book-recommendations

[tribal crow]

indeed, which is why I was taken aback

this is a 100% legal way of downloading thousands of books

[molten mason]

Same

I haven't found a single one yet that it wasn't available lol

I even have a few 2024 textbooks

[tribal crow]

I've found many

am I getting school gapped?

[molten mason]

Maybe send me one you find

[tribal crow]

not being able to legally get a textbook has never stopped me before anyways

[molten mason]

Actually. You're in Canada? I wonder if it is based on school and/or country

Like different licenses

[tribal crow]

possibly!

[tribal crow]

here's one
https://link.springer.com/book/10.1007/978-1-4612-1210-2

logging in doesn't work

[molten mason]

I'm extremely positive I have that one already lmfao

[tribal crow]

in general, if I see this, I can't download it via institution

could be a country thing ig

it doesn't matter because I have the book anyways

just not through Springer

[tribal crow]

interesting

[molten mason]

[tribal crow]

seems like I am indeed getting institution gapped

or country

[molten mason]

Super interesting indeed.

[tribal crow]

we all know you've done this too

[heady ember]

🗿

[gray gazelle]

read Grillet instead

[past flame]

why were you chanting my name

[tribal crow]

why not?

[trail hemlock]

HI GRASS

HI (GHER!)

[past flame]

i dont think you can say that

[trail hemlock]

?

[tribal crow]

hm?

[trail hemlock]

i’m saying hi to higher

but it’s just gher

cuz hi

[loud cradle]

what time is it in india?

[spice stag]

How long should it take to complete Stewart calculus?

[willow merlin]

depends on u

[trail hemlock]

2 hours should suffice

[fast bone]

that's 2 hours on copium

[glad elm]

Slowpoke, 1 hour is the median.

[vast steppe]

hi guys i am from 10 grade any good books to intrudoction to analytical geometry?

[uncut crater]

Ah yes, that thing

[gray gazelle]

im looking for a multivariable calculus 3 book for engineers. I want to book to have lots of problems (ranging from easy to test question). I want it to contain hard problem so that I have no surprises on the final exam. I dont need the book to have rigourous proofs since its a course for engineers.

[molten mason]

Check out Art Or Problem Solving's Introduction to Geometry

[knotty kestrel]

I need a best book for vector calculus

[uncut crater]

Marsden Tromba?

There's also Shifrins text

[maiden glen]

good books for statistics and probability?

[maiden glen]

ah Erwin Kreyzig!

the author of "advanced engineering mathematics"!

[trail hemlock]

i read callahan's "advacned calculus a geometric approach"

its a good text by all means

[lone valve]

Hi all I'm someone who just finished a course in Axler's LADR but in the course we skipped half of chapter 8 and all of chapter 9. Next semester I'm going to take Calc III but a more proof based version (I have knowledge of computational calc iii and some applications but idk why anything works). As I go through the book right now, I feel like I want a book that somehow seemlessly blends some of the more abstract concepts I learned in linear algebra along with some calculus. Is there any one text that does this, or will I have to wait for more advanced courses and/or just wait a long time until I'm comfortable with everything in order to make those connections? If my initial question has no good answer, any good multivariable calculus books would be appreciated.

[trail hemlock]

my assumption is that Apostol's Multi-Variable Calculus and Linear Algebra will do this.

[remote sparrow]

you can read hubbard and hubbard, although they do not employ much abstract linear algebra

[maiden glen]

Response please?

[remote sparrow]

https://stat110.net

wackerly is good for stats

[maiden glen]

thank you

[fresh skiff]

I watched only first lecture. And personally I liked it, hopefully soon (after doing my all HWs) maybe I will watch the entire lecture series

[remote rain]

Anybody out there have a solution manual for do Carmo Differential Geometry of Curves and Surfaces? I can't get Chegg to work anymore. I'm a self-studier so I have to check my own work and usually try to grind most of the problems so the solutions in the back aren't enough...

[maiden glen]

are there any other good books one may recommend me for beginning statistics?

[velvet fable]

hubbard and hubbard will probably be good for this

[willow merlin]

sorry to interrupt, but can someone point me towards an elementary abstract algebra reference

[tribal crow]

I keep hearing from others that Pinter is probably the gentlest introduction to the subject

[willow merlin]

quizlet apparently

[trail hemlock]

you can make infinite accounts with temp mail, slap a 7 day free trial on that mf, and access these for free

[gray gazelle]

looking for a cal 3 book with lots of hard problems. no rigorous proofs

its for engineering, not pure math

[trail hemlock]

Stewart's multivariable calc should be good

Thomas multivariable calc is also good

larson's multi

[vital bane]

Shiffrin's Multivariable Mathematics is also good for this

[noble swan]

hi

what is a good ap calculus bc book ?

[elder atlas]

what is best number theory book for beginner prepare for high school competition?

[elder atlas]

I think coursebook is enough

Becuz senior calculus is not difficult, just need know complete sample done, and do enough paper

[fervent crypt]

do you have any background in number theory

[elder atlas]

nope

[violet ore]

hey everyone, is Thomas' calculus a good book for a beginer?

[elder atlas]

so idk how to get in

[fervent crypt]

elementary number theory by david burton is what i use for competitions

[elder atlas]

is it cover all of knowledgement?

[fervent crypt]

wdym

[elder atlas]

I mean

If I konw everything in this book

do I still need study another book

[fervent crypt]

obviously

its a good book for getting into number theory

after that you could try, arthur engels problem solving strategies

[elder atlas]

alright thank you dube

[strange tree]

Join MODS server, its dedicated to Oly Math

I also did use Burtons book. There is a mainstream book for oly NT, Modern Olympiad Number Theory, but in my opinion it is not for beginners even if the book start at divisibility and "basic stuff"

[sacred sorrel]

I need just a few books about hyperbolic geometry

[raven quarry]

completely true man I tried to read it you may understand the theory but the level of ques skyrocket

[sudden kindle]

@remote sparrow what book would you recommend for teaching vector calc?

[remote sparrow]

to what audience

do they need to know proofs

[sudden kindle]

Undergrads

[sudden kindle]

No

[remote sparrow]

stewart, larson, thomas, etc. aren't good enough? you can look at colley if you want. colley has a slightly more advanced and detailed look, but there are plenty of computational problems

[sudden kindle]

The default course textbook for this course is Vector Calculus by Marsden and Tromba

If not familiar with the books you mentioned

[remote sparrow]

i've heard of that

colley is a good choice if that's the default textbook

[molten mason]

Just browsing through the ToC, the book you mentioned seems isolated to just multi-variable/vector calculus.

The books that Sour Drop mentioned contain your book in the final 1/3 of the textbooks. The first 2/3 of the textbooks are single-variable calculus

IMO they're all the same

[true escarp]

Hey guys, is there a good physics (or math) discord (or irc/xmpp/matrx/whatever) server that doesn't require you to verify your account with your phone number?

[silver moss]

Hey guys can I get a good math book pdf to learn function, trigonometry, differentiation and integration?

[willow merlin]

can I ask which book explain hilbert space for dummies

[knotty kestrel]

@maiden glen yes bro

[uncut crater]

Literally any college calc book

I'm assuming you're in 11th grade rn?

Anyways Lang's A First Course in Calculus is a much better read than slogging through hundreds of pages of Thomas or Stewart

Spivak is good too

[slender cargo]

I thought Lang would produce a thinner calculus text but holy hell it's 700+ pages

[remote sparrow]

that's pretty thin as far as single variable calculus books go

also how long are the appendices?

[gray gazelle]

https://www.amazon.com/Invitation-Combinatorics-Cambridge-Mathematical-Textbooks/dp/1108476546

https://www.amazon.com/gp/aw/d/1482249480/ref=dp_ob_neva_mobile

These are on sale in my library anyone know if they’re good

[gray gazelle]

Were these on the math schedules list for the Maths Tripos?

If so, they're most likely great.

[stoic crane]

Hello guys! Is there any beginner friendly book to get started with linear algebra

[outer wing]

https://link.springer.com/book/10.1007/978-1-4613-0077-9
See this

[weak solstice]

Anyone have any beginner friendly book recommendations for fractional derivatives and fractional sobolev spaces?

