book-recommendations

[gray gazelle]

Best beginner book for algebraic geometry? Starting off with 0 experience in it whatsoever. I have some knowledge in (Algebraic, a little) Topology, but not much else.

[grim ore]

Hottake, but Royal road to AG by Audun Holme; but vakil stated there is no royal road to ag so you can read his text for supplementary (he like explains sooo much indepth to a point of maybe even over explaining, some may say)

Beltrametti lecture on curves is good too for beginners

Shafarevich - Basic Algebraic Geometry series is pretty good with some comm alg background

[gray gazelle]

Thank you! I’ll look into those, I’d especially like as much detail as possible, so I’ll probably like that one especially

[grim ore]

This was what i used for my class

If you want i guess like a formal education textbook

[mossy flume]

I assume you've taken abstract algebra courses?

[gray gazelle]

I haven’t had any courses(homeschooled, and I doubt I’ll even be able to go to college), but I’ve read some group theory book(don’t recall which one, didn’t pay much attention, regrettably), and I’ve read a little on rings, but that’s about it algebra wise. Also some basic category theory, if that counts?

[mossy flume]

If you want a computational introduction, I like Cox, Little, and O'Shea's text Ideals, Varieties, and Algorithms which doesn't assume much algebra past linear algebra and so that'd be a good start and I think computational stuff is interesting. I also like Fulton's Algebraic Curves which you can find on Fulton's site

[gray gazelle]

Alright, thanks!

[mossy flume]

but Fulton's text assumes you know abstract algebra to a good level

and IMO before learning algebraic geometry, learning abstract algebra would be a better start

[gray gazelle]

Yeah that’s probably a good idea

[pulsar quail]

@ionic zephyr Yes,I have an e-mail. I can write my e-mail in PM. 🙂

[ionic zephyr]

ok thanks

[hollow peak]

actually learn complex geometry to start

[molten gulch]

complex geometry seems fun

[grim ore]

Huybrechts is one i recommend

Atleast it was the one i learned off of, idk if there are better ones

Currently looking at Voisin's complex geo and hodge theory text

[molten gulch]

what are the prerequisites to complex geo? hartshorne? diff geo?

[grim ore]

Id say just complex analysis tbf

It doesnt really have much of a need outside of that and everything else you can pick up here and there without too much hardship

Oh and probably a strong linear algebra background but the text does a good job to fill in both of those gaps in knowledge

The first chapter is there to fill in the gaps

[molten gulch]

Okay makes sense, frankly I was just concerned with the homology/cohomology stuff + several complex vars stuff, that I know at-least eventually that you're kinda expected to know; also perchance have you read any of Griffiths and Harris Alg Geo book?

[grim ore]

I have been recommended that so many times but no ;-; i havent gotten to checking it out yet

[molten gulch]

What is your mathematical background?

[grim ore]

Im just a third year ug, I finished all my undergrad course work and just sit in grad lvl classes as I am doing my second major

Definitely not at the lvl of like a grad student

[molten gulch]

Ahh nice, we're in our 3rd year of uni too (CS), just finished up mutlivariable calculus and linear algebra; self studying real analysis...very slowly

[grim ore]

Yooo im doing cs too

[molten gulch]

yoooo

mind if we send you a friend request?

[grim ore]

Yeah sure thing

[fresh skiff]

Oh i thought you are math major

[worn monolith]

What is a rigorous introductory textbook to representation theory? I am not familiar with the subject but it appears that there are representation theories for different classes of groups one is interested in, is there a common foundation for these theories? I am interested in a textbook on the foundations before delving into a particular branch.

As for my (relevant) background, I have taken an introductory group, ring and fields course, and read Axler

[cursive orbit]

fulton harris seems to be the classic

[worn monolith]

I see, may I ask is my assumption stated before correct? The introduction of Fulton harris says that it introduces representations of Lie groups and Lie algebras which has me a bit confused, is this the foundation?

[cursive orbit]

well iirc it begins with finite groups

which is typically the introductory case

[worn monolith]

ok, I will take a look

thanks

[floral lantern]

a slightly lower-level book than Fulton Harris is etingof's book

which is very general

https://math.mit.edu/~etingof/reprbook.pdf

this has quivers and categories and all of that as well

[worn monolith]

thanks

[grim ore]

Im a math and cs major

I finished my math major and now doing cs

[grim ore]

Im also taking alg top and a hodge theory course

which sounds counter intuitive as hell but hopefully itll work out

[fresh skiff]

wow impressive

[old elk]

Nice book of representation

[remote sparrow]

maybe matsumura? there's also this new book i found online. here's a link: https://bookstore.ams.org/view?ProductCode=GSM/233

[remote sparrow]

https://www.amazon.com/ALGEBRAIC-GEOMETRY-ROBOTICS-CONTROL-THEORY/dp/1800610459

apparently this exists

[fossil elk]

Hi im in year 12 are there any book recs??

[normal crystal]

that could mean different things different places, or even the same places
so add a bit more to what you're looking for

[vital bane]

actually one must learn infinite dimensional kahler geometry to start 🗿

[vital bane]

"Emotional Intelligence" by Daniel Goleman, and "The Alchemist" by Paulo Coelho

if you're refering to math books, "Inside Interesting Integrals" by Paul Nahin, and "Understanding Analysis" by Stephen Abbott (pure math book)

[molten gulch]

You have to be more specific than this

[molten gulch]

Assuming they've gotten through algebra and know some trigonometry

[vital bane]

Yes, I would assume a year 12 student would have that knowledge

[molten gulch]

This whole time I thought they said "12 years old" and not "year 12"

Hence my panicked reply

[obtuse topaz]

any book reccomendation for learning advance calculus for putnam

[grim ore]

I recommend looking at "Putnam and Beyond" by Gelca

Its a pretty well known text

[obtuse topaz]

yes i have that book but i think its very challenging and not enough theory given something to start from theory and have more examples

[obtuse topaz]

.

[grim ore]

Oh im glad I found this url, but I also read this when I was preparing for the putnam exam: https://math.stackexchange.com/questions/1170456/books-preparatory-for-putnam-exam

The Art of Problem Solving is also another well known text

[grim ore]

.

[obtuse topaz]

thanks for the info dude

[obtuse topaz]

how did your putnam exam go?

[grim ore]

not great, but i also didnt really study as much as i should have

like i didnt study until the week before

if i had more time i definitely could have done better but i also just got busier as my years went on

I also did it my freshman year lol

[obtuse topaz]

ohh i see

hardly i can solve 1 or 2 questions that too taking lot of time

a day

[grim ore]

Usually these texts do the mid lvl to harder lvl questions, there is this site that has all the putnam exams in previous years and you can try the easier questions and realize you shouldnt stress too much and should be able to get atleast a 10 if you got far enough through these two texts

https://kskedlaya.org/putnam-archive/

[obtuse topaz]

Which is that website

Ohh ok

[dull fog]

Tryna get good at those tricky problems they give in math Competitions, any recs?

[hybrid scroll]

Hello, I’m a random guy who’s wondering how I can self study math efficiently without discouraging myself. Can anyone recommend some resources?

Oh and I finished high school btw, and I started a math textbook, but the few exercises in it are very hard

[gray gazelle]

Which AOPS book should I begin with first? I'm in 8th grade and I'm taking algebra 1.

[gilded shuttle]

prealgebra

[oak zodiac]

I'm second year CS degree, and I'm looking for some problembooks or textbooks that are niched to some spcific filed (e.g. lin alg, abstract alg, discrete math, etc.) but focuses on problem solving and interpreting the field in broader acpect. I really like Evan Chen's infinite napkin as he leaves some "harder problems to thing about" at the end of every chapter, but there aren't many, and not all fields are completely covered in napkin.

[craggy shore]

What sort of maths are you learning?

[deft reef]

I recommend a short history on nearly everything if your looking for a good read it's about the creation of the universe and chemistry and physics written by bill Bryson

[craggy shore]

I believe @oak zodiac is looking for maths problem solving books.

[oak zodiac]

as I mentioned, some classic field that are covered in normal math degree like lin alg, topology, analysis, discrete math, abstract algebra... I wouldn't mind some more CS related topics like algorithms, complexity theory etc. In general, I'm looking for problem-related textbooks that cover university level mathematics

Bonus points if problems are olympiad-like, because with those I usually get most intuition

[craggy shore]

Actually I was asking @hybrid scroll

[oak zodiac]

lmao, I'm dumb

[craggy shore]

No worries mate

[fresh moat]

any book recommendations on good pure math for a motivated high school student? could be about anything I just want interesting theory hard problems

[dim sierra]

Number theory might be good, check out Burton’s book

[crimson needle]

Hi! I'm in 9th grade I need to improve everything, can you guys please give me a really good book recommendation ?

