book-recommendations

[marsh ingot]

Take your time to assimilate the stuff before doing exercises, its at least what I do

The last is one is quite deep, because in some proofs there some arguments that look like magic

What we call here a "happy idea"

[plain barn]

yeah

sometimes it's part of a bigger pattern of proofs an area has

sometimes it just seems like a specific person had a specific thought because of very specific reasons and the textbook will never tell you why

that's why I like cummings' (hihi) proof sketches

[marsh ingot]

Yeah exactly that

I just saw a few happy ideas during the degree but damn some specific argument that make the proof very easy

[plain barn]

friedberg's linear algebra textbook exercises has a lot of happy idea as hints

[marsh ingot]

Like for example dunno while proving Fundamental algebra theorem using Galois theory suddenly pick a 2-Sylow group because of yes

[plain barn]

like
prove something (hint: consider substituting x by TG(x- 2y)*)

[marsh ingot]

Lol what a hint

[plain barn]

it's full of these weird ass hints

[naive trellis]

Algebraic / Topological K theory recomms?
Also, how much cohomology theory do I need for K theory

Also sheaf theory

[plain barn]

anyone has complex analysis textbook recomendations?

[gray jungle]

second half of rudins book real and complex analysis

[broken meadow]

conway

[heady ember]

Yamin shills their prof's textbook: Zakari iirc

[gray gazelle]

I'm starting my undergrad studies in math, any book that you recommend for beginners?

[molten mason]

Depends, did you just learn what sin and cos are last semester? Do you already have 3 semesters of calculus under your belt? Have you read on linear algebra or proofs? Everyone comes in with a different background, list your current math background and what your goals are and we can guide you.

[plain barn]

that's like the third recommendation I ask tonight but
anyone has any recomendations for multivariable calculus books (or calculus that have multivariable calculus in it) that isn't stwart's?

[gray gazelle]

thanks, I don't know: trigonometry, calculus, linear algebra

my math background is algebra and basic geometry.

it's been a while (10+ years) since I studied math in a school setting.

I'm familiar with some concepts in computer programming and recreational math.

just got into a bachelor in science with a focus on math

my long term goal is to have enough math proficiency to use it as a language to describe and solve problems

[molten mason]

Start with Basic Mathematics by Lang, pdf is online somewhere, or Amazon has it for $41 USD. Depending on your fluency and how fast you go through it, you can do the whole thing in a week or spend a couple months going through it. It covers elementary algebra, geometry, and trigonometry. Basically everything before calculus. After you finish that book, pick up literally any single variable calculus textbook. There's also courses online like MIT OpenCourseWare that you can go through Calculus on. Dr. Leonard and BlackPenRedPen are also great YouTube videos to go through.

This website also has a great trigonometry PDF: https://mecmath.net/trig/

[molten mason]

Lmao @ Stewarts There's Spivak

[plain barn]

ty

kinda dislike stewarts

is this like, common? not liking stewert?

[molten mason]

You can type it in search at the top of Discord and that's like 80% of this server lmao

[plain barn]

lmao

why do most people don't like stewert? just to be sure

idk if it's the same reasons as me

[molten mason]

Personally I dislike it because the textbook is geared to everyone who takes Calc, such as Engineers, Pre-Med, Biologist, etc. It's not a textbook for math majors, but that doesn't mean I hate it or anything. It's just a textbook.

I think the commentary I see a lot in this server are similar: there's more rigorous books to truly learn and study calculus.

[plain barn]

hum

makes sense

[molten mason]

Because so many students take stewart, if you're ever stuck, there's almost always an answer to your exact question/problem online somewhere

I think there's YouTube videos going through the problems, literally the answers are given with work shown

[plain barn]

there's a spivak book with multivariable?

didn't find it

is it that one?

[molten mason]

Yes but I wouldn't actually recommend it for now lol it's a heavy text. Have you taken multivariable calculus yet? Have you gone through Stewart's? Is this self-study?

And what do you dislike about Stewart

[plain barn]

no
a little bit
yes

[plain barn]

basically, not very rigorous and idk I just don't vibe with it
also I feel like the exercises are too easy

tho I like some application exercises

I don't hate it I just kinda dislike it

[fierce hedge]

Herstein is almost a problem solving book, at times there's more pages of problems than the theory itself

Not to mention he gives some questions where you're supposed to use some standard techniques before they are introduced making simple questions much harder unless you use yet-to-be-introduced theory.

[vital bane]

you will love "Multivariable Mathematics" by Ted Shiffrin

[marsh ingot]

Manifolds

Calculus on manifolds seems to be a little dense if you didnt take differential geometry before

[median saffron]

oh god spivak

[lyric forge]

anyone have good pdfs?

[marsh ingot]

About?

[marsh ingot]

Just for curiosity Im gonna search it

[plain barn]

I like this

[plain barn]

it was recommended to me by a teacher and he already warned me that I shouldn't force myself to do literally all exercises cus they reapear later

[remote sparrow]

@rustic grove what do you think of carothers

[rustic grove]

I am only using it a a supplement, but I think it is very clear ye. I do quite like it.

[rustic grove]

why u ask?

[remote sparrow]

wanted to know if my recommendation was good

[rustic grove]

It is. The only reason I am only using it as a supplement is that there is no solutions to the exercises 🙂 . The other two books I have, (sutherland and Michael O'searcoid) have full solutions. They don't cover as much as Carothers though as they only focus on metric spaces and pure topo.

So ye, they all work well together.

[ancient bison]

Does anyone have read Amann? Is that a good book for review Analysis and some basic Algebra? I have already finished babyRudin and linear/abstract Algebra, but that's could be one year ago

[remote sparrow]

probably not a great book to directly review classical analysis (for example, if you're preparing for comprehensive/qualifying exams for certain graduate programs), but good if you want to see old material in a new, more general light

[zinc walrus]

Can anyone recommend any 1st year collage books.

[ancient bison]

yeah, I just want to see the old in new, so I can start advanced course after reviewing .

My another choice is Godement, but it's too thick

[remote sparrow]

that's what she said

[remote sparrow]

most advanced courses don't assume you've read amann/escher

[ancient bison]

It's just that I haven't studied for too long, and I've been preparing for the entrance exam for ETH, high school level in German change my brain

Actually, I don't know what I should to read, that's the end of my knowledge

[plain barn]

guess I'll stick with stewart...

[remote sparrow]

for calculus?

[rustic grove]

Vector calculus by Susan Colley or Marsden and Tromba are both good. Also Hubbard.

[plain barn]

yeah

actually I'll go with guidorizzi probably

[plain barn]

will research

[plain barn]

since it's more of my vibe

[plain barn]

does this have multivar?

gonna search it

idk if I should learn the non-rigorous version of multivar first

like, get used to it

it's probably going to be quick tho

[pure solstice]

any book for hard problems on modular arithmetic?

the harder the better. with solutions if possible

[plain barn]

hm

gonna think about that

[molten mason]

I don't know that author. I mean there's nothing wrong with Stewart, and either way you shouldn't just use one textbook. I would 100% recommend sticking with Stewart and supplementing with another book. Apostol Volume 2 (Multi-Variable Calculus and Linear Algebra) is a great textbook, some people pretty much claim Apostol as the Calculus holy book. Shifrin was recommended up, that could be a good one. Based on what I gather from your understanding in math and calculus, that would probably be an appropriate book especially for future topics of study.

if Calculus is easy and you want to learn more, +1 to just moving up to Analysis, which there are a bunch of textbooks pinned in this channel

[plain barn]

I know real analysis, but only with one variable

[pure solstice]

no. actually I want to learn how to prove things like this
\frac{4^n-1}{3}=odd

[plain barn]

ty

[pure solstice]

ok, any books specifically?

[molten mason]

Perfect, just keep going and diving deeper. If you have all the resources (aka downloading unlimited pdfs) just go through as many textbooks as you can. Don't need to stick to one textbook/author/school of thought

[plain barn]

don't stick to one school of thought?
on my way to study john gabriel's calculus

[plain barn]

sure, thank you

I think I'm to obsessed with the concept of finishing a textbook as kind of a mark

[pure solstice]

topics in algebra?

[plain barn]

I think I need to be more free

allow myself to learn in less ordered manner

[molten mason]

I haven't heard that name in a minute lmao

[plain barn]

ony limits are my ssd's space B)

[remote sparrow]

schroeder and browder cover multivariable calculus in the second half

[dusk wind]

all the resources, automation

write a script to download the worst 50 page books ever

[plain barn]

passing my eyes through spivak's calculus on manifolds, doesn't seem that hard

seems like my type

[marsh ingot]

Wait until see differential forms

Green and Stokes theorems

[plain barn]

excited for red theorem

[viral crypt]

Is Group theory doable in one week?

