book-recommendations

[remote sparrow]

what about your old textbooks?

[dim pendant]

Paul's online math notes

[old terrace]

My undergrad institution had a lot of anti-textbook profs, so DE and multivariable never had books. I have still have my class notes though

[old terrace]

Thank you! These are great

[dim pendant]

Let's gooo

Have fun

[coral bison]

Dead mathematicians society

[foggy wolf]

thomas calculus wooo

[hearty grail]

thanks

[vital bane]

@median fossil

you said this book was actually good right? Or were you checking out some other source?

[median fossil]

Too short to call it a book

It's like 20 pages max

[median fossil]

But yes I like it

I know that Rudin's variant of Streater--Wightman's proof of the easy (non-distributional) case is now standard

It's e.g. the proof you can find in Krantz

[median fossil]

Obviously the book has nothing to do with stats though

[summer stone]

Missed opportunity to call it
'Lectures on the w_edge_ theorem'

[vital bane]

Why?

[foggy wolf]

anybody know any good complex analysis books

i wanna dive deeper into it

[prime merlin]

guys im starting to read bartle and sherbert real analysis, anything to keep in mind?

[prime merlin]

i used brown and churchill

[vital bane]

When you read a theorem or a lemma or a corollary, instead of looking at the proof in the book, try proving it by yourself first

if you are unable to do it, try again, if you are still unable to prove it, try reading the first few lines of the proof to get a hint

[prime merlin]

alr ty

[bleak slate]

hi guys (or hello again) i'm looking for some french contemporary novel. i don't think it has to fit in a certain age group nor level (since i'd say i'm fluent enough to read most stuff). my fav genre is prob mystery, but i can read other stuff too. however, i do prefer melancholic or even dark-ish over light-hearted themes.
anyone got suggestions?

[old terrace]

I used Complex Analysis for Mathematics and Engineers by John Mathews and Russel Howell in undergrad and liked it

[foggy wolf]

ok

[dim pendant]

Someone calls you, claiming to be from the US border patrol. They say that they intercepted a number of illegal substances (usually drugs and fake IDs) and claim that your personal information was found in the postal data. They go on to say that you're a victim of identity theft, but that to protect yourself you must appear in court. After confirming you understand, they ask you to speak with another person over the phone, and that person tries to verify your identity, setting you up for the very scam they pretended that you've already fallen for.

I read that as "what's the new scam format"

now I look like an idiot

good morning

[dim pendant]

nice try

[foggy quest]

https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[warped steeple]

i want to self-study multivariable calculus, what is a good book for this? right now im using "single and multivariable calculus"

[plucky hedge]

I am looking for a good textbook on Riemannian manifolds. Could be in the context of machine learning, but that is optional. Any recommendations? Thanks in advance.

[naive lava]

do carmo is a standard intro

petersen and jost are more advenced

[plucky hedge]

Solid. Thanks man, appreciate it

[plain belfry]

Terence taos notes are good

[vital bane]

he has CA notes?

[tender river]

ive seen pty say good things about zakeri for complex analysis and if pty likes it its probably good

[plain belfry]

https://www.math.ucla.edu/~tao/resource/general/132.1.00w/

[shell merlin]

I was thinking about Arabic and read this as theyhORRemm

smh

XDDD

[fiery hamlet]

does anyone else think pugh is really weirdly organized

[timber mesa]

yes I think this is true

it's not a bad text to get intuition and maybe some exercises from but not one I'd follow for a course

[fiery hamlet]

yeah and the text just doesn't define some things

Do you have recommendations for a first text in real analysis? preferably not too easy

[timber mesa]

for something to take right after

calculus*

I think Abbott's Understanding Analysis is a good one

it's not in one-to-one correspondence with the topics in Pugh but I think that's kind of hard given how unique Pugh is

[timber mesa]

if I wanted to cover all material in Pugh maybe I'd do this or Rudin first, then something like Munkres' Analysis on Manifolds or any decent vector calc book for multivariable, then some book for measure theory would could either be Royden, Stein-Shakarchi or Folland depending on taste

[craggy arrow]

what about AoPS

[molten gulch]

AoPS does not cover analysis, to my knowledge

[fiery hamlet]

ill try abbott thank u

[gray gazelle]

does anyone know any books for starting to learn linear algebra and differential equations?

[molten gulch]

friedberg, insel, spence for linear algebra; got nothing good for diffeq sadly

[timber mesa]

you could check out Hirsch-Smale-Devaney's Differential Equations, Dynamical Systems, and an Introduction to Chaos, the first half of it is kind of an unified introduction to both and the second half covers more advanced topics in qualitative theory of ODEs and dynamics

I also like Kreider's An introduction to linear analysis as an ODE book that tries to give some insight into why linear algebra, or really functional analysis is useful

[timber mesa]

more normal recs for LA are what TCC said here lol

or e.g. Axler

though maybe you want a book that focuses more on matrices and stuff

[molten gulch]

For that we'd just suggest the standard Lay Lay Macdonald textbook which is used at too many unis here because it's all fucking matrices and drives me a bit mad

[gray gazelle]

thanks guys!!

[cerulean steppe]

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

[cerulean steppe]

For linear algebra, https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ works

[normal crystal]

mtaylor is back
other recommendations be warned

[gray gazelle]

what's a good reference for the inverse function theorem?

with a self-contained and easy-to-follow proof, while keeping things rigorous

[merry sphinx]

howard anton for LA, and yeah idr know anything good for ode, i guess zill is a common one thats used

[cerulean steppe]

Tao's book 2 has a detailed proof. This book has it less detailed: https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/analmv.pdf

[gray gazelle]

thanks

[jovial sky]

I need a book to review Algebra 1-2 that focuses on problems but has brief explanations because I understand everything (it's just to refresh my memory).

Wait is there a website do to algebra problems?

[molten gulch]

khan academy

[jovial sky]

Already done it but I dont think its enough

[sterile pelican]

Basic Mathematics by Serge Lang?

Or if you want Gelfand’s Algebra

[dim pendant]

you don't understand problems by listening to their solutions

you understanding by trying them until you give up, and then using the solution to give you hints to try again

[sterile pelican]

I am in agreement it's why I prefer books than apps or sites like Khan Academy

Nobody can process that information for you rather it's the struggles that help you get it, sometimes videos and apps can help but it's mostly really one struggling through a book

[vital bane]

pay attention in class, even if they are bad

[dim pendant]

yeah you never know what might be discussed in class that doesn't align with book structure and the likes

[stone heart]

What's best book to start class 11th

[sage python]

Oh that brings back a memory

[violet tapir]

anyone know any good resources for introduction to complex analysis/functions and also one for transcendence theory

[vital bane]

What is transcendence theory?

Theory of Transcendental Numbers?

[violet tapir]

yea

[wraith ember]

I wanna self learn complex analysis (UG level) and I am confused between these two: Stein, Shakarchi - Complex Analysis or Visual Complex Analysis by Needham. Does anyone have soft copy of these books? Which one should I follow?

[sage python]

Stein is more of a standard serious treatment

My impression of Visual complex analysis is that it's a lot of geometry, a lot of yapping, doesn't do much of the analysis or really get very far in finite time

[gray gazelle]

i have infinti time

[wet sentinel]

is it recommended to study multivariable analysis from pugh after being done with the single variable part from rudin, ie up to chapter 8 of rudin?

or are there better options

[molten gulch]

<@&268886789983436800> user intends to distribute pirated material

[plain belfry]

ono

[plain belfry]

also take a look at lars ahlfors book

[zealous coyote]

Please don’t talk about piracy here, we’d rather the server doesn’t get shut down

I’m going to delete this message. You’re not in trouble but please don’t do it again

[muted quest]

Any book for stochastic calculus any1?

[vital bane]

I thought only posting download links to pirated content was against discord TOS?

[foggy quest]

https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[remote knoll]

I've heard good things about "Brownian Motion and Stochastic Calculus" by Shreve and Karatzas

[foggy quest]

Karatzas and Shreve is good

[wraith ember]

Dang, didn't know that (new to discord) thanks for the help👍🏻

[vagrant trout]

Hi, i was looking into encryption and RSA, this led me to number theory (Euler's totient and Carmichael functions ...)
i am now looking for resources; ideally books (videos are ok too); that introduce the subject in an intuitive way rather than just simply
stating definitions and formulas.

[molten gulch]

Introduction to Modern Cryptography - Jonathan Katz and Yehuda Lindell

This is what we've used at uni

[grim ore]

Look into Silverman's works

[violet tapir]

ty

[wet sentinel]

?

[wet sentinel]

any recommendations?

[grim ore]

I am a little lost @wet sentinel, usually Rudin's text can be generalized to R^n anyway?