[pastel shale]

how to prove it by velleman and then linear algebra done wrong in that order

[vital bane]

"Understanding Analysis" by Stephen Abbott

literally the best undergrad pure math ever written in all of human history

it teaches you how to write proofs along with teaching you analysis with beautiful and illuminating exposition

[fresh moat]

thanks. I’ve already done some number theory with AoPS but I’ll look through this

[fresh moat]

👍

[tender cobalt]

yes you can start with a precalculus book

[gray gazelle]

i need help with finding a calculus book which covers topics in great depth but is fairly simple to understand (i know the basics of calculus)

i know functions, differentiation, limits (including L'Hospital's rule), implicit differentiation and some integration

[tender cobalt]

Michael Spivak calculus

limits differentiation integration are covered in insane depth

with all the theory and proofs

or actually you can use Thomas Calculus (a bit less difficult than spivak) too, it also covers these in good depth

[gray gazelle]

is the language simple enough for a beginner to undertsand?

[tender cobalt]

yes

[tender cobalt]

Thomas calculus is what i used when i knew these ^

[gray gazelle]

oh

thanks man

ill try these books

[tender cobalt]

keep in mind michael spivak calculus book is going to be hard

[craggy shore]

Mathematical Proofs A Transition to Advanced Mathematics is also pretty good. It teaches you how to write proofs and then goes to common undergraduate maths and it's proofs topic by topic.

Also How to Prove It A Structured Approach by Velleman is also good to start learning formal maths and proofs. This one is shorter and brief.

[gray gazelle]

okay

[vital bane]

it's more of an soft analysis book lol

[tender cobalt]

any general biology textbook?

[ionic zephyr]

yes let me find

https://www.amazon.com/Miller-Levine-Biology-Level-Student/dp/0133669513/ref=sr_1_4?dib=eyJ2IjoiMSJ9.D_-QyVFW_BiqqG6j_urZQHCugZSyRJPRySG0viUUjcLOgG6cytBLJP4RXKGVotITaSz3TPzMQx6t1DXboNxXwzJZLW4HCKfJbC-plCe5-KihSr7tRbv4HKCDZCiWuoeXFwkA67sQVurfi5SJAahLLpc2UWoopmfMJixJRMyt0OYD2QzWRPFQBdG-EVFG91-BoilZlFGGBwk6LWBQrM6sY6VPdLrmsfCtxszS13ZmQiw.YT-l-mrXswFXwtqRjUKmlr8vC_9CWt947SZ5nubWYKk&dib_tag=se&keywords=biology+textbook+high+school&qid=1736859472&sr=8-4

theres this one but idk

i dont remember the one i used in high school

i actually only took high school bio

i never took ap bio

i did take bio in college tho

but it sucked compared to the one in high school

in fact, i got a perfect score on the end of course exam

the governer rewarded me a certificate

[ionic zephyr]

the one in college was just busy work

https://tenor.com/view/abus-sicherheit-security-schloss-padlock-gif-23573070

[tender cobalt]

Thanks

[ionic zephyr]

ofc, its no problem for me

[vital bane]

what?

[ionic zephyr]

of florida

for perfectt score on bio eoc

i could find it

[vital bane]

The Governer of Florida gave you a reward for getting a perfect score on a biology exam in college??

[ionic zephyr]

yeah weird ik

[vital bane]

no it's fine

[vital bane]

lol yeah 100% that sounds like a bad movie plot

[ionic zephyr]

https://tenor.com/view/deep-snow-doggo-cute-dogs-funny-animals-gif-13079834

[vital bane]

it seems tenor is down again

[ionic zephyr]

oh hmm

its ot for me

thee wifi at my gym has been out for a few day tho

ppl have to sign in by writing their name

and phone numbe

[vital bane]

RIP

[ionic zephyr]

on a chart

yeah

idk how thats supposed to work

[gray gazelle]

its got calculus in the name, good enough for me

[vital bane]

yea the author even says "it's supposed to be named "intro to analysis" but it's too late to change the title now" in one of the later editions lol

[gray gazelle]

oh lol

well it will let me learn some analysis then

knowledge is knowledge

[hollow shore]

Peter Lax's book is a good quasi Analysis book

but if it's for a normal calculus course, then I'd suggest smth else

look into https://ocw.mit.edu/courses/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/

[gray gazelle]

i'll look into it

[vital bane]

🙏

[flat plaza]

Any good books on 0-1 order logic?

[molten gulch]

<@&268886789983436800> inappropriate

[split portal]

Keep things sfw here

[vital bane]

was it furry pron again?

[molten gulch]

no

[vital bane]

I remember some rando coming in and spamming that in all channels

[molten gulch]

lmao

[boreal sedge]

Can anyone recommend me a beginners book for learning graph theory ?

[formal bronze]

Try 'Graph Theory' by Diestel

[boreal sedge]

Okay !!

[mental helm]

a textbook recommendations for Complex Numbers

[molten gulch]

chruchill and brown's complex variables covers complex numbers in chapter 1, the rest of the book is for complex variables (calculus with complex numbers) (complex analysis but with far less proofs and far more computation)

[dull fog]

my brother is in 7th grade and he's trying to get really good at those questions in math competitions. He's done everything up to quadratics, he's going to start trignometry soon. But these tricky problems really get to him.

[vapid badge]

Can someone recommend me a good book for functional analysis based on applied problems from calculus of variations?

I'd like to not get too deep into the theory

[wheat remnant]

Is there a good book for learning proofs/being able to prove things in math or should I just roll with my discrete math course book and hope it’s in there and not assumed

[molten gulch]

Hammack's book of proof is available for free online

(Legally)

[brittle mesa]

thanks!

[wheat remnant]

Oh let’s go!! Preciate!

[gray gazelle]

intro probability with set notation? best intro probability book?

[real marsh]

Stochastics: Introduction to Probability and Statistics by Hans-Otto Georgii, de Gruyter

[old elk]

The treasure that came to me

[gray gazelle]

so blurry

[gray gazelle]

is this good for undergrads

[real marsh]

Yes

[vital bane]

BRO WHAT???

How did you get that???

Drop the link....please

[old elk]

I would sell it to you but I just received it

[thorn ember]

DnF ftw

[dim pendant]

No way

Are those pages glued in

💔

Oh I didn't see the bottom, they look sewed in

[old elk]

jajaja

[vital bane]

no I mean

where did you buy it?

drop the link

[sonic aspen]

Is there a really good textbook for linear algebra?

[vital bane]

yes

Gilbert Strang or FIS

depending on whether you want applied or pure

[formal bronze]

Hoffman and Kunze

[flat marten]

Where are you filming that, a sewer?

[tender cobalt]

it seems like his floor

[grim ore]

Why do you have to do them like that, dang

They were just proud of the new book

[ebon cedar]

good textbook to self study Algebra 2?

[split portal]

@odd spoke Before I forget I wanted to recommend some specific books rather than just kicking the can down the road. When I first learned elementary algebra I used this book https://www.amazon.com/Beginning-Algebra-11th-Margaret-Lial/dp/0321673484/ref=mp_s_a_1_11?crid=2HROHB359R0P6&dib=eyJ2IjoiMSJ9.GxKWMYk63H56Or0zqUgtfvvtC5KfI1BwSxWcC6WCGRnf40vcQxE1ORVaFiD1B3DV-fCgTl0MqQg2R6ikoUIDOozlO-_7LnhQ7WBT6N9lkvpMSMxoIaymEL7SnsxoPCZy4B-H-EqAkGz8r9l0VWmXXbjSzBWX2tobKeU5Wi4-AxMYHiLOIj-P1ZPTMgO26IICHnULGsYkhp1JyrT2tKXJew.bDC6QtnkONzimER7aHQ5zFOPahUcCpGcVFbKJLNpjNc&dib_tag=se&keywords=lial+beginning+algebra&qid=1736977850&sprefix=lial+beginning+algebra%2Caps%2C92&sr=8-11

New copies/editions can be pricey but used older editions can be found for cheap. Also it is possible to find this book online if you look around.

