book-recommendations

[shadow river]

if only for the culture

[safe horizon]

yeah I'll just read cantor's stuff since that's the only thing I remember not getting in my discrete math class

[maiden glen]

Something better?

[glad rampart]

its one of the best there is for in depth learning and practicing problem solving

you arent going to find perfect

[maiden glen]

@remote vortex had you suggested something?

[remote sparrow]

the rules of arithmetic are also easier to show with cauchy sequences. however, it is easier to show the reals have the least upper bound property with dedekind cuts.

[shadow river]

I will say I think the cuts construction better captures the key insight, like basically being able to name a "hole" and a "filled hole" in a uniform way, so that just talking about "holes" in general gives you completeness, like I think it's easy to dismiss what a crazy insight that was, or must have been in the 1850s

[cobalt arch]

Do you know of any books that use mutlisets in combinatorics?

[cobalt maple]

Hey, I would like to read the paper "Shapes of polyhedra and triangulations of the sphere" by Thurston, but I don't have the prereqs. I'm currently reading Lee's smooth manifolds and Bredon's Geometry and Topology. I've read chapter 1 of Hatcher and most of Armstrong's topology. I'm also reading Kühnel's Differential Geometry.

Would these be enough to eventually read the paper, or is there something else I should read as well?

Here's the link to the paper: https://arxiv.org/abs/math/9801088

[maiden glen]

what books may i use to expand my familiarity of mathematical notation in fields like algebra (relating to universal algebra and group, ring, set theories) logic, and other notation for elementary algebra?

[maiden glen]

really?

[marsh ingot]

Yes? For elementary algebra

[maiden glen]

by elementary algebra, i mean linear equations and polynomials

not formal and abstract algebra

[marsh ingot]

You mentioned groups, ring and set theory too

[maiden glen]

oh right, i had.

sorry, i have been occupied quite a bit

thank you

are there any other books you may suggest?

[earnest wolf]

but like idk
prob the easiest way would be to learn that along the way, no?

[violet shuttle]

if you already know algebra

it will be easy to learn the notation

thus it seems that you don't already know algebra

and thus you should read an algebra textbook

[earnest wolf]

u see a symbol like

$\therefore$

ask someone what it means and try to use it on ur own

[hasty eagle]

Sweet Tea 🧋🥥🍍🥭

[maiden glen]

Sorry, I should have specified that the notation that I am searching for is uncommon notation

[earnest wolf]

could u mb just show us an example of what u mean?

[maiden glen]

I will.

[earnest wolf]

||but personally i like 'there four' more||

[maiden glen]

notation i.e. $\N_- = (\inf, 0]$

[hasty eagle]

𝓫𝓮𝓬𝓸𝓶𝓲𝓷𝓰
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[maiden glen]

integers with an index minus sign

jd what I was trying to put on the lhs

[earnest wolf]

i meannnnnnn
that depends on the author

some think zero is (not) natural

for example

[maiden glen]

i meant integers

sorry

[earnest wolf]

nah, the point I'm making is that this kind of notation should be stated somewhere in the book since it differs from author to author

[maiden glen]

I see.

[maiden glen]

may you give me such books?

besides dummit and foote, milne Armstrong and rotman?

[maiden glen]

I figure, could you give me some suggestions please?

[maiden glen]

besides those listed herein?

[violet shuttle]

people like dummit andnfoote

[violet shuttle]

lang's algebra

[maiden glen]

i assume your response was instantaneous and without thought given that you didnt read the statement i made after that 'reply' (reply function) i made to you

[maiden glen]

ooh, who else

[violet shuttle]

read me like a book

Artin has a book I think?

#book-recommendations message

[maiden glen]

am i really not worth a infinitesimal portion of your thought ;(

[maiden glen]

oh yes, thank you

[violet shuttle]

what?

[maiden glen]

you'd confirmed that you responded to me instantaneously and therefore without significant thought

[violet shuttle]

and?

what is there to significantly think about

[strange sentinel]

To be fair, Dummit and Foote is kind of an objectively correct recommendation

There's not much thought to put in

[maiden glen]

well evidently to recall your memory about books you may have read or books others within this server could have suggested to you, the review "Daminable group" made, etc.

[maiden glen]

to be fair, i already have and have read the book

[strange sentinel]

The entirety?

[maiden glen]

i never stated that it was objectively incorrect

[violet shuttle]

this is not significant thought

[maiden glen]

frankly, no

maybe i shouldnt have used the word 'read'

[violet shuttle]

i have also only read one book here

[strange sentinel]

What would be more accurate then?

[violet shuttle]

and recommended the other thing i have seen frequently

so

it's like "ahh! you must have put not even an iota of effort by not instantly seeing the other messages and replying to the first one first and by not finding something to significantly think about despite the lack of the usefulness of doing so given the information provided! how dare you!"

[strange sentinel]

My personal algebra recs are:
Pinter for someone just getting into pure math
Fraleigh for someone with not a lot of maturity or that wants something not super hard
Aluffi (Chapter 0 or Notes from the Underground) is probably the most "fun"
Dummit and Foote for comprehensiveness (and it'll probably make you the best at algebra of these)

[strange sentinel]

Can you clarify this btw

[maiden glen]

sorry

[strange sentinel]

You said "have and have read"

What did you mean, if not that

[maiden glen]

skimmed, i save the books so i can have them and then begin studying the topics correctly if you will

not even skimmed

i just read one page

im quite a klutz

thank you!

[strange sentinel]

Ok, so you know nothing about it and are rejecting it out of hand?

Like, the way I put that is kind of rude, but still

[maiden glen]

no, im rejecting it because i already have a digital copy of it

[strange sentinel]

Ok, then go read that

[maiden glen]

so i can read it later on

[maiden glen]

im going to read your other suggestions, and others first

then i will gladly

[strange sentinel]

I'm not sure this approach makes a lot of sense

Doing several at the same time makes some sense but doing multiple intro algebra texts sequentially is not super productive I think

[maiden glen]

i never said i would read them in simultaneous

i meant in a particular order

obscure to you

[strange sentinel]

Also, I would suggest learning elementary algebra before all of this

[violet shuttle]

read [past perfective, specifically an atomic action as opposed to a continuous/repeated/habitual one]

[strange sentinel]

Right, so you are doing the thing I just said is less productive

[violet shuttle]

(as he reads a single page)

[maiden glen]

could you specify what you mean by elementary algebra

[strange sentinel]

...the thing you said that you meant by it

In your words, "linear equations and polynomials" (ie, high school algebra)

[maiden glen]

oh, well im working on it

[maiden glen]

do you know of any books that provide unique methods approaches and notation for elementary algebra

[strange sentinel]

Not much better for high school algebra than AoPS

[maiden glen]

okay. thank you.

[junior isle]

Is papa rudin a good follow up to baby rudin(after chapters 1-7)?

[gray jungle]

no

[gray gazelle]

Hi people do u have any book recommendation that has all type of exercise to solve

[covert mauve]

any good books on hardware and the kernel? (like how the kernel interacts with hardware, controls it, electrical signals, and all that stuff)

[gray gazelle]

Can calc by james stewart be used for self study ?

[rocky patrol]

Hi Math geneous, I am from India and I study in class 11 is that El Erodo book is best for IIT - JEE exams ?

[graceful moon]

I’d say it’s practically designed for self study

[gray gazelle]

okay,thank you

[spiral spear]

Any good book about math?

[graceful moon]

Anything more specific than that?

Like a textbook or just a piece of non fiction about maths? If the latter do you want more of a history type book or something light and entertaining?

What’s your current level?

[spiral spear]

Undergraduate, middle school. Recommend me books about history of math

[gray gazelle]

yea they are pretty good

[smoky zephyr]

[stuck mist]

i wanna practice some problems on hypothesis testing and probabilty in general. So i need some good recs?

[narrow relic]

https://probability4datascience.com/

@slender cargo @late plinth You both have convinced me to try out Axler and see if I like it better than Lang! About to try some of it right now.

What specifically does Axler like the reader to know before starting his book? Gaussian elimination, but what else?

[spiral sky]

I like axler because it actually prepares you for what's after linear algebra

[narrow relic]

I sunk so much time into the Lang book that it's kind of difficult to just start from page one of a new linear algebra book, but maybe it's worth it.

[spiral sky]

I think you only need linear transformations and its implications, and also knowing that a vector space is simply the generalized version of a Cartesian plane

[narrow relic]

Oh okay, great. When I learn this stuff, I like to be able to have a reference for the previous level just for psychological reasons (and also to be able to give good recs to others).

[narrow relic]

Thank you!

[spiral sky]

I had to go back to s axler when I was in an abstract algebra class, I hope you don't go through the same thing, gl!

[narrow relic]

What do you mean?

[spiral sky]

Thanks to this topic for instance https://en.m.wikipedia.org/wiki/Quotient_space_(linear_algebra)

[narrow relic]

But if I read the Axler book, it contains that material.

