book-recommendations

[coarse frost]

[hallow oriole]

and tbh im not sure what to do then lol

[coarse frost]

im going to travel 200 km for an exam

[hallow oriole]

WHOA

[coarse frost]

tomorrow

so

monke

[hallow oriole]

bro

why

??

[coarse frost]

entrance exam

[hallow oriole]

ohhhh

good luck shyyy

u got this

ez dubs

[coarse frost]

ty!

[tardy walrus]

VALLEY

Where’ve you been you little shiktzei?

[hallow oriole]

slurpppp

ive been w/ ur mum

[tardy walrus]

HWAT

SAMEZIES

[hallow oriole]

AYO

[tardy walrus]

What a coincidence

How’s the medication?

[hallow oriole]

BAD

[tardy walrus]

0:

[hallow oriole]

it doesnt workkkk

all it does is make me less hungry

[tardy walrus]

that don’t sound good

Have you talked with your doc about it?

[hallow oriole]

nope, no appointments yettt

[tardy walrus]

Ohnuuu!

Valley must git gud.

Smh

[compact crypt]

can you recommend best introductory textbooks on graduate level real analysis

like measure theory and lesbesgue but less terse/difficult than rudin RCA or Folland

[cursive gust]

can anyone recommend a book about multivariable calculus and linear algebra

[sage python]

@compact crypt try Bass Real Analysis for Grad Students

@cursive gust Shifrin Multivariable Mathematics

[cursive gust]

thx

[gray gazelle]

What’s the easiest book for differential geometry

[ripe bough]

Is there any site for quadratic equation or function of quadratic equation

[sage python]

@ripe bough try Khan academy? They might have good explanations of the stuff

[ripe bough]

I will try it. Thanks for info

[foggy relic]

Can anyone recommend an accessible book on Lie Algebra, their classifications, and representations?

[sage python]

@foggy relic Try Humphreys

[drifting elm]

I know this has been said but I will second the statement that you do not need calculus for machine learning. You only need to read about machine learning. You are not a developer of the machine learning framework. you are a user and a developer of end use applications that use existing machine learning software libraries and data sets.

[mild cedar]

Yeah. But i have willingness to make my 9wn algorithms some day. Anyways..

[drifting elm]

if you want to contribute to an open source software project you will need to have a lot of practice making clean code that works well. most likely in C++.

https://towardsdatascience.com/the-mostly-complete-chart-of-neural-networks-explained-3fb6f2367464

here is a list of the different kinds of neural networks.

imagine having tested each one of these first many times and being excellent at contributing C++ code to an open source project. you have to work your way up from the bottom. that means you just need to start using machine learning software and reading machine learning books.

for now you only need python and pytorch

nothing else matters

@mild cedar

[mild cedar]

ohok. Thank you. Actually, I have been a programmer for 2 years and I was learning things in a fast phase. So, I am pretty much familliar with programming especially python and C#. Anyways, I am trying to grasp with sickit-learn now. I bought the "Hands on machine learning with ...." the author is Aurelien Geron. And I am trying to go with the book's flow.

So, @drifting elm Let me start with data analysis and make familiar my self with pandas and matplotlib.

[mild cedar]

Nvm.. the book has them combined together. Let me directly work with the book tho..

[gray gazelle]

Any Beginner friendly Disscreate Mathamatics book suggestion ?

https://www.amazon.in/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709/ref=sr_1_5?crid=2LHRMUR04105G&keywords=The+graph+theory&qid=1653198006&s=books&sprefix=the+graph+theory%2Cstripbooks%2C241&sr=1-5

Is this good if i know nothing about discreate maths...

[formal zinc]

Hey guys sorry to disturb, i wanted to ask what is the best complex analysis book?

[runic hatch]

There’s some recommendations in the pinned messages here

[flint inlet]

Hey guys

How are V.Govorov books?

[gray gazelle]

Guys read to kill a mockingbird

Best book eber

Ever

[drifting elm]

that dover book on graph theory is as good as any other book on graph theory. graph theory is only one part of discrete math. you will definitely need boolean algebra. you probably want to learn group theory at a minimum if you don't do abstract algebra. abstract algebra is a larger area that includes group theory. Graph theory has many applications for computer science and algorithms. you also want to learn combinatorics as part of a discrete math education. you can do number theory before or after combinatorics. you should do probability theory and statistics at the same time as combinatorics. if you do statistics before combinatorics that will probably make it easier.

[drifting elm]

that sounds like a good plan. you don't need to do pytorch if you are already doing tensorflow. either one is good. the only reason I mentioned pytorch is that it seems to be gaining popularity in many businesses. you might have a better chance at getting a job with pytorch. but you can worry about that later. but pandas, scipy, numpy is used everywhere in scientific research. that is definitely a good investment for your time.

[mild cedar]

Yeah

[signal cedar]

Anyone know a good book about ODEs and PDEs?

[fading goblet]

Books by J. D. Logan in ODEs and PDEs quite nice, accessible and not that thick.

Standard references for ODEs, I think, would be Ordinary Differential Equations by M. Tenenbaum (I hope I spelled the name correctly) which from Dover.

And standard references for PDEs would goes to W. Strauss's book Partial Differential Equations : An Introduction..

[blazing canopy]

This is a tricky question IMO because both ODE and PDE can be introduced very early in a university education (e.g. more geared towards engineers) but are absolutely massive subjects that have no real standardized list of topics

[gilded coyote]

I am preparing for IMO which books to refer ??

[compact crypt]

https://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1441979395

do you have to know all of analysis to use this book for learning topology or only some parts of it?

like I've read the appendix but it does not seem to require many parts of materials covered by books like abbott/zorich

[slow roost]

it doesnt

[compact crypt]

do you think that knowledge on metric space, derivatives, sequences are enough or do you think that integration and uniform convergence is also required?

its because I'm midway through analysis textbook and I have gotten some time to study other subject so I am thinking about topology

[slow roost]

Unless you want to get into thinking about manifolds as fast as possible, there are better intros to topology

[compact crypt]

thats my goal actually

[slow roost]

But no, integration and uniform continuity aren't needed for it

[compact crypt]

oh okay

so to be clear do you think that content up to chapter 4 of abbott should be enough?

[slow roost]

Probably

If there are parts you're missing background on you can fill them in without much trouble

[compact crypt]

okay thnx

[compact crypt]

one last question: which book would you recommend for intro to topology

[slow roost]

Munkres or Crossley

[compact crypt]

thnx

[sage python]

Actually

I kinda prefer Lee to Munkres

Specifically because for most people the overly specialized stuff in Munkres is not super important

Lee just kinda narrows down to what you need to know

[flint forge]

hatcher notes

[sage python]

That too

[smoky dirge]

hi, any book recommendations for additional practice of combinations/permutations/probability word problems?

[hearty steppe]

Intro to top manifolds by Lee?

[slow roost]

what about it?

oh, yeah above they were discussing that as an intro to topology

[grave thorn]

Is Halmos a good book for measure theory?

[viscid grove]

Has anyone here have used Cohn's Measure Theory?

[loud cradle]

yes, very good book (at least the 2nd edition is, i don't know the 1st)

[sudden kindle]

Id like to learn hodge theory, any recommendations?

@sturdy sail maybe you have some recommendations

[sturdy sail]

Oh

Claire Voisin is a classic reference for this topic

But there are others ofc

Griffths and Harris also discusses Hodge Theory

In sections 6 and 7 of their book "Principles of Algebraic Geometry"

I still haven't gotten that far into Griffths-Harris tho

So idk if their treatment of Hodge Theory is on par with Claire Voisin.

[sudden kindle]

Okay

I'm check out Voisin

Thanks

💓

I think using pdes to study topology of a manifold is cool

[sturdy sail]

There's also "Complex Analytic and Differential Geometry" by Jean-Pierre Demailly, this one focuses more on the differential geometry side of complex geometry.

While Voisin does complex algebraic geometry stuff in more detail

[sturdy sail]

♥️

[sturdy sail]

Oh yeah, it is so awesome. I think that's why I am so excited to learn Kahler Geometry at some point.

There are deep applications of the theory of elliptic operators to studying the existence of Kahler-Einstein metrics and so on

This is still a big area of research

Oh btw nyamin

[sudden kindle]

Hm?

[sturdy sail]

You might like the topics this book covers

It has a brief section on Hodge theory, but is mostly review stuff.