You can also find books of solved problems online along these lines

https://www.amazon.com/Schaums-Outline-Elementary-Algebra-3ed/dp/0071611630/ref=mp_s_a_1_4?crid=CQVIC82ZS6ZC&dib=eyJ2IjoiMSJ9.g91nMXhASRaYjzQn49K6LFGQuC2oEfvBw1rPXNX-cscKOhUZ1D53J-KVuT7t1nHvLyFxqJ4fcYdwqrf15a9eYmvDtrH1wB1iZGV13dYa5Cv43_cLeouWIGZ9zZJPzyUc4JC6Tv9cmBoIaUXVpF-58Q3IfMqgNVPK8l7xA9vWHWo-C5-Hr-wtUUW3zm_luhqgX-fVEotVzB7trqxeyXmc0g.YmVzqYDuvTC1uZm-QQJ3_6Hr21Uf1-cyP_FqfM-oI2E&dib_tag=se&keywords=schaums+algebra&qid=1736977960&sprefix=schaums+algebra%2Caps%2C94&sr=8-4

These can be vaguely good for practice or for seeing methods you are struggling with worked out. They aren't good replacements for full textbooks though.

Lastly openstax has some free online algebra books that seem fairly standard though idk how good they are since I haven't used them personally.

Lemme find you a link to those as well.

https://openstax.org/details/books/elementary-algebra-2e/

[split portal]

What I just posted was aimed at alg 1

But since you are asking these books all also have follow on books for algebra 2

There are also many alternatives to these books since community colleges and high schools all over the world teach this stuff to people all the time.

[outer nest]

K I know it's been like 2 years but how was the book at the end?

[vale nexus]

anyone have textbook reccs for self learning preclac?

[split portal]

Lial, Larson and Blitzer all have popular precalc textbooks.

[vale nexus]

tysm

[outer nest]

yall don't understand that my grandfather wrote that book lol

[crude lava]

never read it lmao

it’s still in my bookshelf

[dapper root]

Real

[vital bane]

Complex

[tender cobalt]

http://alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

This seems like a good starting point for learning differential geometry

[vital bane]

oh yea I forgot shiffrin has a diff geo book

[vital bane]

this is an even better starting point for learning Diff Geo

🗿

[tender cobalt]

Real book

I love shifrin multivariable calculus book

[vital bane]

yea Shiffrin is based

[gray gazelle]

book reccomedations to prepare for STEP exam?

[real marsh]

Isn’t there like a canonical book

[signal mountain]

siklos but its not necessary, just do practise for the most part

[graceful fulcrum]

Hay

Hay

[naive lava]

hey, so, i'm trying to be a physicist, but i also wanna have solid math background, I've read "physicist books" for math before but now i wanna learn stuff i learnt rigorously, so i looked up some books, and i'm having fun currently tbh, but i need some help ordering these books, and i also do not want to spend lots and lots of time on these, because, well, i am not going to be a mathematician, first of all, do i need set theory and graph theory? I know some stuff about cardinality, but not much about graph theory. Here's the list of books:
baby rudin
complex analysis ahlfors
big rudin
functional analysis by rudin
algebra by lang
I have a working knowledge of point set topology from Munkres's book, I have started reading baby rudin and i'm currently at ch 6, how should i continue?

and after i got these i plan on reading hatcher for alg. top and guillemin for diff top. then later something for manifolds and riemann geometry but i haven't decided on anything yet

[vital bane]

hello dogu

[vital bane]

basically don't read anything from Rudin it has bad exposition (only exercises are good)

instead of baby rudin I would recommend "Understanding Analysis" by Stephen Abbott

absolutely amazing book

beautiful exposition

and instead of big rudin (aka papa rudin) I would recommend either Folland or Daniel Cohn

[vital bane]

oh you are at ch 6 of Rudin 💀 then I think you should just finish ch 7

Honestly I think you will get good advice from mathphys people in the physics server

like Dalton

[naive lava]

heeey, long time no see, what's up?

[naive lava]

too late for that now isn't it lol

[vital bane]

nothing much, what's up with you? I think I will join the physics server after summer

[naive lava]

idk much about dalton but most mathphy ppl i know reccomend me mathpy books

[vital bane]

did you ask for pure math book recs

[naive lava]

why ch7 specifically?

[vital bane]

Axler's MT book is also good

[vital bane]

usually people stop doing Rudin after ch 7 or ch 8

as Rudin's treatment of differential forms is awful

[naive lava]

not much, you know, finals week is finally over so hell yeah to that

[naive lava]

worse than nakahara? 💀

[vital bane]

what. 💀 nakahara has bad treatment of diff forms?

I heard nakahara was goated

[naive lava]

it's just

imagine you put a alg top, manifold, riemann geo, morse theo, complex manifold books together

and squeezed it to 600 pages

[vital bane]

oh you mean it's just too compact and leaves out details

I suppose it's for physicists, so it only has the important bits

[naive lava]

it's just definition theorem theorem theorem theorem

you know

[vital bane]

ahh

[naive lava]

wait wait wait let me quote something from it

[vital bane]

Lee is all the hype these days for manifolds, he has 4 books, intro to topological manifolds, smooth manifolds, riemannian manifolds, complex manifolds

[naive lava]

"Although this seems obvious, we have to prove that this is indeed true, but, we are going to omit these proof, an interested reader may consider consulting any algebraic topology textbook"

[vital bane]

complex ones came out recently (2024)

True physicist way

[naive lava]

whoa

4 books?

[vital bane]

indeed

[naive lava]

I have only like 2 years before the classes that i actually have to study for starts

[vital bane]

but I myself will be using Spivak's 5 volumes

[vital bane]

grad school?

[naive lava]

so i might not be able to finish them all beforehand

[vital bane]

I'm sure you won't need hardcore riemannian geometry for those classes

[naive lava]

this is my first year so i take basic stuff like CM EM and QM

next year basic gr, qft and all that jazz

[vital bane]

Based

[naive lava]

then the topics that i am not familiar with will start

[earnest wolf]

what did u guys use for measure theory?

I know about Axler's and Folland's books. Looking for more because that's how I like studying – switching back and forth between books

It could be books, lecture notes, video lectures etc

[vital bane]

but only the first two years are classes right?

[vital bane]

Daniel Cohn

[naive lava]

no, here, we have "research classes"

for example one of them is conformal bootstap methods in quantum field theories

[vital bane]

interesting

[naive lava]

usually only 1 or 2 guys take the class and instead of lectures, you have readings and homeworks

and you have to write a paper if you want a grade

so after my 2 years i will be taking those

[vital bane]

I see

so 3rd year has these research classes

and after that you just fully lock in and do research

[naive lava]

you can take more of those after that but how many areas are you gonna do research in

[vital bane]

https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j

(the same channel also has the dark mode for this course)

[naive lava]

im not landau yk

[earnest wolf]

hmmmm
tbh I didn't like his RA lectures, but thanks for suggesting anyway!

[vital bane]

No one can be Landau 😔

[formal bronze]

Royden and Rudin (real and complex analysis)

[naive lava]

okay i'm kinda getting us back to the point here

i'll drop rudin after 7th ch

then what?

[vital bane]

Folland or Axler or Cohn

for advanced analysis

[naive lava]

why not rudin?

[vital bane]

or maybe Tao as well

[vital bane]

you can do it if you want to, I just think it lacks exposition

[vital bane]

https://www.youtube.com/playlist?list=PLPH7f_7ZlzxQVx5jRjbfRGEzWY_upS5K6 this has a bit of measure theory lectures in between

[naive lava]

and more importantly, can i read lang before that cos i'm more into algebra then analysis

[vital bane]

have you learned algebra before?

[naive lava]

from physics books, yeah

also i've read the first chapter of lang

[vital bane]

Lang is more a grad level algebra book

[vital bane]

and did some of the exercises?

[naive lava]

all of them

[vital bane]

This is what I'm using:

[naive lava]

honestly prob. lang's first chapter covers almost everything i need in physics buy yk

[naive lava]

i looked at that but our libraries copy is missing a cover and a backcover

also ppl called it "dry"

so, can i read it before measure theory? I think I probably can but you know how examples in algebra go

[vital bane]

Lol yea you can

algebra and analysis are usually very far apart sadly

[naive lava]

yeah but examples can be from analysis

that was my issue but since lang says this is a "first year grad course" i would assume he doesn't require measure theory

[vital bane]

do you mean something like ring of continuous functions C[0, 1]

[naive lava]

yeah but also analytical ones or smooth ones

[vital bane]

I wonder if measurable functions on a set form a ring probably does, I think it should be closed under pointwise addition and multiplication

would have to prove it

[naive lava]

isn't is obvious

[vital bane]

I would like to say that it is

but I suddenly realize how many times I got tripped up by seemly obvious facts

I have PTSD

"I've played these games before!!"

[naive lava]

a couple of other things, i go for lee's books after i am done with alg and diff top, right?