It usually specifies in the text what can and what cannot, including general topologies and metrics

Pugh RMA is a good read tho

[merry sphinx]

well it doesnt do differentiation on R^n in c1-8, or integration in R^n, which is probably what they want

[rare moth]

is this book good? *(Calculus: Graphical, Numerical, and Algebraic Hardcover – January 1, 1999 by Franklin Demana (Author),

[grim ore]

If you want to read papers on it, if you want to look into carmichael numbers, look into authors : Erdos and Pomerance heavily

I was obsessed with carmichael numbers for a decent amount of time

[raven vale]

Any book rec’s for geometric algebra? Preferably with a focus on physics application

[cerulean steppe]

Taylor's PDE book 2 covers Clifford Algebras

[trim kayak]

Has anyone read A Mathematician's Lament by Paul Lockhart? Is it worth reading?

[old elk]

I feel that sometimes the books explain a lot of theory and there are few examples and I think that's what frustrates me the most.

[boreal briar]

Hello! Can someone suggest a good book to learn abt Theory of Probability? I’m trying to get a head start for my next semester but I feel lost with every book I’ve encountered so far🫠

[molten gulch]

At what level? With measure theory or without?

[boreal briar]

Without, it’s not a prerequisite

[remote sparrow]

do you have a syllabus or course description handy

[dim pendant]

This is why we use a number of resources to learn

[daring wolf]

It’s an (un)necessary prerequisite
like if you are doing elementary/applied then it is not a prerequisite but if you are doing advanced probability theory then it is

[boreal briar]

Not really😭 I only have a brief description of it:

STAT-3920. Probability
The course will cover the axioms of the theory of probability, discrete and continuous distributions including binomial, Poisson, exponential, normal chi-square, gamma, t, and F distributions, multivariate distributions, conditional distributions, independence, expectation, moment generating functions, characteristic functions, transformation of random variables, order statistics, law of large numbers and central limit theorem.

[boreal briar]

It’s still an undergrad level, I’m assuming not too in depth like using any measure theory

[daring wolf]

not all unis have same syllabus like some unis have measure theory as a prerequisite

[remote sparrow]

https://stat110.net

[boreal briar]

Thank you!

[normal crystal]

idk, her course has 3810 more STAT
ngmi

[peak bluff]

hi guys any book recommendations on higher level olympiad geometry

I already did some

[proud osprey]

Evan Chen's EGMO is very comprehensive

[peak bluff]

okay

ty

[vocal marlin]

Hello, I'm gonna study actuarial science. any books someone can recommend?

[west gorge]

Hey guys, can someone recommend me a good book for practicing probability questions?
It would be good if it starts with simples questions and then moves on to diffucult ones for every topic, and must have solutions/hints

please suggest since Im learning the theory but lacking the practice

[ionic osprey]

a first course in probability by Sheldon ross

[west gorge]

thanks

[full cairn]

When reading big paperbacks I usually have to constantly hold my hand in it to prevent it from closing, which gets pretty tiring after a while. Anyone have experience with something like this that holds the book open for you?

[shut mesa]

That's a skill issue bro

[dim pendant]

Most of the books I end up with have unstable spines that rip open, so I utilize my fast processing to read quickly and then I close the book to work on exercises or statements made along the way

[old terrace]

Never used a device, but have had success with two paper weights. It is a bit annoying to turn pages tho

[full cairn]

Yeah, I have considered using a paperweight, but haven't found any that fits well

[full cairn]

Skill issue I guess

[rough umbra]

What would the recommendations be for with measure theory?

[molten gulch]

generally I believe billingsley is a common choice

[rough umbra]

Thanks

[subtle violet]

or durrett

[subtle violet]

i have something like this, the prongs are quite firm and it takes a bit of force to remove and replace them, but it’s fine for math since i’m not turning pages that often

[full cairn]

I see, thanks for sharing

[naive lava]

yea you just fold the back of it

after breaking the book in

it's not that big of an issue

there will be some wear

but that's generally unavoidable to have over long periods of time

and if you want to use the book as a reference you should buy it as an hardcover most likely

[full cairn]

I followed this guide just now: https://m.youtube.com/watch?v=6cgQiykhkog
which helped a lot It still has a tendency to close, but it requires a lot less effort to hold it open

I definitely prefer hardcovers, but they are often twice as expensive, so most of my books are paperbacks

[brittle quarry]

Easy solution: get all your books used

Then they’re pre-broken in 🧠

[full cairn]

Lol, I wish it were that easy 😅 finding the books I want used is like finding a needle in a haystack

[brittle quarry]

Just find a mathematician who’s giving away his entire collection

Then be the only person to email him on Facebook

And get his entire collection of 1500 textbooks

(Totally not speaking from experience)

(I have 346 textbooks in my basement right now and another 1154 to collect)

[full cairn]

Wtf?? Do you run a library or something?

[brittle quarry]

Im getting all of

Henry Pollak’s textbooks

[full cairn]

For free?

[brittle quarry]

Yep

[full cairn]

Wow, nice

[brittle quarry]

I’m gonna be digitalizing a bunch of them and putting them up on a website for people to check out

Over the summer

It’s gonna take a LONG ass time though cause yk

1500 textbooks 😭

Here go to #chill I’ll send a picture of the current collection

[pliant pollen]

does anyone have any sugges for a geometry book?

[mossy flume]

o wow

that's an insane project

so many books, good luck

[brittle quarry]

Yeah

There’s some good ones

And also a bunch of transcribed lecture notes

From a typewriter

So I’m digitizing a transcription of a lecture 💀

[mossy flume]

hey sometimes those lecture notes have some gems you can't find in textbooks

[remote sparrow]

you should upload them to the internet archive too

also it would be wise to check if some of them have already been digitized

[heady ember]

TeX it up

[brittle quarry]

Exactly

@mossy flume here check it out #chill

I’ll send some photos of my haul from yesterday

Just brought them inside

[mossy flume]

Ya I saw the ones you sent before

Oh are there more?

[sterile pelican]

Has anyone read Douglas Gregory’s Classical Mechanics? He claims only calculus and LA are needed but is it good to add a form of elementary mechanics?

[sterile pelican]

I have a library copy and I just read its preface

My concern is given he states “there is no waffle” implies there is no motivation for these equations and want to hear someones two cents on it

So I thought maybe elementary mechanics can fill that before reading this book

The maths is not the problem for me it's the mechanics bit since I know no much physics, it's why I only asked for the physics not maths, despite mentioning no prior mechanics are needed, but is useful to have, I am a bit dubious after seeing the Amazon reviews

At least the motivation for mechanics I don't think I have the intuition for it, and I seem to like the topics covered here for my self studies

[ancient creek]

Wow I will make sure to follow the progress!😎

[dim pendant]

Fr get me a thread on that

[sterile pelican]

I understand you are being snarky for stating I didn't state ODEs, and it's mentioned in the book, sure it's a failing of not mentioning that here, but the maths isn't the problem here I graduated in stats with a background of those maths, it's why I asked specifically the physics

[brittle quarry]

Oh nice

I got image perms

In book recommendations now

[brittle quarry]

Some books from today’s haul

[sterile pelican]

I understand that but I don't need to worry about ODE I had studied them before

[brittle quarry]

Bunch of interesting stuff

[sterile pelican]

I want to know the physics bit at least

[brittle quarry]

I still need to unpack and sort everything but I think I got somewhere along the lines of another 12 analysis texts

4 transcribed lectures

I took a whole bunch of modern algebra

Some graph theory

Some discrete mathematics

[sterile pelican]

A whole bunch!? meanwhile I am just half way, or likely three quarters, from my abstract algebra book

[brittle quarry]

Like

Maybe 6-8

Maybe more I don’t remember exactly how many I grabbed Monday

[dim pendant]

Oh god how I wish I had a physical copy of Serre's "coherent algebraic Sheaves" in the original French

[brittle quarry]

The pages are actually cut wrong

[ancient creek]

The treasure of humanity

[brittle quarry]

So like the tops of some of the pages are still connected

That’s how old this is 😭

[dim pendant]

Lmfaoo insane

[ancient creek]

That'd be so cool if you release all of them🔥

[brittle quarry]

That’s the goal

I’ll try my best but yk

Obviously I gotta balance this with writing my

College apps

[ancient creek]

I can help you with making all digitization look nice, I can contribute with books I have here too from the country I am from, China 😁

[storm drift]

anyone can help me?

i can send a pdf file of my math book

[ashen ruin]

Hey!, Can someone recommend me books on Integration and Differentiation Calculus

[ancient creek]

Introduction to Smooth Manifolds by John M. Lee but I haven't finished it

[cursive rivet]

I'm assuming you're joking or misunderstood the question, a book on smooth manifold theory is not suitable for calculus...

[ancient creek]

Oh maybe. I just remember it had one chapter covering particularly the differentiation calculus.

