book-recommendations

[strange owl]

A book this is the link

this book may be complex though

Just research a few books and you might find one you like

@maiden glen

[gray gazelle]

Long ass link, https://www.amazon.com/Berklee-Contemporary-Music-Notation-Jonathan/dp/0876391781/

[strange owl]

lol mb

[gray gazelle]

It's fine dw!

[maiden glen]

thank you

[strange owl]

yw

[crude flame]

Guys aops problems is hard and tough then normal problems?

[modern ruin]

good instrument

[grave forum]

Are there any general math books that are easy to understand? I missed out a lot on my year 7-9 math classes , and my fundamentals are very crappy, I'm currently in year 11, struggling a bit.

[gray gazelle]

Um does anyone here have any experience with Klaus Jänich Linear algebra text?

It will be my first intro to linear algebra, I tried hoffman kunze but :).

[left crown]

Hey, so I am a high school graduate which wants to follow a math major program and would want to try to get an Olympiad medal. Does anyone have some book recommendations or resources?
Books that focus on improving your reasoning etc.

[normal crystal]

déjà vu

[lime vessel]

Which olympiad

[unique breach]

Aops alcumus problems can go up to AMC 10 level and Aops alcumus problems are all around Mathcounts level. I don't know what you mean by "normal problems". Yes, they are harder that regular school problems.

[orchid musk]

Reading this becoming guys snarky responses to people while at work really passes the time

[maiden glen]

😊

[sudden kindle]

LETS DO THIS

[pulsar nest]

Anyone have any opinions on Jay Cummings' proofs and/or real analysis long form mathematics textbooks?

[trail hemlock]

@jovial parrot your time to shine

[jovial parrot]

LOL

Our time

[trail hemlock]

mhm

[jovial parrot]

I LOVE THEM

jays writing style is very friendly

[trail hemlock]

jay cummings…where do i even begin …

[jovial parrot]

Especially if you struggle

He really explains everything nicely

[pulsar nest]

Oooh I met the fanboys

[jovial parrot]

lol

[pulsar nest]

I am going into 10th grade with a self-taught accelerated curriculum and his proofs are the very first mah book I've ever bought

[jovial parrot]

I like his proofs book

[pulsar nest]

And so far I'm loving it

Also love that he gives 10 exercises' solutions for every chapter

I've heard there isnt that luxury with the real analysis

[pulsar nest]

Dont have to worry about what exercises to do and what to skip, just do an exercise and check solution

10x

[real marsh]

I'd recommend picking up a book/book pdf that covers some more discrete math type proofs - intro to mathematical thinking is the one I somewhat learnt from. They're also a good intro to proofs that real analysis won't give you.

[real marsh]

you should do at least 1 or 2 without solutions - learning to judge when you feel like you've proven something is an important skill

[pulsar nest]

I mean I still re-read my solution and try to be as rigorous as I consciously can be

But I see your point

[real marsh]

pretty much any maths textbook that isn't for high school students doesn't give solutions, so being able to judge your own solutions is quite useful.

[normal crystal]

4 out of 5 tadpoles approve

[jovial parrot]

I’m the fifth and I approve

[pulsar nest]

First time googling what discrete math is 😅basically its math that you dont need calculus as a prereq?

[pulsar nest]

And do you mean that I should read up on intro to mathematical thinking while I'm reading prooofs?

proooofs

[real marsh]

like its a textbook

that's full of problems

on like discrete stuff

[real marsh]

its anything that's not continuous 🙂

I'd think of it as maths where theres a finite amount of stuff

[pulsar nest]

Ok ill have that in mind then I guess

[fair mortar]

How is Stewart James' Calculus

[molten mason]

Fine, covers 3 semesters of Calc

Answers are on Quizlet Plus

[fair mortar]

What level of calc would it be if i finish it

is it like beginner or slightly higher

[remote sparrow]

enough to advance to future coursework

it's a staple of the curriculum

[fair mortar]

I see

thanks

Any recommendations for intermediate level number theories

[molten mason]

It covers Calc 1,2 and 3 in order

[civic birch]

i am beginner in math any book recommendations

[stuck zephyr]

depends on which topic you want

[civic birch]

algebra

[stuck zephyr]

algebra 1 or 2?

probably khan academy is best for this since I don't know any good books

[civic birch]

thx

[stuck zephyr]

your textbook is enough

maybe

[trail hemlock]

khan academy is the best for alg 1-2

but aops publishes really good algebra books too

lang's Basic Mathematics and Gelfand's Algebra are also good

[civic birch]

thx man

[gray gazelle]

the name is "everything u need to ace for pre algebra maths in one big fat notebook"

[gray gazelle]

..

[violet hearth]

I'm new to elliptic curves and those stuff, and I want to learn about L functions, do you have any recommendations?

[dull fog]

any books I can do to learn math?

[marsh ingot]

What kind of math?

Calculus, algebra, geometry, real analysis, complex analysis, algebraic structures,...?

[normal crystal]

next question, "is there a math discord" 🤡

[remote vortex]

there isn't 🥷

[gray gazelle]

i googled a book title and the first link that showed up was a harvard pdf link, does this mean i can use the book for free legally or is it only for their students?

[normal crystal]

what book
if it isn't locked on canvas or whatever, it's fine

[gray gazelle]

i just searched "advanced calculus" waiting for a wikipedia page or something to pop up but got a harvard link

[normal crystal]

that book is fine to download
if you looked on the Professor's page of that link, it says that

[mellow wren]

if it's on the internet it's free

[gray gazelle]

just to make sure we're talking about the same book
it's by lynn h. loomis and Shlomo Sternberg

[gray gazelle]

meh

[normal crystal]

yes, but again, if you looked at the page hosting the pdf
you would already have your answer

[gray gazelle]

dang..

[gray gazelle]

my bad, will do that next time
thanks

[normal crystal]

np, just encouraging

[quasi dock]

haiya! came to ask, hows stanley i grossmans multivariable calculus, linear algebra, and differential equations? im advance studying for my calc 3, diffeq and my linear algebra courses and it semt like just the right book for me rn considering i think i have a good enough grasp on the calc 1 and calc 2 material

[autumn fox]

hello, can someone recommend me some books on the topic of algtop / dynamical systems / topological dynamics, preferably with some focus on numerical/computational methods? i'm taking a gap year and want to snatch something to read from digital library before i lose access to it for a year

[gray gazelle]

what are some books about techniches? (problem solving, but not just strategies , but rather on how to understand)

[deft thistle]

i am trying to find a book that covers a little more advanced algebra and another book that covers precalculus, someone has a recommendation for me?

[gray gazelle]

algebra by Gelfand, or maybe basic mathematics by serge lang

[willow merlin]

best intro to linear algebra that is not anton

and not c lay

???

[gray gazelle]

you can check this #book-recommendations message

or maybe umm

!bookrecs

[hybrid sparrow]

Check out the official Mathematics Discord website, or ask in #book-recommendations. If you want to submit your own book review, please DM ModMail.

[gray gazelle]

much more reliable @willow merlin

[remote sparrow]

#book-recommendations message

[foggy quest]

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

others like https://www.math.brown.edu/streil/papers/LADW/LADW.html (I haven't read it, but it looks good)

[molten mason]

If you already know the basics, Basic Mathematics by Serge Lang covers pre-algebra through Pre-Calc and is at an advanced level.

[molten mason]

FIS

[gray gazelle]

Hoffman LA

[deft thistle]

I am seeing here and it seems a little easy for me, I would like something more advanced and a saw a book called algebra by serge lang. Do you guys think is a good choice? @molten mason @gray gazelle

[gray gazelle]

uhh that's abstract algebra i think..

[lime vessel]

You mean high school algebra?

Lang Basic Mathematics is probably more appropriate

[gray gazelle]

yes2

algebra by serge lang is abit more harder

i suppose you really want hard problems in the book?

then

algebra by Gelfand

[lime vessel]

Lang Algebra is like another subject entirely

[gray gazelle]

It's like gelfand's algebra but harder

[lime vessel]

Gelfand is high school algebra

[gray gazelle]

Gelfand might have a abstract algebra book in mathematical encyclopedia series if I recall correctly

Serge Lang has 4 algebra books: 1. Intro to LA, 2. LA, 3. Undergrad Algebra, 4. Algebra So @deft thistle you probably need to clarify.

[deft thistle]

The fourth

[lime vessel]

Well they mentioned precalculus so I'm assuming high school algebra

[deft thistle]

Yes

[gray gazelle]

What

[lime vessel]

Lang Algebra is for postgraduate students btw

[deft thistle]

Good to know

[lime vessel]

Like the phase after 4 years of uni

[gray gazelle]

I think probably a bit more than that, needs to be an outstanding postgrad or smth

[deft thistle]

wow

well so ill probably search for this one, algebra by gelfand

[gray gazelle]

Yeah surely

[deft thistle]

does it talks about precalculus too?

i think i would need a book about combinatorial analyses, permutation, combinatories et cetera

[gray gazelle]

What have you done in math? I would like to know so I can help you.

