book-recommendations

[marble seal]

Guys pls read this book, it will open your mind

[gray gazelle]

oh wow. so it wouldn't cover a course a math major'd do in abstract algebra, correct?

[tepid prairie]

You do love Spivak. :)

[karmic thorn]

The amount of abstract algebra a math major would see varies heavily, based on the institute and preferences of a student. My institute for instance covers less than what Gallian does, at the undergrad level.

[gray gazelle]

I see. Gotcha. I guess I'll use it as a supplement for D&F

[karmic thorn]

(D&F is a fine standalone text too, by the way)

[tame rampart]

any recommendations for maths school year 10 books?

[lyric night]

No need for books. Just do past papers over and over again. I got an A* in Mathematics without using the textbooks at all and only papers

Try and do at least 2 per day

The supply of papers may vary

From which exam board you do

[tepid prairie]

Actually the best advice ever. Wish I knew this when I was younger.

[gray gazelle]

what do you mean papers

[lyric night]

Past exam papers for the mathematics subject

[gray gazelle]

that worked in high-school

not in uni tho

for me

[lyric night]

What uni do u study at?

[tepid prairie]

Probably not the best place for this discussion since this is about books. Just go to your exam board and they will probably have past papers to do.

[lyric night]

If you don't mind me asking

[gray gazelle]

I do mind, I don't wanna dox myself

[lyric night]

Cambridge and Edexcel have too many

[gray gazelle]

also how do you study proofs without reading the textbooks

[lyric night]

If Ur studying a levels I recommend this

[lyric night]

You look at mark schemes and see where marks are obtained for certain areas for working out

[gray gazelle]

I don't follow

[lyric night]

You want to study Mathematical proofs

Right?

[gray gazelle]

correct

[lime sapphire]

A levels don't teach proofs well

A level questions are also very repetitive and lack creativity

[lyric night]

Which makes math exams for a levels and GCSEs easy as π

[lime sapphire]

Yea but the point here is to learn proofs and problem solving

[gray gazelle]

I agree with flour

[lyric night]

Yea but you can only learn by doing it right? And getting wrong again and again until you get it right

[lime sapphire]

Uhh

[gray gazelle]

you read the proof you do the exercises

it's not some computational thing

[lyric night]

Off topic but why are most proofs so BS but so necessary?

[gray gazelle]

huh

rigor

[lime sapphire]

I think a book written by a qualified author in the field is able to help you build intuition through their explanations which also helps get better at approaching different problems

[lyric night]

Like for example. Can you prove that there are infinite number of numbers?

[gray gazelle]

yes

[lyric night]

Show how

What proof method will u use?

[gray gazelle]

peano axioms

now constructing the reals on another hand

that's difficult

but you have many methods

dedekind cuts

eudoxus integers

hyperreals

but the main thing is that it's correct

[lime sapphire]

The whole point of higher maths is to prove the littlest things using axioms and then build up from there
We can't just assume something is true because of a pattern as there is the smallest chance that this pattern breaks somewhere along the line unless proven otherwise

[lyric night]

Yes exactly

@gray gazelle how I would go about this is simple

I'll use proof by contradiction

Let's say the largest number is (n)

The biggest number to exist

Now watch this

n+1

That's it

[gray gazelle]

define big and define number

[lyric night]

Big as in the largest number to ever exist

[gray gazelle]

what does that mean

big

[lyric night]

There is no number larger than that number

[gray gazelle]

well you can define it this way

the difference of a and b is in set N thus a>b

N for negatives

[lyric night]

Ok

[old elk]

Hi guys what subject should I study
to get into real analysis

[crimson pagoda]

real analysis perhaps

[winter wraith]

Anyone suggest a good resource for discrete mathematics

[gray gazelle]

Rosen's Discrete Mathematics And Its Applications

[winter wraith]

thanks

[errant swift]

just bought two books one on probability and another on multivariate calculus. math books are cheap when you aren’t in school and don’t need the exact edition

any opinions on serge lang for multivariate calc and degroot for probability

[coarse crane]

But this pushes a rote way of solving problems. An important part of math is conceptualizing a topic; textbooks are perfect for that.

[shy compass]

unfortunately if your goal is doing well in exams, this is the best thing to do

[coarse crane]

If you're a math major, then doing this is kinda pointless, especially in higher levels.

We have computers and software to do the work. Sure, it'll get you an A but what about an actual career.

There are some students that learn to multiply matrices without knowing that it's really a linear transformation, for example. That's insane to me.

[fallow cypress]

The classic is dummit and foote

[fallow cypress]

This proof actually has some subtle details, which one might miss on a first glance. Implicitly evoked is one of the Peano axioms, where you can't form a loop by successively adding 1s, e.g. 3+1+1+1+1+1 ≠ 3. Also, the fact that there is no biggest number does not automatically prove that there are an infinite amount of numbers (you would have to establish that every finite set of natural numbers has a maximum). TBH, a lot of it depends on what you're assuming to be true.

[timber mesa]

opinions on Hirsch's Differential Topology? I'm planning to read the first few chapters, mostly because I want to understand transversality theorems

[sage python]

Hirsch is p good

Pretty technical, chapter 2 is about all of the stuff like smooth approximation except he gets sorta technical/sharp

[river aurora]

need a real analysis book where i can learn about cauchy's first thoerem on limits(https://math.stackexchange.com/questions/3439806/cauchys-first-theorem-on-limits-of-sequences)

i tried rudin and bartle sherbert but the theorem was not there

please help i really need it,
articles/handouts will be helpful but i need a comprehensive knowledge of its related stuffs also so it would be better if it is a book

[hollow peak]

i fucking love hirsch

great book, really gives you a feel for the flavor of diff top

milnor's topology from the differentiable viewpoint is also great

[vague prairie]

Is “Everything You Need To Ace Algebra & Pre-Algebra 1 In One Big Fat NoteBook” a good book for middle school?

[quick hornet]

that's kind of outside the scope of expertise of this server.

[foggy relic]

[brisk ice]

Anyone have an intro math stats book?

Just need something that might be a better cross reference for the book my course is using (don't really like the layout and such)

[runic hatch]

I liked Statistics by Freedman, Pisani and Purves

[brisk ice]

also i am not sure if the book counts as a stats book or probability book

says "mathematical statistics" so I am going with stats

[gray gazelle]

I know nothing about foundations for now. Should I read Enderton first?

[brisk ice]

okay this book is quite different from the context of my book

This is the topics my book has about

anyways I think i found something similar

[gray gazelle]

does anybody have a recommendation for a first course on differential equations for engineers?

[river aurora]

please anyone?

[river aurora]

thanks

[sage python]

Simp

[plain lotus]

not really math, but Superintelligence by Nick Bostrom

great book

[halcyon garden]

Is there a resource that shows examples of constructing Bump functions with conditions like it has to take a certain value at certain points of the domain and derivative must be positive in some intervals?

[icy knot]

Either Saff and Snider’s book or Dennis Zill.

[misty wyvern]

Looking for a dynamical systems text for a practicing SPDEs theory/physics person.

I need to study limiting measures on systems driven by an SPDE and lack the language for it.

Level of sophistication should be high, unless I'm actually missing basic ugrad-level material.

[river tangle]

Guys what books for algebra do you recommend?

High school level btw

[crimson leaf]

https://tutorial.math.lamar.edu Not a book but some notes it starts with algebra and is good for calc as well

[queen beacon]

anyone have any good introductory to stats textbooks?

[queen beacon]

is this book also good for ap stats stuff or intro to stats?

[livid ermine]

I hated this book a lot. It's so bad.

[brisk ice]

So far I hate it also

And I really dislike the layout

[daring leaf]

book for probabilities?

[lucid snow]

what books do you recommend for competition math?

[gray gazelle]

what is better for a first course in linear algebra for engineers, linear algebra with applicatons by gilbert strang or introdcution to linear algebra by gilbert strang?

[crimson leaf]

I would say go with introduction and use MIT OCW Strang has great lectures on there along with a bunch of other resources

[foggy fiber]

What level/grade? University?

