book-recommendations

[queen fog]

https://www.tedsundstrom.com/mathematical-reasoning-writing-and-proof

this approach is very beginner friendly

[wet sentinel]

so basically this is the same content of the book

but as a series of lectures

right ??

[queen fog]

that is correct

[wet sentinel]

ok tysm everyone

[subtle terrace]

.

[molten gulch]

every ODE and PDE book I have is at-least 500 pages long

[gray gazelle]

hey

in the AOPS volume 1

do i just learn the things i don't know?

or i need some supplement for it?

especially if my knowledge is just in pre algebra

[subtle terrace]

damn

but actually now that i think about it

thats really just 7 pages a day

i know thats not easy when it comes to topics like differential equations but i can make it work

so what recommendations do you have for a ode/pde book of this length?

[molten gulch]

Have you taken a course in functional analysis?

[subtle terrace]

nah my only qualifications are algebra, geometry, trig, and calc 1-3, along with a TINY bit of experience with proofs

so im not asking for something too advanced ,just a typical fourth semester differential equations cirriculum

[molten gulch]

Ahhh okay

[molten gulch]

Are you familiar with linear algebra?

[subtle terrace]

oh right yeah i forgot to add that

im not super familiar but i think i know whats nessecary to move on from it
(vectors, eigenvalues, determinants, linear transformations, etc... just the basics)

[molten gulch]

Alr

Well for ODE's there's:

• Nagle, Saff, and Snider-Fundamentals-of-Differential-Equations
• Boyce, DiPrima, and Meade - Elementary Differential Equations and Boundary Value Problems
• Ross - Differential Equations
• Simmons - Differential Equations with Applications and Historical Notes

For PDE's (all of these require functional analysis) there's:
Taylor
Evans

[subtle terrace]

so there arent any books that include both?

btw kinda off topic but what even is functional analysis? is it similiar to real analysis?

[molten gulch]

You need real analysis to do functional analysis

[subtle terrace]

but isnt real analysis usually taken after pdes?

weird

or are these books at a graduate level so they require more advanced prerequisites?

[molten gulch]

all the ODE books are undergrad level

[molten gulch]

PDE theory is considered a grad level subject, the undergrad PDE course is numerical in nature

[subtle terrace]

yeah i was talking about the pde books

[shy silo]

I'd do ODEs after Linear Algebra

Like you lose so much

[molten gulch]

yeah ofc

that's why we asked him if he knew linear

[shy silo]

Ah alr

[molten gulch]

But for PDE's there's Evans' PDE book and oh also Strauss' PDE book

[subtle terrace]

so pdes do exist as an undergraduate subject dumbed down, but at their full scale theyre graduate level?

[molten gulch]

yeah

[subtle terrace]

well do any books include both odes + undergraduate level pdes?

[molten gulch]

we have a lot of books on PDE theory, sadly not much on PDE solutions

[molten gulch]

most of the PDE numerical stuff is in numerical analysis textbooks AFAIK

[shy silo]

What do you mean?

[molten gulch]

I mean most of the books we have don't cover numerical solutions much

[shy silo]

Most differential equations don't have elementary solutions

[molten gulch]

this is true

[shy silo]

Ah

that's what you meant

I mean, that's more suitable for numerical analysis I guess

[molten gulch]

Like something like DiPrima for ODE's or whatnot covers numerical solutions (to a degree) alongside symbolic ones

[subtle terrace]

well ive found a book that seems promising, is
"differential equations and their applications" by martin braun any good?
its 700 pages long but it isnt too textwall-y so i think it wont take that long to finish, and it seems to cover both odes and pdes

[pulsar coral]

Im looking for abstract algebra books or other exercise resources with lots of problems that have a computational vibe to it ranging from easy to hard.
It should cover groups, rings, fields and maybe even modules.
Im thinking of exercises where you have to reason about concrete objects using the general theory.
For example given a Ring and an Ideal, determine the quotient. Things like that.
Ideally it would just be a huge document with such problems that you can grind through over time.