[orchid vortex]

Hi everyone! I'm looking to deepen my understanding of statistics specifically for machine learning applications. Could you recommend any comprehensive books that cover both theoretical concepts and practical applications? I enjoy diving into the theory as well, so a book with a good balance of both would be ideal. Thanks in advance!

[trail hemlock]

Linear Algebra Done Right is the traditional recommendation

this is a very "non math majory" choice

less proofs, more computations

all of these are great choices as well:
#book-recommendations message

[gray gazelle]

Just wanted to add on to the comment about Roman, yes he is indeed v cracked. His Advanced Linear Algebra book goes way beyond what any other LA course teaches otherwise. It's like the one shot to all and any subjects that you may want to cover under LA that's not direct research.

[sage python]

He's already dead but discord took a while to autodelete

[zinc sundial]

pls no deleterino pings @dapper root

[dapper root]

Sorry

I just didn’t want ppl asking me what it was about

[quick hornet]

i agree that is INCREDIBLY annoying

but when i tell people not to do it they act like IM the one being unreasonable

[dapper root]

I get it

MY BAD

[gray gazelle]

I recommend people read the Bible #stay woke

[dapper root]

Thanks for the high quality input in #advanced-lounge and here

[gray gazelle]

ty

[strange owl]

does anyone know any book or website that teaches infinite sums and series really well?

[glad rampart]

youtube

[strange owl]

Thanks 👍

I should have thought of that too lol

[abstract copper]

Any real analysis book should do.

[strange owl]

oh ok

thank you

Can I have an example

[abstract copper]

Abbott's Introduction to Analysis

[strange owl]

ok thanks

[gray gazelle]

you're welcome

[drowsy nacelle]

can i go wrong with any of lang's books

or are they all pretty good

[tribal crow]

@molten mason will tell you that they are all good

take his opinion with large grains of salt

[loud cradle]

i don't much care for his "undergraduate algebra", so there's that

[drowsy nacelle]

LMAO i know people have differing views on him but im more so just asking if there are any particularly notorious ones

[trail hemlock]

lang's algebra is pretty infamous

[cinder shore]

If you like baby rudin, you'll love papa rudin too. Just go for it if you feel like it! Measure theory is super elegant

Some topology background is very helpful though. There is almost no algebra required

Just read some basic point set topology and you'll be able to appreciate measure theory fully

Most of it is already covered in baby rudin (compactness is the most important)

Sometimes you need a notion of convergence, open and closed sets, continuous maps etc. without a metric, that's the only reason you would need to know about topological spaces. In analysis, a lot of the time, you just deal with metric spaces.

[prime oak]

opinions on royden for measure theory?

[cinder shore]

I've read it a little bit. I don't see anything wrong with it. It's all standard material

[prime oak]

my background is just metric space theory, no gentopo

[prime oak]

👍🏾

[cinder shore]

Fairly well regarded book too

[cinder shore]

Good thing Royden has a long intro

Only thing is that it deals with just ℝ for a sizable portion of the book

If you are fine with that, then it's all good

Any notions it needs will be presented in the book itself

[cinder shore]

Since you don't have a topology background, it's actually better that way

[prime oak]

gotcha

[cinder shore]

For self-studying?

[prime oak]

yes

well, self studying under my supervisors recommendation

[cinder shore]

Fun! I love measure theory

Then a gentler book is definitely a plus

Royden seems to fit that category

Papa rudin might be too much of a jump

[trail hemlock]

i’m leaning more folland because of the reviews

but it can’t hurt to learn more algebra which is what i wanna do

[cinder shore]

Oh yeah, if you wanna do it, have fun

[prime oak]

lol i have to read grandpa rudin and i do not have the prerequisite knowledge for it so im trying to push myself to read as much measure and topo as i can

[cinder shore]

Ohh. There's easier introductions to functional analysis than grandpa rudin if that's what you are after

The only thing is that it will be tough to rush topics such as measure and topology, it takes time

These are whole courses in their own right

Plus grandpa rudin will definitely rely on abstract measures (not just on ℝ) so you will have to do some extra reading.

[abstract copper]

Ouch I'm one of the few here that uses Axler lol

[cinder shore]

Axler is great! I use it to reference basic concepts from time to time

I wanted a proof that the square root of a positive matrix is unique and axler has the easiest proof ever

[abstract copper]

I'm talking about his measure theory book haha

[cinder shore]

Ohh

He has one on measure theory??

[abstract copper]

Yep

[cinder shore]

Ooof. Right

Is he an operator theorist by any chance?

Oh yes, he has worked in Operator Algebras!

Hmm, maybe not operator algebras, but adjacent.

[uncut crater]

Guys, any book for studying category theory?

I've dabbled in a few texts, first exposure being Aluffi (and the very little presentation on it)

I've tried reading awodey and the joy of cats but i don't like the wording in both

[gray gazelle]

Can I get book suggestions for abstract algebra for QM and QFT purposes

[uncut crater]

I've liked peter smith's notes but the dude is a convicted pedophile and its way too verbose

Am I cooked?

[gray gazelle]

Liking a person's notes doesn't say anything about you

[uncut crater]

There's Woits text on QM from a mathematical pov that I enjoyed

[gray gazelle]

It just says you have the same study pattern.

[uncut crater]

Yeah, its a bit conflicting

[gray gazelle]

https://www.amazon.com/Quantum-Theory-Groups-Representations-Introduction/dp/3319646109

This?

[drowsy nacelle]

ur cooked fam

better unlearn the pedophilic version of category theory

[gray gazelle]

Amazon is telling me to get this as well

https://www.amazon.com/Lie-Groups-Algebras-Representations-Introduction/dp/3319134663/ref=pd_bxgy_thbs_d_sccl_1/146-3783049-9186258?pd_rd_w=CpBd0&content-id=amzn1.sym.c51e3ad7-b551-4b1a-b43c-3cf69addb649&pf_rd_p=c51e3ad7-b551-4b1a-b43c-3cf69addb649&pf_rd_r=C8ENAZRCGKWX2A2SEYSQ&pd_rd_wg=AY5gB&pd_rd_r=3c8d1860-c9eb-4a74-b516-b0e9fe683fca&pd_rd_i=3319134663&psc=1

[drowsy nacelle]

wouldnt be surprised

his stuff seems very functional analysis oriented

[cinder shore]

Makes sense he wrote books on both linalg and measure theory

[prime oak]

unfortunately i dont have choice over the text

though im reading kologromov and kreyszig because they seem nice and comprehensible

[cinder shore]

Not an issue at all. Grandpa rudin is great, it will just take some work before you can get to it. Don't rush it though, just take as much time as you are able to

[cinder shore]

Kreyszig is good. That's the one I used for basics.

[gray gazelle]

Is #chill message a good book for learning proof-based math?

[fresh skiff]

Yes. Many people like it. However I used two books
Velleman's book (I have read it almost half) and the name of other book was How to think like a Mathematician (didn't remember the name of author)

[gray gazelle]

Thanks👍

[granite lintel]

which book would be best of co-ordinate geometry lvl - iit jee (jee advanced) for theory as well as for practicing ques

[brisk gyro]

Hi guys, I want to study math from the beginning, starting with basic arithmetic (I haven’t learned fractions, squares, powers, and similar concepts). Can you recommend a book or series of books that provides thorough teaching on all foundational topics?

[glad rampart]

im a fan of AoPS

[signal mountain]

serge lang's 'basic mathematics' could be a good option

here's the contents

also has a lot of answers to exercises at the back of the book

im unaware of other textbooks of this nature -thats not to say there are none, im sure there are many
you could look at the curriculum for your country/region/etc, and have a look at textbooks from/endorsed by them

[signal mountain]

ive just found this https://www.youtube.com/playlist?list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb
seems to cover the whole book, so if you prefer to learn through video thats also an option

just be sure to actually 'do math' - its all well and good to read a book or sit and watch videos, but if you dont get your hands dirty, do the work and problems yourself then youre going to severely hamper yourself

good luck!

