book-recommendations

[gray gazelle]

that's no an indicator

but I am asking for books like a transition from undergraduate to graduate math

[molten mason]

Also your question in general is too vague. A lot of answers to this question will probably be graduate-level textbooks, and idk if that's what you're looking for.

Like someone might answer with a book on differential geometry, someone else might answer with a book on Langlands.

Is there a specific subject you want to know?

[gray gazelle]

exactly, that was I am looking for, but my issue is not looking for books that present a topic, but also help to progress into more deep and harder skills

some graduate books are sometimes more appropiate as reference books for researchers rather than a transition into more advanced mathematics for undergrads

by "we have" you mean , in the world, or in this server?

[gray gazelle]

bro how tf is the world in this..

[uncut crater]

Sneak Jojo reference?

[molten mason]

In this server

[gray gazelle]

loool

[gray gazelle]

Za Warudo..

that's really impressive

i think Hall and Knight Higher Algebra is something you're looking for

especially when it's the kind of algebra hardcore

[gray gazelle]

how?

[uncut crater]

Hartshorne

[gray gazelle]

terence tao if he had been born in the 21st century

[uncut crater]

Wait

Tao...is still alive right?

God i need to read this convo again

[signal mountain]

i dont know that necessarily there is a specific book i can recommend, but i read an abstract algebra book before uni that started with a kind of chatty 'heres what pure mathematics and proofs look like' then did sets and relations and then, what i think was the most eye opening for me, they showed constructions of the integers from the naturals then rationals from integers and finally reals from rationals
so it was a very gentle and slow approach to the topic but made me see a lot more of the 'how does this work' behind all of the maths i knew

i also think its treatment, doing sets and equivalence relations first, then doing some modular arithmetic - which showed a nice application of equivalence relations that could later be understand in the frame of groups - (then a bunch of other stuff, including functions, again this was a VERY SLOW book) and THEN groups made it so very easy to digest because it had motivated all these wonderful ideas and notions. especially where this shone through was when i got to quotient groups, idr if they were in the book, but they were super intuitive for me but to a lot of my peers were quite troublesome

i dont think that the particular book i read is that recommendable though because basically all of the math is written inline and could be quite hard to read at times, though perhaps there is some argument as to that forcing me to spend more time thinking about the results and 'filling in the gaps'

anyway (sorry for the wall of text) i suppose my suggestion is a book that take the time to reintroduce these very basic notions thoroughly
iirc tao does this, though as an analysis text rather than algebra

[gray gazelle]

does he have an algebra book?

[uncut crater]

Yeah, its also a geometry book!

[gray gazelle]

i hate geometry I'll pass

[uncut crater]

💀

[gray gazelle]

well sort of

[uncut crater]

You can't escape geom

[signal mountain]

ah missed this lmao

[gray gazelle]

yea never will..

I will face it in the near future..

[uncut crater]

🫂

[gray gazelle]

I'm kinda bias i like trig..

[gray gazelle]

yeah , I am asking this because when I was beggining in math , I read book of proof by hammack, and I was wondering if there is something similar but for undegrad to graduate

[gray gazelle]

which is just a field of geometry..

[uncut crater]

The answer is mostly no

Unless some random author published a book under some unknown Springer subseries

[signal mountain]

yeah i kind of feel like once youre in undergrad (or at least at the end of it) youre kind of just doing maths...

[gray gazelle]

it doesnt have to be exactly as that (not so obvious such a book called "intruduction to whatever graduates do") but maybe a book that has good problems i dont know

[uncut crater]

Hammack, Velleman etc are nice reads, but you won't progress much if you don't get dirty

Best thing to do would be to grab an algebra text, work through the stuff

[uncut crater]

Graduates don't do anything that's visibly different from undergraduates

At least that's my worldview

Im technically a first year math major and I'm reading graduate texts

[gray gazelle]

do harder things , that for some reasonable reason undergradds are not force to do

[gray gazelle]

how?

[gray gazelle]

and nice btw

[signal mountain]

the line from undergrad to grad is blurry, depends on the uni

some unis offer say diffgeo at undergrad, other places you have to wait till grad

for an example

[gray gazelle]

yeah , I have seen that

[uncut crater]

Yeah, in my case, grads study along with the undergrads lol, which is why i have my opinions

[tribal crow]

I don't think there exists such a book

[molten mason]

Undergrad texts are like here's a little bit of these 8 topics

Graduate texts are like, here's 700 pages on one of those topics

[signal mountain]

youre just doing more of the same, just perhaps harder/more specific courses

[gray gazelle]

but how you did it to manage to read graduate texts , how and why?

[tribal crow]

wdym?

[uncut crater]

How did I manage? I don't see anything different about GTMs and GSMs

[glad rampart]

i would assume he opened the book, and like read the words

[tawny copper]

where did you get the quote of your profile from? or did you come up with it

[uncut crater]

Again, i had friends who would solve rudin in their first semester of math

[gray gazelle]

In what topic?

[uncut crater]

So having them made studying easier as well

[gray gazelle]

bruh xD

[tribal crow]

you can be a middle schooler and read GTMs

[gray gazelle]

ohhh, so you mean , your "group" of friends

[tribal crow]

there's nothing about them that's any different from UG texts tbh

[uncut crater]

Yeah

[uncut crater]

Besides the lack of computational examples probably

[gray gazelle]

maybe your "ring" of friends, cause the summ a lot , as it seems

[molten mason]

Somewher else, it's been a while, I don't remember.

[tribal crow]

depends on the topic, I would suppose

[tawny copper]

there are differences btween GTMs btw, but yeah, a GTM shouldn't be understood as "only graduate students can read it"

[tribal crow]

I wouldn't expect an algebraic topology book to have many computational exercises, regardless of who it is catered towards

[uncut crater]

Again, when i use 'solve', there's a lot of blood sweat and tears involved

We weren't casually drifting along the pages, but it was worth the pain

[tawny copper]

I think I heard something like it in the theories of everything podcast with McLarty, he was possibly quoting someone else tho idk. You made me remember of that, that's why I asked :p

[gray gazelle]

btw, what topic are you reading GTM book(s)?

[glad rampart]

math books are hard as hell but very rewarding

[molten mason]

That's awesome lmao

[uncut crater]

Algebra, diff geom

[tribal crow]

which books?

[uncut crater]

Nah I haven't worked out Korner yet so I'm lying

[tribal crow]

I need to add more pdfs to my collection

[molten mason]

All of them. All of the same topics as undergrad.

Abstract Algebra, Real Analysis, Linear Algebra, etc

[gray gazelle]

sorry, are you a genius or what?
you literally said you are on your first year

[uncut crater]

Technically yeah

Fundamentally nope, I'm in third lol

[gray gazelle]

what?

[uncut crater]

The curriculum is messy here

2 years of doing science and baby math

3rd year is where the actual math starts

[gray gazelle]

engineers things

[molten mason]

Yeah same at my school

[uncut crater]

🫂

[gray gazelle]

I have seen that a lot in my country

[tribal crow]

Uta, I'm still curious

[uncut crater]

It's mostly common ones
For rings, I'm casually reading passman and when the sem starts, maybe begin with Reid
For groups, rotman
Diff geom, I'm sticking to Lee

[tribal crow]

Rotman... which book?