[sterile pelican]

Doesn’t that book require his other one called topological manifolds, which then require analysis with metric space?

[daring wolf]

i take this as a joke

[ancient creek]

I wasn't trying to make a joke sorry😅

[sterile pelican]

My goal is to read the topological one it’s only why I know of it :^)

[tribal crow]

you can get away with not knowing anything about metric spaces for ITM

source: I did it

[ancient creek]

Wow.

Knowing metric spaces can create more intuition imo

[tribal crow]

mhm, I don't doubt that

I didn't even know what an open ball was when I started ITM

I would not recommend doing it the way I did

but it's possible, is all I'm saying

[ancient creek]

Isn't it mentioned on the first page lol

impressive what you did tho

[tribal crow]

in the appendices, iirc

[sterile pelican]

I can see after finishing analysis then

I was thinking to do like a tiny section in metric spaces then review it again in the appendices

[torn mesa]

We're having a Calculus with Analytic Geometry course, is there a dumb friendly calc book out there?

[fresh skiff]

higher i will read properly ITM soon. Idk why i do study any subject more than one time to understand it
Right now i am studying LA again (FIS). Now i am understanding better, so a bit demotivated as well. In order to not read again and again i am writing notes as well. After LA i will study AA and ITM (i guess i dont need any other linear algebra then FIS, or maybe Hoffman and kunze if i wanna study LA on side)

[tribal crow]

I wish you the best of luck with your studies

I’ll be following your journey c:

[fresh skiff]

Thank you so much higher
i hope i wouldnt disappoint you at any moment

[sterile pelican]

I propose a fascinating route, does AA->LA sound enticing?

[fresh skiff]

but this route will kill a lot of interesting examples

but LA --> AA --> LA sounds cool lol

[sterile pelican]

How so?! Just get an AA book with rings first then you can do LA after quotient rings

I just want to spread the gospel of Berberian

The morally correct LA book

for mathematicians

Then again I know nothing of the morality of maths don’t mind me

[fresh skiff]

AA --> LA: this path i wouldnt be able to see SL(K), GL(K) groups, i wouldnt understand symmetries properly like this

[sterile pelican]

Oh…

Well that’s fair if you need to see those first

[shut grotto]

Book recommendations for basic topology?

[grim ore]

munkres honestly

its a pretty typical answer and would be surprised to see anything else outside of that for point set

for algebraic, its another story tho

[shut grotto]

Can you help me find a pdf

[grim ore]

youd probs have to go to a library of some kind that has math textbooks; its not publically available on the internet by the author sadly

if you are at a university, they should def have some

[shut grotto]

I see

The book seems rather cheap, I'll just buy a physical copy

lmao all the negative reviews are about how bad the quality of the book is 😭

like the physical quality

[grim ore]

Yeah id recommend the updated 2nd edition with the spirals cover

[shut grotto]

Alright, thanks!

[heady ember]

After you do LA + AA, you might as well just head to CA

[daring wolf]

munkres

[merry sphinx]

mfw i learn all of top from the appendix of ISM 🗿

[sterile pelican]

Why not Lee?

[vital bane]

Munkres also has an Alg Top book though idk what the consensus on that is

[vital bane]

simply generalize metric topology you've learnt in analysis to general topological spaces yourself

all of general topology is left as an exercise for the reader

[sterile pelican]

It's just curious since Lee seems to be a graduate text while I'd assume Munkres is undergraduate

[vital bane]

there is no graduate and undergraduate

there is only math

[sterile pelican]

[molten gulch]

not too great AFAIK

[dim pendant]

I believe Munkres's "Algebraic Topology" is quite dated

[molten gulch]

yeah

[dim pendant]

But I've since discovered that Conway has a book on topology that is extremely short so I don't think I'll ever open up Munkres's "Topology" ever again

[molten gulch]

I think the standard ones these days are like

Hatcher's Algebraic Topology
Tom Dieck's Algebraic Topology
May's Concise Course in Algebraic Topology
Rotman's Algebraic Topology

idk maybe some people like spanier still

[dim pendant]

Spanier does indeed still float around

I think I had it in my super secret electronic collection

For quite some time

[molten gulch]

I still do

[wet sentinel]

is there only one edition of apostol's introduction to analytic number theory which is the first edition published in 1976 or are there newer editions

[willow merlin]

which book explains complementary subspaces

[ancient creek]

😎 They shouldn't make this distinction, really confusing sometimes

[foggy quest]

most linear algebra books do. Subspaces $U$, $W$ of $V$ are said to be complementary if $V = U \oplus W$

[hasty eagle]

L

[grim ore]

we do not speak of this

[sharp latch]

I have a first edition Spanier in my book collection🙏

[gray gazelle]

Munkres and Ronnie Brown

Later half of T&G is Alg Top but first half is mostly pointset

[willow merlin]

that's all to know about complementary subspaces?

[willow merlin]

is the orthogonal complement a unique complementary subspace?

[deep moat]

Book for starting combinatorics?

[foggy quest]

The orthogonal complement of $U$ is complementary to $U$.

[willow merlin]

wdym

[hasty eagle]

L

[foggy quest]

If $U$ is a subspace of $\mathbb{R}^n$, then $\mathbb{R}^n = U \oplus U^{\perp}$.

[hasty eagle]

L

[willow merlin]

is the ort complement unique?

[foggy quest]

By definition, $U^{\perp} = {x \in \mathbb{R}^n : u^Tx = 0 \text{ for all } u \in U}$. What do you mean by unique?

[hasty eagle]

L

[willow merlin]

unique meaning there is only one orthogonal complementary subspace Uperp for the subspace U of V

note that there are infinitely many bases for Uperp, but i mean unique meaning is the only complementary subspace of U that satisfies the orthogonality condition (all of his vectors and his linear combinations are orthogonal to all the vectors in U)

does this hold for the infinite dimensional case? how would you prove is unique? @foggy quest

[foggy quest]

it's pretty easy to show that if $W$ is complementary to $U$ and $W \subset U^{\perp}$, then $W = U^{\perp}$.

[hasty eagle]

L

[desert gate]

I liked A Walk Through Combinatorics by Miklós Bóna

[humble spire]

Is spivak fine for starting calculus? I used aops precalc. If it is not, what are neccesary books to go through for preparation? I am currently going through how to prove it by vellerman

[sterile pelican]

Maybe after Velleman, and better do some single variable calculus at least, like Lang's Calculus

Spivak has excellent exercises for elementary analysis but you need proofs nonetheless, in the preface from his later editions, he realised it would be better to call it an analysis book

As shown here

[humble spire]

yes, thank you!

i was wondering if watching 3b1b's essence of calculus and going through some of rosen discrete math as proof practice with vellerman would be ok prep?

or i will just go through thomas calculus

[sterile pelican]

If you want to go through the main ideas of calculus I think Lang's Short Calculus is good enough and just doing Velleman will do. The rest of watching videos or reading Rosen, which I actually don't like lol, can help but it's best to just do the exercies from Lang and Velleman

Also take note that doing Spivak will be slow and painstaking unlike Lang and Velleman, so be patient of your self and ask help here 😄

[humble spire]

alr

tysm for this help!

i was really just confused on how to approach spivak. this cleared it up lol

[sterile pelican]

No worries that's the path I did for my self studies so I think it is doable to most

[humble spire]

one more thing if you do not mind

how long would you say at the high end is lang's calculus

taking

[sterile pelican]

I am honestly not sure

I am a pretty slow and busy person, before I lost my job, so it took me about a year and a half together with Velleman

[humble spire]

alr

ty

I will try to get atleast some of this done this summer and see how far i get

[sterile pelican]

You can take both Lang and Velleman at the same time

[humble spire]

i was thinking that and maybe some supplementary books to have more practice

and i will be sure to do that

[sterile pelican]

Sure try that at the end of the day it's your interest, and I wish you all the best

[humble spire]

thank you!

[alpine ridge]

Hi can anyone suggest a good book ODE and PDE? also if possible, i really need a proof based linear algebra book

[molten gulch]

for linear alg: friedberg insel and spence or https://linear.axler.net

[alpine ridge]

Thanks!

[molten gulch]

yw

[onyx lily]

yall i need recommendations for calculus books aaaaaaaa

ping me when you got one

[tribal crow]

@onyx lily welcome to the mathcord!

if you're looking for a non rigourous book, Stewart is the standard recommendation

if you want something with more rigour though, Spivak isn't a bad choice c:

[tender river]

https://realnotcomplex.com/analysis/calculus

[onyx lily]

alr ty guys 😋

[fresh skiff]

why not topology

[dim pendant]

Afzal resurrection

[daring wolf]

because next one after AA is commutative algebra

and topology is not prerequisite for it

[fresh skiff]

i guess Zariski topology is something

[daring wolf]

yes but unnecessary tbh

[fresh skiff]

also Atihya's book need top isnt it?