[spiral sky]

In chapter 3 there is a sub topic called quotients of vector spaces

[narrow relic]

I'm just trying to understand what you mean about going through the same problem you had

I don't understand if reading the book will help me avoid that problem or not.

[spiral sky]

Short answer is yes

[narrow relic]

Thank you for the help and kind wishes!

[lethal bronze]

Is there a random funny yellow book (yeah, that publisher) you can suggest for the summer reading? I want to prepare my math skills before I start my Ph.D.

any field in math (that is not geometry, yeah geometry is nightmare to me) would be fine with me

[spiral sky]

I'm going through the same thing right now, did you mean the S word? Lol

[narrow relic]

@spiral sky by the way, do you have a functional analysis book recommendation? (i.e. an Axler sequel)

[lethal bronze]

Yeah, the one that spam you with either 25% off or 50% off every time you don't want to buy one

[spiral sky]

I have no idea, never learned it all I know is a dead end according to AG

[narrow relic]

AG?

[spiral sky]

I'm not prepared to say his name because I don't know enough to say it, but he worked on functional analysis and moved to alg geometry even though it's not really what he intended

[narrow relic]

Okay! Interesting.

@spiral sky So this Axler book is already annoying me. On page 3 he has what he calls "properties of complex arithmetic." He also says C is an example of a field. But he doesn't ever define what a field is. In contrast to this, Lang defines a field and then says that C is an example of a field.

Oh, I see, he defines it later

[spiral sky]

A field is like a space that's all you should

Know

[narrow relic]

I was wrong, he actually has the definition, he just put it at the end of that section, in a "Digression"

[spiral sky]

I really liked in the beginning of the book he says, 1 page should be covered for at least 2 hrs

[old terrace]

Does anyone have any recommendations for an abstract algebra book? I’m currently a third year in undergrad. I’ve linear, but not real analysis or number theory (I don’t know if that matters)

[round shore]

Allufi

[shadow river]

Probably Dummit and Foote for the most comprehensive undergrad level book, Nicholson is also great for an intro text, Lang if you want to see a much more advanced/difficult text

lol I definitely don't recommend Lang, but it's pretty epic in terms of what it covers and it's difficulty

If you're looking for more of a challenge, Jacobson volumes 1 and 2, or Lang, but for learning either D&F or Nicholson

[strange sentinel]

I think Fraleigh, Aluffi, or D&F

Lang is good but not amazing for a first pass imo

[tender river]

nothing beats Rotman

[remote sparrow]

#book-recommendations message

[jaunty sonnet]

Can someone recommend some good books to learn from algebra 1 to algebra 2 and possibly college algebra or pre calculus

[remote sparrow]

college algebra is the same material taught in algebra 1 and 2, just in college

precalculus has algebra 1 and 2 material plus trig

[jaunty sonnet]

But which books can you recommend?

If you can

For algebra 1 and 2 and for pre calc

[strange sentinel]

Khan academy and AoPS are always good options

[jaunty sonnet]

What is AoPS?

[strange sentinel]

Art of Problem Solving

They have a series of pretty decent books that do Prealgebra, Algebra 1, Geometry, Algebra 2, and Precalculus

[jaunty sonnet]

How about khan academy?

[strange sentinel]

They also have other stuff (they have a good but imo not amazing calculus text and their competition math stuff is kinda the gold standard)

[strange sentinel]

It's not a book admittedly; it's a website that's free and has fairly high quality high school math exposition and a large bank of problems

[jaunty sonnet]

Their free courses are highly rated right?

[strange sentinel]

Yeah they're pretty good

[remote sparrow]

https://precalculus.axler.net/

[jaunty sonnet]

Maybe you have something for algebra 1 or algebra 2

[full saddle]

Hey I have never gotten higher than a C in math in my life. I’m 25 love and the dire importance of math and want to learn. Where should I begin?

[marsh ingot]

Jk, Apostol or Spivak for the first approach to Calculus

[violet shuttle]

but if you do rudin you'll get called based

[strange sentinel]

Maybe try something like Pinter's algebra?

[marsh ingot]

Fr fr

[violet shuttle]

likewise if you used lang for algeb+ra@

you could also try dummit and foote for a more beginner friendly reccommendation

likewise tao's analysis

[strange sentinel]

I think something more gentle might be good in this case

Think, say, Pinter or Fraleigh for algebra

[violet shuttle]

i am unfamiliar with either

[strange sentinel]

Pinter assumes like 0 maturity

It's a very gentle intro that was accessible to me as like a 7th grader, but it does get up to like basic galois stuff

I think it's basically good for someone that hasn't done pure math before

[violet shuttle]

sounds great!

[full saddle]

Ok

Thank you

[vocal schooner]

omg i was about to talk about how good pinters algebra is

compared to all the other abstract algebra books ive tried to read his explanations are so clear and easy to understand

especially for idiots like me

i might even reach the second chapter (uncharted territory)

[rigid forge]

what should be done after spivak to get into real analysis? baby rudin or is that too terse?

[dim sierra]

I like Abbott

[jolly compass]

Any good exercise books for calc 2 and maybe 3?

[marble solar]

I think Thomas' University Calculus is just fine

[jolly compass]

Thanks I’ll have a look at it

[willow merlin]

I need anal book, I am reading demidovich for exercises and piskunov for theory

however demidovich has very little theory

and piskunov is more on the engineering side of things

I want theory book, that explains stuff like subsequences and ratio test and root test (Cauchy's and D'Alemberts criterions I believe they are called or something)

any references that comes to mind?

please let me know

[slender cargo]

Baby Rudin would be completely approachable after Spivak. If it were me though I would go for some more advanced book (if I were self studying), or I would learn topology or algebra instead. Spivak covers a lot of what Rudin goes over.

[willow merlin]

help

Demidovich is good for exercises but has almost no theory and explanaitons are little

which book introduces Cauchy's criterion nicely

[rigid forge]

I will admit, i am not very familiar with topology and algebra. i only know them at a surface level.

which book do you recommend for both topics?

[slender cargo]

Munkres Topology is standard for topology. For algebra there is a ton of choices. If I were self studying... I'm not sure of what would be a good recommendation. I would google around to get a view of what there is.

Something to consider also is going through Linear Algebra first, if you have not already yet.

[rigid forge]

thanks

[willow merlin]

which reference explains wtf is a cauchy sequence can I ask

[dim sierra]

I’d like to toot in here and say that I highly recommend Tom Leinster’s notes for basic topology. You can find them here: https://www.maths.ed.ac.uk/~tl/topology/topology_notes.pdf. I think he has some exercises on his website as well.

I’ve found these notes to be more clear than Munkres, at least for a first read.

[slender cargo]

Any introductory Real Analysis book

i.e. Abbott, Ross, Rudin, or Bartle

[strange sentinel]

Take a look at Fraleigh, Aluffi, and Dummit&Foote

[tribal crow]

why not Lang too

[strange sentinel]

And like TopDreg said, Munkres is good for topology

[strange sentinel]

Lang as a first pass of algebra is questionable imo

[tribal crow]

I was joking, but I think there are some users here who would say otherwise

(looking at Xela)

[strange sentinel]

There are, and I disagree with them

[tribal crow]

some people don't like Munkres, but I don't know of any other topology book to recommend besides Lee's ITM lol

[modern ruin]

just read munkres lol

[tribal crow]

too late

[modern ruin]

Tu's ITM is not a general topology book

it's about manifolds

[tribal crow]

hm?

[strange sentinel]

Lee's

[modern ruin]

Lee's is not either

[tribal crow]

ITM does general topology for the first 4 chapters

[modern ruin]

it's about...

manifolds

hm

[strange sentinel]

Yeah

[tribal crow]

this is not his smooth manifolds book

[strange sentinel]

best general topo rec is bredon chapter 1

[modern ruin]

GOOD REC

i love bredon

[strange sentinel]

Bredon is very good yeah

[modern ruin]

such a good writer

[tribal crow]

I have Bredon downloaded...

never read it though

[strange sentinel]

I suggest it!

[tribal crow]

someone told me it was good

[strange sentinel]

After like ITM chapter 6 probably

Or you could just do it now idk

[modern ruin]

you don't have to really wait to read bredon at all

[strange sentinel]

Yeah but he's in an ITM reading group

[fierce hedge]

Do not forget SergeLangFan

[tribal crow]

mhm

I forgot about them

Salagos as well

[violet shuttle]

hi

[violet shuttle]

it's fine as long as you are mathematically mature enough

[willow merlin]

thank you sir

will give them a look

[fresh skiff]

Serge Lang's books are quite fast.