[hollow shore]

looking for a numerical analysis book/lecture notes aimed at engineers

[fresh skiff]

Guys I am thinking to buy following three books

• Topological manifolds by lee
• Axler Linear algebra (4th edition) ----- btw is there some reasonable difference between 3rd and 4th edition?
• Multidimensional real analysis by duistermaat.

do there books look reasonable ? (I have backgroud of analysis upto abbott and a bit of rudin)

[molten gulch]

lee is good and axler is good, unfamiliar with duistermaat

[fresh skiff]

#book-recommendations message

[foggy quest]

you can try chapters 6-8 and the appendix of https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/linalg.pdf

[fresh skiff]

@foggy quest If you don't mind can you please send taylor's web page where he has kept his all notes

[gray gazelle]

Wow there's a 4th edition now?

[molten gulch]

of axler? yeah

been for like a month

[gray gazelle]

I remember 3rd edition being very different from 2nd

[molten gulch]

and axler's book is free on his website now

[narrow relic]

4th edition is excellent from what I've worked through so far. Very different writing style from 3rd.

[fresh skiff]

yes. Even there is 4th edition of Royden too (Real analysis) thats digital and good looking version

[foggy quest]

https://mtaylor.web.unc.edu/notes/

[fresh skiff]

Thank you so much for this

[foggy quest]

worth noting that some of the notes are parts of his 3 PDE books, which are on Springer Link

[gray gazelle]

so by the end of it , I would have already covered some graduate material?

[tribal crow]

I can only speak for Lee's ITM, but I'd say that you have more than enough background for the first 4 chapters (given what I've seen of you)

actually, you're probably more than ready for Axler too in terms of math maturity

about Axler's editions, go for his 4th one

it actually does determinants in a more reasonable way than whatever he pulled in his 3rd ed

[gray gazelle]

https://www.youtube.com/playlist?list=PLdcw5wvaQEomvQjXjBo3L7cEqZ8xNECyA

MIT Godel Escher Bach Lectures Playlist

[fresh skiff]

Ah just checked his PDE1. It's a thick boon with bunch of material. Wow

[cursive orbit]

I would not recommend trying to study PDEs in depth with your experience

you would also want real analysis to study ODEs in depth, so basically the most accessible thing for you is a "cookbook-style" textbook, where they teach you techniques to explicitly solve some ODEs/PDEs

[fresh skiff]

Ah wao that sounds good .
Iirc few days ago I saw first few pages of Lee and I found material reasonable (also maybe it was basic Topology).

[fresh skiff]

I remember i guess one or 2 years ago I tried to study Axler without even a tiny background in proofs
So at the end I stopped.
Hopefully this time it will be an amazing journey

Btw Thank you so much Higher for you and time and these reviews

[tribal crow]

[rain wren]

depends on which topic you're interested in most

lee would server you very well if you wanna go the geometry route

diff topo, diff geo even algebraic topology

I have never read the 2nd and I have never even heard of the 3rd

so I can't speak for them tbh

[fresh skiff]

Personally I would love AG (but without studying that field I cannot decide whether I will enjoy it or not)

[rain wren]

if you wanna do AG further down the line then I would recc artin instead of axler

it covers all the LA you need for a veeeeery long time + algebra

[fresh skiff]

oh I see, np thats completely fine

[fresh skiff]

oh artin algebra!!

[rain wren]

I don't even know what there is to multi var analysis that it would require an entire book tbh

the impression I get is that, the thing that is uniquely multi var analysis and nothing else is differentiation

which can be covered in a single chapter lmfao

integration can be done in a stupid degree of generality through measure theory

and you can learn differential forms and stokes and stuff from any geometry book

this isn't exactly a dig at your book for the record, I'm genuinely curious if my intuition is correct here lmao

[fresh skiff]

So multi var analysis can be done by without actually picking a book on it Interesting

[remote sparrow]

never heard of a place where real analysis needs to specifically be taken after PDEs

[remote sparrow]

fyi, numerical is a fairly well-established term. an undergrad PDE course has little to do with analyzing how good a numerical method is for approximating the solution to a PDE. the course is mainly about finding closed form solutions to very special classes of PDEs.

