book-recommendations

[remote sparrow]

give some natural language examples

[gray gazelle]

'kay

[lost pilot]

My advice would be, pick a textbook meant for a philosopher's.

How the hell is Jech semiformal?

That goes into so much detail

[remote sparrow]

hrbacek/jech is semiformal

not jech

[lost pilot]

Ohh so you're not talking about that one that's like. the 3rd edition Millennium or whatever that recently got a rerelease

[remote sparrow]

i was not

[lost pilot]

ok

I haven't read it, but I want to, but I'm deciding whether to read the 3rd or 2nd edition, because I don't know. I read that the second edition is better.

[remote sparrow]

https://www.amazon.com/Introduction-Revised-Expanded-Chapman-Mathematics/dp/0824779150

[lost pilot]

ty

[remote sparrow]

are you talking about big jech or hrbacek/jech

[lost pilot]

The one that's by just jech.

What do you think about that one second or third edition

[remote sparrow]

i have never bothered to look at the second edition

but since jech is supposed to double as an encyclopedic reference, why not get the one that's the most up-to-date and has the most coverage? it has 100+ pages over the previous edition

i would really just recommend kunen if you're trying to learn formal ZFC

you can also supplement with Basic Set Theory by levy (doesn't do forcing but instead has applications to other parts of math)

they are both reasonably priced

i'd wait until the springer holiday sale (around december) to pick up jech 3rd ed. for $100

[lost pilot]

It's been a while since I've studied formal mathematics, so I was planning to brush up on my colleague. my calculus and real analysis. with Lang. and Spivak. Milineal algebra with Lang. and axler. But the reason I've heard people recommend the second edition over the third one is because the third one omits a lot of information And just prefer you to papers. where's the second one is more self contained What do you think about Halmos naive set theory? I've heard that it's not Naive. even though it's called that

Sorry for the spelling mistakes, I'm just using voice to text

[remote sparrow]

halmos explicitly says that he will not define what a set is on the very first page

[lost pilot]

Nobody defines what a set is though. The definition of a set is always informal. It's primitive. It's always just a collection of things.

[remote sparrow]

@fervent surge @shadow river

looking through halmos a bit more closely, he mentions the axiom of extensionality, specification, pairing, union, substitution (replacement), infinity, power set, and choice (along with a short section on zorn's lemma). he mentions extensionality + specification can be used to prove the existence of an empty set. what isn't mentioned is foundation (aka regularity). in fairness, foundation has little use outside of further exploration into set theory. the axiom of substitution is only given an intuitive definition. a semi-formal description is given in enderton and hrbacek/jech. i find it a bit strange to define ordinals before cardinals in what is ostensibly supposed to be a general exposition for set theory that, to paraphrase halmos, you can safely absorb and then forget.

[shadow river]

Halmos is naive in the sense that 99% of the set theory mathematicians use is naive, like we sort of informally use set theory but don't worry too deeply about the finer details that something like Jech/Kunen covers

like Halmos covers almost all the set theory you'd need as a math student (not studying foundations/set theory obviously), up to the basics of ordinals/cardinals/transfinite induction, it's good but can still be tricky to read as a newer student

[remote sparrow]

@trail hemlock @mystic orbit @rain wren the main thing about point-set is that lots of people need it, but few will use most or all of the results

[uncut salmon]

Any book that talks about geometric inversions in terms of projective geometry?

[open verge]

any horror/thriller novel like a girl on a train or silent patient

[foggy canyon]

Hi, I’m 23 and I have a learning disability. I want to learn math for the job I want.

What resources would you recommend for learning diving physics (such as Boyle’s Law and Charles Law), basic algebra, multiplication and long division? Like what books or apps/website should I use?

[gray gazelle]

khan academy, serge lang’s book on basic math, mathematics for the practical man, Axler’s college algebra and trig

professor leonhard has a good algebra and trigonometry series if you’re looking for something more university style

[gray gazelle]

idk much about diving physics

do u need fluid mechanics?

u probably need to master basic physics first?

u can look at university physics by young and freedman that’s a standard undergraduate physics textbook but you need calculus

u probably also need coding

[timber mesa]

from the sound of it they don't really need any advanced physics, just simple algebraic proportion kinda things which are what Boyle and Charles laws are about

[gray gazelle]

ohhhh

[timber mesa]

an "algebra physics" type course might suffice

[gray gazelle]

yea

bunch of those online

[timber mesa]

there's some textbooks like that written to not require calculus

idk any specific ones but yes there's plenty online lol

[gray gazelle]

i took algebra physics in hs 🙃 taking calc based physics rn

im cooked for my exam

errrr what are free body diagrams fr ?

tf is a normal force

[foggy canyon]

I want to join the Navy with a SEAL contract. The second phase of SEAL training is combat diving and they have to pass a dive physics test which is basically just basic algebra, Boyle and Charles Laws are on the test

[foggy canyon]

So I should just take basic algebra classes on Khan Academy ?

[gray gazelle]

u can yea

all the options are good

[timber mesa]

oh I see. Yeah it seems like you could read an "algebra-based physics" type textbook and find a section on this

you probably need these specifics as an heuristic thing as a diver

[trail hemlock]

i see

[gray gazelle]

giancoli

[north nexus]

Is there a book that deals with actions of topological groups on spaces and like with lots and lots of examples

[vital bane]

Lol yea this came out a while ago

I'm still here with my 4th edition of Griffiths and 3rd edition of Axler's LADR

[gray gazelle]

Dead

[remote sparrow]

u should really get the 4th ed of axler

[copper warren]

is LADR really that good? I've been thinking about reading it for a while

[remote sparrow]

i think it's good

[copper warren]

Any prereqs?

[remote sparrow]

nothing, technically, but LADR is explicitly written for students who have already had a first course in linear algebra on euclidean space

[stable flicker]

For a first course, maybe ILA instead?

[copper warren]

So Im a high schooler, what should I be doing first?

[remote sparrow]

have you done calculus

[copper warren]

to what level

[copper warren]

will check out

[remote sparrow]

umm...the average curriculum?

like, have you done single-variable calculus

[copper warren]

Very vague, its different in every country

[copper warren]

yeah pretty much

[remote sparrow]

the baseline is stewart's calculus or some similar text (i don't really think business calculus or calc for life sciences is adequate)

some schools use apostol or spivak

[copper warren]

I've never heard of a high school using stewarts yet alone spivak for calc

maybe im just misinformed

[remote sparrow]

i did

you might have used larson

calculus books are mostly the same

[remote sparrow]

#book-recommendations message

[copper warren]

I go to a british school so we just use the textbook for our a level course

no external books

[remote sparrow]

i'm sure your A-level is roughly equivalent to any high school calculus class

[copper warren]

Probably, I'm taking a level further maths though so maybe its alittle harder

The last few topics in calc are taylor, leibnitz theorem, weiestrass sub, some numerical analysis, reducable differential equations then finally advanced integration techniques

[signal mountain]

you can probably just jump into a linalg book, i dont have a personal recommendation but halmos' finite dimensional vector spaces is classic and even if you dont use his book he has a book of problems which is also very well regarded, i see a lot of people here also talk about FIS (friedberg, insel, spence)

[pearl cobalt]

@copper warren if u want harder try
Jee adv 47 year maths by disha u can get on amazon

[signal mountain]

though i dont know how well either of these would serve as a introduction to proof-based maths - normally for that i would recommend tao's analysis i, which is very gentle and takes you through a lot of very basic stuff. abbott again is recommended here with i think similar goals (also an analysis text)

[copper warren]

Isn't that the indian test JEE? No thanks

[pearl cobalt]

Ye but it have hard problems

[copper warren]

Thought baby rudin was preferred/known for analysis

[pearl cobalt]

And gaokao china exam also have toughf problems

[signal mountain]

it is "the anaylsis book" and many people argue over whether thats a good thing or not
but my point was less about recommending you an analysis book but instead recommending a book that gives you a graceful introduction to proof-based maths, they just so happen to be analysis texts

[signal zenith]

No lol

Baby rudin is very much widely disliked definitely for people who are new to proofs it is especially disliked

[signal mountain]

my introduction was through an abstract algebra text, and im sure that there is also a linear algebra text out that would serve you well too

i just dont have reccomendations for those

[signal zenith]

I personally didn’t mind it but that’s a very controversial take and I would never recommend baby rudin as a first proofs book

[daring lake]

papa rudin is a good first proofs book

[signal zenith]

It’s significantly harder than the other recommended analysis books which is good for a challenge and probably more in depth but again, terrible for beginners

[molten gulch]

I think the first time we ever touched a proof was a linear algebra book

[copper warren]

Either way Im going through adam's calc right now so I'll probably take on LADR or ILA for LA and Im interested in logic so math logic by enderton. What do you think?