[torn blade]

Best way to learn group, ring and module theory? Can be one book or multiple books. Something with lots of examples and motivation for stuff, and a lot of exercises so i can try some more difficult problems

all i know is introductory group theory stuff like the axioms, homomorphisms, order, subgroup, quotient group etc and some stuff with rings and fields but not much else :^) i wanna learn from the start again

[torn blade]

is Artin good to this end? i was looking at the pinned and it sounds right for me. Also has some lin alg which i might be interested in later on. Although the lin alg part seems to have mixed reception

[strange sentinel]

Sure and almost anybody doing a first path through algebra isn't!

[strange sentinel]

I think D&F or Lang would probably be the answers here

Since you have nonexistant background I think you can probably handle either

[torn blade]

ah, what do other books assume that these dont?

[strange sentinel]

I more meant maturity as opposed to prerequisites

[torn blade]

ic ic

[strange sentinel]

Specifically with regards to Lang, it's a fast book

Which is why I personally think it's not great for a first every algebra experience, but you'd probably be fine

[fierce hedge]

Rotman (advanced modern algebra) or DnF, both are very comparable. Try both and see what suits you better. There's also Aluffi if you wanna go down the category theory route.

[mystic orbit]

it is

it's more topology than manifolds honestly

it's like

topology with a slight emphasis on manifolds

[remote sparrow]

dummit and foote, aluffi's Algebra: Notes from the Underground, rotman's Advanced Modern Algebra

[round shore]

I've never seen DF recommended outside this server and I don't understand. It doesn't look very good

(personal opinion blabla)

[strange sentinel]

Does notes from the underground do modules

[round shore]

I don't think so

[deep epoch]

yes

[round shore]

Oh mb I thought it was only done in chapter 0

[deep epoch]

it does structure of modules over euclidean domains rather than over pid though

which is arguably fine as an intro-level undergrad book

[remote sparrow]

yes

notably it has a rings-first approach

the order of topics is rings > modules > groups > fields

[torn blade]

category theory is something that interests me yeah. but i am still a beginner as far as algebra goes, is Aluffi hard?

[strange sentinel]

Yeah I think this is fine

[strange sentinel]

Given it’s one of the most common algebra texts this surprises me

[remote sparrow]

there are two algebra books written by aluffi

[remote sparrow]

i guess you don't use reddit?

or math stackexchange

but the thing is, most introductory texts don't introduce modules; dummit and foote does

[strange sentinel]

I’ve had multiple profs IRL recommend it to me and my first alg course used it

[round shore]

I don't. But I realised that's maybe because in general I see people recommending more advanced books (and it's often Chapter 0, Matsumura or Eisenbud-Harris)

[torn blade]

oh, which one do u think they were referring to

[remote sparrow]

i don't normally recommend dummit and foote, but the individual already has some experience with group theory and they did ask for modules

[remote sparrow]

Algebra: Chapter 0 since they mentioned an explicitly category-theoretic approach

[torn blade]

ok

this is half for fun half for uni prep so idk how much category theory im gonna be doing

plus Artin’s has lin alg which is a course i’ll inevitably need to take

[remote sparrow]

you can read a standalone linear algebra book if you like

[slender cargo]

It gets used all the time at American universities

Also I'll just say that going rings first is a weird thing to me now, after having done groups first

[torn blade]

so category theory is introduced before groups, that’s interesting

whats the advantage of this

[fierce hedge]

It's not introduced before, category theory is the approach that is used. Basically it is used to generalise algebraic properties common to rings, groups etc. Homomorphisms on algebraic structures are generalised to morphisms over categories etc.

[torn blade]

ok cool cool

[fierce hedge]

Rings first has the advantage to being introduced as number systems. In a vague sense commutative rings with unity behave kinda like integers and is used to motivate them. Since they have more structure that groups, it's generally slightly earlier to digest for a beginner.

[slender cargo]

I can see that argument. I feel like I appreciated groups having fewer conditions though. And being able to go to rings and then say "rings are sets with an underlying additive group and some multiplicative structure" was nice.

Granted, I think I could use more exposure to rings... I'm still not entirely comfortable with them.

[fierce hedge]

Honestly same, I have a set of groups that I usually use to test group theory stuff with but nothing like that for rings

[tawny copper]

Does anyone know a way to view pdfs in google with some dark mode?

[agile blade]

Hello everyone! I'm about to enter a scientific preparatory school (one of the best in France). I understand what I'm taught in high school quickly, I don't have any difficulties, but I don't really know if I'm gifted, the problems of high school have never really challenged me and I confess, I haven't had the will until now to really go further. Could you recommend a book or resource that would help me get the hang of maths and see things more clearly? I'd really like to make progress in problem solving before the pre-prep, so this would be ideal. Thank you for your help and have a nice evening!

[marsh ingot]

For Chrome?

[past depot]

I have got a script, you put it in console and it inverts the colors.
var cover = document.createElement("div");
let css = position: fixed; pointer-events: none; top: 0; left: 0; width: 100vw; height: 100vh; background-color: white; mix-blend-mode: difference; z-index: 1;
cover.setAttribute("style", css);
document.body.appendChild(cover);

[marsh ingot]

From default page there is an option to change into a dark mode

I already have dark mode on it

[tawny copper]

can you elaborate? I don't understand what you mean

[tawny copper]

yes

[tawny copper]

idk why it's not working for me, but you have to do that everytime right?

[marsh ingot]

When you open chrome the part where says "Personalizar Chrome"

[past depot]

yeah, i couldnt make it work in a tampermonkey script

[tawny copper]

dark reader extension does something to pdfs but the outcome is not the best. It will look like this

but the backround is still bright, and also this dark mode where the background is just full black and the letters are full white is not the best imo. The letters shouldn't be full white, they should be grayish

[past depot]

that what the script i sent does

i just zoom in all the way to the content itself

[tawny copper]

yeah I did use some similar script some time ago, but it's just pretty annoying to do it everytime

I find sumatra's dark mode perfect for reading, it looks like this

[marsh ingot]

Oh you meant that

[tawny copper]

it would be ideal if I could have something like that for google. I mean it's not the biggest of problems, just asking in case anyone knows a way

[past depot]

hablas español?

[tawny copper]

sí

[past depot]

eres de españa? o de latinoamerica

[tawny copper]

de España

[trim kayak]

I have so many math books, textbooks and pdfs that I want to read. I don't know where to start!! 😟

[tribal crow]

isn't that all of us

[fluid skiff]

What are your interests

[trim kayak]

Algebra, geometry, trig, stats, and general teaching books

[fluid skiff]

Oh cool. You can start with some group theory books.

[trim kayak]

I have some of my own books and received several recommendations from people here too. Now I have so many to read through. Start with group theory before anything else?

[gray gazelle]

Have you done any proof writing before?

[trim kayak]

No

[gray gazelle]

Start with some elementary number theory or combinatorics then

Assuming you’re already familiar with basic algebra/calculus

[trim kayak]

Yeah I am. Start with elementary number theory before reading anything that I have?

[tawny copper]

imo just start with whatever you want. I would also recommend that you try sticking with a single book for a while, not that you can't read other books, but have one as your main objective

[trim kayak]

I thought about that too. One book will take me awhile to get through. Should I take some notes as I go even if its just for my own learning for fun?

[gray jungle]

I'd recommend your own section summaries instead

[gray gazelle]

I’d recommend, as you go through the book, when you reach a theorem statement, write it down and try to prove it before looking at the book’s proof

Then, once you’ve had an attempt at it, compare with the book’s proof, and correct any logical errors

Rewrite the proof in its final form, and keep an organized notebook full of these

[trim kayak]

Ahh okay. Books like Algebra and Trig don't have proofs...

[trim kayak]

Just a short summary?

[gray jungle]

yep, just summarize ideas and proofs you understood

thats what i did with my very first book

hoffman kunze

and how i started learning latex

lol

[trim kayak]

Ahh okay. I'll try that. Thanks

[strange sentinel]

For real

[strange sentinel]

Taking notes is good because 1) it helps you make sure you understand the material and 2) you have a good reference

[trim kayak]

Ahh okay

[gray gazelle]

any recommendation for calculus 3 or above?

book

I need a book that includes proofs

[remote sparrow]

hubbard and hubbard or shifrin

[gray gazelle]

Thanks

[slender cargo]

Oh I'm just seeing this. Awesome! What convinced you though? Also, it's nice to know someone else is working on Axler's LADR at the same time!

[spiral sky]

Can someone please recommend a book about galois theory with a view towards class field theory, I know some ring/field theory, I'm also interested in galois actions

[slender cargo]

Also yes, the only thing he expects a person to know is Gaussian elimination. He seems to go over everything else.

I'm just starting Ch. 3 now! So, linear transformations.

[willow merlin]

book that explains inverse function theorem in a easy way?

[violet shuttle]

an...entire book?

[willow merlin]

sure

[violet shuttle]

okay my point is that you could find it in any relevant book but you aren't going to get a whole book devoted to it

i think spivak's calculus on manifolds has it

you just need the contraction mapping principle and some algebra bash

[willow merlin]

got it

thanks, but I wanted to ask

if you would have to choose one book for analysis that it isnt too complicated to follow? what would it be

[vestal osprey]

Would anybody have any good books on interior algebras and generalized topology?