[remote sparrow]

you mean fifth edition?

https://www.pearson.com/en-us/subject-catalog/p/real-analysis/P200000007113/9780136853473

[fresh skiff]

ah yes. A brain fart
Thank you for correcting me

[molten gulch]

ahh yeah

[rain wren]

yea, I literally just did like

a chapter from spivak on manifolds

not even that

implicit funciton theorem I did from lee

[fresh skiff]

what were you doing
studying multi var analysis without from specific book on that subject

[remote sparrow]

typically, multivariable analysis textbooks limit themselves to the riemann integral

[molten gulch]

^

[fresh skiff]

oh

so what about measure theory, does it contain integration of R^n?

[molten gulch]

Isn't integration of Rn generally covered in differential geometry?

[tawny copper]

All of it could be reasonably covered in undergraduate courses. But note that a typical first course would pretty much just be the first 5 chapters (up to and including quadratic reciprocity), at least that's what I have seen. Also keep in mind that the exercises are important

[cursive orbit]

measure theory covers R^n, yes, and more general domains

[fresh skiff]

idk

[fresh skiff]

oh cool thats why measure theory is kinda abstract

[covert mauve]

Whats a good linear algebra book for graphics and stuff?

I don't wanna learn it formally yet because time but I would still like an good short introduction

[molten mason]

This definition is oversimplified, but you can think of linear algebra as the study of vector spaces in finite dimensions while functional analysis studies vector spaces in infinite dimensions. Functional analysis requires a very strong real analysis background (My university doesn't even offer it to undergrads, it's like a 2nd year graduate course). It's a little more complicated that that and gets deeper but thats the gist of it.

[maiden glen]

good economics books?

[foggy quest]

I liked Taylor's linear algebra book more than Axler's. Before you buy a book, try reading the first two chapters to see if the book is at your level and whether you would continue reading it.

[foggy quest]

Functional analysis is the study of linear maps between infinite-dimensional topological vector spaces.

[gray gazelle]

Sorry if this is a pedantic nitpick but I think that is misleading. It studies topological vector spaces, not vector spaces.

[foggy quest]

True, Hamel Basis is not part of functional analysis

[gray gazelle]

Well, their cardinality still gives an invariant of topological vector spaces

[alpine ridge]

Hello, is there a free pdfs book on discrete maths and vector calculus? Thanks

[foggy quest]

Here is one on vector calculus: https://mtaylor.web.unc.edu/multivariable-calculus/

[alpine ridge]

Thanks!

[maiden glen]

how did you learn of the borel equivalence relation

[gray gazelle]

Kechris, Classical Descriptive Set Theory

[maiden glen]

i assume from the wikipedia reference page?

[fresh skiff]

Surely i will take a look! Thank you.

[normal crystal]

the 4th edition is legit free from Axler, if you're ok with digital

[fresh skiff]

Yes. I am ok with that too but much more comfortable with physical copy

[vital snow]

Whats are good books to study proof writing and number theory

[remote sparrow]

https://bookstore.ams.org/view?ProductCode=AMSTEXT/61

[vital snow]

thank you

[vestal magnet]

any book recommendations for permutations/combinations/probability?

also how do you master pnc + probability

im 19 and i get confused easily

[pallid briar]

out of the topic but how did you make the Document Viewer UI dark?

