove things is similar to essentially pattern-matching logical arguments based on previous proofs or proof patterns that you've studied. Anything that's truly original is always going to be challenging.

[west sedge]

But how can I practise properly when, for example, most of the problems I get stuck and probably have to seek help on stackexchange or look the solution up

And after doing that I say: Okay hopefully I got the idea, maybe I can do most of the others

But then the next problem comes and its a loop

Of course there are some simple problems with proof by direct definitions, contradictions and stuff

But I want to be able to intuitively assume what something should be at the end or intuitively introduce a definition at the start of a proof (a function for example)

I don't want to recognize these things as magic

[blazing canopy]

Well, at least as far as exercises go, there's a limited number of essential examples, so in theory if you look up how to do all of them, anything else should be like a variation. Perhaps you only struggle to see the pattern.

It is not always possible to intuitively obtain the answer first before proof. Sometimes one can only intuitively recognize the deductive strategy itself.

[west sedge]

Thank you :) Is it okay if I add you if I have questions at some time?

I am self studying in my free time, I graduated from university and planning to start a master's in mathematicsl physics, I only will need to ask questions regarding ways to think

[blazing canopy]

Yes. I would start by finding a textbook with exercises whose solutions are available somewhere

[west sedge]

The thing about looking up solutions is as soon as I read the first or two lines, I immeditely regret it because maybe I could've came up with that solution

[gray gazelle]

Khaled each genre of math (analysis, algebra, etc) has a certain set of tools that you use to prove everything. You just need to know how and when to use them, which comes with practice.

[gilded lark]

Anyone have any suggestions for a secondary 3 mathematics book?

[sterile remnant]

@west sedge I kinda get what you feel, I'm in a similar position. I'm a physics undergraduate and I've developed a strong interest in abstract math and mathematical physics. I can read the books and understand most proofs but when it comes to solving exercises/doing proofs on my own I just can't seem to be able to wrap my head around anything but the simplest stuff. That being said, I do think it's a matter of practice. It's cumulative, you slowly build up knowledge, experience and intuition. But it feels way too slow if you're working on your own. I feel like I'd need to work by myself the entire summer to be able to get through 1-2 books/subjects on my own properly....

[remote ginkgo]

i was not able to read abbott and found it the worst analysis book i have ever tried to read

i never had trouble with any other book

i really think it is unfortunate that his book is popular.

to make things worse, it barely covers anything at all to begin with

[livid ermine]

What did you not like about it?

[sage python]

The writing, the organization, the content, the exercises, the font...

jk

[livid ermine]

I agree it doesn't cover all that much material compared with many other books, but I think the stuff it does cover, it explains more clearly than any other book. I also think the exercises are decent. I mean, they are not super difficult, but if real analysis is the first proof-writing class you are taking maybe that is not so big a deal.

[sage python]

Oh I'm just talking shit lol

Like imagine that as a hypothetical response given by gristle

Idk Abbott too well tbh

Lately I recommend Schroder for analysis

[smoky zephyr]

i can totally see it happening

[gray gazelle]

I think Abbott is a great book for a first pass. I mean the book is literally called “understanding analysis” it isn’t meant to be a super advanced text.

[smoky zephyr]

yet i still can’t do it

[gray gazelle]

Still can’t do what? Read Abbott?

[smoky zephyr]

i can’t do most of the exercises

[gray gazelle]

There’s tons of solutions online, have you tried studying those?

[sage python]

If you struggle then consider how ready you are atm

[smoky zephyr]

i already have proof experience and stuff, what else could i possibly need

[gray gazelle]

I think the other thing is just really understanding the material. Proofing comes from a 100% mastery of what you are learning and reading. If you miss a concept or don’t truly understand why something is true, you won’t be able to prove why something else is true.

It doesn’t work to “follow” a proof. You need to literally be able to write it yourself and understand every step that they do intuitively.

(Of course once you get good enough you don’t have to be this tedious, but the leap from computation to proofs is significant and takes work)

Here’s an example in the context of Abbott: are you able to prove the nested interval property by yourself? What are the main tools that you can use to prove it?

[smoky zephyr]

if i was given that with no context at all, i’m pretty confident that i wouldn’t be able to prove it

[gray jungle]

does a 1st book for real analysis really needs to do that much analysis tho? i feel like its enough to get whats needed and learn how to handle proof based courses and by the time you are a done with it you can pretty much tackle something at the level of rudin and learn everything you need from analysis

[gray gazelle]

Then I would start reading Abbott again using the mindset I wrote about in my previous post.

It’s not that hard of a book. You just need to learn how to read it and study it. Those habits will translate to any other mathematical book you read.

[crimson leaf]

I kinda like Tao's writing so far even if we haven't done analysis yet but the ++ thing was kind of funny to read I feel like it's all explained pretty well though

[gray jungle]

i enjoyed tao as well

[gray gazelle]

Tao is a wonderful author, I haven’t read his second analysis book yet, though.

[gray jungle]

at least what i did from it because at some point i dropped it for a higher level book

but its very well written and i love how he explains things

despite the argument that he can be a bit more efficient its a good introduction point

[crimson leaf]

Yeah I picked it up as my first kind of "advanced topics" book since I'm a little over halfway through calc 2 right now and about half through my book on proofs

[arctic creek]

alex rider books anthony horrowitz

[livid ermine]

Tao spends to much time going through foundational stuff like proving stuff about sets, functions, construction naturals, rationals, reals etc.

If you find that interesting, then its good, but I think many people would be bored with it.

[gray gazelle]

would you recommend it over spivak's ?

[flint forge]

spivak is not an analysis textbook

[gray gazelle]

it's an intro to analysis, no ?

[livid ermine]

I haven't looked at spivak, sorry. I would recommend rudin. If rudin is too hard I would recommend Abbott. If you have a whole lot of time on your hands I would recommend Amann & Escher.

[gray gazelle]

baby rudin right

[livid ermine]

Yes

[crimson leaf]

I do like that aspect myself. Idk I think that's useful though for someone who has very limited exposure to proofs in general though iirc the whole reason he did that is because he would teach students who weren't as strong in the basice before analysis and they would do poorly so he decided to start from the top to say

[flint forge]

No

Its too informal to be called analysis at all.

[gray gazelle]

i see

so it's a transitional text ?