Dont want to have too many books

[daring lake]

i read rudins pma alongwith bartle and found it to be a pretty neat combo

[molten gulch]

you can never have too many books

[signal zenith]

I’m surprised y’all didn’t have a separate intro to proofs class

[daring lake]

for measure theory i only used papa rudin though

[signal mountain]

whats ILA?

[signal zenith]

All math majors at my university have to take one

[daring lake]

i am an ee major

[signal zenith]

Ah

[copper warren]

introduction to linear algebra if im not mistaken, was mentioned by ^

[molten gulch]

we're CS

we don't have to take the proofs course

[signal mountain]

ah strang ok

yh lots of ppl rec that

[copper warren]

It gets messy dont want too many things to be doing, got ECs, other subjects and social life to manage at the same time

[daring lake]

you can only have math xor social life

[copper warren]

I've managed it pretty well tbh

Most people just say that and cope when they very well could have a social life

[signal mountain]

doesnt sound absurd, generally logic is a course offered later into an undergrad when you have more maturity but absolutely dont let that stop you, at least give it a go

[molten gulch]

burn your social life

it's so worth it imho

[copper warren]

Honestly its mostly just curiosity, I was interested in how "proper" logic works. I may just go with the more informal/philosophical way of approaching logic because Im probably too daft to understand the formal rigorous stuff now

No point in not trying though

[daring lake]

all books?

[copper warren]

30.5 gb of what??

[molten gulch]

yeah

[daring lake]

sheesh

[copper warren]

I thought it was something else 💀

[daring lake]

how many have you actually read ?

[molten gulch]

a few, and used a few for class

[copper warren]

0 he just looks at the pictures

[molten gulch]

they* and no

[copper warren]

mb

[daring lake]

i am kinda guilty too since i have like 10 real analysis books and 5 measure theory books but havent even completed one

[copper warren]

reminds me of when I used to look at my moms old textbooks and just stare at the diagrams trying to understand a single thing

[molten gulch]

we have like..20 or 30 RA and 20 MT

[daring lake]

i only have hardcopies, so its collecting dust atm

[molten gulch]

lol that was us like 15 years ago

they were all harmonic analysis and signal processing books

[copper warren]

I still have one of my moms old numerical analysis books

[marble solar]

This was me a while ago. I've now went through almost all of my real analysis & complex analysis books. It took a long time, however

[molten gulch]

oh niceeeee

[copper warren]

I understand the first few bits then it just starts turning into hieroglyphics

one day

[molten gulch]

numerical analysis is just...a lot of calculus and linear algebra

[marble solar]

The best way to get into thinking about analysis is probably spivak's calculus

It is the gentlest way

[copper warren]

Cant find a good quality pdf, and I already have a calc textbook so I dont wanna purchase another one

[marble solar]

Understandable

[daring lake]

I think they were sarcastic? I don't associate spivak calc with gentle at all.

[copper warren]

Barely anyone knows the textbook I have, I've searched alot about it online, any of you have experience with adams calculus

[copper warren]

Maybe I don't really know, I just heard its rigorous

[daring lake]

Yeah it is. It's in an odd place between calc and RA.

[remote sparrow]

some unis do, some don't

[remote sparrow]

i think leary/kristiansen and the recent book by westerstahl are accessible introductions to mathematical logic

L&K is available for free online too, but both are reasonably priced

[marble solar]

Not gentle calculus, but gentle real analysis

[pseudo lotus]

Thus Spoke Zarathrusta - Frederich Nietzsche

oh math books

oops

[timber mesa]

no literature recs are fine to discuss

[sage python]

Lol this could be parsed as having opposite meanings

[timber mesa]

yeah I realized

[molten gulch]

LMAO

needs a comma

[timber mesa]

it's fine to discuss literature recs here, there's also the https://discord.com/channels/268882317391429632/1213613211459256411 thread though

which might be more apt

[pseudo lotus]

It’s more philosophy

[timber mesa]

true

[sage python]

Yeah math and philosophy are spiritually quite close

[pseudo lotus]

Real

[gray gazelle]

https://courses.csail.mit.edu/6.042/spring18/mcs.pdf need basic single variable calc knowledge beforehand (integrals, differentiation at fundamentals) - this book also has supplemental lectures on mit’s ocw under math for computer science

id recomend watching 18.01's lectures / professor leonard's calc 1 playlist to get up to speed

https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328 the bar is lower for this book tho

[molten gulch]

Please do not distribute links to pirated books

[gray gazelle]

sry, ill reformat

[molten gulch]

thank you

we're using epp's book for our discrete maths class, it's not that bad

but we can't rlly share our opinions because we don't have anything to really compare it to

[ripe root]

where can I find notes for introduction to real analysis bartle?

or in general where can I find notes on specific textbooks

[hallow oriole]

epp is good!

i prefer rosen but epp is good

@remote sparrow do u have any hardcover linen books from lulu? i want to see one

[remote sparrow]

never used that option

[hallow oriole]

hmmm ic

[remote sparrow]

@torn crypt have you read pillay's book on stability theory?

it's a dover

[torn crypt]

I have a physical copy but no

[inner quartz]

Artin algebra and introductory to real analysis by W.R. Wade is a great combo book

It’s been 2 years since I’ve done pure math and started going thru it recently and it’s the best

[grim ore]

For a standard ug real analysis class, would Real Mathematical Analysis by Pugh be a good book? I was looking for something similar to rudin but with a lot more diagrams for i guess like an intuition. The figures in here look really nice upon skimming but I also dont know if there are better books

For context my class does lectures, readings, and problems out of rudin

[marble solar]

Pugh is good, but I'd focus on just following what your professor wants

If I were teaching my own analysis class I'd probably teach out of Rudin or Pugh

[hallow oriole]

theoretically if you are doing rudin from a class you will be gaining intuition from your professor's lectures

[grim ore]

honestly i wish; like i do go to every class but it feels like word by word whats written from rudin instead of adapting more

but idk if thats a personal skill issue

[hallow oriole]

do u go to office hrs?

[grim ore]

yeah i do, hes actually really good at answering questions

so giving credit where its due

[hallow oriole]

if you're going to office hours and lectures and it's still not enough then sure go for a supplementary book imo

[marble solar]

Read rudin ahead of time, prepare questions, ask during class or office hours

[hallow oriole]

but maybe consider that you aren't asking the right questions or something

[marble solar]

I think Rudin is actually enough, the details really aren't that bad to fill in

[hallow oriole]

🤷‍♂️ some ppl will just learn differently

[grim ore]

I havent thought of that, ive just been racking my brain having trouble understanding rudin

[hallow oriole]

ask ur prof how to think abt it etc etc

bashing your head against a wall will eventually get you through the wall but you'll hurt your head

ur paying tuition to have phds give you help, use that

[grim ore]

true

thanks for the advice frfr @hallow oriole @marble solar

[quaint arch]

Can someone suggest me a good book on PDEs where I can get the topics like, "Homogeneous Wave Eqns, Vibration of Finite Strings with Fixed length, Nonhomogeneous Wave Eqns," etc

Till now I've been studying the book Linear Partial Differential Equations for Scientists and Engineers by Tyn Myint -U and Lokenath Debnath but the explanations or the language of the book seems horrible imho

As for my background, I am an undergraduate student pursuing a Bachelor's degree in Mathematics.

Now, coming back to my issue, it seems the syllabus of the course in our university is directly designed using the book I mentioned. So, if the recommended book that has the same sort of contents as this book, then it'll be very helpful in my case.

[fresh skiff]

I like Rudin, but it gave me a hard time or maybe the hardest time

[cinder magnet]

i share the same sentiment but only difference is that it is giving me the hardest time

[grim ore]

Thanks for affirming me 🥹

[gilded olive]

what are some niche topics in algebra I can explore after taking a course in groups, rings, and fields? and could you also recommend some books to read after a general introduction to group theory (and rings and fields)?

[grim ore]

I am liking the dialogue nature of pugh so far if you want to look into it

[trail hemlock]

yes rudin …. challenge me 😩😩

[grim ore]

honestly lie algebra is a nice place to go to

Or commutative actually

Commutative then Lie ✅

[vital bane]

I have the PDF, I'll finish 3rd ed first

[tribal crow]

asking on behalf of @zinc turtle: she's looking for an undergraduate statistics book to study from. does anybody have a recommendation?

[tender river]

wackerly?

[stuck zephyr]

does anyone know which book is best for discrete math?

[uncut nest]

I am guessing you want an introductory book to discrete maths?

[molten gulch]

For intro discrete, epp or rosen and decent afaik

[gray gazelle]

Has anyone read Galois Theory Through Exercises? If so, is it good? Worth it to solidify some basic knowledge about Galois theory?