[vital bane]

but yea good luck with your math journey! we shall meet again back in physics land

[naive lava]

and since rudin lacks exposure, what could you reccomend me for functional analysis

[vital bane]

I think all you need for lee's book is knowledge of real analysis and linear algebra

[naive lava]

what

[vital bane]

since lee's first book out of the 4 is essentially a topology book

"introduction to topological manifolds"

[molten gulch]

Lee's books lead into each other, you can read intro to topological manifolds with just rudin level analysis

ISM expects some linear algebra

[vital bane]

so if you have experience with topology from Munkres, you could go straight into Lee's 2nd book

ISM - intro to smooth manifolds

[naive lava]

yeah but not all topological spaces are manifolds, no?

[vital bane]

No but this book develops topology specifically for use in diff geo

[naive lava]

but i need some actual topology sooner

[naive lava]

okay so i'll skip 1st one then go to smooth, riemannian and complex

after i'm done with hatcher and guillemin

[vital bane]

Munkres you said you've already gone through some of it

[naive lava]

no i meant i will need alg top sooner

[vital bane]

you know there is also this interesting book "Differential Forms in Algebraic Topology" by Loring W. Tu and Raoul Bott

it might pique your interests

[naive lava]

yeah but i have no idea what category that book falls into lol

[vital bane]

idk how good it is though

[vital bane]

@remote vortex

func anal book recs? I only know Peter Lax's functional analysis book and I don't know how good it is, I've never gone through it

[naive lava]

imagine if he said rudin

also, do know know if i will ever need alg geo? I've never seen it mentioned anywhere in my books but you know physicsists

[vital bane]

String theory is where I've heard of alg geo popping up

you could ask bubs

[naive lava]

okay than i''ll need it

damn

[vital bane]

but he'd probably say something along the lines of "I've never learned algebraic geometry"

[naive lava]

I'm gonna have to go trough hartshorne

[vital bane]

@median fossil book recs for dogu?

[surreal heart]

any thoughts on Bressoud's Radical Approach to Lebesgue's Theory of Integration?

[naive lava]

also, thank you so so much, this has been much help

[median fossil]

I'd recommend approaching the topic from distribution theory (and perhaps also PDEs)

Streater--Wightman has some of the basic stuff

[naive lava]

probablity theory

[remote vortex]

don't really know anything in English, Folland's Real analysis covers some normed spaces in the middle chapters, maybe that will be enough footing to get through Rudin with

[median fossil]

With some QFT motivation
A great text is, naturally, Reed & Simon
Another good math reference that minimises jargon and Bourbakism is Generalized Functions by Gelfand et al.

Reed & Simon also have very neat physicsy applications

[median fossil]

Why probability theory?

[remote vortex]

I think Rudins functional analysis is the least questionable of his trilogy, anyway

[median fossil]

If you're talking about 'distributions'

Then I meant distributions like the Dirac delta

Weak derivatives stuff etc

[naive lava]

i didn't have a good exp with prob theory when i was in ug

my lowest grade was prob theo

[naive lava]

whoa what is that

i can google

i will google

[remote vortex]

Dirac delta is also a probability distribution

[median fossil]

I knew you'd say that

[remote vortex]

i aim to please

[naive lava]

that actually makes a lot of sense

didn't know there was a name for that

[remote sparrow]

richard bass' Real Analysis for Graduate Students and stein and shakarchi volume 3 are both worth looking at

[timber mesa]

yeah I think these are good complements to Folland

[trail hemlock]

prob nice to know some group theory aswell

[vestal hazel]

book recommendations for linear algebra?

[vital bane]

what kind of linear algebra?

applied or proof based?

[vestal hazel]

applied

[vital bane]

Gilbert Strang "Introduction to Linear Algebra"

also

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

[vestal hazel]

thanks a lot

[vestal hazel]

ohh

[spark jay]

I need proof based book on it any recommendations

[vital bane]

Friedberg, Insel and Spence (FIS) or Hoffman and Kunze (HK)

check out both

choose whichever one suits you

[tender cobalt]

bro really hates axler 😔

just like how he hates determinants

[vital bane]

nah you can check it out after learning LA

it's a fun book

has a lot of FA-esque problems

[runic obsidian]

Any book for probability and statistics?

[spark jay]

Thanks alot

[fresh skiff]

Up vote, for FIS.

[acoustic cliff]

You guys got recommendations of relatively obscure books on Linear Algebra that usually don't come up when recommendations are asked for?

[tender cobalt]

steve roman advanced linear algebra maybe

[gray gazelle]

Harvey Rose - linear algebra
Frederique - Linear algebra I, II.

[vital bane]

not sure if I can call Shilov's Linear Algebra book obscure but that's another book that at least I don't see coming up often

[molten gulch]

FIS is awesome

[vital bane]

https://www.youtube.com/playlist?list=PLISEtDmihMo2i5tj7UCmz43dORdpG_SMY

[remote vortex]

Billingsley's "Probability and measure" is solid, especially if you are interested in the probabilistic direction

There's also Shilling's book which I don't recall the title of, something about measure and martingales

Plus of course there's Rudin's "Real and Complex Analysis"

[stable flicker]

what level?

Grimmett Stirzaker for general, cool hard undergraduate
https://probability.ca/jeff/probstatbook.html for more applied, less topics, but should still be solid

[normal crystal]

👍
that channel has so many playlists

[vital bane]

half of them don't seem useful

[normal crystal]

yea, it's chaotic

[tender cobalt]

is loomis and steinberg advanced calculus literally an intro to functional analysis

[real rapids]

anyone got any book reccomodations for someone who hasnt read a single book in math and only studied in school ( 10th grade) - more of like the math "basics" u can add up on . or just like your fav math book , i am just bored out of my mind and interested in math

[vital bane]

Lol this seems like a fun book, it's basically an intro to DG

[vital bane]

Khan Academy is honestly really good for this

but I'm not sure about a book at your level

[tender cobalt]

wow

[vital bane]

I'm sure there are lots of good books, I'm just unaware of them

[vital bane]

there's also rigorous classical mech

last chapter

[tender cobalt]

I could suggest how me as a 10th grader self study math if you're willing to take my path

[tender cobalt]

Yeaa

[tender cobalt]

as neamesis said you start out with khan academy, what you do there is do their algebra and trigonometry courses

and after that, you can pick up any book that has the name "Precalculus" , i used the one by James Stewart and you can find them free online by searching

[vital bane]

I actually never went through a calculus book, and I learned calculus from Khan academy

[tender cobalt]

these books have lots of exercises on algebra, trigonometry , you can do them

[vital bane]

and like 3blue1brown

[real rapids]

tysm , might aswell try it - i either bore myself to death or do something actually good for my brain lol ( i also am not a native speaker nor am i good in speaking english so we google translate here we are )

[tender cobalt]

crazy

[vital bane]

your english is good

[tender cobalt]

I went through Thomas' Calculus for calculus (single variable) and well before that i learn calculus from khan academy organic chemistry tutor blackpenredpen

[vital bane]

goated channels

[tender cobalt]

Fr

[tender cobalt]

loomis steinberg says it assumes spivak level calculus

but this book looks harder than rudin

[vital bane]

Lol Rudin isn't hard

it's just bad

🗿

[tender cobalt]

pedagogical skill issue?

[vital bane]

indeed

but the exercises are cool though

[vital bane]

This seems like a strange book though

[flat marten]

Greub linear algebra

[vital bane]

Ooh yea Greub

[flat marten]

My fav

[vital bane]

Greub - I've been saying "Gerub" all this time

[tender cobalt]

Yeah its a book from like a course taught in harvard back in 70s

[vital bane]

obscure

[tender cobalt]

but I wonder if I actually go through loomis and steinberg

doing all chapters

how will I come out

[flat marten]

Greub was how I taught myself linear algebra and it's made me dogmatic

[tender cobalt]

this book has homology??

[flat marten]

:3

[versed wraith]

can someone recommend me a book?
i can only read 1 book ever, which one?

[blazing rune]

If you have a bit of linear algebra and calculus with any interest in the math of physics, I'd suggest The Road to Reality. Penrose builds up a lot of tools across fields of math with examples for the first several hundred pages with a lot of drawings.

[night pilot]

baby rudin changed my life (for the better)

anyway i came here to ask for geometric measure theory recommendations

[earnest wolf]

So, since this channel isn't only for math books..