The thing is that it like

Develops a bunch of the theory of elliptic operators and index theory

And uses these results to prove results in topology

Really cool

Ultra recommended me this book a while ago

[sudden kindle]

Interesting

[sturdy sail]

For instance, it gives proof of the Hirzebruch-Riemann-Roch theorem using these tools from analysis, some stuff on Morse Theory and it also contains a section on Atiyah's index theory.

[modern aurora]

Hi there, I wanted to prepare for IMO. I am a total beginner. Can someone recommend me some books that might be helpful at different stages of the preparation?
Thank you so much.
Have a nice day.

[worthy karma]

So, I have the Springer Texts book Understanding Analysis by Stephen Abbott. I am looking to use it to do a heavy review of the topics covered in my undergrad, and I was wondering if anyone has any opinions on the book. Would I be better off using a different book?

I also own Advanced Calculus (2nd Edition) by Fitzpatrick, but I find Abbott's text really easy to follow.

[loud cradle]

Abbott's book is good. If it has the material you want then it should be fine. The only possible downside is that it assigns a fair number of proofs as exercises to the reader - good for learning, not great for reference

[worthy karma]

Hey, thank you for this response!!

[timber copper]

Also would recommend apostol if you wanna go further into riemann-stieltjes and stuff like that

[atomic hound]

Guys, there is a book that teach about matrices in general?

[slow roost]

Basically any linear algebra book

Unless you have something ultra specific and unusual in mind

[grave thorn]

https://linear.axler.net/

[limpid gazelle]

What's a good geometry book for high schooler

[queen lake]

hey. i have a couple people who are asking for resources about complex numbers, as well as intros into them. any ideas? i know nothing other than the education I've had back in school about 6 years ago but im vague on the details, so me teaching them is a no-go lol

[turbid moss]

What books/resources are good for aspiring comp sci majors

[limpid gazelle]

If you're an aspiring cs major you shouldn't be reading books you should be coding stuff, like go on leetcode to practice problem solving or code something

[sage python]

I mean the term "aspiring" suggests that they still need to learn the utter basics

[turbid moss]

Oh no I do stuff on hackerrank,leetcode and exercise daily

But I want to prepare for the math side of it

[limpid gazelle]

Oh

[turbid moss]

Oh shit

[cursive orbit]

I'm a big fan of sipser's theory of computation book

[sage python]

Ah hmm

[cursive orbit]

although you will most likely want a discrete math intro before reading that

[sage python]

I was gonna say that the sorta "Intro programming books" that seem best are SICP, HTDP, and CP

[turbid moss]

Ah, I’m still finishing pre calc and getting that down

Should I finish that first and then move to discrete maths?

Or is their anything else I should learn besides pre calc or discrete maths

[cursive orbit]

linalg and calc are important for applications like machine learning or graphics or whatever

[limpid gazelle]

I think you should get started on calculus, then discrete and then linear algebra

[turbid moss]

Should I learn just Calc 1 and then discrete, linalg?

[limpid gazelle]

Yeah the order is not very essential but I'd still recommend calculus before the other two

These topics like alphyte said are very important in cs applications

For calculus going through steward's calculus is honestly pretty good

[cursive orbit]

I don't really like the standard calc textbooks, cuz they're so unnecessarily huge

[turbid moss]

I’m just going through stuff on khan academy

[limpid gazelle]

That works as well

[limpid gazelle]

That's fair but I still think steward is pretty good and especially good for having a lot of exercises

Steward is large because it contains multivar calc as well

[gray gazelle]

Any learning sources for probability, stochastic process. I am preparing for an internship which includes quant trading. Any input is highly appreciated.

[atomic hemlock]

What's CP?

[gray gazelle]

Competetive programmin

[sage python]

Composing Programs

I know Berkeley uses that for their intro to CS course

@glad prairie confirm?/what do you think of it?

[still jay]

Anyone have any recommendations for books on Riemann Surfaces?

[solemn rover]

I really loved the book by Forster, "Lectures on Riemann surfaces"

I think "Algebraic Curves and Riemann Surfaces" by Miranda is a common recommendation. I don't know anything about it

[still jay]

thanks, I'll check both out

[fluid skiff]

I am currently reading forsters

It's nice

Feel free to discuss

[remote ginkgo]

thank you celeryk

[gray gazelle]

any algebra 2 (quadratic equations, exponential equations, logarithms ect..) book that is well written?

[lime sapphire]

openstax

[gray gazelle]

Thanks

[lime sapphire]

or hall and knight's higher algebra

or gelfand algebra

[gray gazelle]

Thanks and im open to more if you have lol

[thorn cloak]

Hey all, I’ve recently self-learned AP calc BC, (basically a dumbed down version of calc 1-2), but really want to learn more before college as I enjoy math (and might double major, if not then a minor, in it). Should I go straight to learning MV calc or learn something like linear algebra? I mainly want to get better at thinking mathematically and learn I guess a “real” math class. By the by, are there any book recommendations that I should start with?

[loud cradle]

hard to go wrong with linear algebra imo. It doesn't require much in the way of background, you probably already know something about it, it's far less grungy than multivariable calculus (and any good treatment of MV calculus requires linear algebra anyway!) And linear algebra is used everywhere in the sciences/engineering etc, as well as in other mathematical disciplines. The book by Friedberg, Insel and Spence is a fairly widely used intro, and it's pretty good

[subtle mango]

lin-alg first will help a lot with intuition in mvc

[solemn rover]

Yeah they're not totally independent

Actually I know of a multivariable calc textbook whose entire first five chapters are nothing but linear algebra.

Apostol's Calculus Vol. II

[subtle mango]

wish i knew lin alg before mvc

would've made stuff like jacobians actually make sense

[wicked trout]

Geometry has Euclid Elements. What is the cult classical book for the mathematical analysis?

[thorn cloak]

I see, thanks for the help everyone!

[loud cradle]

hmm, maybe hardy's "a course of pure mathematics"? it's obviously nowhere near as old as euclid but it is over 100 years old (first published in 1908) and probably one of the first fully rigorous textbooks for calculus/analysis, or at least one of the best-known early ones

[wicked trout]

Are there any greeks who tried to think about that?

[loud cradle]

yeah, archimedes for one, check out his "method of exhaustion", which was basically a form of integration to find areas

[wicked trout]

Thanks!

[loud cradle]

cheap dover book with some of archimedes' stuff : https://www.amazon.com/gp/product/0486420841/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

[blazing canopy]

It depends on what is the definition of analysis. If we allow calculus, then the first part of Newton's Principia outlines the basic concepts of calculus in the context of mechanics. There's also L'Hopital's book in calculus that set the groundwork for the study of the topic at the university level for decades to come

As far as classics go, those two books were some of the most influential math books ever

[slate quarry]

Lang & Murrow

[flint inlet]

Hey guys, I am not doing math as a school/student but out of curiosity. I have good foundation in school level math. Now, I wish to read some books on the topic. Any recommendations?

[gray gazelle]

@flint inlet book of proof

[hallow oriole]

anyone know any number theory books that start off from like basic number theory and work their way up? same for combinatorics

[flint inlet]

for that i will have to study logic and not interested in that

i am asking for a book where i can apply my existing knowledge

i don't wish to train in new math

[gray gazelle]

@flint inlet i don't follow

you want something to strengthen your knowledge on hs math ?

[flint inlet]

i completed my school and didn't study math seriously after that and don't wish to (concepts like rank of a matrix, fourier series, etc). I wish to study a book which is fun and I can apply my existing knowledge

i mean, you understand that these are college math concepts, right?

[gray gazelle]

i see

[hasty turret]

Well,I suggest going through rabbit holes

Are you interested in anything in particular?

[flint inlet]

nope

i like calculus and equations though. and sometimes a few number games are fun

[hasty turret]

No,I mean like applications

Stuff like graphics

Or simulations

[flint inlet]

no. i have no knowledge about these

[gray gazelle]

kaleshi

do you know about gelfand's algebra ?

[flint inlet]

heard about it. don't know what it is

[gray gazelle]

it's a challenging book that covers topics in hs math

maybe that's what you are looking for

[flint inlet]

ok.

and what is your review of recreational math and essays book

that alan turing one

[gray gazelle]

i didn't finish any

[hasty turret]

If you are just gonna do recreational math,I don't think you will ever get into real math

[flint inlet]

i wish to take a break from real math for quite some time. and presently too, i got into real math through recreational math

[hasty turret]

What real math do you do

[gray gazelle]

oh

i have an advice

do you know linear algebra ?