[spiral sky]

Analysis I, II and III by Herbert amann has been in my wishlist for a long time, cmdoes anyone have any references about these books?

[sick sonnet]

hi, everyone. im new to math (started about a week ago). i went through all the basic concepts related to arithmetic, numbers, a bit of geometry, pre algebra. now starting with algebra. i have a number of textbooks (algebra, trig, geometry, precalc) stored on my hard drive, but im a bit unsure about which one to use. and i know that i should just pick one and go with it, but im curious to hear your recommendations or resources you personally used and why. im looking for material that delves deeper into the why behind the concepts. thx.

[lethal bronze]

actually, I would suggest you against using the same textbook over and over. Yes, it is definitely good to complete one at a time. However, different textbooks have different kind of explanations to the same concept and can provide you with the well-rounded picture that can reinforce your foundation better.

I can't suggest much of the book here as I don't really re-read the high-school-level books. For the precalculus, my personal experience would be Ron Larson's book. That is also biased, as this was used during high school. However, I find that it is readable, and the problems are interesting.

[sick sonnet]

i thought about doing that. mb that's how i should go about it and not overthink things. skimming through various resources at the same time and solving lots of problems i find interesting.

[sick sonnet]

kay, thx, will check it out

[lethal bronze]

another good book that I heard a lot of good things (and some bad things) about it is Stewart one.

Like, educators generally love it but students generally hate it.

[sick sonnet]

i have James Stewart books (algebra and trig, precalc). so far i've heard only good things about them.

[lethal bronze]

Yeah, people have a mixed opinion about it. Some said it is more suitable for pre-calc in college. some said it is suitable for high school. some said the explanation is too long. and this goes on

And if you decide to dedicate yourself to one book, that is okay too. Sometimes, if you like the vibe of the author, go with it. One of my friends love Lang's book and they stick with it while I found myself unable to solve even the first exercise in Lang's book without referring back to the materials.

[slender cargo]

Lang Basic Mathematics is recommended here frequently for people who care more about "why" behind pre-calculus concepts (which includes artihmetic, geometry, etc). To get to the actual "why" though, you need to just get through those subjects and start learning more advanced material.

[sick sonnet]

that's a familiar name, Serge Lang, oh, he's the author of the Basic Mathematics book, that's where i first heard about him

[lethal bronze]

Yep. His algebra books, however, is a "fun" read.

(as someone who is more a stat person would said)

[sick sonnet]

i skimmed through the Basic Mathematics book long time ago when i first thought about learning math for fun, but i found it to be either a bit too advanced or not my vibe, don't remember (btw, im not a native speaker, so sry if i make any mistakes)

[sick sonnet]

noted

[lethal bronze]

well, this algebra is not the same kind of algebra you might think tho. This is more of the abstract algebra. The graduate level book one

[sick sonnet]

i see, that's what im probably going to do

[slender cargo]

imo you should just try to get through those subjects as fast as possible. The goal right now is to gain intuition, and not to prove everything rigorously.

[sick sonnet]

for later then

[slender cargo]

You can start to learn the "why" as early as calculus if you want. Spivak's Calculus is a good book for that.

[sick sonnet]

makes sense, thx for the advice

[lethal bronze]

Yeah, that book is later later. Like, I would say master's degree later lol.

[willow merlin]

which book goes hard into sequences

[slender cargo]

Any (introductory) Real Analysis book?

Abbott, Tao, Rudin, Ross, Bartle to name a few.

[willow merlin]

subsequences too, recurrent sequences

?

[slender cargo]

Yes all those

[tiny epoch]

I'm looking for a book to introduce Galois Theory, any sugestion?

Idk what this emoticon means c:

I'm trying to understand what a Galois representation is without understanding Galois Theory and what a formally is a representation lol

(btw, I'm learning English so sorry by my childish grammar mistakes )

[round shore]

I'm afraid this is impossible, and if it is, you shouldn't do that

What even is your motivation to learn about Galois representations ?

[narrow relic]

Nothing really convinced me except that Axler might be worth a try and the fact that you and a couple of other people are currently working on it. I decided it wasn't good for my needs though. I can elaborate more on what I'm doing now if you would like me to.

[narrow relic]

Thanks 🙂

[willow merlin]

does someone have a review for courant

Introduction to Calculus and Analysis, Vol. 2 (Classics in Mathematics) John Fritz, Richard Courant

nah im not buying that book

[stuck zephyr]

search it up

or else buy it

[willow merlin]

I was about to buy it used

but saw a youtube video of a review and I ddidnt like it

[trail hemlock]

there is prob a better modern alterantive tbh

by the looks if it, doesnt seem TOO bad

hey theres some nice pictures in here too

[maiden halo]

I got Courant & John volume 1 when it was on sale... I'll review it when I get through it 😅

[narrow relic]

Glad you liked it, it was the book from which I learned a lot of the single variable stuff.

[slate chasm]

Hi all 🫡, For those interested in quantum chemistry and how to get started: Well, chemistry is intimately mathematical and is built upon functional analysis, probability, linear algebra, Fourier analysis, group theory, distribution theory, Green's functions, combinatorics, complex analysis, asymptotic analysis, differential equations, and integral equations. This cannot be done without mathematics. There are also solutions to the Schrödinger equation for molecules and atoms and the treatment of chemistry with quantum effects in general. Normally, you need to know basic physics, basic chemistry, formal quantum mechanics, linear algebra, Fourier analysis, functional analysis, combinatorics, probability, calculus, among other things. You would then focus on polyelectronic wave functions, hydrogen-like bases, STO, GTO, Gegenbauer, etc., and aim at different basic theorems such as the variational or the general Aufbau theorem. Next, basic Hartree-Fock, Density Functional Theory, Moller-Plesset, etc.

Some recommended books:

Quantum Chemistry

• Basic introductions to chemistry and quantum theory
• Szabo, Modern Quantum Chemistry
• R. Weeny, Methods of Molecular Quantum Mechanics
• Coulson, Valence
• Springborg, Methods of Electronic Structure
• Martin, Electronic Structure
• Mayer, Simple Proofs in Quantum Chemistry
• Linderberg, Propagators in Quantum Chemistry
• Weitao and Parr, Density Functional Theory
• Helgaeker, Quantum Chemistry
• R. Daudel, Quantum Theory of Chemical Bonding
• Minkin, Quantum Chemistry of Organic Compounds
• Quantum Chemistry, Ira N. Levine
• Elementary Quantum Chemistry, Frank L. Pillar

Well, I can make an immense list of books and applications: quantum mechanics, quantum condensed matter physics, open quantum systems and quantum chaos, quantum statistical mechanics, quantum field theory, quantum phase transitions, quantum many-body theory, quantum Monte Carlo, thermal quantum field theory, string theory.

[candid creek]

Does anyone have any linear algebra textbook recommendations that tells you how to compute the JNF/jordan normal/canonical form of a matrix?

All of the textbooks that I have for reference are too abstract,..., and don't include this

i.e., sheldon axler LADR

[tribal crow]

my course notes

[spiral sky]

I think algebraic geometry and commutative algebra by sigfried bosch has been a greater exp than Galliani or Herstein, will this be enough background before going to eisenbud's book?

[tribal crow]

@candid creek if you would like, I can DM you the course notes that my professor made

they include notes on how to compute the JCF

[candid creek]

That would be amazing if you could!

[tribal crow]

done.

[stiff tulip]

Anyone know a book about measure theory written in a style similar to zorich's analysis I and II

[remote sparrow]

what aspect of zorich would you want the book to also have?

that it generally writes things out in detail?

maybe look at Real Analysis: Theory of Measure and Integration by james yeh

it has a full solutions manual too

[stiff tulip]

Incredibly comprehensive with thorough intuition building

He also has very good style

[stiff tulip]

I'll check this out

Just feels "solid"

[remote sparrow]

i heard bogachev is very comprehensive too

https://www.amazon.com/Measure-Theory-Set-Vladimir-Bogachev/dp/3540345132

[cobalt arch]

There is also Fremlin

[remote sparrow]

https://www.amazon.com/Real-Functional-Analysis-Moscow-Lectures/dp/3030382184/ref=pd_sbs_d_sccl_2_1/135-8592441-9602648

[stiff tulip]

They were colleagues I think

[remote sparrow]

not sure if this suits your needs, but this is a newer book by bogachev

[stiff tulip]

Well I am also looking to study functional analysis this summer, so that is surprisingly helpful

[remote sparrow]

most measure theory books include elementary material in functional analysis

you can check out conway for functional analysis too

[cobalt arch]

Fremlin is the most comprehensive but it is 5 volumes long. The first volume is the absolute minimum

[stiff tulip]

I wonder what text they use at my uni

[remote sparrow]

folland is a standard text

[stiff tulip]

yeah

[marble solar]

Schaum's outline to Linear Algebra

[remote sparrow]

Differential Equations and Linear Algebra by goode and annin

also friedberg, insel, and spence

[cunning elk]

goode/annin was dreadful to work through 😭 and the lower div linalg class i took just stopped at diagonalization, didn't even go over jordan canonical forms or gram-schmidt

[remote sparrow]

i don't like it much either but it is organized well

[cunning elk]

ig yea

[candid creek]

THE DIFFERENTIAL EQUATIONS ONE IS PERFECT

THANKS

[willow merlin]

is mardsen tromba any decent for vector calc?

is there any review for this that I am not seeing?