Wanna satisfy my resent interest in finance. Some topics I'd like to read more abt:

• HFT / quant trading
• How and what math is applied in finance (the purer the better! :D)
• general economics / finance:
  • why golden standard was eliminated
  • what caused 2008 crash
• how is money created in finance industry [they literally don't produce any products]

Any suggestions are appreciated

bruh

[timber mesa]

one book I've seen rec'd and have still yet to read () is The Complete Guide to Capital Markets for Quantitative Professionals

[remote sparrow]

maybe read some measure-theoretic probability with an eye towards stochastic calculus

[night pilot]

the thumbsdown was intended as lighthearted

apolgies

[earnest wolf]

i wasn't offended
I literally just called u by name

[remote sparrow]

bruhh

[timber mesa]

@earnest wolf a friend doing finance-ish data science stuff says two essential books are this and https://onlinelibrary.wiley.com/doi/book/10.1002/9781119457176

surely someone else in this server might know better given your goals and interests though

[thorn cloak]

Shreves stochastic calculus for finance series is very good, especially the second volume. Hulls options futures and other derivatives is considered the gold standard on the finance side but is less mathy. Liars poker is a must read if you’re interested in history and culture of Wall Street. This one is about bonds (a more boring product). The big short, also by Micheal Lewis, is about 2008. Too big to fail is also another one (wait, aren’t these just movies??) i don’t really understand what you mean by “how money is created” but a history of Wall Street by Charles Geist goes through the phases of the finance industry. Hulls book also includes many products they offer clients. I would personally look up “prime-brokerage.” That is one service they offer that makes them quite a bit. Most of the “products” are traded among the traders. It’s mostly services nowadays. I don’t know any specific books on HFT, but there are quite a few in algorithmic trading. HFT is kinda saturated nowadays. No more alpha left. There aren’t many books on quant trading outside of prep books as it depends on the firm. QT is either systematic/algo trading or just a discretionary trader using algos developed by the quants (or a mix). I don’t know any books on golden standard sadly :((

Sorry this is fairly long lol. TLDR:
Very Mathy- shreves stochastic calculus for finance
Derivatives - Hulls OFD
History of Wst - Geist
2008 - big short, too big to fail
Other - liars poker

I have also heard of Malialvian calculus being used (he has his own book) it’s like stochastic calculus of variations but that’s a little beyond me lol

Some other good books are in this thread https://quant.stackexchange.com/questions/38862/what-are-the-quantitative-finance-books-that-we-should-all-have-in-our-shelves#38872

[slow roost]

Saari - Mathematics of Finance is a pretty good undergrad text

[earnest wolf]

oh yeah
thank you So much!

[thorn cloak]

Of course. I also forgot to mention the book on Jim Simon’s ! I think it’s called like the man who solved markets or something. That is absolutely a must read for quant history and also when genius failed

[earnest wolf]

already on my to-read-list in notion haha

[thorn cloak]

[willow merlin]

which book covers projection operator, identity operator, but most importantly Matrix representation of linear transformations with respect to different bases?

for example I have this Matrix

M_EB(f) = [f]_EB
like where the columns of some Matrix mean that for example
(f(e1))_B = (1,1,1)
(f(e2))_B = (...,...,...)
and etcera and I want to multiply by a change of basis matrix so I get
M_EE(f) = [f]_EE
where E is the standard basis

which book explains how to find the image of a linear transformation when I am not given a linear transformation but I am given the matrix representation of the linear transformation with respect to different input and output basis
for example I want an explanation to this formulas

M_EE(f) = M_BE(id) . M_EB(f)
[f]_EE = [id]_BE . [f]_EB
and this formula
M_EB(f) . [v]_E = [f(v)]_B

where E is canonical basis

which book explains why the Image and the kernel of a projection operator are in direct sum

why if a vector that is part of the image of a projection then it means the preimage is that vector

why a projection pop=p
why p(v) = v for v in Im(p)

which book explains that using proofs??

[frozen minnow]

resent

[slow roost]

Friedberg, Insel, & Spence - Linear Algebra

[orchid echo]

basically any book on linear algebra covers these topics

FIS is good but in the pinned somewhere there is a whole bunch of other references too

[visual sedge]

favorite functional analysis books? currently using rudin's functional analysis looking for something to go through once i'm done with this book

[remote sparrow]

maybe look at conway

but you could also consider applying that knowledge to PDEs

[muted tusk]

I'm taking an Optimization course this semester and looking for a textbook/video course to supplement the class. Preferably an open-source book.

MAT 4800 - Introduction to Nonlinear Optimization

Course Description: Development of the theory, algorithms, and applications of nonlinear optimization, including unconstrained optimization, convex optimization, iterative methods for unconstrained optimization, and constrained optimization.

Topics:

• Single Variable Optimization
• Linear Regression as Multivariable Optimization
• Classifying Symmetric Matrices, Quadratic Forms
• Unconstrained Multivariable Optimization
• Convex Functions on Convex Sets
• Arithmetic-Geometric Mean Inequality
• Newton's Method for Multivariable Optimization
• Method of Steepest Descent and Modified Newton's Method
• Convex Programming and the Karush-Kuhn-Tucker Conditions
• Linear Programming Problems as Convex Programming Problems
• Nonlinear Optimization with Equality Constraints

[vital bane]

resent means to hate something, you mean recent

[vital bane]

Peter Lax?

[vital bane]

What about "Introduction to Stochastic Calculus with Applications" by Klebaner

I think you might've been the one from whom I got to know that book

[fresh skiff]

Recently I found a book on AA
https://www.cambridge.org/pk/universitypress/subjects/mathematics/algebra/abstract-algebra-comprehensive-introduction?format=HB&isbn=9781108836654

[vital bane]

the only book you'll ever need

[fresh skiff]

It seems nice. Does anyone have any idea about it?

[fresh skiff]

So true

One of the reviews

[vital bane]

"simplified version of D&F" smh smh

we don't need that

D&F is 👑

[slow roost]

it's a great book, massive, lots of topics, lots of exercises. The writing style is a bit long-winded compared to most grad algebra books, which I actually like. Good book to self study from

[vital bane]

yea exactly the long-winded writing style is perfectly fine, idk what people are talking about when they say it's "dry"

that kind of style makes it enjoyable to read

[slow roost]

yeah D&F "dry" is crazy

have a look at Matsumura if you wanna see dry

[dim sierra]

Neamesis you and I seem to have the same taste in textbooks

Abbott and DnF are 👑 lmao

[dim sierra]

I don’t understand how anyone says this lol

I guess Artin might be more exciting and that’s there reference point but 🤷

Atiyah-Macdonald or like you said matsumara or any other dense commutative algebra textbook is dry af

[vital bane]

[vital bane]

or like Rudin

[dim sierra]

yeah that too

[remote sparrow]

thoughts on complex made simple by ullrich?

[storm tusk]

hi! i'm looking to work up to understanding the proof of monstrous moonshine for a reading program im doing. im wondering if people have suggestions for places to start. general notes / background

• im not familiar with modular forms.
• i am familiar with simple groups, but i am not familiar (more than by name) with the monster group or the proof of the classification of finite simple groups.
• courses taken: undergrad algebra, undergrad analysis, undergrad point-set topology, undergrad complex analysis (very computational), undergrad linear algebra, grad measure theory, grad group theory, in-progress grad ring theory / grad functional analysis

please ping me if you respond :) thanks!

(also any commentary on the plausibility of this project in a 3-4 month time frame / how much progress i should expect to make is very welcome!)

[remote sparrow]

https://bookstore.ams.org/view?ProductCode=GSM/250

there's a new book by eisenbud and harris

[slow roost]

ooh

[fresh skiff]

Rudin is fun.
Once you read it, no matter whether it's dry or not, you will love to continue studying.
(I have skipped a lot of Rudin. But i am talking according to experience what i have read)

[slow roost]

yo that new Eisenbud & Harris is free as an ebook, sick

[remote vortex]

If Rudin was the only analysis book available when I was in my first semester, I would probably have bounced off and not become a mathematician.

I appreciate this book now for what it is, but I think recommending it as a learning resource should come with a lot of caveats and alternatives.

[fresh skiff]

oh yeah, for the first course it might be not good. This book is kinda challenging but worthy.

[vital bane]

you would've been saved from this cruel fate

[vital bane]

Only after you learn analysis

[tender cobalt]

what are really good books for learning analysis

other than abbott

that doesn't really get recommended quite often

but is a solid good book

[vital bane]

most of them

[slow roost]

Pugh

[tender cobalt]

Pugh is what i am currently trying to read

[vital bane]

trying?

https://tenor.com/view/starwarsday-gif-5413758

[slow roost]

there's also Tao

[tender cobalt]

well i didnt do the exercises yet that's why I said "trying"

[tender cobalt]

tao analysis II covers multivariable right

[earnest wolf]

yes. and I don't care enough to correct it

[gray gazelle]

Looking for a book that will introduce me to more advanced topics in algebra and representation theory. I have what most would consider a full algebra sequence behind me and I'm particularly interested in it compared to analysis. I've gone through most of Judson's book which I thought was fine and also my university's lecture notes on galois theory.