[storm fossil]

I'd like to read a book that might be titled "why mathematics." Not "what is mathematics," but why study it, why it's beautiful, and a more philosophical approach. Preferably from a serious mathematician. Could be from Ancient Greece, Rome, or modern day. But I mean a pretty strictly philosophical book. Just a mathematician's personal philosophy on studying mathematics.

[plain barn]

that'd be cool yeah

[spring cave]

Not a book, but some youtube channels try that approach while teaching concepts in maths

[storm fossil]

This is true, but I don't think what I'm looking for is anything particularly educational. Ideally, it would be something like "Why Do I Do Mathematics? by Euler." He would talk about how he started to study maths, why he finds it interesting, what the pursuit of a mathematician should be, his struggles with various problems, etc. It would be fine if there's not a single equation in the book.

Really, it would just be a purely meditative, philosophy book.

You can find similar books in philosophy, physics, art, etc.

[spring cave]

I can only recall one professor, not that famous, but remarkable nonetheless, who talked about his motivation for going into maths in an interview, Elon Lages... Don't know if it's enough for you though...

[fierce hedge]

Absolutely no

[gentle arrow]

no

[finite gale]

no unless you're reviewing or something

[modern ruin]

yes

(this is not true, but i mean whatever i say here won't really affect what you do anyways)

[tribal flame]

To what level of depth?

[vital bane]

group theory would be doable in one month

another month for ring theory, and then another month for field and galois theory

and that's basically one semester of abstract algebra

[remote sparrow]

https://www.amazon.com/Mathematical-through-Python-Yannai-Gonczarowski/dp/1108949479

recently heard about this book

seems neat

[fleet solstice]

How good is Algebra 2 by Timothy D. Kanold?

[plain barn]

elon citado

where does he talk about it???

btw just remembered elon has a book on analysis with multiple variables

I think I'll use it

[spring cave]

I'm using his book on Analytical Geometry

[spring cave]

Are we allowed to share youtube links here?

[plain barn]

idk but you can dm me

[cold sun]

anyone know any great books for probability and statistic for University level maths first year?

[magic spade]

Are you learning for science/data science or are you learning for pure math?

[plain barn]

would y'all recommend herstein for a first time in abstract algebra? why?

[marsh ingot]

I think this is better

[cold sun]

Pure maths

[viral crypt]

To the level of I can use it in other fields to solve problems that would have been really difficult to solve otherwise

[fierce hedge]

If you're using it as main book No, if you're using it for self study Absolutely NO

It's a problem book, also it uses the notation xf instead of f(x)

[magic spade]

Weighing the odds by Williams

[plain barn]

why

[plain barn]

I see, there are a lot of problems lol

[plain barn]

will check it ou

[fierce hedge]

I'd highly recommend Rotman

[magic spade]

You can also look at statistics for mathematicians by Panaretos

[plain barn]

will check this out too

[plain barn]

for self-study?

I'm self-studying it

[fierce hedge]

Yes, I'd also recommend books like Gallian for self study

[plain barn]

didn't know he did something other than being a hollow knight boss

ty a lot

[fierce hedge]

That's Galien right not Gallian. It's been long I played HK

[plain barn]

🤓 ☝️

[dusk wind]

Any good accounts of ancient mathematicians ranting about the beauty of math?

[alpine tusk]

Not that I know of but try reading "The Dialogue on Great World Systems" By Galileo.

[dusk wind]

Sure

[alpine tusk]

There is a lot of gravitas in that book.

[plain barn]

I think I'll main artin for studying abstract algebra

thank you all for the recommendations

[novel obsidian]

As someone maining artin atm

Artin is really cool

Make sure to use Benedict Gross' lectures on YouTube. They follow the book until chap 9 or 10 ithinl? (He ends with rings)

[cold sun]

does anyone know any in dept books for vector algebra and geometry for first year uni

[fierce hedge]

He doesn't go into fields or Galois theory?

[marsh spear]

ws everyone i want to start calculus from 0 can someone give me a book recommendation

[novel obsidian]

Gross' lectures don't. Artin does in chap 16

[thorn cloak]

wanting to get into Data Science. Was wondering if there are any books on the math side (intro levelish)

[magic spade]

What's your math background?

[thorn cloak]

i am in undergrad. So far, I have taken(ing) lin alg, multi var and vector calc, intro to prob theory, and intro to real analysis

[magic spade]

Have you checked out Introduction to statistical learning ?

[storm fossil]

Rigorous intro probability textbook for the undergrad level?

[remote sparrow]

the most rigorous approach that can be taken requires measure theory.

but then, it wouldn't really be introductory

[graceful moon]

Yeah you kinda do introductory probability or rigorous probability, you can’t really have both

[storm fossil]

That's fair. Appreciate it

[thorn cloak]

I have not! Ill make sure to look at it

[remote sparrow]

you could look into feller's two-volume work on probability if you want. the first book restricts itself entirely to discrete probability (thus avoiding measure theory altogether), while the second book introduces the necessary measure theory to talk about continuous probability. they're pretty hard going though. blitzstein and hwang is a great modern introduction to probability. the book is free online at this link: https://stat110.net

[storm fossil]

Thanks, I'll look into it 🙂

Any idea if this is any good?

https://www.amazon.com/Introduction-Probability-Textbooks-Mathematical-Sciences-ebook/dp/B000SB5QXC/ref=sr_1_16?crid=1EI03R441RYX6&keywords=springer+introduction+probability&qid=1701467414&s=digital-text&sprefix=springer+introduction+probability%2Cdigital-text%2C73&sr=1-16

I've seen a few texts that are intro to probability+measure theory, but no idea if that's considered pedagogically sound.

[dusk wind]

'rigorous intro'

maybe have a 2 part course from the sea of immaculate info on probability

literally just use blitzstein though

[gray gazelle]

I bought Hammack’s book of proof to self teach myself proof.

A site that I read mentioned not to fall into perfectionism and try to do every exercise

But how many exercises are enough?

Also what book is best for learning logic on your own?

[fleet solstice]

How long on avg do ppl take to read a textbook?

[vital bane]

as much as you can do in a reasonable amount of time

[vital bane]

as long as you need

dw about how long it takes, just focus on learning the content well

[fleet solstice]

What if theirs something on the book that confuses me?

[vital bane]

that will happen a lot

[fleet solstice]

Do I jus search it up and hopefully the internet can elaborate even better 😭

[vital bane]

you just spend some time trying to understand it

maybe a few days

[fleet solstice]

Oh

[vital bane]

or even 2 weeks

if you want

[fleet solstice]

Dang, for that piece of info

[vital bane]

you can move on to other stuff

just make sure to come back to the things you dont understand

and try to understand them later

[fleet solstice]

Ohhh I see

I think I might jus understand something, before moving on 😭

How do you remember the info you've read?

Also another thing I've struggled with

[vital bane]

you dont

you will forget things

but it's okay

you can just look it up in your book and in your notes later

[fleet solstice]

Eh fair

[vital bane]

that's why you take notes, it helps with retaining what you've learnt

[fleet solstice]

Ig that's what notes are for 💀💀

Yeah

How do yk what to write down for your notes?

[vital bane]

you dont

you take really bad notes at the beginning

you slowly iterate and get better at taking notes

I still suck

[gray gazelle]

I don’t have exams. I have all the time in the world

[long sigil]

Hi there, math experts!

Does anyone know what books are good places to start for getting a formal grasp of the fundamentals of mathematical notation?

I know it sounds weird... but even after going through graduate school, I just studied for the assignments, but my knowledge is patchy and incomplete, because we only focused on preparing for exams, but not studying all the other extra stuff not directly related to it.

My lecturer did teach us about those other fundamental stuff, but I've mostly lost my notes/forgotten about them.

TLDR: A single comprehensive source/a set of books that offer a complete view of the basics of formal mathematical notation and logic would be amazingly helpful 🙂 This is probably something on the level of 'foundations' or 'math pedagogy' I guess?

[marsh ingot]

Mmm I dont think there is a specific book for it. You just get used to math notation while reading any book about math. Because some authors tend to say what notation means. Some notation are not universal but is a few

At the begining of some books there is a page about the notation and meaning in the book

[long sigil]

I see, I see. Could you/anyone name me a few of your favorites then? Might as well start there. If you like that book, maybe I will too.

[long sigil]

*personal favorites

[vital bane]

You may be interested in this book then "all the mathematics you missed but need to know for graduate school" by Thomas Garrity

[long sigil]

I'll give it a go!
Any other recommendations?

[marsh ingot]

Just saw a chapter 0 or section for notation in 2 books but one is for alg topology and the other about algebra

And sometimes depend the context and the branch

[wintry bison]

Sometimes u need to understand rhe concept of the theory and/or make your own simplified definition of it as to keep it in mind

[gritty gale]

varies wildly by person, subject matter, length of textbook, and their other committments

[gray gazelle]

are there any good algtop resources like lectures with assignments and stuff?