[uncut crater]

Aluffi, D&F and rotman are a staple

[gray gazelle]

is lee for graduate?

[uncut crater]

Intro to groups

[tribal crow]

wdyn "for" graduate?

[uncut crater]

Again

You're better off not creating this division

Take it as a challenge

[tribal crow]

Lee is "for" anybody who is interested in manifold theory + has the prereqs to learn it

that is all

[molten mason]

Have you started it yet?

[uncut crater]

Yeah

Nowhere near cohomology

😭

[molten mason]

Any fresh takes from it so for compared to a regular algebra book?

[gray gazelle]

so basically, any book as long as it is hard, and I can manage to understand is a good book?

[molten mason]

Yes

[uncut crater]

It's actually impressive

[gray gazelle]

oh, ok then , sometimes I dont feel sure if risking all to one book, since I have the experience of learning (before going to university) differential equations from a book of schaum outlines, worst error , just loose time, that's why I ask for books

[uncut crater]

It's D&F bite sized

Still has good problems

I think the initial chapters serve as a brilliant revision for people who have seen the stuff

[molten mason]

Neat

[uncut crater]

I just want this vacation to end

I can't read PDFs 😭

[cursive orbit]

there's less hand-holding typically

[uncut crater]

I NEED to feel the book, SMELL it

[sage python]

Lmao

[molten mason]

Schaum outlines are great

[sage python]

More advanced correlates with less hand holding but there's no hard line

[tawny copper]

can't you get the books from your university library?

[cursive orbit]

yeah but on average GTM has less handholding than UTM is what I was tryna say

[uncut crater]

🥺it's summer vacay here

[sage python]

Is measure theory an undergrad topic or grad? What about differential topology? What about representation theory of finite groups?

[uncut crater]

And I'm back home 😭

[uncut crater]

Rep and measure are slowly creeping into ug territory

[tawny copper]

and so where I am. But I can still borrow books from the library

[uncut crater]

How far are you from your library?

[tawny copper]

rn I'm pretty far

[uncut crater]

I wish that was possible

[uncut crater]

Im pretty far too

[tawny copper]

but I can borrow books for quite long time

[uncut crater]

Well

The profs hog the books for half a year at times

Undergrads get only a month at most

[tawny copper]

I can "refresh" the returning date via phone, as long as no one demands the book, can't you do that?

[uncut crater]

Only twice

[sage python]

Some measure theory books are very handholdy and in a way easier than Baby Rudin

[cursive orbit]

fair

[tawny copper]

interesting. I can do it indefinitely (there is a limit date, but that's like 2 years from the initial borrow or something)

[gray gazelle]

mine smell moldy..

[uncut crater]

Lucky you

[gray gazelle]

why are we mentioning a baby?

[uncut crater]

Dw there's a papa too

[gray gazelle]

nah

no way

[sage python]

Yeah it seems like they're not expected for undergrads, so grad analysis at most places starts from 0. But then they're common for undergrads to do

[gray gazelle]

finally after grinding asking questions in #prealg-and-algebra I've got the active role

[tribal crow]

and a grandpa too!

[gray gazelle]

ehh

[uncut crater]

It's a weird family ik

[sage python]

Also great grandpa and great uncle

[tawny copper]

What's the lore here

[sage python]

Great Grandpa is Fourier on groups

[tawny copper]

Ah, neat

I'd like to learn that material

[sage python]

Great uncle is function theory on the unit ball of C^n

[signal mountain]

my course had rep, measure, algtop, alggeo and diffgeo courses in third year (of three, uk)

but it also had algtop, alggeo and diffgeo courses in the masters

[sage python]

Yeah those are often available as electives

Just that I think especially measure theory and algebraic topology have become kinda common for undergrads to do, they're sorta "the obvious next thing after what you would expect undergrads to have done"

[signal mountain]

yeah that makes sense

[sage python]

AG less so I think, since depending on how you wanna do it you might need a lot of background. It also kinda completes with rep theory of finite groups for the banner of "The next algebra thing to do"

[uncut crater]

They can swap AG with comm

AG is still seen as a grad topic here in India

[glad rampart]

@signal mountain whats a good book for intro set theory?

[signal mountain]

#book-recommendations message

people also talk about 'naive set theory' by halmos

[glad rampart]

is there any in particular youd personally recommend?

[signal mountain]

i think halmos is meant to be a gentle intro, but i cannot personally make any claims

[glad rampart]

ill give it a shot

[signal mountain]

gl !

[remote sparrow]

#book-recommendations message

[gray gazelle]

Try Elias Zakon analysis 1

[uncut crater]

Goldrei and enderton

Peter smith also has a book on set theory iirc but…

[vital bane]

Like "A User Friendly Introduction to Lebesgue Measure and Integration" by Gail S Nelson

[vital bane]

it is seen as a grad topic everywhere lol

of course any sufficiently motivated undergrad can learn anything but that doesn't say anything about the average of the population

[vital bane]

I do wonder what you guys think of Halmos' measure theory book?

Outsider and others said it was a bit too old school

using sigma rings instead of sigma algebras and a few other stuff

[uncut crater]

Yeah, i based that off how electives are offered these days

Its still a grad topic

[vital bane]

but it's really cool how your uni offers grad topics as electives for undergrads

oh nvm it wasn't your uni it was Acman

it's still pretty cool, I wish more unis would do that

[quick laurel]

I will be starting differential equations this semester, so can anyone recommend some good books to start it with?

[vital bane]

what kind of differential equations course is it?

mathematically rigorous ODE course or computation oriented ODE course?

[quick laurel]

Mathematically most likely

It hasn't started yet so I have no idea and I cannot find my course syllabus anywhere till then :')

But it's going to be the first proper seperate course on differential so far

[willow merlin]

hammack book of proof and velleman how to prove it, is there any other intro to proofs resource?

[foggy quest]

Discrete Mathematics and Its Applications
Book by Kenneth H. Rosen

[stray veldt]

i wrote a short intro myself that is pinned in #proofs-and-logic

there is also https://math.hawaii.edu/~pavel/Aluffi_notes.pdf which is more focused towards "actual mathematics"

[gray gazelle]

hi, I have heard really good comments about "the art and craft of problem solving" book, so I was wondering if this is one of those books that investing in it is incredible beneficial (in other words , they make a before and after)
(like rudin for analysis)
so, how is it?

[outer wing]

there's also rotman's journey into mathematics: an intro to proofs

evan chen recommends it

[hallow oriole]

im starting to think "intro to proofs" as a concept is kind of extraneous

students could totally learn proofs from a course

proof based linalg or ra

either would be better than "intro to proofs"

[sage python]

Generically I do agree yeah

[vital bane]

only if the course/book had new students in mind who have no idea how to write a proof

Like you can go into Understanding Analysis by Stephen Abbott as a complete beginner to proofs and learn both real analysis and proof writing basically by yourself

it's so well written

but if you go into Baby Rudin not having a single idea about how to write proofs I think it would be very difficult to do anything on your own

[lime vessel]

They should teach ordinal induction and model theory

[remote vortex]

Transfinite induction is great fun and I'm sad I so rarely get to use it

[elfin narwhal]

Please suggest books to practice for imo (math olympiad)

[gray gazelle]

Spivak Calculus

[heady ember]

Just become a set theorist ez

[molten mason]

I don't think some type of Intro to Proofs is bad, I think it's bad if people spent a whole semester on it without moving forward, but the concept itself isn't bad depending on where people are at in their math journey.