I'm going to be taking a class next semester called modules and homological algebra so if you have anything mind that could get me started on that path that would be nice

After that I plan on learning about lie algebras and representations of finite groups

[vital bane]

have you considered the 2nd half of D&F

it has some homological algebra, module theory, representation of finite groups

[gray gazelle]

I have trepidations about buying an entire book for what will probably be less than half its contents but I'll give it a look

Pirates are free, after all

[vital bane]

I'm just using the PDF because I'm unable to find a cheap copy of the behemoth

[vital bane]

also tbh it's a nice reference as well

for the earlier algebra, if you forget some details (groups, rings, fields that is)

[gray gazelle]

In general I like to have physical books to study from but I can tolerate a pdf every now and then

[vital bane]

same

[tender cobalt]

why dont you get a book printing service and reprint

[vital bane]

i should

[flat marten]

i would like to throw my hat into the algebra book ring and say my favorite book is grillet

[viscid dome]

Anyone got any literature that touches on the concept of generalized metrics (in the sense that its over an ordered field instead of R)? I haven't had any luck finding some as of yet.

[tender cobalt]

what literature have you already seen?

[viscid dome]

none, wikipedia I suppose?

[tender cobalt]

check out Rudin's principle of mathematical analysis chapter 2

[viscid dome]

Baby rudin only covers regular metrics: distances using the reals unfortunately

[tender cobalt]

munkres topology is the way to go then

covers metric very generally

[remote vortex]

Still only metric with values in the nonnegative reals

I presume IV is relating to what's in this article https://en.wikipedia.org/wiki/Generalised_metric

[viscid dome]

Yee

[remote vortex]

But it almost feels like it was written by one person to put their idea out there

Which explains your difficulties finding the literature, there isn't any

[tender cobalt]

Oh

[balmy pike]

I was reading Born A Crime by Trevor Noah for school and it ws a very good book

[viscid dome]

Oh, cool. But a shame, I'll still be looking so if there are any suggestions which anyone finds please hit me up

[remote vortex]

Why are you looking for it?

Is it relevant to a problem you're solving?

[tender cobalt]

make the stuff up 😎

using knowledge of topology and algebra

then make an article on it and post it for peer review

ez

[viscid dome]

I'm studying ordered fields, so it feels very natural to extend the idea of metric spaces to be what we're restricting ourselves to.

[tender cobalt]

any deep learning textbook recommendations for beginners? (Something that isnt fully practical like using pytorch but rather discusses the theory and ideally have exercises)

[brave burrow]

Does anyone have a probability and statistic cheat sheet for a typical undergrad course on the subject? Stuff like probability theory, random variables, probability distribution, confidence interval, hypothesis testing, simple and multiple linear regression. Thanks in advance

[restive nexus]

You here too? 🧐

[sturdy shore]

damn good imo, not a beginner book though

by that I mean, would be good if you have mathematical maturity, you can be complex analysis beginner no issue with that

better way to explain what I meant: the book is intended for a graduate level audience

[cursive orbit]

bishop

[mellow wren]

https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/understanding-machine-learning-theory-algorithms.pdf

[molten gulch]

<@&268886789983436800> scam link

[remote sparrow]

https://link.springer.com/book/10.1007/978-94-007-2636-9

today i found this book on the web

@sage python

https://old.maa.org/press/maa-reviews/the-linear-algebra-a-beginning-graduate-student-ought-to-know

i have to agree this book seems a bit overkill for its intended purpose (to remediate perceived deficiencies wrt to the linalg background of incoming grad students)

but this seems useful for quals prep or a topics course in advanced linear algebra

[slow roost]

looks cool, good rec

[remote sparrow]

@crimson leaf were there any noticeable defects with your international edition copy of friedberg?

[crimson leaf]

Not that I can recall

[tender cobalt]

Thanks Ill check it out

[tender cobalt]

Thanks Ill check it out

[heady ember]

Mine (5th ed) was smelly 😔

When I read it, I hope I'm not breathing in carcinogens or something

[gray gazelle]

anyone hear of book recs from putnam fellows? or anyone who did well in comps in gen

doesnt have to be maths necessarily

no springer pls i dont like the pages

unless its really good

[remote sparrow]

i mean like missing chapters or whatever

[gray gazelle]

So I've signed up for a course in functional analysis that starts in a couple months and I need a refresher on my linear algebra and Fourier analysis skills. I took those courses about 2 years ago now and I've been told that the course in functional analysis uses a lot of stuff from those courses. I'm looking for some material to refresh my memory and skills in those subjects (I don't even necessarily need book recommendations just any resources you guys think are good will do)

I must say I didn't do very well in either of those courses (especially Fourier analysis), I did fairly well in the general linear algebra courses they have for engineers and stuff but then I took an advanced course and only barely passed. In particular things like normed vector spaces, convolutions, dual spaces, and inner product spaces were very difficult for me and I wouldn't be able to solve much in reference to them currently

I have had some more time to improve at mathematics in general since then however so I'm pretty confident that I'll do fine this time around

So yeah any kind of undergrad crash course in the prerequisites for functional analysis would be appreciated

[remote vortex]

<@&268886789983436800> self-promotion in #book-recommendations

[daring lake]

Deep Learning by Ian Goodfellow

[tender cobalt]

ive seen it and it seems to be what i am exactly looking for but it has no exercises though

[daring lake]

what kind of exercises?

[tender cobalt]

like problems

[daring lake]

people usually don't do rigorous math calculations for deep learning (especially in a course)

[tender cobalt]

like how will i test myself i understood something?

[tender cobalt]

oh so its not like any physics or math courses where you got problems to do after learning something?

[daring lake]

not really

most courses would be hands on with sklearn, tensorflow

[tender cobalt]

ah, thought i would be learning some underlying mathematics for deep learning and be making my own ML trainer or something

from scratch

[daring lake]

ig you can

but it would be complex

a small DL model i made last sem has 3 million nodes

I doubt anyone would do rigorous calculations to make that

[tender cobalt]

yea from scratch its hella lengthy

[tender cobalt]

any books for that?

[daring lake]

https://arxiv.org/abs/2310.20360

still no problems

but many advanced concepts

[tender cobalt]

looks insane

[topaz berry]

Can anyone suggest me a good book for olympiad level proofs?

[vital bane]

grass WHAT?

[real marsh]

Problem Solving Tactics

[distant nacelle]

Has anyone gone through Algebraic topology-Homology and Homotopy by Robert M. Switzer

How difficult is it..say compared to Hatcher?

[tender river]

https://link.springer.com/book/10.1007/978-3-030-36721-3 don't know what this is like but it can't be nothing?

[teal prairie]

This is kind of an awkward request since any book that follows a non-practical/theoretical approach would probably be targeted towards grad students and thus it is not easy to find books that target beginners with exercises etc.

Foundations of ML by Mohri and Talwalkar has some good chapters on computational learning theory targeted towards beginner that you might find interesting.

Sanjeev Arora has a graduate level text on algorithmic ML (I have not read this) but I am pretty sure it has exercises

A course could be a better way to learn (there are slides/lectures generally available for MIT/Berkeley etc.), I recommend this for beginners in Deep RL (my field) with the course from RAIL, Berkeley delivered by Sergey Levine which has some challenging exercises that can test your mathematical skills and understanding of the content

[rain wren]

why should you care about the difficulty? just worry about the quality of the exposition

[distant nacelle]

It looks fine on a skim through, but i haven't delved in tbh

[fresh skiff]

Hi DarQ

[gray gazelle]

Harder exercises than James Stewart. Explanations are often wordy, examples are poorly explained. I would recommend using James Stewart Calculus for understanding, and doing problems on Essex for mastery.

Rarely any proofs

Same thing

What university do you attend? UBC or UWO?

Canadian universities, the authors are from there

I'd would suggest using James Stewart for explanations and then using Essex for word problems -- are you forced to use this textbook?

Calc 1 is decent, Calc II is horrible, Calc III is just bad.

At my university, we switch over to a different textbook for Calc III

The only reason we use this textbook is because one of the author taught this course at my university

[stark turret]

any books like Nathan Carter’s “Visual Group Theory” but for other areas?

[slow roost]

Visual Complex Analysis and Visual Differential Geometry by Needham?