[marsh ingot]

Depends on the subject and my emotional health

[visual sedge]

anyone have any good recommendations for a book on topology?

[magic spade]

You don't like Munkres? Or what kind of book are you looking for?

[magic spade]

You could try John Lee Introduction to Topological Manifolds if you don't like Munkres

[visual sedge]

i honestly don’t know much about topology books. just starting to look around cause i’m taking topology next semester but i’ve heard of munkres is that the go to topology book?

[magic spade]

Yes

It's focused on point-set topology not algebraic topology. but you might not know what that means yet

[visual sedge]

i have a general idea of what the differences between the two are, but i'm definitely not looking for algebraic topology so i'll try that book out. Thank you!

[gentle arrow]

munkr*s

[dusk wind]

100 pages a day or 100 tiktoks

[heavy pelican]

Textbook or storybook?

[smoky zephyr]

storybook?

[heavy pelican]

Munkres is a good one for former. For the latter, I like 'How surfaces intersect in space' by J Scott Carter

I'm a big fan of https://pi.math.cornell.edu/~hatcher/Top/Topdownloads.html because it has all the essentials and is not as big as Munkres

[visual sedge]

what are the contents of the topology storybook? is it more like intuition building rather than rigorous mathematics?

[heavy pelican]

More intuition

You can look at the table of contents

[visual sedge]

thank you for the recommendations i'll look into both of those

[vital bane]

yea of course but like 10 years later when you switch to a different field you might forget all I'm saying is dont be afraid of forgetting something

[wintry bison]

Hmm true u might need a little push or like a string to pull the rest of the info

[vital bane]

yess

[novel tusk]

Should I try Hatcher’s algebraic topology? I’ve almost finished the group theory section of Dummit and Foote.

[lime vessel]

You can, but knowing rings and exact sequences will help from ch.2 onwards

Also make sure your algebra/visual intuition and point-set (e.g. Munkres 1-3) is solid

[vocal peak]

looking for books on advanced calculus, modeling, number theory and combinatorics

[signal charm]

looking for a good texbook on (algebraic) geometry

[plain barn]

y'all would recommend calculus on manifolds by spivak for self-study?

[vital bane]

@mystic orbit darQ did it

[mystic orbit]

Nope

I quit two chapters in

[vital bane]

[mystic orbit]

I wouldn't tbh

It's great as a supplement maybe, the exercises are awesome

But the exposition is suuuuuuuuper terse

[plain barn]

lmao

[plain barn]

would you recommend another book on the same subject?

(note: I'm confortable with 1-dimensional real analysis and with linear algebra)

[daring lake]

Munkres has a book, Analysis on manifolds, but i have never read it

[heady ember]

Maybe this would be somewhat helpful

[plain barn]

wdym terse

soo anyone else would recomend munkre's analysis on manifolds for self-study?

[rain wren]

I dunno what I would recommend honestly

I think I'm going to do a differential geometry book to cover that content instead tbh

if diff geo is something you're interested you might wanna take a look at Tu

[plain barn]

I am interested in it yes

[rain wren]

I think you might find this book to your liking then https://im0.p.lodz.pl/~kubarski/AnalizaIV/Wyklady/L-Tu-1441973990.pdf

[plain barn]

ty

[rain wren]

terse means it's super concise and spends little time motivating/commenting on stuff

[plain barn]

oh

[rain wren]

it's just straight to the point definition/theorem/proof kind of style

[plain barn]

besides linear algebra and analysis, is there any pre-requisites for this?

[rain wren]

good question

I think not

but you might need prior familiarity with pointset topology

[plain barn]

by the preface, I don't

I mean, I'll need the appendix on the subject

but apparently it's assuming you could not have studied it

[rain wren]

yea I was gonna post the same thing lmao

[plain barn]

aa finding the books to study is so hard

self-study has these things

[rain wren]

what's wrong, is tu not what you're looking for? :(

[plain barn]

no no

just that

I'm not sure it is

I think I'll like, start studying it (since it seems my vibe) and if I don't like a chapter I'm going to another book and so on

also I've seen a lot of different books to the last 3 days never sure which one to use

but this one seems good

[rain wren]

you're not gonna find the perfect reference and even if you did you wouldn't know it

[plain barn]

yeah fr

[rain wren]

my advice is to stick to a reference as long as you think it's serving you well

and I think tu would do that for you :D

[plain barn]

well I did this with linear algebra

started with a book, than changed into another, almost finished the another, now I'm reading the other book again for a different perspective

[rain wren]

lmfao

I've done that myself, I think that's completely natural

just make sure you're not changing references every week lmao

[plain barn]

ye

it's so cool that I've come to this point tbh

I could learn real analysis and linear algebra

now I'm going to learn all these insanely cool stuff

[vital bane]

spivak's diff geo

[rain wren]

ikr!

real analysis and lin alg legit unlock so much it's crazy

[plain barn]

I feel like I have unlocked all of math

[vital bane]

slowly unlocking the tech tree

[plain barn]

like

the ability tree

yeah

[vital bane]

only to see that there's infinitely more to unlock

[plain barn]

I had only the two before now a whole tree has appeared

[plain barn]

happens

[magic spade]

Duistermaat and kolk multidimensional real analysis is the ultimate source for what you want to learn imo

[plain barn]

will check this out later

[magic spade]

A lot of the content of the 2 books is in the exercises, so make sure you look at those

[plain barn]

oh damn I think I should practice a bit of multivar calculus before that

before that book

also apparently it assumes yk abstract algebra

sooo I'll go to that later I think

[mystic orbit]

Wait huh

Is that true? I thought chapter 1 starts developing multi var calc from 0

[modern ruin]

oh i did not see this earlier yeah i really like Tu and i recommended it independently

i love that book

[forest forum]

Any recommendations for books for improving computations? just quick puzzles that require computations cuz I'm trying to get better for next putnam.

[modern ruin]

Putnam and Beyond is the book i like

jump to the section that you want it’s got some puzzles

[forest forum]

i got that one already and i like it a lot but I think I need a book with a large volume of A1/A2 or less difficulty problems so i can get really fast at doing computations and that will probably make doing intemediate steps on harder problems easier for me

[modern ruin]

i mean there is a book of previous putnams idk what it’s called

but it literally has a bunch of putnam problems that are not on kedlayas site

[forest forum]

ok ill look into this

[plain barn]

well it already has like

partial derivatives

and integrals on them

[plain barn]

oh and I think I was wrong, I looked at a part that cited abst. alg stuff but it was defined before

in the book

so its ok

I think I'll read it alongside practicing some multivar calc

[plain barn]

I think the first chapter is just feeling kinda overwhelming

my head literally got hot real quick

I got dizzy and had to rest

but I think it's just because it's new math feeling

or because I didn't sleep well

lots of factors

I'm gonna see if I'm fine with the exercises

[empty nest]

Can someone send me challenging problems in an 8th to 9th grade level

[mossy lily]

richmond osmands thursday murder club

[tawny crater]

Gabi maybe you're jumping the gun a bit

Did you do real analysis materisl or a calculus I material

[plain barn]

yes

both

[tawny crater]

If you defined derivatives and serieses and integrals it's a calc

[plain barn]

ye

I'm think I'm fine with diff geo

with a bit of simple multivar practice

[tawny crater]

Ok gl

You can also do some combinatorics or set theory or logic

Tend to do some of those at year 1 uni it's nice if you want to go a bit wider some of it is pretty easy-going and gives good rewards

[remote sparrow]

maybe consider checking out Mathematical Analysis II by vladimir zorich

[plain barn]

I know these

[rustic grove]

Do you have an answer to this or would you like me to share with u what I have so far?

dm me

[glacial coyote]

Do you guys think it's possible to read artin with only knowledge of pre calculus, trigonometry and matrices(determinants, row reduction and stuff)?

[subtle mango]

probably

but it may be a leap if you don't have the "mathematical maturity" to read it

[glacial coyote]

I guess i'll give it a try

[subtle mango]

[viral crypt]

Guys I want to study abstract algebra with Gallian's book do you think it's a good idea or it's a waste of time compared to other choices and the book is too long and shallow?

[remote sparrow]

not a waste of time

you can always read a harder book after a simpler one

[molten mason]

Anton

[valid marsh]

someone can recommend books of algebra and circumference with their angles

[rare estuary]

Does anyone have recommendations for optimal control theory? I'm hoping for at least one more applied text and something that's more rigorous but may require "heavy machinery"

[remote sparrow]

@silver herald

[dusk wind]

what if I dont want to read

[uncut nest]

write

[topaz berry]

fair

[civic nebula]

can someone suggest a good book for learning random distribution in probability???