[brisk gyro]

I'm currently doing this, solving some exercises from my country's mid-level exams to see where my biggest lack of knowledge is and make progress based on that.
Thank you @signal mountain and @glad rampart , I hadn't known about the AoPS series nor Serge Lang's, I'm looking at these contents

[signal mountain]

nice! thats a good way to do it

[heady ember]

It can't hurt to learn more set theory too

[trail hemlock]

yeah i’m reading jech

[heady ember]

Which one

[granite lintel]

pls someone help me

[trail hemlock]

little

[heady ember]

Nice

[uncut crater]

Yep

[uncut crater]

It's a cute book

[uncut crater]

No

[trail hemlock]

any book that develops introductory micro and macro economics with calculus? I looked around, most books mention calc concepts (marginal revenue) but no actual math

something like this perhaps for both micro and macro, and a little more ... modern 💀

[remote sparrow]

you should know there's a fifth edition out now

[remote sparrow]

try leinster and riehl

[soft patio]

Hello guys, Im not sure if this is the correct channel to ask, but I want to buy a book called "First Course in the Theory of Equations" by Leonard E. Dickson. Since this book is in public domain, there are a few different publishers to buy from but one called "Forgotten books" has caught my interest. Has anyone bought a reprint of old mathematics text from them? They have a sample of the book in amazon, but the text seems a bit fuzzy and hard to read, and I don't know if its an amazon issue or the text in the book just looks like that. Any advice on where to buy welcome. Also any other book recomendations on equation theory is very welcome

[gray gazelle]

💀

aint no way u called a lie algebra book cute

[fresh skiff]

Guys I have a bit of confusion. Recently I am studying CH7 of abbott (section 7.4), but its pretty tough so I am thinking to either move on to another book or reread abbott and do those exercises that I skipped (bcz 50%+ of exercises after ch2 I used to skip, precisely I was following lectures of some prof on YT who was using Abbott and assigns problems)
Idk what to do at this moment

• I tried to read Axler measure theory, and I found I am able to do 40%+ problems from first exercise set ( cuz I read first 4 sections of CH7 from Abbott).
• I have another option, carothers too.
• Or reread abbott with bertal
  Idk what to do now.

---

I read rudin too (instructor is using it, I mostly do HW problems from it).

[gray gazelle]

abbott is the most laidback intro to RA

i would not at all suggest even opening axler measure theory before completing abbott

[gray gazelle]

which qs do u have problems in

[fresh skiff]

wdym by completing Abbott?
Do you mean doing all problems?
Or covering atleast 40% of all sections ? or something else?

[fresh skiff]

There is no particular one. Even I have skipped many problems from previous chapters too.

[gray gazelle]

completing = being able to pick a random problem from the book n being able to do it with ease

like say if i randomly asked you to prove the existence of an irrational number w the dedekind cut construction, you should be able to use the property that dedekind completeness implies the existence of a supremum and infimum for any bounded set

[fresh skiff]

Oh. This seems something strong.

[gray gazelle]

thats the point of reading a maths/physics book

[trail hemlock]

afzal ur not gonna use folland for measure theory?

[gray gazelle]

if you pick a random problem from one of the topology books im reading, id be able to solve it

[fresh skiff]

I don't think so Abbott introduces Dedekind cuts (or maybe introduced with other name)
But I userstood your example

[trail hemlock]

wb from rudin? regardless of how well i study, it takes me a while to do the later problems (18-20) because they are soo unintuitive and not obvious at all

[fresh skiff]

I wouldn't use it as a first book or main text (maybe as a reference) cuz it is hard
But surely I will use it whenever James will start Measure theory reading group

[fresh skiff]

did you prove/solve all problems?

[gray gazelle]

i have done 3 chapters of it

theres 5 total chapters

yes i can do any problem from the first 3 chapters

any problem i skipped was sth i was able to prove in my head

[daring lake]

I did MT from RCA Rudin, haven't seen folland yet

[gray gazelle]

@fresh skiff come into #real-complex-analysis

[fresh skiff]

Oh wow probably thats impressive. Btw what book are you using?

[gray gazelle]

Mendelson

Intro to Topology

it's mostly proofs from RA itself but in a more general setting

like your prove f is continuous uses the epsilon delta def

[trail hemlock]

who is james

[gray gazelle]

in the second chapter they're working with metric spaces

so they make you use d(x, y) where your metric isn't specified

[fresh skiff]

oh wow. Thanks for letting me know

[fresh skiff]

James Banach (one of our instructor in the PMA reading group)

[gray gazelle]

idk i never used rudin

[slender cargo]

I'm guessing that you're having issues with uniform convergence. I think that's one of the more challenging topics in introductory real analysis. I would say check out a different book for help if you're confused with Abbott's treatment.

[gray gazelle]

i dont see how tbh

but fair ig

[fresh skiff]

Seems reasonable. From your and bombastic side eye's suggestion I guess it will be better to use Abbott with some other book like Bertal maybe.

[native cradle]

just wondering, is it generally a bad idea to use multiple books for the same topic?

Like I'm currently reading vellerman's book on proof writing

but it's kind of dense, so wondering if I shoudl switch books

[tribal crow]

no, it is not a bad idea

[native cradle]

thanks!

[slender cargo]

Maybe check out Ross Elementary Analysis, or Jay Cummings book. I think both of those books use the Darboux integral (which is what Abbott is using). I like Bartle's book but he primarily uses the Riemann integral. Abbott calls his integral the Riemann integral but it's really the Darboux integral.

[fresh skiff]

Oh yes Bertal is using Riemann's original definition of integral, surely I wil check these both too thanks

[molten mason]

Maybe Mac Lane?

Besides what you and Sour mentioned, can't think of any others

[uncut crater]

I mean, that's currently my topic of interest

[uncut crater]

Yeah, i think next sem I can actually hop on Mac Lane

[remote sparrow]

any algebraist born after 1993 can't cook, all they know is mcdonalds, charge they phone, twerk, be bisexual, eat hot chip and lie algebra

[uncut crater]

Lmao

I do have a thing against purists tho

[molten mason]

1993

I'm safe

[uncut crater]

I think algebraists today are more open-minded? Idk most of the relics in India (at least) were more into alg geom, com alg and hom alg when talking of algebra

It's only after Langlands popularized the work of Harish Chandra that it got spicy here

With that being said, while hunting for a project guide, is it necessary to work under someone who's in the specific topic of interest? I've always thought about writing a thesis topic tangentially related to my interest at least and branching away in the future

This increases my options of selecting affable people. There's like 2-3 chill people in the department and the rest are either applied or cranky/egoistic asf

[molten mason]

Yeah I don't know if I'll have time anytime soon but I have the PDF of Mac Lane and I'm planning on going through it in the near-future

[uncut crater]

I've gone through the book and I definitely lack a lot of algebra to comprehend it

A saner treatment was in Jacobson surprisingly

[molten mason]

Probably better question for #advanced-lounge maybe?

[uncut crater]

Yeah

[wintry hornet]

what are thoughts on west's graph theory?

vs diestel

i think my class will use diestel, but i took the undergrad graph theory with west

[uncut crater]

West was definitely a more verbose read than diestel

Definitely a good book for undergrads

[wintry hornet]

is diestel more succinct?

[uncut crater]

Yeah

It's a gtm

It has to be

[remote sparrow]

have you gone through more of Galois Theory by cox?

[wintry hornet]

okok but how good is like

the “teaching”

?

[uncut crater]

Well, you could check out a pdf of it? I have a terrible memory

I've heard that Diestel is the canonical reference for graduates (?) besides Bollobas

But I remember it being a good read (vaguely)

[trail hemlock]

u give off crazy millenial vibes

[sage python]

Yeah I didn't learn off books so much as a class and then a bunch of piecemeal things

But Diestel seems to be the standard

I do need to get around to reading stuff about expanders systematically though. I kinda just wing it

[uncut crater]

Tf? I'm literally 20

My terrible memory is a result of years of suppression and three traumatic years full of depression and surgeries

But that's actually funi because I don't remember stuff unless they have a traumatic aspect

[uncut crater]

Man bless your profs then, ours are literal shit

[sage python]

Well this is specifically graph theory, my graph theory prof was great

In general it was a mix

[uncut crater]

Why is it that the 'purer' the math gets, their teaching gets worse?