[deft thistle]

perfect . i started to learn math by my self for 2 months and i am struggling with algebra, equations and some of them are really simple. I am studying to make an exam and my biggest problems are algebra and combinatories

i am studying math with previous exams and youtube

[gray gazelle]

I see. I think you should use ask a question here about your situation: https://matheducators.stackexchange.com/

[gray gazelle]

Hello there, I am searching a book for discrete maths, I get Concrete Maths but I feel sometimes the level is too high for me in some aspects

I don´t really know what to do, it is normal that it just hurt my brain and my working memory doesn´t understand it?

It goes too fast

[weary kestrel]

Hey guys

Anyone has a good resources for solving complex problems

I just wanna practice calculus and simplify some equations

thanks in advance

[weary kestrel]

https://www.khanacademy.org/

that's a really really good resource it provides good explanations and quizzes to test your comprehension

[glad elm]

Algebra of set theory: Definition of concepts, laws of algebra of sets, Venn diagram and application. Real Numbers: Rational numbers, theory of surds, sequences and series (including AGP), binomial theorem, theory of quadratic, cubic and quartic equations, indices and logarithms, mathematical induction, partial fractions, theory of equations, inequalities and polynomials (including factor and remainder theorems). Complex Numbers: Algebra of complex numbers, Argand diagram, multiplication and division of numbers in polar form, nth root of unity, and DeMoivre’s theorem, expansion of sin nØ, cos nØ, tan nØ.

Anyone know a book/books that cover these topics at the 1st year undergrad level?

[molten gulch]

Can't think of a single book that does this and esp not at year 1 level. Can think of multiple books that'd cover all this info when out together

[glad elm]

Oh, okie. Could you please name a few?

[molten gulch]

Once I get to my laptop, sure but they're all like upper undergrad books

[glad elm]

Oh, if their uppergrad books, there's no need to send them. Thank's for the offer!

[molten gulch]

Alr

I mean, for some of em I might have some intro stuff

Lemme check

[foggy gorge]

Can someone suggest a book about geometry and set theory?

I'm learning to apply for a computer science bachelor and I also want to dive in mathematics olympiads

[molten gulch]

Algebra of set theory: Any discrete mathematics textbook should introduce this to a good degree. We have a copy of Rosen's Discrete Mathematics but again, any discrete math book should have a good amout of info on this. If you want to go more in depth, you have Jech's set theory book but it's very much a Definition, Theorem, Lemma, Proof type book. From what we're aware of, discrete maths books (sometimes) have chapters on the binomial theorem as part of a chapter on combinatorics and counting. If you want something a bit more combinatorics-only focused, there's many good books on combinatorics that are good if you know proof strategies

For sequences and series, again, some discrete books have a small amount of info on them, but for a strong intro, we'd recommend going through the chapter on sequences and series in a calculus textbook (stewart's calculus, thomas' calculus, etc...) or hell even a real analysis textbook (though that may be a bit too much at once) (Abbott, Pugh, Rudin, etc...)

For quadratic, cubic, quartics, general polynomials, ln, exponentials, equations, and inqualities; we learned most of that from a precalculus and algebra textbook. Again, there's many you can look for there.

For complex numbers: the main books we have are on complex variables and analysis so we can't really be of much help for a basic introduction.

[glad elm]

Thank you so much, I really appreaciate the help!

[molten gulch]

you're very welcome

[molten gulch]

For set theory, our recommendation is the same as we gave to @glad elm

We sadly don't know any good geometry books

[foggy gorge]

No problem, thank you very much

[molten gulch]

oh also, this is a complex variables textbook but the first chapter goes over complex numbers: Brown and Churchill - Complex Variables and Applications

but yea, wouldn't recommend tbh because the rest of that book is very heavy calculus

legit would just say go look on khanacademy or such

[foggy gorge]

Have you any clue if "axiomatic geometry" is a good one?

[molten gulch]

can you provide a link

or isbn or author name

[glad elm]

Thanks!

[glad elm]

yeah, that's probably what I'll do

[candid creek]

which book can i lose my virginity

[glad elm]

...

[molten gulch]

you can't lose that to a book

[candid creek]

i nearly lost it to abstract alegbra last sem

[foggy gorge]

Here

[glad elm]

lmaoooo

[candid creek]

but i clutched the exams

[candid creek]

it takes it from u forcefuly

reading baby rudin rn

feeling this might be it

[molten gulch]

We know Lee's manifolds books are very good but we didn't even know he made a geometry book

[foggy gorge]

Which books he made so far?

[molten gulch]

there's probs more than this, but the ones we know of are

• Intro to Smooth Manifolds
• Intro to Riemannian Manifolds
• Intro to Topological Manifolds
• Intro to Complex Manifolds (this one isn't out yet)

[foggy gorge]

They seem books for ones that knows calculus

[molten gulch]

oh absolutely

[foggy gorge]

I am still in precalculus

[hollow peak]

Intro to Complex Manifolds is out

I love it so far, I'm 4 chapters in

[molten gulch]

ooh well then

[dapper root]

Does it only use ISM

Or do you need IRM too

[maiden glen]

books concerning order theory?

[hollow peak]

The Kahler stuff is saved for the end

You definitely have enough background at least

[sturdy gust]

does anyone know of a book on constructive group theory?

[sturdy gust]

maybe:
S. Roman, Lattices and Ordered Sets (2008)
G. Grätzer, Lattice Theory: Foundation

have read some of them, but didnt finish

[maiden glen]

thank you

[maiden glen]

what is "constructive"

[sturdy gust]

as in constructuve mathematics

[maiden glen]

oh

a constructivist

interesting

[sturdy gust]

not sure, i just think its an interesting area of mathematics

that can coexist with classical

i dont necessarily consider myself a constructivist

[gray gazelle]

!bookrecs

[hybrid sparrow]

Check out the official Mathematics Discord website, or ask in #book-recommendations. If you want to submit your own book review, please DM ModMail.

[tall karma]

Can someone recommend an introductory numerical analysis text?

For background: I took an undergrad numerical optimization course and did major in mathematics with the intent of going to grad school for combinatorics (but chose to go into CS instead)

I would like something that goes more in-depth assuming I have a good working understanding of linear algebra, real analysis and complex analysis with a bit of exposure to harmonic analysis

not entirely sure what all is relevant here, but I just want something that lets me get a better understanding of what was going on in my undergrad course and helps me solve numerical optimization problems that are coming up in work and hobbies

[cobalt arch]

Maybe try Ray Mines, Fred Richman, Wim Ruitenburg - A Course in Constructive Algebra. It is not on Constructive Group Theory but close enough. You may find other books on constructive math in the bibliography.

[sturdy gust]

haha i am currently reading that one. that was what led me to ask that question.

unfortunately it doesnt seem like theres a textbook on constructive group theory listed in the bibliography.

[cobalt arch]

This is currently the only book on my list of constructive math books pertaining to Algebra

[sturdy gust]

sad

[cobalt arch]

Along with one which is more advanced, on commutative algebra

[strange siren]

Hi guys I want to be able to take multivariable calc, linear algebra, and a intro differential equations class but I feel like my calculus 2 knowledge is weak, particularly with polar coordinates, parametric equations, and sequences and series. Do you guys have any books and/or resources you guys would recommend using to relearn calculus 2? And how would you recommend thinking about such materials/how would you approach learning calc 2

I haven't tried to learn math content entirely by myself, so I'm wondering how much to focus on understanding proofs/how the important theorems connect with each other, and how I can evaluate I've done enough problems in each textbook section to have a good grasp of content

[sturdy gust]

just out of curiosity, which one is that?

[cobalt arch]

Henri Lombardi, Claude Quitté - Commutative Algebra, Constructive Methods

[molten mason]

Professor Leonard or Brian McLogan on YouTube. BlackPenRedPen on YouTube also has probably hundreds of questions you can try to go through. Paul's Online Notes has a Calc 2 section. You can also just go through any Calc textbook's Calc 2 section all over again

[strange siren]

What are your thoughts about the second part of my question? I was thinking maybe it would help me to take an intro to proofs book so that I can understand the logic of proofs related to calc theorems better

[gray gazelle]

hello guys any recommendations how to do proofs from like basic mathematics by serge lang?

having a hard time what is really a proof

you know the deep meaning which i really don't know..

[mossy flume]

You'll probably get better advice asking about specific problems in #proofs-and-logic

[gray gazelle]

no I want some guides how to do basic proofs

i really don't know what's the context of proofs and how to use them xd

[strange siren]

Try looking up on YouTube what a proof is and what relevant books there are

[gray gazelle]

i dont even know what are axioms and stuff...

[strange siren]

Again, you should look up basic resources and then if you have questions for basic definitions try searching on wikipedia

[molten mason]

What page? What question?