[queen beacon]

books for introductory to stats

[rain hound]

Looking for a good resource on lambda calculus. In particular I'd like to learn the rules of the game, basic computability theory and algorithms, as well as computational complexity. It's something that is quite unintuitive to me and I just don't understand. Circuits and TMs seem much more clear.

[gray gazelle]

does anybody know a precalc book that covers these topics?

need a resource for a math competition

[drifting elm]

I don't see how the two are related. there is an equivalence between TM and lambda calculus according to the church turing thesis. but complexity theory does not require lambda calculus. maybe the only point I can think of is recursive complexity. This could also be examined with pseudo code without lambda calculus.

[drifting elm]

https://www.amazon.com/Schaums-Outline-Mathematics-Applications-Technology/dp/0071611592

[rain hound]

You’re correct computational complexity does not need lambda calculus. But the whole point of it is what it studies is supposed to be independent of your arbitrary choice of a reasonable model of computation. I just want to learn it from a lambda calculus perspective for another look at how it all works. Also, it’s ever important with the rise of functional programming languages, not purely academic.

[drifting elm]

ok sure. there are a few different kinds of lambda calculus actually. you can divide them into typed and untyped or "type free" lambda calculus. wikipedia can get you started. I have always found this topic to be difficult no matter what book I use as a reference text. you are probably better off learning haskel first. SK combinators are also interesting and somewhat related. peano axioms and the von neumann construction of the ordinals are perhaps related to start thinking about functional programming and trees (graphs) as representations of sets in axiomatic set theory. a book on algorithms might also be prerequisite. for example depth first vs breadth first search. binary search. solving problems in graph theory. natural language processing. this is the motivation for lambda calculus.

[rain hound]

Thank you. Sounds like I need to learn a lot more graph and set theory. And just have fun with Haskell

[halcyon garden]

Bump

[fallow cypress]

omg I love haskell

simply typed lambda calculus is probably not what you want since I don't think it's turing-complete

although they are useful for thinking about programming languages like haskell

untyped lambda calculus is REALLY cool

[gray gazelle]

does anybody have a book recomendation for discrete math but with a computer science focuse. I tried concrete math but my pdf version of it is bad compared to pdf versions of some newer books

[slender dragon]

@gray gazelle https://discretemath.org/

[gray gazelle]

thanks

[fluid bay]

discrete math by kenneth rosen is pretty standard in comp sci

[granite blade]

hey, would someone be able to recommend me a statistics book to learn/cite for ensemble averages?

[muted oyster]

statistical inference by casella

[granite blade]

thanks

[lucid snow]

university / 12th grade

[hearty steppe]

https://tenor.com/view/yes-nod-agree-yup-oh-yes-gif-13439264

[arctic hemlock]

Hey, does anyone have any book recommendations for learning coalgebra? Maybe something nice for beginners

[sudden kindle]

Zakeri

[sage python]

Wait that actually looks good damn

[cursive orbit]

tfw no pdf online

[hallow oriole]

^ a tragedy

all i can find is his book "rotation sets and complex dynamics"

[uneven moth]

Books for AIME

Plz

[desert thorn]

So i've been googling for undergrad Linear Algebra textbooks, but i was hoping for some human feedback... is there anything as good for LA as Stewart is for Calculus?

[runic hatch]

What exactly are you looking for in an LA book

Computation-focused stuff?

[desert thorn]

had my first LA course a few months ago, and i'm going to have to revise basic concepts because i didn't do great on the final

[runic hatch]

There’s a list of recommendations here in the pins (with a small review for each one)

[desert thorn]

oooh i didn't even know that was a thing.

i'll have a look at those, thank you.

[blazing canopy]

If we're taking the comparison with Stewart's Calculus to mean very introductory level, suitable for high schoolers or first year college students, then the equivalent of this would be either Strang's "Introduction to Linear Algebra" or Lay's "Linear Algebra and Its Applications"

[sage nebula]

I'm trying to look into combinatorial optimization and it seems I don't have the background knowledge to understand much of it. It seems that graphs are an intuitive way to go through solving these problems.

Mostly I think I want to get the gist of the terminologies and the core fundamentals. My problem is sorta niche.

Any good suggestions for combinatorial optimization, ideally focusing on applications?

[gray gazelle]

any good books with hard exercises to read along tao's analysis I ?

[karmic thorn]

[karmic thorn]

You can find several "problems in analysis" kind of books (see Kaczor-Nowak or Demidovich), but it's hard to say if these are good supplements to Tao's books

You can use a secondary analysis text for its exercises too

[gray gazelle]

any suggestion for the latter @karmic thorn

[mystic orbit]

Rudin

But like

Unironically

[gray gazelle]

@mystic orbit baby Rudin?

[runic hatch]

Yeah I’d say it’s a good source of problems

[mystic orbit]

Ye

[gray gazelle]

Im new here, i want to start learning calculus and found jame stewart's book and wondering how much calculus does the book cover.

[gray jungle]

i feel it it would be hard to work on rudins exercises coming from tao because you would not be familiar with notions from metric spaces.

[mystic orbit]

As if rudin explores metric spaces outside the exercises much

[karmic thorn]

Any book that you vibe with, really. One issue I take up with this is, if you have to end up going through a different textbook for analysis anyway, what purpose does Tao serve in the first place? It has good explanations and wordy proofs that help a lot with the "thinking process" of coming up with arguments, but you can decide if that's enough to make it a primary textbook.

[gray gazelle]

I want both wordy proofs AND good exercises

and like grothendiek said "One should never try to prove anything that is not almost obvious"

[halcyon garden]

Try Pugh, maybe you'll like it. (Sometimes) "a picture is worth a thousand words" plus good excercises

Lots of good excercises

[gray gazelle]

thanks

[gray gazelle]

how is this math

well i reccomend how to be good at math but it is for like K-6

i remember reading it back at second grade

[halcyon garden]

If someone has a solutions manual for Fulton Algebraic curves, pls dm me

[blazing garden]

There are some excellent companion notes to baby rudin with exercises graded by difficulties

It’s from a professor called Greg or George something

[dull ruin]

Anyone have a recommendation for a book that works towards the classification of simple groups?

[soft drift]

wtf does sloth completely read all the books they review?

[timber mesa]

tbh you don't need to read each math book you come across entirely -- they're just references

just focus on the chapters you need to learn

do a few relevant exercises, not all of them

anyway -- I need to take a qual-ish exam in complex analysis in about a month, what are some good resources for exercises and such?

my prof recommends Conway and Alcides Lins Neto (in Portuguese)

[timber mesa]

(I agree that this one looks very interesting, but it's very recent and I'm short on money rn)

[sage python]

Nah, so for that rec in particular

I've referenced Bass and Folland a fair bit, my measure theory class pulled a liiitle bit from Stein-Shakarchi. The others I looked up for the sake of the review + used impressions from people I know (e.g. the "miss a comma miss a theorem" quote from one of my undergrad analysis profs)

re @soft drift

[remote ginkgo]

big rudin + royden best

need to look at folland though

[gray gazelle]

https://link.springer.com/chapter/10.1007/978-1-4614-3618-8_1

what is your opinion on this book?

[glass wren]

but it’s graduate level, should i do ahlfors as my first complex analysis textbook, or do you have another recommendation

[glass wren]

same to you, for the above

[sudden kindle]

I recomend to avoid ahlfora

Imo its a bad book

[glass wren]

do you have any suggestions

[sudden kindle]

Zakeri

[glass wren]

that said graduate textbook

would it work as an introductory book?

[sudden kindle]

Yes

[glass wren]

also do you know any analysis books that i could go through which would be more advanced than rudin

(after covering rudin)

[sudden kindle]

Begining graduate students = undergrad

[glass wren]

ah

thank you

[hallow oriole]

say pty did u buy it?

or did you find it online somewhere

[sudden kindle]

I did not buy it

Zakeri was my complex analysis prof last fall and he gave pdfs of the chapters to us because the book wasn't published yet

[hallow oriole]

huh

sounds like a pretty nice guy

[sudden kindle]

He's great

Really knows his complex analysis

And the history too

[foggy relic]

dang where can a pdf of it be found

i dont see it on libgen

[hallow oriole]

there aren't any rips online

[sudden kindle]

On one hand i think it would be a benefit to society if someone put the pdf on libgen

But also it was just recently published last fall

We can wait a bit

[hallow oriole]

yeah i'd give it a bit longer

plus there are other ca books out there

that are decent from what i'm told

which are also online

[glass wren]

this looks fun

[hallow oriole]

don't post direct links here pls

dm it to ppl you wanna give it to

<3

[fallow cypress]

can I recommend non-math books in here, aka the portrait of an artist as a young man by james joyce

[runic hatch]

Yeah that is a good book

[fallow cypress]

like damn, joyce can write

that christmas dinner scene had me in chills

[nocturne marsh]

after this, can I now proceed with precalc? or straight onto calc?