Please ping me

[stuck zephyr]

yes

[stuck zephyr]

can you link them

[formal parcel]

Is introduction to linear algebra by strang a good book for someone brand new to linear algebra

[formal parcel]

im going in blind into linear algebra so if there is any books anyone reccomends for absolute beginners it would be appreciated

[oak patrol]

I have a good book

[formal parcel]

what is it?

[oak patrol]

https://ruor.uottawa.ca/items/f66a4ede-e276-486c-9067-9621d5347440

It's the book called "vector spaces first"

A group of professors at my university wrote the book

[umbral field]

strang has video lectures posted on youtube that you can follow as you go through the book

[shadow river]

hey fellow UOttawa friend

[oak patrol]

Heyyy

What year are you in?

[shadow river]

i graduated a few years ago actually, what about you?

[oak patrol]

I'm in 1st year

I'll send you a friend request @shadow river

[fresh hull]

any good books for learning graph theory for the first time w/ topology

please reply to this msg or @ me if u reply

[gray gazelle]

Excuse me, I'm going to start studying at college, but I graduated from high school many years ago and don't remember anything, any good resource to learn by myself?

[sage python]

Try Khan Academy

[gray gazelle]

Ohhh..

Pre K, high school & college.. and even the get ready courses?

[sage python]

I mean depends on what exactly you need to learn. If you're comfortable with basic algebra and just need to do some more advanced algebra and some trigonometry, go through that

If you're iffy with adding fractions or with the equation of a line

Then you'll need to dig deeper

[sand path]

Doing the same thing right now. I recommend 2 books that I’m currently working through. Basic Mathematics by Serge Lang & Precalculus: A prelude to Calculus by Sheldon Axler. I don’t know any good pre algebra books but I’d imagine khan academy would be ideal. You can also check out Organic Chemistry Tutor & Professor Leonard on YouTube

[lucid badger]

any good books for mathematical proofs?

[timber mesa]

Richard Hammack's Book of Proof, it's available on his website for free

[grim ore]

refuses to comment further 😂

[gray gazelle]

mathematics for the practical man I forgot the author tho but his stuff is good it’s an old book but good illustrations and examples for arithmetic and algebra

https://www.aproged.pt/biblioteca/mathematicsforthehowe.pdf

[gilded olive]

thoughts on Algebraic Combinatorics: Walks, Trees, Tableaux and More by Richard P. Stanley?

[trail hemlock]

it’s the message right below that ?

[hallow oriole]

it's great

[gilded olive]

can i read it simultaneously while taking a course in group rings and fields

i mean after the group theory part of the course has passed, can i start reading

[grim ore]

I loved reading this personally and it was more of a dialogue between stanley and the reader rather than being dense

it’s also great for introduction into research topics and the tableux section opens a lot more doors

[grim ore]

you for sure can, but also just be wary that you may have to look into a couple of things outside of realm of algebra to really understand

[grim ore]

i did rings and fields first and it was fine for me to read without group theory but that’s my background

[oak patrol]

Yo I sent the book a long time ago

[gilded olive]

i see thank you for the reply!

[gray gazelle]

Can someone recommend a book to learn about hyperbolic functions in depth? i believe its part of complex analysis but my prof just started with the heading then wrote down some forumlas and then we were solving questions using the e^x "expansions" of sinhx and coshx (no introduction, no explanation)

[hallow oriole]

mm yeah you'll be fine. just look up anything relevant you don't know yet in ur alg textbook

[steel cloud]

I already covered Rudin up to differentiation and Tao I and also did Carothers up to six chapters now I am just looking at Basic real analysis by Sohrab, any advice how can I approach this book?

[vocal egret]

is complex analysis by Deshpande worth reading through?

[late pivot]

wasserman’s “all of statistics”?

the first book is like 200ish pages and very light

and not fully rigorous

@zinc turtle

[zinc turtle]

hello there bif

[late pivot]

hi POKEDANCE

[zinc turtle]

im doing john a rice statistics book and ill probably stick with that for now

[late pivot]

o nice

yeah at intro level there are

lots to choose from

[zinc turtle]

thank you for the recommendation

[late pivot]

so doesn’t matter too much which u choose

np!

[zinc turtle]

would this be more advanced?

[late pivot]

i’m not sure

i’ve never seen the book by rice but that was one of the main books that got me interested in stats

[fervent wyvern]

Hello! I want to ask for reccommendations on what materials/resources to use to study abstract geometry(specifically i can't wrap my head around the proofs of the theorems of hyperbolic geometry). send help😭. Thanks!

[stable flicker]

Yes it is more advanced

I recommend anything that is math stats and sufficiently established. Anything that is completely descriptive (and zero math) is not good for future study of stats. For something free and what I think is decent, I recommend Evans and Rosenthal.
For something that is not free I recommend Panaretos Statistics for Mathematicians

[sage python]

At a glance it seems like most of this book is redundant for you anyway. Why not just continue to Rudin chapter 6/7 and then do a measure theory book?

[steel cloud]

I have to prepare for my master college entrance exams so....I want to do measure theory but also I have to revise this stuffs

[quick hornet]

your best bet might unironically be to find a set of lecture notes

[gray gazelle]

Bump

[trail hemlock]

sounds like rudin

ive heard over and over that its a great reference text

[heady ember]

I basically use Rudin as a list of theorem statements and exercises

[remote sparrow]

"contain all the proofs for all the theorems"

mr. left as an exercise may not necessarily be ideal

i don't think a single volume or even a set of volumes can necessarily cover everything, but zorich generally spells the main results out

[trail hemlock]

a "proof outline outline" 🙏

[late pivot]

zorich’s books are the closest to that for early grad real analysis

i don’t know why you would want such an analysis book though

[remote sparrow]

why do people want encyclopedias (or reference works more generally)? although information exists on the web, a reference work collects all that information in a single volume or volumes and presents that information in a consistent and organized fashion. part of that consistency comes from having the same notation globally.

[merry tiger]

Dude.

Someone please read shadow slave

If you’re into fantasy stuff

It’s very good

It’s an online novel, read it on webnovel, or find some other pirated website, and if you want an audio book look for “Anya Audiobook” on YouTube

It’s an AI voice but that’s the best you’re getting…

[keen vale]

do yall have a rec for graph theory?

[tribal crow]

@hallow oriole

[hallow oriole]

intro?

diestel!

[keen vale]

yeah

[keen vale]

hm, let me check that out

[hallow oriole]

https://diestel-graph-theory.com/basic.html

[keen vale]

does exercises come with it?

[tribal crow]

of course lmao

Diestel has tons of problems

[hallow oriole]

lots and lots of exercises, not much in the way of solutions! feel free to ask in #discrete-math or #combinatorial-structures for solution verification or something

[keen vale]

hm, ill take it, thanks!

[keen vale]

by the way, would i need linear algebra as a prerequisite?

[hallow oriole]

not for a good amount of the sections really

any linalg needed could be learned on the side i guess

having said that you should pick up linalg as soon as possible really, you'll never truly be able to avoid it

[late pivot]

yeah exactly idk

[remote sparrow]

are you agreeing with me or are you saying you don't know why someone would want a reference work?

[late pivot]

yea

especially for analysis

Where it’s like u can find everything on wiki/encyclopedis of math anyhow

[remote sparrow]

but my point is exactly opposite that

it's that there are good reasons to want a reference work

[late pivot]

oh okay

hmm

i feel like such a thing may not be practical in analysis

because like

you often get slight perturbations of a situation

that cannot be encyclopedicslly written down

but if u recognise the scenario/method morally

you know what to apply

this is in contrast to say algebra

where theorems are more precise

analysis is more guided by principles

I don’t know what an encyclopaedia of analysis would look like, if not just a collection of bounds and methods

Which is not really compelling

since there are too many

[crimson pagoda]

it’s a lean theorem prover that gives you the best bound known by all current methods

[late pivot]

i guess that sounds pretty promising

although current methods may only be known

to the minds of some deranged analysts

nazarov, tao, pinelis, …

[crimson pagoda]

The deranged analysts are in this chat right now.

[late pivot]

Lolno

[drowsy nacelle]

i might be deranged

[crimson pagoda]

Heyyyyyy

[drowsy nacelle]

definitely not an analyst

[crimson pagoda]

ur not

[drowsy nacelle]

yeah i dont think i am

[crimson pagoda]

Yay

[foggy gorge]

What is a better book for precalculus? Art of problem solving or James Stewart's?

[gray gazelle]

hi everyone, im trying to learn math even tho i think i aged so much ;-;. but the intrest of mathematics really developed slow on me , so can anyone tell me the book of mathematics which allows u to understand how nature works and things expands like nature,space, or in future i really dont know much about maths and im sure u do, so please can anyone suggest me book which will be available on public domain for freee thank you future wishes!