[flint forge]

Roughly yeah

[gray gazelle]

alright, i'll use it as such

thanks

[tender cedar]

strang's

linalg

Is strang's linear algebra a good book for a first course on la

also

can you guys recommend me a good book for a first course on ODEs

[remote ginkgo]

both amusing and correct

[remote ginkgo]

yes

[remote ginkgo]

partial differential equations by the popular author whose name starts with s but i cannot remember

just the first chapter

[crimson leaf]

What are your thoughts on Tao's Analysis gristle, just curious

[remote ginkgo]

i respect tao greatly but i haven't read his intro real analysis book

at any length

i get the impression from what people have said about it that it's fine

but of course different books are readable for different people, so his style may not suit you

[crimson leaf]

I like his style really keeps me engaged in the reading

[remote ginkgo]

then run with it

[crimson leaf]

I do regret buying rudin though lol

[remote ginkgo]

it'll come in handy later.

i prefer rudin personally

but yeah they each cover some things the other does not

[crimson leaf]

Have you read stein and shakarchi? I was thinking about picking up that set sometime after introductory analysis

[remote ginkgo]

i just read their fourier analysis

i actually find axler's book on measure and real analysis the best after a 1st course in analysis

and ahlfors for complex analysis

@crimson leaf it would pay to pick up some topology in the meantime btw

[crimson leaf]

I have Munkres on deck

[remote ginkgo]

good

speedrun the whole first half (not the algtop section) then the last chapter (which is in the algtop section)

do lots of exercises

[crimson leaf]

I also have fraleighs first course in abstract algebra and contemporary abstract algebra

[remote ginkgo]

idk any good intro texts to algebra

i was just taught directly. i did use pinter a bit when i first started, but it's very basic. i got taught it at uni then just used lang's algebra after that

[crimson leaf]

Yeah that's what I'm doing with graph theory

But I'm interested in building up to functional analysis after hearing about graphons

[remote ginkgo]

topology and analysis pay dividends in every field tbqh

functional analysis is a weird subject

definitely worth pursuit

[crimson leaf]

Why's it weird?

[remote ginkgo]

you have to make lots of odd compromises

i haven't learned a ton of it, just have come into contact with it from messing around in other topics and with applications of other things

it has a distinctly geometric side that's kind of mysterious

but also really beautiful and entertaining to think about

[tender cedar]

perfect

thank you so much

[crimson leaf]

Stanley Farlow?

[remote ginkgo]

no

it's like

david spade or something LOL

oh

it's by Powers

sorry

@tender cedar

[tender cedar]

wait

what's the name again

is partial differential equations the same as ordinary differential equations

?

[crimson leaf]

No but the first chapter in this book just about ordinary differential equations

[tender cedar]

oh ok

what is the name of the book?

[crimson leaf]

Boundary Value Problems : And Partial Differential Equations by David Power is the one I found

[tender cedar]

nice I'll check it out

[crimson leaf]

Oh also gristle is there something you recommend after Lang's intro to LA

[heavy vector]

Taking pre calculus next year but honestly my math teacher this year was a very good teacher, makes me interested in mathematics a lot more, any book recommendations for pre cal to read over summer?

[crimson leaf]

I think Basic Mathematics by Serge Lang is pretty good but you can always take a look and see if it's for you

[remote ginkgo]

yes this is it

[remote ginkgo]

i dont rec lang's linalg. i rec shilov and strang instead

[crimson leaf]

Any particular reason for not liking Lang?

[remote ginkgo]

i love lang he has the same birthday as me

and i love how he writes

but trust, strang is just easier

[tender cedar]

btw

is axler good for a first course

Linear Algebra Done Right

[crimson leaf]

I do think Strang is one of the best lecturers I've ever seen

[remote ginkgo]

i absolutely hate this book

try kostrikin&manin instead.

[crimson leaf]

Man strang sure wrote a big book

[heavy vector]

Late response but ty man I’ll look into it :)

[grand thistle]

hoffman and kunze is also good

[compact crypt]

for abstract algebra

I think the best book is to use topics in algebra by herstein

combined with dummit foote

also topics in algebra has full solution manual

which helps tremendously

tho topics in algebra is old it has never felt outdated

[compact crypt]

I recommend friedberg

axler has non orthodox approach

which I recommend checking out ofter completing a course in linear algebra

[teal heart]

Hey guys what are some good resources for calculus II?

[runic hatch]

Paul's Online Notes are good

[sage python]

@tender cedar Axler teaches you how to think about e.g. determinants and characteristic polynomials like a moron

Kostrikin-Manin seems rather interesting actually

I haven't seen it before

I used Hoffman-Kunze

[remote ginkgo]

probably

[remote ginkgo]

i think KM is part of the verbitsky curriculum actually

[gray jungle]

not the best for a "1st course" but great for a 2nd exposure + reference

[sage python]

Honestly idk if I buy the whole first and second course business

If you're at a place where all math majors are sorta pushed through the service LA course that's one thing

But if you can just do it once do it right

[lime sapphire]

"right" pretty much depends on who's doing it, does it not?

e.g. an engineer would be better of going with a less rigorous approach since they might not care too much for it and don't see any relevance for rigour in their career

but yh tbh if you're a math major and rigour is the world then just go for the "right" choice

[steel pumice]

Best books for prmo and rmo?

[gray gazelle]

@slim peak sorry for the ping. Did you ever use baby rudin for your first analysis course

[fluid halo]

hey guys what books should I get to start calculus ?

[stone storm]

Any calculus book is good, all the popular texts are about the same. You can honestly get away with using Paul's online math notes and youtube videos for Single and Multivariable Calculus

[solar anvil]

Do you need a background in linear algebra in order to read Hoffmans book on linear algebra

[sage python]

Not really

[solar anvil]

you sound hesitant

[brittle breach]

no

[gray jungle]

the book is self contained but it does require a certain level of mathematical maturity.

[subtle mango]

its good to have proof writing experience

[slim peak]

I never used Baby Rudin in my whole life

[marble solar]

FR reax only

[slim peak]

For undergrad stuff yeah, I only know about French litterature.

[coarse crane]

What are some good books for undergrad Linear Algebra?

[broken meadow]

see pinned messages

the second pin has a list and some opinions

[coarse crane]

What does the description "Lol" mean under Roman?