[fallow cypress]

prob just straight to calc

idk what precalc really entails, it varies dramatically from school to school

[hallow oriole]

https://www.amazon.com/Mathematical-Induction-Powerful-Elegant-Method/dp/0996874593

someone tell me if this is a good induction book i am so fucking done with not understanding induction

there are rips online

[cyan prism]

don't understand induction?

what part

[hallow oriole]

i know like

basic induction

i'm talking about understanding how to extend said basic induction

to other things

[mystic orbit]

I think you'd be fine if you went straight to precalc

even calc if you're feelin frisky

you can always ask for directions if you come across something you didn't know and precalc's curriculum isn't particularly bloated

[gray gazelle]

Hello, i am looking for something (hopefully a book) which covers all trigonometric formulas along with their proofs, thanks in advance for anyone who helps

(or suggest something better)

[mystic orbit]

you don't really need a book for that

here: https://www.purplemath.com/modules/idents.htm

you don't even need to memorize all of these

you can just use the above as a reference

[gray gazelle]

I actually want the proofs and stuff for these too, if u have any, thanks

[mystic orbit]

oh

these don't have proofs?

I thought they did

[gray gazelle]

Nope

Don't see any atleast

[mystic orbit]

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

this uses right triangles to prove most identities

[gray gazelle]

Ah thanks

[split cradle]

whats an interesting book 4 alg 2

[mystic orbit]

Kan academy

[normal sandal]

serre rep theory

[granite viper]

is there a way of working through a textbook? i make sure to read it through until i understand the concepts. But i feel bad if i don't commit to memorizing all the little details. for example, i've started learning calculus and there is something called the mean value theorem. I understand it conceptually, but cannot define it as rigorously as they do (with sets and all these inequalities). should i focus on working through the book conceptually and doing problems? or meticulously remembering proofs too.

[gray gazelle]

this is very natural

i'm going through it myself!

you just keep on studying

and if you forget something you go back

and skim it

[granite viper]

some of the theorems i feel are irrelevant to the major problems. so skipping isn't too bad right?

[gray gazelle]

proofs are important

[granite viper]

isn't that analysis?

[gray gazelle]

is it spivak's ?

[granite viper]

no keisler's. it's an infinitesimal approach instead of epsilon delta

[gray gazelle]

i see

[granite viper]

but still has proofs

[gray gazelle]

well it depends on what you want

[granite viper]

to get by with engineering mathematics, it's not too bad to skip some details right?

[gray gazelle]

that's up to you

but if i were an engineer i'd read the proofs at least

understand them

[granite viper]

alright, i'll try to keep it up then

thanks

[gray gazelle]

np

[remote ginkgo]

do problems

mvt does not become very obviously useful to you until you see where it comes up and gets used

it actually gets used in court cases regarding speeding tickets

the speed meters cops use just check distance traveled over some finite amount of time and get the average rate of travel. MVT says rigorously that you were traveling at that rate of speed at some instant while the measurement was being made so that you can be properly charged with the speeding crime

[crimson leaf]

It can also be used to derive many results in calc 2

[granite viper]

all right. every single one?

[gray gazelle]

wdym

[gray gazelle]

Which would be the most basic book about math for start

[fallow cypress]

what do you mean for start

what do you want to learn

[quick hornet]

find any preschool worksheet on how to count to 10

alternatively, read russell-whitehead

[loud cradle]

this is ambiguous as they don't define "item"

[gray gazelle]

calculus

[fallow cypress]

maybe early transcendentals? or just use khanacademy, khanacademy is really good for calculus

[runic hatch]

Paul’s online notes are also good

[fallow cypress]

^^

[heady ember]

If you want to learn it with proof based exercises you can try Spivak

But be warned, you'll spend hours to no avail often

[gray gazelle]

or taos analysis

@heady ember have you looked at tao?

[heady ember]

Im not at analysis yet

[gray gazelle]

it's an intro to it

you know how spivak uhh defines addition and the like at the start of the book ?

[sage python]

Tao does that in much more detail yeah

I haven't looked super deep into it, obviously that guy is talented as hell and probably has well thought out and quality opinions on pedagogy

Someone said it takes a couple hundred pages to get to limits, which feels a lot but perhaps it's a mix of verbosity and frontloading foundations heavily

[gray gazelle]

@sage python yeah 234 iirc

it's the definition of a functions limit

he defines limits of sequences first

[sage python]

Oh that's pretty fair

[winter echo]

good

[gray gazelle]

whats a good easy to understand first book for numbr theory

[stray veldt]

silverman's friendly introduction to number theory

[crimson pagoda]

Any number theory books for an arithmetic geometer? I'm a 6th year undergraduate student

[hollow shore]

6th year

[runic hatch]

Any good books on axiomatic set theory? For reference, I’m looking at Suppes right now and am interested in alternatives

[sudden kindle]

Maybe Neukirch

[crimson pagoda]

Read it, it was terrible

[sudden kindle]

What was bad about it? I didn't read it

[crimson pagoda]

I don't like number theory

[sudden kindle]

Liu Algebraic Geometry and Arithmetic Curves is an intro to ag and arithmetic geometry

[crimson pagoda]

yamin it's me gabe I'm trolling

[sudden kindle]

Arithmetic geometer who doesn't like number theory

[crimson pagoda]

It's called geometric langlands

[thorn cloak]

This might be a little ambiguous but does anyone know any good books I can read just about I guess theory? Just a book to help me in thinking and being a “mathematician,” not necessarily one actually teaching a core subject with problems. I just want something I can read casually without pen/paper and problems

[rancid ivy]

Does someone here have a PDF about arithmetic of integers ?

[grand osprey]

Even when one comes to limits in Tao, he does it in a grossly detailed way which imo is a lot of info(many non standard definitions for example) to keep in one’s head

[remote ginkgo]

@rancid ivy sure. https://www.jstor.org/stable/3072368

[gray gazelle]

any short intro to number theory, like just the very basics and overview of some topics < 100 pages

[orchid musk]

i really like Elementary Number Theory by Jones and Jones

[sage python]

Why'd you send a bunch of pictures? I don't see a point in blowing up chat like that

[wet holly]

Book recomendation?

This entire collection is amazing

Cover all elementary math in a very deep way

[sage python]

I mean can you just send the name then and say it's a 9 volume series rather than send pictures? Or links?

[wet holly]

mb cuse of the flood i tought the images would have grouped themselfs

[sage python]

Makes sense

Anyway we'll note that you recommended "Fundamentos de Matematica Elementar" vols 1-9 (except 8? guessing that was an omission)

And I'll delete the images so not to blow up the channel

[wet holly]

8 it's derivates

introduction to calculus

Im not on that

[sage python]

@crimson pagoda "Hey can I have a number theory book? I do arithmetic geometry"
"Here's a number theory book"
"Eww number theory"

[gray gazelle]

Thanks, i will look into it

[shut bane]

recommend me a good story book to read before night night

[delicate hemlock]

where the wild things are

[coarse frost]

[rancid ivy]

Thank you but don't you have that is free ?

[remote ginkgo]

i do but i can't provide it to you

[restive falcon]

the stormlight archive
some very light reading

[crisp river]

Hello I am reading Complex Analysis in One Variable by Narasimhan. Therr are no exercises. How should I go about reading the book?

[ebon umbra]

Isn't narasimhan the most difficult book on that subject?

I recommend Serge Lang's complex analysis my favorite book on complex analysis

[cosmic drift]

You guy have any book recommendation for calculus?