The first half of How to Prove It could be done in a week, maybe two at most. There's not much effort wasted in the grand scheme of things.

Isn't Analysis With an Introduction to Proof by Lay a mix of Intro to Proof + some baby Real Analysis? I haven't gone through it personally.

[gray gazelle]

you could check the notes (if there are) of your national team olympiad, past tests, etc
anyways, you should chek the MODS (mathematical olympiad discord server) , since it's more appropiate for getting help in olympiad than this server

[teal perch]

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

good stuff

[gray gazelle]

I was thinking exactly on that

math is somewhat esoteric

since more advance math books are like: "now we assume you know this X topic that probably you never has heard of, and we assume you have this skill you weren't tell you should have"

[remote vortex]

A reasonable advanced book will discuss its prerequisites in the introduction.

[gray gazelle]

yeah , that's were begins the travel for references

[remote vortex]

Yep, you can't jump into advanced topics without familiarity with the prerequisites.

And a book can't reasonably include all of the prerequisite as part of it since that would be quite unwieldy

[gray gazelle]

you can , indeed , that's how research is done, what you can't (or you should not do) is to assume something , or not being sure about something

[gray gazelle]

evan chen tryied XD

[remote vortex]

I mean, you can, it's a free country (possibly), you're just not likely to get anywhere.

[gray gazelle]

you tryied doing that before? (jumping into topics you knew were too hard)

[remote vortex]

It's not about difficulty, it's about lacking basic required skills.

[tribal crow]

agreed
#book-recommendations message

[vital bane]

Like trying to climb a mountain without even getting to the base of the mountain first

it's not hard, it's just that you have to get to the base of it first

[cursive orbit]

evan chens book is at most a summary of a lot of fields

[primal pollen]

hello, i wanted to ask if there are good free resources on the internett about arithmetic and logic? i want to research the foundation of proofwriting, logic and arithmetic.

[robust dust]

Hi. Anyone know good introductory books on differential equations and probability/statistics?

[robust dust]

There are the Open Logic Project books. They are introductory books on logic, sets, computation …. They are free on their website. However I’m not sure if this is what you need

[strange owl]

does anyone know any good resource to learn Calculus?

[remote sparrow]

#book-recommendations message

[robust dust]

Thank you!

Anyone heard/read Differential Equations and Their Applications by Braun?? Is it good for a first course?

[trail hemlock]

Anything on this list will suffice:
https://www.amazon.com/shop/themathsorcerer/list/SKD9TCJQOZAI

spivak and apostol are more rigorous and i used spivak as an intro

[cursive orbit]

search up "MIT OpenCourseWare Calculus I"

[maiden glen]

good books for point set/general topology?

[foggy quest]

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

[foggy quest]

"Real Analysis" by Folland

[maiden glen]

just "Real Analysis" or "Real Analysis: Modern Techinques and Their Applications" by Gerald B. Folland

[foggy quest]

yes

[maiden glen]

wrong

he wrote two

at least two

[trail hemlock]

oh

my bad

[maiden glen]

thank you

[foggy quest]

modern techniques

[trail hemlock]

anyway A course in Point-Set Topology by Conway is pretty good, if not a little dry

[maiden glen]

thank you aswell

[cursive orbit]

hatchers notes are pretty good

contains like basically the minimum knowledge you need to know

[remote sparrow]

this is a measure theory book. there is a chapter on topology, but is that all you need to know?

[remote sparrow]

munkres, gamelin/greene, willard

[maiden glen]

not really searching for minimum as I am self studying but thank you, it is more of my fault as I was not specific

[maiden glen]

thank you, once more!

[cursive orbit]

I see. usually people study topology as a prerequisite to another topic, so in that case hatchers notes would be the quickest path

[maiden glen]

thank you, in humility

[robust dust]

Thank you

[foggy quest]

Yes it covers the topology needed for further study in topology, e.g. functional analysis, PDE, differental geometry and topology. The typical next step in topology beyond Folland's book would be differential geometry/topology.

[remote sparrow]

what if the individual does not wish to do functional analysis and PDEs? i suggest qualifying your recommendation so that others don't get the wrong idea

[zinc thistle]

I also think Stewart's calculus is good

[gray gazelle]

also Spivak

[grim wolf]

Do you have textbook recommendations for learning geometric algebra \ Clifford algebra ?

[gray gazelle]

i think there was one

hartshorne algebraic geometry

or maybe I'm wrong

[grim wolf]

That's algebraic geometric,

Not geometric algebra,

[gray gazelle]

oh i thought they were the same sorry..

[rigid fable]

Any good books in set theory/discrete math?

[gray gazelle]

the math sorcerer youtube channel is only good at that

lol

could help you with book recommendations and taking a quick look at the book

[normal crystal]

Epp's Discrete Mathematics

[rigid fable]

Why is it not good at other things?

[gray gazelle]

in my opinion it exaggerates for example in roadmaps and what to follow to learn something doesn't seem to be correct all the time

[rigid fable]

Makes sense

At least it's good at one thing though

[normal crystal]

I do think he tends to have clickbait-y titles then shows a mess of books in old editions that he happens to own

[gray gazelle]

math sorcerer just randomly recommends books

i hope he do something like analyze and then summary

[fossil crescent]

Can someone recommend a book that has a lot of tricky olympiad style integral problems?

[narrow prairie]

Inside Interesting Integrals

[vital bane]

yooo that book is dope!

[foggy quest]

page 299 of https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/linalg.pdf

[vital bane]

@fickle whale

[grim wolf]

Thanks :))

[fossil crescent]

Thanks

[queen fog]

is there anyone on this server who has experience with both Charles Pinter's: A Book of Abstract Algebra, and Dan Saracino's: Abstract Algebra a First Course, and could briefly compare the two?

trying to decide between the two which one to get

i already have Gallian as a primary resource, but would like a supplement

[uncut crater]

Go for pinter

Tbh it doesn't matter

Just pick one and go on with your day

[queen fog]

did you have an experience with either of these?

[uncut crater]

No sadly

But I've heard good things about pinter

Saracino is dated

[queen fog]

ah, no worries

[uncut crater]

No one should read old books in algebra

[queen fog]

that's an interesting perspective

[uncut crater]

I mean

The more technical you get, the older are your available resources at disposl

So you can't really fret

However, when you're starting stuff, it's better to follow modern books that are more sound and pedagogical

[queen fog]

ok, so the idea is, since pinter is newer, maybe there would be more resources available to help if i ran into a problem?

[uncut crater]

Even tho I'm seeing really good texts in alg geom and rep theory popping up these days

[gray gazelle]

how do you maintain active role?

[uncut crater]

Idk

[uncut crater]

Yeah

Or you can just hit MSE

Even chatgpt works

[gray gazelle]

hey @uncut crater I'm halfway done with this course

[uncut crater]

I've seen chatgpt conjure mostly correct proofs

[uncut crater]

Which course?

