book-recommendations

[steel frost]

i thought its obvious that i mean the best ones in someone's opinion 💔

[cursive orbit]

boas

[true sail]

Knuth - The Art of Computer Programming

[sharp goblet]

What is an example of a book that does not need to be read in order and that focuses on problems rather than theory (like physics books that assume calculus as a language but focus on physics, the same but for mathematics)?

[wheat remnant]

Goated.

[near jewel]

Then I would focus on mental imaginary (unless you have aphantasia), which is the ability to imagine something. This kind of abstract ability is essential for math and other STEM subjects. I don't really know any book on that, so maybe other got one, or that you imagine things lot ofter (say a ball, why does it roll, what affects its roll, what will happen in other circumstances, etc.).

[wet sentinel]

i recommend this especially if you want something light and with minimal prerequisites (no prereqs)

[sage python]

Yeah it's just a combination of 8th grade algebra and 9th grade geometry

(Editor's note: Daminark is a lyre and a harp)

[daring wolf]

lmfao

[crimson pasture]

I actually own this book and tried to get into AG earlier this year, I stole my dads copy since hes has a phd in some field of algebra

[wet sentinel]

ohhh thats nice

i still have a long way to be ready for AG lol

[remote sparrow]

anything?

[wet sentinel]

but now unironically speaking, i would recommend apostol's introduction to analytic number theory if you havent done ANT yet. Actually i am currently studying ANT from this book and i am enjoying it.

[wet sentinel]

(currently i am doing exercises of chapter 2 so i am still at the beginning)

[remote sparrow]

complex analysis and some familiarity with basic nt

[marble solar]

You should know real analysis, complex analysis, and some abstract algebra

[wet sentinel]

usually it is complex analysis and elementary nt, but apostol doesnt assume knowledge of elementary nt and as far as i heard you can get away with knowledge of multivariable calc

[remote sparrow]

analytic number theory
look inside
analysis

???

[wet sentinel]

actually idk complex analysis and i am using it, although i havent reached the part where complex analysis is needed yet

but deltoid told me that you can get away with multivariable calc (instead of CA) if you use apostol

[remote sparrow]

probs just spamming green's theorem or smth?

complex analysis wasn't as hard as real for me

[wet sentinel]

i am not sure tbh, rn i am still at the end of chapter 2 which is about arithmetic functions and there are no analysis shenanigans yet

until now its basically playing around with sums lol

ohhh i see, well i have done until chapter 6 of rudin's PMA before and now i am revisiting it to jump into complex analysis

also because i didnt feel like i understood chapters 5 and 6 (about differentiation and integration) very well. So basically we are in the same boat

@fair fiber this is from apostol

ohhh. Actually i am studying algebra for algebraic NT

well not only for that but thats a main reason (the other being that algebra is very nice and important for many interesting advanced stuff)

who knows, actually you may like nt if you study analytic/algebraic nt

[regal ore]

Does anyone have a book recommendation for the bo-Adams spectral sequence or a book that covers it in addition to additional material?

[velvet flax]

what is the most comprehensive book on commutative algebra

[cosmic kiln]

anyone ?

with some recommendations

[remote sparrow]

i would guess eisenbud

[regal ore]

Not an expert on competitions so take my advice with caution. I wouldn’t pick up a textbook - instead I would practice on questions from previous years. A simple google search gave me problems and their solutions for hmmt, but you could probably find bmt as well. Hope this helps 👍

[cunning elk]

also keep in mind HMMT is hard compared to its peer team-based competitions for HS students

[daring wolf]

eisenbud

[bitter knot]

Do you guys have any pre-calculas practice problem books recommended?

[sour cargo]

For anyone interested, Prof. Ralph Cohen has made his (soon to be published) book Bundles, Manifolds, and Homotopy available on his homepage.

[obtuse walrus]

nice ill sure to check it out after it comes out

[stray badger]

whats a good book on inequalities

[supple mirage]

An Introduction to Inequalities by Edwin Beckenbach and Richard Bellman

[foggy quest]

what kind of inequalities? Probability? PDE?

[stray badger]

math olympiad sorts

[stray badger]

i dont think this will help in math olympiads

i want something link bj venkatchala but a bit simple

idk if thats ez and im just dumb

nothings gonna help

[supple mirage]

I heard Arthur Engel also covers that topic but I'm not sure if its Olympiad level

[pliant drum]

any good books for basic statistics?

[molten gulch]

blitzstein and hwang does some probability and statistics, wackerly's mathematical statistics is slightly more advanced and more into statistics AFAIK

[pliant drum]

ooo ty and do u know any good math inspiration books? possibly an autobiography ?

[molten gulch]

Some others here might know of some, I do not

[slow roost]

Ed Frenkel’s book Love and Math is supposed to be nice for that

Ive been meaning to check it out

[blazing holly]

Yes
This is the one i used

[blazing holly]

I’m not able to give an isolated review, as this well as notes from Triester were the texts my NLA courses used.
We didn’t cover it entirely but I liked it as it gave me a new way of thinking about processes like leasts squares & svd. It was also really interesting as some of the stuff in here are used by like google & amazon

Highly recommend if you’re an applied person as well as if you’ve taken a LA course already

[shrewd talon]

Which textbook is best for learning point set tooology (want to do algebraic topology after)

[blazing holly]

You should be good then
I’ll also send the triester notes

[shrewd talon]

Gl bro fr

[full cairn]

I like Lee's intro to topological manifolds, it contains basically everything you need for alg top. A lot of people like Munkres, it's more comprehensive, but I prefer the exposition in Lee

[shrewd talon]

Any group theory

[full cairn]

huh? In Lee?

or are you asking for a book

[foggy quest]

It's a clear book that covers classical algorithms for linear algebra, such as Cholesky factorization and singular value decomposition

[young thorn]

secrets in inequalities by pham kim hung

is absolute gold

it has 2 volumes

he solves lot of imo problems as examples

also if u wanna look at geometric inequalities i would say titu andreescu book is p good for that

[remote sparrow]

cauchy-schwarz master class

[remote sparrow]

blitzstein and hwang previews some important statistical ideas, but it does not meaningfully cover any stats material

wackerly does both probability and statistics, but i prefer blitzstein's treatment of probability

[young thorn]

i literally put olympiad style book above lmfao

[tardy bough]

I’m taking cal 1 honors, do you think self learning real analysis on the side is fine and will strengthen my calculus skills? What would you do after finishing the book, the book I’m using is introduction to real analysis Robert g.

[near jewel]

It depends what you want to do later. If you're a CS student, you probably won't need any more advanced math than linear algebra.

[tardy bough]

not even in hs yet 😭

[near jewel]

Then it's worth thinking what you want to do later. If you're thinking of doing something in math later, then doing real analysis simultaneously with calculus is doable (and maybe you'll have a stronger abstract mind), but since a lot of the stuff uses calculus and linear algebra, it won't be a smooth learning experience.

[wet sentinel]

well real analysis is proof based while calculus is calculations etc so doing real analysis may not really help you be better at evaluating integrals for example, but it does tell you why integrals can be evaluated this way or when is a function is integrable etc..

this doesnt mean that you should or shouldnt study real analysis, it depends on you. rn you are trying real analysis from what i understood, if you like it then continue and if no then you dont have to

[tardy bough]

Yeah I like it so far

[wet sentinel]

yea then ig you dont need further reason to decide whether you want to study it or no

also keep in mind what Good said, you should think about what you want to do later

for example in uni

you may think that its too early or whatever, that may be right and i am not saying that you have to think about it all day. But having a sort of a sketch of a plan for later is never bad

[tardy bough]

I didn’t research the different branches of mathematics yet so I don’t really know

[tardy bough]

🤔

[wet sentinel]

yea thats natural, you need to explore

[tardy bough]

I was thinking of pure maths but I haven’t explored the other branches

[wet sentinel]

can i know in which grade you are if you dont mind

[tardy bough]

8

[wet sentinel]

like at the end of middle school

[tardy bough]

Ye

[wet sentinel]

ohhh very nice

[tardy bough]

Just started

[wet sentinel]

yea then there is still along road ahead of you

[near jewel]

If you have a lot of spare time, do learn real analysis. Just take it as a extra bit.

[wet sentinel]

just explore many different things and enjoy the adventure

[tardy bough]

As an actual course?

[tardy bough]

U right!