[ebon umbra]

I think it has similar contents and also serge lang has solutions

[ebon umbra]

which level?

rigorous or technical

[cosmic drift]

Both if possible but i would go with technical

[ebon umbra]

tbh I don't think theres much difference between calc books

get the cheapest one from bookstore

my favorite is calc book by serge lang

it doesn't go oveboard like spivak

[cosmic drift]

thanks

[ebon umbra]

btw I'm kind of serge lang simp

but serge lang is infamous for love it or hate it

so take my recommendation with grain of salt

[sage python]

Schlag is definitely harder than Narasimhan

@ebon umbra what kinds of stuff are you working on btw?

[ebon umbra]

I actually took complex analysis right after real analysis

and am planning to take measure theory next semester

[sage python]

I heard you have 2501 projects going simultaneous

[ebon umbra]

no?

what are you talking about

[sage python]

I can't tell if you're deflecting me or actually not an alt of that other guy

[ebon umbra]

I came here today

[sage python]

There's someone here who hard shills for Serge Lang

[ebon umbra]

I am not an alt

welp interesting

[sage python]

Nickname here is sergelangfan42069

[crisp river]

🤷

[ebon umbra]

oh lol

thats interesting

[crisp river]

I just want a supplement for exercises

[ebon umbra]

I thought that I was being suspected of alting

[sage python]

Actual username is project 2501 lol

I mean this person is not banned

I just thought like

Lmfao

[crisp river]

Should I just use two different textbooks?

[ebon umbra]

isn't serge lang pretty popualr though?

[crisp river]

Or is there a nice method for this

[ebon umbra]

especially ones who study algebra?

[ebon umbra]

I recommend using multiple textbooks

[sage python]

Kiiiiinda

[ebon umbra]

I used 3 textbooks for real analysis and it helped a lot

[sage python]

Lang algebra is the king ish

[crisp river]

Id prefer not using multiple textbooks. Can you suggest anything else?

[sage python]

But controversial

[ebon umbra]

ask your professor

[sage python]

Lang algebraic NT is also popular

[ebon umbra]

I think that's the best way

[crisp river]

I dont have a professor lol

[sage python]

@crisp river a newer version of the book has problems

Look up Narasimhan and Nievergelt

[ebon umbra]

I'm not really an algebra guy and I've only taken course using fraleigh

[crisp river]

Thanks! That is helpful to know

[sage python]

Might be spelling it wrong

[ebon umbra]

so I don't know much about algebra books by lang tho

[crisp river]

Maybe Ill purchase the book

[sage python]

But it's the second edition and it has problems (hence the second author)

[ebon umbra]

I like the insight that lang's textbook has

though it is a bit disorganized and terse

[sage python]

Now fwiw I'm not gonna double down and say oh this is necessarily your book

I'm more saying if specifically the only problem was lack of exercises, that has been resolved

[ebon umbra]

actually i'm kind of interested about this sergelangfan guy

[sage python]

Narasimhan is kinda my pick though if you know some measure theory

[crisp river]

Im just scared about lack of exercises

Ive read a small amount of papers before but it’s different because the pength

[ebon umbra]

I think that you should know how to pave your own path if you are at the level of narasimhan

like you are much higher than me

[sage python]

Well okay I haven't read much of it to know if it does measure theory

But it feels like it does in harmonic functions bit

[crisp river]

Im only trying to get to chapter 9

[sage python]

It incorporates ideas from algebraic topology which is the objectively correct way to do things lol

[crisp river]

Im trying to use it as a prerequisite for complex geometry

[sage python]

Nice

[ebon umbra]

this is kind of unpopular but another good option is the book by freitag& busam but the book has focus on number theory

so it might not be for everybody's purpose

[sage python]

To me Freitag-Busam is one of the "correct" answers

Basically my shtick is

Gamelin if you don't have much background

[crisp river]

Are there nice ways to go about books with no exercises? Or do I read and come up with my own?

Because there are no examples either

[sage python]

Freitag-Busam if you're at baby Rudin level

Narasimhan if you're more serious

[ebon umbra]

using multiple textbooks

[sage python]

And Schlag if you're actually cracked

[ebon umbra]

I felt like freitag was a bit softer than lang's version

maybe because freitag was targeted towards undergraduate

also I mean vol 1 not vol 2, vol2 is graduate level

[crisp river]

Im at baby rudin level. I have a good algebra background but poor analysis

I took courses in real analysis

About to take a grad course this coming semester

[ebon umbra]

i won't say that baby rudin level is 'poor'

[sage python]

Okay to be fair I don't know Lang much. Lang and Greene-Krantz and Bak-Newman are high profile books that I'm less familiar with

But Lang strikes me as just boring

[crisp river]

I liked some parts of Lang’s Algebra

I havent read all of it of course

[ebon umbra]

how difficult is lang's algebra though

[crisp river]

But it is very good reference

[ebon umbra]

my friend really hated the book

[sage python]

I only read a bit on field and galois theory

[crisp river]

It shouldnt be your first course in algebra

[sage python]

And very much like that

[ebon umbra]

he said it took 5 days to read 2~3 pages

[crisp river]

If its your first time seeing things then yes.

[ebon umbra]

tbh I'm not planning on studying algebra further

but yeah

lang's algebra shouldn't be first algebra course

[heady ember]

"Differential Geometry" as prerequisite

[sage python]

Yeah lol

I know the man himself

He's a master teacher

[ebon umbra]

how are math professors like in person?

[sage python]

But he's also fucking wild

[heady ember]

What do you mean by that

[sage python]

So my undergrad has a course titled "Introduction to Differentiable Manifolds and Integration on Manifolds"

Topics include exterior algebra; differentiable manifolds and their basic properties; differential forms; integration on manifolds; and the theorems of Stokes, DeRham, and Sard.

This is the catalog description

Also we have "Basic Complex Variables"

Topics include complex numbers, elementary functions of a complex variable, complex integration, power series, residues, and conformal mapping.

[ebon umbra]

mind sharing syllabus?

kind of curious what that course is about

[sage python]

The description is the best thing you'll get because the class changes drastically each time

I'll give some details later but for now

[ebon umbra]

which textbook did you use

oh okay share it later

[sage python]

Notice those two classes and their descriptions

And they're numbered as undergrad classes

[ebon umbra]

latter one seems much more lenient

wait they learn diff manifolds undergrad?

[sage python]

Yeah

[ebon umbra]

thats pretty surprising

[sage python]

I didn't have him for either, I had him for honors analysis

And to be fair it was nuts

But that class was marketed as being hard

We had what we called the Jesus Christ pset

set3.pdf

[ebon umbra]

did they use lee's book of tu's book?

or something else

[crisp river]

I took two courses in differential topology

[sage python]

Else, be patient polygraph

[crisp river]

So maybe this book would be better in future

[sage python]

So

[crisp river]

I think problem with Narasimhan is that it lacks exposition

Atleast thats what im finding right now

Too quick to give definition and result

[ebon umbra]

is there a reason to stick with narashimhan?

[crisp river]

and remarks seem infrequent

[sage python]

Yeah basically when this guy taught complex he taught it at a level close ish to his honors analysis class

[ebon umbra]

i've heard the book is very challenging

[crisp river]

I dont find reading through it chapllenging atm but im only on page 8 on first day

[sage python]

And people were like bruh

[crisp river]

I just find some things unmotivated

[ebon umbra]

how do students catch up?

[sage python]

For instance

This is one of his complex analysis psets

set7.pdf

This is not billed as an honors or grad or anything

It's "Basic Complex Variables" lol

[ebon umbra]

how was the grading?

was it harsh?

[sage python]

I'm not sure

Anyway so when he taught manifolds

He was like alright last time I taught complex analysis people complained it was too much

So I'll tell you day 1 what I consider reasonable

We will cover Nash embedding theorem

[crisp river]

That is unreasonable

[sage python]

Yeah lol. For undergrad manifolds

Obviously he did not get there

[ebon umbra]

my uni's graduate course on diff manifolds

[sage python]

But yeah that's what I mean when I say Schlag is wild

[ebon umbra]

doesn't even go there in 2 semesters

maybe he is too enthusiastic

how did you manage to study through those courses

[sage python]

@heady ember

Lol very much so. But yeah what he actually did was like

[crisp river]

Well thats weird

We got there maybe 6th week

[ebon umbra]

tbh my uni's graduate school

[sage python]

Nash?