[subtle terrace]

yeah thats what im planning to do, like not a graduate level analysis of differential equations, just your typical 2nd year 2nd semester course on them

[subtle terrace]

yeah ik it doesnt NEED to be taken after pdes, but it is the usual way it goes im pretty sure? math, engineering, and physics majors go through the calculus series in the first 2 years(including differential equations), and then math majors go on to take more advanced math courses in the rest of their college studies; ie real analysis. so i dont understand why you would take real analysis before differential equations
(correct me if im wrong on anything though i havent been to college yet so this is only through word of mouth)

[subtle terrace]

interesting, thanks for letting me know

[remote sparrow]

that is unusual too

usually you're free to take real analysis after calculus 3

could even be after calculus 2

[subtle terrace]

oh

so what youre saying is i can do real analysis before differential equations?

[remote sparrow]

yes

[subtle terrace]

since ive already taken calc 1-3 and linear algebra and i think those are the prerequisites

[molten mason]

ODE and Real Analysis are two separate things. You can take either or both, any order or together.

[subtle terrace]

Ik yeah i just thought it was rare/strange to take real analysis before differential equations, but it seems its more common than i thought

[molten mason]

Engineers take ODE and don't have to take analysis

[subtle terrace]

but for a math major the order doesnt really matter in this case right?

(except for taking calculus 1 and 2 before ofc)

[dense pumice]

Yeah they're pretty different topics, though both work around calculus concepts

Real Analysis is gonna be more theoretical, why can we say these things about limits

ODEs is probably more applied, how to solve those sorts of equations

[subtle terrace]

btw kinda off topic but if i start a book like abbots "understanding analysis", should i apply for advanced/postgraduate math role or do i wait till i move onto more advanced topics?
(since real analysis is in the advanced mathematics section here, but usually it is an undergraduate course)

wait forgot to add the word role mb

[dense pumice]

What, you mean like the role?

[subtle terrace]

that kinda changes the meaning

[subtle terrace]

yeah

[dense pumice]

Yeah, go for it

[molten mason]

Realistically the roles I don't think mean too much, but probably stick with undergrad role until your mastered the undergrad topics.

[subtle terrace]

seems theres a conflict of opinions

but eh im not in a rush to decide, im only gonna take real analysis after i finish vector calculus which i still have a few weeks left on

[novel hound]

you can add the real-complex-analysis channel (from channels and roles on the top left). Don't necessarily need to add advanced role (I think).

[molten mason]

Yeah advanced role was phased out. Undergrad role should give you access to those channels.

[gray gazelle]

Can you guys give me a free textbook on highschool maths? Thanks in advance

I mean, recommend

[subtle terrace]

yeah i already have access to all of the advanced math channels dw

[stuck zephyr]

topic?

[buoyant badger]

Any good textbooks on early University level statistics, preferably Business orientated ?

[gray gazelle]

it largely depends on the ODE class, if it's computationally oriented, then there's no reason to take ra beforehand, in some places you'll even take them concurrently (like at UK unis)

[gray gazelle]

at what level? with mathematical undertones I assume?

[molten gulch]

on GNOME? Just set your UI theme to dark in the system settings

[molten gulch]

for us you can take real after calc 3 + discrete math (proofs) + a separate advanced math course (more proofs)

[gray gazelle]

For all topics every highschool students need to master.

[gray gazelle]

there is

[gray gazelle]

Is there?

[gray gazelle]

Openstax has that one. I guess

[gray gazelle]

there is

A Guide To Econometrics
Peter E. Kennedy

[gray gazelle]

The VNR Concise Encyclopedia of Mathematics
Book by Walter Gellert

[molten gulch]

The VNR book is uni level maths

and even then it's just a quick rundown of topics

not proper textbooks

[gray gazelle]

my bad dont buy vnr

[gray gazelle]

Wow. Thanks. Is that free?

i thought vnr was good for someone who wanted to build intuition of high school maths

[molten gulch]

no

[gray gazelle]

almost every maths book is $10 on ebay

at least older ones

[molten gulch]

we got a copy for free because our uni has access to springer

but that's about it

[gray gazelle]

I don't have international bank account. Like the cards. I have no card.