[broken meadow]

Roman is not designed for a first course in linear algebra

it is better used after one has had some time spent learning linear algebra and abstract algebra, maybe even some analysis

[coarse crane]

Ok.

[broken meadow]

idk if its a bad book though i haven't started reading my copy of it 😵‍💫

[coarse crane]

Well, my experience is at most Calculus II. My teacher is exposing us to Linear Algebra at the end of the year now and I'm interested and want to study more.

[smoky zephyr]

some analysis? really?

[broken meadow]

well what else are you going to have to think about when you deal with infinite dim vector spaces

its hard to pinpoint exactly what the prereqs are

but as it is it's meant for graduate students so like

[coarse crane]

Yung cofe, would you recommend Artin for me as a relative beginner to the field?

[broken meadow]

i didnt read out of artin myself but if it's meant for beginners it should be fine

the book i read out of was Friedberg insel spence

which i think is written in an easy to understand manner

and has nice exercises

[coarse crane]

I'll take a look at both. Thanks for the input and assistance.

[broken meadow]

np

[gray gazelle]

piskunov

[foggy relic]

cover checks out

[crimson leaf]

Are like fake copies of Spivak floating around

[foggy relic]

@gray gazelle What do you mean by coding? Like typing out code in some language?

or like coding theory

[night prism]

Those are generous margins for notes

[crimson leaf]

I like that

[cursive orbit]

cs50 is not coding theory

it's just programming

but if you're looking for an introduction to programming, I'd recommend Berkeley's CS 61A

lectures are available here https://www.youtube.com/playlist?list=PLoRTsGsOgdQvAPI33fDL2bpPYtLRrhFyp

https://inst.eecs.berkeley.edu/~cs61a/su19/

website here

[fluid halo]

should I get "Thomas' Calculus" ? I want to learn calculus from scratch

[hollow shore]

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

try this one

[polar terrace]

Anyone has any recommendations for ressources to learn ode?

[slim peak]

Viorel Barbu's book

[gray gazelle]

Anyone have any more advanced logic textbooks?

I just went over most of Kalish' Logic: Techniques of Formal Reasoning

But I'm looking to go further I guess

[heady ember]

@gray gazelle

[viscid grove]

Oksendal vs shreve

Which do you think is easier

Or are there other more friendlier book

[jaunty wasp]

Hey! Looking for some proof writing books, if anyone knows any good entry ones that'd be cool. Preferably undergrad level

[dapper root]

Uhhh @karmic thorn has a few he likes I think

[smoky zephyr]

book of proof

[night prism]

Formal or informal?

(Proof writing)

[jaunty wasp]

oh informal

[night prism]

How to prove it Is very popular

Also look at Roman’s transition to advanced mathematics text on his personal webpage

[jaunty wasp]

Thanks! will do

[brisk walrus]

http://nozdr.ru/biblio/edu/math/high

[safe horizon]

looking for good books on history

doesnt matter what kind as long as it isnt too esoteric

[karmic thorn]

Book of Proof seems to be a popular choice, as mentioned above. Other stuff include How to Prove It and virtually every introductory text on discrete math.

[hallow oriole]

book of proof, how to prove it, how to solve it - top three

there's also Proofs From the Book

which is maybe not very useful but is definitely worth a look

[heady ember]

Loch's summary

[timber mesa]

of mathematics?

Stillwell has a decent one, it's structured like a textbook with exercises which might seem a bit odd but it's a good summary of the early history of mathematics

[safe horizon]

sure and perhaps things like Guns Germs and Steel

[brittle latch]

trying dummit and foote and im finding it a bit dull - admittedly on chapter 1 but should i stick with it or does it just get worse

[timber mesa]

you can probably skip the first few chapters tbh

doesn't it start with like, the integers

ah, chapter 1 is an introduction to groups

well, it's known that the writing is a bit terse and while some sections have a ton of exercises, you don't need to do all nor most of them

DnF is a good reference, I'd stick with it

[brittle latch]

i know most of the early stuff

took a class on algebra last semester but it was literally only basic stuff tbh

so what im gonna do is try and just summarize all the material i know from chapter 1 already in my own words, and then compare that to chapter 1 to see if there are any gaps or things i got wrong

that, along with some problems, should give me enough confidence to just move forward

[night prism]

You could also just see how prose-like you can read it

If you know it there won’t be a lot of pauses to stop and think or fill in steps

Trying a medium-level problem from the chapter could also be a good indicator

[brittle latch]

http://math.stanford.edu/~akshay/math120.html

probably gonna be yoinking this and just treating it as actual hw

[night prism]

Are you starting D&F?

[brittle latch]

yeah i started it today but got frustrated

im gonna try and stick with it though

one day of frustration shouldnt be enough to cripple me

[gray jungle]

alternatively you could consider trying something more efficient (e.g artin)

[rain fjord]

Anyone have book recommendations for inbetween algebra2 & precalc

[brisk ice]

I don't think there is much of an in between

Maybe trig if your algebra course didn't cover it.

[runic hatch]

Either way Khan academy is probably your best bet

[coarse frost]

based

[livid ermine]

Bummit and foote is great ngl

[lime sapphire]

does anyone know of a university linear algebra course/ lecture series that follows hoffman and kunze?

[compact crypt]

has anybody seen viro's elementary topology?

https://www.amazon.com/Elementary-Topology-Ya-Viro/dp/0821845063

if so what are your opinions regarding it

[compact crypt]

isnt it dummit and foote

[livid ermine]

i don't know. i've only read bummit and foote at least

[compact crypt]

welp anyways its a good book

[desert herald]

Need a recommendation for a proof or discrete math book for a computer science student that wants to learn a bit more behind the math of theoretical cs. Already did a basic discrete math course at uni but it didn't cover much about proofs.

[brittle latch]

book of proof

[gray gazelle]

Discrete Mathematics with applications by Sussana Epp has some beginner friendly proof writing. Not sure if it's good for more advanced stuff

[smoky zephyr]

seconded

[desert herald]

by Richard Hammack?