[gray gazelle]

how nature works and things expand like space?

thats physics

not mathematics

well still learn pre calculus then calculus(its the way to understand motion of any kind)

then pick up a book on university physics

start doing it

[tardy phoenix]

There's always youtube. You could watch a brief video on what maths can be used for, same for physics.

A lot of physics is just maths applied, to phenomena that can be observed.

Can anyone recommend Polya's How to solve it? I just bought it but I'm ill and lazy and haven't gotten through the foreword yet 😂

[strange sentinel]

Haven’t read Stewart but I can vouch for aops

[humble kiln]

I'm torn between two textbooks to start learning linear algebra, one is elementary linear algebra by howard anton 12th edition which ik is well known and the other is linear algebra by jim hefferon 4th edition, any notes or recommendations on which to choose?
im learning linear algebra for graphics programming if that helps also

[vocal egret]

gonna be fr, Precalculus is a bit wordy some peeps, but it a good book

[vocal egret]

grab an online copy in libgen and compare the contents, both books are for diff peeps

[humble kiln]

yeah i have both textbooks downloaded already but i was still wondering if there was something that makes one a more obvious choice

[vocal egret]

lemme check uh-

same thoughts

@humble kiln Anton for computational, Hefferon is more abstract (some goes to calculus).

Honestly, Hefferon fills in what Anton doesn't, you can't go wrong with Anton

But it's less beginner friendly afaik, Larson is more friendly

das all ik, cjkdcmmemd

[humble kiln]

ooo okay thank you

[vocal egret]

honestly, just check out the syllabus of the book and compare with the curriculum's

[foggy gorge]

Hi

[vocal egret]

olla

[foggy gorge]

Tbh, I'm totally lost on what to read
I'm already at the chapters about trigonometric functions graphs of the Stewart's book, but I'm not understanding anything

[vocal egret]

bprp

[foggy gorge]

I understood some key points but there is still some points I didnt

I understood like what each variable in A sec(Bx - D) + Z does, but idk how to graph it or reach it through a graph

Or why is it that the function is undefined at x = C/B + (kPi/B) for some k integer

[vocal egret]

my brain ain't braining

[vocal egret]

I got an odd question to ask

math book author who isn't afraid of going to complex stuff with rigor, or an suthor who prefers to write in a more diary-like way to a reader?

[gray gazelle]

best way is to have

graphing calculator physical or computer

keep graphing with different values as u learn

u will learn to draw them on paper eventually

[viscid valve]

What book would anyone recommend for learning ODEs (assuming I'm a beginner with them, with a sufficient enough background with calculus to start on it)?

[gray gazelle]

Elementary Differential Equations and Boundary Value Problems by william Boyce and richard

[viscid valve]

Alright thank you!

[marble solar]

Boyce & DiPrima is my favorite beginning book as well

[barren turret]

What books would you recommend for a beginner new to mathematical logic?

[gilded olive]

I want to read an algebra book next semester that will introduce me to different fields of algebra. Currently, I am taking a Groups, Rings and Fields course. The group theory potion will be done by the second semester. After the suggestions on the server, I narrowed down my choices to two books:
1 - Algebraic Combinatorics: Walks, Trees, Tablaeux and More by Richard P. Stanley https://link.springer.com/book/10.1007/978-3-319-77173-1
2 - Representation Theory of Finite Groups: An Introductory Approach by Benjamin Steinberg https://www.amazon.ca/Representation-Theory-Finite-Groups-Introductory/dp/B01FEKU6N6

My (hopefully final) question is if there is a particular order I should follow in reading them, or are they two entirely different things? And which one is more fun to read?

[finite shale]

What are some good AG books?

[mellow wren]

Hartshorne

[finite shale]

Any others?

[gray gazelle]

Does anyone have any opinion on “A Concise Handbook of Mathematics, Physics and Engineering Sciences?”

Only knowing basic math, I wonder how good of a book this may be.

[remote sparrow]

#book-recommendations message

[ashen socket]

Question... which resources / books would you recommend for learning graph theory?

[hallow oriole]

diestel

[strange sentinel]

I liked Chartrand and Zhang's First Course in Graph Theory

[hallow oriole]

one of my grad friends swears by that book for intro and he's a graph theorist so i'd trust that too

[plain barn]

sooo I've finished jay cummings' real analysis last year and am intending to get into baby ruding which seems to go deeper
am I safe starting at "differentiation of vector valued functions" from chapter 5 or am I losing too much because of the use of general metric spaces in the rest of the book?

[strange tree]

https://agag-gathmann.math.rptu.de/en/notes.php

[heady ember]

Have you learnt metric space topology? If not, you shouldn't skip the chapter on it (which is chapter 2 iirc).

[plain barn]

well, not deeply, I kinda only know the definition of a metric space and some random theorems

ig I'll at least skim the chapter to see if I know enough

[heady ember]

You should read the chapter, then.

[plain barn]

yeah probably

[plain barn]

omg weaving2 hiiii

[plain barn]

only that or are other things important to not skip too?

[strange tree]

OCW use baby rudin, you can skim through the problems on metric spaces and see if you have enough knowledge

[strange tree]

👋 👋 long time no see you gabi

[plain barn]

yeahhh it's been 38 minutes

[heady ember]

It doesn't hurt to take a look at the exercises of each chapter, since Rudin is well-known for having interesting ones. But you should be fine for the other chapters (1-4) if you read another analysis book already.

[plain barn]

👍 ok sure

[heady ember]

Oh but chapter 4 covers continuity in metric spaces, so maybe skim that.

[plain barn]

ty grass

[heady ember]

Yeah there are some neat theorems and proofs in that chapter.

[heady ember]

Np

[gray gazelle]

can anyone recommend books on the theory of entire functions?

[remote sparrow]

plenty of complex analysis books cover entire functions

but idk about books that only cover entire functions

[gray gazelle]

Any opinions about Pure mathemathics by Godfrey Hardy?

[gentle jasper]

Anyone have a good geometry book? Euclidean Geometry.

I’m doing a reading course in measure theory, and I realize that I’m geometrically inept. I can’t really think in geometric terms, I’ve forgotten a LOT of high school geometry, and it is very hard for me to visualize.

I’m looking for a Geometry book that is Geometry for its own sake. Basically a modern Euclid’s Elements. The Hawthorne book isn’t particularly good in my opinion, but otherwise I’m open to suggestions.

[quick hornet]

part of the issue here is that a lot of lecturers for euclidean geometry either make their own lecture notes or just recommend an annotated copy of euclid

so theres a weirdly low amount of textbooks relative to the historical importance of the topic

[trail hemlock]

its great

i couple friends of mine have read teh entire thing, ive skimmed it on occasion, and from what ive seen its good

[heady ember]

John M. Lee has a book on geometry iirc (not his manifold books). But I'm not sure if its Euclidean Geometry.

[gentle jasper]

This has been my experience as well.

Lang has a high school geometry book that I might take a look at, seems like a relatively uncommon book.

[gentle jasper]

Thanks! I’ll look it up.

[trail hemlock]

of course lang has a book on it 🙄

[heady ember]

Indeed, the repertoire of his penmanship is very langthy

[trail hemlock]

A somewhat recondite joke is the query “Why did Bourbaki stop writing?” The answer is that they discovered that Serge Lang is one person. Lang’s output of text connected to his many political disputes was voluminous. He also has some unpublished books of a political nature (others of his political tracts were actually published). Lang liked to say that the best way to learn a new topic is to write a book about it
😭

oh, i guess in emeritus now (?)

[gentle jasper]

As a matter of fact, I might have answered my own question. It seems like quite a good book. And I like Lang’s books. So, mentioning it here if anyone

else ever looks it up. *

[strange tree]

Classical Geometry
I.E Leonard , J.E. Lewis , A.C. F. Liu ...
I cant send images so I send this info d:

[remote sparrow]

you might say that, but i'm sure you remember some basic results. if you really do not remember, i suggest having a look at kiselev. otherwise, i do recommend weaving2's suggestion

https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

[echo tendon]

Anyone have some recommendations for books on axiomatic set theory? Should I read jech?

[ashen socket]

Thank you 🙏

[ashen socket]

thank you!

[remote sparrow]

have you read a textbook on logic beforehand?

[echo tendon]

No, do you recommend it?

[hallow oriole]

i don't think you need a logic textbook before a set theory textbook...

you should be able to pick things up while you need them

[remote sparrow]

no, you can be recommended different books based on your background

[remote sparrow]

#book-recommendations message

[remote sparrow]

it depends on the textbook

[heady ember]

Tfw you try to read Big Jech without knowledge of ug logic

[gray gazelle]

any good introduction to real analysis book

which i can read along with standard calculus?