is there a high school encyclopedia book like vnr

[trail hemlock]

theres no such thing as "high school math" so no

[molten gulch]

not that I'm aware of

I have some precalculus books lying around I can recommend

[gray gazelle]

stewart

[molten gulch]

also basic mathematics by serge lang is p. popular afaik

[gray gazelle]

ryan whats a similar book to vnr thats good

[trail hemlock]

aops precalc is nice, lang's basic mathematics and hardy's a course on pure mathematics back to back would prob cover "high school math"

[molten gulch]

yeah

[gray gazelle]

Mathematics: Its Content, Methods and Meaning

[molten gulch]

I don't know

[gray gazelle]

ok

for some reason my college doesnt have great selection of books

Highschool maths is just precalculus and calculus?

maybe underfunded

high school maths r u in olympiad?

join olympiad they will train u to be a beast at high school maths

[trail hemlock]

[gray gazelle]

beast mode

excuse me a beast is coming through

background beast music

[gray gazelle]

I'm neither in highschool or in Olympiad. Just a late learner to improve my knowledge and skills in maths as a hobby. But I don't feel happy my matriculation exam score was 40%

vegetarian if u even graduate high school read vnr book to become college beast

u know algebra and trigonometry?

khan academy is free and good

i just think they only teach one method of doing things and expect you to recognize patterns

which i think is bummer

[gray gazelle]

I know basic algebra. but I don't understand trigonometry a bit. I'll try khan academy first then. Thank you.

ok u gotta get a book called precalculus by stewart

and the beginning it teaches the foundations

and a lot of problems in that book

by the end u will become high school beast

[trail hemlock]

other than khan academy, i see https://mecmath.net/trig/ here a lot, and its pretty good

[gray gazelle]

Thank you

yes u will become the best at maths trust

[gray gazelle]

Yay. Thank you so much! ❤️

theres a really good book called princeton companion to mathematics

if u can ever buy it its $40 on ebay used

[gray gazelle]

eBay doesn't even work in my country

if u become a beast at maths then reading this book will make you 2x beast

[gray gazelle]

Yay.

i think the book is like $70 brand new

[gray gazelle]

That's cool.

its kinda expensive

Yes. But worth it. Just I don't have any card

😦

if u live next to a university

i think u can just go in the library

or wait at the door for someone to leave and walk in when they walk out

thats what i do

[gray gazelle]

Lol. Okay

[molten gulch]

yet again, just an overview of maths

[maiden glen]

no, just plain economics which assumes the negligibly acknowledgeable mathematics

whatever builds upon micro and macroeconomics

[gray gazelle]

well there's international economics chapters in Ellie Tragakes' Economics for the IB Diploma

[maiden glen]

self studying

i don't want school books

[gray gazelle]

you can self-study from that

that's what I did

and it worked out perfectly

it doesn't assume any prerequisite knowledge

I need a quick complex analysis book that only covers basics and has undergrad-style problems, can anyone help with that?

I'd devote myself to big books but sadly I don't have a lot of time so I need something quick and easy

wait I'll read the stuff in "All The Mathematics You Missed" book for now

[gray gazelle]

idk about easy, but Narasimhan is certainly quick

ToC looks like that of a graduate level book's

either that or I'm living under a rock

[maiden glen]

ok then

[molten gulch]

Aurora and Barak? Sipser? Yeah that's (kinda) a grad book

[molten gulch]

churchill's complex variables?

[gray gazelle]

I was referring to Narasimhan but now that I looked past ToC it looks more exciting and I might actually not be able to hold myself back from reading it

[gray gazelle]

will look at that one too

wish I had more time to read these thoroughly

thanks for the suggestions

[molten gulch]

ahh the only ToC I know of is "Theory of Computation" by Arora and Barak Sipser, which is a book on complexity theory

[gray gazelle]

ToC is also short for Table of Content

[molten gulch]

ahhhhhhhhhhhhhhh

[gray gazelle]

since you mentioned it I shoud ask, is Aurora and Barak a good book for complexity theory?