[smoky zephyr]

yes

[gray gazelle]

Rosen

[remote nymph]

Does anyone know about any book which is full of algorithms for machine learning

[gray gazelle]

People say it's good

[gray gazelle]

Either Rosen of the MIT book

[ocean ledge]

are there any books that could help me get a grip on calculus

[hoary onyx]

burn math class might be good if u like math but are struggling with calc (me)

its just a decent read overall but it really shines when you understand everything

tries to invent calculus from (mostly) the ground up which is cool but the last few chapters are a little hard for me

[hallow oriole]

im gonna assume you mean like computational calc (finding value of integrals, differentiating functions, evaluating limits, etc)

a good book is Stewart's Calculus

just do all the exercises

or at least until you feel you have a good grasp on it

[crimson leaf]

Paul's online math notes can be a good resource too if you're enrolled in a course right now

[heady ember]

Spivak's Calculus

[gray gazelle]

Looking for something for Putnam/IMO level maths (competition maths) other than Putnam & Beyond

[sharp latch]

Problem solving through problems

[wary compass]

can anyone recommend any textbook about functions of two variables? I'm currently reading Trench's introduction to real analysis but it's about n variables, and I would like a book more focused on the case when n=2...

[cursive orbit]

why specifically n = 2?

because things in the case n = 2 and the general case aren't really super different

[wary compass]

ah okay, it's actually my professor who suggested me find a textbook like that, cuz he says the proofs that may come up in the final will be of the case of functions of 2 variables.

But you do have a point

[weak violet]

what are some good books for a self-study through complex analysis?

[heady ember]

Look at pinned

[static bolt]

Do you guys know any good books that teaches vector math especially for absolute beginners?

[fervent magnet]

same i need this too

are u in highschool?

[static bolt]

Yeah why’d you ask?

[fervent magnet]

im 12th grade too rn

we'll study vector algebra this year in maths

[static bolt]

Ahh for school

[fervent magnet]

like 2d

3d*

[static bolt]

Oh 3d, thats much more complex from what I was going for haha

I didn’t specify that I wanted it to be about euclidean space

[static bolt]

What course or track did you go for?

[fervent magnet]

stem

in my country u have like much broader streams

i chose phy + chem + math + cs

[runic hatch]

Khan Academy is probably your best bet

[shell geyser]

I don't know any entire book that does vector algebra. I think that's usually only 1 chapter and most of the standard calculus texts (like Thomas) have it.

[night prism]

How deep do you want to go?

I have a few books but they get deep into it

Oh you said vector algebra

Yeah might be best to check general texts on physics or math

Intro physics texts actually do a fantastic job with vector algebra because it’s so useful for them

[eager crater]

Anyone know any books to learn discrete math

Keeping in mind I'm a complete idiot

[subtle mango]

discrete mathematics by rosen

[eager crater]

Thanksssss!

[honest pagoda]

Anyone have any interesting computer science books they might recommend?

[cursive orbit]

SICP

[compact crypt]

are there any stochastic calculus book with solutions

or is it too advanced to have solution

[stone storm]

Probably, I don't know if there are any stochastic calculus books that are purely computational so solutions aren't really necessary. If you're looking for a non-measure theoretic book, you can try Stochastic Calculus and Financial Applications by Steele

[blazing canopy]

very few advanced textbooks provide solutions. However, sometimes for popular textbooks you can find some diligent student online who has posted their own solutions.

[hard bronze]

Any good introductory books on optimal control theory?

[south salmon]

Do you want to go more for theory, if so, getting a book on calculus of variations would be good. A book like Gelfand and Fomin is good.
For an introduction in optimal control theory in general, this intro by Evans is good https://math.berkeley.edu/~evans/control.course.pdf

Or Kirk’s introduction to optimal control theory

[timber copper]

, also liberzon's book is quite decent

also take a look at bertkesas's dynammic programming + optimal control; didn't like this book, but I think still a good resource to have (mostly bc of typography)

You may also want to look at Sontag's MCT which touches upon the topic in the final chapters. You may like this if you enjoy Evan's book

[inner token]

This is a reach but I want a Portuguese translation of Serge Lang's "Basic Mathematics"

[remote ginkgo]

all of bertsekas' stuff is really bad

[remote ginkgo]

kirk's is the classic. you can also read sutton&barto for another perspective. alternatively read bellman's dynamic programming and milnor's morse theory

[whole sage]

Hello, I am preparing for a bunch of highschool mathematics competition, Do you have any books that could have a wide range of topics with exercises and solutions?

[timber copper]

Sutton and barto for optimal control

[rancid marten]

I'm a 28 year old accountant, got no degree and I have a very basic education in math. I want to become a Math Teacher for secondary education. What's a good place to start (book) and what do I need to master?

[lime sapphire]

You might need to check what your country's requirements are for becoming a math teacher

you will most likely need a bachelor's degree depending on where you are

[sage python]

Like high school?

[viscid grove]

What is your country

Thats the most important part

Some countries require degree

Some countries yiu have to take exam

[undone echo]

Any cool book recommendations. mathematics that might come to be under 5 dollars right now? I have a 3 dollar coupon. I guess what I'm saying is I want a free book to run through right quick. My store is Google play books but I'd be willing to go to Barnes and nobles. (Do they even have a math section?)

[undone echo]

It's an open ended questions. I'm sure I'll see more worthy of read in this chan. I just got tired of scrolling

[sharp latch]

That’s a pretty low price if you’re looking for a physical copy. For the best price-to-selection ratio I’d recommend going to any local or used bookstores you have in your area and seeing what they have

[undone echo]

Yeah everything is 20 bucks. Again I looked through Google play. Again. Too expensive

[flint forge]

Yeah the best you can hope for would be used bookstores

they often have ridiculously good deals

[runic hatch]

I third used bookstores

It’s probably the only place where you can find good books under 5 dollars

[flint forge]

of course, if all you want is a free book to run through, you can get many books on mathematics for free online

[sharp latch]

Could also try the library

[rapid lily]

any opinions on this book?

[dreamy cove]

cool books rip

[empty mortar]

JEE

[lime sapphire]

out of curiosity, how are you finding amann and escher? thoughts?

[split snow]

Hi! sorry if i interrupt any discussion. do you guys have any recommendations for an introductory graph theory book? i consider myself to be proficient in writing and understanding mathematical proofs.

[serene reef]

But this is what I am interested in knowing.

[dreamy cove]

also if i get time i would like to understand more math

(programmer here)

[calm saffron]

zetamac is garbage

[empty mortar]

please tell me you did not unironically recommend this garbage.. (kids game?) zetamac lol

[dapper root]

Why the fuck are you replying to something from four months ago?????