[crisp river]

but definitely not a day 1 thing

[ebon umbra]

isn't that famous

tho undergraduate is pretty good

[sage python]

That's not common choice of topic in manifold theory

But yeah he ended up doing a bit of "generalities on smooth manifolds"

[crisp river]

It was talked about for one lecture

[sage python]

Then differential forms and Stokes' theorem

And then did curves/surfaces and moving frames

[ebon umbra]

which textbook did he use btw

[sage python]

I think official book was Barden and Thomas

But then he was like wait up

[heady ember]

Yeah i get what you mean lol

[sage python]

I totally forgot Do Carmo's book on differential forms exists

So he used that and then Shifrin curves/surfaces for the latter part

But yeah my year it was Guillemin-Pollack

And we covered more differential topology than geometry

The year before me I think it was Lee

[heady ember]

Lee

[crisp river]

Lu Toring is my favorite

but Lee covers more

[sage python]

Honestly both of those books induce this reaction in me

[heady ember]

[crisp river]

Its not Hatcher

[vital bane]

is that the one that says you can't isometrically embed a riemannian manifold of dim n in a euclidean space of dim lower than 2^n + 1?

[sage python]

I think it gives you when you can rather than can't

[shy compass]

mfw there is no identity map from R^n to itself

[fluid crow]

Can anyone recommend me a book, I want to cover High School Math.

[gray gazelle]

not a book but

[gray gazelle]

khan academy

[fluid crow]

no offense, but i tried khan academy and now specifically looking for a book

thanks tho

[thorn cloak]

I think the math sorcerer has a good video on math from the beginning

https://www.google.com/search?q=the+math+professor+learn+math+from+start+to+finish&client=safari&hl=en-us&sxsrf=ALiCzsZlAh24woPs918HVl9zvqU95yV1PA%3A1657131471795&ei=z9HFYtDwL9ykptQP2fKjsA0&oq=the+math+professor+learn+math+from+start+to+finish&gs_lcp=ChNtb2JpbGUtZ3dzLXdpei1zZXJwEAMyBQghEKABMgUIIRCgATIFCCEQqwI6BwgAEEcQsAM6CAghEB4QFhAdSgQIQRgAUIoDWOQYYKMaaAFwAXgAgAHGAogByBSSAQg1LjE2LjAuMZgBAKABAcgBCMABAQ&sclient=mobile-gws-wiz-serp#fpstate=ive&vld=cid:41f47f05,vid:pTnEG_WGd2Q,st:0

I think it covers some high school math in there

[gray gazelle]

What's wrong with your textbook? I assume you're in high school.

[gray gazelle]

suppose I know proof writing well, should I go for LA first or discrete math?

[fluid crow]

I passed high school 3 years ago

Didn't study after that

@gray gazelle

[crimson pagoda]

Lee is so easy to read tho...... Even the problems r easy enough that one could just intuit the solution most of the time....... Or whenever a difficult calculation comes up you could just imagine it in your head and carry on with your day........ I still don't know what a manifold is........

[fluid crow]

I am self studying from these books.

I have learned and practice 80% of the book "preAlgebra 2e" they have further books but I am not sure which ones I need to cover in order to be high school level.

[fluid crow]

Thank you i will take a look

[fluid crow]

https://openstax.org/subjects/math

[gray gazelle]

Just do both.

[gray gazelle]

What's wrong with them? I was going to recommend them because we want to stay legal and free. Also https://aimath.org/textbooks/approved-textbooks/

[cyan scroll]

Hi everyone, what book do you recommend for introductory course in combinatorics?

[gray gazelle]

For self-study? Or are you taking a course now?

[cyan scroll]

For self-study

[fluid crow]

I love them, just want to know which of these books I need to cover for high school math

[warped cedar]

does anyone have a recommendation of a book covering Markov chains

[sage python]

Try Lawler

[warm glen]

people use bona's book a lot it's pretty standard and well written, u could probably find lectures to go along w that book

https://cseweb.ucsd.edu//~dakane/Math184/

this site has lectures and problem sets and follows bona

[gray gazelle]

Does anyone have a high quality Spivak PDF? I can only find low quality ones, a little bothersome to read

I saw this message but sadly the sender deleted their Discord account

we must respect TOS

[gray gazelle]

Hi, I want to learn about mapping, functions, sets, mathematical logic and proofs. What books do you recommend? (for beginner but in depth )

[heady ember]

As long as you don't send it in the server its fine

[empty orchid]

hi guys I completed sophomore and have done all of HS math other than few topics in advanced algebra and most of calculus. What fields can I branch into learning now? My interest is mostly number theory. Any books and some free resources would be helpful thanks

[stray veldt]

you can read a number theory book, like silverman's friendly introduction

[gray gazelle]

proofs maybe

[empty orchid]

i also forgot to mention I wanted to start to understand and read research in number theory , so if there is anything that can start me on that too

[stray veldt]

well, understanding current research will take a while

you would have to learn linear algebra, abstract algebra and then you can start learning modern number theory

[empty orchid]

i see, thanks for the help

[stray veldt]

by algebra i mean abstract algebra*

[empty orchid]

and i think my hs will have an advanced course on group theory soon. What are the pre-reqs

*not graph , group sry

[stray veldt]

hm?

group theory has no prereqs

at least not formally

if its advanced group theory, the prereq is probably basic group theory

[empty orchid]

gotcha thanks

[ebon umbra]

what are some good rigorous probability textbooks

that does not require measure theory?

also is the knowledge of measure theory the only prereq to stochastic processes or do I also need to know rigorous probability?

[unkempt plank]

Any good book for learning geometry from zero ?

[remote ginkgo]

what do u mean by geometry

u can try khan academy exercises

if u know calculus u can try shifrin's classical theory of curves and surfaces book

[primal mica]

What’s the best analysis track to prepare you for other fields without being too intrinsically analysis-ey.

Like what’s a good track for putting you on good footing for algebra/geometry/topology

Or should I suck it up and dive in deep

[gray gazelle]

Why do you think you need extra preparation?

Just take the courses after you've taken the prerequisites. Or in case of self-study, just open a book on algebra/geometry/topology start working on it.

[gray gazelle]

Try your local university library. Most likely have a copy and allow you to borrow it. Since we want to stay legal. Also pdf collecting and studying only from the "best" book are easy traps to fall into. Most books would work fine, no need for spivak.

[cyan scroll]

"Discrete mathematics with applications" by Susana Epp is good

[gray gazelle]

thnx

[thorn cloak]

Good books to brush up in calculus 1 2 before taking multi variable calc? Preferably not a full fledged textbook

[serene reef]

Not a book but Paul online math notes is good for that.

[gray gazelle]

I love the way Spivak teaches (building up from axioms), which is why I was hoping for it.
I'm 100% sure my local library won't have it, and it costs $100 on Amazon in a country where the average wage is $400 a month, I can't afford it.

Thanks anyway, I won't ask again if it's against this server's rules, I will just read the PDF I already have

[gray gazelle]

Check first. It's pretty popular book. As long as your local uni has a math department, it will have it most likely. At least the translations.

[gray gazelle]

good mathematical books of general relativity?

[forest sleet]

Wald

Or try https://mathoverflow.net/questions/217565/modern-mathematical-books-on-general-relativity

Wald is a pretty standard classic gr textbook

[forest sleet]

It's going to be tough to do without measure theory if you want to work with continuous random variables

A number of probability textbooks will start with intro to measure theory though

[trail kernel]

Does anyone know any good differential geometry books (with tensors/tensor fields) which also have exercises like these? I mean computational exercises, not just "show that" or "prove this" exercises

[amber pumice]

What's a good book on computational geometry in 3D concerning piecewise linear complexes? I've tried "Computational Geometry Algorithms and Applications" but it mostly stays abstract and concerns 2D

[primal mica]

I don’t know either of those books but with knowledge and basic foundations in derivation and integration, multi variable is the next natural step

Later in single variable texts they do cover some more techniques like Integration by parts, partial fraction decomposition, and substitution might also be covered here? Those are great to know and necessary for differential equations but most multi variable texts don’t require much of that, unfortunately.