[nova lotus]

hey idk if this belongs here and ill move it if asked but does anyone have a link to the paper referenced here https://media.discordapp.net/attachments/811392135885750322/1265767903459020950/image.png?ex=66a35e79&is=66a20cf9&hm=b889036eb17522c9d68e9abbc87d27a7ed7432b66f9da5776dc3699066ce2319&=&format=webp&quality=lossless

googling wH young year didnt do much for me

[gray gazelle]

page 26

24

[normal crystal]

this is a free book
https://www.people.vcu.edu/~rhammack/BookOfProof/

[gray gazelle]

can you give the title?

i dont trust link

[molten mason]

Page 435 starts the answer key to the book so you can look at how answers are to similiar questions. The answer to that specific question is on page A-5.

Utilize the #proofs-and-logic channel and the #precalculus channel for that textbook.

A lot of learning proofs is just trial and error, when you see the answer try to work backward to see how it was made. Then try to recreate it yourself from memory. Try to explain to yourself why every step is there.

Most people learn proofs just from doing it out of a book exercises, but there are plenty of Intro to Proofs textbooks. Daniel Velleman has a common one, Jay Cummings has another.

[gray gazelle]

answer key doesn't make sense lol... i mean what's the purpose of proofs

[normal crystal]

It's a real mystery what the title could be🙄

[molten mason]

Specifically when it comes to Calculus, normally your Calculus textbook is more computational, and you do the proofs and theories in Real Analysis. I feel a lot of what you're asking for would be in Real Analysis, which you can easily start with Calc 2 knowledge.

[molten mason]

In math we can't just say something exists or that something does something. We must prove it. This makes more sense the higher in math you go.

For Basic Mathematics I wouldn't stress too much about it. I would simply review the questions and answers when it comes to the proof questions in that textbook so you can just become familiar with what they look like. You need to get the actual pre-calc knowledge down first.

[molten mason]

https://math.hawaii.edu/~pavel/Aluffi_notes.pdf

This is probably a good start

[molten mason]

https://youtube.com/playlist?list=PLBh2i93oe2quABbNq4I_-hyjhW8eOdgrO

And this one

[gray gazelle]

but you gotta try to solve it first right?

[molten mason]

Polar Coordinates and Parametric Equations I would just keep going down the YouTube rabbithole to get practice. They were used a lot in multivariable Calc. A lot of trig identities and trig integrals. Not so much series/sequences

[molten mason]

Sure

[magic knoll]

is haese green book for math aahl gud?

[trail hemlock]

ong yess i love this dude

[maiden glen]

unique and extensive proof writing books for self study?

[molten gulch]

Velleman's How to prove it, Hammack's Book of proof

[gray gazelle]

Hello there, I am searching a book for discrete maths, I get Concrete Maths but I feel sometimes the level is too high for me in some aspects

[trail hemlock]

what is concrete math out of curiosity

[gray gazelle]

Math to lay concrete roads

[tender river]

a book by knuth

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

[median fossil]

From the Springer series Graduate bricks in mathematics?

[gritty gale]

so i graduated a while back and ive been wantng to get back into things by having another crack at my weakest subjects so i guess what im asking is if there's a good angle to attack electromagnetism from as somebody coming back (i'd ask the physics discord but they want my phone number)

also idr what i was reading last time around. i think it was probably just the course notes with supplementary tipler+mosca

[median fossil]

I'd recommend either Purcell or Griffith

[gritty gale]

oh yes

griffith. i remember griffith

well. i remember it existing. idr how much i used it

ok i'll try those thx

[maiden glen]

thank you

[molten gulch]

yw

[maiden glen]

have you any good introductory universal algebra texts for self study too?

better yet

[molten gulch]

UA? no

[maiden glen]

differential equations?

[molten gulch]

Boyce and DiPrima Differential equations and boundary value problems; Nagle Fundamentals of Differential Equations

[maiden glen]

thank you

[remote ginkgo]

jackson maybe

[gritty gale]

isn't that more suitable for graduates who were good at it the first time round?

also while ur here what do u think of using feynman?

[remote ginkgo]

idk i learned from it

[gritty gale]

ah fuck how is it 1am already

[remote ginkgo]

i think feynman and susskind both leave out too much

[gritty gale]

shit

[gritty gale]

ic. what about grant?

[remote ginkgo]

i would say probably landau is the 'graduate book' that is maybe too hard for young people

idk who grant is

[remote ginkgo]

but one should aspire to it anyway

[gritty gale]

tru but one should also aspire to not being thoroughly mediocre the first time around. but here i am

[gritty gale]

this baby?

anyway im gonna sleep. thx for the advice

[remote ginkgo]

hm idk it

[remote ginkgo]

i didnt study physics at school fwiw

other than a graduate quantum class i took

[livid lintel]

Any good book on the history of magick and that sort of practice?

[molten mason]

Yea

Griffiths is a pretty standard undergrad text, Jackson is pretty standard graduate text

Jackson isn't exactly user-friendly if you don't know how to get the answer... like you should probably review a few things before going through it.

[foggy quest]

"Introduction to Differential Equations" here: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/

[drowsy nacelle]

Any recs for diff eqs from a more Lie theory standpoint?

Preferably something that has a good amount of computation problems as well

[trail hemlock]

i read that in captain holt's voice

[remote ginkgo]

olver

is the only "proper" one

i and a friend went through like half of the book and are familiar with the subject as lie knew it, but another friend of mine finished the book and does research in that area now and says that the later parts are rehashings of the earlier parts on steroids

and are way more powerful

it has lots of computation problems

there are other books that are not as deep, like hydon's, which can be a source of good easy practice problems too

this is olver, the main one that covers the history & methods

here's hydon

the difference in exposition is pretty insane, hydon basically has like 5% of the content

no development of the theory at all

regarding that friend i mentioned who does research in this now, his undergrad advisor apparently wrote some books i am seeing for the first time now, which talk about this. don't know what's in them, but might be worth a look as well

there are various collected papers published from conferences you can find around

[drowsy nacelle]

thank you for these details, i'll check these out

most likely i'm not gonna use only one book regardless esp for problems so this is helpful to know

[remote ginkgo]

sure, sure

i will say the whole first chapter of olver you can likely skip

he just covers basic analysis on manifolds there

[drowsy nacelle]

ah okay

yeah i'll probably just assess as i go

[remote ginkgo]

and right after that it gets pretty immediately computational & interesting

he's a great writer ^_^

[drowsy nacelle]

damn let me take a look at oliver

this def sounds like what i was asking for

[remote ginkgo]

i had some trouble when i tried to go a different route, looking at equivariant diff eqs

like in the vein of golubitsky

i didn't find much interesting there, though this was likely mostly because of writing style

[drowsy nacelle]

yeah, its taking a little bit to download but im hyped to check this out

[remote ginkgo]

it was too algebraic -- the olver approach is directly what Lie himself was doing originally & is extremely geometric

[drowsy nacelle]

yeah fair

yeah looks quite good @remote ginkgo

i'll check the others you mentioned as well

[queen fog]

^ deleted my message, moving it to groups chat (to avoid cross-posting)

[maiden glen]

any pirate copies?

[daring silo]

Is Schilling's book good for measure theory? I finished Rudin's Principles of Mathematical Analysis and now I want to learn measure theory

This book: https://www.amazon.com/Measures-Integrals-Martingales-René-Schilling/dp/1316620247

I know essentially nothing about measure theory but in the preface the author says

I tried to avoid topology and, when it comes in, usually an understanding of an open set and open ball (in R^n ) will suffice
And I'm not sure if this is a bad or good thing. Rudin's book had a chapter about topology

[livid lintel]

Don’t ask here, ask Anna

[foggy quest]

there are

[foggy quest]

libgen dot rs

[livid lintel]

Wait saying that out loud is allowed?

[tender river]

no

delete the above conversations

[foggy quest]

it seems good.

[foggy quest]

You can look at Folland's book for Topology/functional analysis background when you need it.

[daring silo]

Okay, so I will use this book as the main source but also look at Folland's and Gogachev's books

[maiden glen]

libgen is overrated

thank you though

if libgen has it then anna must

[queen fog]

did you ever read How to Think About Abstract Algebra by Lara Alcock?

[remote ginkgo]

idk

[nocturne swallow]

so as a high-school student I face a problem that is losing old rule like in geometry algebra coordinates and stuff (sorry for low vocab) so what i need is generally a summery that just hold the rules

[remote sparrow]

yes

[remote sparrow]

if nothing else, schilling has written a full solutions manual freely available on the web for everyone

[daring silo]

I found the manual but for some reason the solutions are wrong

[queen fog]

thank you for answering, what did you think about it?