[shut matrix]

Hey guys, what are the best books for maths foundations?

I know basic maths, basic alegbra and geometry and some trigonometry stuff

Edit: I also know pre uni maths, like factorization, basic coordinate geometry, quadratic equations

I want to work on these so I can master basics and move on to higher level maths.

I'm a premed student, but I want to learn maths as a hobby, since my syllabus has a lot of physics.

[willow merlin]

did you checked out Higher mathematics: Textbook for Technical Schools by suvorov

[shut matrix]

Not yet, I'll check it out rn

[willow merlin]

I bought it physically last week, looks lowkey like what you might be looking, either that, or Handbook of elementary physics by koshkin

also by mir

[shut matrix]

Does it include practice questions?

do u know which book would be best for practice questions for my level?

[willow merlin]

higher math has exercises and solved examples

has some solutions but not solutions to everything though

[shut matrix]

That's fine

Tysm

[willow merlin]

I would like to hear other opinions aswell, if someone else can recommend something

[shut matrix]

at the moment, I don't have any maths textbooks, but I was thinking of buying the NCERT Class 12 Maths (Part I and II)

[stiff tulip]

Does anyone have recommendations on books to prepare for the Putnam

[stuck mist]

i wanna practice some problems on probabilty in general. So i need some good recs?

[gray jungle]

what level of probability are we talking?

[stuck mist]

im an undergrad student, so required recs according to it.

[glossy zealot]

The classic is one by Ross

There is a good free one from a professor in Havard

The one by Blitzstein

Another common one is byAnderson

[lethal bronze]

There is also another one from Rick Durrett, I think it is called Elementary probability

[strange sentinel]

Lang’s Basic Maths

[fallow cypress]

Hey! Can anyone recommend a statistics book for people who are comfortable with measure theory/probability but don't know much about statistics?

[blazing vine]

ik I am reposting this, but in a better place for this ques mp
I need some resources on discussions on equilibrium in game theory (currently working in rl and I need to check the convergence of an equilibrium, the model is similar to a very generalised tit for tat)

[willow saffron]

sup yall, I was wondering if anyone has a book recommendation regarding elementary linear algebra with explained applications in computer science?

[gray jungle]

the goat gilbert strange has a lovely book and course on MIT ocw, not sure how far the applications go

emphasis on strange @vital bane

[glossy zealot]

I guess you can use Casella Berger if you are at grad level of mathematical maturity

It is a standard grad text for statistics

[fallow cypress]

👀 Cool thank you

[glossy zealot]

Iirc it has both probability and inference, if you want a harder text for mathematical statistics only, you can search the book by Bickel

Also well known I think

[willow saffron]

ohh ofc gilbert lol, thanks! Ig imma just have to search up the applications separately

[fallow cypress]

which book by bickel?

[glossy zealot]

Mathematical statistics: basic ideas and selected topic volume 1

By Peter J Bickel and Kjell A Doksum

[fallow cypress]

ty :)

[glossy zealot]

Np

[remote sparrow]

it does not use measure theory

[remote sparrow]

Mathematical Statistics by jun shao, Theoretical Statistics by robert keener, and Theory of Statistics by mark schervish are standard references

shao has a solutions manual

[fallow cypress]

oooh thank you!

this is very helpful

[remote sparrow]

bickel and doksum also does not use measure theory

[fallow cypress]

kk, I'll probably still briefly look through them then

[gray gazelle]

Any good books for solid mensuration?

[hearty aspen]

how to start learning elliptic curves

[willow merlin]

whoevers recommendings tao for intro to anal is high

[hearty aspen]

really?

why

i thought it was good

[willow merlin]

5th page has double integrals wtf

maybe its good but not intro

[tribal crow]

it's definitely an intro

also, that double integral stuff is just an example used for motivation on why analysis is worth studying

it's not "real" content, so to speak

[willow merlin]

Ill keep reading then, ty!

i was about to give up

[tribal crow]

chapter 2 is where Tao actually starts 👍

[gray gazelle]

Hey I need book recommendations for Combinatrics Olympiad level

http://rads.stackoverflow.com/amzn/click/0817642889
Does anyone have a online pdf to this book?

<@&286206848099549185>

this server is not piracy help

jesus christ

$60

how tf

ok

i can help you pirate

one second

Exactly why :([Also the fact that shipping cost increases it]

it's on the archive\

https://archive.org/details/pathtocombinator0000andr/page/n9/mode/2up

you need an account

Yeap Done, thanks 🙂 [I shall give the author the money he is owed once I have my own source of income xD]

lol

[gray gazelle]

Trigonometry essentials practice workbook by Chris McMullen is $13 on amazon and great to get better at trig. I saw math sorcerer recommend it first

[gray gazelle]

number theroy by hardy

[fossil locust]

what do you think about galois theory from joseph rotman? is it good? https://link.springer.com/book/10.1007/978-1-4612-0617-0

[gray gazelle]

Which book should I pick to understand linear algebra in deep
As in matrices in my class started but i am struggling in it... Reason is because I can't do math untill unless it makes sense to me

So to get answers like ** "what are matrices? What's geometric representing of it? Why it is the way it is? What actually is determinant?" **
Which book should I prefer

[gray gazelle]

My recommendation would be to study linear from the coordinate-free perspective

Matrices are just representations of linear transformations, after all

Halmos would be good for this

[slender cargo]

There's several choices. Halmos being one as indicated. A pinned post has several books to showcase. I would say you should just go to your professor's office hours and ask your questions, and follow the class book. But if you really want another book that is heavy on theory, Friedberg Insel Spence is widely used. Axler's Linear Algebra Done Right is also very popular (maybe the most popular?). I'm currently going through Axler's book right now.

[stuck pike]

I know this is the book recommendations but on YouTube you have some amazing visualizations about lineaire algebra on the 3blue1brown channel just go to playlists and lineair algebra

[remote sparrow]

#book-recommendations message

[gray gazelle]

Sure, I have just started it

[gray gazelle]

No use of following class textbook because....Umm well... since I am preparing for a competitive exam, here the popular notion is to use formula and just solve it
Even I can do the same, but because I don't know the reason behind doing it, this constantly keeps on going behind my head, thus affecting my studies.

And yeah, I'll definitely go through the books mentioned by u, just a confirmations I need, I think I went through linear algebra done right's index and most chapters were vector spaces and vector field etc
So is matrices there in that book Or not?

[gray gazelle]

Sure! I went through, but since it starts with linear transformations, I need to learn that ig
I only know simple operations like adjoin, add, subtract, multiply, determinant, transpose , etc

[gray gazelle]

Thanks😅

[gray gazelle]

Every vector space is isomorphic (essentially equivalent to) some coordinate space (think R^n)

When you choose a representation of a vector space, you also get a representation of the linear transformations on that space

In that representation, linear transformations correspond to matrices

But vector spaces are needed to have an environment that linear transformations can act on

[gray gazelle]

Vector has only 3 components right, i j k
So it would make sense for 3×3 matrix
What about 9×9 or any such?

In other words, understanding matrices essentially amounts to understanding vector spaces and the structure-preserving functions on them

[slender cargo]

Yes. Ch. 3 covers matrices, although that book does not cover Gaussian elimination. I'm not sure what competitive math in this context entails though. Axler's book (and the other recommendations) are more for preparing someone to pursue a PhD.

[gray gazelle]

A vector can have any number of components

Actually, vectors only really have components in coordinate spaces like R^n

The set of all polynomials with complex coefficients is a vector space as well

As is the set of all continuous functions on the interval [0,1]

[gray gazelle]

Example

[foggy quest]

The best I've read is https://mtaylor.web.unc.edu/notes/linear-algebra-notes/. It's very solid.

[gray gazelle]

9x9 matrices correspond to transformations between 9-dimensional spaces

[gray gazelle]

The set R^9 of all tuples with 9 component

[gray gazelle]

Thanks!
Competitive math is nothing but learning math and just solving tricky questions
It doesn't really emphasize on understanding it..

And word competitive is there because many students compete for a good college and in these exams marks don't matter
Because seats are limited so here seats are given according to rank

Hell, you can even think about the space $\mathbb{R}^{\infty}$ of all infinite sequences of real numbers, which are essentially vectors with an infinite number of components

[hasty eagle]

eigenpuppet

[gray gazelle]

Oh, some high level math I suppose 😅
I don't know much about it

[gray gazelle]

You’ll learn about it quickly if you study linear algebra

[slender cargo]

Is your class simply computations? No proofs?