[gray gazelle]

what's your opinion for algebra with this..

[uncut crater]

Nice

[gray gazelle]

is it enough?

[uncut crater]

Hmm, what kind of opinion do you want?

[uncut crater]

And what level are you aiming for?

[gray gazelle]

well if it's enough prerequisites towards precal then calc

[gray gazelle]

higher level calc-based physics

[uncut crater]

Towards precalc? Yep, seems enough

[gray gazelle]

after is lin alg

[uncut crater]

Assuming precalc has more algebra?

And/or trig and stuff

[gray gazelle]

yes trig

[uncut crater]

Hmm, I'd say to get some more algebra under your belt if you can

Especially stuff with functions

[gray gazelle]

umm yea

well the course end at inverse functions

[uncut crater]

Also, a bit of complex numbers too

[gray gazelle]

...

[gray gazelle]

is it enough?

[uncut crater]

That should be in precalc

[uncut crater]

Yeah, but idk the amount of content in the course

Lang's Basic Mathematics should be a good companion

[gray gazelle]

I don't like lang's taste..

[uncut crater]

🤝

Us

[gray gazelle]

i like something like Stewart's

[uncut crater]

Oooh yep you can go ahead with it too

[gray gazelle]

Sadly he doesn't have algebra 💀

[uncut crater]

Stewart tends to be verbose but if it helps, then it's all good

Oh

[queen fog]

@uncut crater what algebra books did you read for undergrad abstract algebra?

[uncut crater]

d&f, aluffi

Actually I read more

But it's just going thru the pages

[queen fog]

wow, D&F, really?

[gray gazelle]

well after I've read his precalc book especially like the Distance, Velocity, Time problem it's a freaking enlightening

[uncut crater]

Not the whole book

Just the relevant chapters, stuff in groups and rings

[gray gazelle]

now i have a different thinking of solving this type of problems

[uncut crater]

Nice

[gray gazelle]

well the algebra course actually has precal course too

[queen fog]

@uncut crater did you like Aluffi? i heard about it, is that more for graduate level? how does it compare with pinter?

[gray gazelle]

but it doesn't really end well with physics if i ever think about it

[uncut crater]

Well, the comparison shouldn't be made 💀

Pinter is an entry undergrad book

Aluffi is an end ug/grad book

[gray gazelle]

Uta this is the precal course

[uncut crater]

I absolutely LOVED aluffi

[gray gazelle]

https://youtu.be/eI4an8aSsgw?si=T4pP87TRrToHuLXk

[queen fog]

what did you like about it?

[uncut crater]

This looks sexy ngl

Yep, it's covered everything

[uncut crater]

Use of categories, easy prose, informal language, nice structured proofs

It's the readability of the book

[gray gazelle]

but considering I've done like umm a course should i do stewarts or this?

[uncut crater]

Cons, easy exercises

[uncut crater]

It doesn't hurt to review the material, see the vid and check your progress

[queen fog]

cool, i'll take a look at it. gallian has plenty of exercises, i just need something for a supplement

[gray gazelle]

I really like to get accustomed with books as early as possible as the course may be shitty rather than a book

[gray gazelle]

i see so i should supplement both..

[uncut crater]

If you're okay with the categorical notions, aluffi can be a good option
Otherwise artin

[uncut crater]

Yep

[queen fog]

i heard artin was grad level

[uncut crater]

It definitely didn't feel like a grad book

[queen fog]

@uncut crater how are the proofs in that book?

[fickle whale]

For an introduction either:

MD Taylor's book, Introduction to Geometric Algebra and Geometric Calculus,

As well as Alan MacDonalds two books,
Linear and Geometric Algebra
Vector and Geometric Calculus.

If you want to know it more deeply I'd recommend something like
Clifford Algebra To Geometric Calculus by Hestenes,
Or Clifford Algebras and Spinors by Lounesto

[fickle whale]

There's also a new book out by GA Pariah Eric Lengyel which I have yet to peruse or collect opinions on

[hollow peak]

...GA pariah?

[karmic tangle]

Nice I just came here to ask about him

Is there anything covered in his UG book (Notes From the Underground) that is not in Chapter 0?

[uncut crater]

Yeah he's doing well

Oh

[karmic tangle]

Is he? Nice

[uncut crater]

Hmm...

[karmic tangle]

XDD do you actually know him?

[uncut crater]

Okay I didn't read notes completely

[uncut crater]

Just playing along 😃

But the thing is, notes and chapter 0 will go along well

[karmic tangle]

My set theory prof told me last week he met Lawvere once

[uncut crater]

Not a lot of overlapping material

[karmic tangle]

Wait really?

[uncut crater]

Damn

[uncut crater]

Well how should I put it?

0 being a graduate text, is more dense

Notes is pretty light on the material

But hey

I didn't read notes properly

It's better if someone who's read notes just pitched in now

[karmic tangle]

I've done a course that covered groups up to the ispmorphism theorems and then rings and a bit of fields and extensions the latter of which was veryyy quick

[uncut crater]

Damn

Do read fields and field extensions again

[karmic tangle]

So far I liked Chapter 0 but I only got through the first chapter plus a bit of the one on groups

[uncut crater]

Nice

[karmic tangle]

So like idk if to keep going or to do notes first

[uncut crater]

Since you've done a course already

0 is better

There's way too many books to do dude

We need to leave some behind 😔

[remote sparrow]

Algebra: Notes from the Underground starts with rings, so if you feel weak on rings, you can read it

there are also full solutions to some exercises in the back

it's nice

[karmic tangle]

I know almost nothing about modules or galois theory or solvable groups or whatever the 3 group theorems named after a guy whose name starts with S

[remote sparrow]

there is a pretty long list of errata though

[karmic tangle]

Foe real

[remote sparrow]

Galois Theory by cox is a good book to read

[uncut crater]

For notes?

[remote sparrow]

yes

also chapter 0

[uncut crater]

Cocks

[remote sparrow]

he's the namesake of the cox-zucker machine

[uncut crater]

...damn

I love this typa humor

[karmic tangle]

Ah I might do that I suppose, I feel very weak on fields and field extensions and idk what all is there to know about rings from the basics

Xdddd

[uncut crater]

What if I incorporate a groundbreaking proof into a commutative diagram that looks like a penis?

[remote sparrow]

the order goes rings > modules > groups > fields

[karmic tangle]

Ah so I wouldn't be missing out on stuff this way right?

[uncut crater]

As in the canonical way of studying?

I do agree

Lmao

[karmic tangle]

Have you seen the cover of Conceptual Mathematics

[remote sparrow]

no i'm talking about Algebra: Notes from the Underground

[uncut crater]

[remote sparrow]

that's the order the book does

[uncut crater]

no

[karmic tangle]

You will be blown (hahahahaha cock reference) away

[uncut crater]

LMFAO

It's subtle

He tried slipping that in 😭 🙏

[karmic tangle]

Had it on my table onr of the first things a friend said to m was he asked if that was a cock?

So I decided on this order of study LADR + Conceptual Mathematics -> Algebra: Chapter 0 so I guess I sneak a bit of notes in-between those too?