[civic hollow]

What do you guys think about this calculus textbook? Calculus: A Complete Course
Textbook by Christopher Essex and Robert A. (Robert Alexander) Adams

[gray gazelle]

anybody has exercises/past papers for algebra 1? (websites)
imo khan academy's exercises are way too easy and straightforward

[timber mesa]

this depends a lot on what "algebra 1" is in your institution

you could check out Paul's Online Notes https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

he has sets of practice and assignment problems for every section there

[gray gazelle]

middle school algebra is what I call it

thanks

[timber mesa]

yeah Paul's seems to have overlap with what Khan covers I think it'll help

[gray gazelle]

what about Arts of problem solving textbooks?

[timber mesa]

I've seen these recommended as a first read for competition math type stuff, if you're into that sure

haven't really read them only skimmed a bit

[slender wasp]

Spivak will do both - calculus and intro analysis

[gray gazelle]

ohh

will check it out!

[left galleon]

Meditations, Obstacle is the way, Moral letters.

[strange violet]

need a book which covers elementary block matrix transformation in detail

[faint fractal]

Need a book for limits and derivatives sums ( beginners side ) .

[faint fractal]

Kindly send asap

[molten gulch]

stewart's calculus

[faint fractal]

Thanks for the help

[gray gazelle]

Any good calculus I-III books for reference

[molten gulch]

stewart's calculus, thomas' calculus

[humble spire]

what is a good number theory textbook?

[remote sparrow]

#book-recommendations message

[humble spire]

I have silverman, was just wondering what to do after it

am halfway through

[remote sparrow]

have you done abstract algebra?

[humble spire]

no

[remote sparrow]

maybe you should learn some! i was going to recommend ireland and rosen if you had background in abstract algebra

https://link.springer.com/book/10.1007/978-1-4757-2103-4

[humble spire]

yeah i have to get on that. I just had a focus on chem for some time and decided to come back and learn more math

[stoic hamlet]

I think even without abstract algebra, Ireland-Rosen is by far the best NT book. It grows with you -- the first few chapters assume no algebra, then the later chapters start using some algebra and some analysis.

[signal zenith]

Elements of set theory by Enderton was fine for me

Wasn’t anything special either but perfectly good enough

[smoky nest]

the rosen book on discrete math is fire

i really liked it

[smoky nest]

I have thomas' calculus its like soo good

[remote sparrow]

different rosen

[smoky nest]

oh

[remote sparrow]

@blissful shore have you ever read The Dialectical Biologist by levins and lewontin?

[gray gazelle]

Any texts for measure theory at the introductory level?

[remote sparrow]

https://measure.axler.net

[gray gazelle]

Thank you guys

[half robin]

Hi y'all, I'm an undergrad senior and I took a course based on Dummit and Foote but we only covered groups and rings and I really want to learn commutative algebra do you think I could just jump into AM's book and learn modules that way. I was also wondering if I could just jump into Milne's notes or Hungerford to learn fields and Galois theory?

[daring lake]

Yes, AM starts from rings, but its very terse

I am not familiar with Milne or Hungerford. For field theory I used M artin & Dummit and Foote. For galois theory I used Emil Artin.

I was kinda traumatized by following AM ngl

[trail hemlock]

the cover for emil artin's galois theory is so pretty 😋

[daring lake]

It is

[remote sparrow]

who is AM? also david cox's Galois Theory is good

as far as commutative algebra goes, eisenbud and matsumura are standard references

[ionic osprey]

atiyah macdonald

[remote sparrow]

oh i heard that book is a bit old-fashioned now

you could probably get some use out of it

[gray gazelle]

anyone know like GOOD trig book like i was doing these epsilon delta proofs and stuff and |arctanx| <= |x| showed up lmao

idk from where that came

[remote sparrow]

it doesn't seem like you're doing this proof in the context of a real analysis class since i don't see any messages in #real-complex-analysis

what sort of calculus class is this

if you know the graphs of arctan x and x, the bound is fairly easy to intuit

[trail hemlock]

its also kinda overkill to go to a trig book based off of 1 misunderstood inequality. u can just ask in the appropriate channel tbh

[remote sparrow]

i'm not aware of an elementary way that doesn't use calculus to prove this bound

i tried to think a little bit but i need to get back to my other work

[gray gazelle]

well i don't have access to that channel lmao but the problem was
prove lim x-> a tan^-1 x = tan^-1 a

for all epsilon > 0, there exists del > 0 such that
|x-a| < epsilon => |tan^-1 x - tan^-1 a| < del
|tan^-1 x - tan^-1 a| = |tan(x-a/1+xa)| <= |(x-a)/(1+xa)| (by the |arctanx| <= |x|

in the last step*

😭

[daring lake]

I used AM for comm. algebra

[gray gazelle]

Arithmetic mean?

[daring lake]

Atiyah & Macdonald

[gray gazelle]

oh thats a book 💀

nvm

[remote sparrow]

just grab the undergraduate role

[gray gazelle]

oh

oh cool i have access

[daring lake]

its still on my backlog

[blissful shore]

I havent, but i might take a look now youve mentioned it

[remote sparrow]

@halcyon mesa i think you might be interested as well

[novel hound]

I came across this free book/supplement to Atiyah MacDonald (A term of Commutative Algebra by Altman and Kleiman) which has solutions to all problems in AM and aims to update and improve upon AM. https://dspace.mit.edu/handle/1721.1/116075.2 I haven't used it but curious if anyone has and found it useful. Edit: nvm I found a mention. This post could probably be pinned: #book-recommendations message

[ocean oyster]

Dudes, recommend books for a detailed immersion in the topic of fractals?

[gray gazelle]

I'd like to start studying probability theory and statistics from the very beginning but I don't know how to start, any book recommendations?

FYI: I'd like to have something like a roadmap, not just a beginner's book, because I want to know what to study next until what can be considered "the end".

Thanks

Yes

https://github.com/TalalAlrawajfeh/mathematics-roadmap?tab=readme-ov-file

This GitHub webpage specifies it

Not much

In real analysis you don't focus much in solving integrals

You focus more in concepts like uniform continuity, uniform converge and other fancy stuff

You could study calculus along with real analysis

[blazing dagger]

Imo one of the main purposes of analysis is so you can do calculus

Smoothly

So it's not a hard prerequisite

You can in fact do both simultaneously

Actually if you're like capable I would say this is the best way

Yeah like

You can do analysis without too much focus on calculus per se

The converse is actually not true past a certain point

[gray gazelle]

.

[sacred nova]

I need an analysis (in R^n) book that covers:

• Topology in R^n
• Sequences in R^n
• Limits of vector functions of vector variables
• Continuity of vector functions
• Differentiability of vector functions of vector variables
• Implicit Function
• Double Integrals
• Triple Integrals
• Curvilinear Integral
• Surface Integral
• Gauss’s Theorem and Partial Derivative Equations

Any recommendations?

[timber mesa]

Munkres' Analysis on Manifolds?

I'm not sure whether that covers PDEs at all but I'm sure it covers the rest

[sacred nova]

oh ok! thx ;)!

[timber mesa]

maybe complement it with some other book for vector calc and stuff

[sacred nova]

okok! thanks for the help ^^

[blazing dagger]

zorich

i prefer that to munkres/spivak

[sacred nova]

Ill check it out:)

[rugged sleet]

Hi guys, i'm searching for a book for practicing calculus proof, one that focuses mostly on that, with exercises and examples

Been searching in my language without success, most books have very few exercises of this kind

Thanks in advance people

[gray gazelle]

Any problem book with focus on multivariable analysis?

[molten gulch]

thomas or stweart calculus should have more than enough problems

hubbard and hubbard has more theory

[gray gazelle]

https://www.amazon.com/Calculus-James-Stewart/dp/1285740629 this one?

[molten gulch]

yes

but that book has single and multivariable

keep that in mind

[gray gazelle]

Ok I see, there is also a "Multivariable Calculus" by the same author

[cold sun]

can someone give me a good book for linear mathematics , i'm in second year of uni and i really want to work hard and secure that 70%

[plain barn]

ym linear algebra?