[quick hornet]

the record has went uncorrected for 4 months too long

its never too late to do a good deed

[flat lantern]

time to set an alarm

[calm saffron]

who

[hearty sluice]

yall are replying to something from four months ago, I think the better question is how did you see it now? Are you reading every message since the start of this channel and just got to four months ago?

or are you going backwards one day at a time?

[calm saffron]

i spend all day reading on here

[serene reef]

Bumping this.

[shy compass]

I haven't learned from it but I did do some exercises when I was learning rings & modules

they were good

and the broad consensus here seems to be artin is a good aa book

[rancid marten]

Yea I'm from Luxembourg so it does require at least a bachelor.

[rancid marten]

I'm from Luxembourg!

[lime sapphire]

Lmao

Why's zetamac bad

[calm saffron]

eyesore

and limited options

[lime sapphire]

Right

I mean i don't use it anyway
I use a program almost like it but with better ui/ux

[calm saffron]

alphamac?

[lime sapphire]

Yea

Wait is alphamac a big thing?

I didn't expect anyone here to know it

[calm saffron]

i used to use it

im on the leaderboard

no i dont think it's a big tihng

not at all

[lime sapphire]

I see

[placid pollen]

This is bigger than it needs to be lol

[night prism]

Huh

I have his finite dimensional book

Never seen that one

[remote ginkgo]

this book is kinda bad

just read munkres instead

[pale scarab]

I'm teaching precalculus next year and I am looking for a good textbook to review and use for good problems. I am not looking for Khan academy level but also not quite AOPS level.

[pale scarab]

I remember liking the linear algebra problem book he has.

[remote ginkgo]

a hilbert space problem book?

[heady ember]

Lee's Intro To Topological Manifolds is also good from what I have heard

[pearl path]

lmao

[heady ember]

[dapper root]

It works pretty well as an intro to topology

Doesn’t cover the separation or metrizability stuff as in-depth

But if you want to learn general topology for other classes and to later take manifolds it’s good

[pearl path]

I too thought that

but then searched it up

it is not bad

when I hear lee

I only think of smooth manifolds (maybe if you push me, diff manifolds)

[mystic orbit]

We need more math textbooks with similar cover styles

Simple, modern looking, charming.

[coarse frost]

chrew

[coral narwhal]

why does the title say Linear Algebra when its just FDVS?

[empty orchid]

hi guys, I come from the main chat, Completed sophomore year of HS, started IBDP just now, Know most of all topics of HS math other than Calculus. I want to get started next on Number Theory or Discrete Mathematics or anything else suggested next. Preferably Online or affordable books(sub 50 Dollars) but will check out everything. Thanks

[gray gazelle]

Actually

Nvm

[empty orchid]

wow thanks man looks pretty interesting, what is considered next after that

nvm deleted i see

ah

[runic hatch]

Do you have plans to major in math?

[empty orchid]

yeah planning on majoring Math and Physics and tho I am doing good with school, I do not think I have the rigor in Math that I see other HS students around here have. And more importantly its fun and I want to get deeper

(forgot to mentionl,also preferably self contained the books)

[runic hatch]

I’d say that learning some abstract algebra could be cool; I’d recommend Artin’s Algebra for this topic

Spivak’s Calculus is also a nice introduction to analysis

[empty orchid]

i am yet to start calc btw

[runic hatch]

I think it may be doable without prior calc knowledge

If you don’t feel confident though you can start with Artin

Both topics are useful in math

[empty orchid]

what are the "higher level" things I can do if that makes any sense, not by complexity but I mean stuff overarching all of math like number theory

[runic hatch]

Well both of the books I mentioned get you ready for the “higher level” stuff

[empty orchid]

ic, thx also any alternatives to the spivak book its 100+ dollars equivalent in my country

[runic hatch]

Oh damn lol

Apostol’s Calculus series is also nice, although that may also be pricey

Alternatively there may exist online copies

[empty orchid]

understood, thanks a lot ab

[runic hatch]

Looks like it

Although you may want to delete your message with the link because we don’t want links to piracy sites here

Anyways have fun

[empty orchid]

thanks for the help mate!

[runic hatch]

Np

[lime sapphire]

there's an IB server and their maths channel may help you get started since a lot of people there are into math in general and have done IB before so they might help you know what overlaps nd what doesn't etc.

[empty orchid]

yeah i am aware but they need phone verification 😦

[lime sapphire]

rip

[restive falcon]

would the content in browder and rotman be enough to understand schlag

or is more real analysis assumed

[gray gazelle]

IS there any online resource to begin physics

I know this is a math sesrver

[restive falcon]

you will get more help in the physics server

i guarantee

[gray gazelle]

I cannot join it

[restive falcon]

were you banned

or sth

because you should be able to join

[gray gazelle]

I need to verify a phine number

[restive falcon]

oh

[smoky zephyr]

i heard that if you dm the mods they’ll let you in

[gray gazelle]

im a student that will start IBDP in a year but I've pretty much mastered the topics covered in the two years for AA HL. So essentially I'm looking for book recomendations that are like strarting universtiy level

[gray gazelle]

I’m confused: does AA mean abstract algebra here? If you’ve studied it why are you asking for starting university books?

[placid pollen]

It's the same book you mention. The editorial just changed the name

[placid pollen]

In the Amazon article website says "many students have missed on this one because of the non-conventional name" or something like that

"This book, originally published as "Finite-Dimensional Vector Spaces" has been regarded as a masterpiece of linear algebra. Due to its non-standard title, the book was often overlooked even by math majors. Now the book appears with the new title, new typesetting, and corrections."

[hybrid chasm]

Prolly means “analysis & approaches higher level”

Yknow not every letter string only has one acronym

But its ok

[gray gazelle]

I mean BLT can mean a sandwich or something else, but it’s mostly used to imply the sandwich

[rocky jay]

Book(s) to work out on proofs?

[hybrid chasm]

The implication of it not being “abstract algebra” is quite obv
Because he’s talking about hs level and also mentions some other acronyms
Sorry if that msg came off as condescending

If you’re ever in doubt ig you should turn to google

[coarse frost]

Two popular ones are "how to prove it" and book of proofs

[gray gazelle]

You know, I probably should next time. You’re absolutely right!