[hasty turret]

By "real math" I mean fields like analysis,algebra, topology, combinatorics, logic,number theory or like more specific subfields

[flint inlet]

well, i don't see anything as real math or pseudo math honestly

[gray gazelle]

if you want recreational maths

[tight crag]

If they haven't done something on the level of book of proof then they wouldn't have done that drake

[flint inlet]

because everything just gets derived by logic

[gray gazelle]

you can try learning how to code

and make some animations

[flint inlet]

i am a btech graduate buddy

[gray gazelle]

perfect

you can make animations then

that's really cool

[flint inlet]

umm.....honestly i am not that much drawn towards coding and computers tbh

[hasty turret]

Ok,Animations will lead you into a rabbithole

[flint inlet]

animations

[hasty turret]

Which is good

[flint inlet]

do you mean blender?

[hasty turret]

Could be anything

Blender is a subset

[gray gazelle]

i meant manim, drake

like 3b1b

maybe i can recommend good math youtube channels ?

and you can look up concepts you find interesting

[flint inlet]

good idea

[hasty turret]

Ok,sure but you need some motivation to do math

[gray gazelle]

• numberphile(any of brady's work is good)
• 3b1b

help me here drake

[flint inlet]

3b1b is too complex for me.. numberphile is meh

[hasty turret]

I guess Micheal Penn?

[flint inlet]

i mean not too complex but sufficiently complex

[gray gazelle]

black pen red pen

[hasty turret]

bprp is not really a good channel to learn math

It's just integrals

[flint inlet]

it is academically inclined

i believe

[gray gazelle]

it's entertaining tho

[flint inlet]

i want something more recreational

[gray gazelle]

mathologer

he's really cool

[flint inlet]

ok let me check out

[flint inlet]

he sounds mystical to me

not into that kind of stuff

like astrologer

very elementary

[gray gazelle]

i don't know then

[weak violet]

? he "sounds" mystical?

[flint inlet]

like an astrologer

[hasty turret]

Are you sure you want to do math for recreation?

[flint inlet]

yes

[heady ember]

Then start reading some math books and do the exercises

Like you can start with calculus or LA

For instance, if you are dedicated enough to mathematics and you like maximal pain and suffering, use Spivak's Calculus

[random raptor]

I think the classic recommendation in this case is Martin Gardner's books and puzzles.

Another idea would be to try out problem books on combinatorics.

[modern aurora]

Hi, can anyone recommend me beginner level competition math books?

[random raptor]

How beginner-level are we talking?

[modern aurora]

starting just after the standard school material?

[random raptor]

If we're talking high-school mathematics competitions like the Olympiads and such, then you'll already need to have a rather unusual repertoire of techniques at your disposal.

[modern aurora]

there is just so many resources, i find myself really confused

[random raptor]

I would recommend checking out Art of Problem Solving.

[modern aurora]

after aops?

[random raptor]

One recommendation I can give you is this:

https://www.maa.org/press/maa-reviews/browse

Look up the problem book category.

There's extensive reviews provided for a lot of them.

[modern aurora]

thank you so much

[unreal elm]

Imo this is the best calculus textbook ever written and should be used in every calculus class

[cursive orbit]

imo not every calculus class is (or should be) geared towards mathematicians

[unreal elm]

I’m just mememing lol

Ik

[foggy relic]

Whats a good book for a second course in differential geometry? My class used Andrew Pressleys book which ended with the global gauss bonnet theorem and I liked the subject so I want to learn more.

[compact crypt]

don't you usually learn about manifolds after that?

like j lee's introduction to smooth manifolds

[foggy relic]

no clue lmao

[light solstice]

only if they learn about proofs before taking calculus, otherwise no

[light solstice]

regardless of whether they are mathematicians * but only if they had a math fundamentals class

[flint forge]

Intro to proofs classes and the like are not a prereq to spivak

But spivak is a poor choice for most students

Just because the approach is really not that relevant to people who aren’t interested in mathematics for it’s own sake

Which is (shockingly) most people

[gilded thistle]

Anyone have any suggestions on books for learning discrete math? I'm planning on using the eighth edition by Kenneth H. Rosen and was wondering if that is good enough

[slow roost]

Do Carmo's Differential Geometry of Curves and Surfaces if you want a deeper dive into classical diff geo

or either Boothby, Tu, or Lee if you want to get into manifolds

Visual Differential Geometry by Needham is also fantastic and can be read without knowing manifolds

[hearty steppe]

What do you mean here? I think I find a lot of value in venturing into abstract mathematics and applying it to STEM research working with data sets

[flint forge]

Most people are also not interested in that hahahaha

I just mean that most people learning calc probably don’t need anything at the level of spivak

[hearty steppe]

Oh

[flint forge]

And that it would be a poor pedagogical choice for them

It’s a great choice for like

An honors calc class

I’d wager most people in stem have at least a little appreciation of math for its own sake / why it’s true

[hearty steppe]

It’s an intuition thing I guess

I keep taking my own experiences for granted

I need to stop doing that, cuz I gotta appreciate my experience as my own

[slow roost]

yeah most people who have just taken precalc aren't really ready to jump into spivak

but could handle a more gentle calc course

[tepid prairie]

At least Spivak has solutions online.

[unreal elm]

I was mememing but yeah gotta agree with this, as a pure math ppl

I think every honours Calc class tho for the pure math majors and maybe for mathematical disciplines with lots of proofs, like CS, should use Spivak tho

I will die on that hill

[subtle mango]

rosen should be enough. i liked the book

[mystic orbit]

You do?

Huh

[hallow oriole]

not true

my stance is as such

why would you ever ruin math by applying it??

[robust marlin]

[coarse frost]

josh feels attacked

[robust marlin]

i'm not angry just disappointed

[coarse frost]

understandable

[broken meadow]

applied math is Good

[coarse frost]

i havent done any pure maths or applied maths to agree or disagree

[blazing canopy]

There's a well known essay about how there are two kinds of mathematicians. Those who seek to understand mathematics to solve problems, and those who solve problems as a way to understand mathematics

(I'm 100% in the first category)

[subtle mango]

i seek to understand math so i sound cool online

[hearty steppe]

Don't worry, josh will go for the red pill soon enough

I mean what I do is applied but I still focus on the pure route

[hallow oriole]

applied math is good yes

but like

it's still ruined

[robust marlin]

This is such a terminally dumb take I'm not even gonna bother

[hallow oriole]

ruined isnt bad per se

it's just

"reduced to a state of decay, collapse, or disintegration" such that it's not the same

but hey i could very obviously be wrong about this my hate comes from a whole fucking year of ap stats and ap phys online

im sure engineering is cool

[cursive orbit]

[hallow oriole]

maybe

[cursive orbit]

"applied math" is neither of those things

[hallow oriole]

stats and physics aren't applied math?

[cursive orbit]

they overlap with applied math, but neither ap stats nor ap physics are applied math

[hallow oriole]

what's applied math, then

also if not applied math wtf was i being taught lol

[cursive orbit]

stats and physics

[hallow oriole]

actually i do know what i was being taught in stats

fucking english

stats was a reading comprehension class

[hallow oriole]

.

[cursive orbit]

mathematics for the purpose of application in other subjects

[hallow oriole]

subjects like statistics and physics?

[cursive orbit]

yes

however, you don't learn any mathematics in either ap physics or ap statistics

[hallow oriole]

hmmm

so the math is good

but warped into abomination by the machinations of physics and statistics and the ap curriculum

[robust marlin]

Lmao what

[hallow oriole]

i just really hate physics and statistics tbh

[robust marlin]

I'm not sure that M-theorists would agree that they have warped mathematics into an abomination

[hallow oriole]

and i thought they were applied math

[robust marlin]

Quite the contrary in fact

[hallow oriole]

so i guess i thought applied math was bad

[hallow oriole]

that's fine, this is a matter of opinion

they don't have to agree with me

[robust marlin]

How exactly does physics warp mathematics into an abomination

[hallow oriole]

hm

i just don't like it

¯_(ツ)_/¯

[robust marlin]

Lmao OK well that's a very different thing to what you were saying

[hallow oriole]

i like math and i hate physics

and physics uses a shit ton of math

which i thought made it count as applied math

but now im told that's not what applied math is

[cursive orbit]

ap physics does not use a "shit ton" of math

[hallow oriole]

so applied math is good

but physics is still bad

[cursive orbit]

it uses basic calc at most

[robust marlin]

I mean physical models are mathematical models

[hallow oriole]

i have the same issue with other things that are similar

like

hmm

[flint forge]

ap physics is well known to be a strong upper bound on the field of physics in general

[hallow oriole]

idk but im sure i will lmao

[cursive orbit]

kekw

[hallow oriole]

also im ngl i thought fucking algebra-based physics was too much

gods

i hate physics so much

[robust marlin]

I think you're maybe a little early in your career to be saying you "hate physics"

[hallow oriole]

no, i'm absolutely not lmao

i have literally talked with a psychiatrist about it

[robust marlin]

You don't know even know what physics is?