[cold sun]

i think so that's the only thing i can find but the module is called linear mathematics

but it involves matrixes etc

[plain barn]

weird

[brave burrow]

If it involves matrix then it is likely linear algebra may be different countries use different names

[cold sun]

ah i see

do you have any book recommendations i could use

because the lecture notes are per week so i can only do so much

like only 3 out 10 are unlocked right now

[remote sparrow]

start with blitzstein and hwang's Introduction to Probability. for mathematical statistics, use wackerly, mendenhall and scheaffer. you may feel free to do grimmett and stirzaker's book on probability and random processes, or you can do some measure theory/read certain measure-theoretic probability textbooks that develop measure theory from scratch (in the context of probability spaces) such as billingsley or ash/doleans-dade. i would recommend eventually doing measure theory proper at some point, though. something you can do after measure-theoretic probability theory is stochastic calculus. one such reference is le gall. however, i'm not a probabilist, so i'm not aware of other topics. for further mathematical statistics, you can take a look at casella/berger. measure-theoretic treatments of mathematical statistics include keener, schervish, and shao. as i'm not a statistician, i'm not very familiar with books for topics like time series or experimental design.

[brave burrow]

Some people here use "Introduction to Linear Algebra" by Serge Lang but I haven't read it. Personally, I use "Linear Algebra and its Application" by David C. Lay, which focuses on the computational sides of linear algebra

[remote sparrow]

shifrin does cover most of this material in an orderly fashion. hubbard is a little harder to reference, but it's a great read. i don't quite recall applications to PDEs in either.

[gray gazelle]

I vouch for ILA by Serge Lang

great book, smooth read, and covers most if not all the things typically taught in a first treatment of the subject

for something more advanced, LADR by Axler is the go-to

or you could continue with Lang's LA (which I personally have only read a bit of)

[gray gazelle]

I really appreciate your answer, thank you!

[cold sun]

i see , thank you so much!

sorry one more book recommendation , do you guys have any for vector calculus

[remote sparrow]

hubbard or shifrin for proof-based introductions

[cold sun]

tysm!! have a great day :)

[stable flicker]

Sour gives good introductory.
For 'The End' of probability I think Probability by Shiryaev is a good final boss. Once you defeat it, you are well equipped to handle any probability

[trail hemlock]

hi guys, quick question. sorry if this is a stupid question, but what is the difference between Lee's smooth manifolds book, and spivak's diff geo books?

[thorn hinge]

What are some books to accompany switzer's Algebraic Topology - Homotopy and Homology?

[thorn hinge]

The books look similar, but Lee writes more

[trail hemlock]

yeah lee's yapping is getting a bit old in his topological manifolds book

[half robin]

Aityah Macdonald my professor told me it's what I should read before Hartshorne but when I asked the same question as before he kind of just shrugged 😂

[mellow wren]

If you wanna read hartshorne atiyah macdonald will not be enough
Ideally you should read something like mataumura's commutative ring theory

[limpid hearth]

Hello, good day, I have a question. My teacher recommended the book Mathematical Analysis by Rudin, but I have read that this book is very, very difficult. Do you recommend that I read something else first? Or just read it? Thanks.

[restive bloom]

Can anyone point me to any good resources to learn about Koopman Operators?

[foggy quest]

I would not recommend Rudin. The exercises in Rudin may be good, but the exposition is not. The one variable book here is good: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[limpid hearth]

Thanks

[open merlin]

Abbott's Understanding Analysis is recommended pretty often

[trail hemlock]

i also like tao for being gentle

[strange tree]

friends have told me that Pugh´s book is about the same difficulty but better explained than rudin

[grim ore]

I also recommend Eisenbud comm alg, if someone wants to verify. Its def a lot more terse but it really builds a solid foundation into comm algebra with algebraic geometry in mind so I mainly use it as a supplemental for finding results. I dont know much about mataumura tho tbf

[marble solar]

My favorite part of Pugh's analysis isn't the exposition, but the exercises that really make you think

[floral lantern]

If you want an open source book (yay open source!), Jebz’s analysis book is pretty good - we use it at my school for our analysis class.

[grim ore]

i love both, using it as a supplemental to rudin ; but the nice thing about pugh is that they build enough of a framework where you can solve the theorems from rudin on your own in the exercises

[grim ore]

this is also in reply to

[gray gazelle]

any books for math oly especially for the IMO and my national olynpiad? I'm just starting out and exploring the worlds of math competitions I'm in 8th grade dk where to start

[torpid flint]

Which book for undergraduate graph theory?

[tribal crow]

@hallow oriole recommends Diestel, usually

I'm not sure about others

[torpid flint]

I was alr using it but thnx btw

[olive ocean]

I've heard that ''Mathematics for the International Student'' by Robert Haese and ''The Art and Craft of Problem Solving'' by Paul Zeitz are great books to start with.

[trail hemlock]

ur learning analysis?🥳🥳

[strange sentinel]

Chartrand and Zhang’s A First Course in Graph Theory is nice

I can’t tell whether or not the 18+ message was a joke

[gray gazelle]

Brother Artin it wasn't

That's why it was deleted promptly.

[remote sparrow]

@split portal did you read anything before working with soare's Turing Computability?

[floral lantern]

No

That’s that book I’ll use next year

[trail hemlock]

oh

[split portal]

Sipser, but also, I'm not particularly competent with this stuff so maybe I'm not a good role model for this. I sorta see Soare so far as like, terse and requiring some effort to really parse through stuff. It kinda depends on how long you're willing to scratch your head at things. Rogers, Cutland, new Soare, Boolos/Jeffery, and Epstein/Carnielli have been nice to have around I guess.

My class is using old soare fwiw

My experience right now is all my other classes really dominate my time so I can't actually study for this class as much as I'd like lmao.

I guess out of the above Hartley/Rogers seems the best as a secondary reference.

[woeful rock]

Which book is like the Bartle's Introduction to Analysis, but for multivariable calculus?

[remote sparrow]

were my previous recommendations unsatisfactory?

[trail hemlock]

🥺

[dusk wind]

any reason why there's no pins here

[molten gulch]

There are, they may just take a second to load

[woeful rock]

SORRY, I DIDN'T REMEMBER THEM 😭

[dusk wind]

ahh, hopefully other commonly recommended material also get pinned

[molten gulch]

I defo think some of Sour Drop's reccomendations should be pinned

[dusk wind]

definitely not, let's pin reviews instead

[molten gulch]

yeah, that's a better idea

[signal mountain]

i dont know how much it matters 😭 so many people dont check

[dusk wind]

it matters to people looking for something

theres a lot of buried stuff that should have been pinned here

instead you get stuff like this #book-recommendations message

of course that answers the dilemma doesn't it

[gray gazelle]

Opinions on precalculus by James Steward?

[signal mountain]

oh yeah im not saying its useless by any stretch

just .. perhaps there is a better way

not sure what that is but pins are markedly tucked away

[remote sparrow]

they're just lists tbh

[molten gulch]

true

[marble solar]

Sour drop camps this channel 24/7

[tribal crow]

real

[dapper root]

Spawn kill

[wheat remnant]

does anyone have a great book recommendation for probability

[sage python]

Measure theoretic or nah?

[wheat remnant]

yeah I'd be down for that! it's for personal, i've already passed my class but im unfamilar with measure theoretic actually

[signal mountain]

billingsley maybe

folland or axler tend to be recommended for just straight up measure theory, folland going deeper

and i was told billingsley is comparable to folland but with a probability focus

[compact storm]

hlo

[mystic orbit]

I can vouch for billingsley

if you want something comprehensive

it covers the necessary measure theory along the way too which is nice

if you want something quickers there's uhhhh

Rosenthal

[blazing dagger]

Rosenthal is ok but sooo dry

Imo

What does @sage python think of bredon?

I am thinking of using that after going through hatcher ch 1

And 2

[mystic orbit]

your mileage may vary I suppose

I know people that absolutely adore rosenthal

I personally haven't read it so you can take my suggestions with a grain of salt

[mystic orbit]

dami loves bredon

others would recc rotman

[sage python]

Bredon is imo the best mid level algebraic topology book

Early level is Rotman, advanced is tom Dieck or maybe Concise

[mystic orbit]

hmm, rotman is early level?

where does bredon start?

I know rotman goes up to singular cohomology

[sage python]

Well they start at the same level

Contentwise

[mystic orbit]

concise is for people that already know at lmfaooo

[sage python]

I guess I mean difficulty/maturity

[mystic orbit]

inchresting

[sage python]

Like Rotman spells stuff out more and moves gently

[mystic orbit]

I dunno what I should use if I go back to AT

[sage python]

So the advantage of Bredon for you would be that it does a bunch of smooth manifolds stuff

[mystic orbit]

inchresting

very inchresting in fact

[sage python]

It has a differential topology chapter, and then I think it leads into cohomology using differential forms

[blazing dagger]

Based

I felt so too after reading a bit of it

I liked the manifold focus

[vestal flume]

Anyone pls explain what cohomology is like it's so confusing

[mystic orbit]

you take the duals or smth I dunno

[vestal flume]

Shit now im curious

[mystic orbit]

dami, I'll do de rham stuff using lee (yes, I still haven't reached that lmao)

what I need after that is like, the content of hatcher chapter 2 and 3

but maybe not from hatcher

[sage python]

Yeah sure I just mean that it tells you something about Bredon's focus that he builds to cohomology using forms, instead of just jumping to singular

[mystic orbit]

I'll give it a look!