[rocky jay]

Thank you.

[gray gazelle]

How could you mock Wizard’s timeless wisdom?

books for math competition grade 9?

Shame on you Shyshu.

if there are any

[gray gazelle]

Please clear up this question it doesn’t make sense.

[coarse frost]

what

[smoky zephyr]

just so you know, it’s actually called “book of proof”, not “book of proofs”, by hammack

[gray gazelle]

I’m confused do you seriously agree with what wizard said

[gray gazelle]

Like are there any books that could be useful for grade 9 maths competition ( mostly algebra, geometry, set stuff and basic trigonometry ) but like more complicated problems

[rocky jay]

I'll take that into account, thank you.

[gray gazelle]

In what country

[tiny stone]

anyone have terrences book on mathematical problem solving

[coarse frost]

kinda

[tiny stone]

Aops books most definetly, also join the mathematical olympiad server

[gray gazelle]

Well I am in Serbia but that is why I put the topics that are most likely in brackets

[coarse frost]

oh yeah

[gray gazelle]

thanks

Yeah I would go with AoPS

[tiny stone]

anyone have the book terence wrote at 15

im really freaking bored and too tired to solve problems

[gray gazelle]

is 6 months enough to work through an AoPS book

[gray gazelle]

An explanation of my joke: I was being sarcastic in response to their blatantly condescending message.

🤦‍♂️

[tiny stone]

you could do each one within a month if you tried, or a week or two if you really work at it, but you have to use the knowledge and keep solving problems

but yeah taking 2+ weeks is a good idea so you can sink time into the challenge problems

[gray gazelle]

alright thank you

Good luck with your competitions @ interested!

Thanks!

[coarse frost]

ik

[gray gazelle]

You threw me for a loop Shyshu

[coarse frost]

lol

[glad prairie]

Shyshu is so mean today

Bully bully

[coarse frost]

i am not mean!

what are u saying

https://tenor.com/view/kuch-bhi-gif-24530809

[alpine rover]

Hey guys, I'm in my second year of math at university, and I've taken real analysis and linear algebra, but I'm not very good at proofs. What's the best book to get better at proofs?

[gray gazelle]

For real analysis, do Understanding Analysis by Abbott.

For linear algebra, do linear algebra done right.

Those are two introductory books that explain proofs well for those genres IMO.

[lime sapphire]

How to prove it by velleman
Or
Book of proof by hammack

[gray gazelle]

As a note for proofing in general: the way to get better at proofs at first is to prove things! I always recommend that people try proving the theorems the author does in the text side by side. This introduces you to the “machinery” of the subject that all the other proofs will use. It also helps for motivation of certain tricks or ideas that are common.

[sage python]

Absolutely not

[subtle mango]

i suggest hoffman kunze

it is a bit difficult in some places but is a great book

[gray gazelle]

As an intro to proofs?

Please don’t kill me sloths

[subtle mango]

hk also has a lot of "proof left to reader" exercises that have hints

[brazen steeple]

On the converse, I have 2 LA undergrad courses under my belt as well as a numerical computation course and I would love to study linear algebra more specifically to see applications and uses in ML and data science; i.e. I want a good LA book for my background that isnt overly theory heavy but will give good and rigorous insights into machine learning

any suggestions for someone in my case

[foggy relic]

@alpine rover I did LADW and it was really great

alot of the excericses are "proofs" but only require a couple of steps so its not too hard

[grand thistle]

i also did ladw and i found hoffman/kunze to be much more comprehensive after switching in the middle of the book

i don’t really like ladw that much to be honest

it focuses a lot of pivots of a matrix and frequently uses them in proofs as well which i didn’t really find very motivated tbh, but maybe that’s just me

[foggy relic]

2 LA undergrad courses
well what else do you really need to know

[brazen steeple]

I'd love to see how I can specifically use techniques for ml applications, I mean everyone says linear algebra is the most important field in ml

from my classes I can compute eigenvectors and multiply matrices and I know factorizations but I want to apply them

[foggy relic]

okay, but which applications

what have your classes covered

[brazen steeple]

SVD, QR, LU factorizations. eigenvalues/eigenvectors, norms, ill and well conditioned matrices, hessian, jacobian

idk, I just want to be able to understand how it works underneath models and how it applies to datamining more in depth

my classes have been less application heavy but more LA for the sake of math if you know what I mean

[foggy relic]

I think Strang has some book for lin alg with its applications to ml

forgot the name

havent read it so also dont know its quality

[brazen steeple]

I'll look that one up

[coarse frost]

based dami

[zenith cobalt]

any recommendations for a good elementary number theory books ?

[solemn rover]

|| Just a joke. this book is probably very hard. ||

[karmic thorn]

Silverman, A Friendly Introduction to Number Theory is a very informal but nicely presented book. For something more concrete, try something like Burton's Elementary Number Theory or Niven's An Introduction to the Theory of Numbers. There's also the one by Titu Andrescu (called Number Theory) but I don't know much about it.

[zenith cobalt]

Thanks a lot

[zenith cobalt]

does this books contain proofs as well ?

[karmic thorn]

Yes

Silverman is probably slightly informal, but the rest do.

[zenith cobalt]

Thanks a lot

[tulip blade]

Just look at ML books.

Textbooks that focus more on theory

[gray jungle]

just wondering if these 3 chapters in artin algebra provide anything not given in a linear algebra course ?

looks the same to me, just making sure

[cursive orbit]

systems of linear ODEs might be one topic that isn't commonly covered in an LA course

[placid cove]

Hi guys I am currently in High school and want to get started in uni math (not patient enough to get to uni), tbh I don't even know what topic to choose, any recommendations ?

[cursive orbit]

discrete mathematics if you're just getting started out

[placid cove]

Alr I see

Any specific book recommendations?

[cursive orbit]

discrete mathematics and its applications by rosen

[modern stone]

Thoughts on Topology by Jänich?

[gray gazelle]

Burton is great. Has a historical account of NT and basically covers a first course in NT

That actually brings me to my question; any book recommendations for an undergrad course in graph theory?

[gray gazelle]

Probably more advanced calculus first

I'm also in hs

[gray gazelle]

Does anyone know of a full solutions manual for the Galois Theory chapter in Dummit and Foote?