[daring silo]

For some reason I can't send images here but I can send images in other channels

[remote sparrow]

i think it's good

[daring silo]

The first exercise of this book is to calculate the area of a circle and the solutions show the result 2πr^2 lol

Then in the solution to another exercise he uses a geometric sum r/2^(n - 1) from n = 1 to infinity, and says it is equal to r

Is this really the author's solutions?

[queen fog]

i did a search on the server and saw that you mentioned it. would you care to share anything you liked from the book? i am thinking about buying a copy. i thought that it looked like it could be a good supplement to a standard abstract algebra book.

[daring silo]

Well for some reason the one I just found online doesn't have this mistake

[daring silo]

But it has this one

Here is is: https://motapa.de/measures_integrals_and_martingales/solutions-mims-2e.pdf (not piracy)

Look at the sum in the solution to problem 1.3

[frail hollow]

If anyone is interested in tensor calculus, I recommend Tensor Calculus for Physics, by Neuenschwander

[trail hemlock]

$\oiiint$ himself

[hasty eagle]

BlackBeard

[trail hemlock]

!bookrecs

[hybrid sparrow]

Check out the official Mathematics Discord website, or ask in #book-recommendations. If you want to submit your own book review, please DM ModMail.

[trail hemlock]

...doesnt have it, nevermind lol

[daring silo]

These is no way to reach this page starting from the site's homepage

[trail hemlock]

its hiden

🙈

[sonic hill]

Hi

[tall karma]

any recommendations for introductory texts on convex optimization?

[gray gazelle]

Any recommendations on rigorous Analytic Geometry?

[primal zodiac]

any recommendations for pre-univerisity maths (11th std) preparing for a competitive exam called IOQM

[trail hemlock]

looks to be amc/aime level, so the aops serise would prob help

Aops Intermediate Algebra, Geometry, Number Theory are all good

as well as vol 1 and vol2 as reference

[trail hemlock]

well actually its a bit higher than amc

mid level aime or HMMT or SMT more likely

[leaden lark]

I am prepping for it too

nice to find someone who knows about it

[livid lintel]

Book on mathematical simulation for biology (or just general introductory book on that)?

[vital bane]

what do you mean by "mathematicial simulation for biology"?

Do you mean something like this? https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#Variations_on_the_basic_SIR_model

[livid lintel]

Sorry I meant mathematical modeling, yeah something of that sort

[stable flicker]

There's multiple math modelling books, but I don't know about any that specialise in biology

[stable flicker]

Brauer and Castillo-Chavez is well-cited, but I can't find any academic reviews. Amazon reviews says it's ok.

[livid lintel]

Thank you so much

[stable flicker]

https://www.math.unl.edu/~jlogan1/MathBioS07.html
Try the one listed as Textbook first, rather than the references? Brauer and Castillo-Chavez is listed here as a reference

[primal zodiac]

Thank you

[narrow relic]

It's dense but good. It does help to know about topology but I think you can do without it if you've seen metric spaces. The topology helps for understanding his definition of the Borel sets.

[daring silo]

Cool

[narrow relic]

I've worked through a number of chapters of it.

[daring silo]

I skimmed over the first two chapters yesterday since they are things I already know (operations on sets, countability, etc)
I might actually start studying today

[narrow relic]

Oh, I just saw you mentioned you've worked through the Rudin book, you'll be fine then if you have studied some linear algebra as well.

To understand the d-dimensional Lebesgue measure material you need to know linear algebra (and probably for some of the other things I didn't get to).

[narrow relic]

Great! 🙂

[fickle whale]

Is there a book all about algebras over the quaternions

[remote sparrow]

https://math.dartmouth.edu/~jvoight/quat-book.pdf

also available for purchase from springer

https://link.springer.com/book/10.1007/978-3-030-56694-4

[fickle whale]

Is this what I asked for? I'm not sure

Precursory glances seems to me that it discusses Quaternion Algebras over a Field(/Ring?)

I'm referring to Algebras over the Quaternions

Are both included?

[fickle whale]

I.e. M_2(H)

A quaternion algebra over the quaternions, maybe a bad example

But obvious how to generalize

[fickle whale]

Regardless of whether this is what I asked for, I do quite like what I've skimmed so far and I thank you!

[marsh ingot]

Oh

[haughty walrus]

@maiden glen What's that pfp? It's something about math?

Anyway, i need recommendations for Analysis books. Maybe something "international", that I can find in Europe.

[maiden glen]

try Terence tao's analysis 1 and 2

[haughty walrus]

I need something exactly for analysis 1, thank you.

[remote sparrow]

#book-recommendations message

[sudden kindle]

Jaquet Langlands

[fickle whale]

I'm sorry?

[sudden kindle]

From Wikipedia: Jacquet–Langlands correspondence is all about "relating automorphic representations of GL_r(D) and GL_{dr}(F), where D is a division algebra of degree d^2 over the local or global field F."

[fickle whale]

indeed

[fickle whale]

no way is that like

exactly what I'm asking for

[gray gazelle]

hi

is linear algebra by georgi shilov considered a good book

i know general & basic stuff about the topic

[loud cradle]

it is a good book, a bit unusual because it starts with determinants

[gray gazelle]

yeah that was surprising

good thing i already know about them

thanks bungo

[molten mason]

A couple of people in the server have gone through the book, it's a good book

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[fresh skiff]

Is using Munkers (Topology) and Lee's book (Topological manifold) together a good idea?

[trail hemlock]

Munkres topology or analysis on manifolds

[gritty cloak]

Hi

Best book for jee mains

Trigonometry

[fresh skiff]

Munkers Topology

[trail hemlock]

is there a syllabus for the trig covered on jee ?

a book like this
https://www.amazon.com/Skills-Mathematics-Trigonometry-Main-Advanced-ebook/dp/B09RJZ8LRQ
is prob ur best bet

responses to this quora post seem to be in line with your request

[minor shoal]

Greetings everyone. Excuse me, why is it not possible to download the worksheets?

[trail hemlock]

seems to work for me

[minor shoal]

Do you know is there another way I can download them? It's seems impossible for me, I'm afraid

[gritty cloak]

S

[minor shoal]

What does "S" mean?

[molten mason]

This is free and online

https://mecmath.net/trig/

[molten mason]

Are you on mobile?

[molten mason]

That whole website doesn't work for me when I'm on Mobile, nothing opens up. I have to open the website on a computer for it to work.

[minor shoal]

I think you might be right. You're correct, I'm on mobile. I will try on my computer now. Thank you so much, Sal!!

[vital bane]

Sal...from Khan Academy

[tribal crow]

[molten mason]

What

[vital bane]

The guy who made Khan Academy is "Sal Khan"

short for Salman Khan

[willow merlin]

Wdym

[brave burrow]

Good to know. The guy who made Khan Academy is Khan

[molten mason]

Oh shit

Ghengis Khan really be making an impact centuries later

[trail hemlock]

o nah

HIGHER!

I SEE U

[tribal crow]

perhaps Salagos is Sal Khan

hello BlackBeard

[trail hemlock]

🫵

higher!

[tribal crow]

this is #book-recommendations, just a heads up

[gray gazelle]

Book recommendations for ML math? I've already taken calc, probability, and linear algebra. mainly looking for a refresher and optimization

[maiden glen]

my not so light review of the review of d&f's abstract algebra book therein server website may have been a misunderstanding of the intention of the reviewer or the sources

the review is likely assumes the reader is capable of the abstraction, and modeling that comes with abstract algebra

then omitting elementary algebra and calculus as prerequisites for obvious reasons

especially since the "new math movement" was not too long ago

[trail hemlock]

d&f is boring

use artn or jacobson

[maiden glen]

overrated texts

[trail hemlock]

who needs melatonin gummies when yo have d&f

[trail hemlock]

expand on this

[maiden glen]

d&f is good

[trail hemlock]

i didnt say it wasnt food

good

its just boring

[maiden glen]

okay.

[maiden glen]

they're popular and people recommend them out of bias

often

[molten mason]

This is a common sentiment I hear

[maiden glen]

uncannily so

it was also uncalled for

[molten mason]

Also on the basis of abstraction in general, some people have an intuition for algebra or analysis. Abstract algebra comes easy to me for example, so I feel that's user-dependent.

[maiden glen]

that's exactly what I was saying

[molten mason]

Nah, part of book recommendations is what will help someone learn the subject. For some people, this matters greatly. If they can't get past the first chapter without falling asleep, then they won't learn the material. Other people ||(Lang gang)|| this is irrelevant.

The boring level of a book means absolutely 0 to me, but I still let others know how the motivation is inside the book in case it matters to them.

[trail hemlock]

help wait i like lang 😭

[molten mason]

Their second comment if you scroll up

[molten mason]

but you find D&F boring?

[trail hemlock]

yeah

[trail hemlock]

whoops didnt see that, sorry becoming !