[uncut crater]

That's heavy

But if you can do it, sure 👍

[karmic tangle]

It's fun so far though the 200 exercises at the end of each LADR section are something

It's not too heavy though is it? It's like basics kinda right? Without the notes I suppose

Wew there is a looot of text in notes

Could I maybe read them simultaneously?

decisions decisions

[modest saffron]

Heh what are people’s thoughts on basic mathematics by serge lang? Just started getting into it but I would like to know if there’s a better substitute for self study

Oh just saw the pin lmao

[hollow peak]

Gud book

It's like all you need to prepare for first and second year university

Then you can start doing calc and linear algebra

serge lang was not a very nice guy though

[fickle whale]

His views are a minority in the modern GA landscape

And he's somewhat hostile to other authors

[modest saffron]

I’ve heard… hiv denialist apparently

Thanks for your thoughts

Greatly appreciated! C:

[remote sparrow]

i don't think Basic Mathematics is in pins?

[modest saffron]

As in a review of general introductory-ish maths texts

The oldest pin I believe?

[remote sparrow]

those are abstract algebra books

[modest saffron]

Oh

[grim wolf]

Thank you a lot ::))

[stiff lodge]

any reallly good linear algebra books?

[fickle whale]

No problem, GA is the only reason they keep me around here

[willow merlin]

is huffman kunze and anton aswell as david c lay good enough for LA? what would be a classic book for this

[foggy quest]

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

[willow merlin]

who is michael taylor and how does he have a book for every math

[muted maple]

I'm a college student who's taken your basic undergraduate mathematics courses like calc and linear algebra and whatnot, but I'm extremely fascinated with the art of math. I've always found geometry extremely beautiful, so if you guys have topic suggestions for me to dive into I would love them. Whether it's a textbook for a class that was interesting or something recreational about like fractals or packing problems or anything, really, I'm interested in learning more 😁

[foggy quest]

He's a matematician. He doesn't have a book for everything; it's mostly analysis.

[molten mason]

More than enough

[fierce hedge]

Chapter 0 has easy exercises? Or are you talking about notes from the underground

[winged bluff]

Also page 10 of Visual differential geometry and forms

The google books preview includes that page

[uncut crater]

Chapter 0, as far as I completed it (till groups second encounter)

[fierce hedge]

I see, how does it compare to say DnF or Herstein

[uncut crater]

Herstein, no idea cuz I dropped it because of terrible notation

DnF was a supplement

So yeah, dnf + aluffi is now the standard ug treatment (or should be imo)

[fierce hedge]

I see

[rain hound]

Undergrad 😓

[vital bane]

I'm using D&F and supplementing it with D&F atm

it is going good

[remote sparrow]

using dummit and foote and supplementing with dummit and foote?

[vital bane]

yup

[remote sparrow]

did you mean to say you're using a different book to supplement D&F?

[cursive orbit]

Artin should be the standard ug treatment

[vital bane]

no

D&F is all I need, my ug algebra Bible

[nova lotus]

But does Artin have everything that DF does?

[cursive orbit]

no, but you don't need everything d&f has for undergrad

[nova lotus]

Ah I agree, but is good if someone wants to explore imho

[gray gazelle]

good beginners books to study diff eq, pdes, vector calc, and dynamical systems/chaps

chaos

[foggy quest]

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

[wooden tartan]

based

[cedar crypt]

Ikr

[gray gazelle]

hi

https://www.amazon.in/gp/product/1107044103/ref=ox_sc_act_title_8?smid=A15DBATYR506U3&psc=1

is this a good book to buy

[ornate sierra]

Any recommendations for starting competition geometry?

[willow merlin]

for euclidian geo? maybe egmo

although is not easy intro, maybe someone else can recommend

[brave lotus]

aops intro to geo -> do some past problems until u cant do -> train from egmo

euclidean geometry in mathematical olympiads by evan chen

[maiden glen]

Good group theory books for self study?

[maiden glen]

i have this and am currently reading it already, any other suggestions?

[marsh ingot]

Nope, sorry. Thats the only one I know

[foggy quest]

The contents are core mathematics to learn, and it looks good from the pages I looked at in my pirated pdf.

[gray gazelle]

Can you send it to me?

[foggy quest]

the formatting is a bit weird

[gray gazelle]

(you might wanna delete the post)

[foggy quest]

also one proof about compact operators was missing?

table of contents is also missing

[echo spear]

hey yall, what are your opinions on strang for linear algebra?

[maiden glen]

does anyone at all know of any good books for a person who is self studying

[mossy flume]

What math are you interested in and what math have you done so far?

[maiden glen]

im interested in formal algebra, and so far I've done real analysis

[mossy flume]

Ah so you wanna do some abstract algebra?

[maiden glen]

and algebraic topology

[mossy flume]

Have you done any abstract algebra before?

[maiden glen]

is that also of abstract algebra

[maiden glen]

my only experience is with dummit and foote and gtm211

[mossy flume]

You need to know abstract algebra to tackle algebraic topology

Ohhh ok how much of D&F?

And how much of Lang?

[maiden glen]

i have only went to chapter 7 of lang, but I completed d&f

[mossy flume]

Ok if you completed D&F then I think the standard intro to algebraic topology is Hatcher's text

https://pi.math.cornell.edu/~hatcher/AT/AT.pdf

[maiden glen]

are there any additional prerequisites

that were not mentioned in d&f

[mossy flume]

Maybe someone with more algebraic topology experience will have better reqs

[maiden glen]

in what branch is algebraic topology of

[mossy flume]

According to the review here: https://mathematics.gg/books/algebraic-topology no other prereqs

[maiden glen]

so I can continue exploring

[mossy flume]

I mean it's a combination of algebra and topology idk what you mean by branch. The idea is you apply tools from algebra to better understand topology

[maiden glen]

given that the website suggested there were no prerequisites required for df the last time I checked, I would rather search for another source

[mossy flume]

Fair enough but hopefully someone else has a better idea

[maiden glen]

i thank you

[mossy flume]

AT is not a field I'm too familiar with

[maiden glen]

and again, what branch is at of

i want to continue exploring

[mossy flume]

idk what you mean by branch. It applies abstract algebra to better understand topology

So whatever that means to you in terms of "branch"

[maiden glen]

is there a list you know of of abstract alg subbranches

and you never gave me a book for group theory

[molten mason]

More group theory than D&F and Lang...?

Rotman's An introduction to the Theory of Groups would be the only other book I can think of, I'm sure there's more specific ones

[maiden glen]

what about homological algebra

[remote sparrow]

rotman has also written a book for that

also weibel is another standard text

[maiden glen]

i didn't see that

in d&f that is

[molten mason]

End of Lang

[maiden glen]

thank you

thank you all

[mossy flume]

D&F and Lang cover a ton of group theory and iirc D&F has some homological algebra

And probably Lang also?