[wet sentinel]

well technically its still a long road ahead of me too

[tardy bough]

What grade you’re in

[wet sentinel]

first year in uni

[near jewel]

No, more like other do sports in their spare time, you do math in your spare time.

[tardy bough]

Ohhhh

[cunning elk]

the earlier you get comfortable with nontrivial proof writing the better

if you're planning to study math beyond HS

(i say "nontrivial" bc frankly the "proofs" they go over in HS geometry are really fucking boring and/or obvious)

[tardy bough]

Yeah

The proofs I did in geometry were so boring and easy

[wet sentinel]

well euclidean geometry is boring

[tardy bough]

U think so?

[cunning elk]

oly geo goes hard

me when the diagrams start looking more like gang signs than actual diagrams

[wet sentinel]

bro all olympiad stuff is meh

all competition math tbh

[cunning elk]

idk im washed in contest math, only barely made AIME my last year of HS 😭

[wet sentinel]

well i havent done any competition math ever so you are safe

[wet sentinel]

yea i mean i hate geometry

even in multivariable calc for example when everyone gives an advice to draw figures to get the multiple integral bounds for example i never draw any figures

i try my best to find any way that doesnt involve drawing figures

[cunning elk]

LMAO real

[wet sentinel]

the only "figures" (diagrams) that i will willingly draw is when i study category theory

well maybe you cant call these figures to begin with but whatever

[remote sparrow]

there can be interesting books on synthetic geometry, like pamfilos' two-volume book on the subject, kiselev's two-volume work, or Classical Geometry: Euclidean, Transformational, Inversive, and Projective by leonard et al.

it's not necessary to study it in much depth though

[heady ember]

https://tenor.com/view/obi-wan-so-uncivilized-attack-of-the-clones-star-wars-gif-19823075

Imagine not spending days on one figure

[wet sentinel]

its easier for me to imagine death

[wet sentinel]

i mean imagine doing that

[heady ember]

I don't need to imagine

Two versions of the same diagram made in Asymotote.

Another two made in TikZ because why not. But TikZ doesn't have true 3d so it was a pain getting it to render properly

[wet sentinel]

wow bro is good at torturing themselves

[heady ember]

I have upgraded since.

Instead of spending days on one figure, I now am spending months on a TeX project 👍

[wet sentinel]

this upgrade is apparent from your pfp, tag etc..

[last cipher]

Thoughts on this book everyone?

I love the large amount of exercises and i think its well balanced

[queen lynx]

never read it but i recommend if it's linear algebra :D

[haughty tendon]

Anyone got book recommendations on the math of astrophysics

[gray gazelle]

Has anyone read Godel Escher Bach?

[remote sparrow]

https://www.math.uci.edu/graduate/current-students/examinations

https://quals.math.uci.edu/

https://www.math.uci.edu/~nckaplan/graduate_algebra.html

more resources

[remote sparrow]

this from the library or a used book?

[pulsar veldt]

I guess you'd like to ask it here https://discord.gg/physics

[tardy bough]

hm

[fathom topaz]

umm i want to start studying calculas from scratch .can anybody tell me from where to start

[gray gazelle]

It’s standard pretty much everywhere, I had positive experiences with Khan Academy and Stewart’s book. Although the latter is expensive, there are ways of circumventing that

[fathom topaz]

can you give me the pdf of stewarts book?

[gray gazelle]

I cannot

[fathom topaz]

kk

[gray gazelle]

I haven’t used the book in years and that would violate the server policy

[fathom topaz]

u could dm me

[gray gazelle]

Well, I could do a lot of things, as could you

[fathom topaz]

mb

thanks for the advice

[gray gazelle]

Happy to help

[last cipher]

Uni library

[stray badger]

guys any reviews about inequalities by bj Venkatraman

[languid bloom]

anyone know the difference between Dolciani's Introductory Analysis and Modern Introductory Analysis?

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-031-63665-3

https://www.math.uwaterloo.ca/~krdavids/FAOA.html

was googling some references for FA and operator algebras and found this recently published book

@sturdy shore

[sick kelp]

What are some good books on quants and financial related stuff?

[tardy bough]

Does sm1 know any books that talks about special sequences

and like why the Fibonacci sequence for example is important

[cunning elk]

overromanticizing and glazing the fibonacci sequence (and by extension the golden ratio) is a favorite of crackpots who dont know what theyre talking about

for example i once heard someone try to insinuate that some debussy piece was precisely written around it which was

just hogwash

[remote sparrow]

@sage python

[old elk]

Do you have exterior algebra?

[old elk]

A question: are the exams that universities post for admission or for master's degree students?

[remote sparrow]

idk, i think it's a requirement to get either a master's or phd

[old elk]

I understand, because I see exercises that are quite complicated, even with my level, I can't manage to do some exercises.

[molten gulch]

You have ben given several texts which introduce exterior algebras over the past several days

[old elk]

Hahaha, I know, I've found what I need, I've become a bit obsessed xde

[balmy crown]

Im taking a ML course, anyone have reccomendations for a solid introduction to the area?

[coral comet]

for anyone seeking calc

[worthy kindle]

ur acc not allowed to post pirated content on the server. discord doesnt like it, esp for partnered servers

[coral comet]

oh my bad, didn't know that

[normal crystal]

I'm 99.99999% sure they weren't asking about Meta Language

[balmy crown]

Lol mb Machine Learninh

A textbook for machine learning

[last cipher]

Wdym

[remote sparrow]

brian hall actually has a book on lie groups, which mainly focuses on matrix lie groups. i saw the string "adjoint representation," but not "coadjoint representation." i also looked at knapp's Lie Groups: Beyond an Introduction, which also mentioned adjoint representations, but not coadjoint representations

[still jungle]

what is interior algebra

[tardy bough]

So it isn’t that important?

I always hear sm1 glazing it so I thought it was important

[south cairn]

Adjoint representations are relatively standard and would be covered in any book on Lie groups I guess. Coadjoint representations are dual to the adjoint ones, and one context in which I have seen them crop up prominently is Kirillov theory/orbit method. You can take a look at Kirillov's book "Lectures on the Orbit Method" for details (the book assumes some understanding of Lie group representations).

A less geometric but somewhat drier account, specifically in the setting of nilpotent Lie groups can be found in Corwin-Greenleaf's "Representations of nilpotent Lie groups and their applications".

[cunning elk]

contrary to what pop culture tells you it's not that interesting by itself? but can lead to some other interesting related topics: linear recurrences, various geometric relationships, continued fraction/infinitely nested square roots, etc

[tardy bough]

Oh

[vital chasm]

Not fibonacci (thats boring) but a sick book with techniques to deal with sequences is generatingfunctionology2

[tardy bough]

Yes!

[vital chasm]

I just used generating functions today for to deal with a probability question

Like i apply law of total probability to get a recurrence relation for a sequence and then I used generating functions to nuke the problem

[wispy bison]

does anyone have any recommendations for a rigorous book covering flat modules and Ext and Tor?

[remote sparrow]

https://www.amazon.com/Introduction-Module-Theory-Graduate-Mathematics/dp/0198904916

https://link.springer.com/book/10.1007/b98977

https://www.cambridge.org/core/books/an-introduction-to-homological-algebra/AAA3F16482097015CD12D4376D505282

i would say rotman and weibel seem to cover more on the topics you mentioned specifically

[wispy bison]

which one of these do you think is better?

[remote sparrow]

rotman's easier. covers less compared to weibel. assem and coelho is a more general intro to modules if you care about that, but ctrl-f doesn't yield as many hits for ext and tor.

[wispy bison]

Thanks!

[daring wolf]

weibel's homological algebra is a hot take imo

i dont like rotman

[wispy bison]

is it your take?

[daring wolf]

yes i studied with weibel

skimmed some of rotman's book but i didnt like his text

[wispy bison]

hmm I’ll check out weibel

[full cairn]

There's also a book by Scott Osbourne which is apparently pretty good: https://link.springer.com/book/10.1007/978-1-4612-1278-2

[full cairn]

<@&268886789983436800>

[twilit pulsar]

i found a book from 2020 on it, An Introduction to the Circle Method by Murty and Sinha, vol 104 of AMS' Student Mathematical Library

no idea if ur still interested in such a book but

it's good so far

[blazing holly]

Im looking for books/notes on floquet theory. If anyone has some please lmk

[tardy bough]

is this not the method 🥹

[restive pecan]

Any book recommendations for pre algebra?