[trail hemlock]

lang had nice exercises

like wait lemme

[loud cradle]

D&F is boring, of course
it's good though

[molten mason]

Yeah

[trail hemlock]

ok idk where my pdf went

but hte problems arent really interetting

jacobson has nicer problems imo

[molten mason]

I haven't gone too much into D&F except skimming some parts, but the general opinion agrees with that

[loud cradle]

jacobson seems too hard for an undergrad course though

[molten mason]

I don't mind hand-holding, but I hate when textbooks are unnecessarily wordy. I just want the knowledge, then exercises to apply that knowledge, then to move on.

A lot of "reference textbooks" I like for that reason

[loud cradle]

i don't think it's unnecessarily wordy for the amount of stuff it covers, i just think it covers too much to be a great first book if you want to learn primarily from the book

[trail hemlock]

yeha thats why i like lang

granted it may be boring

[molten mason]

Aluffi and Hungerford are pretty good in that regard though I think?

[trail hemlock]

but he doesnt waste a lot of words

the psets are interesting and not obvious (to me lmfao)

D&F has like 2 paragraphs of yap which is alright, its just not what i like.

[molten mason]

To none of us

[loud cradle]

i haven't read aluffi, i've read a bit of hungerford, but only after i knew some algebra
(also, i think there may be more than one book by hungerford?)

[heady ember]

Why have exposition when you prove everything yourself and ask yourself questions, which you then answer yourself

[trail hemlock]

then again, i dont really know algebr well enough to comment on textbook A vs textbook B in terms of coverage.

[molten mason]

Oh maybe, to be fair, Aluffi and Lang both have two algebra textbooks, one is more "intro" and one is more "advanced"

[trail hemlock]

doing this with rudin

[loud cradle]

ah ok i only know the "obvious" ones by aluffi and lang ig

[trail hemlock]

line of questioning has lead me down a 3 hour path

but

i dont wanna leave

[heady ember]

Rookie numbers

[trail hemlock]

so ive devcided to forget abt sat practice and just do rudin a little bit longer

[heady ember]

Mfw proving one theorem becomes a whole problem set

[trail hemlock]

yeah

[heady ember]

It's fun though

[trail hemlock]

rabbit hole of l-hop

and i tried a bnunch of bullshit with neighborhoods

[molten mason]

Chapter 0 is the Advanced one, Notes From the Underground is the Intro one

[trail hemlock]

which lead nowhere

😭

[heady ember]

I like reading books this way. Its way more fun to me than just reading it and being like "oh ok."

[trail hemlock]

"yep... that sounds about right"

dude i tried to prove a random theorem yesterday in a way differnt to rudin

[loud cradle]

ah, i was thinking the first one, i vaguely recall that the other one exists 🤣

[trail hemlock]

like completnle diff

it was really fun

but challenging

:(

[molten mason]

I like the journey, and then going back to something a few chapters back and having the "oh ok, duh" moment lol

[maiden glen]

sat?

[trail hemlock]

yeah

im in america so i gotta do sat

[heady ember]

Yeah

[maiden glen]

how old are you

[trail hemlock]

16

im old :(

[heady ember]

For instance, I couldn't prove that all perfect subsets of reals were incomplete. But then I proved Baire's theorem and used that result to prove it

pretty nice

[maiden glen]

evidently you think you're too old for something

perhaps recognition?

[trail hemlock]

nah

all these newgens

8th and 9th grade

learning more stuff than ive ever learned and ever will learn

cough arti cough

[maiden glen]

how old are they

[trail hemlock]

14

[maiden glen]

i assume you mean the fox person

[trail hemlock]

no

their @ is springonion smth

[molten mason]

I'm not at Baire's theorem yet

But that sounds enlightening

[maiden glen]

chmology?

[molten mason]

Yeah

[trail hemlock]

wait arent perfect subsets of R complete?

[molten mason]

He's 14 doing like grad-level math

[heady ember]

oh typo

I wanted to write

uncountable

[trail hemlock]

yea cuz

i remember making a joke abt

[heady ember]

idk how I made that typo lmfao

[trail hemlock]

"you are perfect just like subsets of R"

whoopsie daisy

[heady ember]

[trail hemlock]

lmfao

idk my questions just arent interesting enough for me to answer

maybe im not creative enough for ts

[maiden glen]

guy's around my age assuming month gap

not very impressive

[molten mason]

I'm like twice y'all age, not doing grad-level math

[trail hemlock]

bro is ancient

gramps

[maiden glen]

obviously impression isn't what he's seeking

i assume

[trail hemlock]

?

[maiden glen]

i said "not very impressive"

it was unnecessary

that may not be a quality he's pursuing

[trail hemlock]

i mean ok?

[maiden glen]

depends

it's a regurgitated review

you can find something like that everywhere in this channel

an apparent trend is that: assuming the user exhibiting the review has been a member for at least a year, you are likely to have established some sense of ignorance in passion

within that time you will have seen a review not very different than your own of the present day

now assuming the user is new to the material

you become optimistic when you see some promising looking guy with a promising looking role throwing out reviews

so you read it with this initial optimism and it eventually evolves into a perhaps faulty conception of "semi-original" understanding

then you regurgitate the review about 5 months later because you're comfortable with your newfound conception

my point is

they are overrated herein

now I could use a good and long number theory book for self study

im feeling theoretical.

[trail hemlock]

https://tenor.com/view/yapping-yapping-level-today-catastrophic-yapanese-gif-13513208407930173397

[molten mason]

What exactly do you mean from that entire paragraph you wrote?

The reviews in this channel aren't adequate? Or are you concerned that people are giving reviews without knowing the material first-hand? Or something else?

[molten mason]

This depends entirely on your background, and which NT. Do you want theoretical elementary number theory? Have you done any before?

[gray gazelle]

I gotta say, I have an envy for people above my level. But I don't think achievement score (which level of math you are doing) transfers directly to aptitude. People lie to you or mostly to themselves when they say they are doing blah blah blah. They don't know if they are good at blah blah blah, they are just doing blah blah blah for the sake of doing it. If they got into a real college, they will doing everything anew with guidance. So doing blah blah blah doesn't mean a lot. To conclude, don't compare. You're the BEST!!!

That being said, lots of kids claiming to be doing grad level stuffs, might not be able to solve grad problems at a grad ability

I knew a guy who's 13 and claiming to be doing QM. I only got to find out how he's lying to me a year later. Now I blocked him.

[trail hemlock]

doing? i prefer "struggling through"

like rudin, his fucked up sense of humor, and whatever the FUCK he was doing whne he wrote his proof of l-hospital

[gray gazelle]

Rudin is quite selective at his contents. He talk about things he is familiar with, but seems like he is not making a comprehensive approach

[trail hemlock]

but my pookie wookie precious math stack exchange

(the apple of my eye)

hath saved me

[gray gazelle]

Well yeah, everything is available there for PMA

Almost

[trail hemlock]

in excruciating detail

like this is amazing

[gray gazelle]

Indeed

Amazing

[trail hemlock]

anwyay

back to regular book-recs

[gray gazelle]

I am using Zorich analysis and baby Rudin together. I am only using baby Rudin because it got lebesgue measure which I'll need for Papa Rudin.

Like Zorich is fr a canonical mathematical analysis textbook!!

Hoffman Kunze also!!!

for Linear Algebra!

[trail hemlock]

im using baby rudin, and the uc davis companion notes

when rudin stops making sense, i look at the notes proof

[gray gazelle]

I see, baby rudin has a complete solution guide, you know that?

[trail hemlock]

yeah ill bet

it was published in 1953 (1st edition) so i hope theres a soln guide

[gray gazelle]

Yes there is!!!

Let me send the Amazon link!

https://www.amazon.com/Complete-Solution-Principles-Mathematical-Analysis/dp/9887879711/ref=sr_1_1?crid=330D82D16TW4S&dib=eyJ2IjoiMSJ9.7DmSdtpqRqE_xBtaxGdNEfJGVAer3vgwz8QIA4mcyGgcsfAkXUOWhCdb6Im918JaGYzSI0F5UWXLrLnoJ6j7CA.XSau_f2pVDu5d7MmZ2FykOGuxaFJhhsSTHSnONLGJXo&dib_tag=se&keywords=rudin+solution+guide&qid=1722147961&sprefix=barudin+solution+guide%2Caps%2C483&sr=8-1

[trail hemlock]

oh cool

used for 13 dollars, not bad

usually when i need help with a hw, ill just ask a friend in uni

[gray gazelle]

Nice that you have friend in uni, I don't

[trail hemlock]

well theres mathcord

mathcord is your collective friend in uni

[gray gazelle]

Well yeah lolol

[trail hemlock]

oh wow this same dude wrote a soln guide for all of rudin's books

[molten mason]

Amazing

[gray gazelle]

I actually pirated it somewhere lol

[trail hemlock]

yo thats illegal

big corporations have feelings too

[gray gazelle]

I am in a we call Greyzone Country

[trail hemlock]

oh ic

[gray gazelle]

China

Lol

Anyways

Let's get back to legal stuffs

[trail hemlock]

[vital bane]

okay BlackBeard

I'm sick and tired of this D&F slander

watch your back.