[gray gazelle]

Math subjects that will be useful for quant jobs?

[ebon umbra]

actually i am interested in it too

professors told me to aim for courses in 'stochastic calculus' and 'probability theory'

+'measure theory'

[gray gazelle]

Oooo measure theory is useful for quant, I am trying to get there but have to finish all the analysis leading up to it first

[ebon umbra]

yep I have to do it too

[hearty steppe]

I think the most important areas of higher level math for most subjects are going to be measure theory and topology. That’s depending how far down the hole you need to go for what your doing

[crimson pagoda]

🤔

[hearty steppe]

Topology has a very nice appeal in terms of trying to gain a sense of for instance the integrity of your data clusters when compared to eachother or even when comparing structures that may have extremely similar designs

[lime sapphire]

Surprisingly, dedicated courses in topology aren't taught until last couple semesters of undergrad for most ppl

[hearty steppe]

Your not gona gain much from math I don’t think if you don’t study the theory mostly. I think people tend to try to get a surface explanation and then look into how they can take formulas and stuff they don’t understand and do stuff with them

[lime sapphire]

Ig you can say that

[gray gazelle]

I mean the other way around also true, right? You read the text, you learn ||(memorize)|| how to proof the results, statements, theorems, etc. But in the end you can't solve any problems in the HWs and exams. Not even talking about original research.

[quick hornet]

i dont understand the point

on either "side" here

[gray gazelle]

No need to understand. Just silly internet discussion. Both of us are probably ESL too.

[primal mica]

Any standard PDE book?

[gusty smelt]

good books/papers for cobordism/bordism stuff? I am familiar with some homotopy theory so something from that perspective might be nice (i am interested in general in applying AT stuff to differential topology)

[austere osprey]

any book suggestions for Complex Analysis

[loud cradle]

there's a pinned message with some recommendations. stein and shakarchi would be one popular suggestion

[blazing canopy]

In addition to the pinned suggestions, I like Greene and Krantz's Function Theory of One Complex Variable which treats complex analysis in a much more analytic way (more like analysis on R^2), rather than in a geometric or topological way. This has some severe limitations but I thought it made the presentation fairly straightforward. I also like Ablowitz and Fokas' Complex Variables: Introduction and Applications which has a focus on what kinds of mathematical problems can be solved using complex analysis.

Lastly, I found Rudin's Real and Complex Analysis a decent reference for describing some of the key highlights of the theory, but I haven't read it through entirely in a long time.

But if my memory serves you wouldn't want to use it as a primary text on the subject.

[loud cradle]

two others that aren't in the pinned list which I think are worth checking out (depending on your level - these are probably introductory grad level?): Marshall's Complex Analysis and Ullrich's Complex Made Simple

[austere osprey]

thnx .

i will give stein a try..

[dull bramble]

Please share some reviews on this book if someone has gone through it: https://a.co/d/3qxLbnp

[vital bane]

ooh

[dull bramble]

did you go through it?

[vital bane]

sorry, no this is the first time i've even heard of it, it seems interesting

[dull bramble]

oh

[gray gazelle]

in the AMC 10 exam, the last 10 questions are always really hard. Does anyone what aops books they come from??

[fallow cypress]

I used bak+newman, it was pretty clear

stein-sakarchi is also great though

[remote ginkgo]

ahlfors

[runic hatch]

Pins here have some more recommendations

[warm storm]

Book reccomendation to help me qual for JMO pls

[lime sapphire]

Whats JMO

[broken bison]

Junior math olympiad. I used AOPS's volume 2 to prep. From there, it's just practice.

[warm storm]

Ok, Ill go through the two volumes.

[hazy flax]

any one can suggest the best math textbook?

[loud cradle]

on what subject?

[hazy flax]

algebra and calculus

[heady ember]

Spivak's Calculus

(it will absolutely slap you in the face )

[runic hatch]

Paul’s Online Notes is also good (and free) for calc

[narrow copper]

thomas and finney's calculus

[gray gazelle]

really is that so hard

[heady ember]

Depends on your personal experience with rigorous math textbooks I suppose (proofs)

But it is one of the more/most challenging calculus books out there I suppose (obviously not including anal)

[river tangle]

Guys any books for sting theory and m theory?

[ebon umbra]

Hi

What are prerequisites for Hubbard& Hubbards vector calculus?

is a course in single variable calculus enough or do I need further courses in analysis?

Or is knowledge in multivariable calculus assumed?

[gray gazelle]

hmm

[gray gazelle]

any linear algebra stuff that is not too long, easy to understand and introductory? with not much prerequisites

[primal mica]

GSW is the standard and I’ve heard D-Branes by Clifford Johnson affectionately called Volume 3

Zweibach is also quite good, so I’ve heard

(Although thats at a lower level)

[solar anvil]

does anyone know of any books on computational geometry

[earnest gazelle]

joseph o rourke, discrete and computational geometry (2011)

CMSC 754 computational geometry (2021 notes) can be found on google, they are great

[elder wolf]

hey everyone, I am going into Calculus II in the fall and don't want to forget all the stuff i learned in Calc I, does anyone have any recommendation of books or resources to use as sort of a precursor to it?

[novel obsidian]

pauls online math notes 🙂

[elder wolf]

oh i used this site in calc I! thank you much

[heady ember]

Yeah POMN is good

You could try Khan Academy too

Or Spivak if you're really feeling it

(Spivak is more proof based though not as much as Anal)

[ebon umbra]

can you use shifrin to learn multivariable/vector calculus for first time?

with only knowledge of stewart level single variable calculus and some linear algebra

[gray gazelle]

Yes

But supplement with khan when necessary

[grand thistle]

khan academy?

[gray gazelle]

What is the prerequisites to learn Probability and Statistics? Is there good elementary book(s) on this?

I am interested in learning about AI and data science in general, which are prob and stats heavy. I only know up to Calculus

[gray gazelle]

https://math.dartmouth.edu/~prob/prob/prob.pdf - Calculys

Stochastic Calculus = Real Analysis, Measure Theory

[gray gazelle]

What about statistics?

[primal mica]

High school / basic statistics you can learn with basic algebra skills

[gray gazelle]

Uni statistics

[karmic crater]

To start with university probability and statistics you only really need to know calculus and some basic linear algebra and multivariable calculus

[gray gazelle]

Thanks! And what books are recommended, if any?

[karmic crater]

For prerequisites or prob/stats?

[gray gazelle]

prob/stats

[karmic crater]

I took my introductory courses in swedish so I don't know too much about the introductory material. I have heard good things about "a first course in probability" by Sheldon Ross which is free online but I haven't read it myself

Casella and Berger has a nice book on statistics which is at an intermediate level but you can probably find books more suitable for an introductory level

I like Klenke's probability book aside from some weird notation but the text is more advanced

[gray gazelle]

Luckily I'm swedish

[gray gazelle]

You read 3 books on stats? That's like 2k pages

[hollow nymph]

If I wanted to get into numerical mathematics or differential mathematics more, what would you guys recommend? I am a mechanical engineer by education and I had an interest in PDEs through fluids and heat transfer, and I also had an interest in differential geometry and regular old topology while I was doing some undergrad electives. I don't have formal training in those latter two fields, however.

[blazing canopy]

@hollow nymph Are you simply trying to learn some interesting things about numerical computations, or are you trying to expand your skillset as an engineer?

[old elk]

Spivak or Apostol?

Spivak or Stewart?

Apostol or Stewart?

🧐

[broken meadow]

spivak, apostol seek to do something very differently from stewart

the former is more rigorous

the latter is just like standard material and a lotta problems

[fluid skiff]

Any book for algebraic geometry which teaches by examples and then introduces definitions

[hollow nymph]

Definitely both. I'm interested in using numerical computations in my career, hopefully. But I also want to learn more about PDEs and ODEs. Differential math is interesting to me.