[cunning elk]

don’t really need a book for that

[normal crystal]

I get by now you feel this way about all math up to calc
but it doesn't really help to answer that to someone who is asking and wants a book

[normal crystal]

Openstax has a free one

[sour cargo]

Mac Lane's Homology might interest you (if you love abstract nonsense, because of the author)

Also Manin's Methods of Homological Algebra uses category theory and sheaves freely.

[fresh vale]

What's that?

[wispy bison]

I’ll look at those too, I just hope they don’t skip over a lot of details

[restive pecan]

Oh okay

[lofty comet]

Books are good!

[remote sparrow]

@narrow relic

https://www.logicmatters.net/2021/05/19/mathematical-logic-from-a-compsci-angle/

I’ve had Mordechai Ben-Ari’s Mathematical Logic for Computer Science (Springer 3rd edn 2012) recommended to me. But I thought this pretty second-rate. The level of exposition is poor, and indeed at points seemingly outright confused (e.g. about the status of the Deduction Theorem for a Hilbert system). Someone who already has a grip on the standard math logic approaches could, I guess, get something out of the book by diving straight into the chapters on propositional resolution, SAT solvers, and first-order resolution, for example. But I didn’t find this material well explained: it is surely treated more pleasingly elsewhere.

i'm looking at huth and ryan and it seems good

[remote sparrow]

https://www.amazon.com/Logic-Computer-Science-Modelling-Reasoning/dp/052154310X

[tardy bough]

Did you read everything bro 😭

[umbral lagoon]

yo

everybody

[gray gazelle]

yo

[thick ore]

Somebody can suggest me problem sets from basics to advanced in probability and statistics...
As I can do easy questions
But the hard questions for me looks way to harder than actually it is...

[oblique hatch]

What level in general are you looking for?

[thick ore]

I am looking for papoulis and pillai level book

I have heard it from my professor

But it's not from basics to advanced

[bitter knot]

Does anyone have a book for preparing for IMO for beginners? ;-;

[orchid robin]

is there good book to study all arithmetic or a very good foundations in math for beginner

[stray badger]

yea start egmo by chen evan

[obtuse inlet]

hey all
hope you are doing well
so this semester I'll be studying topology for the first time
(- 𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙 𝑠𝑝𝑎𝑐𝑒𝑠.

• 𝑐𝑜𝑚𝑝𝑎𝑐𝑡 𝑠𝑝𝑎𝑐𝑒𝑠.
• 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒 𝑚𝑒𝑡𝑟𝑖𝑐 𝑠𝑝𝑎𝑐𝑒𝑠.
• 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑 𝑠𝑝𝑎𝑐𝑒𝑠.
• 𝑛𝑜𝑟𝑚𝑒𝑑 𝑠𝑝𝑎𝑐𝑒𝑠.)
  and would like you to suggest some beginner friendly books

[molten gulch]

i believe munkres is the standard for topology

[obtuse inlet]

thanks Ryan

[molten gulch]

no problem

good luck in your studies

[grim ore]

Topology and Groupoids i think it’s called

I like it personally but it’s not the most beginner friendly and it rises through the point set section as if you already know it

has great exposition for the intermission between point set and alg top

[gray gazelle]

bert mendelson's book covers all of the above minus the normed spaces and is perfect for a beginner

and it's short but dense and you prove a lot of cool stuff

i enjoyed it a lot during my studies, although yeah you might want something else for supplemental purposes / exercises

[north summit]

I really liked gamelin topology

[velvet flax]

kelley's general topology is quite nice

though it is somewhat dated

[velvet flax]

what is the most comprehensive analysis book

or series

i am looking for something analogous to lang's algebra

[young thorn]

may i ask whats that

i mean what website

[marble solar]

Possibly Barry Simon's Comprehensive Course in Analysis is what you're looking for

More elementary, there's the Stein and Shakarchi series: Fourier, Complex, Measure & Integrals, and Topics

[velvet flax]

basic mathematics lang maybe

[slow roost]

Lang - Real and Functional Analysis

but I don't really know if it's as comprehensive

it is almost 600 pages

[flat plaza]

ODE recommendations? Like i tryna find that book that does not throw some method at me without any derivation/proof because I want to understand what is lying underneath those methods,

[heady ember]

Arnolds’ is well-liked as a rigorous ODE book

[rancid fjord]

Book recommendations for class field theory? ideally with a lighter AG background, although I have galois theory

[swift topaz]

does anyone have books that are just integral problems

[viral knoll]

Solely integral problems? Try caczor and nowak third volume

[swift topaz]

is there one thats more like friendly i am just like 1st year undergraduate im interested in learning more integral techniques and things beyond those taught in classes

[viral knoll]

Alright, try I A maron problems in one variable calculus

You have almost everything there

And one advice:- don't solely rely on techniques

Rely on your intuition

[remote sparrow]

did you look at huth and ryan?

[cursive orbit]

a lot of the methods used are reliant on the symmetries of the ODE, so perhaps you can try a book that emphasizes techniques involving the symmetry group

[remote sparrow]

just have it printed with lulu

also used paperback copies don't seem particularly out-of-reach price-wise either

could be $17-25 pre-tax and shipping + handling

[remote sparrow]

not too bad for a book that's been in print for 21 years

[visual latch]

guys
i want to freshen up my
knowledge of number theory
like the basic number theory
i dont have any reference book sin my mind
what should i do?

[remote sparrow]

#book-recommendations message

[visual latch]

thanks bro

[restive pecan]

What's that?

[stuck sparrow]

I am looking for a modern introduction to proof based linear algebra, with a more concise style compared to sheldon axlers discussionary style.

[heady ember]

Uh perhaps Greub? Iirc it covers quite a lot of stuff in ~300 pages, but its not an easy read from what I have heard.

[gray gazelle]

Intermediate calculus?

[molten gulch]

Greub is more concise but as grass has said, way way harder, at-least of the bits I've read it seems almost like a reference of most of the pure linear algebra you'd need but condensed quite a bit

[slate peak]

guyss i need a book for class 9 maths cbse that goes from basics to advanced (imo olympiad level)

what's aops?

ah

okay

[foggy quest]

https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[cosmic haven]

Does anybody have some book ideas for more advanced higher mathematics? I know how to do stuff taught in school like calc, trig, et cetera. But I want to get a jump start on more university topics like modular arithmetic, number theory, group theory, linear algebra, etc. Is there a book which explains these topics at my current level? I don't mind how long it is.

[young thorn]

anyone went through conway complex analysis - 2 ?

i have done ahlfors complex anal and i m planning to look at conways book soon can someone tell what prerequisites book assumes

[quick crane]

Thomas' Calculus, maybe ? I have one

[gritty cliff]

Is lulu a book?

[unique pier]

Discrete mathematics book recommendations pls

[molten gulch]

Rosen

[chilly geyser]

Try indian book like R.D. sharma for class whatever you are in.

[remote knoll]

If you haven't taken a proofs course, I would recommend it. Generally, a proofs course will involve some introductory number theory.

Perhaps this?

https://bookstore.ams.org/view?ProductCode=AMSTEXT%2F61

[flat plaza]

not solely, but Demidovich fs is a good problem book

[alpine mist]

Hi, I'd like to get a little familiar with this world. Can you recommend a book that could help me learn a little bit about everything? A book that could teach me the basics of everything and help me learn.

I want to know what awaits me in the future and go prepared and with prior knowledge.

[cunning elk]

try lang’s basic mathematics and/or the princeton companion to mathematics ?

[lone matrix]

Does anyone have a book about Propositional Logic?

[rigid trail]

Why do you need a book for that

[lone matrix]

The one we use in college has a HUGE amount of errors and when I'm trying to study with it, I get discouraged by problems that seems impossible

My classmates have the same situation

[cunning elk]

any basic discrete math text should have a section on that

[lone matrix]

Could you share some books?

[restive pecan]

I have

You may like this

[gray gazelle]

Hello

[slow roost]

The Princeton Companion to Mathematics is an amazing book, but I don't think it's the right recommendation for an engineering major who wants "to know what awaits [them] in the future"

or for learning "the basics of everything" (which, to be fair, isn't a reasonable expectation from one book, but anyway)

it's more of a coffee table book for math grad students. Also rather expensive

don't get me wrong, I'd recommend anybody check it out at some point for fun, it rules. But I could imagine this engineering major ordering this cinder block of a book, opening it and being like "wtf is this"

[alpine mist]

So what do you recommend, my friend?