[cyan valve]

Anyone checked out Gortz and Wedhorn's newly released volume of their algebraic geometry book? It's on the Cohomology of Schemes

[fringe torrent]

Hi guys as a beginer i need a good book for analysis .. i'm waiting your answers

[magic spade]

What's your background? Have you looked at the usual suspects? Abbott, Tao, Rudin...

[silver herald]

What is your current background and what is your current target with optimal control?

[stuck apex]

Hey guys I hope you’re all doing good, can anyone advise me in a book in combinatorics and combinatorial proofs and where I can find a lot of exercises so I can practice.

[molten mason]

There's a whole list in the pinned posts of this channel

[narrow tide]

Does anyone have any opinions about Bass's probabilistic techniques in analysis. I know a friend who's been preaching about using probability to do analysis problems and I think he'd really like the book.

[sage forge]

Do yall got any recommendations for books where I could practice "translating" words into math cause when Im faced with a problem i make errors cause i translated the problem wrong. Im looking for ones with HS algebra

[reef escarp]

So I have been focusing too much on geometry and forgot my algebra basics, can anyone recommend a book for alegbra 1? i would prefer ones that explain stuff nicely, but still have some good practice questions.

[uncut salmon]

If you are talking about basic abstract algebra, I'd suggest you the book of Herstein, it has good explainations and a decent amount of exercises, or Algebra by Artin, even tho it covers more than the necessary I believe. You should find the free pdf online. In case you want really hard exercises, take a look at Selected Exercises of Algebra by Chirivi, Del Corso and Dvornicich.

[glacial oar]

is analysis 1 a good tetbook for real analysis ?

[rare estuary]

I have an undergrad degree in engineering and currently trying to prepare for grad school in applied math. I'm trying to get a more rigorous/general look at the controls I learned in school. So my goal is general curiosity and scouting out potential specializations in grad school. I would guess that I will need a pretty easy text to start, but it's ok if I have to sidetrack to get some prerequisites that I lack currently.

[gray gazelle]

Is Basic Mathematics - Serge Lang rigorous? Does anyone recommend any other books that are as if not more rigorous?

[remote sparrow]

author?

[remote sparrow]

yes

[viral crypt]

Let me guess: T. Tao, in that case the answer is yes

[strange vortex]

That’s the best analysis 1 text book in my opinion

T tao

[glacial oar]

Terance tao

[magic spade]

It's a great book

[dusk wind]

no one knows how to actually use discord

or google for that matter

it would require reading more than 100 pages

[molten mason]

There's many questions here asked almost daily that can be answered in search. I constantly use the searchbar <book name> in:#book-recommendations

[dusk wind]

discord literally has filters

[molten mason]

That's probably the perfect amount of rigor for a pre-calc book. I have it on my desk and I recommend it to everyone. I don't know of a better book.

[dusk wind]

if you trust anyone read more than 100 pages of a certain book you're looking for, search for posts by them in x topic

[molten mason]

Yup

[dusk wind]

literally just search sour drops posts

[molten mason]

And you can jump to that message and read the whole convo around it to see what else was said

[dusk wind]

unfortunately we are on autopilot so we can't do that

[molten mason]

Speaking of Lang, Basic Mathematics by Lang would help with this.

[dusk wind]

if you want to pin anything, pin how to use discord and have a bot link said pin

[glacial oar]

Is it good if i dont have a strong foundation in proof writing ?

[tawny copper]

it is specially good in that case. Like read the preface

[glacial oar]

Thank you so much 😍

[crimson leaf]

Yeah I would reccomend tao if you're not good at proof writing otherwise I would personally pick up a different book

[stuck apex]

Hello guys, so I’m studying groups and rings in abstract algebra I want to find a book where I can practice and do some exercises can you help me and send me a good book in this field if you can.

[graceful moon]

Artin or Dummit and Foote

[heady ember]

Look in pinned

[mystic orbit]

Artin is very good

[silver herald]

Typical references tend to be - Bertsekas's Dynamic Programming and Optimal Control Vol. 1 & 2 along with Ross's Primer on Pontryagin Maximum Principle (This is what Doom's optimal control course is using as main textbooks).

If Bertsekas is not upto your liking - Try out Kirk's Optimal Control book (It is also a Dover one, so cheaper to purchase)

As for applied texts. - It depends on what you are looking for in terms of applications. For say - Robotics, not found anything beyond Russ's notes on Underactuated Robotics

https://underactuated.csail.mit.edu/index.html

[rare estuary]

Thanks!

[rustic grove]

Does anyone know any books on basic number theory that can be 'dipped in and out of' .

[magic zinc]

Any book for class 9th geometry

ncrt based?

[gray gazelle]

any good book for starting off linear algebra in the mathematical way (not the applied way)

i have little-some experience in linear algebra so im not fully new

but basically new lol

Does anyone know about quadratic functions?

I mean a book about it

no

tbh for something like quadratic functions ur better off just using youtube or smth

if it's just the basics u need

[placid canopy]

i haven't read it myself, but #books recommends Friedberg, Insel, Spence (past professors in my school have used it before for their LA course)

[gray gazelle]

ye i saw friedberg a lot

[graceful moon]

LADR is the usual recommendation these days I believe

[placid canopy]

can be (reading rn!), not sure if it's great for a first course

[graceful moon]

I mean if you already know the basics (like calculations) I think LADR should be fine, provided you take your time with it

[gray gazelle]

ladr?

[placid canopy]

linear algebra done right by axler

[gray gazelle]

oh right

[placid canopy]

4th edition pdf is free!

[gray gazelle]

i have to choose and idk which one to choose

aaaaaaaaaaa

[placid canopy]

ehhh, if you can, try going through a bit of axler first and see if you like the cut of his jib

[gray gazelle]

question

is it fine if i dont do some chapters eg start at like chapter 6 and then move to chapter 4 (reason is i wanna prioritise the tpics which will prob come up in my jan exam and have a firm understanding of them)

then learn the other stuff in my free time

[placid canopy]

still on chapter 3 :(

[gray gazelle]

😦

[graceful moon]

For Axler I wouldn’t recommend that, especially if you’ve not done much else in the way of university maths

And if it’s for an exam axler probably won’t help much either because he hates determinants so he does a lot of stuff very differently to most books

[gray gazelle]

f

what do u think i should do

also it's not necessarily for an exam

buyin it just cz i wanna delve deeper but it would be nice if it helps for my exam too

lol

[vital bane]

didnt he fix that in the 4th edition?

[graceful moon]

I mean it’s less deranged, he now has a chapter on multi linear algebra and just rigerously defines the determinant but I’m sure it’s the final chapter, which is far later than most LA books will define the determinant

[vital bane]

hm alright

also why friend req

[graceful moon]

Fully accidental lol, didn’t even realise I did, not sure how I did tbh

[vital bane]

Oh lol alright

[molten mason]

Basic Mathematics by Lang

[molten mason]

Chapters 5-12

[molten mason]

I'm not an expert in this but I do have Friedberg's 5th edition and I'm going through it now, I like it a lot. I also have LADR 4th edition as a .pdf but I haven't gone through it extensively enough to have an opinion

[desert oriole]

hoffman kunze for first time lin alg? (only lin alg i know is the lin alg ive needed in multivar calc)

[desert oriole]

egmo by evan chen

idk

aops geometry is highschool geometry

[tame sphinx]

I need a book for functional analysis, that refers to proofs and things used throughout the book, it's to learn hahn banach

[magic spade]

Have you done measure theory?

[marsh ingot]

Rudin Functional Analysis

Or Conway

[tame sphinx]

I have done a course on measure theory, but I wasn't very good at it

[marsh ingot]

Megginson is good too

[tame sphinx]

it's only now that I'm starting to get better at understanding/learning math, after real analysis, measusre theory, and them topology made it kinda click

[magic spade]

I agree that Conway is a good option

[rustic grove]

I have not done FA yet I am still doing metric spaces. However, Linear functional analysis (Rynne and youngson) or Introduction to functional analysis (James C Robinson) or 'Linear Analysis ' Bela Bollobas are meant to not require measure theory and both 1 and 2have full solutions in the back. I realise I am not really qualified to answer but when I get around to it, one of these is what I will use.

[magic spade]

Robinson is great, agreed

[tame sphinx]

might be good, because I'm forgotten a fair bit of it... and never truly grasped the stuff

[marsh ingot]

Fabian, Habala, Hajek, Montesinos, Zizler - Banach space theory

Another one

Very extensive

[rustic grove]

Just out of interest, what is the depth difference between Conway and Robinson?

[magic spade]

Robinson is more beginner friendly, Conway is a bit more advanced

[rustic grove]

Does Conway cover more content I mean?