[daring wolf]

while com alg books have some topology concepts or algebraic geometry things, they are not strict prereqs

[fresh skiff]

oh, but i still i will learn top at some point i would need it (at least basic general top)
Oh wait i meant, After doing LA i will continue Top and AA

[fresh skiff]

oh interesting

[dim pendant]

Usually the correct move is to pay good attention to metric topology while studying analysis, and then you learn some really basic general topology as an extension of metric, and only later do you take a full course when you need to be caring about abstract spaces or manifolds

[gray jungle]

i mean you already did rudin no? the step from metric topology to general topology isnt that hard for you

the only new difficulty you have to deal with is what you lose when you drop hausdorffness

rest is pretty much in the same spirit

[fresh skiff]

Ah so it requires some of topology, I was about thinking for Lee's book on ITM

[fresh skiff]

oh, maybe it would take some time, but i know basis topology from rudin very well so i guess wouldnt take much time (maybe some efforts)

[dim pendant]

Yeah you'd be fine

[fresh skiff]

yay

thank you

lemme read LA , it is frustrating when i cannot prove some statement that i proved months ago. But i guess i should move on

[pallid crypt]

is there a book/online resource to learn plane geometry from the ground up?

[heady ember]

... Because you said LA -> AA -> LA. If you wanted to do LA after doing LA and AA, you might as well do CA. Or did you not catch that CA abbreviates comm alg?

[fresh skiff]

oh gosh
i misunderstood it

i thought complex analysis and was wondering why so random

this makes sense now

[heady ember]

[ancient creek]

From Los Angeles to Alaska is tough, After Alaska going to California is not bad

[reef granite]

Is I.A Maron too much for beginner

Concept wise beginner not understanding wise

[full pier]

Hello, is Lang's undergraduate algebra a good textbook?

[twilit field]

Higher algebra by hall and knight pretty generic but still one of the best for secondary school algebra

[normal crystal]

<@&268886789983436800> doing this again, not sure if same account as before

[remote vortex]

<@&268886789983436800>

Also can we please ban modern day gatsby

[dim pendant]

It's fine. A lot of people find Lang to be a dry writer but such statements reflect people's preferences about the study of mathematics. In reality, the book is perfectly fine.

[remote vortex]

<@&268886789983436800>

[sterile pelican]

Mods?

[remote vortex]

What the hell is going on?

[sterile pelican]

We are under attack by this scam thing

[echo knot]

Was it some random screenshots ?

[remote vortex]

Yes, some kind of scam using James Donaldson's name as the draw

[peak dew]

To self study any decent book on set theory for beginners?

[celest trellis]

I need a good hunger games like book

Or like the maze runner

[dim pendant]

What do you mean "set theory"

Are you leaning the basic language of sets so you can start studying advanced math

Or do you want to learn real, axiomatic set theory

For the basic, naive language, any popular real analysis book is sufficient. For actual set theory, Jech is a common shout.

[molten gulch]

<@&268886789983436800> scam is back

[timber mesa]

trying to figure out an automated solution to this

[remote vortex]

Very worryingly at least one of them weren't new users but existing ones.

[timber mesa]

yeah it's common for hacked accs to start spamming stuff

so remember children if someone offers you a 50 usd gift you're about to be part of a botnet

[peak dew]

Yeah that
Btw I got good book already someone helped me

[sterile pelican]

But imagine the books you can buy with 50usd!

[remote vortex]

Like half a page!

[molten gulch]

Whoa

[normal sandal]

Someone have a rec for an introductory alg geo book? I'm pretty familiar with commutative algebra and I've done a little geometry abt a year ago at the level of fulton's algebraic curves, I'd like to go somewhat fast bc I feel I have the background, any recs?

[molten gulch]

Hartshorne?

[floral lantern]

Shafarevich?

If you know your commutative algebra and have done Fulton’s algebraic curves you could probably just read Hartshorne though

Or maybe Vakil

Sort of in ascending order of difficulty and depth would be shafarevich < vakil < hartshorne

[earnest meadow]

Does anyone know where I can find the errata for Sullivan's Precalculus 11th Edition (Global Edition)?
I've been noticing some wrong answers in the answer key, or I'm just an idiot. But take chapter 2.1 exercise 108 for example. It's as simple as it can get:

[normal sandal]

Yeah makes sense. Hartshorne does look intimidating though, I'll try looking at vakil aswell

[floral lantern]

Well any graduate level book is pretty intimidating at any level I think

Harthorne is much more compact than vakil for what it’s worth

800 pages long

[normal sandal]

Do you think it's worth looking at fulton again? just to get used to the objects and basic computations?

I'm probably going to keep it by the side while studying anyway just wondering if it's worth a refresher at this stage or if I should just start

[floral lantern]

i think you could probably just start - Hartshorne will redefine everything but in more general contexts of course. Just keep Fulton on the side for concrete examples you find too abstract

[normal sandal]

Awesome, ty!

[mossy flume]

I recommend Harris's Algebraic Geometry text just as a repository of examples (I find the text itself quite hard to follow just on its own). I will also recommend Cox, Little, and O'Shea's text Ideals, Varieties, and Algorithms for a computational angle to things. For scheme theory, I actually prefer Gortz and Wedhorn to Hartshorne by a great deal but of course being familiar with Hartshorne is invaluable

Oh how can I forget

https://agag-gathmann.math.rptu.de/de/alggeom.php

these notes are fantastic as well

[ebon gulch]

Can anyone recommend any book on Trigonometry (covering basic to higher understandings step by step & conceptually)?

[vapid quarry]

I mean a regular precalculus textbook usually has some good trig

[ebon gulch]

I see.. thanks

[vapid quarry]

you could also try Prentice Hall Trigonometry

haven't checked it out in a while but I think it's pretty good

[ebon gulch]

oh.. heard

[vapid quarry]

I can send the link if you want

[ebon gulch]

sure.. thanks

[vapid quarry]

https://archive.org/details/prenticehalltrig0000hayd/mode/2up

you might have to make an account and borrow the book

[ebon gulch]

yea.. got it

[still oriole]

Hey everyone! 👋 I'm starting Algebra 2 and was wondering if you have any good book recommendations. Looking for something that's clear and good for building strong fundamentals. Would love any suggestions!

[vapid quarry]

I'm assuming algebra 2 is like 11th grade math right

[still oriole]

Yehh it is!

[vapid quarry]

alright I think I got a book

https://bim.easyaccessmaterials.com/index.php?level=13.00

[still oriole]

Greatt ty

[vapid quarry]

this is our im3 (11th grade) math textbook

[trail hemlock]

prolly your best bet is khan academy. it will help you build fundamentals and they have practice. openstax has an algebra book for more practice problems, but khan academy is great for learning

[vapid quarry]

make sure to look through the contents to check it fits your algebra 2 curriculum

[fresh skiff]

i am about to ask a silly question.
If i study Linear algebra and do can do all homework problems (from oxford archive and example sheets from cambridge) then should i be satisfied and move to other subject? (maybe can back to lin algebra again for further study like Roman etc but surely after doing some maths)

[vapid quarry]

look for some stuff on mit ocw

[still oriole]

Really appreciate the suggestions!

[vapid quarry]

their linear algebra course has some pretty good problem sets (I'm using them rn lol)

and the exams are good as well

[fresh skiff]

oh they use Gilbert's book i guess, idk but i feel like its for applied purpose

[vapid quarry]

yeah it kinda is

[fresh skiff]

oh, surely i will check the exams

[vapid quarry]

ok

have you tried the problems in a textbook?

[still oriole]

Good idea, I’ll make sure to check the contents first. Thanks!

[fresh skiff]

ahh, but i will check exam and homework (certainly the new think i will find would be LU decomposition maybe idk)

[fresh skiff]

yes, till now i guess i was able to do 90% from each exercise set (i am about to finish the revision of chapter 2 from FIS -- friedberg)

[vapid quarry]

ok that's good

tbh if you want more reinforcement of the ideas just look through diff textbooks and do some problems

[fresh skiff]

this makes sense, i pick up Hoffman and kunze but i was unable to do last three problem from the first exercise set so i demotivated lol

[vapid quarry]

😭 omg I was just about to open hoffman and kunze

[fresh skiff]

also i have LADR, its full of challenging problems lol

[vapid quarry]

I was looking for a theoretical lin algebra book so I thought hoffman would be good

[vapid quarry]

yeah it's pretty good

[fresh skiff]

damn 😭
well i will read it again and will skip those problem (will revisit again)

[fresh skiff]

i guess so it is good

[fresh skiff]

yeah

[molten gulch]

hoffman is good, axler is good, FIS is good

[vapid quarry]

yeah I was thinking of axler

tysm 🙏

[signal mountain]

ive heard a lot of good things about halmos before but i never see it get rec'd here, anyone know why that is? is it seen as outdated or smth else ?