[brisk prism]

I’m a professional power engineer. Back when I was learning, my boss actually had me work out iterative numerical methods—like the Newton–Raphson method—by hand on paper just so I could really understand how PSS®E power flow converges.

Honestly, the math you’ll need depends a lot on which engineering field you’re going into. For example, linear regression is handy for short-term weather data forecasting or filling in small gaps of missing data, but it doesn’t really cut it for complex weather predictions. I’m not too sure about what’s most useful in other engineering fields, though.

[brisk prism]

I agree

CS reminds me of those complex logic gates... wait that's for EE... like semi conductors...

Let's move this to discussion since it's book recommendations chat here

[velvet flax]

the book "basic mathematics" by serge lang

[restive pecan]

I tried using it, but i totally failed to understand it I need maybe something more basic

[velvet flax]

hmm

the aops book maybe?

[plucky finch]

Not a book recommendation but a yt recommendation

Check out prof lenoard

he does detailed guides from pre algebra to differential equations

and then check out Paul's math notes

[plucky finch]

You also have open stax

don't buy books if they can be found as pdfs of pdf drive

[restive pecan]

Full title

[restive pecan]

Thanks ♥️

[slow roost]

it's really written for a math major who wants to go back and review all the basic stuff

the presentation assumes mathematical maturity

it is very good

but not necessarily easy

[restive pecan]

I think that's why it's so tough for me

[restive pecan]

Exactly

[cerulean thicket]

Hello nerds and bibliophiles

[restive pecan]

So ,do you have another basic book for recommendation?

[slow roost]

honestly, any school textbook for that level of material is alright

the presentation of those books tends to annoy math major types, which is why a book like Basic Mathematics is nice for them

but for, for lack of a better word, "normal" non-math major people, any basic algebra, geometry, and precalculus text is fine

you want to have lots of repetitive examples and highlighted boxes displaying the definitions and theorems and color pictures and stuff

and no books like that are particularly better than any of the others

in my experience

or just use youtube and khanacademy and other online stuff, if that works for you

you can learn all of the basic stuff from those alone

[void temple]

What books would y'all recommend for learning homological algebra and algebraic topology after having taken first courses in each topic?

[alpine mist]

So what do you recommend, my friend?

[slow roost]

the last bunch of stuff I wrote was written for you in mind

[alpine mist]

oh, thanks

in that case do you have any books of that type that you recommend or any YouTube channels?

[tardy bough]

I copied the original message ngl

[slow roost]

https://www.youtube.com/@TheOrganicChemistryTutor/playlists

https://www.youtube.com/@blackpenredpen/playlists

[velvet flax]

art of problem solving's "prealgebra"

maybe that professor dave channel has something

[restive pecan]

Wow that's a good book

Thank you so much

[robust tartan]

200x2001288281

20010101x2020101=4.0422×10¹³

[mortal ore]

Cool bro

[cunning elk]

my honest reaction:

[robust tartan]

Told u I was Albert Einstein son

202929299191+12882=2.0293×10¹¹

292928281x292928=8.581×10¹³

29828282+828282=30,656,564

292929x299282=8.767×10¹⁰

[primal flare]

guys im albert einsteins son

also

8282882828282828828288388383x82828282882828282882=6.861×10⁴⁷

73737377373738828282828838383838x828288383838388484848488483838=6.108×10⁶¹

7373773838383838838383838738388282838288283+82838388383838838383838838383838388383838383883=8.285×10⁴⁶

[robust tartan]

Yes rgn is my brother

[primal flare]

this is so ez

redo why are u he/she

@robust tartan go to #chill with me

[regal kettle]

I checked the basic integral basically calculus playlist its 331 videos 😭, if i wanna learn, functions, itf, limits continuity, differentiability then differtiation integration is that a great source or are there any better organised lectures?

[slow roost]

I prefer learning from books, and if there's a particular topic I'm having trouble with, then I'll check out videos about it

[molten gulch]

Just use an analysis textbook

[velvet flax]

dieudonne’s treatise on analysis if ur really mature

spivak’s calculus (not on manifolds) if this is ur first exposure

maybe papa rudin in the middle

[regal kettle]

It's my final year of h.s.

[velvet flax]

then spivak fs

[regal kettle]

alright, thanks qchs!

any lectures I might find?

[regal kettle]

I found one called calculus on manifolds is that it?
I'm sorry it's my first time hearing about these references

[velvet flax]

no

that ones the advanced one

he wrote a book called just “calculus”

[wild blaze]

Any book or website recs to learn python I know basic C stuff

[molten gulch]

yes, the python tutorial

https://docs.python.org/3/tutorial/index.html

[native cradle]

Would a first group theory course be too early for Roman's fundamentals of group theory

I'm just going through it, looks really fun

[loud cradle]

looks fine, he says he doesn't assume any group theory knowledge, just mathematical maturity
i haven't read the book but skimming it, it seems fine
i'd probably put the sylow theorems earlier but hey, he's the author

[native cradle]

Awesome, looks like I'm going to have a lot of fun! :D

btw bungo, somehow I was able to download random springer books directly from springer link yesterday for free

Was able to download books worth around 500 EUR I'd say

[loud cradle]

nice, was there a glitch or something?

[native cradle]

I have no idea

[loud cradle]

can't argue with free

[shrewd talon]

Do you study analysis yet

[native cradle]

Doing it this semester

[shrewd talon]

And abstract alg?

[native cradle]

This is my first abstract algebra course

[shrewd talon]

What’s your thoughts on the cantors diagonalization method

[native cradle]

Idk, It's cool I guess

[shrewd talon]

Sup…?

[shrewd talon]

When u studying topology

[shrewd talon]

Wha you reading

From

Without

*author

[void temple]

Well, I will try again, seeing as my last question was in the middle of a discussion round. I'm currently taking first courses in Algebraic Topology, and Homological Algebra. These classes are mainly covering the topics:

• Homology
• Very basic homotopy theory
• Singular & Cellular Cohomology
• The cup product
• Poincaré Duality
• Basic category theory up until derived and triangulated categories

I then wonder what do you recommend I read next, once finished with said courses. Thanks in advance!

[cosmic kiln]

Hello I am doing calc 2 right now, but I am interested in reading an introductory real analysis book

Any recommendations?

[remote sparrow]

how about spivak

[cosmic kiln]

Spivak's calculus?

[verbal bolt]

Is it possible to read in through a browser?(like opening a. Page of this,not purchasing the digital book)

[remote sparrow]

yeah

[cosmic kiln]

Hmmm piracy isn't permitted

So it is likely that they won't answer this

[cosmic kiln]

I will give it a try

[remote sparrow]

speaking generally, pdfs can be read in browsers

[velvet flax]

dieudonne treatise on analysis volune 1

or baby rudin

[coral temple]

Hello, some book of techniques of proof that they recommend?

[velvet flax]

also perhaps simon’s course

[velvet flax]

polya’s how to solve it?

[coral temple]

Never heard it, thanks look so good

[remote sparrow]

https://richardhammack.github.io/BookOfProof/

[coral temple]

Thank you

[velvet flax]

note: this does not cover riemann integral

but only cauchy

2nd vol covers lebesgue iirc

[cosmic kiln]

i only want to give it a brief read

i will do it in detail once we reach there

thanks for the help

[remote vortex]

Riemann is skipped altogether?

[velvet flax]

yes

dieudonne said it was braindead and decided to completely disregard it

[remote vortex]

Eh, definitely not an approach I agree with.

[gilded cave]

Anyone know any good introductions on PLT? I'm currently working through https://plfa.github.io/

[gritty cliff]

This book is on which topic?

[molten gulch]

it's in the name, it's a treatise on analysis

[late sundial]

does anyone recommend Mathematics for Machine Learning by Marc Peter Deisenroth?

[wet sentinel]

i hear good things about abbott's understanding analysis.

[arctic yarrow]

i hear good things about schroder's mathematical analysis

[foggy quest]

empirical risk minimization is an important topic, and the book has a section about it, so that's a good sign

[regal arch]

I want to get good at mental maths, specifically with radicals and exponents.

Any book recommendation?

[shrewd talon]

Did it come from me

[pine tundra]

I don't think there are books specific for this
I'd say it's just a matter of practicing

[wet sentinel]

tbh it comes from many people in the server

[wet sentinel]

personally i prefer rudin's PMA but i wont recommend it here, but maybe if you dont mind struggling for quite a bit then try it out

[tiny gulch]

Careful, you’ll summon outsider

[wet sentinel]

i had this thought too

oops, maybe i should delete before its too late

[shrewd talon]

I read it and couldn’t finish the first page lmao

[gray gazelle]

Fellas, got a good book on physics?