[molten mason]

Yeah the last 100 pages of the book

Mf read Lang and is asking for more like Kylo Ren

[heady ember]

Have you looked in pinned

[molten mason]

Can also lurk the AT server

[mossy flume]

the AT server is for like

much higher level stuff

at least as far as I can gather

[molten mason]

It is that's what I meant by lurk, maybe look around convos or use the search feature and see what the people in there are doing

[maiden glen]

where

[molten mason]

https://discord.gg/HDdzcK6w

[maiden glen]

this is fun

thank you

[hybrid iris]

is strang's linear algebra a good linear algebra textbook or should i go for the one that was recommended on the website

[foggy quest]

I think differential geometry entails a good bit of algebraic topology, and if not a good prerequisite, is good motivation for it.

[maiden glen]

good!

anyone disagree?

so I don't dive into gold coins?

[willow merlin]

which book explains crt intuitively

[vital bane]

no it is true! Algebraic topology is used a bunch in Diff Geo and it is awesome!

De Rham Cohomology

[vital bane]

doesn't strang have two Lin Alg books?

they are both good

[molten mason]

It's fine, it's just Strang. Plus side is you can follow MIT Courseware with it

[vital bane]

but it depends on what kind of LA you want to learn

rigorous or general use

[molten mason]

Oh, he does!

[molten mason]

What have you used so far?

[willow merlin]

i’m using montgomery intro to nt

someone helpp

I need easier intro to crt

[molten mason]

Give me a min

[molten mason]

Probably the most intuitive would be Elements of Number Theory by John Stillwell, CRT is on page 171. Books alternative to Montgomery would also be Elementary Number Theory:
Primes, Congruences, and Secrets by William Stein or Number Theory by George Andrews.

There's also a couple good videos on YouTube that you can check for yourself

[trail hemlock]

whats crt

[broken meadow]

chinese remainder theorem probably

[warm arch]

metal what happened to your book list

[broken meadow]

It got moved to the website

!books

[warm arch]

to what website

[broken meadow]

ok idk the thing

gimme a sec

[warm arch]

,books

[gray gazelle]

!books

!website

.books

hi

hello

[broken meadow]

!bookrecs

[hybrid sparrow]

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

[warm arch]

類books

[broken meadow]

there we go

[warm arch]

oh cool u have a website thats barely advertised?

[gray gazelle]

Does anyone know if "College Physics" By John A. Eldridge is good?

[broken meadow]

Yep...

[gray gazelle]

why no algebra?

[broken meadow]

i actually always forget we have a website...

[gray gazelle]

also precal

[broken meadow]

i think we should make some kind of announcement or at least have the bot post !bookrecs once every 30 minutes...

[warm arch]

not only that, you can't access the books link from the frontpage. it's literally a hidden url

[broken meadow]

Oh fr

i think its still under construction then

i handed off the books list project to @fallow cypress

[warm arch]

maybe if you check the github source lol

[vital bane]

what is your opinion on "Introduction to The Theory of Numbers" by Niven, Ivan and zuckerman

[warm arch]

oh wow it's Ruby on Rails

[broken meadow]

it's decent and what i read originally

requires no background

[vital bane]

yea both my prof and Richard Borcherds recommend it

though I feel like you would have at least a bit of exposure to proofs and pure math to go through it

which I do have, and it does seem like a nice book

[warm arch]

huh weird, for some reason I thought there were more stuff in AlgGeo section, but i guess this is it:
https://mathematics.gg/books/algebraic-geometry

[vital bane]

also it's pretty cool we have an official website now

[warm arch]

it'd be cool if it could become something like the /sci/ wiki, though I don't know if they want that burden.

i think it was exonium or someone that runs a model theory wiki

[gray gazelle]

anyone? :P

[warm arch]

never herd of it

[gray gazelle]

damn

I got it today

helping somebody move their dead fathers stuff

[molten mason]

Pretty standard text, pretty low barrier to entry. Resources everywhere, many have gone through it.

You can pop into Ireland and Rosen afterwards

[heady ember]

What about Poland?

[short urchin]

Hello I am in a hospital rn was in a coma for like two weeks can’t really move but I have an ipad to read books and would like to do some math anyone got a pdf of spivak or something that they can send on discord

I am able to think and write I think that is all I need and math would be more fun than watching sitcoms and doing rubicks cubes

[trail hemlock]

pdf sharing is not legal so people here can’t

spivak is on internet archive for free tho

[short urchin]

Some books have free pdf editions

[weary trellis]

the ones i found on google are unusable

[maiden glen]

are you the person who does the reviews on the server website

[gray gazelle]

why no algebra and precal?

[fickle whale]

@fallow cypress

[gray gazelle]

<@&268886789983436800> ?

[stray veldt]

@weary trellis please keep mentions of piracy out of this server

ill delete the message

[broken meadow]

i do not do all of the reviews, i did a few. They are crowdsourced

[broken meadow]

?

[maiden glen]

what is "crowdsourced"

[broken meadow]

People used to write reviews and send them to me

[maiden glen]

i see.

[gray gazelle]

in the website..

[foggy quest]

See this paragraph from Hatcher's Algebraic Topology book:

[rain wren]

@broken meadow are you still accepting reviews?

I can give a review of folland

[fallow cypress]

DM it to ModMail

I'll add it

[broken meadow]

Yes

dm modmail

[broken meadow]

You should be more clear when you ask questions. In any case, there are no sections for highschool algebra/precalculus probably because we didnt anticipate any reviews to come in for those subjects anyways. Usually we divert people to khan academy/organic chemistry tutor/professor leonard/etc, so i see no need for those categories unless there really are canonical textbooks for those subjects

[gray gazelle]

oh i see... and sorry for not making it clear..

[trail hemlock]

jacobson's Basic Algebra is an excellent high school algebra book...

[gray gazelle]

nah i alr have one i will just look out

wtf is basic algebra by Jonathan's lol

[mossy flume]

who is Jonathan

[gray gazelle]

son of baby rudin

[uncut crater]

Like the name suggests

Basic algebra

[fresh sage]

Does anybody have any book suggestions on Pre-Algebra?

[trail hemlock]

khan academy/organic chemistry tutor/professor leonard

Aops sells a prealgebra book which is good

[fresh sage]

Gotcha, thanks!

[gray gazelle]

or elementary algebra by hall and knight

or maybe algebra by gelfand

[rain hound]

Euler’s algebra book isn’t bad actually

(surprisingly pedagogical for who he was lol)

[molten mason]

Just like Yeh is great for intro analysis

[trail hemlock]

isnt Yeh like

pretty hand holdy compared to other books

i mean not for intro but

ykwim

[molten mason]

I'll let you know in ~6mo

[trail hemlock]

https://cdn.discordapp.com/emojis/1166347571527155722.webp?size=48&quality=lossless&name=salute

[gray gazelle]

I read through all of Loring w. Tu's "An introduction to manifolds" except for the de rham cohomology and I'm thinking of getting Tu's differential geometry book. I've heard John Lee's "Introduction to smooth manifolds" is good, should i get it before starting differential geometry?

[uncut crater]

Dude

If you've done Tu

You've already done a lot

You can conveniently start diff geom

[gray gazelle]

https://mathoverflow.net/questions/475004/how-to-choose-a-good-textbook-that-is-pedagogically-optimal-for-a-student

[uncut crater]

Why did you link this?

Oh it's the same person who asked the question lol

[gray gazelle]

Yeah lol

[uncut crater]

Russian texts are terse

[gray gazelle]

did you hear the news of trump?