[magic spade]

Somewhat, is has a few topics Robinson doesn't I believe.

[rustic grove]

Ah, ok thanks 🙂

[magic spade]

Not a huge difference I believe

[marble solar]

At the undergraduate level for ODEs, I like Boyce & DiPrima

For PDEs, the go to text is Walter Strauss

For Fourier type things, I am a fan of Stein and Shakarchi's Volume 1

[marsh ingot]

For PDEs also Evans

[graceful moon]

I really dislike Boyce but there’s no denying that it’s comprehensive

[fallen bronze]

what’s a good book for algebra or precalculus.

[molten mason]

Basic Mathematics, Serge Lang

[gentle arrow]

algebra, serge lang

[crimson leaf]

This is a horrible recommendation

[gentle arrow]

yeah i was joking
dont use this book

[heady ember]

Read Damni's review in pinned

Friedberg has been great in my exp

[gray gazelle]

any good combinatorics book?

[remote sparrow]

A Walk Through Combinatorics by miklos bona

[gray gazelle]

read pre calculus by sheldon axler

[junior isle]

Algebra book for someone with linear algebra background?

[sage python]

Try Jacobson

[glossy zealot]

Guys which real analysis book for undergrad that teaches strategy to solve problems?
Or which one is more explicit with the proofs (more explanations, includes guidance, etc.)

[junior isle]

Take a look at jay cummings real analysis or understanding analysis by greg abbott

Both try to explain properly

[crimson leaf]

Schroeder mathematical analysis

[glossy zealot]

Thank you all

[heady ember]

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

[crimson leaf]

Honestly the only thing I don't like about Schroder is how late he introduces topology of R iirc it's like chapter 17 or something

[hollow shore]

I used a different book but I skipped that chapter. Is it important?

I thought id eventually do metric spaces later on

[crimson leaf]

I mean I guess it depends on the book lol like the book I've been reading uses the topology it developed early to develop everything else so it was very necessary but I really like the way it works out

[remote sparrow]

https://www.reddit.com/r/math/comments/18bmo09/best_springer_books_for_the_following_topics/

[glossy zealot]

It looks great, I like the additional details for each step

It is exactly what a beginner needs!

[hollow shore]

there is no good pdf of schroder out there

or at least I haven't found any

[vital bane]

Abbott

[rustic grove]

Kenneth Ross 'Elementary Analysis'

[graceful moon]

@stray veldt

[sharp cosmos]

Guys what books can be paired with Thomas' Calculus in order to properly understand the concepts covered? I've lost both my touch with calculus (been a solid six months since I've had to use it) and hopes from the assigned faculty for my calculus course. I'm basically looking at a for-dummies version, I guess

[daring lake]

Thomas Calculus is something that a new student to calculus would use, I can't really think of anything to compliment it.

[maiden halo]

Morris Kline's Calculus (it's a Dover book) is very good and comprehensive

[kind torrent]

any1 has class 11 math(straight lines) formula sheet?

[remote slate]

Singularités des systèmes différentiels de Gauss-Manin by Frédéric Pham has any english translation?

[cobalt maple]

Looking for a book on algebraic geometry that is mathematically rigorous and explicit in details; has lots of well selected problems and, ideally, the possibility of finding solutions to those problems somewhere. Does anyone have any recommendations?

Further details: I've had an undergrad course in algebraic geometry focused on curves with the book by Fulton which I wasn't the biggest fan of as it was too dense and lacked motivations for stuff. I therefore already know quite a bit of the material (stuff like alg sets, nullstellensatz, morphisms and coordinate rings, Zariski topology, local rings and geometry, tangent spaces, intersection multiplicities, projective space and projective alg sets, projective nullstellensatz, homogeneous coordinate rings, veronese and segre embeddings, projective rational functions, local geo of projective varieties and Bezout's theorem)

However, the course was very scarce on problems and fast paced, so I feel like my understanding of most of the above things is lacking. I therefore would be happy if the book would cover some of the above in greater details and with lots of problems.

[dusk wind]

With how much you have written here, writing your own book seems optimal

[cobalt maple]

My understanding of those topics isn't the best, which is why I need a book with lots of problems (ideally addressing some of the above topics)

I also wanted to ask: is Vakil's notes approachable as an introductory text?

[sage python]

Vakil seems to be fairly good

[crimson leaf]

Not algebraic geometry but it might be good to read some commutative algebra, Eisenbud's book might be a good fit for you, but it's a tome

[mellow wren]

Hartshorne
It fits all your requirements
It's a challenging book but it has so many wonderful and useful problems

[fallen bronze]

roughly how long would it take me to read basic mathematics by serge lang

[marsh ingot]

Any book that talk about complex differential forms in a friendly way?

[strange lava]

Any book recommendations on algebra II, precalculus or imaginary numbers?

[cobalt maple]

Thank you. I was considering it too. Seems like a nice book with lots of exercises

[cobalt maple]

Thanks, I will take a look

[strange vortex]

Pre calculus By ron Larson

If u want it on computer search up pre calculus by Ron Larson pdf

[strange lava]

thank you

[pliant falcon]

Book in SCV (several complex variables) with a primary emphasis on differential topology?

[vital bane]

Lol what?

The topology of your space would be the same regardless of whether you're dealing with C^n or R^2n right?

topologically they're the same

or am I missing something

or do you mean the differential topology of complex manifolds? (stuff like in the complex case the transition maps being holomorphic etc.) wouldn't that be covered in one of the complex diff geo books you were looking at?

[sage python]

If this person was looking at complex geometry and is now asking about SCV with a topology bent

Then I'm guessing these complex geometry books referenced SCV background

And he wants to learn that background, ideally from a source that emphasizes topology over analysis

[pliant falcon]

Thats exactly it!

[pliant falcon]

Like the guy above me said, the complex diff geo books heavily rely on the theory of SCV

[pliant falcon]

The differential aspects

Complex tangent bundle

Dolbeault cohomology

[sage python]

Unfortunately I don't actually know very many such books 😦

[vital bane]

implying that he knows at least one such book

[pliant falcon]

if only my lord and savior Lee did a book on complex geometry

[sage python]

0 isn't very many 🙂

Hmm

Poking around on Google a bit

What do you think of this?

https://bookstore.ams.org/view?ProductCode=CHEL/368.H

[pliant falcon]

hmmm, so...I don't know much sheaf theory at all

are they like fiber bundles?

[sage python]

The basic idea is that sheaves sorta remembers local information

So for instance, let's take CP^1

There aren't any non constant holomorphic functions to C

Because its image is bounded, by compactness, and thus its restriction to C would be a bounded holomorphic function, therefore constant

[pliant falcon]

okay okay, Im following

[sage python]

But if I consider functions defined on open subsets, for instance those which aren't defined at infinity

Ah now all of a sudden we have the theory of entire functions

This book seems like it starts from 0 on the sheaf theory front

[pliant falcon]

okay, so this isn't entirely different from the concept of fiber bundles, just deal with more arbitrary collections of sets

[sage python]

Yeah I mean, if you give me a bundle

I can talk about the sheaf of sections

Which is just, oh here's an open set U in the base space, I attach to it the set of sections of the bundle defined on U

And then in the other direction, given a sheaf you get something called the etale space

(Also sorry I'm a bit scattered since I'm heading home from campus)

[pliant falcon]

that makes some sense now

I will have to look more into it

it seems very categorical in nature

[sage python]

Yeah it is

[gray gazelle]

Is there any better version or similar book like "mathemathics for the practical man."

I was forced to study at religious school without math, but before i goes to dormintory i was a math national olymphic winner at my primary school

I wanted to relearn

[rigid flint]

Anyone got any good textbooks on geometry; specifically geometric proofs, circle theorems, and maybe vector proofs?
I am pretty mediocre at them, and its definitely not the best part of my math.

[remote sparrow]

Kiselev's two volumes on geometry, Lang's book on geometry, and Everything You Need to Ace Geometry in One Big Fat Notebook

[rigid flint]

tyty

[glossy zealot]

Someone told me I can use this as supplement, has anyone read through this?

The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Raffi Grinberg

The title attracted me a bit

[gray jungle]

that title is a red flag for me , but ile skim through it

[daring lake]

I believe that one should understand and construct proofs in their own way. Sure, book may break down a proof or give some steps to write a proof, but one should be able to read between the lines and completely understand the process laid out in a proof. It's not a easy thing to do, but comes with effort.

[dusk tapir]

Goal: Want to get better calculating integrals using lebesgue/riemann integration theory and techniques.

I identify as unskilled in that regard, so ideally the exercises range from simple to hard(er) and maybe there are worked out examples/problem solving approaches.

For this recommendation I only care about calculating these integrals and using convergence theorems and not about proof exercises.