Especially thermodynamics and electromagnetism, since i want to deepen what i learned at school

[wet sentinel]

well you would have to struggle too much especially at the beginning

but i chose it especially for this reason, idk why but i deliberately chose books that i know i will struggle alot with for many subjects

maybe i find such books much more fun than ones where i wont necessarily struggle much with

[shrewd talon]

Just choose abott fr fr

I love this

[wicked fractal]

[wet sentinel]

i wouldve considered it if its title was misunderstanding analysis

[radiant marlin]

is it worth reading baby rudin after abbott for new material? or would another text be better

[grim ore]

new material?

like, you already studied real analysis?

[radiant marlin]

like after going through abbott

[grim ore]

Oh sorry, thought that was baby rudin and abbott

No

Don't do that honestly

You dont really gain much out of an undergrad text from other sources bc tbh, its pretty standardized

[wet sentinel]

i havent used abbott before but from what i hear it doesnt work on metric spaces in general for example (at least not from the get go). But either way i wouldnt recommend doing that

i think it would be a waste of time

[radiant marlin]

what would you recommend? is papa rudin too far up

[grim ore]

How far are you in your ug career?

[radiant marlin]

im a soph

[wet sentinel]

have you studied linear algebra and or abstract algebra?

[radiant marlin]

yeah dummit and foote and axler

[grim ore]

What is missing from papa rudin that you are not understanding?

Also being a 2nd year in ug is kinda early for grad lvl. I am not saying its not possible but the point of ug is to get mathematical maturity, which you will hear a lot about in this server if not already

Chances are if you took analysis and not getting real and complex by rudin, then there might be a gap missing in the comprehension / math maturity between the two levels

[radiant marlin]

lesbegue and hilbert stuff i havent really seen

[wet sentinel]

maybe try complex analysis

[grim ore]

This is an option, but imo not needed ^

I would personally say, a lot of the time in taking grad lvl classes, i am a ug and you realize they are literally no different than undergrads except those who are close to finishing their thesis/dissertation ofc (imo). But you will have to always self study concepts you dont understand

[wet sentinel]

yea sure, i wasnt recommending that as a prerequisite for papa rudin or something like that. just a random recommendation

[grim ore]

If you are always self studying every time you learn something, then it probs isnt the right time for you to take that class, but once in a while is pretty normal

[radiant marlin]

got it, any book recs then?

[grim ore]

for analysis?

like grad measure theory?

[radiant marlin]

yeah second book after abbott

[grim ore]

https://www.youtube.com/playlist?list=PLp0hSY2uBeP8hajKOVGZ9oIPjG3HKMfoY

This is a playlist i skimmed through and can understand after ug algebra and analysis

It seems pretty good tbh

But this might help you much more than a textbook, but Folland isnt a bad text either

[radiant marlin]

thanks!

[grim ore]

Dont be afraid to find playlists on yt, its my goto thing to do; and ocw is also a good resource

[radiant marlin]

oh yeah i saw ocw uploaded a real analysis course recently, but it was an introductory course

[grim ore]

Look for measure theory on there

[radiant marlin]

i see an analysis II course tho

oh ok

[grim ore]

Yeah I also got lost trying to find grad ra lmao

nws

[grim ore]

this is basically intro to measure theory at mit

you can watch it, but it should not be needed

[radiant marlin]

ok thanks!

[shrewd talon]

What

[gray gazelle]

Is there any book with all the math you need for comp sci?

[molten gulch]

Not one book but you'd want quite a few

[gray gazelle]

Feel free to suggest

I havent touched maths since high school

[molten gulch]

Something on analysis, linear algebra, probability theory and statistics, theory of computation, some on various aspects of programming, if you want to do crypto or ML you'll need some other books and for crypto it helps to know some abstract algebra alongside the linear algebra too

[normal crystal]

if you mean for a CS degree, you likely will need/do through Calc 2 maybe 3, Discrete Math, Prob/Stat, Linear Algebra
there are plenty of recommendations asked repeatedly here to search

[near jewel]

You need to be specific. But Boolean algebra is sure some math CS has.

The more hardware of CS you’re referring to, the more math it’ll be.

[wintry spire]

hi, someone can recommend me some books about thermodynamics, please?

[cunning elk]

might be better to ask this in the physics server

[molten gulch]

intro thermal or stat mech

[native cradle]

I was just wondering is " All of statistics" really that great of a book to read form?

[remote sparrow]

out of sheer coincidence, a little over a year later, i picked up a copy of the first edition today, which is instead titled Real Analysis with Real Applications. it appears the edition you were asking about cut down a lot of the first part (at least 85 pages). supposedly this is meant to give "greater emphasis" on the latter half of the book, which seems to have plenty of nontrivial applications, but the table of contents for the second part of both editions don't seem to differ. there are other organizational adjustments (one notable adjustment is deciding to cover least upper bounds before limits, which is more in line with other books i've seen) and some new examples. i suppose in practice the authors didn't cover some of that cut material as often as they'd hoped (for example, there is some discussion of what's generally considered more advanced material like L^p norms, L^p spaces, and abstract integration in the first edition). a short review of proofs was cut as well. the cut content is available here: https://www.math.uwaterloo.ca/~krdavids/RAA/real.html. i think the first edition is better if you're looking for more content. from skimming my copy, i wouldn't quite recommend this book as a first course for the average student, but it could be a good alternative to rudin for stronger students.

[blazing holly]

Are there any go to texts if i want to learn helmholtz’s theorem/decomposition?

[wintry spire]

I didn't find where to put it, where do I can?

[wintry spire]

Intro thermal

[cunning elk]

#old-network has invite link to phys

[heady ember]

@remote vortex

[native cradle]

Roman's algebra book is so good

[near jewel]

It's a book specially aimed for CS applications, such as AI.

If you want to have good foundation, read it. But usually using it as a reference is also fine.

[topaz rampart]

Can I get some combinatorics books reqs?

[sage python]

There are quite a few options here. Where are you at in math rn?

And is there any particular angle you're hoping to take on the subject? (eg linear algebraic methods)

Generically I have been recommended "A Course in Combinatorics" by van Lint and Wilson

[balmy zephyr]

anyone has any book recommendations on polynomials? preferably not a very advanced one

[topaz rampart]

apologies for the late response. I just got into uni and we have a course named intro to combinatorics. Our professor told us that she will teach the subject without having to get too deep into the whole theory-proof shabang. I dont rly know what that means, but you prolly do. I am not very familiar with combinatorics

[topaz rampart]

I dont know any of the angles I could potentially take

[topaz rampart]

I'll give this one a read

[sage python]

Okay my combo class was very proofsy and upper level so this book (which we didn't realize use but which the prof said is good and an "advanced reference") may not be as useful

Try "Introductory Combinatorics" by Brualdi

That's the book my uni's combo class which isn't hyperproofsy uses

[topaz rampart]

okayyy thank you

[north heron]

hello, i got a good background in bilinear and linear algebra, do you have a book with a good chapter on convolution to understand it deeply ? i'm following a signal processing course but i'm very curious on convolution

[shrewd talon]

What

What even are metric spaces btw

Topology?