[remote sparrow]

maybe lack of interest in all but the most neurotic/obsessed people

[uncut crater]

It's a hellhole

Everyone should undergo a course on math pedagogy

[remote sparrow]

generally professors were also exceptional students themselves, so they might not necessarily relate to struggling students

[uncut crater]

Bunch of professional tards

Back to greub i go

[true escarp]

this ong fr no cap

[sage python]

Eh I think some of my teachers even in pure-ish topics were great

Hell a lot of the topics in my graph theory class were heavy on theory as well. It was a mix of things

So we talked about info theory and Shanon capacity, orthogonal polynomials, probabilistic methods, spectral graph theory

But also my measure theory class was incredible. That, combo, differential topology, and graph theory were my favorite classes

Especially combo

[fierce hedge]

I feel like only folks at CMI do pure algebra like algebra for the sake of doing algebra

[uncut crater]

Yeah, the last bastion of algebra here

It's a pity that we don't have many math schools here in the country

[uncut crater]

Oooh sounds interesting

[uncut crater]

I'll comment on that once I audit my measure and R^n analysis courses this sem

I feel like auditing com alg too, but...i don't have any specific reason to study it?

[sage python]

Lol to be fair mine was... I don't think any other class is like it

What are your interests Uta?

[uncut crater]

Mostly rep theory, geometry

[tacit crow]

hi dami

[uncut crater]

And harmonic analysis

I've been reading projective geom for that smooth transition to alg geom later on

[trail hemlock]

gosh i didnt know people got that old

[uncut crater]

Bruh

Tweaking

[trail hemlock]

im jk btw

no offense ofc

[uncut crater]

[abstract copper]

Ik I've been 13 for years now

[uncut crater]

Damn...

[trail hemlock]

yeah when i was ur age i was a year older than u

[uncut crater]

Pretty consistent

It's 6 30 am here and I'm still up with my phone

Wtf is a stable sleep cycle lmao

[trail hemlock]

yeah ur sleep schedule def more fucked up than mine

i fixed mine 🥳

[uncut crater]

🫂

[trail hemlock]

bump 🥺

[willow merlin]

which book for linear algebra is the best?

[trail hemlock]

#book-recommendations message

i like lang personally

(second lang)

[willow merlin]

is there a pin like this for multivariable? any other rec apart from mardsen tromba?

[trail hemlock]

ive seen hubbard and hubbard recommended a lot

.

[uncut crater]

LADR

[willow merlin]

fr?

I have read it a bit, and was a little too much for me, but will give it a second try

also, I dont understand why determinant is not so present in the book

[tacit crow]

determinant is a shortcut to most results. you should get into the habit of proving things without resorting to an argument using the determinant.

[uncut crater]

Definitely one of the LA books of all time

[sage python]

@uncut crater eyyyyyyyyy

I also like rep theory

[uncut crater]

Oooh rep of what exactly?

[sage python]

P-adic groups

[uncut crater]

Oooh that's close enough

[sage python]

Specifically stuff in the vein of Bruhat-Tits buildings, Ramanujan/expander complexes

[uncut crater]

Expanders? Like expander graphs?

[abstract copper]

Tits hehe

[uncut crater]

Tits are good

Oooh wait a sec, this is the second time I've seen buildings

[sage python]

Yup!

[slate hearth]

any good abstract algebra book recommendations?

[narrow relic]

How is your Lang progress recently?

[trail hemlock]

terrible

havent done math in days

[daring lake]

I uhh have been seduced recently by quantum mech and non linear dynamics, so no

[slow kindle]

Any good books on physics relating to every day life like biking and swimming?

[dapper fossil]

is stewart the best calc book why does every prof use it

[tribal crow]

it's a very popular book used for non-rigorous calculus courses

that doesn't mean it's the best though, obviously

though truthfully, most calculus books are all very similar

so not much would change if you replace Stewart with a different book, most likely

[molten mason]

Because all the answers along with walkthrough/explanation, odd and even, are online

Also it's on Cengage and they can assign homework/quizzes/exams online and it's graded automatically without instructors having to do too much

[heady ember]

wtf is that profile pic

blocked.

[lusty escarp]

You can move to Ch2 with the knowledge that there are functions which are not Riemann integrable.

We can do axler together.

[fresh skiff]

Oh really? Btw I tried CH1 it was same as Abbott and I was able to progress

[vivid bridge]

bhai kisine cmi exam diya yaha pe

[uncut crater]

No hinthi

And yes, i did, some time back

@vivid bridge

[vivid bridge]

this year?

[vital bane]

he does, in the last section of the last chapter

[uncut crater]

No, two years back

[vivid bridge]

oh

[fresh skiff]

oh I am still on 7th

[uncut crater]

Why do you ask? Have you been selected?

I saw the paper this year, kinda on the easier side

They're slowly bringing in non-standard Olympiad material into the exams

[vital bane]

which CMI exam do you mean?

[uncut crater]

BSc?

[vital bane]

ah okay

I thought you meant MSc

[noble swan]

is the barron ap calculus book better than princeton review’s one ?

[uncut crater]

Oh MSc, i have no idea

I mean tifr is better for an MSc imo

But that's my bias

[lusty escarp]

Tifr does not have an exclusive msc in maths.

[uncut crater]

An iPhD then?

[lusty escarp]

Yes. IPhD and PhD.

[uncut crater]

I think they'll allow an MSc exit

NEP 2020

But what use is exiting with an MSc if you're guaranteed a PhD there

[lusty escarp]

Yeah, exit the program with a MSc.

[uncut crater]

One would need good grades to pull that move off

[lusty escarp]

I don't know.

[noble swan]

is the barron ap calculus book better than princeton review’s one ?

[vocal violet]

Getting back into math for mathematics degree after several years after high school. What do you guys recommend to prepare

[signal mountain]

what did you cover up to in high school

[cinder shore]

Linear algebra is always a good bet.
If you are comfortable with calculus, real analysis would also be a great place to start.

[cinder shore]

It's something you pretty much do all the time the more you advance. Feel free to use as many reference material as you want to.

If one book isn't cutting it for you, you can go back and forth between two and study both of them.

[native cradle]

Thanks

[foggy quest]

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

[remote sparrow]

#book-recommendations message

[next condor]

Could someone suggest an introductory book on graph theory for mathematicians and another more informal book discussing the historical aspects and applications?

[narrow relic]

I'm sorry to hear that! I haven't done any in days either, been too busy with work.

[uncut crater]

West for an introduction

The one by Ciaoba and Murty is a fun read too

[sage python]

"Discrete Groups, Expanding Graphs, and Invariant Measures" by Lubotzky

[uncut crater]

Sharad Sane's combinatorial techniques should be the new OG reference for ug combinatorics imoo

[sage python]

Nah but yeah Uta's recs are good

I like the notes from my graph theory class but

They won't discuss history and such

[uncut crater]

Its tragic that i left studying combi

I'll pick it up someday during my PhD when I'm not ridiculed by the faculty for it being 'lesser' and 'fun' math

[sage python]

Still though: https://people.cs.uchicago.edu/~laci/19graphs/

[sage python]

Wait that's so lame of them

Combo can absolutely be sophisticated

[uncut crater]

Yep

[sage python]

I mean just look at this. I dare them to call these topics lesser

[uncut crater]

I tried giving a few talks on incidence geometry and partitions but no one seemed to join the combi group

It got relegated to Olympiad math for eternity, and the senior who was highly into combi is in PDEs so i have no support

This single-handedly stopped the math circle in our institute tbh

[sage python]

If you're doing rep theory and enjoying it you should try the connections between that and combo

[uncut crater]

Ooh, my first exposure to rep theory was actually a bit combinatorial

[sage python]

Rep theory of S_n has connections via stuff like Young Tableaux, which I do wanna learn at some point

[uncut crater]

Yeah

[sage python]

Random walk even has connections to rep theory, see Diaconis style math

[uncut crater]

Alrighty

[sage python]

My stuff is similar but in the setting of graphs, and using p-adic groups instead of finite groups

So yeah you'll enjoy it I think

[uncut crater]

I'm pretty confused atm

I hope the department gets better here

Otherwise it's just personal effort that's driving me (and others) so far

[sage python]

Which year are you?