[hearty viper]

Best book on trig? I BARELY passed trig this semester.

[night knot]

Not sure if this is necessarily what you need, but what about Krantz' Function Theory of Several Complex Variables? It gets to stuff like sheaves and Chern classes by the middle

[fallen bronze]

how long will basic mathematics by serge lang take to read, roughly?

[stuck zephyr]

depends

[rain ore]

anyone have any algebra 1 book recommendations?

more teaching, less questions

[spiral glade]

Hello. Noob here

I am trying to decide between two different textbooks

I have Sullivan precal 11th or Cengage Precal 5th

Anyone know if either of those are better?

[plain barn]

any recommendations for books on point-set topology?

[marsh ingot]

I found Andre - Point set topology and topics

[plain barn]

ty

[marsh ingot]

[gilded shuttle]

Does anyone know any good textbooks for studying calc 3 I have done all of single variable calc and i’m finding that I need to know multi variable and vector calc to get deeper into physics

[graceful moon]

For physics I’d say probably just go for Stewart, should be good enough

[gilded shuttle]

james stewart?

i see that a lot online

the book seems to have a lot of single variable when i saw the contents

so i didn’t know if it was really a calc 3 book

in university courses do they generally use stewart’s book?

[cold mortar]

In mine yeah, although we mainly use the notes of a teacher that just retired

[graceful moon]

Half the book covers single variable the rest is multiple variable and vector calc. It’s definitely used in many universities

[cold mortar]

It was a calc III class with the physics, astronomy and statistic buds

[gilded shuttle]

ok then ig i should get it

would u say it’s good for self study

[graceful moon]

It’s not a super rigorous book for like pure maths students but for applied maths or physics students it’s ideal

[cold mortar]

Oh absolutely

[gilded shuttle]

yea that’s what i’m looking for

[cold mortar]

The explanations are great! From what I've read

[gilded shuttle]

does it matter which edition?

cheapest or newest

[cold mortar]

Oh you're planning on buying it? I would say one that's not super old will do

[graceful moon]

Probably not, I’d just get whatever you can get, Stewart is very ubiquitous so you can probably find pretty recent editions for very cheap

[gilded shuttle]

yea

[cold mortar]

make sure to google the erratas

they should be free to look up

[gilded shuttle]

they range from like 120-300

[graceful moon]

Look for them used because that’s pretty insane e

I saw a copy of Stewart used for £10 last month

[gilded shuttle]

😳

for a whole textbook?

wow

quality must’ve been horrendous

10 is dirt cheap

[graceful moon]

Yeah there’s a charity shop just off of my campus that tends to get a lot of used textbooks and they go cheap, it was in perfect condition

But even new here Stewart is only £40-50 I’m sure

[dusk wind]

mecmath.net ?

[gilded shuttle]

this has calc 3 material?

[dusk wind]

should yea

[cold mortar]

Mi uni actually gave copies of Stewart away cause they were getting newer versions. EDIT: Hm now that I think about it idk if "gave copies of Stewart away" is quite correct. Maybe "gave away copies of Stewart" is better. I'm still learning english.

[graceful moon]

Ok I lied it’s £80 new but still I’ve seen it cheap used a few times (also there are plenty of PDfs hosted online)

[dusk wind]

not a fan but theres also https://www.whitman.edu/mathematics/multivariable/

[gilded shuttle]

what was wrong with that one

[dusk wind]

nothing

I'm just not a fan of it

authors all write differently

[gilded shuttle]

yea i’ll probably get stewart’s book

[gilded shuttle]

u mean the explanations weren’t as good

[dusk wind]

noooo

there is nothing wrong with it

I just don't like it fmpov

[gilded shuttle]

there’s just better

[dusk wind]

theres no clear distinction between books of the same relative levels

better is subjective

[gilded shuttle]

true

[dusk wind]

if you want to talk about better though, would you rather read a book from the 1980s or 2020?

[gilded shuttle]

recent books tend to have easier explanations imo and better wording but i also read a book from the 1940s when i first taught myself single variable

and i liked it

[dusk wind]

yeah but how common is that

[gilded shuttle]

not very

[dusk wind]

how often is it you can read a book not written for your time

[gilded shuttle]

that book did have a few exercises that didn’t make much sense either

the wording was strange

[dusk wind]

just as we do today

so a timejump of 50 years seems too risky to recommend to somebody, unless its on sale

[gilded shuttle]

true thank you tho

[dusk wind]

and yet, we still have people courageously providing these recommendations

[gilded shuttle]

usually i stick to youtube recommendations

mathsorcerer makes a lot of book reviews

he recommended books like stewart and larson

there wasn’t as many videos for calc 3 so i came here

werent

[cyan sequoia]

Hey man anyone at the collage algebra level of maths willing to be study buddy’s with me?

[hearty viper]

Your English is better than a lot of native speakers, honestly. But yeah the second version is slightly clearer.

[molten mason]

Same as any other textbook, if you know all the material, a week, if you don't and struggle a couple months

[remote sparrow]

i assume munkres is not to your liking? everyone knows that book

[glossy zealot]

Guys this is only remotely related to the topic of book recommendation. But do you usually do all the problems in the chapter/section of the book? I want to ask the same question for real analysis book too

[crimson leaf]

No unless there's a small amount of problems

[finite gale]

No

[heady ember]

So far, I normally do most of the exercises + self-proof just about every result given by the author

[remote sparrow]

have you had a professor assign all the problems in a chapter?

@glad prairie you mentioned that you had read Computability and Logic by boolos, burgess, and jeffrey. was this for a class? do you remember what class this was for? i am writing down alternative textbooks to Introduction to Mathematical Logic by mendelson for my professor to consider.

[vital bane]

my guy is inventing analysis by himself as he goes

[silk apex]

Mother by Maxim Gorky, very good book

anyways, what you suggest for calculus 1-2

[heady ember]

NaBrO I'm not coming up with the results myself

I'm not god

[glossy zealot]

Thanks everyone for the input. I am self studying a book and not sure if I should be doing few problems then move on or insist on doing all before getting to the next chapter

[glossy zealot]

I am self studying a book so I don’t have anyone assign me homeworks

Though I do problems that an open course suggested

I have been working on Real Analysis by Jiri Lebl, and following MIT real analysis course

[remote sparrow]

okay, but have you ever had a teacher assign every single problem in a chapter, unless the total amount of problems is very short?

no, right?

[glossy zealot]

Yea I did not

I think I understand your point. Do you have any ideas of which problems I should be doing when self studying?

[vital bane]

one thing you can do is mark every problem you do with a pencil in the book, and then a couple months after you've finished the book and want to review the subject or something, you can come back and do all the unmarked problems

[vital bane]

roll a dice!

[glossy zealot]

Good ideap

[glossy zealot]

Very nice idea too

[vital bane]

it's okay to not do every problem but at least take a look at every problem yk? like at least think a little bit about how you'd solve it before moving on

[glossy zealot]

Thanks for the advice. This is why I struggle with self studying, not sure when to move on or if I studied enough

I will just think about the problems within a set amount of time then

[remote sparrow]

https://dl.acm.org/doi/book/10.5555/1146297

https://www.amazon.com/Classical-Mathematical-Logic-Semantic-Foundations/dp/0691123004

found a couple of reviews for this book

seems neat

i have a library copy with me

might buy this book

this book places more emphasis on how logic can be used to formalize mathematics than other books, which try to stick to the main ideas: propositional logic, first-order logic, soundness completeness of propositional and first-order logic, a bit of model theory, deductive calculi (e.g. hilbert systems or natural deduction), godel's incompleteness theorems, axiomatic set theory, and computability

[vital bane]

[remote sparrow]

proof theory generally gets shafted in introductions to mathematical logic, but avigad's Mathematical Logic and Computation bucks this trend, although it seems too advanced for a beginner in logic

[glad prairie]

@tardy oasis this might be for you

[plain barn]

I don't know any book

well, besides one that I found in a youtube video and the one another person recommended me

[daring lake]

From what I have seen, he has a review video for every math book in existence and praises all of them.

[daring lake]

I did it for bartle (2-9) and rudin (1-7) but took me like 5 months
I tried the same for dummit and foote but gave up 2 sections in

[tardy oasis]

Dunno logic, sorry

[remote sparrow]

i was sure i saw someone with a bird pfp with ryc in their name mentioning that book

[orchid mortar]

Too many birds fluttering about

[gray gazelle]

I wanna become math wigard which book has potential to make this a reality

[graceful moon]

If you glue like a full UG worth of books together you might be able to count that as a single book

[marsh ingot]

Wigard?

[graceful moon]

But seriously there isn’t a book that will do that, you just need to study and keep at it and you’ll get good at maths

[opal fossil]

I read that for a course, I think just titled Computability and Logic. Interesting book, more readable than most. It seems like a bit of an exercise in "just how many powerful results follow from some version of the liar paradox?"