[trail hemlock]

you could say that now i am your nemesis 😭

[molten mason]

You can give becoming your D&F review then

[trail hemlock]

good luck

[vital bane]

i have no enemies

[trail hemlock]

i read the text on the gif too

smh

[vital bane]

D&F is the best UG algebra book of all time

[vital bane]

it didnt load for me lol

[trail hemlock]

lmfao

[trail hemlock]

i just find the exercises in jacobson to be more fun

[heady ember]

our*

[trail hemlock]

yeah fr

[remote sparrow]

fyi, most think baby rudin is not good past chapter 8

[proven lantern]

I see. Thanks for the info.

[grand gulch]

https://reactormag.com/excerpt-the-quantum-thief-by-hannu-rajaniemi/

[gray gazelle]

when does your perma-studying! role ends?

[trail hemlock]

in a year

[gray gazelle]

in November 7

[fresh skiff]

I have friends but none can help with math stuff lol
Even not teachers (we don't have pure maths teachers , and TAs used to watch YouTube videos before lecture and then they improperly deliver the lecture (if someone asks question, they say use Google lol) -- Except ODEs I can't remember which other subject we studied correctly

[molten gulch]

Hey chat. We've recently considered rebuilding our arithmetic foundations a bit and so were wondering if anyone has any problem sets or even a light book discussing the complex numbers and the complex plane. Many books on complex variables and analysis that we have also cover the material in an introductory section but we'd like a little bit more than a chapter discussing the properties. We know overall they're quite simple but at times we struggle actually doing calculations with them.

(No khan academy or such, we'd just prefer having a book so that we can review it when we're offline too or can just put the PDF into our book folder)

[maiden glen]

why do you have "perma- studying" but still talk

[maiden glen]

thank you

[gray gazelle]

#book-recommendations is the No access channel still

why would you talk when you study?

bruh

for sure sometimes you get out of the zone and come back

[maiden glen]

how do I know if I truly like mathematics and just hadn't tricked myself into liking it

like yinuo said

[stray veldt]

whats the difference

[maiden glen]

i like it and I hadn't liked it but want to think I like it

respectively

[stray veldt]

but in practice

[maiden glen]

how should I know if I truly like the practice and not just like it initially because it makes me feel better about myself

how do I know im not liking it for the wrong reasons

[stray veldt]

you probably just dont

[maiden glen]

don't what

[stray veldt]

dont know

[gray gazelle]

why does it matter?

[gray gazelle]

Any (HS) algebra or trigonometry books? Finished Basic Mathematics, already.

Prefer and appreciate rigor.

[scarlet saffron]

Hello, is there any book that could recommend to me to learn about functions of bounded variation in several variables?

[molten mason]

You'll enjoy this then

https://mecmath.net/trig/

[gray gazelle]

Thank you!

[molten mason]

That's the most rigorous book I know for HS Algebra though, but I think Sour has a couple of recs. Maybe AoPS? Not sure tbh

[gray gazelle]

Well, do you have any other algebra books in mind, in general?

[molten mason]

Nope. They're all the same IMO

You get a lot more algebra practice in Calculus. I would recommend just moving up to Calculus at this point.

[woeful rock]

The Spivak's Calculus and Bartle's Introduction to Real Analysis are at the same level of complexity?
And if want to study a more rigorous Calculus, which one I should choose?

[woeful rock]

It is worth reading Spivak first and then Bartle. Or even read them together?

[remote sparrow]

spivak assumes no prior exposure to calculus. it will teach you calculus. bartle does assume prior exposure to calculus.

[trail hemlock]

because, and this might blow your mind, nobody studies for 24 hours straight

[tribal crow]

a bold assumption you make there

[normal crystal]

methamatics

[scarlet saffron]

Hello, anyone can help me with this?

[gray gazelle]

Sure. I'll probably hit some AOPS books while I'm at it, though. Thanks for the recommendations, Sal & @woeful rock.

I believe Rapidoso recommended to me... lol.

[woeful rock]

WHAT?... I was asking as you XD

[gray gazelle]

Anyone have recommendations number theory? Currently struggling to get the grasp on number theory. I passed my class with a B but there are some holes in my knowledge

[molten gulch]

Our university uses Rosen's Elementary Number Theory

Personally we've also seen Hardy's Intro to the Theory of Numbers and Burton's Elementary Number Theory

Oh also Silverman's A Friendly Introduction to Number Theory

[gray gazelle]

Thank you. I will look into these

[gray gazelle]

I got confused, lol. You said “it is,” which made it seem like a statement. I presume, an accident. My bad.

[gray gazelle]

that's what I'm saying lol unless you're Einstein or maybe Gelfand

or any famous physicist

[molten mason]

Einstein enjoyed a lot of downtime and had hobbies, such as hooking up with various women. No one devotes their life just to study.

[remote sparrow]

one of which was his cousin!

[gray gazelle]

ah i meant to say isaac newton lol

[molten mason]

Call that relativity

[drowsy nacelle]

any recs for variational calculus?

[remote sparrow]

https://www.amazon.com/Calculus-Variations-Dover-Books-Mathematics/dp/0486414485

https://www.amazon.com/Calculus-Variations-Applications-Physics-Engineering/dp/0486630692/

[drowsy nacelle]

ty

[remote sparrow]

https://www.amazon.com/Calculus-Variations-Universitext-Bruce-Brunt/dp/0387402470

[proven lantern]

I think there isn't a difference.

Either way its kind of liking it. You are yourself, you can't trick yourself, Right?

[verbal furnace]

What would you recommend for ring theory, was going through T.Y. Lam A first course in noncommutative rings, but it feels like I am missing a lot of prerequisite knowledge on modules and ideals

[stoic sentinel]

what do ppl know abt linear algebra topics for a second course by shapiro

[remote sparrow]

maybe read dummit and foote

[verbal furnace]

Tyvm, I'll check it out!

[spice stag]

Can you tell me some questions resource for highschool level calculus which progressively toughens the questions ?

[remote sparrow]

i heard the standard text is Convex Optimization by boyd and vandenberghe

[daring lake]

Yes, I can also suggest that

[trail hemlock]

spivak

[spice stag]

Ok thanks

[fleet veldt]

what're the go-to book for linear algebra, real and complex analysis, partial differential eq, and harmonic analysis?

[grand gulch]

we used friedberg for lin alg, but people also like lin alg done right, lin alg done wrong

some combination of these

[fleet veldt]

thanks

[foggy quest]

Linear Algebra: https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ Real anal: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ Complex anal: https://mtaylor.web.unc.edu/notes/complex-analysis-course/ PDE: https://link.springer.com/book/10.1007/978-3-031-33859-5

[molten mason]

Linear Algebrq, Real Analysis, and Complex Analysis: Check the pins in this channel, Dami has a list for all three of these

[fleet veldt]

i found there linear and real analysis but not complex

also is harmonic analysis a niche subject? i don't see it discussed much

[fleet veldt]

thanks for that!

[fleet veldt]

btw is there some big book that deals with both ode and pde in great detail for both?

[cursive orbit]

depends what you mean by on great detail

[fleet veldt]

enough for new student (EDIT: sorry not sure it was the fitting word) to UNDERSTAND (caps in purpose) both subjects well

[cursive orbit]

Taylor deals with ODE in his pde book in chapter 1 in sufficient detail

but if you are undergraduate level you should not be using Taylor as ur PDEs book

[fleet veldt]

I'm a first year and we skipped a lot of content so i want to understand what we didnt learn

[vital bane]

how much of ODE theory is used when studying PDEs? it feels like PDEs are a whole another beast

[fleet veldt]

undergraduate means first degree, no? or is it something else?

[vital bane]

So you want a ODE/PDE book that is computational?

[cursive orbit]

for like a standard graduate course, only thing I needed was like existence and uniqueness and smooth dependence

[vital bane]

I see, yea PDEs seems way different

[vital bane]

yea it's like your first college degree, it's also called "Bachelor's degree"

[fleet veldt]

i want a good mix of computational and theory, i love theory and see how things were derived

[molten mason]

#book-recommendations message

I don't know anything about ODE and PDE textbooks. I'm new myself to the Harmonic Analysis rabbithole to discuss anything confidently about that either but I will say yes it's pretty niche.

Like my uni uses an in-house for ODE, Strauss for undergrad PDE, and Evans for grad PDE.

[vital bane]

I wanna find time to do Strauss

it seems like an interesting book

and useful for physics people

[fleet veldt]

i want time in general lol, im just writing these books for myself and hopefully someday i'll have time to review them

[foggy quest]

There is an intro to ODE here: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/

[fleet veldt]

im procrastinating learning for an upcoming test that i just don't see myself passing, i hate it when that "anti-motivation" vibe settles

[molten mason]

Yeah that's one thing I think I want to do self-study and not as a required class lol

[short urchin]

This has been asked 143894389^3 times but guys

Is it possible to self-study stewart's calculus book?