[gray gazelle]

Sadly, yeah

The nice thing about linear algebra is that it’s basically the same no matter what (finite) dimensional space you’re in

[gray gazelle]

Thanks a lot man!
Will definitely check out

[slender cargo]

Ah okay. Personally I'd talk to your professor about how you want to learn more. I imagine they would be happy to hear that.

[gray gazelle]

we have discovered 3 dimensions only.. Isn't it?

[gray gazelle]

we live in 3 dimensions

but objects of interests may be in many more (or infinite) dimensions

for example, 3rd degree polynomials live in a 4 dimensional space

[gray gazelle]

They will be but answer would be
"That's good but useless, you just want answer"

The graph of a function from the complex numbers to themselves lives in 4 (real) dimensions as well

[gray gazelle]

damn!
As in x^3 +x ^2... Like this?

[gray gazelle]

yeah, polynomials of the form ax^3 + bx^2 + cx + d

[trim kayak]

I have several math textbooks and pdfs as well as various teaching books that I want to read through. I plan to take notes on the math ones just for learning for fun. I know it depends on the content and how much time I need to learn it, but how much time should be spent on one book? Should I learn one and then move to another or alternate between two books at once so I can get through them faster? I need suggestions. Help!!!

[slender cargo]

I think it's important to know what your goal is for these books, and what kind of (math) books they are (proof heavy, higher or lower level math)?

[trim kayak]

Just to learn and study the math for fun. Algebra II, Geometry, Trig, Stats

[slender cargo]

Just go at your own pace then. The process should be fun! You don't need a lot of books for those subjects. For example, one book that is often recommended here, Lang's Basic Mathematics, would be more than sufficient for Algebra II, Geometry, and Trig, and it would give an ordering to the topics so you don't have to decide on what the proper order is. At least in the U.S. though, people usually go Geometry -> Algebra II -> Trig, if you were using a separate book for each.

Just do a number of problems until you feel comfortable with each concept. And I would stick to just working on one topic until you feel ready to move on to the next. No need to flip around.

Statistics is its own thing so I can't say much there.

[trim kayak]

Thanks!! 🤓

[thick kelp]

Are there any book recommendations for Probability? I will be taking AP Prob & Stats in 2 years so I want to get used to the material.

[fierce hedge]

Every *finite dimensional vector space is isomorphic to Rn

This is not true for infinite dimensional spaces

[gray gazelle]

Yes

Was writing on my phone, forgot to note that

[sturdy shore]

(finite dimensional real vector space)

[fierce hedge]

Any counterexample for non real FDVS?

[tribal crow]

to be isomorphic to R^n, a vector space need not be real, just finite dimensional (with dimension n), no?

[formal bronze]

F^n for some field F that isn't ℝ

[tribal crow]

ah, that is true

[tender river]

finite fields

[formal bronze]

Or even ℚ

[tribal crow]

another reason why F^n is better than R^n

[sturdy shore]

no

[tribal crow]

yes, I saw my error

I now agree with you

[fierce hedge]

This should still work with C as C^n is isomorphic to R^{2n}

In fact the only issue is that the FDVS should be defined over the same field

[formal bronze]

Consider a finite field

No vector space over it will be isomorphic to ℝ^n for any n

[fierce hedge]

I mean yeah it works for any finite field

Probably if and only if

[formal bronze]

Consider ℚ^n

ℚ isn't a finite field

[fierce hedge]

Fair enough

[balmy crown]

Has anyone here read The Way of Analysis by Robert Strichartzs?

[fresh skiff]

@glossy zealot

My friend dalliance is currently studying analysis from this text book.

[glossy zealot]

I half hate half like it

Very wordy

[balmy crown]

Ya, Im not a fan of the text font of the book

you didnt take the class at JHU by any chance?

[glossy zealot]

Oh you are talking about real analysis 1? I did take it in spring

Gonna take the second course in Fall

[brazen tapir]

Opinions on "the art and craft of problem solving" by Paul Zeitz? Is it worth a read?

[balmy crown]

Howd you like the class overall?

Im taking the first this upcoming fall

[glossy zealot]

I think it was beginner friendly, being slow at the first few weeks then picked up the paced after first mid term

I don’t think you would have any problem taking the course

Just make sure that you complete your coursework and review regularly

[soft ivy]

can anyone suggest me best book for linear algerba for super begginers please

[gray gazelle]

you want a PDF or?

[soft ivy]

no i can buy it

[gray gazelle]

one sec so

[formal bronze]

Hoffman and Kunze

[soft ivy]

salam valekum brother

[gray gazelle]

wallekum al salam

[gray gazelle]

https://www.youtube.com/watch?v=_EZ4Dg-kr3k
I didn't buy these books but this guy is good and I assume lots of people know it here

https://www.youtube.com/watch?v=nH3ArpZt0Uw&t=148s

[soft ivy]

i saw his video

thanks

[gray gazelle]

https://www.youtube.com/watch?v=T-n3D-JRSKA

[gray gazelle]

you're welcome

[broken drift]

hi can anyone give me some free article that contains derivative and physics related for my scientific work

i need some article for my highschool scientific work

like online article

[void pelican]

https://www.nist.gov/ https://physicsworld.com/

[naive cove]

Are there good books for pre algebra with many exercises to work on a solid foundation?

[vital bane]

[foggy quest]

There are a lot of physics examples here: https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2020/10/diffeq.pdf

it's a math book primarly, though

[plucky plume]

Does anyone know a free book that covers Engineering Maths - I?

[tribal crow]

you’ll have to clarify what you mean by “Engineering Maths I”

[plucky plume]

I guess that refers to basic maths used in engineering, hence the I

[graceful moon]

This is possibly the least helpful answer you couldve possibly given

Could you share the syllabus for the class

[plucky plume]

okay...

I can't post pictures

Shall I DM it

[wild grail]

basic

at what level

for what type of engineering

lots of ODEs in my lower-div structures and circuit analysis classes

some PDE stuff when I took materials

perhaps try perusing math methods for physics textbooks, Riley is the most popular

[solar flint]

I've just finished my degree in Physics, I want to continue to study mathematics but I want a much more solid foundation, is there any books on changing perspective of mathematics anyone can recommend? As low-level as how to visualise complex numbers and operators etc.

[vital bane]

do you mean you want to study rigorous mathematics or do you want a mathematics book written by a physicist?

for visualizing complex stuff, definitely "Visual Complex Analysis" by Tristan Needham

[solar flint]

rigorous mathematics but I want to look back at the basics and see if there's a better point of view for understanding them, rather than learning how they behave knowing what they are and why they behave that way

[solar flint]

I'll have a look at this as well ty

[real sapphire]

What do you guys think of the teach yourself calculus book by P Abbott? I have a copy in hand. Main concern is that it was released around 1999. If I want to prepare for college calculus 1, is this a good book?

[candid turret]

can anyone suggest me books on Number Theory (basic to advanced)?

[modern ruin]

everything recent is sort of the same. if you want to actually be prepared for calculus, learn more algebra

you also don’t need a textbook to learn calculus (maybe a hot take)

https://tutorial.math.lamar.edu/Extras/AlgebraTrigReview/AlgebraTrigIntro.aspx make sure you know everything about every topic on this page

[real sapphire]

Oh ok bet

Will this also teach me if I don’t know?

[modern ruin]

yeah, it has a lot of information on each of those pages

[warped kayak]

Is it overkill to read through all of these Topology related texts?

Topology by Munkres
Differential Topology by Guillemin and Pollack
Intro to Topological Manifolds by Lee

I assume there would be some overlap, but maybe they all cover a fair amount of unique stuff?

[gray gazelle]

munkres and lee have a lot of overlap

[tribal crow]

Munkres and Lee both begin with point-set topology, and cover somewhat similar material (though not entirely); G&P is very different

pick either Munkres or Lee imo

read G&P afterwards

[sage python]

And pick Lee over Munkres

[warped kayak]

Thanks everybody!

[maiden glen]

may anyone suggest a book that discusses functions in the perspective of set theories?

not just specifically that, but something containing it

[modern ruin]

i am a GP hater

[tribal crow]

what do you prefer?

[modern ruin]

idk just at the point where I had to read GP i didn't get much out of it

it's worth looking at becuase it isn't completely bad, i just hate the way it's written

[warped kayak]

If I wanted to read up on Algebraic Topology, would Lee's Intro to Topological Manifolds be enough before a book like Hatcher's Algebraic Topology? Or would another book be necessary to bridge the gap?

[violet shuttle]

what gap?

you can just jump into hatcher if you eant

note that chapter 0 is harder than chapter 1 and it perhaps makes sense to use it as a reference as you read chs 1-

[maiden glen]

response?