[blazing canopy]

@hollow nymph How is your linear algebra? Underpinning many numerical methods are algorithms for linear algebra.

[opal oasis]

Adult level books for visualizing mathematics, the more subjects the better, especially if they use color, especially if the colors serve a purpose, like getting more opaque and changing hues depending on amplitude or frequency or whatever. Different ways to visualize limits besides graphs. Like what those limit graphs represent in physics, like matter approaching light speed, or an object going half the previous distance it traveled each second, etc.

I know some websites, but it’d be nice to have like a 400 page book I could progress through each night.

[gray gazelle]

What does adult level mean, it sounds a bit funny lol

[storm harness]

[hollow nymph]

I'm gonna be honest, it's basically non-existent. My education didn't require a full linear algebra class, only half of one, essentially. And on top of that, my professor was god-awful. I suppose I could give another look through my linear algebra book.

[remote ginkgo]

neither. do khan academy then read rudin

[grand thistle]

i think that's gonna be a very very huge jump in difficulty

[remote ginkgo]

it's what i did

wasn't that bad, though i did whine to my mentor a lot when making the switch

[manic rose]

Any recommendations for math that I’ll need for programming a 3D Engine? Such as Vectors, Matrices etc. ?

[serene reef]

LearnOpengl.com has the basic stuff in the math section of it. Also watching 3bluebrown is nice for intuition. If you want more resources the book 3d math primer for graphics and game development is good. There more resources like that.

Although I will hold of on making 3D engines unless your comfortable with the math. So you won’t be frustrated. I recommend writing a raytracer first since you get to do 3d math faster.

[serene reef]

Going back to this, if you want learn LA there are several options. For without proofs there strang two linear algebra book.

[manic rose]

Okay sounds good. Yeah I’ll make little steps. I’ll also check out the resources you recommend me. The thing is that I got a 50€ coupon for a very big book store and I want to use it. :D

[manic rose]

Okay LA is also what I’ll need

[serene reef]

Learn vector stuff and linear transformation well.

[serene reef]

This is also decent https://textbooks.math.gatech.edu/ila/. Interactive linear algebra. Now I am done.

[manic rose]

Okay.

Is there another book for around 50€, that has the same topic like the 3D math primer for graphics and game development?

But the resources you recommended me are already good enough.

But I still want to use this coupon, I’ve got as a gift.

[old elk]

oooh

[remote ginkgo]

?

[hasty forge]

Does anyone know sources to start studying aerodynamics.

Books... courses...videos anything(free if possible)

Even names of books if you know

[old elk]

I am afraid of ruddin's books
and more from springer publishers
I feel I have learned nothing
I feel bad for myself

[remote ginkgo]

you need a considerable amount of training before such books are digestible to you

[old elk]

I haven't learned anything about linear algegra
I'm a mess

[remote ginkgo]

try shilov

[old elk]

yaay!

[remote ginkgo]

also if you have questions i have a bunch of very good mathematicians in my server that can help you all the time

and will give you the training necessary to read harder stuff

mind me inviting you?

[stray veldt]

[old elk]

I am interested, you can send me the invitation to private 😄

[remote ginkgo]

it's a relatively big pure & applied maths server but has some people that speak in a way that is usually considered rude in big public spaces

[lime sapphire]

Strange im on a server with the same description

[surreal phoenix]

that sounds kinda awesome, how do I get in on some of that

[meager turtle]

anyone got any introductory books to ramsey theory

i've got a decent amount of graph theory and some probability under my belt atm

and some research experience related to complex analysis and probability

(introductory still ideal tho i'm not very far in math just yet)

[heady ember]

Or just persistence to stare at a page / a question for hours without making any progress

[formal tinsel]

does anyone here know what math you'd need to understand before learning about etale cohomologies?

[tulip blade]

If you know some basic ramsey Just read papers. You can look at the ramsey theory chapter in diestel and ramsey theory related chapters of the lecture notes graph theory and additive combinatorics, probabilistic methods in combinatorics both by yufei zhao

[meager turtle]

i’ll check those out! by any chance, do you know if there is a textbook about ramsey theory?

[tulip blade]

I think there is. Ive never meet someone that read it though.

[meager turtle]

this is a long shot but once in a university library i saw a book titled Ramsey Theory but i dont think i caught the author’s name

[tulip blade]

You can start reading papers. There isnt a deep cohesive theory.

[meager turtle]

never got to read it but i would absolutely love to someday
i see

makes sense that there’s not a cohesive theory, it seems to pop up in a lot of places

[white kraken]

Hey guys

Does anyone has a book suggestion for homological algebra (for self study)

(w/ a good amount of exercices if possible)

[delicate hemlock]

Weibel + Rotman for more details if needed

The last chapter of Aluffi also does a good job, or at least that's what I'm using for the moment

[main void]

What is the usual “standard” recommendation for an introductory text in mathematical logic?
A lot of texts I’ve found were somewhat oriented towards philosophy students and the pdf given in #books apparently isn’t an introduction.

[white kraken]

hehe I'm currently reading the last chapter on Linear Algebra of Aluffi xD, if it's good then I'll definitely check it out. Thanks 🙂

[small pilot]

is there any place i can buy books about Algebra that chinese 9th grade students use?

oh and the US too

[hallow oriole]

i wouldn't buy a textbook for that kind of algebra

i recommend just khanacademy

[hallow oriole]

https://www.logicmatters.net/tyl/

remember that everything is free on the internet ^^

[main void]

Nice thanks ill look into it

[coral marsh]

anyone have good textbooks for advanced multivariable/vector calculus? i have some knowledge (about the level of stewart's) but the vector fields portion didn't stick too well the first time

ideally would want a book that covers like chapter 16 of stewart's but also later goes in-depth enough to cover what would be needed for differential geometry

bonus if it's more application/computation based instead of purely theoretical

[gray gazelle]

atomic habits

[velvet crag]

I'm currently a high school student in the UK, I'm applying to university this year and need to read a few books over the summer for my application.

Which books would you recommend that are elementary enough for me to understand yet are still actual books and might seem like a good fit on an application?

[novel obsidian]

math textbook or math exposition books?

[velvet crag]

Like a readable textbook, I guess

(As readable as a textbook can be)

[lime sapphire]

Are you applying for maths? If so what area of maths are you interested in?

If you have no preferences, i can recommend how to prove it by velleman

Or numbers and functions: steps into analysis by burn

[velvet crag]

Yeah, I’m applying for just maths courses. Both books sound great, will get reading.
Thank you so much.

[lime sapphire]

Np

[night prism]

From what I’ve found, this can depend on your level of mathematical sophistication. It would help to share some details in this regard

[median shale]

Pls Guys any or textbook pdf that explain functions deeply I mean piece wise function and those stuff

[main void]

Im entering my last year of undergrad (but im in europe so this might be misleading since the american system is a bit behind I believe)
So im looking for a textbook/pdf which is at the level of maybe a first graduate course or last year undergraduate course

[quick hornet]

...for what subject?

[main void]

Oops sorry i was responding to @night prism

[quick hornet]

ah i see

[night prism]

Okay; also, are you looking for books aimed at aspiring logicians, or just “logic for (other kinds of) mathematicians”

[main void]

Definitely for other kinds of mathematicians, though i dont mind having more specialized references

[night prism]

Alright gotcha

I think some common introductory ones aimed at math students are Enderton and Van Dalen; I’m reading Van Dalen currently and find it fairly straightforward. Mendelson is also a good standard treatment. In truth I cycle through about 4-5 logic books just because the matter is so technical that I sometimes find different authors’ treatments to be more lucid than others for even the identical subject matter

Some of my personal favorites: Van Dalen, Andrews, Stoll, Tourlakis

[safe salmon]

hey

[main void]

Awesome, thanks for the response and your time, ill make sure to look into them

[safe salmon]

does anyone here know a book about conics and quadrics in Geometry?