Or is it written for classroom settings

[ruby lodge]

Howdy math people! I want to learn multivariable/vector calculus rigorously, but without learning abstract differential geometry (i'm first year undergrad, i've got a solid understanding of basic real analysis, by which i mean like all of Abbott, the first 4 chapters of munkress topology, and some basic linear and abstract algebra algebra). I can't seem to find a book, i either find very simple and computational multivariable calculus books or stuff that is too advanced

[grand gulch]

khan academy

spivak calculus

[ruby lodge]

I can find some theorems and proofs here and there, but for some topics it's really hard to find a rigorous construction or proof (e.g. divergence theorem of greens theorem)

Khan academy is not rigorous enough, it's just intutition and computations

[grand gulch]

sorry i cant read

spivak covers vector calc i think

[ruby lodge]

I think you're talking about Spivak's calculus on manifolds, because i read the calculus book and it stops at series of functions

I'm gonna give it a try

[remote sparrow]

hubbard or shifrin

[grand gulch]

maybe check https://www.amazon.com/Vector-Calculus-Paul-C-Matthews/dp/3540761802/ref=sr_1_1?s=books&sr=1-1

[cursive orbit]

try Terence Tao Analysis II, or Pugh's book

for vector calculus, you can certainly prove the main theorems without learning differential topology, but honestly it's not really worth reading an entire book for that, you can probably find the proofs somehwere online

[short urchin]

Hello guys please answer my question too :/

[cursive orbit]

yes

[short urchin]

Really? Book looks like it has very brief explainations and is written for a classroom setting

[cursive orbit]

the book is over 1000 pages, so I'm not sure what you mean by "brief explanations"

[short urchin]

Majority is figures and pictures?

[gray gazelle]

the questions are good

[cursive orbit]

not really

[gray gazelle]

just try

[cursive orbit]

^

there's very few books that are less concise than stewart's book

[molten mason]

Yes, maybe even better. The classroom speed runs the book and skips a lot.

[short urchin]

I have a hard time believing this, but I will give it an honest try and report back to you guys

[molten mason]

Apostol Volume 2

[short urchin]

Can I use apostol instead of stewart? or is apostol more like analysis

[remote sparrow]

you can

[short urchin]

O.o

[molten mason]

Quizlet Plus has a walk through of every problem in the textbook, both even and odd. Pay the $8 USD a month for it or just use random emails for the free trial.

There's a million Calculus lectures on YouTube and there's Paul's Online Notes. It's not bad.

When I took Calculus in University we used stewart all 3 semesters and I did the class online, our instructors didn't give us any lecture they basically told us to watch YouTube and gave us assigned problems and skipped a lot of sections in the text. So we all pretty much did it directed self-study

[molten mason]

Apostol is great

[short urchin]

WOW

You're a great help Sal!

I am more interested in pure math, but my primary goal is to get into university and pass the entrance exams which requires calculus, I am not sure if it's better to use Stewart or apostol, the problems look like this:

cant embed image :')

plz let me send one image 😭

[molten mason]

I don't know if any of us can answer that, look through both and see which one you understand easier.

[short urchin]

I want to know which book is more in line with the problems of the entrance exam

[molten mason]

Like Stewart does have a lot of proofs in it

[short urchin]

Oh

[molten mason]

Send the image in #chill

[remote sparrow]

stewart will probably have problems that are more like the ones in your entrance exam

[short urchin]

Ahh okay thank you½!

[short urchin]

Done

[molten mason]

Yeah either one is fine

I would say for you, just stick with Stewart for now. You can supplement with Apostol later

[short urchin]

Which stewart book is it? he has so many versions and early transcendentals

[cursive orbit]

in practice the version doesn't matter

because basically all that happens between versions is exercises get reordered, and the pages get reformatted slightly

[short urchin]

lol

edition doesnt matter either?

[cursive orbit]

yeah that's what i meant

like the difference between the n and n + 1 edition is that problem 6.11 is now 6.12

[short urchin]

Ahh okay, I meant versions as well he has two versions Calculus and Calculus: Early Transcendentals

[molten mason]

Early transcendental, any edition

The most recent editions are on Quizlet Plus

[acoustic turret]

I am going into grade 12 and will be taking advanced functions as well as calculus and vectors. I loveself teaching myself and thought it would be a good idea do learn on my own a bit to prepare for my final highschool year. Is there any good textbook anyone reccomends for this. I know khan academy has good stuff but I generally prefer books. Something that I could read and then do any excercises it says. Thanks.

[short urchin]

signing up on quizlet plus now

[molten mason]

We're in the middle of talking about Stewart's Calculus textbook, very commonly used. You can scroll up to see what has been said.

[acoustic turret]

ty

[short urchin]

huuh

it has solutions

[molten mason]

With explanations on how to get to the solution, yes

[short urchin]

Oh I had to press show steps 🤦

[slender wasp]

How does chegg compare to quizlet?

[molten mason]

Quizlet feels more like an official textbook solutions guide. Select your textbook, select chapter, select question number: follow walkthrough and solution.

Chegg felt more like quora, open questions, multiple possible answers, some are wrong. Great for randomly generated homework questiond though like from WebAssign

[marsh ingot]

Some book to start with differential algebras?

[drowsy nacelle]

any recs for generating functions

ik about wilf so i guess other than that

[foggy quest]

Is Lie groups and algebras part of that? https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/

[gray gazelle]

Hi, I’m looking for a book recommendation, I’d like to study Categories (Category Theory Categories) of simple graphs (I think they form the category “SimpGrh”). Is there a book dedicated to this? If not, are there any books that go into some level of depth of this Category?

[trail hemlock]

bro someone answer dude has been asking for a while 😭😭

[gray gazelle]

Oh, this channel wasn’t listed, I had to search, thanks.

[rain hound]

Godsil and Royle Algebraic Graph Theory is really good. Not everything is done as category theory as possible but they dress it all up in the categorical language. Very algebraic. Filling in the rest of the category/nlab style stuff as desired is no trouble.

It’s also just a really good graph theory book period.

[gray gazelle]

Thanks!

[rain hound]

Oh another word I can share is Quiver. Feel free to look up any formulation of graph theory using the word quiver. It realizes a general multidigraph as a certain functor from the free quiver. Graph homomorphisms then are exactly natural transformations between these functors.

[gray gazelle]

Okey, is that similar to a sheef?

Oh, nvm

Okay, yes, also, does the HOTT book have any graph references that anyone know about?

Also, yes, a quiver, great suggestion.

[thin needle]

Recommend some books on probability

[marsh ingot]

Idk thats why I was asking, but I gonna think that yes. Thanks for the link

[sacred nova]

Do you guys think that Tao's Analysis II book is good for Analysis in R^n? or at least for its basics?

[spark jay]

Best books for calculus

[signal mountain]

stewart or thomas for more computational first pass
spivak or apostol for rigour

[spark jay]

Thanks

[sudden sparrow]

hey anyone know a good book for amc 8 or amc 10 test preparation

[foggy quest]

looks fine

It covers similar material to other similar books on this topic

[sacred nova]

okok, ty L!

[rain hound]

Probability theory by Rozanov is good. I also recommend Axler’s Measures Integration Real Analysis to learn measure theory (and it’s a good exercise to rephrase everything from Rozanov in terms of this).

After that feel free to go wherever you like, there’s a lot of possible directions for probability.

[rain hound]

Yeah it’s really good for that imo.

[sacred nova]

Thanks!!!

[untold pecan]

Bertsekas for beginners. There is also Grimmett as a standard reference. Shiryaev is for theoretically minded.

[rain hound]

Calculus made easy by Silvanus thompson for basic calculus (freely available online). For the rest I like to just use a math methods book. The multivariable calculus and vector calculus chapters of Mathematical Tools for Physics by James Nearing is really good. You can also check out David Tong’s lecture notes on vector calculus.

Both are freely available online if you just search for them

[spark jay]

Thank you for the recommendations I'm thinking to start with Thompson

[gray gazelle]

"Calculus: Early Transcendentals" by James Stewart, "Calculus and Vectors" by David G. H. O'Sullivan, "Advanced Functions 12" by M. L. B. Fitzpatrick, "Precalculus: Graphical, Numerical, Algebraic" by Franklin Demana, Bernard B. Price, and David L. Cohen, "Vectors and Matrices" by John B. Fraleigh

[open gorge]

http://christophebertault.fr/cours-et-exercices/ a website who contain courses of "prépa MPSI/MP2I", it's like very high freshman math level courses

[primal mica]

i am trying to get good at Real analysis and related proofs, is there a book you guys would recommend to me, to get a touch of what these proofs are like and get better?