[blazing canopy]

Not officially, but if you Google there are some diligent students who have provided their solutions

I think that's pretty much the best you can do, and of course there's no guarantee of correctness

[trail kernel]

Does anyone know any good books that explain how tensors work and what they are? A book that could be understood by someone after some basic linear algebra, one which would also explain the concept of multi-linearity and dual spaces

[thorn cloak]

A little bit of a different question but I still think it fits here. Does anyone know a good client for reading/annotating eBooks/PDF textbooks? My college is using them, but pdfs on their own are just really clunky and I feel that adjusting to college will be hard enough let alone with annoying textbook clients. Thanks!

[last sail]

Hello do you guys have a good recomendation for a book introducing cohomology?

[solemn rover]

There are a few different homology and cohomology theories. Some are for spaces and some are for algebraic gadgets like modules over a ring.
I think the two most important theories to learn for spaces are simplicial homology and de Rham cohomology. Simplicial homology, maybe the book on algebraic topology by Rotman would be good. It is also treated in chapter 2 of the book by Hatcher.
de Rham cohomology is treated in the book by Bott and Tu, "Differential forms in algebraic topology", and treated in the book by Warner "Foundations of Differentiable Manifolds and Lie groups."

If you like complex analysis, I can recommend "Lectures on Riemann surfaces" by Forster as a first introduction to sheaf cohomology/Cech cohomology with applications to Riemann surface theory. This is a beautiful area of math. It requires a little background in complex analysis but no prior exposure to cohomology theory

I think i recommend rotman and forster to start with

[dense wren]

What’s a good text to go through after Aliyah and Macdonald?

[dapper root]

For what?

[dense wren]

I guess I’m just trying to figure out which topics to go for next

[dapper root]

I mean

For what lmao

It’s like if I asked what’s a good dish to eat after finishing A&M

Like idk, do you want more commutative algebra?

See applications of A&M?

[dense wren]

Yeah I get it’s vague lol

More commutative algebra I guess

I know it’s a book people usually go through before algebraic geometry

[quiet forge]

Everything that man writes is (chef's kiss).

[dapper root]

I like Matsumura Commutative Ring Theory, but it’s a much more… difficult book?

In terms of actual difficulty relative to prereqs it isn’t bad I think, it just uses some highbrow techniques

So you need to know direct limits (which you should!) and some homological algebra like derived functors

There’s also Eisenbud

For me, the book is just too big

[dense wren]

@dapper root for some background I just finished my MS in math and am looking for some interesting topics in algebra to study on my own, I don’t have a particular direction in mind other than “more algebra” which I know isn’t super specific, just trying to explore. I’ll check those books out though thank you

[dapper root]

There’s a lot of fun topics in commutative algebra!

[karmic thorn]

I've only read a little bit but I'm definitely a fan of his exposition.

[dense wren]

@dapper root yeah I think it’s pretty interesting, i think A&M is a great book. Do you know what I could look for if I wanted some sort of intersection between that and more category theory intensive stuff?

[dapper root]

Oooo

Uhhh

You start heading towards homotopical stuff probably

Things involving E_infinity algebras and stuff

Maybe model category stuff

[dense wren]

Do you think it would be a good idea to learn category theory on its own before looking into that stuff? My background in cat theory is pretty weak

[dapper root]

Definitely

For model categories you maybe don’t need too much…

But like if you go into homotopical algebra stuff with E_infinity stuff you’re doing infinity category theory…

So you should have a solid base of 1 and maybe some 2-category theory under your belt

That being said, I can’t imagine studying category theory on its own

¯_(ツ)_/¯

[dense wren]

@dapper root lol yeah most of my professors who I’ve asked have said all the category theory they’ve learned was learned as they needed it

[dapper root]

Yup

[solemn rover]

bro

ok

I hate you people

[subtle mango]

it's okay. i love you diligent clerk.

[solemn rover]

Thank you anamono

[subtle mango]

of course

[solemn rover]

Try not to trip over your huge dick while you're boasting of your ignorance

[dapper root]

I literally just can’t, it seems too boring to me lol

[solemn rover]

Ok.

[dapper root]

I don’t have anything against people who do

[solemn rover]

This is how I feel about proof theory so I understand

Anne Troelstra is a genius

but I will never have the motivation to get through one of his books

[solemn rover]

There is more to category theory than homotopy theory, for example there is the line of research pioneered by the australian school.

[gray gazelle]

Hello, can anyone recommend a book for comp math?

To improve skills in such type of problem solving

[solemn rover]

You should learn homological algebra, I think, it's a good complement to comm alg

[dense wren]

@dapper root that’s a good idea! What’s a good book for that? Rotman? Or weibel?

Woops meant @solemn rover

[solemn rover]

Both are good. Rotman is a really good expositor so I recommend that one first. Weibel's book is more substantial/goes further, it has good computational exercises but is also rife with typos.

In general homological algebra is somewhat dry, I hope that Rotman makes it more engaging. I first started to get really into hom alg when I studied Dold Kan

Also try to like, look at the applications of these homology/cohomology theories in various places in algebra to get a feel for why you're doing this stuff and what the motivation is

@dense wren for a recent research topic getting some activity you could consider "Koszul Cohomology and Algebraic Geometry" by Aprodu and Nagel

[quiet forge]

Agreed!

xD

[dense wren]

@solemn rover I’ll check them out thank you

[solemn rover]

Category theory is a noble and beautiful discipline.

[quiet forge]

I'll believe it when I see it.

[dense wren]

@solemn rover what would you recommend for straight category theory texts?

[solemn rover]

You can read whatever to get the lay of the land, the standard recommendations are probably fine. I don't have anything against Riehl's book. The book by Mac Lane has good stuff in it but category theory is also very dry unless you have stuff to apply it to, so go back and forth between learning category theory and collecting examples.