[uncut crater]

Uhh

3rd

BUT

[sage python]

‼️

[uncut crater]

Given that it's an integrated MS

I'm kinda equivalent to a freshman

[sage python]

Ah so you'll still be there for a while

[uncut crater]

Yeah, 2 more years

And I'll have to squeeze in a LOT

[sage python]

What kinda things do people there work on which you still like?

[uncut crater]

💀

Harmonic analysis and quantum information

[sage python]

That stuff is pretty cool tbf. Rep theory harmonic or more the singular integrals kinda stuff?

[uncut crater]

Yep

[sage python]

(or both)

[uncut crater]

Rep theory harmonic

[sage python]

Eyy

[uncut crater]

Although I'd need singular integrals regardless

[sage python]

Tru

[uncut crater]

I've had only 6 courses in math so far lmao

Most of the stuff, i had to pick petty fights with the faculty for readings

[sage python]

Oof, wait like they said no and you convinced them?

[uncut crater]

Yep

They were of the opinion that as a first/second year, i had no business studying topics which I would cover later on

I spent more time studying chem and bio than math and physics lmao, and the LABS OMG they were terrible

[sage python]

Labs are the antichrist

Though also we should keep this for books and resources, we kinda trailed

[uncut crater]

Yep

[modern ruin]

we should have labs as part of lower level math classes instead of discussion

[remote sparrow]

labs for calculus classes do exist at some places

[gray gazelle]

I’ve seen labs for ellipses where you’re given two points and a rope

[willow merlin]

are u from the Us catgos?

[harsh moat]

Does anyone know good books to start learning mathematics on my own?

my level is pre-university

There may be several recommendations to read in order

[trail hemlock]

aops series gets you from pre algebra to calculus

although there are many many better calculus books than aops calculus

[torn crypt]

Anyone know good references for dual of L^\infty, \ell^\infty stuff, and finitely additive measures (including C valued)

[harsh moat]

thanks, I'll keep that in mind

[remote sparrow]

@remote vortex

[torn crypt]

I’ve found a bit but some more systematic-y stuff is the goal, since all manner of “this is well known” type results, or spelling out some particular technical details

[weak solstice]

Do you have any beginner reading recommendations?

[sage python]

Do you know measure theory/functional at all?

[weak solstice]

I know a bit

Currently going through axler

[sage python]

Hmm, okay Folland Abstract Harmonic Analysis is good. People also like Deitmar-Echterhoff

[weak solstice]

I've also done some rep theory of finite groups and lie groups

[arctic hamlet]

Hi guys, do you have any recommendations to build good math foundation for Quantum Mechanics or Quantum Computing?

[remote sparrow]

learn linear algebra

[abstract copper]

Measure theory and functional analysis would be good as well.

Planning on studying QM properly after finishing measure theory

[remote sparrow]

it is not so bad getting your hands dirty by thinking like a physicist

if you would rather read a book written for physics students, do so after meeting its mathematical prerequisites

[arctic hamlet]

I am thinking about improving my linear algebra one, I just know basic of matrices calculations

do you have any book recommendation for my level?

[daring lake]

Hoffman & Kunze

or Linear Algebra Done Right

[arctic hamlet]

thank you, will give it a try!

[marble solar]

I think if you just learn linear algebra, and some differential equation & fourier stuff, then you should be good to go. Don't get caught up on the "right" mathematical background for QM. If you've passed most of your lower division math classes, then you just pick up the math you need along the way

You can spend a lifetime trying to learn all the math you need for QM or you can just start learning QM and pick up math along the way

[remote sparrow]

#book-recommendations message

linear algebra done right is good too

[willow merlin]

Best measure theory book

[remote sparrow]

for beginners, https://measure.axler.net is a good choice

[willow merlin]

Thank u

[gray gazelle]

Can someone recommend a exercises book that would go along nicely with professor Leonard's precalc playlist?

[uncut zealot]

Khan Academy will auto-generate them. Lang's Basic Mathematics is another option.

[analog lava]

probably paul's online no tes

has exercises

[uncut crater]

Harmonic analysis is sadly not beginner friendly
The only text that comes close is Deitmar's Introduction to Harmonic Analysis

A semester of functional analysis imo is essential for harmonic analysis

[weak solstice]

Yeah I've done functional. I meant like a book to get started with harmonic. Sorry if I was unclear

[uncut crater]

Oh then it's finr

Jump straight into Deitmar's principles of harmonic analysis

[uncut crater]

Nielsen & Chuang deals with the required math in their book

As someone who's into QIT and foundations, I'd say that you don't need much math for QIT

Foundations is a different game tho

[digital pelican]

Hey guys- is the Sullivan AP Calculus book good?

And also- since I’m barely dipping my toes into wanting to learn Math for myself, what are some good “entry”-level books going into Calculus, Linear/Abstract Algebra, and so on.

[uncut crater]

Entry level linear algebra: strang (for matrix computations, mostly)

Entry level abstract algebra: Gallian/Pinter

[digital pelican]

For Linear Algebra, Gilbert Strang?

[uncut crater]

Yeah

It's a good entry level book barring proofs

And abstract vector spaces

[covert mauve]

does anyone have good short notes on geometry topics? (mainly menusuration, circles, and coordinates). I have an exam coming up, and I have forgotten all the formulas.

[native cradle]

is reading, writing and proving by Ulrich Daepp

Pamela Gorkin
better than vellerman for proof writing ?

[gray gazelle]

Book for the AIME or IMO?

[willow merlin]

Best book for zfc set theory?

[uncut crater]

Which level?

[willow merlin]

Undergrad

[uncut crater]

Hrbacek and Jech is good, although it's not complete (for an introduction); i had to fill in the lines a bit

Might try goldrei or enderton?

Enderton is too chatty (for me)

[willow merlin]

Okay

[native cradle]

any suggestions for books on number theory ? Assume I know nothing

[foggy quest]

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

[vital bane]

Niven, Zuckerman, Montogomery is the usual recommendation

[stuck swallow]

Elementary Linear Algebra, Howard Anton
Introduction to Linear Algebra, Serge Lang

[native cradle]

any cheaper books?it's around 250 USD here

[gray gazelle]

Took a break from math and I know the author of this book through a friend. Got me into doing math for fun. Starts with arithmetic and goes to some advanced level calculus like Feynman integration and the gamma function

You Can Do Calculus: Math for Anyone, Shawn Cogan https://a.co/d/04QJH23b

Written like a story and it’s only $25 for about 5 years of Precalculus and calculus in 400 pages

[vital bane]

??

you can get the pdf and print it

[native cradle]

That's piracy , no?

sorry

[vital bane]

perhaps, but what's better than spending 250 USD on a book?

[remote vortex]

Sadly we are not allowed to encourage piracy in this server.

But yes, the prices of textbooks and journal access are absurd and I also don't encourage anyone to pay 250 USD for a book

I've posted this before but I will post it again:

[vital bane]

oh yes I definitely do not encourage googling the title of the book you want and downloading the PDF and printing it out and using it to study

no way, I'm not that disingenuous

[remote vortex]

Other than piracy, which we do not condone, libraries are a good option if you're near an academic institution.

[vital bane]

this is true

[remote vortex]

Even if you're not a student/faculty; at least my university library allows non-students to borrow books.

[vital bane]

some libraries have a lot of books and are very based

[remote vortex]

Just in fewer numbers and with shorter deadlines.