Aw fuck

Well I’ll learn it later

[wet sentinel]

basically sets equipped with a notion of distance

[tiny gulch]

yes

[mortal ore]

Yes

It would have to be i think as theres no norm without a metric

[drowsy thicket]

with d(x, y) := ||x - y||

[wet sentinel]

yes, but the converse isnt true

[mortal ore]

Ah wait no im misremembering

The norm comes from an inner product not a metric right

[tiny gulch]

well there are normed spaces that aren't inner product spaces

norms that come from an inner product have to satisfy the parallelogram law

[wet sentinel]

the last one is =< not =

triangular inequality

[mortal ore]

Oh I see

I never learned about norms so im not well read on the definition and all the things they do

[wet sentinel]

bro spams it all the time in real analysis and then forgets about it

[drowsy thicket]

d(x, y) = 0 <==> x = y is how I learned the first one

What you wrote is only <==

[mortal ore]

I split that one in two parts when I learned in analysis 2

[wet sentinel]

yea, in rudin its written as d(p,q)>0 if p neq q, d(p,p)=0

[mortal ore]

Same in tao

[wet sentinel]

but yea mq only wrote a part of that

[drowsy thicket]

it's the same for normed spaces, ||v|| = 0 <==> v = 0_V

[wet sentinel]

np all good

[wet sentinel]

yea well since norms are metrics

[drowsy thicket]

Yeah well atleast they induce one

[wet sentinel]

i dont think that i am the best to say things about these since i havent fully studied LA (probably strange), i started but then stopped

i will get back to it soon

how did you know that i am doing that

actually i am studying AA rn

[wet sentinel]

thats why i said its probably strange here

i am near the end of group theory part of lang's book, currently at actions

yea its very nice

[mortal ore]

Oof lang

[wet sentinel]

i was waiting for someone to take the bait

its lang's undergraduate algebra

not lang's algebra

[mortal ore]

Nah i said "oof lang" because he's notoriously dry

Or rather his texts are

[wet sentinel]

ohhh i see. I actually enjoy his style tbh

thats why i will use his CA book when i start with it

[mortal ore]

Boring and some concepts being left unmotivated

[wet sentinel]

he more or less gets straight to the point, contrary to D&F for example which is too chit chatty imo

[west flame]

Ello

[mortal ore]

Though maybe I should cut some slack bc i myself haven't read him

Yeah i cant agree

[wet sentinel]

tbh i dont really get what people mean by the ideas being motivated/unmotivated

[mortal ore]

I find things like cayleys theorem very enlightening

[wet sentinel]

what exactly does that mean

[mortal ore]

Motivated meaning a lot of substance to use as intuition

Philosophically it confirmed group theory as a continuation of the study of permutations that had been happening earlier

[wet sentinel]

i see

hmmm i think i get what that means now

thanks for the explanation both of you

[mortal ore]

Its more that group theory is the study of permutations at all

Groups are more just those particular permutations that behave well

Before group theory there was some study about permutations being done

But then as people got more comfortable with abstracting the concept of permutations, they realized that it elegantly explains a lot of strange concepts in what was algebra then

And as we keep giving sets more structure those new objects explain some new things

So the reason why group theory is important is not just that its cool math, but its that in any situation where you have things permuting, group theory can save the day if needed

And I dont think it needs convincing that permutations come up often

[remote sparrow]

miklos bona's A Walk Through Combinatorics

[wet sentinel]

but that only applies to finite groups no?

[mortal ore]

You can still look at permutations on infinite sets

[wet sentinel]

sure, but is there an isomorphism between any infinite group and some infinite permutation group?

[wet sentinel]

so like is every group (finite or infinite) isomorphic to some permutation group (finite or infinite)? or does this fact only hold for finite groups?

[topaz rampart]

okeoke i'll check this one out too, thank you

[cursive orbit]

all groups are isomorphic to a subgroup of a permutation group

[wet sentinel]

ohhh i see, now thats interesting

[mortal ore]

You just have to use ordinals to make that sensical

But mathematicians made ordinals so that we could do that (at least I assume thats why ordinals exist)

[remote sparrow]

https://link.springer.com/article/10.1007/s00283-019-09898-4

[primal elm]

Any recommended books on statistics?

I’m about to do a masters in bioinformatics, my bachelors was in biochem, but I want to strengthen my maths skills beyond what the course will offer

[cunning elk]

look for texts in “mathematical statistics” specifically if you want more rigor

my stats class used wackerly

[remote sparrow]

https://www.youtube.com/watch?v=jO0xKqHXCvg

jay cummings has a youtube channel now!

[primal elm]

Thank you I’ll take a look

[foggy quest]

Do you know probability at the level of "A First Course in Probability" by S. Ross?

[primal elm]

I haven’t read it, let me look it up and see

[normal crystal]

yea, in the spring/summer he said he was gonna start with videos for his real analysis book
but he started with proofs his book instead

[primal elm]

Having skimmed through a bit of the book and looked at some of the questions, I’d say I’m maybe around that level. There’s definitely stuff in there I don’t know but I reckon I could work through most of the exercises

[deep moat]

Oh hoh

I have a lot of stats book that I can recommend you

Beginner:
Schaum's Outline in Statistics
Mendelhall Statistics
Naked Statistics
Mathematical Statistics

Well.. uhm... idk any advanced and other elvels

[deep moat]

but in genral this is valid since all the contents are the same

[foggy quest]

Something somewhat advanced is https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www.di.ens.fr/~fbach/ltfp_book.pdf&ved=2ahUKEwiZpu_AhPiPAxWnSjABHT3MFHAQFnoECCgQAQ&usg=AOvVaw0UAUxy8wDGamS40sm3bDZy

It covers more modern-ish topics rather than what would be covered in a classical statistics book like the one by Casella and Berger

[dawn socket]

i’m looking for a free online textbook to self study real analysis, any suggestions?

[normal crystal]

look here
https://textbooks.aimath.org/textbooks/approved-textbooks/

[dawn socket]

lebl, trench, zakon, or thomson & bruckner?

[sage python]

Approved? Lmao

Oh that's just a way of saying it's open source and good for a full blown class

[deep moat]

I got a reprint version of the "How to Prove It" book by J. Velleman

Best $12 purchase

[nocturne badge]

does anyone have books on history of the math tripos, especially about the old ones before reform, the history of reform. id also appreciate detailed biographies of hardy and littlewood, or books on the general cambridge mathematics in the era of 1890+

[glossy cove]

is titu's complex numbers from a to z recommended for first read? i mean i know the basics, i have done some analytic geometry and mecmath's trig, but wouldnt say i know a lot of polynomials stuff or have had a formal introduction to complex numbers.

[true sail]

What's your opinion about the book?

[deep moat]

Really nice! It reassures you that you don't have to worry if you don't know where "this and that" came from since they go through it

thoroughly

[dawn socket]

for real analysis

[true sail]

Thoughts on the book "Fundamentals of Data Structures in C"?

[molten gulch]

Never heard of it

[shrewd talon]

Abott

[mortal ore]

Yo could I just start humphreys's book on coxeter groups right away or should I read that one intro to geometric group theory book first

Intention is to work with a professor that does coxeter group stuff

[oblique hatch]

Neither are really a prerequisite to the other in any way

I’d read the Humphreys’ book first bc that seems much more relevant

[trail hemlock]

what is the point of responding wit this 😭

[gray aurora]

What are the best books for these field:
Complex analysis
Real analysis
Proof writing
I want to get better

[scenic sequoia]

1. Ahlfors
2. Rudin
3. Hammack

[wet sentinel]

1.#book-recommendations message
2.#book-recommendations message

you can choose what you like from these 2 lists for CA and RA respectively

as for proofs i dont think you really need a book dedicated for that tbh

personally i will go for lang's complex analysis when i start CA soon, and i do agree with brandon about rudin for RA

(although many people wont agree on rudin )

[gray aurora]

Rudin is not basic at all so hard to understand 😔

I can't see the list

[wet sentinel]

so if you click on the link it doesnt teleport you to the message?

[gray aurora]

I can't find any list

[wet sentinel]

in that case open the pinned messages

and scroll down

[gray aurora]

Yes

[wet sentinel]

scroll until you reach "what you should use in analysis"

go to that message, this list is for real analysis books

and then scroll down a bit more until you see "Ahlfors", this will be the list of complex analysis books

do they appear to you?

[gray aurora]

Okay I've seen them thank you

I'm just trying to get into pure math, in school we are not really taught properly so I've to start self studying

[scenic sequoia]

That’s good

[wet sentinel]

ohhhh nice, yea in school you wont learn proof based math

keep it up, and whenever you have any question you can ask in the suitable channels like #real-complex-analysis for RA and CA

also you should keep something in mind, dont give up if you find things hard because things are hard at the beginning

especially since its a totally new transition to proof based math which is different from the math you've seen so far

but eventually things will better with lots of practice

good luck on your journey!

[gray aurora]

I've been doing some proof by the way I'm not entirely new to pure maths, took Abstract Algebra 1 and Real analysis 1 and 2 last session

Groups , convergence of a sequence , Riemann integral (but not the proof aspect )

[gray aurora]

But I will put this in mind

[wet sentinel]

ohhhh i see, yea then you are probably more than prepared

[molten gulch]

Rudin
Rudin
Unnecessary

according to some friends

[mortal oar]

In my number theory class we basically started at axioms and then proved some of the fundamental theorems from the ground up, are there any books like this for optimization?

[trail hemlock]

as an alternative to rudin check out abbott's understanding analysis.