[heady ember]

Enderton

For logic, Manan likes A Friendly Introduction to Mathematics

Seems quite good

The exposition seems pretty awesome from the first few pages i read

[night prism]

A bit of a shit book to me because of all of the typos

But sure, feel free to recommend based on having read the first pages

[heady ember]

Manan recommended it last time. I did not reccomend it solely based on that i read the first few pages

I just put that as a disclaimer since I have not read that much of the book but Manan said he/she liked it

So the person might wanna give that book a go and see if it suits their needs and preferences

Or if they like Enderton more

[night prism]

Oh, you were being a mouthpiece; then it’s alright

[hollow shore]

I am looking for video lectures on introductory combinatorics. Does anyone know of any good resources?

[heady ember]

In the case of highschool level combinatorics, perhaps you could try Khan Academy

[hollow shore]

no I am looking for undergrad level material

[safe salmon]

[heady ember]

Oh you said introductory so i thought you meant hs level lol

[karmic thorn]

I've only watched the first couple of lectures, but this is probably at the level you're gunning for:
https://youtube.com/playlist?list=PLhkiT_RYTEU3dNiYxNIICOG6zQUsJuRdt

https://youtube.com/playlist?list=PLFlhMm_qks4It1dvfww0rssfC5w4HIHNc

Here's another

Honestly I'm just using the playlist filter on "combinatorics" on YouTube

Just try doing that

[hollow shore]

thanks Manan <3

[cyan scroll]

I don't know a book in this topic, maybe you can find one here https://link.springer.com/

[safe salmon]

thanks

[novel obsidian]

does anyone have any strong opinions on proof-based lin alg textbooks?

actually dami pin

nvm

[near leaf]

Are there any all-encompassing introductory book recommendations with theoretics rather than just formulas for Pre-University level maths? I want to get back into the subject for personal interest. Or do y'all recommend I pick one particular set like Alegbra or calculus and slowly work my way up?

[surreal phoenix]

You'll kinda have to anyone cause they build onto eachother, and subjects that dive into the details of stuff you've studied before, like how analysis dives into the details of calculus, it's assumed you're familiar to some degree with the elementary level of these topics

If you have some level of familiarity with calculus, you can try analysis

Or you could try something completely new that doesn't depend too much on a typical school curriculum, like abstract algebra, some of whose books are pretty self contained

[next wolf]

Does anyone know any good books for learning statistics rigourously

[loud cradle]

how rigorously? do you already know measure theoretic probability for example?

[next wolf]

not that rigourously - just rigourous enough to explain proofs for statistics results and show how hypothesis tests work, etc, and not just presenting all the theorems and methods and purely applying.

[lime sapphire]

Basic mathematics by Lang helps you build up until just before calc iirc

[warm storm]

any book recs for learning books about advanced analysis

[analog lava]

wdym by advanced analysis

measure theory

?

harmonic analysis

pdes

functional analysis

[tame plaza]

did you use it?

[lime sapphire]

No

I don't think i need to

[glad prairie]

When you say "advanced analysis" based on what you were saying in the other channel I'm guessing you're looking for an introduction to real analysis?

Abbott's Understanding Analysis is really good

There's also the "classic", rudin's Principles of Mathematical Analysis. It's a very difficult, terse book.

And then if you want something more like advanced proof-based calculus, Spivak's Calculus is very good.

You can def find pdfs of all 3 so maybe take a look and see what you'd like

[warm storm]

Ok, thanks!

[halcyon garden]

You can check out "Pugh, Real mathematical Analysis" too. It's a great book with a lot of pictures and lots of exciting problems. It's also a lively book.

But I believe it's a bit more advanced than Abbott.

[timber copper]

All of statistics Larry Wasserman

I like the book

It's also online for free

[grand thistle]

uh

[mystic orbit]

nani kore

[royal bobcat]

A book for complex numbers pls?

[mystic orbit]

there are complex analysis books

[serene reef]

Thoughts/review for Herstein topics in algebra?

[analog lava]

good

[mystic orbit]

but complex numbers don't hold up much on their own

so you won't find a book specifically for complex numbers

[serene reef]

I mostly thinking about it since I want to learn abstract algebra but I am familiar with LA but not the latter LA stuff. Which Herstein covers.

I see thanks.

[hasty forge]

@remote ginkgo yes I'd love to...link please...

[hasty forge]

Is that a book?

[remote ginkgo]

author of a book yes

[hasty forge]

Ok give me an hour and I'll be back

[loud cradle]

It's a well written book, but it covers much less material than say Dummit and Foote. Also, he likes to throw exercises at you at the point where you have the bare minimum machinery to solve them (with difficulty and cleverness) even though they become much easier or even trivial once you have a few more theorems available. His proofs of theorems are that way sometimes too. So I don't think I would want this to be my only exposure to the material. The group theory content is pretty good, but the ring and field theory coverage seems a bit sparse compared with other undergrad books.

[gray jungle]

artin good

[next wolf]

Thank you!

[serene reef]

Thank you, I go for it.

[warm glen]

is learning ab determinants via that formula involving the sign homomorphism the "wrong" way of learning them? i remember someone here saying that axler teaches determinants the wrong way and i noticed that the book im using defines them the same way as axler

and if so, can anyone recommend a book that treats determinants "correctly"

[loud cradle]

imo the best way is to list a set of properties that we want the determinant to have, and then prove that there is exactly one function that has those properties (the one involving the permutations). this is done in a number of books, including Linear Algebra Done Wrong, which is made available for free by the author: https://www.math.brown.edu/streil/papers/LADW/LADW_2017-09-04.pdf

[wooden dock]

Any cheap books that go in depth on a subject?

[hallow oriole]

all books are cheap

[warm glen]

ah alright, i thought the preferred way to learn it would be using multilinear algebra or something but if its fine to learn the usual permutations formula ill see if my book explains it well and lists the properties we want it to have

[fallow cypress]

this is a good way too

[warm glen]

ok good to hear, i was worried ab learning it incorrectly, thanks

[sage python]

So here's the thing about determinants

[hasty eagle]

Sloth King Daminark

[sage python]

Is a formula

The issue is that it comes off as "take a matrix beep boop beep here's a magical number that does our stuff for us yey"

[slim peak]

In my world it is forbidden

Teached to 2nd year student as the unique up(to a multplicative coefficient) n-multilinear alternated form over Endomorphisms of a finite dimensional vector space E

[sage python]

Honestly I kinda prefer that

Just teach multilinear algebra they should learn it anyway

[slim peak]

You don't really need a lecture on multilinear algebra

just say well this is a n-multilinear stuff

this is a alternated multilinear stuff

count stuffs, then dimensions

and here comes the magic

You can skip a huge part of (not so) deep multilinear algebra stuff and still have a proper definition

that gives a perfectly defined, without plot hole, determinant

[warm glen]

yeah i was thinking about that

the usual definition just seems like some number, not a real definition, like it doesn't say what kind of object it is

[sage python]

I mean I just think the answer is do multilinear algebra straight up

LIke it's not thaaaat hard

[warm glen]

idk im pretty dumb

but i'll consider doing it that way

[sage python]

This is how you become smart 😛

[warm glen]

since anatolysis says u don't really need all of multilinear to learn it

im using valenza's linear algebra book to learn the subject

determinants are chapter 8 and im halfway through ch 6

im thinking once i finish 7 on inner product spaces i'll go back to reading artin until ive learned ring theory (im gonna skip the chapters on linear algebra, symmetry groups etc and just go from basic group theory straight to rings)

and then read blyth's module theory cos it looks cool

[sage python]

Idk Valenza

[warm glen]

it does multilinear stuff and determinants

yea i didnt know it either til i saw some random reddit comment about it

he gives the definition of groups and rings and whatnot first before introducing vector spaces so that he can just define them as abelian groups wrt addition that are closed under scalar mult

instead of listing a bunch of axioms

[sage python]

Honestly if you're already doing it then like

Finish it off yeah

[warm glen]

alrighty sounds good to me

[sterile remnant]

What would be a good source for that?

[analog lava]

hoffman kunze does determinant this way

i cant remember much but its the unique bi-linear something something that sends the identity matrix to 1

etf

etc

and is multiplicative

and just goes on to derive it from the properties

[serene reef]

I think friedberg also does it?

In the last section of the determinant chapter.

Let me check.

[grand thistle]

hoffman kunze does multilinear but in the last section of determinant chapter

[analog lava]

yea isnt this the same?