[hallow oriole]

ap physics ruined my mental state for months lol

[cursive orbit]

ap physics != physics

[robust marlin]

AP physics is not physics

[hallow oriole]

field of science that studies the way the world works

[cursive orbit]

I hate group theory but that does not mean I hate mathematics

[hallow oriole]

sure, maybe there's fields of physics i will like

i agree

that is possible

but, to get to them, i will have to learn the physics i do not like

and i won't do that to myself

[robust marlin]

Don't rule out an entire field of study because you don't like some high school level course about it

And certainly don't make claims that physics is an abomination of mathematics lmao

[hallow oriole]

bleh, that's subjective so i can

you are probably correct though

[flint forge]

this is literally every physical field of science

[hallow oriole]

it might be too far-reaching

[robust marlin]

Like the standard model of particle physics is a group-theoretic model

It's the purest of pure mathematics

[hallow oriole]

hmmm ig the field that studies matter and it's behavior then

wait

[flint forge]

thats chemistry as well

[hallow oriole]

i think that def applies to everything too

yeah

what's physics then?

[flint forge]

physics is a field invented to assist with mathematical research grant proposals

[hallow oriole]

that's cool! i love that! i love noether's theorem and all the weird shit you get from quantum mechs!

[robust marlin]

This definition is also true of mathematics if you're a Platonist lmao

[hallow oriole]

i just don't like any of the physics i've been taught

[robust marlin]

Sounds a bit like you do like some physics lmao

[hallow oriole]

and im pretty sure i will need to learn it if i want to get to the fun stuff

[robust marlin]

A lot of theoretical physics is great and mathematically beautiful

[hallow oriole]

but i cannot learn something i dislike lol

so it's barred from meeee

[robust marlin]

That seems like something you'll need to get over if you're looking to pursue mathematics as a field of study

A lot of the foundational shit you need to know is drab and boring and ugly

[hallow oriole]

hmmm like what

i like everything i've learned so far

i've started on like

multivar calc

and linalg

and loving it so far

[robust marlin]

Well it'll vary from person to person obviously

[hallow oriole]

i love proofs too

i dont think ive run into a part of math i dislike

[robust marlin]

Basic real analysis, for example, is my least favourite shit ever

But I need to know it to do anything interesting in analysis

[hallow oriole]

i think that's fun too

same with algebra

[robust marlin]

Perhaps you won't run into any mathematics that you don't enjoy ever

All I'm saying is that it's not a guarantee

[hallow oriole]

hmm

that is

a very good point

a very very good point

i guess maybe i shouldn't discount physics

[robust marlin]

So if you so end up in that situation it's important to step back and see the bigger picture

[hallow oriole]

completely

[robust marlin]

I mean high school physics is a boring slog through the nitty gritty computations of classical mechanics

[hallow oriole]

oooh i figured out what i dont like

computation

[robust marlin]

It bears no resemblance to quantum theory or general relativity or anything like that

[hallow oriole]

oh shit im coming to a realization here

[robust marlin]

Yeah I hate computing stuff by hand

That's why I'm an applied mathematician. So I can get computers to do it for me

[hallow oriole]

wait wait wait

my entire perspective just shifted

lmfao

[robust marlin]

Howso

[hallow oriole]

my issue isnt with the physics

or the statistics

my issue is the fucking mindless computation

[robust marlin]

Lmaon

I think a lot of mathematicians and physicists would agree with that

[hallow oriole]

if a problem is is form 1 then plug numbers x y and z into ur calc

that

is what

ap physics and ap stats are like

[robust marlin]

Yup

It's mind numbing and tedious

[hallow oriole]

the only reason i like computation in specifically math is because im forced to work through the actual solution steps and that's the fun part

omg

[robust marlin]

But very very few theoretical physicists or mathematicians actually do anything with actual numbers lmao

[cursive orbit]

physics is arguably the least mindless class of all the classes in high school that require significant amounts of computation

[robust marlin]

I hated high school physics

But actual real physics is, imo, a very beautiful mathematical description of the world

Nobody does mindless numerical calculations

Literally everyone gets computers to do it

[hallow oriole]

i took it last year and this is categorically false

maybe it was my teacher idk

but that is just a wrong statement

[robust marlin]

I mean what you're experiencing here is something that I think the vast majority of people go through

The mindless computations of physics and mathematics during high school are generally very dull

Most people hate it and leave high school assuming that's what mathematics and physics are

Which is why I said earlier you might be too early in your career to make those kinds of decisions

Like, you haven't even got to the good bit yet

I don't mean to be condescending; rather, take a look at where all this stuff leads to instead of assuming that what you're doing now is representative of everything that's potentially ahead of you

[cursive orbit]

maybe 20-25% of my physics questions on my physics c tests required more computation than adding like 50 and 25 together

[robust marlin]

Though fwiw I also think stats is a snoozefest and i've done several graduate courses in statistics lmao

Different strokes for different folks

[hallow oriole]

no you didnt come off that way at all lol dw i found this very interesting

[hallow oriole]

not my experience

[robust marlin]

Jolly good. I mean yeah you're at an exciting point in your mathematical journey. Going into undergraduate is exciting because there are so many doors open to you.

Take courses far and wide and in anything you like the look of is my advice. I did a bunch of compsci and physics courses in my undergrad and while none of it is relevant to my research it broadened my horizons for what's out there, which I think is really valuable.

[heady ember]

Yeah i said the pain part jokingly

[hasty turret]

I guess you did too much sylow stuff

[supple knot]

Guys can you recommend me a series of books since basics till calculus ig?

like openstax one

but i get bored of it after leaving it by a week or 2

[heady ember]

You can try these (they are no books but still good resources) Khan Academy and Paul's Online Math Notes

You can use Spivak's Calculus for calculus too. It's a good book, but do be warned that you need to be determined enough to do it as the exercises are known to be challenging

[fervent lava]

serge lang basic mathematics does highschool stuff, for calculus I really liked paul online math notes.

[wary compass]

could anyone recommend a textbook that covers sturm-liouville systems(preferably friendly to someone who has a weak background in ode)

im a second-year undergrad

my ode prof is teaching this, and 90% of the class are not understanding anything. We don't have a textbook to follow so its kind of hard

[blazing canopy]

This is actually quite a tricky question. There are plenty of books that cover Sturm-Liouville theory but it is not usually an introductory topic. However, there are probably a lot of textbooks that introduce some of the absolute basic concepts. I can browse my library and see if anything pops up. More generally I think it's tough to find good ODE books at the undergraduate level. Does your course have any notes?

So the absolute most introductory book on this would be Boyce and DiPrima's Elemental Differential Equations and Boundary Value Problems. It's not a great book, but I taught out of it some time ago for an engineering-oriented differential equations class. It includes a short section on Sturm Liouville problems that might be fairly barebones but the explanations might help you understand more intuitively what's going on

I found another book that I've never used, but which seems to have a decent and more thorough coverage of S-L problems, which is Adzievski and Siddiqi's Introduction to partial differential equations for scientists and engineers using Mathematica

You might find it easier to use online resources; there are online course notes and videos that might clarify some of the concepts. Probably the most challenging thing about doing this is that different resources may use different notation, which is always tricky when you're first learning any mathematical subject.