[foggy quest]

Real analysis: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/. Complex anal: https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[upper patio]

Can you recomend me some beginner friendly combinatorics books?I am kind of aware and can solve some very simple problems realted to NCR and FPM/FPA

[remote sparrow]

https://math.vanderbilt.edu/peters10/students.html

[gray aurora]

Thanks a lot

[trail hemlock]

read this messgae and forgot to reply to it. thanks for the in depth review, and actually this is very useful to know.

yeah after reading the ToC this seems really cool

wonder why its not talked abt as much

[remote sparrow]

well, there are dozens of competitors out there. sometimes books just fall by the wayside cuz not many people use or talk about them. it could also be because the core material is covered pretty rapidly, while many professors may not be interested in teaching applications or would rather teach different applications.

[trail hemlock]

hmm ok

[willow merlin]

any recommendation for learning combinatorics

[indigo blade]

books for undergraduate level math logic

[remote sparrow]

bona's A Walk Through Combinatorics

[willow merlin]

thanks

[remote sparrow]

#book-recommendations message

[remote sparrow]

https://www.amazon.com/Complex-Analysis-Cambridge-Mathematical-Textbooks/dp/110713482X

you might like this; it's rather concise

[restive pecan]

Can someone recommended some good pre algebra books?

[fresh hull]

What’s a good book(s) to bridge the gap between lee’s topological manifolds & lucks surgery theory (bordism rings, transversality whiteheads theorem etc. are required)

[wet sentinel]

I will check it out tysm

[ivory talon]

Any good books for quant finance?

I'm an ML engg, any good book recs?

[pale totem]

Can anyone suggest me a book for high school

[molten gulch]

What have you already studied

[pale totem]

Everything that is in High school except quadratic equations

[old elk]

Introductory books on measure theory other than Sheldon Axler's book

[pale totem]

Ty

[kindred jacinth]

do you mind me asking where youre from? cause how is it possible youve done evrything else and not quadratic equations

[pale totem]

India as u know

[rigid trail]

don't

it was a joke

For quadratic equations, don't really need a book

[sage python]

Try "Real Analysis for Graduate Students" by Bass

Or "Real Analysis" by Folland

[regal arch]

https://archive.org/details/modernintroducto00dolc/page/n1/mode/1up

[regal arch]

I'm looking for a PDF of this book, it's currently unavailable on the site.

Unless I'm being an idiot and don't know how to use it.

[molten gulch]

That person was ASKING for books, not recommending you one

if you really want one, try https://www.stitz-zeager.com/Precalculus4.pdf

[molten gulch]

Bass, Folland, Royden, Cohn, Schilling

[worthy kindle]

cohn

angus taylor's general theory of functions and integration is really nice as well

[molten gulch]

Billingsley is common to my understanding

[restive pecan]

YouTube

Then practice and practice practice practice practice practice practice practice practice practice

[foggy quest]

This book is good: https://sites.math.duke.edu/~rtd/PTE/pte.html

[sullen wigeon]

I second this curiosity

Quadratics are like alg 1

Aren’t they

at least factoring

and other stuff stems from those ideas

[cunning elk]

“everything except quadratics” casts serious doubt on your claim of having learned everything else in HS math

[old elk]

I hadn't remembered that I had this book. It also explains differential forms and exterior algebra very well, although it doesn't mention them in those terms.

[remote knoll]

I'm so used to several different math authors making innocuous sounding titles for grad level texts. So imagine my surprise when I see this book and open it to find it is actually basic math.

[low swallow]

https://www.bing.com/images/search?view=detailV2&ccid=l9h7PiTT&id=F0DC2F54577867CE0932BAEC89762D26F793C4C9&thid=OIP.l9h7PiTTrFIIBMJD0J14jQHaJl&mediaurl=https%3A%2F%2Fm.media-amazon.com%2Fimages%2FI%2F71HO01kCO3L.jpg&cdnurl=https%3A%2F%2Fth.bing.com%2Fth%2Fid%2FR.97d87b3e24d3ac520804c243d09d788d%3Frik%3DycST9yYtdonsug%26pid%3DImgRaw%26r%3D0&exph=2200&expw=1700&q=square+root+of+4+to+a+million+places&FORM=IRPRST&ck=CAFA213DE2D85693A4403F38C7C9F94E&selectedIndex=0&itb=0

[wet sentinel]

yea imagine lang having a book on basic math

[low swallow]

best math book ive ever read

enthralling, captivating

hooked from digit one

[worldly brook]

I hate cauchy

he keeps popping up

with all his random stuff

how can I for once get rid of this annoyance

where can I learn what the heck does it mean when someone mentions 'cauchy this, cauchy that'

what the hell did he even do

[cunning elk]

real asf

[molten gulch]

Well he has a bunch of results in analysis

I can't tell if this is ragebait or someone genuinely wondering what cauchy did, because if it's the second; look into real and complex analysis please

[worldly brook]

😭 def not rage bait

[molten gulch]

cauchy sequences, cauchy kernel, cauchy-goursat lemma, cauchy's integral formula

[worldly brook]

just tryna sum up the reqs for rudins

[worldly brook]

yep, those are a lot of cauchys

[molten gulch]

He was a very prolific mathematician, I'd assume biographies of him can be found, and a lot of his work is in analysis, so if you learn some analysis you should more-readily see his impact

[worldly brook]

how do you even get into analysis

also what sort of analysis sorry

[molten gulch]

Pick up rudin/abbott/amann and escher/whatever and start reading

[worldly brook]

I did

I can kinda understand some of it

[molten gulch]

Analysis is a lot to chew and it takes time

[worldly brook]

the neighbors part is impossible though

I suppose I need some topology or something

[molten gulch]

what neighbours part

[molten gulch]

Well rudin should cover the topology you need within the text itself

[cunning elk]

neighborhoods im guessing

[worldly brook]

this doesn't cut it as a self contained topology intro

wait really?

[cunning elk]

is that papa or baby rudin

[molten gulch]

yes

wait

if that's papa rudin you're gonna suffer

[worldly brook]

functional analysis, I think It's baby rudin

[molten gulch]

........

[cunning elk]

[worldly brook]

is it not

[cunning elk]

baby rudin is "principles"

[molten gulch]

You want "Principles of Mathematical Analysis"

[worldly brook]

ew

[molten gulch]

then you read "Real and Complex Analysis"

[worldly brook]

😭

oh

[molten gulch]

then you read "Functional Analysis"

[worldly brook]

but I need functional analysis

[molten gulch]

for what

[worldly brook]

do I really need the other ones

what do they even do

[worldly brook]

hilbert spaces supposedly

[molten gulch]

Yes because FA is built on measure theory which is built on basic analysis

[worldly brook]

and kernels

and God knows what else

[molten gulch]

What is your eventual goal

[worldly brook]

applying hilberts to latent spaces in ml

[wet sentinel]

bro jumped to grandpa directly

[worldly brook]

damn, that’s crazy

[wet sentinel]

real

[worldly brook]

I'm not doing this dudes entire heritage

how can I make up for funct analysis?

[wet sentinel]

i mean you dont specifically need to do the 3 books of the same guy

[molten gulch]

That's the thing, you don't

[wet sentinel]

but yea you should do intro real analysis before functional analysis

[molten gulch]

There's several well known texts on functional analysis

but all of them assume you at-least have done the content of baby rudin or equivalent, most also assume some measure theory, though AFAIK Kreyszig doesn't

[wet sentinel]

so you actually dont really need the second book

[molten gulch]

One of my friends did a course out of Kreyszig last semester and only had the equivalent of baby rudin

[wet sentinel]

but maybe you should know some measure theory, i dont really know since i havent done FA yet

[molten gulch]

AFAIK you lose some generality though

[worldly brook]

measure theory

what even is that

welp

[worldly brook]

what BCs is he doing?

or at what point in academia do you do that

[molten gulch]

Was a CS major, switched to maths

[molten gulch]

Mid-late UG or early grad school

[worldly brook]

mid late? 😭

[molten gulch]

yep kreyszig only assumes intro analysis

[worldly brook]

this preqs seem great

what is that book called?