[uncut crater]

Ofc

[gray gazelle]

WW3 was about to happen..

[uncut crater]

Not necessarily

[dim sierra]

Stop fearmongering lmao

[uncut crater]

Trump isn't occupying any position of power atm

[gray gazelle]

sorry bout that

[dim sierra]

It’s crazy but it’s not gonna blow up the world

[gray gazelle]

well my imo

[dim sierra]

I still can’t believe it happened

Like it genuinely doesn’t feel real

[gray gazelle]

but lots of secrets

[dim sierra]

We’re literally living in a historic time

[gray gazelle]

i have no proof writing experience whats a good

book for it

[narrow relic]

What is the background required for that book?
Also, how did you choose which problems to do?

[molten mason]

This happens every few decades over the last 200 years, nothing new, ww3 isn't happening

[molten mason]

Also mainly, this is book recs not discussion

[gray gazelle]

huh

lol

[halcyon wasp]

What is a good resource to study coordinate-free treatment of diffgeo?

I found Tu's "Connections, Curvatures, and Characteristic .." a bit slow. Is there a faster-paced one? Preferably also introducing infinite dimensional constructions.

(Or maybe one with more exercises could suffice)

[gray gazelle]

what is a a good multivariable calculus book/course like spivak's calculus and is spivak's calculus on manifolds is good

[vital bane]

spivaks's calculus on manifolds isn't a calculus book lol

it's more analysis + diff geo

[lime vessel]

Calculus on Manifolds: A Speedrun to Stokes Theorem

[marsh ingot]

Basically

[broken pecan]

any quant/financial math people here? I want to learn math of quant. I only had Rudin and spivak. Never reached measure theory. I'm going to read probability theory myself.

I'm using Seydel's book for computational side of things, Shreve's two books for theory. I understand these two books are already quite advanced. Anything else I need to read before truly master the subject?

[heady ember]

Schroder TLDR:

[stiff grail]

Nihao

Any book for beginner level calculus to advance

Same for algebra

Pls thanks 🙏🏻

[heady ember]

Holy shit this author actually released his book open source, with the latex source code and all.
https://digitalcommons.trinity.edu/mono/7/

[sage python]

How many real analysis books...

[halcyon wasp]

Seems like "Tu's connection" might be just too slow, feels like Lee's Riemannian would be faster

[vital bane]

too many

[normal sandal]

looking for a recommendation for a representation theory text, something not too dense perhaps?

[hollow shore]

has anyone here worked through Hoffman and Kunze?

[normal sandal]

for my background I'd say I'm comfortable with group/ring/field theory and decent familiarity with galois theory and a lil commutative algebra

[gray gazelle]

you might enjoy this https://textbooks.aimath.org/textbooks/approved-textbooks/

[sage python]

Serre Linear Representations of Finite Groups is good

Steinberg has an easier rep theory book (doesn't ask for any background beyond group theory and linear algebra)

[thorn hinge]

Does anyone know a source that has the proof that the operator ( e^{A} = \sum \dfrac{A^{i}}{i!} ) is (C^{\infty}) around the origin?

[hasty eagle]

tales

[thorn hinge]

A is a invertible linear operator in a banach space

I found the book Lie Groups, Lie Algebras, and Representations, but I am looking for other sources

[normal sandal]

thanks!

[mystic orbit]

aaaand thankyu

was looking for something like this

OMG

manan

sorry dude, just considering my options

[karmic thorn]

Introduction to Representation Theory by Etingoff is quite novel in its approach. For finite groups specifically, check out Peter Webb's book on representation theory of finite groups (available online). Steinberg's book does things more concretely in the setting of C, while Serre was too hard for me to read.

[karmic thorn]

Dw, Strichartz will disappoint you soon enough

[mystic orbit]

pfffffft

I'm only hesitant coz SS doesn't use the measure theory I know

[karmic thorn]

Mfw doesn't even define what it means for a distribution to be a continuous linear functional

John reccomended Folland

[mystic orbit]

even tho I hear the lebesgue integral is indispensable when treating fourier stuff

[karmic thorn]

And I honestly think that's a better treatment

[mystic orbit]

oh, right, folland

[karmic thorn]

Chapters 8 and 9

[mystic orbit]

I could just go full on folland tbh

(I don't think john has read those chapters tho LMFAO)

[karmic thorn]

I think it's pretty clean in terms of writing

Strichartz gets too lost in the motivating examples for my taste

I don't like giving examples at the expense of formal definitions altogether

[mystic orbit]

alright

ig I'll just try them out

[hybrid iris]

i'd prefer general use with applications

is strang's linear algebra and its applications good

[karmic thorn]

Not cover to cover, but several chapters

[normal sandal]

ty! webb's book looks quite nice

why did you think serre was hard? just the exposition is hard to read or

[karmic thorn]

Yeah, mostly that

(and the lack of LaTeX typesetting )

[normal sandal]

fair enough haha

[glad prairie]

:manancoping:

[gusty smelt]

I did!

[mystic orbit]

bruh

why

surely you knew that stuff already when you taught us measure theory last year

[gusty smelt]

oh i mean a bit

i didnt really know the distribution stuff

is the main reason

the fourier stuff yeah

[mystic orbit]

[gusty smelt]

also the reason i taught that class is cause i sucked at measure theory

[mystic orbit]

[gusty smelt]

now i dont!

[mystic orbit]

alright then

ig I'll just use folland

https://tenor.com/view/cute-cat-pout-gif-23544621

[iron badge]

Anyone got recommendations for introduction to model theory?

[remote sparrow]

Model Theory:

Model Theory by Chang and Keisler
A Shorter Model Theory by Hodges
Model Theory: An Introduction by Marker (notoriously filled with typos)
A Course in Model Theory by Tent and Ziegler

[weary fox]

Not sure if this is the right channel but does anyone know of a good place to buy math books secondhand (i.e. cheaper than new)? I am aware of thriftbooks and ofc ebay but I would like to check out other places if there are any

[remote sparrow]

generally deals aren't much better than amazon's

[normal crystal]

eh, that depends on the title
alot of the used book sellers post to all the sites
the three sites mentioned cover most bases
but also biblio, bookfinder.com

[weary fox]

bookfinder looks amazing!! thank you

[gray gazelle]

precalculus recommendations

[trail hemlock]

khan academy/organic chemistry tutor/professor leonard

Aops sells a precalculus book which is good

[trail hemlock]

Guys is "A Companion to Analysis" a good companion to baby rudin

[uncut crater]

Silvia?

Or erdman?

I'd rather read another book

[trail hemlock]

Körner

full disclosure i googled this qeustion and i got this

[trail hemlock]

i just need a good companion

and a companion book to rudin would be nice as well

[uncut crater]

Körner...