[wary compass]

we do have the professor's handwritten notes, but it's not particularly well-organized as he just uses it as his own reference in his teaching. Also I just checked out the second book you mentioned and found some practice problems, and that's exactly what I need....Thanks so much

[broken meadow]

another source which might be okay is my professors notes too but they might suffer from the same problems ur professor’s notes have

oh you asked for systems i think mine is a little too basic

[wary compass]

I would be grateful

[broken meadow]

its just single SL problems but ill share

[wary compass]

THANK YOU

God this community is so much friendlier than my university's, people here in the maths program basically never share anything, even if some courses are so hard and everyone is suffering

[broken meadow]

ok i am realizing now that the SL theory i had was in lecture form

[wary compass]

it's alright

[broken meadow]

and they’re not available in full since they’re being reuploaded

[wary compass]

thanks regardless

[broken meadow]

so here is basically a course which is happening Right Now

and so not all the lectures are up i think but these are all recorded from back when i took this a year ago and they should all be up in about 2-3 weeks at most

[blazing canopy]

Good. I did notice that the book does have a fair number of worked-out examples so I'm glad that it looks suitable.

[broken meadow]

i can post the PDE notes as well since we do sturm liouville there too but i think u want ode

ok idk where they went on his webpage oog

wait i dont even know if you can access the lectures without being a student

[blazing canopy]

Sometimes professors don't like their notes getting disseminated outside their course, I would point out

[broken meadow]

im kind of dumb

[blazing canopy]

this includes myself

[broken meadow]

yeah i think that these lectures are locked within a login

im in pain

but yes

good point

[blazing canopy]

Even if they weren't, I personally don't think it's good practice to disseminate material which is somebody else's

[hallow oriole]

out of curiosity, why? (not knocking you im genuinely curious)

[broken meadow]

ok i removed it because it does link to other places which i think definitely do not need to be shared and also they should be stuck behind a login thingy

my professor posts grades publicly

[wary compass]

yeah, I think you need to login to see those contents

[broken meadow]

alright i would alternatively suggest the nagle saff snider textbook to do some of these problems, it should be similar to boyce diprima

[blazing canopy]

A combination of (1) the material is sometimes kinda crappily organized so I don't want that being a permanent "publication" of my mathematical writing and (2) keeping the course materials in general local to the class

[broken meadow]

as an ode text

[wary compass]

cool thx

[blazing canopy]

I have never actually kept anything actually locked only to current students though. But if I knew my students were going to disseminate those materials, I might be less pleased.

[sage python]

I guess (1) makes sense. I don't know if I buy (2) as a sentiment but 🤷

Still (1) is fair enough that I may cease to mentally angry react when profs lock things down

[gray gazelle]

What's the best book for analysis?

[grand thistle]

rudin is hte classic

[runic hatch]

Apostol is also good

[halcyon garden]

Pughs a book written with love imo

[heady ember]

Yeah I think you can look at the standard texts like Rudin, Apostol, Abbott and see which you like best

[gray gazelle]

I'm extremely confused between Apostol and Rudin.

Which one is better?

[lime sapphire]

doesn't really matter

you can use them both simultaneously

or just either

[gray gazelle]

Apostol is 30k bucks here lmao

[tardy walrus]

pirate

[gray gazelle]

other than khan academy, is there a book that explains the basics of mathematics for a complete newb?

i prefer writing than reading on a computer screen

[runic hatch]

Maybe try Basic Mathematics by Lang? Those sort of books tend to be a bit pricey tho

[gray gazelle]

ill look forward

its just that i barely understand mathematics at all

but i find it absolutely fascinating

[gray gazelle]

✍️

[rocky jay]

Book for modular arithmetic and basic number theory?

[worldly crane]

what should i read after ken binmore's mathematical analysis a straightforward approach?

[timber copper]

Reviewing my real analysis for measure thry in the fall and seconding apostol; book just feels good imo

[worldly crane]

to get some further grasp of analysis

[frail lava]

There are some interesting E books on Sale including Math books like
1.Practical Discrete Mathematics
2.Hands-on Mathematics for Deep Learning.

https://www.packt.com/?utm_source=Ali-Abidi&utm_medium=influencer&utm_campaign=spring_10_dollar_2022

[sudden kindle]

Mumford's writing is so clean an elegant

I'm reading Tata Lectures on Theta II again, and its so smooth

[gray gazelle]

http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf

I just finished this what next

Im looking for pre calclius and trigonometry

[cursive orbit]

you could go on khanacademy

[gray gazelle]

I cannot

I need a book

[karmic thorn]

Basic Mathematics by Lang might be worth looking into.

[gray gazelle]

I alreay have it but the book covers most of it

[noble prawn]

Lippman-Rasmussen and Stitz-Zeager are both quality open-source textbooks that cover pre-calc and trig. The writing styles are quite different, so I suggest checking both to see which you like better.
https://www.opentextbookstore.com/precalc/
https://www.stitz-zeager.com/

[manic drum]

Hi guys. I failed exam from combinatorics. I need to be confident with basic combinatorial structures and principle of inclusion and exclusion. I need to learn it so I'm searching for some document with explained a and step by step solved problems. Do you have any recommendations ? Thx.

[gray gazelle]

Leisurely read on diophantine analysis or prerequisite texts algebraic geometry?

[karmic thorn]

Miklos Bona, A Walk Through Combinatorics

[hearty steppe]

Yea that book is a beast I recommend it too but I need to put in some work with other texts first before getting back to it

Bona very hard tho. Do Knuth and Matousek first, I’m working thru those currently in my combo journey

I’m all for another combo book rec that can make Bona a bit more approachable in terms of how difficult the exercise problems are >.>

Maybe knuth and Matousek are good enough for now

[compact crypt]

https://www.amazon.com/Real-Analysis-Theory-Measure-Integration/dp/9814578541

has anybody taken look at this book

if so is it a good book for measure theory? or are there any better books?

[eager shoal]

Has anyone used Discrete Mathematics and Its Applications (Rosen)?

Looking for a solid self study book.

[compact crypt]

it has a lot of contents

but I found them to be pretty good

previous editions also have solutions

[gray gazelle]

https://www.amazon.com/Manga-Guide-Calculus-Hiroyuki-Kojima/dp/1593271948/ref=asc_df_1593271948/?tag=hyprod-20&linkCode=df0&hvadid=312152840806&hvpos=&hvnetw=g&hvrand=6762320924197184007&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9003594&hvtargid=pla-454396476612&psc=1&tag=&ref=&adgrpid=61316181319&hvpone=&hvptwo=&hvadid=312152840806&hvpos=&hvnetw=g&hvrand=6762320924197184007&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9003594&hvtargid=pla-454396476612#customerReviews

just read this

easy

i now know that d/dx(2x) = x^2 😻

[compact crypt]

wow the art style is very old

[gray gazelle]

wdym its a timeless classic

omg i just downloaded it

[blazing canopy]

What is a good and comprehensive survey of combinatorics at the graduate level? It does not need to be a textbook, a reference-level book is fine too. I'm already familiar with some basics but I never took any discrete math courses when I was in school so this is a gap I'm trying to plug. A book that contains good examples of applications to other areas, especially those that have more of a geometric flavor (e.g. algebraic topology, computational geometry, graph algorithms, parallel computing, etc), would be ideal.

[timber mesa]

Thompson's Calculus Made Easy

[gray gazelle]

clearly a biased review

also it was their fault for drinking while reading such a masterpiece

ruins the experience imo

[hollow shore]

[loud cradle]

children have to learn to drink sometime

[gray gazelle]

exactly

what if u forget to drink water

a classic mistake

obviously just a spy for thompson and his calculus

[hasty turret]

I think the later parts of Bona might be the answer for this

[blazing canopy]

I will take a look more closely later. On first impression it looks too low level, but I'm also fine with using multiple books, especially since combinatorics is a fairly diverse topic unlike certain areas (e.g. complex analysis)

[manic drum]

Thanks, i will check it

[grizzled cypress]

any book recommendations for precalculus?

[forest sleet]

For textbook you could look at Stanley's enumerative combinatorics although I don't remember how many geometric applications it has. But it's for grad combinatorics

[hollow shore]

Serge Lang's Basic Mathematics and Sheldon Axler's PreCalculus.

[grizzled cypress]

thanks! and for calculus stewart should suffice?

[hollow shore]

For Calculus if you want a proof based approach Spivak and the likes would be a better option. Stewart is good too but it stresses more on concrete applications. So it depends on what you really need.

[grizzled cypress]

Well I want to work my way up to Spivak or a Real Analysis book, but I am concerned I don't have the fundamentals. What would you recommend

[coarse frost]

well u can use pauls online notes

[hollow shore]

for fundamentals Lang or Axler would suffice. for calc you don't need to do a compuational text prior to a proof based text. You can just jump right in with Spivak and use some supplementary proof writting text like Velleman or Hammack (optional).