[vapid quarry]

who tf are these people that keep posting the same scam 😭

[slender cargo]

Just wanted to give a slightly different opinion on this. I think using Spivak's Calculus is fine after what you studied, but you would just have to trust that the difficulty spike is a bit high. Just don't get too demoralized about how much harder some problems might seem at first. Spivak did write that book to be a first exposure to calculus, after all (even if it's a hard first exposure). I feel like the suggestion to supplement it with a book like Velleman is good though.

[cerulean steppe]

The linear algebra book?

[tribal crow]

@still oriole welcome to the mathcord!

@ebon gulch and welcome to the mathcord too!

[signal mountain]

yah

'finite-dimensional vector spaces'

[humble spire]

Yes, thank you!

[floral lantern]

Halmos is like old

And also very functional analysis pilled

Axler isn’t quite the same but is a “modern” functional analysis-oriented linalg book

[molten gulch]

What makes it FA oriented specifically? (About both books)

[remote sparrow]

functional analysis, loosely speaking, is "linear algebra" but on infinite-dimensional vector spaces

[humble spire]

referring to the pinned message, why is schroder analysis doable without calculus and only proof background?

[remote sparrow]

so arguments with determinants don't really hold (since they only apply to finite-dimensional vector spaces)

axler does most proofs without determinants

he's also a functional analyst

[scenic sequoia]

Any substantial differences to baby Jech and Enderton ?

First set theory book, freshman undergraduate currently taking calc from Apostol

[remote sparrow]

former has more topics

it's a bit denser as well

[scenic sequoia]

Oh okay, thanks

[humble spire]

if anyone has read schroder, could they reply about the approximate difficulty compared to, lets say, spivak?

if not also its fine.

[unborn pewter]

I'm studying precalculus which textbook should I get

[molten gulch]

stewart is fine, stitz and zeager is fine, lang's basic mathematics is fine, etc...

btw why are you named riemann zeta when you may not even know enough to know what it means or why it matters as much as it does?

[normal sandal]

ooh this is really helpful I'll take a look at cox's book, I've used gathmann before but totally forgot it existed now. tysm!

[mossy flume]

I think knowing some basic computational AG really helps to compute examples

The CLO text is written for undergrads who know linear algebra

So you'll pick up the math very quickly

[floral lantern]

Axler wise, the reason he de-emphasizes the determinant is because the determinant doesn’t exist in infinite dimensions. Halmos tries to do most of his proofs via the more general infinite-dimensional arguments (he likes using inner products a lot and such) instead of “cleaner” finite-dim argument.

[molten gulch]

I see

[floral lantern]

Books like Hoffman and Kunze or FIS are more “algebraist-pilled” in the sense that they emphasize the determinant, finite
dimensional arguments, and finite dim applications

[normal crystal]

marlins really prepping with his Ross Sensei cap on

[tiny gulch]

Tell that to a physicist lol

We be taking determinants of differential operators~

[floral lantern]

🥀

[unborn pewter]

Thanks. The reason why I named myself what I named myself is for kind of a dumb reason that of which being I like the way it looked on a graph.😅

[molten gulch]

I see

[wraith cave]

it looks kinda funny

asymptote near the origin and then shoots off to various infinities for high |z| and low Re(z)

red is θ = 0 for x + iy = re^{iθ} btw

[normal crystal]

<@&268886789983436800>

@green aurora
that's why you're ChipperPotato
not QuickerPotato😎

[molten gulch]

<@&268886789983436800> scam again

[remote sparrow]

<@&268886789983436800> scam

[dapper root]

Dang there’s a lot

Maybe I should preemptively ping once for the next one

[molten gulch]

yo smugcat

[coral bison]

That’s a cool idea

[full pier]

Hello, I am currently going through Lang's undergraduate algebra textbook which I have found to be quite good, I was wondering if his linear algebra book is also good, I currently have linear algebra done right by axler

[remote sparrow]

maybe img perms got turned on for the thread

[sterile pelican]

If you are doing abstract algebra first mind if I introduce to Berberian's linear algebra?

But you need to know quotient rings first before you start that book

[ebon gulch]

Thanks

[misty frigate]

hi, I am a grade 12 student, are there any books I can read to learn more about 1. geometry (circle properties, cooridnate geometry, 4 centers of triangle...) and also 2. probability (Bayes theorem, Binomial distrubution, poisson distribution...)

[abstract bear]

Anyone know of any books that provide unorthodox methods to approaching problems in math? for example using lagrange multipliers to "solve" an optimization integer problem (I know this doesn't always work but it does work most of the time :p)

[deep moat]

1. Introduction to Geometry — Schaum's
2. Geometry by Jurgensen (friendly book, I recommend!!)
3. Sheldon Ross' book about Probability — A First Course in Probability

By any chance, are you studying about Geometric Probability?

[misty frigate]

yea i think my syllabus includes that too

[misty frigate]

thx, ill check it out

[shut grotto]

y'all sure that rudin is a good pick for analysis? like if I can understand the concepts, fill the gaps in the proofs and do most of the exercises on my own that's good enough for introductory analysis?

[tender river]

give it a try, you can always fall back on a gentler text

[shut grotto]

I've done the first 3 chapters at some point

except the exercises from the 3rd chapter

Kinda forgot why I quit though, guess I'll give it another go

[daring wolf]

I used it as my first book to analysis and there was no issues

it's totally okay to start with it imo

[shut grotto]

What books did you use to go deeper into analysis? (after rudin)

[daring wolf]

deeper means by?

you mean measure theory?

if you mean classical analysis rudin is enough for it

no need for deeper one and i wonder if there is one

[shut grotto]

Like multivariable analysis or smt idk just whatever people usually do afterwards

[shut grotto]

I see

[daring wolf]

there are some ways

like
topology
abstract algebra
and what you said

[shut grotto]

I see

thanks!

[heady ember]

LESSGOO

My sewing materials have arrived

300m long, 0.8mm thick nylon waxed thread for just ~5 S$
(*casually ignores the child labour involved )

[gray gazelle]

So I am gonna start calculus, including calculus one two and three, which book should I purchase for the absolute practice plus I want to make my calculus kinda good so I want it to be in levels for example basic then moderate then advanced questions, and the number of questions should me much more so that I could practice plus I want notes inside the book too

[patent canopy]

hi chat, is there a small list of books that could help me prepare to strengthen my basics and prepare for grad school interviews by the end of this year ?

[gray gazelle]

By grad school what do you mean? You mean like entering uni?

[patent canopy]

for a PhD in Math, focusing on GGT and Modular forms

i have read office hours of a GGT book, its nice and Kapovich too

[gray gazelle]

So you're undergraduate?

[patent canopy]

i completed my math undergrad a year and half ago, completed my master's in AI

[gray gazelle]

I mean it's pretty obvious I'm sorry

[patent canopy]

will work for a year in Data Science

and then prepare for PhD

[gray gazelle]

Can you help me with stuff? I need help in calculus

[patent canopy]

sure

[gray gazelle]

You're ok talking here?

[patent canopy]

you can DM me too

i am fine with anywhere

[gray gazelle]

Sent you a dm

[old terrace]

I have never read this book, but people say good things about Stewart’s Calculus:Early Transcendentals.

I’ve enjoyed Active Calculus and Paul’s Online Math notes, but those are both free online resources (although active Calculus sells paper books too, iirc). In a similar vein, Khan Academy has lots of calc problems, although their multivariable is a bit incomplete

[gray gazelle]

@old terrace thank you

[vital bane]

peak

[celest jacinth]

Any probabilities book recommendations?

[open elm]

I self taught myself calc I-III solely using Stewart's Calculus during high school and it's pretty easy to grasp and has some good computational questions I do suggest it if you want to learn the basics of computation before diving into the proof-based side

[gray gazelle]

I'll go with stewards then baby rudin,thanks for the rec

[molten gulch]

At what level

[open elm]

baby rudin is a pretty tough analysis textbook

I think people normally start with something more introductory then move on to rudin after

[celest jacinth]

university, i wanna study this summer

[open elm]

if baby rudin is too difficult I would suggest Analysis I by Terence Tao (more formally written proofs) or understanding analysis by abbott (more intuitive)

[molten gulch]

yes, but do you know measure theory?

[celest jacinth]

yes, kind of

[vital bane]

Probability was so good that they released Probability 2

[molten gulch]

buh

[stable flicker]

[stable flicker]

This book shouldn't cause "too abstract for me" symptoms too

There's a ton of suggestions for probability, even at the graduate level

So I do recommend either A reading them all or B explaining more what kind of book you want

[celest jacinth]

Thanks!