[violet shuttle]

wdym by this? like deep foundations stuff or just like basic sets

[formal bronze]

Use Kunen for set theory

[north lion]

Any math book recommendations? I need to learn math as soon as possible. I'm not ready for college.

[tribal crow]

what topic do you want recommendations for, specifically? what is your math background like?

[north lion]

I can do algebra 1 right now no more

[humble vortex]

Can someone help me in Quadratic equations ??

[tribal crow]

Serge Lang's Basic Mathematics sounds like a good idea then

it should get you ready for the mathematics you'd see in college

[north lion]

Will it teach me the foundations of algebra 2, geometry, triginometry, etc....?

[tribal crow]

yes, and more

[north lion]

Okay, thank you so much. Care to answer more of my question?

[tribal crow]

e.g real/complex numbers, induction, determinants, etc

[tribal crow]

I can certainly try

[north lion]

I barely know history, science, and statistics. Care to show me some books for those as well?

I need to study a lot and get ready for college.

[lethal bronze]

like, the book? If not then this is not the place to ask.

[humble vortex]

NCERT CLASS 10

chapter 4

[tribal crow]

that's much tougher for me to answer

[humble vortex]

@lethal bronze

[north lion]

No problem; I can find out! 🙂

Oh and English as well! I really need to work on my grammar.

I can do all of that, thanks a lot for your help

[maiden glen]

'deep foundations stuff'

[lethal bronze]

I think one of the standard ones would be Thomas Jech Set theory book

[north lion]

I found books, thank you so much for your help @tribal crow

I'm going to wait on buying those books

In the meantime, I'm going to learn Japanese!

[lethal bronze]

Japanese sounds fun. Actually, there are a lot of educational manga about mathematics too if you are into the manga

[north lion]

I love manga, but I don't read it often

Japanese is my favorite language

[lethal bronze]

I remember reading Doraemon (that probably tells my age), which has couple of series dedicate to mathematics

like algebra stuff

[north lion]

I want to get my education degree and move to Japan

[north lion]

Everyone has their own preferences, do what you enjoy!

[maiden glen]

May anyone suggest any books which discuss functions in the perspective of set theories and linear algebra? homomorphisms, linear maps, transformations and such please someone

[gray gazelle]

sounds like any algebra text would fit the bill

[maiden glen]

give me one

an example

[gray gazelle]

#book-recommendations message

[covert mauve]

what exactly is the difference between graduate and undergraduate-level text? I see a lot of supposed graduate-level texts being recommended as an introductory text to a topic, whats the difference?

[marble solar]

Broadly, the difference is that graduate texts largely pre-suppose most (if not all) of undergraduate standard curriculum {Real Analysis, Complex Variables, Algebra, Topology, Linear Algebra, ...} whereas undergrad texts try to keep the pre-reqs to a minimum

[strange sentinel]

There's not necessarily a hard line or anything, lots of books say "for graduate students or advanced undergraduates" or whatnot
The main difference is mathematical maturity expected

There's also often more prereqs for graduate texts

[lethal bronze]

From my experience, if it is an introductory graduate-level book, it often requires you to have prior or previous exposure to the topic.

[gray gazelle]

This, but also it's a bit weird sometimes, for example Aluffi as a whole is considered graduate, when it is actually used as an undergraduate book in the institution it was written, really only the final chapter is Graduate level

[warped spoke]

look up manga guides

by Masaharu Takemura

[lethal bronze]

I read LA and stats one. Really fun

I also heard that regression analysis is hilarious.

[warped spoke]

Im planning on reading the LA one

Im gonna do a summer course

and they cover some linear algebra there and im gonna use the LA manga guide as supplementary resource

[lethal bronze]

LA is a nice read. And yeah, you probably need some exposure before reading the manga

you have to understand the original novel (i.e., LA in class) before reading manga

The Doraemon one I read is really old. Like early 2000. I still thought it is 10 years ago but it is actually >20 years at this point lol

[warped spoke]

I've had a small amount of exposure to LA

but it's not substantial

[lethal bronze]

then you would be fine reading that

because the advanced part of the book will go relatively quick

[warped spoke]

Hell yeah

I mean I don't really mind parts of books going quicker than others

In fact I would probably prefer a faster book than a slower one

Do you know where I could find a large amount of exercises on linear algebra?

well

not necessarily a large amount

but just exercises in general

[tribal crow]

any textbook would suffice for this purpose

[warped spoke]

any books in particular that you would recommend?

[lethal bronze]

linear algebra done right or linear algebra done wrong both are good books

strang one is also good

Lay is also good. I actually used that in the LA class before and problem is moderate

[tribal crow]

Friedberg, Insel, Spence; but do also take a look at the books printName suggested

here's some more books to consider

#book-recommendations message

if you're looking for more computational problems, then Strang or Lay are good, yes

[warped spoke]

thanks guys

I really appreciate the recommendations

[glossy zealot]

If you want more abstract stuffs, try Axler or Hoffman and Kunze too. If you want more computational stuffs, I heard people also recommend Anton

[dense loom]

Hi there, any book that deals with convergence (simple, uniform CV etc) ?
I have read Rudin's chapter in PMA, but got stuck

[glossy zealot]

You can read any other intro analysis book

Abott, Sherbet, Jay Cummings,…

Hop on to another one when you find the one you are reading difficult to understand

That’s what I usually do

[dense loom]

Ok thanks 🙏

[echo inlet]

📌

[balmy crown]

Finally read the entirety of Book of Proofs. Overall my favorite math book ive read

[foggy quest]

The one variable book here: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[foggy quest]

Book here is good: https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[willow merlin]

I need easiest book for learning ordinary diff eqs

Integrating factor at the very least needs to be covered

if possible considering special cases of diff eqs

[formal bronze]

Perko is a good book for ODEs

[sage python]

Lol I referenced that book a bit when my analysis class did ODEs but somehow I'm... ever so slightly skeptical

That this is what that person is looking for

Just slightly idk maybe just a hunch

[formal bronze]

Eh, maybe. They'll do their research and see if it fits their needs

I just suggested it because it did a great job of teaching me ODEs

[willow merlin]

you mean perko isnt the easiest book for learning diffeqs

xD

[remote sparrow]

it's generally regarded as a graduate reference

[willow merlin]

I figured

[remote sparrow]

#book-recommendations message

[maiden glen]

when should i read joseph. j rotman's advanced modern algebra?

[remote sparrow]

after you've read an introductory undergraduate textbook

[maiden glen]

like what?

[gray gazelle]

Artin’s Algebra is a nice transition to algebra from linear algebra

One can argue you don’t even need to read Rotman after completing Artin and you can start reading special topics

[maiden glen]

thank you\

[remote sparrow]

#book-recommendations message

[formal bronze]

I see, it was used for my first course in ODEs

And in any case it only needs a bit of linear algebra and analysis

[fierce hedge]

Depends on the edition you're using. 3rd edition explicitly states chapters for used in ug level. 2nd edition is more of an encyclopaedia but it is still very very readable. You can try it and always refer back on the ug book by Rotman for detailed proofs (he often tells you which part to look at). 1st edition is very similar to 2nd so there's that.

Although I think 1st edition should be friendlier as he does full proofs and doesn't refer back to his ug book.

Also note that 3rd edition does rings first approach.

[sturdy shore]

rotman: basic number theory -> commutative rings -> groups -> galois theory

[fierce hedge]

This is for the ug book, advanced modern algebra doesn't start with number theory

[fresh skiff]

Hello guys. Is there a good reference book for for Abbott?
I was using Ross but after covering few sections (recently i did section 9), the stuff is getting horrible. Also I have a Cummings book too I used when I was doing chapter 1 of abbott, but since Cummings has given all problems together so it is bit difficult to see either I have covered that xyz topic or not to attempt the problem

[remote vortex]

What do you mean by a "reference book for Abbott"?

[fresh skiff]

The book that I can use as a reference. Meaning, if I want more problems on that topic then I use that book (so ig the books should be equivalent to Abbott in terms of level of difficulty and mathematical maturity or slightly higher).

[remote vortex]

I'm going to go against type and recommend Rudin

He's got very good exercises, and if you go in having the intuitions and tools from Abbott, it should be a bearable read.

[fresh skiff]

Thank you so much.
Also currently I was doing problems from Rudin (homework problems).

[gray gazelle]

has anyone read Lang's Undergraduate Algebra? Thoughts? I really like the author so I bought it from Amazon and super excited; wanted any advice for going through it? How does thisbook compare to the Algebra graduate-level book by Lang (aside from difficulty of course)?

[violet shuttle]

against type? anti recommending rudin is at this point standard

[remote vortex]

Yes, and I did recommend Rudin

[fresh skiff]

Well my experience with first chapter of Rudin was good. Out of 10 assigned problems i am able to do more than half

Also done remaining but have some doubts

[vagrant rose]

Calculus book for beginner?