[coarse frost]

and grind problems from there, after that u can try doing spivak

or even apostol

apostols book is basically analysis

while spivaks is semi analysis

[grizzled cypress]

okay thank you @hollow shore and @coarse frost much appreciated

[coarse frost]

[blazing canopy]

Thanks, I grabbed a copy from my library. It has the level I'm looking for, but definitely its focus is less on the applications. That's OK, this can still serve as a reference for me while I look at other resources.

[grizzled cypress]

@coarse frost any advantages of Pauls math notes over a book like Stewart?

[coarse frost]

hmmm

stewarts book as far as i have heard isnt very "abstract" its much more applications based, while pauls online notes seem less biased in either side to me

[grizzled cypress]

sounds good!

[coarse frost]

[livid ermine]

van lint is more advanced than bona and covers quite diverse topics

and pretty much sets out to do what you are asking for

bona is an extremely good textbook also, but less comprehensive

[flint inlet]

can anyone suggest some good books for high school level math students which isn't about teaching math lessons

[heady ember]

Not a book but Khan Academy is a good resource

[blazing canopy]

OK great, this looks very promising, thank you. Will pick it up shortly and look through it.

[compact crypt]

https://www.amazon.com/Introduction-Analysis-Graduate-Texts-Mathematics-ebook/dp/B07WFWGG5Q

has anyone used this before?

the reviews in sites like maa seem to be good but I dont think its a very popular book

[livid ermine]

I don't know if its any helpful, but I've read metrics, norms and inner products by the same author, and I think that book is very well written.

[compact crypt]

oh

how was the writing style and difficulty

[livid ermine]

I think it was very well-written and had good, but not too difficult problems. It reminded me a lot of terence taos analysis 1&2 books if you've read those.

[compact crypt]

okay thnx

[viscid grove]

Is measure integral and martingale good book for novice?

Also, is it as extensive as Folland or does it have lesser content?

[gray gazelle]

Which is better in your opinionor which has more

[noble prawn]

Both are excellent. Iirc, Stitz-Zeager also covers some basic linear algebra stuff (in addition to the usual precalc/trig material) and some sequence stuff that is usually covered sometime in Calculus.
But I'd say the writing style is the true difference between the two books. Both are very well-written, but different people have different tastes in mathematical exposition. Hence why I recommend taking a look at both books (compare how they each teach a particular topic) in order to pick the one that's a better fit for you

[gray gazelle]

OK thank you

[compact crypt]

https://www.amazon.com/Real-Analysis-Theory-Measure-Integration/dp/9814578541

has anybody had experience with this book?

if so can you tell your opinions about it

[gray gazelle]

Any practice test textbook recommendations for Year 11 Math Extension 1?

any french mathematicians around? could you suggest some libraries to download french maths textbooks? in particular, i totally fell in love with this series: https://www.editions-ellipses.fr/218-mathematiques-a-l-universite
I love their teaching style and that they have problems at the end of each chapter with solutions. if you can recommend other such series i would also be grateful (i'm not actually french, but I haven't seen any similar series in other languages)

[hallow oriole]

hammock should be done anyways tbh

everyone should know the very basics of set theory

[tardy walrus]

Good morning valley!

[coarse frost]

[hallow oriole]

hi slurppp

hi shy >.>

what's with the :hmmm: >.>

[slim peak]

You may find a part of it on several websites like libgen

The Analyse de Fourier dans les espaces fonctionnels is a very good one

The one called Extension de Corps - Théorie de Galois too

[gray gazelle]

Good books on Partial fraction decomposition?

[hallow raptor]

I doubt anyone's ever written a book for that. I imagine Khan Academy should do the trick. Partial frac is actually just chinese remainder theorem for polynomial rings so, if you want to learn more, it might be worth picking up some ring theory

[gray gazelle]

@hallow raptor any book you'd recommend?

[hallow raptor]

Khan Academy is good; I dont know any specific precalc/calc books

[gray gazelle]

Thanks

[hallow raptor]

Anyway, I was wondering if anyone had any good recommendations for probability books for undergrads. I'm reading probability with martingales, but there aren't all that many problems in there.

[tepid prairie]

Ordinary Differential Equations by Morris Tenenbaum actually has a nice section on it and you can read it in about 10 minutes and just do some of the problems and you'll be set.

[gray gazelle]

@tepid prairie thank you

[warm glen]

i heard that lovasz' combinatorial problems and exercises is very hard but it looks like it gives a pretty good overview of lots of combinatorics stuff

[forest sleet]

oh looking at the cover of van Lint and Wilson I think my uni's grad combinatorics class also used this book

[blazing canopy]

Yeah looks familiar, probably it was the standard text in my school too, I just never took the course

[quick hornet]

Hey, FYI that this room is now visible to users with the Studying role, which is an opt-in role intended to prevent being distracted by the "social side" of the server; so we're going to be a bit more strict with enforcing the "no off-topic conversation" stuff here from now on. We won't ban you or anything, but if you're asked to move to another discussion channel, please do!

[blazing canopy]

A similar policy for other channels might reduce the frequency with which people ask for help in the general channels

[quick hornet]

it doesn't.

people asking for help there is invariably due to them either not reading the rules or ignoring them

adding more rules wont help

[blazing canopy]

If they can't post in or even view that channel without taking a role, then they'll never know how to take that role without reading the rule

I'm in a few servers like this, where every channel is opt-in, where the very act of opting is more or less gated by reading an instruction

The benefit is that the user is navigated clearly towards their goal. Users looking for help would check off "I'm looking for help" and they wouldn't be misguided towards discussion channels, which would remain hidden

[brittle latch]

thank you mods!!

[tulip blade]

You dont need a book devoted to partial fraction decomp. Just look up how to do it.

[fickle granite]

Recommendations on numerical analysis books?

[brittle latch]

https://nhigham.com/ not a book but a good start

[south salmon]

A good book for numerical PDEs is Leveque Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems
For introductory numerical analysis, I liked Burden, Faires and Burden Numerical Analysis

[fervent lava]

Thank you finially.

[gray gazelle]

thank you! shame not all the books are available though, they are such a pleasure to read!

[subtle mango]

texts on C* algebras and its prerequisites?

[gusty smelt]

im liking dana williams notes rn

you probably want to have done a first course in functional analysis first tho

I also read a few chapters of gerard murphys book on the topic, I personally thought the exposition was dry and gave up later

[subtle mango]

https://math.dartmouth.edu/~dana/bookspapers/cstar.pdf

these ones?

[gusty smelt]

yep

[subtle mango]

dope thanks

if i read functional analysis by Brezis would it still be necessary to read a text dedicated to PDEs

considering the full title is “Functional Analysis, Sobolev Spaces and Partial Differential Equations”

[south salmon]

No, just knowledge in analysis is necessary

[subtle mango]

oh i meant this as a different question from the one about C*-algebra

should’ve specified that oops

as in, does Brezis suffice as a text for PDEs as well

[coarse frost]

idk, idt everyone should read a proof book

[south salmon]

I haven’t read the PDEs section of brezis, but for PDEs, Evans is also a good book for reference

[subtle mango]

gotcha thanks

[south salmon]

But for functional analysis, brezis is good

[tardy walrus]

Classic physicist

[coarse frost]

i meant people dont need to read a book about proofs

they should just go straight to a book that uses proofs

[gray gazelle]

And then they can practice using proofs

[coarse frost]

indeed

exactly my point

[heady ember]

Yeah I think I agree too

Personally I read a bit of Rosen for discrete math but found it boring so just read loch's summary of proofs and just went on with reading other books lol

[halcyon charm]

what is the good book for jee advanced

[storm pulsar]

Can anybody recommend me a good book or some nice questions for practicing derivation and integration questions?

[karmic thorn]

Problems in Mathematical Analysis, Demidovich.

[heady ember]

If you want really challenging qns you can see if you like Spivak

[storm pulsar]

thanks

[heady ember]

Taking a look at like the second chapter of integration in Spivak iirc, you'll see one of the questions is on the Gamma Function lol

[compact crypt]

https://www.amazon.com/Complex-Analysis-Graduate-Texts-Mathematics/dp/0387985921

has anybody seen this book

[uncut zealot]

What's a good intro differential geometry book?

For someone who knows a bit of real analysis, some point-set, some complex analysis?