[fickle haven]

I would like a recommendation for linear algebra

I've been searching for a book that covers it well

Thanks

[vital bane]

What kind?

pure LA with proofs and stuff or more applied stuff?

[stable flicker]

Time for me to introduce more applied math
https://textbooks.math.gatech.edu/ila/

[fickle haven]

More applied stuff would be nice, however im not well documented on the topic should id like more of an introduction

[open elm]

typically in unis they would first start with something like elementary linear algebra from Anton

[stable flicker]

If you want applied it's usually one of the Strang books

LADR/LADW are also good to add on as reference for any applied POV

[fickle haven]

Thanks for the resource

[fickle haven]

Thanks

[fickle haven]

Thanks a lot

[vital bane]

Huh?!?!

LADR is certainly not for applied POV lol

it's more like "LA for analysts"

[stable flicker]

That's why I put it for reference

[vital bane]

LADR? More like L

[gray gazelle]

@open elmdont be surprised if I spam you with doubts then lol

[vital bane]

I'd put FIS for reference tbh

[molten gulch]

lanalysts

[stable flicker]

You do want pure math reference as opposed to an applied book (like Strang)

[vital bane]

it has more applied stuff on top of pure math

[vital bane]

Yea imo FIS would be perfect for that

[fickle haven]

I've read LADR is also a good introduction to structuring proofs

which im also eager to start learning

[vital bane]

I think any good math book is a good introduction to structuring proofs

[fickle haven]

I guess thats true

[tribal crow]

@fickle haven welcome to the mathcord!

[tribal crow]

Rudin

[vital bane]

that would require Rudin to be well-written

[fickle haven]

Thanks i had a warm welcome

[tribal crow]

true :p

[vital bane]

learning differential forms from Rudin is the final boss

[tribal crow]

as Dami once said

[fickle haven]

Do you know which field would be more important as a math background for studying physics?

Not that im studying physics, just that i've always been interested

[tribal crow]

I think it depends on what area of physics you want to go down?

[fickle haven]

Specially kinematics and mechanics in general

[vital bane]

Analysis and Geometry mostly

that's about it

[tribal crow]

ah, for mechanics, you'll probably need a lot of geometry

[fickle haven]

I understand

Thanks

[vital bane]

Higher I don't think they mean the kind of mechanics that requires stuff like symplectic geometry

[stable flicker]

To solve these you'd want to look into solving standard differential equations

[rich sun]

for (mathematical) continuum mechanics, differential geometry and functional analysis

[fickle haven]

Yeah ive always been interested on differential equations, involves a lot of calculus too right?

[stable flicker]

It's not a lot of math per se

It's a lot of calculation

But well calculation helps

[fickle haven]

So more practical and less theoretical?

[vital bane]

Yup calculus + LA would be great for ODEs (Ordinary Differential Equations)

[stable flicker]

You can do the theoretical ones

[vital bane]

Multivariable calculus too

[stable flicker]

linear algebra actually creeps in

But you won't need to know why/how

[vital bane]

You can choose which direction you want

[fickle haven]

I really liked the idea of vectors and vector spaces on high school thats why i asked about linear algebra, also matrices

[vital bane]

Yes it's super cool

You'd love LA

[stable flicker]

"Vector spaces" goes really deep

[fickle haven]

So partial derivatives and all of that?

[vital bane]

and more!

[fickle haven]

Yeah, i once watched a video about fluid dynamics with vector fields very interesting stuff

[vital bane]

vector fields come up in multivariable calculus

[rich sun]

sections of a vector bundle

[tribal crow]

next chapter of ISM for me :o

[vital bane]

sections of tensor bundles

[vital bane]

Let's goooo

[fickle haven]

Sometimes i think im deffinetly too dumb for that if im honest

It just looks too complicated at first glance

[vital bane]

All the people who invented/discovered all those complicated ideas were once a student like you, who were confused about certain topics and clear on some others

[fickle haven]

Thanks for the boost of confidence

I think ive seen this symbol once but idk where

maybe logic or proofs of some kind

🤔

[gray gazelle]

$\join$

Man I keep forgetting the latex names

$\wedge$ $\vee$

[hasty eagle]

Eclipso

[gray gazelle]

Yeah the former is used for joins(or meets? Idk) and also the logic symbol for “and”

[vital bane]

wedge product

[vital bane]

yea join is \vee and meet is \wedge

[gray gazelle]

Ic ic

Thanks

Kinda weird their names are basically synonymous..

[vital bane]

basically least upper bound and greatest lower bound (in a poset)

yeah

[cerulean steppe]

is it different than $\lor$ and $\land$?

[hasty eagle]

L

[cerulean steppe]

$\vee$ and $\wedge$

[hasty eagle]

L

[upper estuary]

What's that one quote by von Neumann, "One doesn't understand things in mathematics, one gets used to them". math is hard and it is often a struggle even for the geniuses

once I understood that it made it much easier to not lose faith in myself when I'm stuck

[fickle haven]

thanks a lot for the motivation

[severe blade]

Is abstract algebra by dummit & foot an appropriate first exposition to rigorous group theory

[old terrace]

It’s probably readable without any previous experience and more in-depth than most other books suitable for undergrads

[severe blade]

Okay that's good to know, my objective is to learn this for physics so I'll probably have to read it sooner or later ig

[old terrace]

I don’t really much physics (TIL group theory is in physics), but D&F is one of the classic algebra books for a reason

[severe blade]

I learned that when looking at QFT and string theory and I was quite surprised as well!

And thank you for the recommendation!

[wicked fractal]

https://tenor.com/view/cirno-touhou-cirno-touhou-touhou-memes-touhou-meme-gif-1856342627816926458

[wicked fractal]

Rudin is not bad

[plush rain]

maybe, but i would certainly not use rudin as an “introduction to structuring proofs”

[quartz stirrup]

what is the best book to really learn math for a guy who has difficulty learning math

[old terrace]

What kinda math are you trying to learn?

[quartz stirrup]

the most basic one

[molten gulch]

This tells us nothing

[cunning elk]

for low level math it's not worth fretting over a specific book

there are plenty of resources online

[quartz stirrup]

well im completely new to math

[old terrace]

If you are trying to learn arithmetic, prealgebra, algebra, precalc, or single variable calc, Khan Academy is great

[quartz stirrup]

i didn't was interessed learning until now

[molten gulch]

Yeah don't go read Weil just yet, use Khan Academy

It's a useful website with many practice problems

[tribal crow]

@quartz stirrup welcome to the mathcord!

[floral lantern]

In book recs is crazy work

[tribal crow]

[open elm]

sorry what do you mean by this? XD

also you should prolly learn how to do proofs before analysis

I think "How to prove it" by Velleman is the one most people suggest

my school curriculum taught how to proofs so I never did it though

otherwise you could instead pick up a book in discrete mathematics which teaches how to do proofs as well as a bunch of other stuff which is hugely helpful in understanding more abstract books

I read the one from Susanna Eep and it's super easy to read! I also self taught myself during high school using it

[molten gulch]

I had to read epp kast semester, I didn't like it a lot, but it was okay IG

[open elm]

I think it's a good starting book

[molten gulch]

I don't like those big fat books like that, I generally prefer specific books for specific topics

Burton for ENT
Blitzstein and Hwang for Probably and Stats
Bona for Combinatorics
Sipser for Automata

[open elm]

haha that's true! I prefer specifics too but if you're new to higher maths it's more intimidating

[molten gulch]

Ehhh personally I didn't find it too bad

I also learnt how to do proofs by doing linear alg, and it didn't feel too bad, well alongside having to take a discrete maths course last term

But in the end, basic "discrete maths" is too shallow IMHO to do enough of anything

[open elm]

it's supposed to be a starting point to just improve general mathematical maturity before later specializing, discrete mathematics is a huge field

[molten gulch]

Yeah

I guess

[open elm]

Your approach may suit certain students better I agree though but it does depend

[molten gulch]

I just feel like each of those fields is so vast, but I get the intention of a class like that

[sterile pelican]

I think it's doable to touch some fields

But to go in-depth you kind of need to dedicate your life on one or three things

[rocky berry]

can u recommend good book for self studying number theory

[vital bane]

tbh you don't need discrete group theory

you need Lie Groups for QFT

[severe blade]

Wouldn't I have to first learn about more "general" groups then go into a more specialized topic like lie theory though?

[vital bane]

afaik no, since Dummit and Foote or any UG Algebra book for pure math students mostly covers finite groups (sure it also has group theory results for general groups but most of the focus is on finite groups)

So you'd see a lot of things relating to the order (basically cardinality) of a group (which is most of the time finite)

I think you'd benefit more from a "Lie Groups for physicists" book

or something like that

[severe blade]

I see, I see so it's not really worth the detour and I might as well jump right into it

Do you have any recommendations for such books

[vital bane]

Yes, that is what I've heard physicists say, and I'm going through group theory using Dummit and Foote right now and I'm seeing mostly finite group theory

[vital bane]

I don't really know I want to learn both physics and pure math so I haven't really looked at books like that

but you might find some helpful recommendations here:

https://math.stackexchange.com/questions/1154018/lie-theory-for-physicists

[severe blade]

thank you!