Nope

[trail hemlock]

like a dog maybe

or a cat named giggleshitter

[uncut crater]

Gigashitter

The thing is

If you need a companion for rudin, just don't do rudin

Read the stuff from somewhere else and then do the problems

Ez

[trail hemlock]

i just want an alternate approach to the

proofs

ykwim

differnet perspective

[uncut crater]

Hmmm, you need a different analysis text then

[uncut crater]

This one's not a first read

[trail hemlock]

i see

[uncut crater]

There's a lot of notes floating around

Based on rudin

That fills in the gaps

[trail hemlock]

"second first and first second" confused the fuck out of me

[uncut crater]

Yeah

[trail hemlock]

oh that reminds me of this:
https://siegelmaxwellc.wordpress.com/mathematics/math-notes/

by complexvariable

[uncut crater]

Isn't that the Collatz guy?

M c siegel

Yeah

It is him

[trail hemlock]

yeah

hes also an author iirc

[uncut crater]

If you're comfortable with them, go for it

[trail hemlock]

wait im being dumb

i can just use tao

[uncut crater]

Why?

[trail hemlock]

https://cdn.discordapp.com/emojis/654412877687685130.webp?size=48&quality=lossless&name=facepalm

which i own a copy of

💀

nvm sorry to waste ur time

[uncut crater]

Im wasting my time staying up tbh

It's 9 am and haven't slept

Maybe I'll just study lie algebras

[trail hemlock]

i did this yesterday

didnt sleep at all

[uncut crater]

Ive been doing this for a month

[trail hemlock]

i tried for 5 hours but it didnt pan out

i might buy those sleep gummies

[uncut crater]

Man

Insomnia is real

[trail hemlock]

i dont think i have insomnia

well i hope not

cuz its usually a symptom of another condition according to my psych teacher

[molten mason]

Undergraduate Analysis by Serge Lang 700 pages of pure analysis baby

[trail hemlock]

this is pretty off topic

[trail hemlock]

lang is pretty terse, no?

[molten mason]

He actually has good reviews on this one. I've seen a few random reviews rec it for self-study and it being 100% self contained.

The answer to your question would be personal preference.

[trail hemlock]

i think im gonna stick with tao because i have a physical copy

[compact ore]

if its your first time doing proofs id recommend abbott. if not id recommend zorich.

[trail hemlock]

and i dont want pages of explainstions or i wold use abbott, i just want some more proofs that are fleshed out

[molten mason]

Yeah if you have access to the PDF you can just skip to the proofs of whatever you want. You don't need to actually go through the book lol

[trail hemlock]

im on ch5 of rudin with no problems so far, i just wanna see some more proofs because it takes me a fair amount of time to prove some of the harder exercises in rudin

[compact ore]

that is normal they are hard

[trail hemlock]

i jus like analysis proofs

they are cool

[compact ore]

u can always use multiple sources

my friend raves about how it made his studying much more efficient but i dont like

[trail hemlock]

i tried proofwiki but that shit pissed me off

they used 70 backlinked previous theorems to concluide that everything is actually trivial

[compact ore]

dont bother with proofwiki

its a reference for people who already know

not for learning

[trail hemlock]

aint that the truth 😭

[compact ore]

wikis are never good for learning thats not their purpose

[trail hemlock]

basicslly what im saying is like

rudin style proofs of more theorems

iykwim

[compact ore]

have you considered checking out the companion text "real and complex analysis" which goes into more detail on the things he skips

[compact ore]

in all seriousness youre not gonna find this most likely

cuz why would someone write a textbook thats basically rudin

rudin exists and every undergrad analysis book since then has essentially had to justify its existence against rudin

as such the proofs in most of these books will be more verbose and less to the point intentionally

just use tao since u have it

but keep up rudin if youre not having problems

[trail hemlock]

isnt that a measure theory text?

[compact ore]

no its a book on real and complex analysis

lmao

[trail hemlock]

makes sense

should have gathered that

[compact ore]

im not saying this to be snarky either

theres not a better way to summarize it

[trail hemlock]

oh that reminds me of when my teacher quit her pure math degree to do engineering after 2 days of real variables class

her and my eng teacher were the wrost

[compact ore]

changing textbooks is probably more of a hassle than its worth

[trail hemlock]

but thats neither here nor there

[trail hemlock]

https://cdn.discordapp.com/emojis/1166347571527155722.webp?size=48&quality=lossless&name=salute

ill consult tao and stick to rudin

[compact ore]

good luck

oh wait

pugh also exists

i dont know if it would be what ur looking for

it has lots more exercises than rudin though and is ordered roughly the same way

[trail hemlock]

pugh sounds like a sigh starting with a closed mouth

[compact ore]

i have no fucking clue how to say

[trail hemlock]

"pugggggg"

[compact ore]

every time i try to say it i make a fool of myself

[trail hemlock]

or pug like the dog

is it Real Mathematical Analysis?

[compact ore]

yea thats the one

[trail hemlock]

https://cdn.discordapp.com/emojis/1166347571527155722.webp?size=48&quality=lossless&name=salute

u the goat ty

bruh school is starting in a month and i wont have time to lurk on mathcord anymore

😔

[compact ore]

analysis rocks have fun

[cursive orbit]

this is a feature and not a bug

[compact ore]

lurking mathcord is cringe do math instead

[trail hemlock]

im trying but

i had to give up jech to fit in SAT prep

😔

sad truth

[compact ore]

jech will prepare you better for the sat

[trail hemlock]

the math section is like

super hard ive heard

[tribal crow]

ouch.

I caught a stray

[compact ore]

sorry

i only say the truth

[trail hemlock]

[compact ore]

ur getting lied to

[remote sparrow]

it's mostly simple tricks to do them efficiently

[trail hemlock]

i was kidding 😭

[vital bane]

yes

[hollow shore]

is it good for a first pass given that I have some intuition about Linear Algebra?

[gray gazelle]

Any very good textbook that have a good mixture of real analysis and calculus? It'd better be modern, and I'd greatly appreciate it if you have any suggestions.

[remote sparrow]

spivak?

the fourth edition was published in 2008 which i'd say is pretty modern

[fierce hedge]

There's Silvia's famous companion notes for Rudin

[trail hemlock]

i found one

its great

[fierce hedge]

Which one

[trail hemlock]

uc davis has one

[fierce hedge]

Link?

[trail hemlock]

i downloaded them all and added a table of contents

[remote sparrow]

bergman has a companion to rudin

[trail hemlock]

berger man

🍔 man

[fierce hedge]

This is the companion notes by Silvia

[trail hemlock]

shoutout my homie silvia

💯

[fierce hedge]

The main issue with Tao is that you kinda need to just stick with Tao cause it uses some non standard definitions. At least I found it very hard to back to after few months.

[fierce hedge]

Isn't Zorich a bit too big, also it has a lot of exercises while being more than reasonably hard?

[remote vortex]

Vendor lock-in, mathematics edition.

[fierce hedge]

I was taught Linear Algebra using H&K, it's pretty much the standard in most places in India. That said, it might be slightly hard for self study. Maybe try LADR or LADW with H&K for problems.

[gray gazelle]

Any more complicated ones, for example I have looking for something like Russian textbook Zorich's Mathematical Analysis

Like I really like zorich, but I feel like the pedagogical approach in it is not very good.

[gray gazelle]

what are your thoughts guys about Stewart's precal?

[hollow shore]

I have found an NPTEL lecture series of a prof following h & k. So I think I could complement it with the videos.

[fierce hedge]

Ah, okay okay

[daring lake]

Prof Pranav Haridas?