[sage python]

Like there are a few povs one can have in this subject

[mystic orbit]

kekw

[sage python]

eg Hatcher begrudgingly admits that algebraic topology involves algebra, and likes to do proof by debatably convincing picture

Rotman I think leans a bit algebraic, and spells out details (often verifies continuity of the maps he writes down)

[mystic orbit]

topologists verifying a map is continuous? how ludicrous!

[sage python]

Actually I think I wrote down some reviews in a pinned message here

[mystic orbit]

obviously all maps are continuous

[vocal egret]

http://www.witno.com/numbers/

do y'all think this is a crazy good book for 5 cents?

[thorn hinge]

What are some books to accompany switzer's Algebraic Topology - Homotopy and Homology? https://link.springer.com/book/10.1007/978-3-642-61923-6

[mystic orbit]

Im gonna out on a leg on this one and say, unless it's munkres, it's prolly crazy good for 5 cents /j

It takes a lot to not be worth even 5 cents lmfao

[vocal egret]

the amount of discounts is crazy

The book's contents itself is quite rigorous for a first pass, assumes full understanding for basic proof writing.

Honestly, for the price, this is good for undergraduate level

kinda basic 😦

I mean, olympiad high school stuff ykno

eviehgoiehgerigferf

[floral lantern]

There’s a lot of cryptography

😒

[vocal egret]

tru

algorithm stuff

tbh, Titu's book is alreaedy sufficient

gonna mald rn

not passing olympiad with this one

[floral lantern]

I like Rosen

[floral lantern]

There’s a number theory pdf on aops for this lol

[vocal egret]

damn

w8

[floral lantern]

“Introduction to Olympiad NT” I’m sure you know it

But just google apps ply nt textbook

[vocal egret]

last time I check this covers more contents

It's good

[floral lantern]

Yeah

This is very light

[vocal egret]

tru

[floral lantern]

Idk my personal favorite is Rosen

But that’s bc I used that book to learn ENT

[vocal egret]

das kinda aight imo tho, but it kinda depends

It's good

I feel jealous for aops havers

[floral lantern]

Not good for oly or everything and kind of bloated

[vocal egret]

basically like a very large manual

[floral lantern]

AoPS’s Calc book is great

[vocal egret]

gonna try it out rn

thx

[signal hazel]

Brilliant but Axler is better and not as overwhelmingly long.

Axler has super useful tips that cut out nugatory work and memorisation

[tame tree]

anyone know of a good resource to practice multiple integrals besides stewart or larson calculus

ideally focused around getting good at trickier multiple integration, etc.

the purpose is to prepare for a math stat course in which there will be tricky multiple integrals

[verbal cargo]

https://artofproblemsolving.com/wiki/index.php/Math_books

is that enough to prepare amc or other competitions?

Is there any other list like this?

[flat viper]

is there a good book about stochastic

i want to be able to know how to learn probability for different scenarios

e.g.
10 slot exist to fill,
you role 10-sided dice
-> first role 100% chance to fill a slot
-> second role is 90% chance to fill a slot
---> wtf is third roll chance to fill a slot
---> how to calculate the chance for have 5 slots filled after 7 rolls

etc.

[left cloud]

this question doesn’t make sense

[flat viper]

how so?

[full cairn]

Anyone have an opinion on Lee's Introduction to Smooth Manifolds vs Tu's An Introduction to Manifolds? Or any other book that cover the same material?

[cursive rivet]

Lee is my personal favourite book for it, and I don't like Tu's writing at all, but Lee very much is a book where you have to "pick your battles" and understand it's very packed with material, not all of which you need at first (though I think Lee does an ok job of indicating where this is)

a book similar to Lee in terms of writing style but less packed (and a fair bit older) is Spivak's Comprehensive Introduction 1 which I very much like

in terms of the writing styles, Lee is definitely strongly on the side of "explain everything in full detail" and tries to explain quite a bit of his own intuition (think the polar opposite of Rudin) which isn't to some people's taste, but is definitely to mine

[mystic orbit]

yes

very

I used both and I hated tu tbh

tu's idea is very simple, do the least amount of smooth manifold theory to learn the stuff you actually care about for ph*sics or w/e the fuck

definitions are taken to be the most natural and not the most economic

the development is wordy and comprehensive. It's meant for a mathematician trying to get into modern geometry

[marsh ingot]

Prefer Tu over Lee for some topics. The way Tu introduces his book and how he explains some stuff clearer than Lee. However, I think Lee covers more topics but need patience to understand it. I dont really like the way he explains some topics

[mystic orbit]

also, lee has waaaaay better problems

[marsh ingot]

For me: Diff forms part

Prefer Tu way over Lee one

[mystic orbit]

hmm, fr?

I dunno, I liked how tu offloads a bunch of the theory to diff forms in the concrete case of R^n

but lee's exposition was imo really really good

maybe I sailed smoothly through that only because I read tu's first chapter

[marsh ingot]

I struggle a bit with Lee's explanation, for sumarize it. Tu was better imo, I didnt check R^n forms part since is already trivial for me and I was interested in generalization over smooth manifolds. Liked how Tu explained exterior algebra

[mystic orbit]

honestly, I personally like all of lee's exposition. My only gripe with lee is that it's way too fucking long and covers so much stuff that you prolly don't need for a first read. And I knew that going in.

But tbh, I regret choosing tu over lee at first for that reason

[full cairn]

Thanks for your opinions I liked Lee's ITM, so I think I'll go with Lee again, but maybe look at Tu just for differential forms when I get to that point

[mystic orbit]

what you should do is perhaps read tu's first chapter

and then switch to lee

tu's first chapter is excelent

and also a very light read

[full cairn]

First chapter meaning the entire Euclidean spaces chapter?

[mystic orbit]

yes

a lot of it is very basic, don't worry about the length

also

another word of advice

learn how to skip the bits that aren't super crucial from lee

and then come back to them if you ever need them

[marsh ingot]

Basically this, covers too much and I needed smth more specific. Also his construction via tensors mmmm I didnt understand it the first time

[mystic orbit]

you will need to do that if you want to finish during your lifetime 💀

[mystic orbit]

I mean, he covers both construction

the abstract categorical one and the product of dual elements blah blah

[marsh ingot]

That part was deep and didnt need smth too formal so I choose multilinear functions explanatiom

[hallow pelican]

Does anyone know a book or something with a bunch of exercises about semisimplicity? artin wedderburn theory and such.

[trail hemlock]

why is physics censored 😭

[quartz verge]

what fictional books do mathemsticians read outside of math books?

[foggy quest]

manga

[quartz verge]

i said mathematicians, not weebs

[foggy quest]

novels

animal farm, sherlock holmes series, hitchikers guide to the galaxy.

[hallow oriole]

i just finished infinite jest!

[open merlin]

manga

[hallow oriole]

and i just started american gods

after this i think i will do a discworld reread

probably not the whole thing, just a few

[gray jungle]

manga is the right answer

[hallow oriole]

then i want to try to get back into earthsea

[quartz verge]

guys

i

cracked a joke

[hallow oriole]

yeah but it wasn't funny so nobody acknowledged it

i took your question the way i wish you had written it!

[quartz verge]

thank you for your honesty

[hallow oriole]

you're welcome

it's okay, tough crowd here frfr

[quartz verge]

id say they do be too obsessed with forms for mathematicians

[heady ember]

Me taking two years on intro anal:

[willow merlin]

what is the best book from learning linear algebra non proof based and only computational linear algebra currently going through Anton's Elementary linear algebra but I would like another one

[remote sparrow]

https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/0199654441

[willow merlin]

thank you very much and sorry for being a nuisance to this channel

[remote sparrow]

https://www.maths-for-all.co.uk/linear-algebra/

[willow merlin]

perfect!!

solutions is exactly what I need!

[cold musk]

I am looking for a complex analysis book that is rigorous, starts from the fundamentals, and covers as much as possible

please ping me if you recommend any

[remote sparrow]

#book-recommendations message

you can also look at marshall and other recommendations in pins

[cold musk]

I don't see any in the pins. Is marshall a well known book?