[opal fossil]

Yeah, that's been my experience -- lots of books on model theory and it's relatively hard to get a focused proof-theory text. I'll have to look at this one.

[plain barn]

anyone knows a real analysis problem book?

really want to solve real analysis exercises

lots of them

[marsh ingot]

Rudin Real and Complex analysis

[plain barn]

hm

[marsh ingot]

By real analysis what do you mean?

One and several variables?

[gray jungle]

there are problem books for real analysis

lots of em , look into "problem book in real analysis" dont have anything specific

[plain barn]

one

cus I only know one

[marsh ingot]

Spivak looks good

[plain barn]

ty alex

[marsh ingot]

[dusty slate]

@everyone

@everyone

@everyone

@everyone

@everyone

[graceful moon]

Do you really think you’d be able to tag everyone in a server with this many people?

[marsh ingot]

I was going to ping mods

[stuck zephyr]

Shut up

[daring lake]

wouldn't that be a calculus book?

Anyone here have read Steven Roman's field theory? I would like to know if I would be good for Galois theory (I also appreciate any other suggestions )

[opal fossil]

Problem books are books containing only problems and solutions -- no explanation. The idea is to learn elsewhere and become expert from the problembook.

[daring lake]

Ah okay, I didn't know there were such books

[steel pebble]

helloooo everyone !!!!

[stuck zephyr]

Hello there

What book recommendations do you want

[steel pebble]

what

[daring lake]

You came to #book-recommendations

[stuck zephyr]

Yes

[steel pebble]

oh is there like books of maths to study it ?,

[daring lake]

.. yes

[steel pebble]

ssrry i didn t see XD

[steel pebble]

i wanna some recommandations abt books of trigonometry it will help me

[stuck zephyr]

openstax.com

[steel pebble]

?

[stuck zephyr]

Look up there

[opal fossil]

Here's a weird niche request: Anyone know of a book on measure theory or real analysis, which tries to explain the historical and logical development of the field? Rather than just the results that we currently know in the field? Like: Cauchy thought the integral and sum swap, so-and-so showed "not always", Lebesgue thought to take pre-images (because ... why?) etc.

[steel pebble]

what

[stuck zephyr]

You see something called Google and then type "openstax.com" then scroll down for a trigonometry book

[steel pebble]

i didn t understand anything

[steel pebble]

oh okay

i didn t find anything

it shows a book from amazon

ngl am poor i can t buy a maths book for 89$

[opal fossil]

libgen.is

[stuck zephyr]

There a download and view online

You don't need to buy it

[steel pebble]

OH TYSM

well are u a college student or what ?,

[stuck zephyr]

Who me?

[steel pebble]

yh

[marsh ingot]

Do you think someone here pay for one?

Well if its for collecting and personal purpouses

[stuck zephyr]

No I'm a highschool student

Graduating this year

[steel pebble]

cool

from wich country

[stuck zephyr]

Canada

[steel pebble]

okayy

[remote sparrow]

https://maa.org/press/maa-reviews/a-radical-approach-to-lebesgues-theory-of-integration

https://maa.org/press/maa-reviews/a-radical-approach-to-real-analysis

[plain barn]

I would also be interested in something like that

[trim burrow]

Any book recommendations about the history of maths, specifically algebra and calculus because those are the topics I will dive into then.

ChatGPT recommends these. Any idea?

"Leonhard Euler: Mathematical Genius in the Enlightenment" by Ronald S. Calinger: This biography of Euler covers both his life and mathematical contributions. Euler was a pivotal figure in mathematics, particularly known for his work in calculus and the introduction of several key mathematical concepts​​.

"A Concise History of Mathematics" by Dirk S. Struik: This book offers a straightforward and classic approach to the history of mathematics. It covers various mathematical fields including the development of algebra and calculus, presenting these subjects in a historical context​​.

"The History of Mathematics: A Reader" by Jeremy Gray & John Fauvel: This book places a strong emphasis on the context of mathematical developments, using translated original sources. It's particularly recommended for its coverage of earlier mathematical material​​.

"Unknown Quantity: A Real and Imaginary History of Algebra" by John Derbyshire: This book provides a detailed narrative on the development of algebra, exploring its origins and evolution across different cultures and time periods​​.

"Men of Mathematics" by Eric Temple Bell: Although written in 1937, this book remains a classic in the history of mathematics, covering the development of calculus and other fields through the lives of various mathematicians including Isaac Newton​​.

[mellow wren]

Yes :Chad:

I like having a math library

[dusk wind]

Good bot, at least 2 of those are useful

Unfortunately they are also old

Honestly, maybe a youtube video would be better for this

[maiden halo]

that is a quite incomplete list. but you could try the following. not all will be directly relevant to algebra and calculus, but check their bibliographies.

• Boyer. The History of Calculus and Its Conceptual Development. 1949
• Bressoud. Calculus Reordered: A History of the Big Ideas. 2019
• Grabiner. A Historian Looks Back: The Calculus as Algebra and Selected Writings. 2010
• Grant & Kleiner. Turning Points in the History of Mathematics. 2015
• Gray. The Real and the Complex: A History of Analysis in the 19th Century. 2015
• Kline. Mathematical Thought From Ancient to Modern Times. 1972
• Krantz. The Proof is in the Pudding: The Changing Nature of Mathematical Proof. 2011
• Stillwell. Mathematics and its History. 2010
• Stillwell. The Story of Proof: Logic and the History of Mathematics. 2022

[dusk wind]

[maiden halo]

See also some recommendations here (and probably some other Reddit threads): https://www.reddit.com/r/math/comments/c10xs/any_recommendations_for_a_book_on_the_history_of/

[fluid skiff]

Does anyone know if there is such a thing as math podcasts?

[dusk wind]

They exist

[fluid skiff]

Like audios which help you learn a topic?

[novel obsidian]

read

[fluid skiff]

So you think board etc is not needed?

[dusk wind]

Uhh a youtube video?

[fluid skiff]

Na just audios

[novel obsidian]

i'm being naive and pretentious i apologise

[dusk wind]

Yeah.. extract it..

[fluid skiff]

But that will not be a podcast. That will be audio recording of a video lecture

[crimson leaf]

This seems like a really ineffective way to learn math visualizations are very helpful and being able to look at something over and over also helps both of which you lose by moving to audio only

[dusk wind]

Could you really even call it a lesson at that point. An actual podcast would also be difficult to follow even if it's highly organized

Try a math audiobook and test the results

[fluid skiff]

What are some good audiobooks one can listen to while traveling? Maybe not just related to maths

[dusk wind]

Ah this is more accessible, probably your favorites currently, although math sorcerer is technically video that could be a start

[trim burrow]

wow, thanks!

[hearty steppe]

Anyone heard of this? https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176

[plain barn]

what's your mother tongue?

or well, what languages can you read in

[dusk wind]

DeepL

[trim burrow]

eng, fr

[remote sparrow]

i just mentioned two books

[plain barn]

oh ok

[plain barn]

I saw it sry thank you

[mossy flume]

So my goal is to study algebraic combo

And I know a lot of that is motivated by representation theory

What's a good first book for representation theory of finite groups

I've got this like "Pioneers of Representation Theory" book that's like a historical telling of how this was all developed

But after reading a bit of it, it's light on proofs

Lots of theorems just not a lot of proving them

[pallid nexus]

is spivak the best book from which to learn partial integration? am a third undergrad and i need something that has a mix of integral multivariable calculus and something about topology, i have a weird mandatory class that mixes both

[mossy flume]

Are you taking a course in differential geometry?

[pallid nexus]

would you mind if i showed you a synopsis that way you can judge

cuz idk

[mossy flume]

Sure?