[wet sentinel]

this is from follands "real analysis"

[wet sentinel]

you dont need measure theory for this, he covers it at the beginning

[worldly brook]

... metric spaces

where do metric spaces come from

[wet sentinel]

baby rudin

[molten gulch]

They're topological spaces with a metric, aka a notion of distance

And if you read baby rudin you'd learn them

[wet sentinel]

you will have to go through something like that anyway

[worldly brook]

so I should just read baby rudins intro

[molten gulch]

Both books mentioned, Kreyszig and Folland both assume you know baby rudin equivalent analysis

[worldly brook]

then I'm good to go

[wet sentinel]

exactly

[molten gulch]

no, the whole book up to chapter 7

[wet sentinel]

dont read beyond chapter 7 from baby rudin

[molten gulch]

I've heard chapter 8 and onwards are bad

[worldly brook]

hm?

[worldly brook]

oh

[wet sentinel]

people say its too messy and bad after that

[molten gulch]

There's better sources for multivar

[worldly brook]

glad to hear it now from you guys

thanks

[wet sentinel]

i think you can do chapter 8 if you want

its not multivar

its about special functions like gamma function, power series etc

[worldly brook]

no offense, It's not that I don't like math but I think of it more as means to an end 😭

[sage python]

Chapter 8 is fine/good, 9 is kinda mediocre, 10 is mind virus, 11 is just a bit out of place

[molten gulch]

....disappointing /lh

[molten gulch]

mind virus???? wtf does that mean

[worldly brook]

If I can get to my goal without doing much theoretical jargon that would be great

[wet sentinel]

sloth can give you a more accurate review

[wet sentinel]

like this for example

[molten gulch]

You'll realize that most of it isn't actually "jargon" and that we have specialized terminology for a reason

[worldly brook]

mind virus 😂

[wet sentinel]

"10 is mind virus"

[molten gulch]

😂 is used so much we have a deep fried version just for it

[worldly brook]

yeah this is where engineering diverges from math

we don't find proofs, we just probe it until something sticks

[sage python]

Rudin does not understand differential forms

And chapter 10 kinda exposes that

[molten gulch]

[wet sentinel]

dami, what do you recommend for multivar analysis. Pugh?

[sage python]

Pugh I've barely read, it seems a bit awkward in the topology side

[worldly brook]

can you skip topology all along, or do you have to read one book on it at some point?

[sage python]

Does it define forms via multilinear algebra or using that nonsense about "Oh it's a symbol looking like blah that sends a parametrized surface to this integral"?

[wet sentinel]

depends on what you want to do with topology

[sage python]

Which is the most stupid fuckin thing ever

[wet sentinel]

if its for things like analysis then you can find what you need in a textbook on analysis

[worldly brook]

great

[worldly brook]

this is sick indeed

also, how do you get those roles you have

I've been told I should aspire to learn 'spectral theory' and 'representation theory'

[wet sentinel]

i dont really know, i am actually asking to know what to use for multivar

[molten gulch]

Who told you?

[molten gulch]

what the FUCK???? I've only ever seen the multilinear/tensor way of doing it

[worldly brook]

the ml dudes in some other place

apparently It's helpful to know it

[molten gulch]

Frankly, they just dumped a ton of random fields on you

I do not know where the hell rep theory shows up in ML

[worldly brook]

damn lol

[wet sentinel]

i mean if you are doing engineering then i dont think you would need representation theory for your studies lol. If you want to study math for fun then sure you can study whatever you like

[worldly brook]

I think I do?

[molten gulch]

If you just want an intro to ML, just knowing basic calculus, finite dim linear alg, and (calc based) probability seems enough?

[sage python]

Machine learning foundations mostly just need linear algebra, multivariable calculus, probability, statistics

[molten gulch]

You can kinda build whatever else you need over it

[worldly brook]

pretty sure you can do rep theory on the latent spaces of the data which are learned via an embedding model

[wet sentinel]

but you dont seem like you want to study things that wont really be directly of use to you

[sage python]

For research topics you can lean quite a lot on math

"Equivariant deep learning" is probably a thing

[worldly brook]

well I already know some ml, I wanna get much better at it though 😂

[worldly brook]

well. I don't wanna do unnecessary jargon 😭

topology yells useless for me

[molten gulch]

yet again, jargon isn't jargon for no reason, and I lean quite heavily personally on "learn the general theory then specialize it to examples"

but I know that doesn't work for everyone

[molten gulch]

Yeah...it's very much not useless if you're working on hilbert spaces, doing anything related to physics, etc....

[worldly brook]

that's interesting, cuz I kinda hate physics and general engineering outside of comp sci related

well

[sage python]

Wait so when they said you needed spectral theory

[molten gulch]

anyway I need dinner, bye all

[worldly brook]

anyways, what should I do after 8 chapters of baby rudin

[sage python]

Does that mean functional analysis spectral theory?

Or just spectral theorem and SVD and all?

[molten gulch]

also dami, separate qn, are you still a mod? or did you retire?

[sage python]

Hiatus

[molten gulch]

ahh okay

[worldly brook]

I suppose this

[sage python]

Okay in that case you don't need functional analysis

[molten gulch]

You learn this stuff in a first course in finite dimensional linear algebra

[sage python]

And corollary you don't need Rudin

[worldly brook]

is that normal linalg?

[heady ember]

I'm almost there in FIS ahhh but lin alg feels so dry to me lol

[molten gulch]

Man I love LA

[sage python]

Spectral theorem is about normal operators

[molten gulch]

IDK why but I've found it so nice

I need to learn analysis, I say after not touching analysis AGAIN

[worldly brook]

binary operator theory and all that?

[heady ember]

Personally, I've enjoyed analysis much more than lin alg.

[worldly brook]

ie, vector spaces

[molten gulch]

wrong operator

[sage python]

Linear algebra courses need to juggle points of view more that's the way to make it fun

[worldly brook]

or am I tripping

[sage python]

Operator means linear map from a vector space to itself

Basically a square matrix

[molten gulch]

An operator (T) on a (finite dimensional) vector space (V) is an element (T \in \mathrm{End}(V)), which means that it's a (bijective) map (T \colon V \to V) and when we pick a basis, is represented by a square (n \times n) matrix of full rank/nonzero determinant where (n \coloneq \mathrm{dim}(V))

[heady ember]

A normal operator is a linear operator T: V -> V (linear in the sense that T(au+v)=aT(u)+T(v)) iff T*T = TT*. Easier to understand would to be just consider T to be matrix. Then the matrix T* is just the transpose of T with all entries conjugated

[hasty eagle]

Ryan + skye (TCC)

[worldly brook]

not this again.. 😭 the weirdness from that book I tried to pick up once coming back to me

[heady ember]

Wdym weirdness

[molten gulch]

Did you jump right to the chapter on operators without reading everything else?

[worldly brook]

this is linalg ?

[molten gulch]

yes this is

Normally in linear algebra you learn a lot about matrices, but many times it's not too nice to pick a basis

[heady ember]

Linear algebra is all about the study of linear spaces (i.e. vector spaces)

[molten gulch]

so we generalize our statements to operators and pick a basis when needed

[worldly brook]

not really, I tried doing some book on the maths for ML, and this came in the preqs for linalg

[molten gulch]

Read a plain old linear alg book first

don't just read a maths for ML type book without already knowing the maths

[worldly brook]

true

[molten gulch]

those books assume you know the basics and will jump ahead

[worldly brook]

haven't pushed forward in linalg tbh

I have the book, just haven't finished reading it

[molten gulch]

I mean, deisenroth does the core of linear alg in 40 pages, that might be a bit too fast

[worldly brook]

I love quick stuff 😭

[molten gulch]

see this book is literally intended to be A SUPPLEMENT for students in an ML course at uni who've already taken linear alg and calculus and just need a refresher

[sage python]

Try "Linear Algebra Done Wrong" if you want to understand things properly

[molten gulch]

LADW is very nice I can concur

LADW and FIS are my favourite linear alg books

[trail hemlock]

unc on unc violence 💔

[worldly brook]

which website is this?

[heady ember]

Mandatory warning: Do you actively read? I.e. critically think about why the ideas and theorems make sense, and do a generous number of exercises?

[molten gulch]

it's a book

[worldly brook]

I spend hours reflecting on a single page

[molten gulch]

https://mml-book.github.io/

[worldly brook]

Is it good?, better or worse then Ray Kunze

[molten gulch]

Do you take notes and attempt exercises? With some books spending a day on a page may be normal, yes, but at this level it seems excessive

[heady ember]

How do you find satisfactory intution for lin alg? Sometimes when a theorem/definition, say, of normal operators pops up, I don't immediately understand it. Naturally, I wait and see. But sometimes that intuition never seems to come.

[molten gulch]

Kunze is a good but relatively difficult book