I don't actually know if they're like that Carter book, as I haven't read that. But at least their titles are of the same form

[hollow osprey]

Can i ask something here?

[plush rain]

seems as if you just did

[hollow osprey]

How can i know my math level?

How can i know at which level of mathematics i am ?

I mean i want to evaluate my math skill

[slow roost]

what's your highest completed math class?

[hollow osprey]

After 2 years i'll complete my high school

[quick hornet]

then youre high school level

[slow roost]

Ok, do you breeze through your classes and take hard classes and practice math competition problems, or do you struggle a lot in regular classes, or are you somewhere in the middle?

[hollow osprey]

I think i'm somewhere in the middle

[slow roost]

there you go then

[hollow osprey]

@slow roost which country do you belong?

[slow roost]

USA

fair point - average in some countries is stronger than average here

and by some, I probably mean a lot

[hollow osprey]

You're a post graduate in math, right?

[slow roost]

um, in the sense that I’m post graduation yes. But I’m not a “post grad” in the common sense of someone with a PhD on track for a job in academia

[hollow osprey]

Me brain: 🤡 after hearing all this

What does it means btw?

I don't understand adult stuf

[slow roost]

“Post grad” is a common term here. It refers to someone with a recently earned PhD desperately struggling to find a good job

they often relocate to work at some school they don’t love too much in the hope of eventually getting their dream job of tenured professor

I’m giving a cynical characterization of it, but it’s the reality for most

[hollow osprey]

Hey post graduation is different from getting a doctrate, right?

[slow roost]

in the sense I’m talking about, yes

[trail hemlock]

post grad means after getting masters/phd

[slow roost]

Post grad is a transitional time between getting the doctorate and becoming a full blown professor

but taken literally, post graduation does just mean after graduation. I am in that camp

[hollow osprey]

Ohh

[hollow osprey]

So are you getting a doctorate?

[slow roost]

I’m not ruling out the possibility one day

not in my immediate plans though

I almost got one but things went badly

[hollow osprey]

So to sum up all
You are a full blown adult

[slow roost]

I’m an old yes

[hollow osprey]

How old?

[slow roost]

36

[hollow osprey]

Teen me thinking you were an in you 20s

Man you are way too old then you sound

[slow roost]

yeah it’s been a pretty long time since my masters to still be dreaming about going back

[hollow osprey]

I can't control my laugh 🤣🤣

[slow roost]

that’s probably because I’ve been online chatting with peeps since I was in middle school

[hollow osprey]

So are you married?

[slow roost]

😅 some personal questions. I’m with someone for quite a few years, we’re not quite ready for marriage yet or official engagement or whatever but I expect it’ll happen eventually

[hollow osprey]

Man or woman?

[slow roost]

haha, woman. You know, I’m a pretty laid back guy and I don’t really mind these questions, but some adults would find this overly forward. Just fyi

[hollow osprey]

You're a woman?

[slow roost]

I was referring to my partner

me am man

[hollow osprey]

sorry sorry

you're awesome man
I wish i would have met you in your teens

[slow roost]

heh appreciate it

[hollow osprey]

So you're an adult and a postgraduate in math

Have you ever thought of becoming a mathematician

[slow roost]

glamorous, I know (jk)

well yeah

I was in a PhD program

I guess I didn’t make that clear before

but yeah that’s what I wanted to do, things went wrong and I’m lucky to have gotten out with a masters

[hollow osprey]

By mathematician i mean the real deal

[slow roost]

I wanted to be a professor and prove some good theorems

[hollow osprey]

You know like the big and famous ones

[hollow osprey]

Ohhh

So what are you doing now

[slow roost]

I taught some middle school and high school math for a few years. I wouldn’t teach middle school again, I hated it. I am open to teaching high school again if the conditions were better for me than they were

I walked away from that

I’m currently tutoring kids in math at an after school center, learning some computer programming, and thinking about what I want to do with myself

[hollow osprey]

Nice

So do you know all of high school math

If yes tell me how could i master all of it in a year or so

[slow roost]

I’m comfortable with most high school math with the exception of AP Statistics

I should really learn that stuff

[hollow osprey]

And about my question?

[slow roost]

that’s difficult to do without guidance and it’s hard for me to give advice without knowing your background

[hollow osprey]

Ask me then?

Ok atleast give me an least assuring advice

[slow roost]

Khan Academy is a good resource to learn from and practice problems

[hollow osprey]

Ok

Let's see whether i can accomplish my goal or not

[tender cobalt]

it can be done in 4 months

[hollow osprey]

@slow roost thanks sir loved talking to you

[tender cobalt]

3-4 months

[tender cobalt]

yeah

[hollow osprey]

Really?

[tender cobalt]

yes, at least that's what I did

[slow roost]

If you like learning from books and are up for a challenge that will take time, you could try reading Basic Mathematics by Serge Lang

[tender cobalt]

i started off with khan academy then picked up a precalculus book

[slow roost]

it pretty much covers the entire curriculum from kindergarten to high school, stopping with trigonometry

and it’s written by a legendary mathematician

[hollow osprey]

Ok i'll look into tha

[slow roost]

though it covers elementary topics, it’s written in the style of a math grad textbook, which will take some getting used to

[hollow osprey]

Okay

[slow roost]

but I believe it’s the best exposition of all that stuff in one book

hey look, we got back to a book recommendation!

[hollow osprey]

Yes
Nice way to do business (jok)

Oh then see you some time

Thanks for help senior citizen 😂

@slow roost

[tender cobalt]

books are really good compared to videos

there is a massive difference tbh

[hollow osprey]

Oh well did you learned all of high school math in 4 months

[slow roost]

just look how nice that is

[hollow osprey]

Yes looks like that

Okay then
See you later

[slow roost]

adios

[tender cobalt]

yes

[tender cobalt]

Yea

[hollow osprey]

?

[tender cobalt]

Rigorous precalculus book

[slow roost]

it’s spanish for “goodbye”. Sometimes white guys like me say it to try to sound cool

[hollow osprey]

You white people

[tender cobalt]

should i read something on fourier analysis before PDEs

[gray gazelle]

yo whoever recommended me the calculus books, thanks a lot to you man

[marsh ingot]

What level?

[gray gazelle]

idk what level those books are but i love em
one is Calculus by Spivak and the other is Thomas' Calculus

[marsh ingot]

So you have read those?

[gray gazelle]

i am reading them currently

[marsh ingot]

I see, then those are good for now. Once you want to check Real analysis

[tender cobalt]

think I did

[gray gazelle]

thank you so much brother 🫂

[tender cobalt]

ah yes

[tender cobalt]

Your welcome

[tender cobalt]

Are you reading both spivak and thomas

[gray gazelle]

even though the rigourous proofs are a bit complex for to me to understand in the first read, they are making me fall in love with calc

[gray gazelle]

spivak currently

[tender cobalt]

awesome

[alpine ridge]

Hello, i need to dive deep into imaginary numbers, complex numbers and the Euler's identity. Can someone recommend a good book for it? Thanks

[quick hornet]

how deep

[alpine ridge]

Deep enough to understand circuits

[quick hornet]

i think the usual recommendation for electrical engineers is churchill and brown's complex variables and applications

might be more advanced than what youre after based on how you phrased the question though

the first chapter at least is probably appropriate regardless

[alpine ridge]

Ahh i see thanks!

[alpine ridge]

I got Calculus 1 to 2 and linear algebra under my belt, its enough right to understand this book?

[tender cobalt]

Yea

[gray gazelle]

Hiii I’m new here from the U.K. loved maths but chose a different career and now I want to learn more. Just wondering if you have any recommendations on what I should look into or read? Any ideas would be appreciated and thanks in advance!

[sudden kindle]

Maybe take a look at undergrad curricula and see what you missed.

[weary python]

do u know some good probability theory book?

[vital bane]

Understanding Analysis by Stephen Abbott and Concrete Mathematics by Knuth, Patashnik and Graham

[slow roost]

Feller

[old elk]

This book is simply monstrous both in size and content, I'm going to spend a lot of time on algebra this year.

[fresh skiff]

Looking awesome. I have D&F as well but the binding isn't good enough

[gray gazelle]

city spies a good book if anyone here is under the legal age of discord

otherwise ur too oldfor it

[grim ore]

?

[gray gazelle]

idk

its a recommentation

[slow roost]

that's for sure:

[grim ore]

That is absolutely horrendus

What the hell?