[heady ember]

Ok im obviously not an expert. But what I have heard as an outstanding differential geometry book from many ppl here is Lee's Intro to Smooth Manifolds and his series on manifolds in general

Loring Tu is another I have heard ppl reccomend before

(Lee is the reccomendation I hear of most often)

[coarse frost]

these are the recs i have heard as well

also Lees intro to topo manifolds, he introduces the topology needed for it

[fervent lava]

There's also spivak.

[coarse frost]

spivaks book is mvc

[grand thistle]

spivak also has a large 5 volume set on differential geometry

[coarse frost]

oo

i didnt know about that

[uncut zealot]

I always got the impression that was meant to be more of a reference than an introductory textbook

[grand thistle]

just curious, what book is your profile picture from?

[uncut zealot]

http://math.univ-lille1.fr/~ramero/CoursAG.pdf I think

[cursive orbit]

calculus on manifolds is also intro diff geo

[runic hatch]

It’s really intro stuff, but yeah it can serve as a nice starting point

I have heard that it contains some major errors though, so perhaps find some errata online

[coarse frost]

[compact crypt]

btw does freitag's complex analysis require some knowledge regarding compelx variables?

i've done munkres topology and analysis by abbott but I find some parts of the book difficult to read

could there be another material that I might need to know?

[hybrid chasm]

Depends on your interests

But like

Lee is probably the best all-around text, for some definition of “all-around”

Tus book is a lil more introductory so you might like it more (iirc lee’s book requires knowledge of fundamental groups)
And it contains the prereq material for tu’s other books (“differential geometry” or “diff forms in alg top” the latter seems to be pretty based)

[dusk sonnet]

im trying to self study the pre-ap algebra 1 course, any textbook recs?

[subtle mango]

dunno about textbooks but khan academy should suffice

[cursive orbit]

that should be enough

[foggy relic]

Elementary differential geometry by Andrew Pressley is good, covers material up to and including Gauss-Bonnet

It only assumes calc 3/linear algebra and introduces all the analysis/topology needed

[vestal sphinx]

Does anyone know of a quick and dirty resource to learn about the group algebra of a finite group and also FG modules? In the very beginning of Gordon James' book The Representation of the Symmetric Groups he says the reader should be familiar with it

[night prism]

David Marker Model theory

[worldly crane]

ץ

[night prism]

That’s assuming you mean Group algebra as an algebra; not the group theory itself

[brittle latch]

are the problems in Artin's Algebra usually worthwhile? sorry if this is a dumb question but another algebra book i was looking at had really tedious questions (i understand tedious questions are often needed but still)

[dapper root]

Definitely do not use Marker for that

[night prism]

Did he mean the group theory itself? Or you just don’t fancy Marker?

[dapper root]

I mean that model theory to learn about group algebras is silly

They really obviously mean they want to learn about what C[G] is and some basic facts about them, and about finitely generated modules

[night prism]

Oh ok, I misinterpreted then; I saw ‘quick and dirty’ and group algebra

[solemn rover]

you still shouldn't recommend a book on logic to someone asking a question about algebra

where does marker reference group algebras

i'm looking in the index rn and i can't find it

[night prism]

Are groups not an instance of algebras?

[hearty steppe]

Groups are associations

Mostly

[night prism]

Alright, bad recommendation, then

[solemn rover]

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

this is what we're talking about if there's any confusion left to clear up

[restive raptor]

I think dummit and foote should have exactly what you need, since D&F has a chapter on representation theory whose first section is "Linear actions and Modules over group rings". That and the module section of the text should give you everything you need

[vestal sphinx]

Great, thanks a lot! I'll go have a look 😃

[gusty smelt]

my profs notes are good : https://drive.google.com/drive/folders/13QqswmY7gHF39_YnmV6blcilm3ZZ_tSd

based on lee

we covered ch1-17 this sem

so its that

[brittle latch]

consider these yoinked

[heady ember]

Our notes

[fading goblet]

Is there any recommended resources to learn Semiclassical Dynamics/Semiclassical Analysis, e.g. Quantum Chaos, Quantum Scars, Gutzwiller Trace Formula, etc.?

My background is in Dynamical Systems in the levels of S. Wiggins and Classical Mechanics in the levels of V. I. Arnold and Goldstein..

Any recommendation would be helpful. If there is any recommendation regarding prerequisites (such as I should study Quantum Mechanics, etc.,), let me know..

Thank you in advance..😄

[forest sleet]

for semiclassical analysis there is the (math) book by Zworski

although the quantum chaos part is only really the very last 2 chapters

probably the fastest way to get to a version of the quantum ergodic theorem is notes like https://www.math.univ-toulouse.fr/~bouclet/Notes-de-cours-exo-exam/M2/Shnirelman.pdf

I'd definitely recommend learning some quantum mechanics, like from Griffiths or Shankar

For quantum chaos topics specifically, there is the (physics) book by Haake et al Quantum Signatures of Chaos

[fading goblet]

Thank you for the link, I'll definitely check it very soon..😄

[fading goblet]

Do you recommend to study quantum field theory or relativistic quantum mechanics? Or is it overkill at that point?

[fading goblet]

I'll try to check this one out again, because last time I check, they kinda need to have statistical mechanics ready and my skills is very rusty in both thermodynamics and statistical mechanics..😅

Perhaps I could sniff something out better..😄

Once again, thank you for the recommendation.. I'll take a look to Zworski and brush up my quantum mechanics..😄

[forest sleet]

You shouldn't need qft or relativistic qm at all, just the fundamentals like eigenstates, Schrödinger equation, time evolution, and then some intro to the path integral formulation and semiclassical approximation. If you want to do the supersymmetric sigma models later then those involve field theory but it's the condensed matter kind not so much the qft kind.

yeah the book by Haake might be overkill. There's probably some lecture notes or arxiv review that would be a much briefer introduction. I kind of learned it through quantum graph papers but that's a specific simpler case.

Zworski Semiclassical Analysis doesn't do qm so much, the book is more about pseudodifferential operators in semiclassical analysis. If you want to read it for quantum chaos you probably want to skip around the chapters a lot, just reading the chapters on Wigner-Weyl quantization, Egorov theorem, local Weyl law, and then the last 2 chapters on the quantum ergodic theorem.

[subtle mango]

time evolution my beloved

[fading goblet]

Okay then, I think I would give Griffith a try, although I remembered that Griffith can be quite verbose.

Most of my exposure to QM mostly from my QM undergrad class lecture notes (based on Gasiorowicz) and suddenly changed to Sakurai books in the second course of QM. Although I could follow Sakurai books nowadays, it could be said that I quite traumatized by the experience.🤣

If I'm remember correctly, Haake used Random Matrix Theory in their book, which kinda different from Zworski and most math books in semiclassical analysis..

Thank you for the pointers, this will be really helpful when I try to navigate through the book..😄

[forest sleet]

yeah Haake and Zworksi cover pretty different topics, Haake is definitely more focused on quantum chaos though

the physics quantum chaos books will generally have more rmt I think

but not so much can be rigorously said about agreement with rmt level spacings

It seems the math focus in quantum chaos is more on quantum ergodicity/unique ergodicity

[fading goblet]

I really agree on this.. Most of math paper/articles in quantum chaos tried to focus on quantum ergodicity, when I try to look up for references..

Meanwhile physics touching quantum chaos when discussing quantum optics, quantum information, or open quantum systems..

[shell acorn]

Preap is considered honors in some schools, they are practically the same thing I believe

[viscid grove]

Do I need to do fourier analysis before tackling Steins Complex analysis?

It seems to be heavy on fourier

[forest sleet]

no, you can do complex analysis without it, might just skip some of the exercises or sections specifically about fourier analysis

[gray gazelle]

is there any book that is softer han isaac newtons principia mathematica

[dapper root]

Why the hell are you reading principia Mathematica. I think any book on calculus that was made in idk, maybe at least the last century will be easier 😭

[gray gazelle]

because im just curious on how the foundations of classical mechanics and his theories were made

[golden locust]

If you're interested in it as a primary source you can't really switch to a softer book

[heady ember]

Spivak's Calculus: Hello there

[random raptor]

What is a solid problem book on linear algebra?

Tricky and clever problems are appreciated.

I basically want a counterpart to something like Kaczor and Nowak's analysis problem books.

[quartz ruin]

college algebra & trigonometry book
i'm a highschool student, i want to learn mathematics from scratch

[runic hatch]

Khan Academy is a good starting point and a useful supplement to any books that you may use

[karmic thorn]

I'm not familiar with a single source but Artin and Axler's books have some good problems.