[molten gulch]

What books have you used for analysis so far

[primal mica]

I tried to do some competitively and read Putnam and Beyond, but its still out of my reach

[molten gulch]

Have you completed a course sequence in calculus yet?

[primal mica]

yes

i am proficient in calculus

and differential equations

[primal mica]

calc i calc ii

and i did some complex analysis too

i havent learned entirety of calc iii but i understand it so far

[molten gulch]

Okay, then if you want to do real analysis specifically, pick up a book on proofs like Velleman's How to Prove It or Hammack's Book of Proof (Hammack's book is free) (if your proof skills aren't very good) and then pick up something like Abbott's Understanding Analysis for basic RA

[primal mica]

alright

[molten gulch]

Beyond that you can then go through the problems in a book like Rudin's Principles of Mathematical Analysis and well...from then there's a few paths you can take but focus on the basics first

[primal mica]

alright

thanks

[remote sparrow]

https://stat110.net

[molten gulch]

Blitzstein and Hwang

[molten gulch]

Goddangit you beat me to it

[upper iron]

Hey friends, I am starting to be fascinated by Mathematics.
Aside from that I will soon be starting college as an industrial engineering major.
What books would you recommend me based on the above?
(Mathematics, Physics and Accounting)

[normal crystal]

your major probably has most of that locked up for the next two years, have you looked at what they use

[willow merlin]

Easiest topology book

I need handholding im new

[remote sparrow]

https://www.topologywithouttears.net/

[trail hemlock]

https://artofproblemsolving.com/wiki/index.php/How_should_I_prepare%3F

[upper iron]

Chemistry: general and organic
Mathematical analysis: Integral and differential calculus
Mathematics: Linear Algebra
Physics: I, II

These are the subjects of the first second cycle (the first year).

I would like books that help me to prepare myself and see a little above those topics to be aware and defend myself (and stand out from the others xd).

[glad lodge]

Alright I’m curious if anyone could help recommend to me a list of books that could take someone from beginner all the way into math professor level smart.

Opened to being @‘d since I’m not on discord much.

[molten mason]

If you see what the actual course numbers are called, you can Google the textbook normally

For example, Analytic Number Theory at Stanford is Math 155

So to find the textbook, I would Google Stanford Math 155 textbook or if I want to 100% make sure the search results have a textbook listed use quotes Stanford Math 155 "textbook"

[molten mason]

General answers for these textbooks you can use the search feature in the top right.

So you would type into the search bar in:#book-recommendations physics and you will see prior discussion and answers from prior people who have asked the question. I would do the same for chemistry and Ochem.

Calculus is discussed multiple times a day here, tons of answers. Common authors are Stewart, Thomas, Anton, Spivak, Apostol, and Kitchen.

Linear Algebra, check the pinned messages in the channel.

[upper iron]

Thanks for the information and advice

[upper compass]

Any algebra book recommendations

[marsh ingot]

Ig differential rings are included there right?

[heady ember]

If you're new to proofs/analysis, then reading Rudin first might be a bad idea. Fyi.

But otherwise, Rudin can be pretty good.

[trail hemlock]

i like pugh

[glacial crypt]

rudin is excellent if you are looking to refresh your knowledge

i personally find it quite good for that purpose actually

[molten gulch]

yeah that's why we recommended rudin after a book like Abbott

[heady ember]

Yes I know. I was just trying to make that explicit.

[zinc thistle]

someone answer this dude 😭

[remote sparrow]

@mossy flume

[mossy flume]

I do not know ramsey theory 😭

sorry

I know the statement of Ramsey's theorem and that's it lol

[normal crystal]

he needs to think outside the box
to get his texts recommendations

[hallow oriole]

gasarch, kruskal, and parrish have a nice purely combinatorial exposition of ramsey theory called "Van der Waerden’s Theorem: Variants and
'Applications'" although unfortunately it's unfinished and according to an email i sent gasarch a while ago it will remain so (still good, the completed portions are published on the umd.edu website for free)

graham, spencer, rothschild and landman, robertson have two elementary books as well. they're quite easy as books go, not terrible.

another really really interesting book is the mathematical coloring book by soifer, one of the most unique math books i've ever read.

[tribal crow]

valley

I was gonna ping you for this actually

[hallow oriole]

there's also an intro to ramsey theory: fast functions, infinity, metamathematics by katz and reimann, it's also decent

hiiiiiiii

ramsey theory at higher levels is more specialized and usually there will be dedicated books on the subject

if you just wanted an intro you could probably make do with any combinatorics book like stanley or bona or something

[trail hemlock]

bro FNALLY got his answer

after eons of waiting

[tribal crow]

valley is a true legend

[sturdy gust]

I think the best one I know is
I. N. Herstein, Topics in Algebra (1975)

A shorter, easier one is
I. N. Herstein, Abstract Algebra (1986)

They have a lot of amazing exercises which i really loved. But i guess its a bit subjective.

[livid lintel]

Don’t post that, that’s against the rules

[sturdy gust]

alright, deleted the message

thanks

[main hill]

Hello there 🙂 Does someboy have a valid z-library link? There's a few scam-sites I would love to avoid but after formatting my computer I don't want to risk stepping on a mine

[livid lintel]

DMed

[main hill]

Thank You very much! Really appreciate it! 😉

[gray gazelle]

anyone have any interesting maths novels suggestions

[tired glen]

Pls anyone suggest any book bye which i can do practice for jee main and advanced and syllabus should be aligned with jee main and advanced syllabus

[gray gazelle]

Is there a way to find a list of unsolved math proofs, in graph theory, organized by difficulty? I don’t know how to judge the difficulty, since so many are categorized as NP-hard.

[stray veldt]

this question doesnt really make much sense

NP-hard problems are decision problems and well, finite

they are all solvable, maybe just not very fast

and if you are asking about open problems (that actually would require proof), then who is supposed to order them by difficulty?

[gray gazelle]

hey I'm looking for recommendation for textbooks/websites that cover complex numbers, set theory and functions at a first-year/second-year university level that have problem questions too. if anyone can recommend me anything, would greatly appreciate it :)

[lusty escarp]

Do you go to any coaching institute?

[foggy quest]

Notes here: https://mtaylor.web.unc.edu/notes/, particularly https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ for intro analysis and https://mtaylor.web.unc.edu/notes/complex-analysis-course/ for intro complex analysis.

[dim snow]

Does anyone have any good Putnam recommendations other than Putnam and Beyond? I really want as many books as possible for a wide variety of problems

[covert bane]

does anyone have a good introduction to sheaves (in particular for working with grothendieck topoi)? I'm working through Sheaves in Geometry and Logic, and I'm finding it very useful, but other additional material would be good.

[remote sparrow]

@solemn rover

[stoic hamlet]

What in particular do you want to do with sheaves?

[covert bane]

I don't know enough about them to know what you can really do with them (I basically only know the definition from sheaves in geometry and logic), but they seem to come up in a lot of places, so I'd like to learn more about other general uses since they seem to be important -- I'm really looking for something very introductory

[stoic hamlet]

I am not sure you'll find anything super introductory since the basics tend to only be developed by people who are using them for a particular advanced application.

I use sheaves and topoi a lot to do arithmetic geometry, but I never really studied topoi abstractly in as much as I use regularly a small number of topoi to do work. The 'bible' there is maybe something like SGA4, but I think almost everyone gets by with much less. I personally learned most of the topos theory I know from Tamme's book on etale cohomology; Akhil Mathew taught me a few additional facts as I needed them that he learned from SGA4, though.

[solemn rover]

"Manifolds, Sheaves and Cohomology" gives a lot of motivation, it is a really good textbook on modern geometry with sheaf theory as the basic formalism.

If you know French, there is a book by Godement which is very beautiful, called "Topologie Algebrique et Theorie des Faisceaux".
I did not know French when I started this book but I learned as I went

[remote sparrow]

https://www.amazon.com/French-Reading-Karl-C-Sandberg/dp/0133316033

FYI there are books geared to academically-oriented people that teach you how to read french for academic purposes

[covert bane]

I have a french-speaking analysis friend I'll bother for help 😭

[trail hemlock]

what are the prereqs to spivak's diff geo?

oh wiat someone alr told me nvm

🤦‍♂️

[fresh skiff]

Btw can I know what's the prerequisites?

[trail hemlock]

I'd say Munkres Analysis on Manifolds is the basic pre-requisite
moonbears told me on a diff server

[fresh skiff]

Oh got it. Thank you BlackBeard.

[glacial crypt]

spivaks com

[trail hemlock]

i like munkres analysis on manifolds so far

CoM prob best with a class but im self studying

[tribal crow]

wait, what?

oh.

I see, I mistook you saying "Spivak's DG" for "Spivak's CoM"

my bad

[trail hemlock]

higher why are you green

how does one become "helpful"

[tribal crow]

??

you already know the answer

[trail hemlock]

!

[trail hemlock]

so pretty

wait