I mean, you can say it sure is broken in

[fresh skiff]

mine is in good condition lol

[mortal ore]

is that your copy

i cant decide if that binding means that you love or hate linalg

[fresh skiff]

lemme show you later once i done that Lin Alg problem

[slow roost]

unfortunately

I've been wanting to get it mended somehow, not sure where to take it

I never could understand that stupid Jordan canonical form

[mortal ore]

In my words and definitely NOT wikipedias:
In linear algebra, a Jordan normal form, also known as a Jordan canonical form,[1][2] is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them.

[slow roost]

yeah, I've tried to understand it and kinda sorta get the gist, but I never learned how to actually compute it

[mortal ore]

i dont know either

im currently taking linalg and the last thing i learned was that vector addition is commutative

(the semester just started)

[slow roost]

cool. which book are you using?

[vital bane]

@gray gazelle bro what

I sent that message about 2 years ago

[vital bane]

let me know if you find out how to mend it

[mortal ore]

lemme check

"Linear Algebra and its Applications" by David Lay

6th ed

apparently its supposed to be comparably rigorous to other books

[trail hemlock]

what algebra does to a mf

[slow roost]

for the record I didn't get frustrated and destroy my copy of D&F I got it used and it gradually fell apart

[tender cobalt]

any book recommendations starting off with multilinear algebra right away

like a linear algebra book with emphasis on multilinear stuff

[remote sparrow]

i guess Multilinear Algebra by greub?

[weary python]

tyy

[fresh skiff]

Is he the author of linear algebra book (one for graduate level)?

[flat marten]

That's not really a linear algebra book

To get linear algebra you'd have to read one in conjunction

Th3res also northcotts multilinear algebra

Which does modules from the start

But it suffers the same issue

[fresh skiff]

https://www.google.com.pk/books/edition/Linear_Algebra/jbjfBwAAQBAJ?hl=en&gbpv=1&printsec=frontcover

i was talking about this

[heady ember]

I mentioned it a couple times before: my copy of FIS has an unpleasant smell

[tender cobalt]

ill check that out

[toxic cypress]

I’m studying for amc and I really suck at it rn, does anybody have any book recommendations to get better at it?

[remote vortex]

The aroma of success

[real marsh]

the search function will reveal many hidden truths

[flat marten]

Doesn't have multilinear algebra in it im afraid

But yes multilinear algebra is a good book iirc

[fresh skiff]

Idk honestly. I haven't read it yet.

[fresh skiff]

Cool

[old elk]

A book that already has a story, hehe, mine is just about to start.

[fresh skiff]

good luck, i will first either do real anal or lin alg

then will start it

[wet hornet]

Hi guys, do you have any analytical number theory book suggestion? Thank you in advance ^⁠_⁠^

[old elk]

You can use Mohammad's Advanced Linear Algebra book.

[tender cobalt]

Wow it looks like roman's one except it's gentler

[old elk]

If the book is very intensive, and it comes complete with its demonstrations

[real marsh]

Lin alg is vaguely essential

[sleek python]

You want to learn measure theory before taking the class in order to tackle functional analysis?

Or did I misunderstand what you're asking for

[granite prawn]

Hey, I am someone who isn't very good at maths, and I'm currently only doing quite basic maths compared to what I see here. I am 18, just finishing school, but our maths course isn't too great here. I have an interest in maths, but I'm not sure where to start to start learning some new skills and to learn more about maths in general. Does anyone have any good recommendations?

[old elk]

Starts with calculus and linear algebra, refines linear algebra very well.

[sleek python]

No use comparing yourself to some of the maths done here, there is everything in this server: from hs maths to research level maths

[plain barn]

I feel sometimes genuinely envious of people who have physical books and have them be absolutely destroyed out of use

[sleek python]

But if you want some recs, maybe try to pick a book/pdf that's proof heavy

[plain barn]

my pdf files are still the same after years

[sleek python]

Gotta be at ease with most ways of proving things if you wanna study maths

[sleek python]

Same

I only have one physical book

[mortal ore]

I got a bunch of physical books today

For philosophy tho not for math

[plain barn]

I basically only have history books and fiction

in physical form

[mortal ore]

Fair enough

I only bother getting physical books if they are for school

[plain barn]

btw I just realized for some reason basically all my non-fiction books are about history

[mortal ore]

Taking notes on paper books is so much better

[plain barn]

one about history of maths the other about history of debt

[plain barn]

I think when I enter university I will start to want physical books kinda for convenience and that

and also because I'll have a better direction for what I should buy

[mortal ore]

It also makes u feel smart and fancy

[plain barn]

YES THAT'S IMPORTANT

actually the only math book I bought is coming to my home soon and it's a category theory book

[mortal ore]

That's a wild topic to study considering ur not in uni yet

[plain barn]

it's pretty recent and from the brazilian mathematical society (famous for being very hard to find uh free copies online) so I eventually gave up trying to find a pdf

[plain barn]

I mean all the topics I study are wild considering I'm not in uni so I think I can handle this one

my main motivation is that I'm coming to a point where I just can't escape category theory, every new math topic I go to have some hidden or explicit category theory bit and it's making me pissed off

[mortal ore]

Well category theory seems to be an attempt at abstractively generalizing areas of math

[plain barn]

yeah and that's like the main reason I find it really interesting I love abstraction

[old elk]

How necessary is measure theory for algebraic topology and algebraic topology geometry, speaking of the subject

[mortal ore]

I do too honestly

Ig it's a big reason I study what I do in college

Idk when I would learn category theory formally tho

[plain barn]

probably when you want it too I'm pretty sure people generally aren't forced to do it

also just realized "I study what I do in college" my brain read this sentence as big reason you want to study in college

which makes my last sentence kinda nonsensical

[remote sparrow]

try reading kreyzsig's functional analysis book. it doesn't require measure theory

[trail hemlock]

any measure theory lecture series online following papa rudin?

[remote sparrow]

not sure

[remote vortex]

Doesn't seem to come up much in measure theory or functional analysis

[delicate sandal]

Does anyone know any good textbooks for number theory + logic

[torn blade]

can u give some examples

like i really havent found any reason so far to go into category theory in depth, other than learning some when i was learning homology

[vital bane]

analyst/geometer: what the hell is a category?

[tender cobalt]

wait a min i am still confused whether loomis and steinberg advanced calculus is functional analysis or not 🥶

nahh i am not studying func analysis

im still stuck on real analysis

lmao

i really wanna go to some uni

[tender cobalt]

it feels lonely learning these stuff alone

uni is still literally 3 years away from me

well there's physics which i suck at 💀

not like i am academically excellent student

i just like math

[fresh skiff]

It's normal to be stuck in real anal

[tender cobalt]

although im studying shifrin multivariable mathematics idk if that counts as analysis

cuz it is very rigorous

[fresh skiff]

Yes. You are literally studying a lot of subjects at a time

[tender cobalt]

ye, shifrin multivariable mathematics (analysis) , and linear algebra, and topology

might pause linear algebra for a while though

[fresh skiff]

I usually find real Analysis => topology

[vital bane]

there's no topology in it (as in point set topology)

it's metric topology of R^n

that's found in every analysis book

[fresh skiff]

But studying topology before analysis wouldn't hurt that much i think

[vital bane]

I think doing analysis before general topology is far more helpful as you get motivation for a lot of things

topology is literally about generalizing metric spaces

[fresh skiff]

Yeah that's true

[vital bane]

so if you're good with metric spaces, then....

general top will not be too much of an issue for you

[fresh skiff]

Read Rudin for metric spaces
Ch2 (basic topology) from rudin is kinda my favourite

[tropic nacelle]

I think that as you go beyond first year, the advice given to you becomes less and less prescriptive, which is a good thing, as in you have some sort of foundation so you're more qualified to have an idea of what is reasonable for you

but at the same time like I absolutely don't support students being given bad advice / being lost without any direction

[vital bane]

yea that's the worst

[tender cobalt]

it doesnt!

[vital bane]

Abbott's ch3 is my favorite

[vital bane]

it does

[tender cobalt]

i mean for motivation yeah

[tropic nacelle]

so yeah like there is kind of an order here, definitely do real analysis first I would say, and if you already know some proofwriting then all the better, you'll be able to deal with things more easily

[tender cobalt]

i learnt topological spaces before learning metric spaces

[fresh skiff]

Yeah i like that too. Except last two sections of ch3

[tropic nacelle]

I do think that analysis in R^n is a waste of time if you're just looking to get to topology and then FA / diffgeo or whatever, to fill out the 4 years
Australia has no such requirement for instance in their 3 years

[tender cobalt]

which ? shifrin?

[vital bane]

ye ye

[tender cobalt]

well theres no pointset topology

but contents from abbott are there

typical analysis contents are there

compactness etc

[vital bane]

ye ye

Shiffrin is based