I think my advice is like, when you see a construction in mathematics, be on the lookout for adjunctions, universal properties, etc. and if you find something that seems to be a universal property of some kind but you don't know how to formalize it, then go learn more category theory

[dapper root]

This is what I meant when I said I can’t imagine studying category theory on its own

Divorced from applications or seeing how this is a generalization of blah blah blah

I can’t see myself studying it

[flint forge]

I think riehl gives convincing examples

but you can also learn a lot of what you need as you go

I have spent very little time studying category theory without specific purposes in mind

[solemn rover]

Alright, I see. I personally have just cranked through a lot of it because I believe that the characteristic arguments of category theory can provide a lot of insight, like in homological algebra if i can give a purely categorical proof of something then i feel that the proof has kind of 'written itself' - usually the universal properties only give you like one choice to make at each step, and so the arguments are kind of self-propelling or self-driving in a very beautiful way which i think gives a lot of insight into the problem. So I have studied a lot of category theory on its own just because these self-driving arguments are beautiful to me.

Also with sufficient time with categories they just become ordinary mathematical objects which don't seem intimidating, but just like, naively, you get used to them just like you get used to Jacobson rings or whatever.

[flint forge]

Yeah to me categories are not even like

any more abstract than a ring

[dapper root]

I don’t consider homological algebra proofs done in an arbitrary abelian category to be category theory

[flint forge]

interesting

[dapper root]

I think this is homological algebra done coordinate free

[flint forge]

in a lot of ways category theory is just everything coordinate free

[solemn rover]

Ok, I get what you mean, that's not really what i meant. Give me a second

[dapper root]

Maybe it’s a hot take, but I find that it has a different flavor, maybe because in the background I always have module theory as a backdrop

So it feels a bit more tangible

[flint forge]

Well the goal would be to have enough examples that you always have something to fall back on

[dapper root]

In arbitrary category stuff I feel like it gets too formal for me, I know this is a criticism of commutative algebra and stuff, but to me algebra has begun to feel very very tangible

[flint forge]

i think the issue is this last sentence part lol

like

as you said

these things just begin to feel very very tangible

[dapper root]

Yeah I mean Dold-Kan felt like homological algebra to me

Sure, but I’ve sunk a good bit of time into it and it still feels that way

[flint forge]

into category theory?

[dapper root]

And also, your category theory stuff you study is still really “algebraic”

[flint forge]

that is very untrue

[dapper root]

I mean oky depends on what “good bit of time” mean

[solemn rover]

this explicit construction of the inverse to the moore normalization functor is like, very annoying to me. why this functor? why that definition? why construct it this way? Not talking about R-mod vs arbitrary Abelian category stuff

[flint forge]

I mean consider how much time you've spent on commutative algebra

and compare that to how much time you've spent on category theory

[dapper root]

Sure

[solemn rover]

I find it much more elegant when this is prhased in terms of Kan extensions

[dapper root]

I qualified my statement later

[flint forge]

was this referring to diligent btw?

[dapper root]

It isn’t nearly on the same scale as the other two subjects I studied a lot

I mean I think it’s directed towards you

[flint forge]

I think you don't have a very good idea of what I study hahaha

[dapper root]

That might be true

[flint forge]

It's like, a godsend when the categories I care about end up being algebraic in nature

[quiet forge]

What do you study?

[flint forge]

Stable homotopy theory

and even then its like

""""algebraic""""

[quiet forge]

Is there an unstable homotopy theory?

[flint forge]

Yes

that is more or less the study of the homotopy category of spaces

[quiet forge]

I.. was honestly not expecting the answer to be yes. xD

[flint forge]

so, traditional algebraic topology

[dapper root]

Algebra and AG felt more concrete and lucid to me from the outset. I don’t deny that categories could feel natural and concrete, but there’s a combination of they don’t for me, but these things already do, combined with I don’t think I need to care

[flint forge]

ah

that latter part might change

but there is no reason to force it

[dapper root]

It certainly might

And I’ll study it then

[flint forge]

yeah thats totally fair

[dapper root]

But like, I can stomach learning CA for CA’s sake and have fun

[quiet forge]

I wish I felt that way.

sigh

[dapper root]

And I just can’t with category theory

[flint forge]

I mean, knowing a lot of category theory is basically essential to doing anything in modern AT

so like

I hit that barrier

much sooner

[dapper root]

Like I actively have to stop myself from learning more CA that I won’t use because I just find it fun, and so I don’t really see myself studying category theory on its own until I need it

[flint forge]

I do not study category theory on its own like that either

[dapper root]

But like, I definitely see myself reading HTT at some point

[solemn rover]

I do

[dapper root]

Yeah, but that’s what my initial post was saying which Clerk sees to take offense to

[solemn rover]

I read category theory before i need it, if we are looking for someone to take my stance

[flint forge]

I study categorical ideas that are generalizations of categories I already care about

[dapper root]

Yeah Clerk, and the reason I said what I did is that I think few people can really stomach that

So I wasn’t about to go to tell someone to go try and do it because like “that’s what you do”

And to be very clear, I feel the same way about algebra

[quiet forge]

I think category theory would be more enjoyable / less inscrutable to me if I understood the math it generalizes.

[flint forge]

probably should

[dapper root]

I do not think most people can stomach studying CA like I do

And I wouldn’t recommend someone to do so

Unless there’s some other reason that I think they might enjoy it

[flint forge]

you technically do not need to know anything about infinity categories to study E_infinity rings, but it is a little cleaner

[dapper root]

Basically, my point was that I didn’t want the guy to think he has to go read Maclane front to back now

[solemn rover]

It's fine if you're not personally interested in category. What I read into it (and it's fine if this is unjustified) is like, a general attitude that mathematicians have that you need three weeks of category theory to pick up the basic definitions and then you should never read a category theory book again and wash your hands of it, like it has nothing to offer as a subject beyond just like, the five things you can name
(category, functor, nat trans, colimits, yoneda, adjoint functors)

[dapper root]

Because he finished Atiyah MacDonald and that’s the next step

[flint forge]

well yeah they should read riehl instead anyway

[solemn rover]

Anyway I don't think that was your intention now that you clarified

[flint forge]

I mean if you want to do category theory you should learn category theory, and someone saying they want to do category theory probably doesn't need the response "I think category theory is boring"

[dapper root]

I mean for a lot of people that is a lot of what you need to be able to navigate life. Obviously for a lot of people later on things pop up, and you pick it up then, but for me my approach to math is usually to frontload

So I learn a ton of theory before I need it

[solemn rover]

Ok.

[dapper root]

And I was just saying like, you probably don’t need to do that with category theory to be able to continue with what you want to do

[solemn rover]

No, I agree

[sudden kindle]

Chmonkey is a CA enjoyer