[willow merlin]

thomas calculus

[sturdy shore]

what
I'm literally currently going through the book

I guess technically it starts with quadratic, cubic and quartic formulas

[rain wren]

that's not good advice

[glossy zealot]

I will return to the main textbook after I get the idea

[rain wren]

I think a better strategy is to stick to a single book

maybe 2 at a max

and whenever you're stuck you ask for help for clarification

this server is a really good place to do that

otherwise you'd spend too much time shuffling between and looking for different books and not so much reading them

[gray jungle]

awful idea, use as many books as you need, the different perspectives are essential!!

i rarely use less than 2 books while learning unless the book is just godly written

seeing different approaches is so nice

[slender cargo]

I don't see an issue with using multiple books?

The point is to learn the material. Bashing your head for several hours to understand a single point is not necessarily more effective for learning.

[fresh skiff]

But how do you choose books? I was doing this ( Cummings, ross and Abbott). Suddenly Ross became horrible and Cummings problems were confusing me. But the main text Abbott was good in all aspects

[slender cargo]

Just stick with Abbott if you've gone a good ways through it. It's good.

Sometimes a concept is just hard to understand. Write out your thoughts, try to solve the proof yourself.

[fresh skiff]

And sometimes the proof makes sense (at that moment I can't see the mistake) and I accept it correct and move on

[gray jungle]

i just make a folder with a bunch of books, some i get from here some from MSE recs and some from wiki references

a quick skim tells me if the author is a good writer

[fresh skiff]

Btw thank you. Yes Abbott is like an ideal book.

[gray jungle]

usually ile converge to a single reference i use much more than others

but only after experimenting with different books

[slender cargo]

If you really want another book, I like Bartle Sherbert. That's the book I went through.

[fresh skiff]

Seems interesting. I did with ross initial like 1.5 chapter were friendly and I liked it but eventually it became dry.
Well ig I didn't skim in proper way . Thank you James

[fresh skiff]

Got it. I will take a view. Thank you guys.

[fierce hedge]

Oh this is the 3rd edition, I didn't use it cause does the rings first. Besides, compared to this the ug book does around 100 pages of number theory. I think this is just the stuff that would be used in rings part.

[sturdy shore]

the nt section is essentially stating theorems and citing his other books for the proofs

[remote sparrow]

aside from rudin, you can look at bartle and sherbert or schroeder

[cobalt arch]

Any books on logic that are as exhaustive as metamath's site? I would prefer something that would at least be in English besides formulas so that it can aid intuition.

[sacred sorrel]

is this "Richard Courant, Fritz John Introduction to Calculus and Analysis Vol. 1" a good book to learn calculus?

[fresh skiff]

Ok. Thank you.

[gray gazelle]

anyone?

[celest tulip]

Hello, im new, anyone can recommend me a book for novates pls

sorry for my ortography, im native spanish

[maiden halo]

it's pretty old and is not a typical intro to calculus.

[sacred sorrel]

I was reading and its a good book but has a tough theory to read

I've just read 5 pages in two hours

[willow merlin]

which book goes hard into hard exercises for training convergence test for series

[foggy quest]

https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/anal1v.pdf is good

[maiden glen]

recommendations for informal and extensive tomes concerning elementary geometries (plane, solid, line, Euclidian, analytic, non-Euclidian)?

and other branches of geometry

give me everything (i am aware that the various branches of geometry require prior understanding of other fields, i will find the way, just give me everything, if not a list)

[bright epoch]

Coxeter's geometry text is very good

[glossy zealot]

Is there a book dedicated to matrix calculus?

[vagrant rose]

What's topology?

And why does algebra need it?

Oh wait I didn't read carefully

What's algebraic topology used for?

[stray veldt]

uh, thats a pretty wide question

[lean magnet]

hi is there any book suggestions for ODE and PDE, preferably not theory heavy but I still want to know what's going on. Thanks

[gray gazelle]

#math-discussion will fit more your question but shorty, topology about the study of the changes in space and stuff and algebra is needed in most of mathematics if not all but I am not into topology so I can't be more detailed

[grand thistle]

💀 💀 cooked darq up fr

[lethal bronze]

When in doubt, read Stanley Farlow. By no means is the theory-heavy or even focused on mathematics. But it is a good start I would say.

[bright epoch]

do you mean what is it used for in math (the answer is that all the strongest topology tools are algebraic) or what is it used for in applications (I'm working in TDA and there's tons of TDA to be done with AT)

[lean magnet]

Thanks a lot

[maiden glen]

response(s) please?

[maiden glen]

thank you

[cinder magnet]

Guys any recommendations for undergraduate combinatorics

[bright epoch]

Do you want a text that will prepare you for an undergrad combi class or a book on combinatorics that is approachable for undergrads

[bright epoch]

What do you mean by matrix calculus

[cinder magnet]

The first one

[lapis sky]

I think this is a good book. It does cover combinatorics but I think it also does a good job with preparation. https://arxiv.org/abs/2108.04902

[cinder magnet]

Thank you

[native cradle]

what's the best book to learn RA from scratch and what are the pre-requisites ?

[tribal crow]

Abbott is a very gentle introduction

perhaps check that out?

[native cradle]

Thanks

[tribal crow]

Bartle and Sherbert, Schroder, Spivak, and Rudin are also possible introductions

I think Abbott may be the heaviest in terms of handholding though

which is good if you're not used to analysis at all

pre req wise, intro RA requires almost nothing

[native cradle]

Do I need to know more than High school maths to start?

Like epsilon delta limits

Cool

Thanks

[tribal crow]

maybe the only thing to know is naive set theory, propositional logic, functions, basic proof techniques including induction

but you can also learn all of that along the way

it's definitely not all a hard pre req

[native cradle]

Got it, thanks!

[tribal crow]

[slender cargo]

imo Spivak has the most exposition from what I read through, but some people just don't wanna give it a chance since there's no topology section (and I guess the topics are weirdly ordered)

[tribal crow]

mhm

I liked Spivak

but if one has absolutely no exposure to analysis beforehand, his exercises can be really rough (speaking from personal experience)

[slender cargo]

It felt very well written

[tribal crow]

it is very well written

I don't deny that

his writing is good, his exercises are very hard

[slender cargo]

They're at the exact same difficulty as Abbott

imo

[tribal crow]

oh are they?

[slender cargo]

yeah

[tribal crow]

I've never actually taken a close look at Abbott's exercises

[slender cargo]

the two books can replace one another

Unless you really need that smidge of topology

[tribal crow]

mhm

Little Spivak is much more terse though

[slender cargo]

Yes that is completely different lol

[tribal crow]

this book is a bit brutal

Calculus is a very good book, I agree there

[slender cargo]

I will be taking multivar calc next term with Edwards Advanced Calculus

it'll be interesting to compare that book to Spivak's Calc on Manifolds

[tribal crow]

interesting!

good luck with that course!

[slender cargo]

You as well!

I am trying to speedrun Axler's LADR this summer in preparation..

[tribal crow]

wow, good luck!

[slender cargo]

I'll be taking that course, Topology, and Algebra (with Dummit Foote) next term

Fun times!

[slender cargo]

Just curious, are you self studying it or is it for a course?

[tribal crow]

both

[slender cargo]

Oh, nice! lol

[tribal crow]

I'll have a course that uses it next term

I'm self studying in advance, but also because I'm actually interested in this material

so it's a win-win

[slender cargo]

Indeed

I hear it's treatment of multilinear algebra (which I know nothing about) is not great

[tribal crow]

mhm

[slender cargo]

so I wonder how that material will go in the course

[trail hemlock]

also consider cummings' real analysis book. it requires almost nothing and is very strong in the hand-holding. use it with abbott or something else, not alone

[tribal crow]

supposedly its inverse/implicit function thm proofs are not great either

I've yet to get there though, so I'll see for myself

[willow merlin]

easiest number theory book

?=????????=????????????????????+

[tribal crow]

(this is a joke, if that wasn't clear)

[willow merlin]

what would be the equivalent of "Number theory" for dummies

[willow merlin]

did someone read "Real and Functional Anal"

is it any decent? by Mukherjea and Pothoven

[unborn jackal]

what is the book even about?

class field theory right?

[mystic orbit]

fakke news

[maiden glen]

once again, please give me responses

i need it

[willow merlin]

easiest number theory references?

I need some NT for dummies type of book

[earnest wolf]

btw, I heard u host a rudin study group right?

where could i find it?

[fresh burrow]

is there a list of introductory algebraic geometry books somewhere here?

or recommendations

im moreso hunting for a book i remember from the past, as described here https://discordapp.com/channels/268882317391429632/1136641179719565342/1246965361643880558 but any would be appreciated

[graceful moon]

Miles Reid has an approachable classical introduction to the subject which pairs with his comalg book

[fresh burrow]

ty that looks really good, i think its not what im searching for but if i cant find that book ill most likely use miles reid