[vital bane]

that's actually really cool

[vital bane]

I'm sure public libraries can have a math section as well

a few of them in my area do (and contain lots of very based books )

[remote vortex]

Unlikely to be very robust though

I wouldn't expect to find many university-level books in a general public library

[vital bane]

what if it was a large library?

tbh I can't tell if my experience is the norm since I've only been to 2 libraries and one of them is very old and the other one is very large and well maintained

[remote vortex]

It's going to vary, but the public libraries I've been to mostly have the kind of books you'd encounter at a typical bookstore, so fiction and non-fiction but not much in the way of specialized academic or technical literature.

But it will probably vary considerably by library

A university library definitely seems a better place to try

Some universities even have separate libraries per department, that's the case at mine.

The department of mathematics has our own library with just mathematical books

I've just looked up my municipal library's website out of curiosity; they have Rudin's PMA but none of the measure theory books I've tried.

They also have Papa and Grandpa Rudin, someone in charge must have been a Rudin fan at some point

[native cradle]

I actually am studying before uni starts, so I can't use any libraries

1st year

[vital bane]

lol is there a law that prevents you from going to a library if you're not a uni student?

[remote vortex]

You probably do need to be legally adult, or at least if you're underage you probably need some help from parent/guardian

But it's very possible you don't have to be a student

You might be living away from a city with a big library though, and that would be a problem

[native cradle]

I'm talking about uni libraries

[remote vortex]

You often don't need to be a student to access one.

Doesn't hurt to check

Unless you did and that was the answer 😦

[signal mountain]

there are also a lot of texts that are open access!

i.e. you can download them, generally as a pdf, for free legally

axler's books: https://www.axler.net
wide assortment, categorised by level and topic: https://hbpms.blogspot.com

you might also be able to find some searching https://archive.org

@native cradle

[native cradle]

thanks!

[signal mountain]

and of course there are many more out there than you will find in just those three links, but def a good start

https://textbooks.aimath.org/textbooks/approved-textbooks/
https://openaccesstexts.com/math/

[native cradle]

say for number theory is David M. Burton good?

[native cradle]

thanks!

[north summit]

lang vs conway vs cartan vs alhfors.

[signal mountain]

#book-recommendations message

[north summit]

doesn't speak about lang nor cartan

[signal mountain]

ive not heard of cartan at all, and ive not heard people talk abt lang for CA

doesnt mean theyre bad, just some anecdotal exidence ig

[sage python]

I've heard Lang is supremely boring

[north summit]

i honestly need something for self study

don't care if it's boring

probably an easy book but for advanced undergraduates first year grad

[opal tiger]

Does anyone have a recommendation for a vector/tensor analysis textbook. I've been trying to find one, but often times they just cover the latter half of a traditional multivariable calculus course in the US.

[sage python]

Are you looking for a kinda topology angle, connections to number theory, Fourier, what?

[north summit]

topology angle you mean metric space based?

[sage python]

Even more, stuff like differential forms, covering spaces, building toward Riemann surfaces

[north summit]

not really that much

for example conway's book contents or alfhors even lang is enough

but modern

lol

[sage python]

What do you think of Freitag-Busam?

[north summit]

chapters 1 to 3 covers all i need

how would you compare it to alfhors or conway

[sage python]

Ahlfors' book feels kinda old and I've heard complaints about how he often doesn't label theorems

Just kinda talks and in the middle of talking something happened

[north summit]

kinda hate that

was reading an old book Copson metric spaces

and all theorems where labeless

just writenn in italics

[sage python]

Conway I've heard is very easy (goes over a lot of stuff you prob should know before you open it) but very slow as a result

[north summit]

when you say slow

you mean slow in the boring way

or that it covers to much stuff before the important parts

[remote sparrow]

you can try marshall's Complex Analysis for a power-series first approach

[sage python]

This is second hand so I'm not certain, but looking at it now, it spends 30 pages defining C and talking about basic metric topology before defining complex differentiability

[north summit]

i can skip the basic topology chapter tbh

[sage python]

I figure as much, but yeah that seems like the nature of the slowness

This is where my "the D&F of complex analysis books" shtick came from

Tries to be accessible but if you know what you're doing you might be like ugh get on with it

[north summit]

never used DYF

thought book was too big to carry around

lol

ayways one last book

joseph bak complex analysis

[sage python]

Don't know it

[marble solar]

Having taken complex analysis way too many times, each time from different books

I'd say Conway is probably the most rigorous and precise, but the cost of that is going slow & going over things carefully

[north summit]

please tell me all your experiences

how many times why some many wich books

everything

[marble solar]

I've done complex analysis now 3 times

(Twice in undergraduate, and once for my first year of PhD)

First time we used Stein & Shakarchi, but prof. switched to Ahlfors half-way through. Was kind of a shit show, and the class was too difficult

Second time we used a mix of Ahlfors & Rudin, and that was much better

Part C of complex my first time through it, the Professor typed up his own lecture notes

[remote sparrow]

it's fine. there are answers and solutions to most problems in the back

also power-series first

[marble solar]

This time the first two terms were out of Conway, and the third term was out of Forster's Riemann Surfaces

[north summit]

why power-series first is important?

[remote sparrow]

it's not MORE important, it's just different from the typical approach

[marble solar]

The advantage of power series first is that a lot of the "big theorems" become easy consequences of the fact that holomorphic functions have a locally convergent power series

[dapper root]

I LIKE POWER SERIES FIRST

[north summit]

you have 3 terms per year? also one course for a whole year??

[remote sparrow]

quarter system

[marble solar]

Yeah, Complex ABC

[dapper root]

Shoutout Marshall

[sage python]

Like they develop the theory for analytic functions and then later show holomorphic => analytic?

[dapper root]

Yeh

[marble solar]

More or less

[sage python]

Idk if I like that

[marble solar]

I actually had to learn how to compute Cohomologies for Riemann Surfaces. I was in physical pain

[sage python]

It doesn't take very long to do the holomorphic => analytic story

[dapper root]

It’s a based approach

[remote sparrow]

#math-pedagogy message

[sage python]

So you might as well just do that first week or two and you know how powerful the results you're proving are

[marble solar]

It's a very good approach to complex analysis. My only problem with Marshall is that I wish there was more an emphasis on Linear Fractional Transformation Methods. I think the best general book for learning Complex Analysis that I've read is Stein and Shakarchi. My favorite is Marhsalls, and the most precise is Conways

Rudin is fine, but requires some more measure theoretic point of view that I'm not sure pays off

[sage python]

Wait proving product rule and such using power series???

[marble solar]

Yeah, I've gone through it

The one that sucks is chain rule

[dapper root]

I like POWER SERIES first because you immediately get to do TAYLOR APPROXIMATION-esque stuff which ends up being VERY useful

For making nicestimates

[marble solar]

Also I think Conways Proof of the Riemann Mapping Theorem is the clearest out of any of the books I've read. So the technical precision does pay off

[dapper root]

Like I learned CA first from Gamelin and then from Marshall

[sage python]

This is bizarre to me. I'd rather just establish analyticity of holomorphic functions as quickly as possible

So now you can use any tool that's good for the job

[north summit]

what if i mix bak and conway so i get a litle bit of both worlds.

[dapper root]

And the power series approach in my memory mitigated a lot of the really annoying ass hard analysis I remembered at the start of Gamelin

Where I was like brain melting

And quickly got to “here’s nice theorems to use”

[marble solar]

That's fine. I also really like Conways approach to Cauchy integral formula using differentiation under the integral

[dapper root]

Which is what I liked the most cuz it’s like algebra

[remote sparrow]

bak & newman is meant for undergraduates, you're probably above that level

since you said you already knew some metric space topology

[marble solar]

Conway is a good intro to grad book. It's a little slow & does the details

[north summit]

i'm undergrad

[remote sparrow]

you can read it if you like; marshall is more appropriate

[sage python]

Gonna write my own complex analysis book. Part 1 will be differential topology, part 2 will be elliptic PDE

Part 3 will finally be complex analysis

[marble solar]

Isn't that just Barry Simon's series?