[pallid nexus]

Multiple integrals. Riemann integral of a bounded function on a rectangle. Basic properties. Integrability of continuous functions. Area of sets in R2. Sets of area zero and sets of measure zero. Lebesgue's characterization of Riemann integrability. Integration over bounded subsets of R2. Fubini's theorem. Functions defined by an integral. Change of variables in double integrals. Polar, cylindrical and spherical coordinates. Multiple integrals. (6 weeks)
2. Integration over curves and surfaces. Piecewise smooth paths and curves and their length. Integral of a real function (scalar field) along paths and curves. Integral of a vector field (differential 1-form) along a path. Independence of path of integration. Potential of a vector field (exactness of a 1-form). Angle form and winding number. Green's theorem. Integrating over surfaces in R3. Flux and divergence of a vector field. The divergence theorem of Gauss - Ostrogradski. Rotation of a vector field. Exterior derivative of a differential 1-form (a differential 2-form). Stokes's theorem. (7 weeks)

[mossy flume]

This just sounds like a second course in real analysis

[pallid nexus]

but i took analysis 2

[mossy flume]

[pallid nexus]

1. Derivative. Motivation (geometry, physics) and definition of derivative, connection between derivability and continuity, basic rules for differentiation, derivative of elementary functions. Rolle's and Lagrange's middle value theorem, monotony, local extremes. Derivatives of higher order, Taylor's middle value theorem, convex functions, inflection. Asymptotes, analysis of function flow and graph of function. Some applications. (5 weeks)
2. Integrals. Motivation (plane area, work done by a force) and definition of Riemann integral. Integrability, monotony and continuous functions. Primitive function, Newton - Leibniz formula. Substitution, partial integration, integration of rational functions. Improper integrals. (5 weeks)
3. Series. Definition, criteria of convergence. Power series, Taylor series. Uniform convergence, function series. (3 weeks)

this was analysis 2

[loud cradle]

derivatives and integrals in analysis 2? what did you do in analysis 1 then?

[pallid nexus]

1. Introduction. Sets N, Z, Q, operations and order, geometric interpretation on real axis, proof that , motivation for R. Notion of function, Cartesian coordinates, graph of a real function of real variable, affine functions, simple rational functions. Quadratic function, polynomials, rational functions, composition of functions, injectivity, surjectivity, bijectivity, inverse function. Roots, exponential function on Q, logarithmic function, hyperbolic and area functions. Trigonometric functions (geometric definition on unit circle), arcus functions, solving equations containing trigonometric and exponential functions. Axioms of real field R, supremum and infimum of a set, completeness. (6 weeks)
2. Sequences. Notion of sequence and subsequence, monotony, boundednes, monotonic subsequence, various examples of sequences. Convergence, basic rules, connection between convergence, boundednes and monotony, Cauchy sequence, limes superior and limes inferior. Field C, sequences in C, convergence in C and by coordinates. (3 weeks)
3. Continuity. Limit of function and basic rules, continuity of function and operations with continuous functions, continuity of rational functions. Strict definition of exponential function, continuity of exponential function. Correspondence between continuity, boundednes and monotony, continuity of inverse function. Continuity of elementary functions.

is that...strange?

[loud cradle]

not necessarily, there's something to be said for spending a fair amount of time on topological aspects of R before starting the "calculus" stuff

[graceful moon]

Youve covered everything typically covered in analysis 1 and 2 but its split between 3 courses and then does some introductory geometry. Not the strangest thing ever but not how I did it

[pallid nexus]

yea we do not have a topology class in undergrad

well we sorta do

anyway that aside spivak? or something else

integrals have never been mz strongest suit

[pallid nexus]

bump

[remote sparrow]

zorich's Mathematical Analysis II, munkres Analysis on Manifolds, hubbard and hubbard's Vector Calculus, Linear Algebra, and Differential Forms, second half of browder's Mathematical Analysis: An Introduction

[plain barn]

anyy recommendations of books on measure theory?

[marsh ingot]

Rudin Real and Complex, the first chapters

[remote sparrow]

axler

also check pins

[marsh ingot]

Or Bartle

[plain barn]

lmao

[marsh ingot]

If you want only measure theory, Bartle is better

[plain barn]

not that I think the recommendation is bad it's just that's the second time you recomend me this today

[plain barn]

ty

anyways ty alex

[plain barn]

I am also interested in complex analysis and stuff so I guess rudin

[marsh ingot]

One day you should check one of Rudin's book

[plain barn]

I like the idea of rudin cus I heard he's hard

[marsh ingot]

Tbh Rudin is like love and hate relation. Sometimes is good sometimes is bad and can be even worse

Rudin's measure theory part and Bartle are quite different. Rudins start with relationship with topology and Bartle just start to talk about measurable functions then spaces etc

[remote sparrow]

just do folland if you want something hard

[marsh ingot]

The important theorems like Radon-Nikodym is different in each book

Bartle is soft and Rudin dont care and just uses Hilbert spaces while proving Lebesgue decomposition at the same time

[crimson leaf]

Royden is also good for a gentler introduction

[plain barn]

I think I have collected now books on every math subject I have any interest in and which is in my capabilities

I mean, pdfs

but books

[plain barn]

sure

[remote sparrow]

#book-recommendations message

[plain barn]

ty

[marsh ingot]

Bogachev looks good for the first volume

[plain barn]

I think in the past 2 weeks I have asked recommendations for books on everything I could possibly learn rn

now comes the hard part

reading them

[marsh ingot]

Good luck

Measure theory is pretty beautiful imo

[plain barn]

it does seem so

and also I'm intensily desiring lebesgue

[marsh ingot]

Lebesgue is good for 1 dimension

For n dimensions uhhhh the formalism is a bit delicate

But no rush

If you decide to read Rudin's book I could help if you struggle in some proof. I used it for my thesis

[plain barn]

oh cool

sure ty

[heady ember]

Look in pinned

[daring lake]

I really like rudins RCA so far (have read 2 chapters)

[left cloud]

rudin RCA goes hard

[mellow wren]

[LOUD INCORRECT BUZZER SOUND]

[sage python]

Buzzer canceler noise

Measure theory done right is excellent

[mossy flume]

bumping this

I want something just to get my feet wet in rep theory

something to work through over winter break

my thought was Serre's book? At the least get through Part I, it's only like 50 pages

[sage python]

Serre is good yeah

[mossy flume]

dope

[remote sparrow]

https://www.youtube.com/@mathematicaladventures

https://www.youtube.com/watch?v=UiKgy9rLviA

seems like a cool dude

https://www.youtube.com/playlist?list=PLuiPz6iU5SQ_3Gubdqa1JHBvM0GBFcIV0

this set theory playlist roughly follows hrbacek and jech's set theory book

https://ocw.metu.edu.tr/course/view.php?id=270

here's the associated webpage

https://www.youtube.com/@philipwelch3429/playlists

https://people.maths.bris.ac.uk/~mapdw/teaching.html

resources for logic and set theory

https://www.youtube.com/playlist?list=PLTpJiP-hRaV2ZKBQipaeWp7Yxk_IK5X-5

[stuck zephyr]

You don't need to spam this to every channel mate but there many people need help in #linear-algebra , you can help them

[marsh ingot]

[mossy flume]

I mean

Artin would be a good source

I think the best thing to do would be ask for help with problems from Artin

now if you find Artin hard to understand, then other books are also great

sometimes you just need to read the same thing written in a different way to get it

Dummit and Foote is popular

IMO dry but whatever

[inner token]

Recommended Numerical Analysis book? Both at ug and grad level pls

[rare estuary]

seconded

[gray jungle]

i believe emil artin has quite a good book on galois theory

[halcyon ether]

Does anyone have a good book suggestion for self studying statistics and probability at undergraduate level?

[radiant crow]

Guys I'm in highschool

Could anyone recommend a book that covers all hs topics or it can be one that covers all introductory college level topics?

[gray jungle]

what?

[radiant crow]

Yes

[gray jungle]

its still pretty good , maybe im just a fan of old school books

old $\neq$ bad

[hasty eagle]

James Banach

[gray jungle]

i would not advise using baby rudin if OP hasnt done formal proofs yet

also introductory college topics cant be covered in a single book

The usual math topics at a introductory college level are real analysis , linear algebra , discrete math , probability and multivariable calculus. ( this is a bit subjective btw)

[radiant crow]

Actually I'm in highschool, so I would prefer a book fit for hs students preparing for competitive exams

[radiant crow]

I have only done the basics of calculus in physics xD

[gray jungle]

competitive exams like what?

[radiant crow]

These are Indian exams, JEE and JEE Advanced (this one is one of the toughest exams in the world actually)

[gray jungle]

Ah , im not familiar with JEE exams sorry but try to search for JEE in #book-recommendations search history, i know many people asked about it before

[radiant crow]

Oh alright

[gray jungle]

@arctic hamlet Btw im pretty sure Lang does galois theory , cant go wrong with that book.

its also not that old

[radiant crow]

Does cengage have good theory?

Cuz I would rather just read the book and skip lectures for some chapters

Could u please name the writer?

I haven't watched lectures for some of the chapters. Does the book explain the topics in a proper way? I'm not really after questions at the moment

Ok bro 😀

[daring lake]

That book is as thick as a pamphlet

I haven't read it entirely yet but its on my list

Also it has a really cool cover

[somber prairie]

I’ve done 1 semester of analysis as well as unrigorous multivariable calculus and some differential equations (+a little bit of Lin algebra)
Any good recommendations for statistics books (doesn’t matter whether they’re rigorous/proof-based or not, just not one of those really simple give-you-some-intuition books)?

[keen gyro]

people, has someone read the book by Steven Hocking?

[clever idol]

✨