[karmic crater]

Any tips on more books like this
https://link.springer.com/book/10.1007/978-1-4419-7254-5
where rigorous maths is intertwined with and motivated through problems in physics?

[random raptor]

I see...

It's really a bit surprising to me, because I've found plenty of dedicated problem books on combinatorics and analysis and such, but few involving matrix math.

[restive falcon]

what book is this

[shy compass]

it's not a book

it's my notes for this year

[merry moss]

I am also a high school student in my last high school year I do quite well in calculus but thought to learn math from scratch from ARITHMETIC idk why tho

maybe Its another type of perfectionaizm

[heady ember]

Spivak's Calculus

[merry moss]

it starts from numbers yeah

[heady ember]

Well the first 2 chapters ask you to prove things like

• induction, some inequalities n stuff

But be warned that it is notoriously challenging

[merry moss]

I am planning on reading it

after exams

[heady ember]

Be prepared to spend hours on 1 qns lol

[merry moss]

also I have a good thing about it one of my best math teachers on youtube uses it in his calc course (but its in arabic tho)

[heady ember]

Oh ok

[merry moss]

have u done all of them

[heady ember]

no

Im on chapter 2

[merry moss]

oh cool set a goal to complete them then

[heady ember]

Already have 40+ pages of latex lmao, from 10-11 qns of C2 only

[crimson pewter]

name?

[merry moss]

@crimson pewter anaHr

[crimson pewter]

thank you <3

[bitter path]

is there a spivak study group

the proofs are hard and i’m dumb

[solemn rover]

hahahah

[remote ginkgo]

isu vaisman's cohomology and differential forms is really nice

has a good category theory intro

[compact crypt]

do you mean calculus on manifolds?

I recommend using other book

like moskowitz or duistermaat

[graceful cosmos]

I want to learn general topology. Should I get the book by munkres?

[coarse frost]

you can use munkres or hatchers notes

[graceful cosmos]

Instead of buying the book?

[coarse frost]

u dont need to buy the book

u can download it "legally"

[graceful cosmos]

Oh ok

[coarse frost]

if u know what i mean

[smoky zephyr]

you definitely can’t download it legally lol

you can just look up a pdf

[coarse frost]

i didnt say legally quantum

i said "legally"

notice the difference

[bitter path]

nope, the ‘calculus’ book

[gray gazelle]

Ah a fellow pirate I see

[runic hatch]

Lee’s Intro to Topological Manifolds is also decent as an introduction to topology

[coarse frost]

😌

[coarse frost]

yeah a few people have told me this

[remote ginkgo]

munkres + hatcher is best

there is also the book by witten et al

[gray gazelle]

Where can I learn more about smooth Banach spaces?

Classical Banach spaces would be good?

By Lindenstrauss and Tzafriri

[compact crypt]

I think the explanation is better than munkres

the problem is it does not have that many topics

[runic hatch]

yeah Munkres is broader

[compact crypt]

but tbh is amount of topology in munkre necessary for most people?

i don't know

[sage python]

The amount of topology you need to deal with depends on what you're doing

Topologists are often mainly interested in manifolds/CW complexes, and those guys aren't too messy topologically

[compact crypt]

what I have to study is stochastic calculus and complex analysis

those 2 are my ultimate goals during undergrad

along with smooth manifolds if possible

[sage python]

But the weird thing is that even if you mostly care about studying manifolds, the methods you might use to study them can push you into territories where you need things

Still, I do think topologists for the most part think less about point-set shenanigans? I know in algebraic topology, for categorical reasons, people like compactly generated weak Hausdorff spaces

Once you start getting into infinite-dimensional things (common in analysis), you need to start getting scared of stuff like countability axioms

Group actions can mess up niceness re separation, and in stuff like AG and number theory you really have to start worrying about messy spaces: Zariski topology, profinite spaces, etc (one can prob argue that you're thinking of the Zariski topology less as a geometric notion and more tracking data, while topology is more etale, but you get the idea)

So to tie this in with books, Munkres does probably more point-set than most people likely need. I like Bredon Topology and Geometry chapter 1

Hatcher notes and Lee Top Manifolds are also good

I guess among those 4 check and see which has enough of what you need

[compact crypt]

okay thnx

now I get the idea

[austere zephyr]

u guys should all read Magic Tree House

[white laurel]

By the meme master sun tzu

[white laurel]

Wow

Can't believe u did me like that

[austere zephyr]

The librarian seeing me sign out the communist manifesto, war and peace, art of war, and my little pony friendship is magic (sparkled pop-up book) at the same time

[wooden nymph]

did you read it?

[compact crypt]

lol

I remember the time when I borrowed bunch of books on various types of drugs

and librarian called my mother because she was worried

[austere zephyr]

She was worried of a possible breaking bad scenario

[compact crypt]

I was obssessed with weirdest things when I was little

[austere zephyr]

Like

[compact crypt]

like execution/torture methods, drugs, germs/parasites

crimes

and supernatural rituals

[austere zephyr]

👀

yikes

[slow roost]

that takes me back to when I discovered the infamous Anarchist's Cookbook online in 5th grade

I was fascinated, although about 75% of it is outdated ways to steal your neighbor's cable TV channels

I tried making their 9 volt battery bomb. It didn't work

[compact crypt]

https://www.amazon.com/Practice-Magical-Evocation-Franz-Bardon/dp/1885928130 I've read this book when I aws little

[compact crypt]

wait wut

[slow roost]

It was written in the 70s, when "phreaking" was big

overall it's an interesting historical/cultural artifact, but full of misinformation and toxic ideology

[brittle latch]

why is artin usually recommended for algebra

[deep bronze]

Does anyone have any book recommendations that can help me with problem solving for maths? I'm planning to prepare for math admission tests for universities in the UK e.g. STEP. Thanks in advance.

[gray gazelle]

Do more problems. You just get better at it over time.

[sacred delta]

Stephen Siklos' booklet and Cambridge's free STEP programme online are a good start if STEP problems are hard to solve right now. Otherwise it is a matter of doing a ton of past papers. And also see if you can get support from your school (can any of your teachers help? Can any previous students from your school give advice?)

[deep bronze]

Thank you so much, I've had a glance at the Stephen Siklos' booklet and I think I'll be investing a lot of time into this. Just out of interest, have u sat any maths admission exams?

[brittle breach]

polya how to solve it

[deep bronze]

thank you

[sacred delta]

Very good, you're quite early if you're applying for next year. Yeah, I have and I know how painful it is, so I'm wishing you the very best of luck

[hollow drum]

Is there another book besides Stewart that's good for multivariate calculus?

[subtle mango]

shifrin multivariable mathematics is commonly recommended

[hollow drum]

Oh shoot it has a chapter on differential forms nice. Thank you

[gray gazelle]

Do they cover all the same thing?

[fickle granite]

Has anyone every used Apostol's Linear Algebra textbook? I'm currently working through his vol. 2 of Calculus, and genuinely enjoying it, so I was wondering if this textbook was also something that other people like.

[night prism]

I don’t think it’s very well known, but I have both his calculus volumes and skimmed the second book and saw some of it and got excited about it. Decided to read up on some set theory first, but I’m looking forward to that for linear algebra (at least as one resource)

[north mountain]

Hi. I'm in middle school and want to learn about algebra. I really find it cool to learn about processes and make new ones out of them. I also think that algebra is quite beautiful, especially factoring. What books would you recommend to a middle schooler to learn algebra well?

[sage python]

I didn't even know Apostol had a linear algebra book

[primal mica]

What books would lead a dumb physicist to be able to understand this in good detail

[gray gazelle]

I thought they just had volume II that taught linear algebra

[night prism]

It’s integrated into his calculus series, so technically not standalone

Whats most people don’t know exists is that Hoffman has an analysis book

[sage python]

I've heard of that one yea

Honestly I've finally found like

3 books that probably just usurp Rudin's throne for analysis

[night prism]

I think it’s true too, it’s just that this place is an echo chamber

Which 3 in particular do you fancy?

[hot dawn]

Royden

[fickle granite]

https://www.amazon.com/Linear-Algebra-Applications-Differential-Equations/dp/0471174211

Honestly also thought that his calculus series were what covered linear algebra with Apostol, but lo and behold

[sage python]

@night prism well, I do like Rudin a fair bit, and honestly this server probably is net biased against Rudin. But I like Browder, Kriz and Kriz, and Schroder

At a glance at least