I'm quite into pure math as well

mostly to complement physics in a way

[sterile pelican]

There are a few I do like Silverman's A Friendly Introduction to Number Theory

Depends on your level though

[vast leaf]

Elementary number theory by Dudley is pretty decent

[fresh skiff]

any comment on zukerman

sorry if i misspell

[sterile pelican]

I never used that so I cannot say

I really like Silverman’s prose though

I wished his algebra book was written in that manner instead the current on

[vital bane]

Zuckerman?

[fresh skiff]

oh yes, i always forget "c"

[vital bane]

It asks for nothing other than "mathematically maturity" from the reader. It's great

[fresh skiff]

ah dont you like his algebra book

[fresh skiff]

goated

[rocky berry]

completely beginner i know calculus 1-2 and trigo. I will also start studying calculus 3 soon but i want to start number theory aside

[rocky berry]

David burton's book is not for beginners right?

[sterile pelican]

I would say doing a proofs book would be better Velleman has a section on number theory for you to be familiar with

[rocky berry]

i will try velleman then btw are u teacher or student?

[remote sparrow]

it is

[sterile pelican]

I am in the camp that one should do some proofs first though if they never read one

[sterile pelican]

Well I self-study maths for fun but I am a stats graduate and I do teach high school maths part-time irl

[rocky berry]

that's some great advice!

[rocky berry]

Oh very nice!

[rocky berry]

so practicing proofs by seeing or without seeing it?

[rocky berry]

can u elaborate mathematical maturity? please.

[vital bane]

https://www.youtube.com/watch?v=zHU1xH6Ogs4&pp=ygUVbWF0aGVtYXRpY2FsIG1hdHVyaXR5

[rocky berry]

because all im doing applied mathematics, i want to study pure mathematics also

[vital bane]

https://www.youtube.com/watch?v=4HFyWC-YtIk&pp=ygUVbWF0aGVtYXRpY2FsIG1hdHVyaXR50gcJCd4JAYcqIYzv

[sterile pelican]

Maturity is kind of hard to define but after painfully interacting with sets, functions, relations, then proving it so much so it feels like it suddenly makes sense is what "maturity" is

You will see those three things a lot in maths alongside logical statements

[rocky berry]

unrelatable 🥲

[rocky berry]

sure i will.

thank u for helping have a good day!!

or night.idk

[cunning elk]

oh pcmi huh

im going to their undergrad program next month lmao

[vital bane]

You've revealed you location, I'm going to track you down

[sterile pelican]

Garrity has an AG book I do want to read

Also his videos are funny but quite relatable

[cunning elk]

me when the self dox 💀

[proper rose]

what is the hardest book you all have solved?

[cunning elk]

I would say baby rudin but my analysis class didn’t even actually follow the book 😭

[vital bane]

They are all equally hard to me

[rich sun]

One with a hard cover

[keen vale]

Joeee no way

[warm jasper]

The best references for calculus

[molten gulch]

for anyone wondering, these are just PDF versions of the Lamar Paul's Online Math Notes website

[warm jasper]

Yes exactly

https://tutorial.math.lamar.edu/

[heady ember]

Better Cal Saul Paul

[desert tusk]

a lot of books are specialized but i was wondering if there was a book that'd be a nice introduction to many different fields of modern mathematics, just to get a taste basically

[warm jasper]

The site that I sent above is the best reference. You will find the curriculum in order.

[vital bane]

https://www.wikipedia.org/

[toxic willow]

modern is a big word

[vital bane]

It has a nice intro to many different fields of modern math

[toxic willow]

ug Calculus is knowledge from two hundred years ago

[desert tusk]

fair enough, i meant ug university level+ for math majors basically. rn im at the point where ive had some bits of galois theory and functional analysis (spectral theorems)

[rocky berry]

im sam not joe xD.

[vital bane]

Hey Joe!

[glacial cloud]

JOEEE

[jolly dawn]

Hello
Does anyone have a book recommendation for spherical/hyperbolic/projective geometry? I only know some basic real analysis (no linear algebra, no group theory etc.), so I would be glad if there was some book that teaches these topics without many prerequisites.
Thank you in advance 🙂

[sudden kindle]

Brannan, Esplen, Gray - Geometry

[jolly dawn]

Thank you

[keen vale]

Ashita no joe!

[weak yarrow]

What would be a good resource for real analysis? I studied engineering so I never touched that lol, but i am very interested

[fresh skiff]

Stephen Abbott's book namely Understanding analysis is the suitable book for first course in real analysis. I used this for learning real analysis in my selfstudy.

[trim kayak]

I just received Mendenhall's Intro to Probability and Stats text today. Is anyone familiar with this one? I want to learn it just for fun. Would you recommend that I read a chapter, takes notes, and then work on the practice problems?

[rocky berry]

Joe yabuki very very strong...

[sterile pelican]

Rudin is popular too

[severe blade]

I love rudin

[weak yarrow]

Oh i was gonna say I found a pdf while trying to look for it legally

LMAO

[deep moat]

at least its something and you get to read the contents :PPPP

[weak yarrow]

Not joking even i just put the title in the search engine and that was the third result

[trim kayak]

No suggestions guys? Sheesh.

[vital bane]

For what? Statistics?

[upper estuary]

I'm not familiar with that specific book, but your plan is good!! I personally spend like 20% of my time reading and 80% on exercises

If you have any background in algebra and mayyybe in calculus that would be super helpful too

[faint fractal]

I am searching a book for differentiation basics problem, which book can j refer

[upper estuary]

Stewart's Calculus is pretty good if you just wanna do a ton of problems and focus on your mechanistic skills. (It's not as good for very deep understanding but still decent)

[gray gazelle]

Calculus by Michael Spivak

[upper estuary]

that is like 8 steps above "basics" lol

[gray gazelle]

Need a material on harmonic analysis for beginners,my target is to learn character theory

[vital bane]

@wicked fractal

[spiral sky]

Is there a book/article/website that has the historical beginnings of higher algebra (waldhausen's view)

[trim kayak]

Prob and Stats

[dim pendant]

This is so evil

[ionic plume]

It's such a good book, though. 😩

Spivak, my icon. 😍

[ionic plume]

PLEASE what is this sticker?!

It's his WIKIPEDIA photo?

Iconic, actually.

[wet sentinel]

wait uh for some reason i didnt see a ping here lol

sorry for not responding but no ping appeared to me so i didnt realise that someone replied

well rudin's text has multivariable analysis but usually people dont recommend that

they recommend to hop to another book for the multivariable part

[cold forum]

What's a good book or subject to dive into to essentially prepare for a pure math major?

[sly jolt]

Stewart's calculus imo

Calculus is a good microcosm of what your degree will be albeit lacking much pure maths and learning it now will be the most helpful when you start your degree

If you really want something more abstract, friedbergs linear algebra or any number theory book

[cold forum]

I do know some single-variable calculus, my class stopped at u-sub integration

[cold forum]

alright, thanks!

[grim ore]

Im talking about his normal analysis text meant for ug?

Perhaps im missing something, but after the second chapter he makes remarks stating things can be generalized to R^n for some theorems or definitions

[old terrace]

If you want to learn more calc, you might like the latter half of Stewart. Active Calculus is a good open access (free) book that has a multivariable calc sequel too. Paul’s online math notes cover a ton and are readable.

Khan Academy is great for single variable calc, although its multivariable is less complete (and it isn’t a book). Some like Professor Leonard’s videos

[grim ore]

baby rudin*

[wet sentinel]

i am talking about it too

so from chapter 1 to chapter 8 he deals with single variable analysis

[cold forum]

I'm already registered for calc 2 and 3. I just want to get my hands on some upper topics so I'm prepared

[signal badge]

Discrete math may be of interests. But it's a little mix of everything.

[wet sentinel]

from chapter 9 till chapter 11 he deals with multivariable analysis, ie derivatives of multivariable functions, multiple integrals, a bit about differential forms... and he talks about lebesgue integrals/measures..

[cold forum]

Isn't that computer science focused?

[wet sentinel]

so usually when people recommend baby rudin for real analysis, they recommend that one picks up another book for the content of chapters 9→11

[signal badge]

Not necessarily. You're introduced to basic proofs, logic, number theory stuff, trees, relation, induction and et cetera.