[remote sparrow]

it's a newer book with a somewhat different take (although not novel)

@marble solar

it's a power-series first approach

[marble solar]

Not super well known, but it does a good job at getting everything across and has interesting problems. It covers two different proofs of the riemann mapping theorem (one non-standard, one standard). I liked its approach to complex, but I'm biased

[obtuse spoke]

Hi, Can I follow this roadmap
https://github.com/TalalAlrawajfeh/mathematics-roadmap?tab=readme-ov-file

[marble solar]

As far as the most rigorous one that covers both breadth and depth I must recommend Conway's two volume set in complex Analysis

But it does have the drawback of being so precise that it is dry

[remote sparrow]

is the first volume all you need if you're not planning to go deep into CA

[marble solar]

Yes

If you want something that incorporates measure theory/real analysis, then Rudin is the obvious choice. If you want calculation then brown & churchill is the go to text

If you want to know how complex analysis relates to other subjects then I'd recommend stein & shakarchi as it has a lot of applications of complex to fourier, analytic number theory, and covers theta functions

It's also not as precise so if you're looking for intuitive proofs with calculation then S&S volume 2 is the one for you

[remote sparrow]

a more advanced book with applications is ablowitz and fokas

freitag and busam is also slanted towards analytic number theory but is considerably faster-paced

[hallow oriole]

no it's really bad

[remote sparrow]

i don't think the books suggested are necessarily bad, but i don't believe all the blue boxes can be considered "essential"

[cold musk]

what are their titles?

[remote sparrow]

like...it's okay not to do some of the stuff

[hallow oriole]

oh the books are fine, i just think the everything else is bad

[remote sparrow]

what counts as "everything else"

[remote sparrow]

a set of reviews for complex analysis is one of the early pins

[hallow oriole]

the things in blue, the things in purple, the order of the things to learn, a lot fo the books too hoenstly actually

like the linalg and combinatorics books are probably not good either

if the goal is strictly for applied math i guess this is probably fine...?

[remote sparrow]

algebraic number theory in applied math?

[hallow oriole]

not a single proof based linalg book?

and not any good combo books either

[remote sparrow]

oh true no proof-based linear algebra book

[hallow oriole]

oh wait it has the proof based linalg in "advanced linalg"

also just the order of some of this

[remote sparrow]

yeah i see it now

[hallow oriole]

intro combo --> intro prob --> intro stats --> advanced prob --> advanced stats

like LMAO

[remote sparrow]

it's probably because discrete probability is most students' first encounter with really simple combinatorics

[cold musk]

what is its date? I for some reason don't see it

[remote sparrow]

march 7th 2021

[hallow oriole]

i don't think you should be starting combinatorics that way tbh

the perfect intro to combo book has already been written

[remote sparrow]

i don't have a combinatorics class at my uni

[hallow oriole]

idk why more people don't just read it

[remote sparrow]

boner

i mean bona

[hallow oriole]

LMAO

yes

bona is so good

supplement it with loehr's bijective combinatorics and you have a perfect combinatorics foundation

[manic crest]

Need a book to prepare for MAT oxford entrance test with similar problems

[exotic comet]

is it me or is lay for lin alg hard to follow

[remote sparrow]

https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/0199654441

https://www.maths-for-all.co.uk/linear-algebra/

if you're having trouble, you can get kuldeep singh's book

[exotic comet]

thanks

[rough umbra]

Intro alg -> alg geo is crazy

[quiet ravine]

Any good book for olympiad problems for 11-12 grade

[keen vale]

any rec for group theory?

[remote sparrow]

just group theory?

[keen vale]

just group theory

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-4176-8

[glad wren]

any good book for mathematical logic (intro)

[grave vale]

I was about to comment that it's a nice dream you have there, but [that previously suggested book](#book-recommendations message) seems cute and is openly available. @glad wren

[slate zenith]

hello, any rec good book for elementary number theory? tyiaa

[deep moat]

Any books that're good for statistics and probability?

Beginner here, no background of such.

Preferably some eBooks and books that contain actual table of contents?

Thanks!!

[rare iris]

Hi I request a book about Disney princesses to read

[deep moat]

I would also like to request a book of To not read

Okay, ima search up the books here

[left galleon]

🤦‍♀️

ANyway here is a book " Cinderella Takes the Stage "

[candid bay]

Any good maths books for like 10th grade?

[deep moat]

Hey! Majority of peeps here say AoPs books are really nice

They kinda cover everything to General Math

Pre Calc*

[sly pier]

hello, is there any good source of information about the Weierstrass Function and how to apply it :)

[candid bay]

Sorry I don't think I know what that is do you mind elaborating a bit

[gray gazelle]

its a set of books which goes by the name

art of problem solving

smth

they are used by high school/ middle schools students for olympiads

and such

[deep moat]

AoPs means Art of Problem Solving. Essentially, it's a book about mathematics that teaches you how to solve and approach problems in a very "awesome" way

[gray gazelle]

aside from that they are

really good

[deep moat]

In other words, AoPs books are for competition math and for self studying!

It is really in depth

[deep moat]

Well said!

[golden quarry]

Good philosophical books ?

[deep moat]

Uhhh... "Math is.."

by Sullivan iirc

[gray gazelle]

oh that is a book

lmao

[golden quarry]

Huh ?

[candid bay]

Ah okay thanks

[deep moat]

My school has that and along with the first edition Calculus book by J. Stewart!

[gray gazelle]

damn

[deep moat]

Sorry, I don't really get your question for "Philosophical Books" because I think you're asking for mathematical-philosophical books. The only thing I can consider as "philosophical" is the "Math is..." book

[golden quarry]

Is the books title "Math is...." ? I got confused with the title

[deep moat]

Yeah

I forgot the name of the author, but that book exists.

[golden quarry]

I will search for it then.

Any good books regarding patterns that ya might know ?

[deep moat]

No, sadly. Maybe try asking an AI to help you with that! That's what I usually do if I people can't help.

As far as I know, Number Theory seems like one that has patterns and stuff. I only have surface knowledge with math so... 🤷‍♂️

[hollow shore]

"What Does It All Mean?: A Very Short Introduction to Philosophy" by Thomas Nagel

[gray gazelle]

hey i only know arthemetic and basic algebra, where should i start to improve from i want to learn more of math

[dim sierra]

Another good intro is the introductory book by Simon Blackburn

[copper warren]

Anyone know any good intro to bayesian statistics books?

[foggy quest]

I heard "Fundamentals of Nonparametric Bayesian Inference" by S. Ghosal and A. van der Vaart is good

[snow plume]

Any intro to control theory books?

[past tiger]

I am self studying Diff equations, and i only have 1 -2 hours after work, so i don't have that amount of time to solve all the problems in the book

so if i solved like 30% of the problems on each topic then after finishing the chapter i solve all the problems in the chapter review section

it contains between 40 problems

so is that ok?

[timber mesa]

sounds good, I think this is how most people study from books anyways

aiming to at least understand most problems is a good thing but it's not unusual to just write out a few

[gray jungle]

can you be a bit more specific on what kind of control theory ? if you want a good intro to control theory for ODEs then checkout lawrence evans lecture notes

havent reached beyond that atm

[remote sparrow]

@silver herald

@silver herald

[humble spire]

Is kiselev planimetry and stereometry good to go through for geometry, or are there more in depth books?

Nothing too advanced though

[gray gazelle]

Hie
Books for in depth theory of calculus
Understanding calculus to last minute details

Any recommendation
( popular ones I saw on internet are spivak and Thomas but want recommendation from people)

[deep moat]

He's the one thats always in the dishes

[deep moat]

"Art of Problem Solving" books. They help you build a better foundation in mathematics and learn how to approach problems in a very "unique" way. You should start off with "Introduction to Algebra" or "Pre algebra". I suggest going through the pre algebra book since it somewhat gives you an additional fundamental knowledge that'll help you go through the Introduction and Intermediate. Do note, AoPs is built for competition math and for self-studying. You can also use their trainer -- "Alcumus" to have a better grasp of a topic you're currently in!

||AoPs is very expensive so go a head and get yourself a copy/download it from the internet||

AoPs is always recommended in this server afaik

I learned about it from here!

[gray gazelle]

If free reply to mine text too pls
Just the name of book(s) would do

[deep moat]

Hi! Sadly, I don't know any books about calculus theory. However, I do recommend asking ChatGPT for books that you're looking for. That's what I always do when the internet can't help.

[hallow oriole]

you can also just use khanacademy

up until calc it will sate you

then you can ask here again for those books

[hallow oriole]

you're asking for real analysis technically which is not what you probably holistically mean

i would use spivak

[deep moat]

Oh, cool, "Calculus Theory" is real analysis? Wow

If I remember, "A Struggling Graduate Student" recommended some Real Analysis books. I think its in the PhD program kind of books :p

[hallow oriole]

there are undergrad analysis books but i judged the asker was probably not ready which is why i recommended spivak

if spivak is still too difficult then they should go through hammack's book of proof beforehand