[remote sparrow]

you can look through marshall too. the geometric aspects of complex analysis are covered better in marshall compared to bak and newman even though both do power series first

[marble solar]

The geometric aspect is somewhat covered. I think if you want the geometric aspect, there's no one better than Ahlfors

[north summit]

sadly i don't have access to a physical copy

[remote sparrow]

yeah but bak and newman is very scant on the geometric aspects

[sage python]

Narasimhan gang

[marble solar]

I haven't read it

Hopefully I can TA complex this year

I'm taking the complex qual, and will have to compute more cohomologies. I didn't realize I could hate computations so much

[sage python]

Neither have I lol, I went off lecture notes for my class whose reference was "Silverman"

Which I think is a quasi-translation of Markushevich

[dapper root]

If u want the geometric aspect of complex analysis

Use an algebraic geometry book

Heyoooooo

[north summit]

Introduction to the theory of analytic spaces?

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-0175-5

[marble solar]

Ah yes just work through Hartshorne then it will be clear what's going on in Complex Analysis

[dapper root]

GRIFFITHS ANS BAREIS

[marble solar]

The correct way is to just introduce sheaves

[dapper root]

I meant a COMPLEX algebraic geometry book

[remote sparrow]

#book-recommendations message

what made you change your mind?

[marble solar]

being in graduate school

[dapper root]

THE GIFT OF BEING ABLE TO LOOK BACK

AND SEEING THE LANDSCAPE FROM A HIGHER POINT

[remote sparrow]

[north summit]

https://link.springer.com/book/10.1007/BFb0077071 yeah this seems like the correct place to start

[sage python]

Wrong Narasimhan

Idk that one tbh

[sage python]

This is the one I'm talking about

[remote sparrow]

i just linked you the correct narasimhan

[sage python]

Much more topologyish

[north summit]

i was joking

[marble solar]

Graduate school, properly done, really changes the way you think & do mathematics. It offers a lot of perspective on what you learned, and you can see through the bullshit that you went through. It puts things in context & perspective in a way that's hard to describe. The best thing that captures is that famous painting of the guy on the mountains looking down at the fog

And I'm sure being a professional researcher is similar

[sage python]

The evolution can happen on a much shorter scale

[dapper root]

This is how I feel about HARTSHORNE

If u think it’s bad it’s SKILL ISSUE

You can have more nuanced takes and say there’s better ways to learn and that’s fine

But to say it’s trash is skill issue

[remote sparrow]

i used to pronounce his name as heart shorn but i learned it's actually pronounced as hearts horn

[dapper root]

In the words of my AG prof

[remote sparrow]

heart shorn is so much cooler tbh

[dapper root]

“The book is heart shorn, the man is hearts horn”

[spare shadow]

Hey guys, i am utter dogshit in Math kinda because of Dyscalculia. Well now is it summerbreak and i want to get better in Math and Physics, etc. Do you guys have any tips, videos, websites i could use?

[north summit]

isn't shorn like past participle of shear?

¨the heartbroken¨

[remote sparrow]

i don't know specific grammar terms but sounds about right

[drowsy nacelle]

lmfao actually yes it is

[mossy flume]

Khan Academy would be a good place to start for math that comes before calculus

I will say that idk how good it is for dyscalculia specifically but in general that site is a really really great learning tool

[spare shadow]

Oh perfect, i just stumbled appon that website while doing the research

Thanks for confirming tho

[torn crypt]

Anyone know anything more systematic about these?

[sleek canyon]

im planning on going to uni this year to study maths, does anyone have any book recs/ online courses that are preferably free?

[spare shadow]

I also stumbled across some free Harvard courses, probably to complicated but maybe interesting to look into in the future

[north summit]

o'neill elementary differential geometry vs do carmo differential geometry of curves and surfaces

[remote sparrow]

tapp is good too

apparently maa is reworking its website? the old maa book reviews page is down

https://old.maa.org/press/maa-reviews

the old layout can still be accessed here

[north summit]

how's the printing?

[remote sparrow]

good, the book is full-color

the pages are like, glossy and thick

[north summit]

and the quality of the binding?

[remote sparrow]

my copy is fine, it's perfect bound though

https://old.maa.org/press/maa-reviews/differential-geometry-of-curves-and-surfaces-2

https://old.maa.org/press/maa-reviews/differential-geometry-of-curves-and-surfaces-1

https://old.maa.org/press/maa-reviews/elementary-differential-geometry

[north summit]

do you know how does it compare to o'neill or do carmo?

[remote sparrow]

tapp? it expects familiarity with real analysis and linear algebra

i quite like the pictures; they're very helpful

[uncut crater]

How are Needham's texts?

[remote sparrow]

they're more supplements than proper textbooks

[uncut crater]

I see

I was particularly annoyed with CA texts until I read VCA for some reason

Maybe because, as the joke (?) goes, that CA is trivial

[remote sparrow]

gamelin is good

[uncut crater]

I need one for a second reading soon enough

I did a bit from Bak and Newman

[remote sparrow]

marshall does more of that power-series first approach if you've gone through bak and newman

[north summit]

how was bak and newman?

[uncut crater]

For a ug book? Fantastic

Better than the competitors (usually engineering texts lmao)

[trail hemlock]

Uta and sourdrop are like the viper of #book-recommendations

[uncut crater]

It's only books I read and no math done unfortunately 😞

[remote sparrow]

viper?

[trail hemlock]

viper is the dude who lurks in #calculus until get got active

hes cool tho

[remote sparrow]

gamelin can still be used for a second reading too

[uncut crater]

I'll see if my library has a copy

@trail hemlock is the onepiece rael?

[sick swallow]

Hi! I'd like to hear an opinion about Felix Klein - Vorlesungen über Nicht-Euklidische Geometrie (the one about non-Euclidiean geometry). Is it good? Will it be enough to understand the concepts of non-Euclidean geometry?

[trail hemlock]

sorry i dont watch anime

[uncut crater]

[trail hemlock]

but im sure it is

if you believe (?) in the power of friendship (???)

[uncut crater]

What's that

[trail hemlock]

oops, forgot this was a math server

friends are like if textbooks grew hands and feeet and connected with you on an emotional level

[uncut crater]

?????

Oh

Holy heck I read that wrong

[trail hemlock]

hope this helps

[uncut crater]

I thought our hands and feet became books and had sentient extensions of their own

[uncut crater]

Well, it's Klein, maybe it's good?

The only book on non Euclidean geom I flipped through the pages of is Sossinsky

[trail hemlock]

myabe its a metaphor for humanities greatest tools seperating them from other animals

Thonk

regardless i continue on my search for a macroeconoics textbook that uses fun calculus

if anyone knows a good 1

[uncut crater]

Hmmmm

[uncut crater]

Oh that's literally impossible to find

Trust me, i tried a lot

[trail hemlock]

dude i like econ

its super interesting

[uncut crater]

I had econ too

[trail hemlock]

my school offers macro and micro over the summer

and i thought fuck it

but our textbook is so dogshit

[uncut crater]

And the most amount of math I saw an econ course use was the derivative of the quadratic function

Lmfao

[trail hemlock]

someone told me about this one, and its pretty decent

its not as outdated as rudin, and since rudin rings true, im sure this one does as well

[uncut crater]

Nice logic

[remote sparrow]

why is rudin "outdated?"

[uncut crater]

Are they using Mankiw by any chance?

[trail hemlock]

rudin and ahlfors were published 71 years ago

[sick swallow]

I don't know to be honest :D Haven't read Klein's books before. Was Sossinsky's book on non-Euclidean good?

[trail hemlock]

this is getting off topic, cya guys

[remote sparrow]

the first edition of rudin was published in 1953, but it's in its third edition

also, the material in rudin has not changed

[trail hemlock]

neither has the brevity

[uncut crater]

Iirc the treatment was similar to Hilbert, it started with Euclidean geometries and finished with consequences of not considering the fifth postulate

I'm reading that book again, the problems were fun

[remote sparrow]

ahlfors may be somewhat dated, but it is still getting good mileage as a standard text in many classes

[trail hemlock]

is stein and Shakarchi is more popular?

only reason i ask is because hte cover loooks cool

[sick swallow]

I think I'll read both of them when the time comes. Thanks!