[wet sentinel]

at least thats what happened with me

[wet sentinel]

sure, some chapters even deal with metric spaces in general

[cold forum]

Alright, I'll check it out. Thank you

[wet sentinel]

like the chapter on limits and continuity

but for differentiation and integration he first restricts himself to only R, and mentions vector valued functions at the end of these chapters for a bit

and then deals with these concepts in R^n in later chapters (chapters 9 and 10)

because things are different when you go from R to R^n regarding differentiation and integration right?

[signal badge]

The reason I suggested is it's usually used as a baby step to something like analysis and whatever. I agree with the other comments on using Stewart and studying calculus first, computation is quite important despite most of your later years in uni will be spent doing proofs. You can certainly do analysis while learning calculus, just with a gentle enough book

I think the book many recommend here is Abbott's Understanding Analysis

[cold forum]

The topics look like those in a finite math class I took, except number theory, I learned basic combinatorics

[signal badge]

Yep

[cold forum]

I own Rudin, Wade, and Hardy right now. I probably should mention, my proof experience is a logic class and some induction

[signal badge]

As long as you've seen some proof, can write it, and knows single-variable calculus well enough I think that's good enough for a first course in analysis tbh

From my experience alone you just need to stare at some of the proofs hard enough and you'll get the hang of it

[wet sentinel]

i think one can directly start with linear algebra. Or real analysis if there is a background in single-variable calculus

[signal badge]

Yeah I think so too

[cold forum]

I've got AP Calculus AB under my belt, and am set up for linear algebra in August

[wet sentinel]

real analysis can even be studied without any knowledge of calculus, but its better to have it because it helps with the intuition sometimes

[cold forum]

That's basically what I did when I first started looking into pure math

[wet sentinel]

and with this background one would have an idea about the concepts even if it is vague and imprecise

[cold forum]

Which of the 3 books would you say is more beginner friendly; Rudin, Wade, or Hardy?

[wet sentinel]

idk what AP calculus AB covers but as long as it covers all of single variable calculus that would be more than enough

[signal badge]

Covers half of it

[wet sentinel]

Rudin certainly is not beginner friendly

[signal badge]

Right before integration methods

[cold forum]

Just up to u-sub for my class, some volume was thrown in because we had the time

[wet sentinel]

although you can try it if you want

[wet sentinel]

ohh i see

even with that you are ready in my opinion

that is, if you want to study real analysis rn you probably can

[wet sentinel]

idk about wade and hardy but i wouldnt recommend rudin as a beginner friendly textbook

although i am currently using it as a first exposure to the subject

but i didnt want a beginner friendly textbook lol

#book-recommendations message

here is a list of recommendations

[cold forum]

Thanks

[wet sentinel]

as for the 2 other books that you mentioned, you can ask about them here in a new message so that someone who may know about them can read your message and reply

[cold forum]

I'll look through the intros/prefaced first to get an idea

[wet sentinel]

Great idea, usually you will find the prerequisites there and you will get an idea about the textbook

[cold forum]

Thank you for the help

[wet sentinel]

np, have a great day

[trim parrot]

anyone have any book recommendations for someone who just finished a bachelor of cs and wants to learn more math? i did a decent amount of set theory, some graph stuff, and wrote my thesis on complexity theory, but want to learn some of the topics i will have missed out on by not doing a math degree + some linalg since i am bad at that. looking for more of a reading list than a single book, i was thinking of starting with spivak and going from there

[cold forum]

What about Apostol's "Calculus"? I forgot I owned it

[signal badge]

I think it's fair to say it's an improved version of Stewart's Calculus

[cold forum]

Probably it over Wade/Hardy then?

[signal badge]

I'm not familiar with those two books so I can't say

[cold forum]

They're both analysis books: Hardy says his for first year scholarship students; Wade says it's a bridge from sophomore calculus to graduate analysis and is sectioned off from one-dimensional to multi-dimensional

[signal badge]

Apostol's book has some theory and some computation. It just depends on what you want

You have a fair amount of books in your pocket, I wouldn't worry about picking a particular one and sticking to it. I'd say just start reading one of them and if you're stuck on something go to the other books if a better exposition exists

[cold forum]

Fair enough. Yeah, I've been stuck on this problem for 1.5-2 years now, so I've built up a small collection

[old terrace]

If you like linear algebra, you might like abstract algebra. Undergrad Hungerford is a good introduction. Dummit and Foote is a more comprehensive introduction

[trim parrot]

yeah, i definitely want to learn some abstract algebra. i touched a (tiny) bit of cat theory for relevant parts of my degree, but wasn't able to go much further with it because of lack of algebra knowledge. thanks for the recommendations.

my wip list of things to read has fraleigh on it, you think i should swap that for either of the two you mentioned?

(full wip list: spivak, linalg done right (axler), understanding analysis (abbott), fraleigh, a first course in probability (ross), statistical inference (casella))

mainly sourced through gpt because i genuinely have no idea what math textbooks are good 😐

[old terrace]

I’ve never read fraleigh, but I have heard good things. I’d start with Fraleigh. If you don’t like it, you could try one of the other books

[spiral sky]

basic abstract algebra by robert ash is really awesome! the best algebra book imo, as for the rest of algebra aluffi is the go to, presentation is clear! AG: vakil, for cat theory i dont have a ref, just caught some of the language from people I know. As for commutative algebra maybe altman and kleiman if you like exercises w/ atiyah of course, after that, i found eisenbud towards algebraic geometry, gives a lot of perspective, but if you find eisenbud a little dense, then miles reid offers you an alterntive in terms of perspective towards more advanced topics/branches. For homological agebra I haven't really found any book, I have weibel's book on the shelf for a long time but havent really opened it, if anyone has a rec it'd be awesome

[remote sparrow]

rotman has a homological algebra book

[spiral sky]

so does weibel, i didnt have a good exp w rotman as i was reading ext and tor I felt information was scattered

[supple ferry]

Maybe this has been asked a couple of times already, but what is the difference in Evans' PDE book versus Brezis' PDE book? I have seen these books recommended for these subjects.

By Evans' PDE book, I mean "Partial Differential Equations" and by Brezis' book, I mean "Functional analysis, Sobolev spaces and Partial Differential Equations"?

[upbeat vine]

It pretty much is in the name. Evan’s book is pretty much a PDE book: it will teach you all about different kind of PDEs and how to solve them etc.
Brezis is a FA book first and PDE second. It teaches you FA rigorously and then develops a small class of PDEs as an application to FA theory.

If you just care about solving PDEs, you should go for Evan’s but that would mean at times, you would be scratching your head making sense of few things (convolutions, embeddings, Fredholm theory, sequences magically having a subsequential limit).
If you go for Brezis, you will spend an inordinate amount of time not doing PDEs

[supple ferry]

Ok, thank you for the information. 👍

[gray gazelle]

do you know its prerequisites?

in the sense that it would be a good idea to know those topics before opening that book

for context I know some very basic algtop but have no idea what homological algebra is

[outer helm]

which category theory book would you recommend for a beginner in this theory?

i saw ppl recommend the mclane book but idk some people says it’s not appropriate for beginners

[full cairn]

I've heard Tom Leinster's Basic Category Theory is good, it's also free online: https://arxiv.org/abs/1612.09375

[outer helm]

thanks

[tiny gulch]

yes leinster is good

i would not recommend the mclane book lol

awodey's is nice too

riehl's is more comprehensive but maybe requires a bit more mathematical maturity

if you know enough programming then bartosz milewski's series is excellent

[proper rose]

did anyone try Hall and Knight's Higher Algebra? Is that book good?

[quiet lantern]

Class is following Milne's Galois theory for course but I can't get it
Any good rec
Urgent Galois Theory book recommendation needed that does it like Milne's notes but in detail

[mossy flume]

https://www.jmilne.org/math/CourseNotes/FT.pdf

is this what you're talking about?

[quiet lantern]

Yes @mossy flume @mossy flume

[mossy flume]

they're just on his site...

so idk why you thought you couldn't get it

[molten gulch]

Maybe by "get it" they mean understanding rather than access

[mossy flume]

ohhh I see

[quiet lantern]

I mean I am finding it difficult to follow the text

He has written it too short/compact
Not many exercises
And I am finding the pacing too fast
I need a better book with these topics that's what i am sayingb

[gray gazelle]

need a book harmonic analysis for begginers

[foggy quest]

Classical Fourier Analysis by Grafakos is popular and looks good to me

[gray gazelle]

is it quick

[foggy quest]

It gets to the good stuff (Fourier theory) pretty fast. You could probably skip some of the non Fourier stuff until you actually need it

[gray gazelle]

my target is representation and character suggest me for that

[foggy quest]

You'll need chapter 2 and 3 of classical Fourier analysis, which covers the Fourier transform on the real line and the torus

This is basic material all analysis should know

[gray gazelle]

in this book there is no rep and char theory

[foggy quest]

yeah that's true. There isn't any in the modern Fourier analysis book either