[uncut crater]

Very handwavy

[trail hemlock]

ehh such is life

[remote sparrow]

it is popular, and i hear the problems are very high quality. but some people here take issue with "toy contours"

[remote sparrow]

it's a good exercise to try to make precise what is handwaved

[north summit]

How's Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts? sounds pompous

[modern ruin]

doesn't make them outdated

[trail hemlock]

wrong choice of words

i meant more than 4x older than me

[modern ruin]

lol

i do find it strange that there has been so much time to improve analysis textbooks and pedagogy but no one can do much better than rudin

[trail hemlock]

ehh "better" depends

most people find abbott to be "better" since u learn the same material in a gentle way

[sage python]

Abbott does way less so idk about same material. And is gentle a virtue? :0

[trail hemlock]

ehhh rudin past chapter 7 isnt the best treatment from what others have told me

[sage python]

Oh yeah definitely. But Abbott doesn't cover that stuff :P

I do think there are books that have kinda beaten Rudin, but they're not as well known

Schroder if you're super new to everything, little to no background in either proofs or calculus

[full pier]

does anyone have much experience with basic mathematics by serge lang? I want to fill the gaps in my knowledge since i didnt much attention in school

[sage python]

(Or even if you have more background it's still good)

And Browder is basically Rudin but organized differently and with multivariable calculus inspired from Spivak Calc on Manifolds (so probably better)

[trail hemlock]

ok i havent read abbott so i dont have the experience to comment on it

but like u siad, i doubt rudin is the best RA book ever written objectively

[remote sparrow]

dami prefers a rough introduction to anal? :0

[real marsh]

the best objectively written textbook in a field is the one that grabs your attention enough for you to finish it

[foggy relic]

yeah rough anal is peak

[sage python]

Gahhhhh

[gray gazelle]

LOL

[molten mason]

I've gone through it, it itself has tons of gaps, but it is a good reference point to get the basics of what you need in preparation for Calculus and it can identify your weak points.

For example it covers the basics of trig, there's ton more trig that you can study and learn.

[ashen flower]

hello. i need documentation/info/texts about dual spaces in the context of linear algebra

math majour

[full pier]

I see, sounds perfect for me then since ive done single variable calculus and really basic analysis (limits, continuity, differentiabilty and integrabilty) but i can tell in some areas im weak

and i want to improve my intuition

[torn crypt]

https://shop.elsevier.com/books/theory-of-charges/rao/978-0-12-095780-4

Any commentary/reviews on this text?

[molten mason]

Oh yeah I've done 3 semesters of Calc and I found the book as great refresher. I think it would be good to go through.

[molten mason]

What have you done so far? What textbooks have you used?

[full pier]

thank you so much, ill definitely go through it then. Do you reckon Langs other books are good? im thinking after this one i do his linear algebra text

[molten mason]

Everyone has different opinions, and for the most part you should use more than 1 textbook anyway.

The unbiased general consensus is his good books are Basic Mathematics, his Calculus textbooks, Linear Algebra, and Algebra (as a second or third textbook)

[full pier]

i see, thanks for all your help!

[molten mason]

#book-recommendations message

Click that to see other great LA books

[slender cargo]

Another member for the Lang club

[left cloud]

i can’t believe you just put general consensus, good books, and lang algebra all in the same message

[molten mason]

So many schools use Algebra for their quals I feel like it's a necessary evil

[slender cargo]

I've seen D&F as the other primary recommendation

[full pier]

now im getting a bit scared lmaao

[mild arrow]

Hiiii, should I use stewart's early trans in conjunction with Spivak's as a way to self study calc 1, 2 and 3?

[molten mason]

Same

[molten mason]

You can, Stewart covers all 3. Spivak I think only covers 1 and 2?

[molten mason]

They asked specifically out of Lang though and that's why I said they should also use another text

[mild arrow]

i think so, but im honestly interested on how spivak goes very deep on some topics, and it may be better if i use it with stewart's

[slender cargo]

No need for Stewart if you're using Spivak, although maybe Stewart can give some intuition if you feel Spivak is lacking somewhere. I think Spivak is fine as is though

[mild arrow]

alrighttt, btw im gonna use it as my reference on MIT OCW

[slender cargo]

And yeah, for Calc 3 you would just need a different book, of which there are several

[mild arrow]

which one do you recommend?

[full pier]

spivak is quite good, but its more rigorous and i think you should be comfortable with proofs

[mild arrow]

i kinda like proofs but i hate them

[slender cargo]

I'm taking a class on the material next term so I can't really say for sure. My class is using Edwards Advanced Calculus of Several Variables.

[mild arrow]

(like literally anyone else lol)

[slender cargo]

I think it works just fine as an intro to proofs, but maybe pair the book with some primer on proofs. Maybe go through Book of Proof or something like that

[mild arrow]

is it weird or too early to study this if im only 16 😭

[slender cargo]

The nice thing about Spivak is he has a full solutions manual

[molten mason]

Normal for 16

[mild arrow]

thanks for the assurance 😭

[full pier]

bruh i had my head up my ass at 16, its really good if you go through it

[mild arrow]

ive done discrete math already, i can do proofs already, it's just im not really comfortable w/ them

[slender cargo]

Just keep practicing

[full pier]

youll be completely fine then lmao

[molten mason]

A real chad would use Apostol

[mild arrow]

what the hell is apostol 😭

[slender cargo]

The other option

[molten mason]

The very expensive alternative to Spivak

[slender cargo]

(I say go with Spivak)

[full pier]

i say go through rudin, i promise you wont cry yourself to sleep every night and quit in chapter 2

[molten mason]

If you use Spivak you'll have a lot of support in this server too

[mild arrow]

i'd go w/ spivak since i already have eyes on the physical copy itself

im just waiting to buy it

[mild arrow]

i'm still a beginner tho 😭

[trail hemlock]

the reward for understanding chapter 2 is chapter 4

everything jus clicks

its iwld

[mild arrow]

i'm interested in spivak cause apparently it goes deep, which is what i want, i tend to remember everything if i study it at their core

[trail hemlock]

spivak is an excellent choice

my intro to calc was spicak

[full pier]

ima hundred percent go through it after i do a refresher on my basic math skills haha, i cant wait for that feeling

[mild arrow]

which is something that stewart's might not be able to provide

[trail hemlock]

its super approachable, all u need is free time

[mild arrow]

also, is it fine if i havent studied hyperbolic functions yet?

[mild arrow]

and i have lot's of it, i might just go with it xD

[molten mason]

Stewart is perfect if you want to go into Physics or Engineering. All solutions are online too

[trail hemlock]

khan academy or i think (dont hold me to this) spivak does them

[trail hemlock]

as previously mentioned, the alteranteive is apostol's Calclus

[mild arrow]

yeahhhh but i don't want to just remember the rules and identities and shit, i wanna learn how they're derived

[trail hemlock]

🥳

my hero

[full pier]

do spivaka then

[mild arrow]

apparently it's too expensive...

[molten mason]

I think you learn that in Calc?

[trail hemlock]

🏴‍☠️

[mild arrow]

oh?

[gray gazelle]

Y'all should read the Bible I'm not sure if y'all heard of it

[trail hemlock]

this is the most important skill in all of math.

[full pier]

do you have any previous experience with calc yet?

[full pier]

no i havent whats it about

[mild arrow]

i have a strong foundation of precalc

but i do know a lil bit about some concepts in calc

[trail hemlock]

a lottt of poeple here read spivak as an intro

[gray gazelle]

Part one about this powerful dude and his people and part tow is about the powerful dudes son and he's really cool

[molten mason]

I mean Stewart is filled with proofs and explanations. It just also has tons of computational exercises.

[full pier]

id say go for spivak then

[trail hemlock]

it rewards hard work, not knowing all the stuff beforehand

[mild arrow]

like how integrals is the area under a curve, and adds up infinitesmal-ly tiny rectangles, and derivatives are slopes of points on the cuvre (very much generalized)

[trail hemlock]

ur gonna have to formalize this

😔

[mild arrow]

you're making me scared of calc 😭

[full pier]

i would say learn some computation first, then go through spivak

[trail hemlock]

"make it more rigorous" echos in my nightmares

in darq's yelly voice