[molten gulch]

it's considered pretty good

[tender river]

i cant find an arora barak book titled theory of computation

do you mean computational complexity: a modern approach

[molten gulch]

oh I was yeah

[molten gulch]

this one

my brain is cooked rn

[gray gazelle]

but wait, is it called "Computational Complexity: A Modern Approach" or "Theory of Computation"?

[molten gulch]

first one

I was thinking of Sipser's book

Sipser - Introduction to the Theory of Computation

[gray gazelle]

damn, I'd better go back to complex analysis

time pressure is real

[molten gulch]

how much time do you have

[gray gazelle]

it's not a fixed amount but I have a lot to learn

[rain hound]

There’s a book on computational complexity and there’s lecture notes on theory of computation and they’re different things

[gray gazelle]

I'll start having classes (+TAship) in september so will have very little time to study and make progress

[rain hound]

Arora and Barak is the best book on complexity imo. (after you learn intro theory of computation elsewhere)

[rain hound]

Sipser is really good, I’d argue the best intro to theory of computation/complexity

Sipser -> Arora & Barak is a good progression

[gray gazelle]

it looked kinda self contained to me no?

[rain hound]

It is self contained technically. But realistically I think it’d be really difficult to follow if you aren’t already comfy with intro theory of computation.

Unless you’re just a lot smarter than I am (fully possible).

[gray gazelle]

makes sense

I've studied some theory of computation but have forgotten almost everything

but my clock is ticking so unfortunately I'll have to let go of it

[mossy flume]

clock is ticking?

[gray gazelle]

I mean I have a lot to learn but very little time

especially when my classes and work start in september I'll have almost no time

[maiden glen]

is this complex analysis

[gray gazelle]

no

theoretical CS, roughly speaking

[mossy flume]

It's the study of how hard certain problems in computing are

[remote vortex]

None of us are getting any younger

[maiden glen]

maybe intricacy would be a better word

and i suppose that's too concise to be taken seriously

[maiden glen]

yes we get it you've aged enough, got a degree and now feel like you're entitled for the "wise" role

[remote vortex]

I mean, I have to get some use out of it

Also I've never claimed to be wise, in fact I have repeatedly pointed out that I'm not

[maiden glen]

so the owl pfp and suggestive username is for nothing

you don't claim "wisdom"

[remote vortex]

Owls are very stupid

Excellent predators, but tiny brains

[maiden glen]

you're confusing wisdom for intellect

[remote vortex]

Fair point

Shows how much I know

[maiden glen]

ok 😌

[gray gazelle]

what are the true prerequisites of harmonic analysis?

[gray jungle]

classical or abstract?

[gray gazelle]

sadly I don't know the difference

[gray jungle]

id say if you really want to do harmonic analysis you need some background in measure theory and functional analysis

katznelson is a great book on the subject

but if you want to avoid that and just want the practical theory

stein and shakarchi have a good book on fourier analysis

you just need to know real analysis and reimann integration

and multivariable calc ideally

but like a lot of the actual theory needs measure theory/FA, its hard to discuss fourier series if you dont know hilbert space theory, and its hard to actually talk about the fourier transform without lebesgue integration

so my personal advice if you are serious about harmonic analysis is to put on hold for now, and get a solid background in measure theory/FA

[gray gazelle]

thank you for your input

[pallid briar]

Hmmm, makes sence,but i use hyprland

[gray gazelle]

Is Sipser a grad book? Idk, the course I had out of it was one of the easier ones I’ve taken

I found the presentation a little lacking, tbh

[stuck zephyr]

you don't usually need a textbook for this unless your school gives you one

I'd recommend khan academy though

[gray gazelle]

thanks

[molten gulch]

huh I'm not actually too sure, I know Arora is considered a grad book

[molten gulch]

well then I'd just use lxappearance to change the GTK theme to dark

you might need GTK themes extra if it's not already there

[gray gazelle]

what's the relationship between fourier analysis and harmonic anaylsis again?

[gray jungle]

i dont know if the distinction matters at early levels, its only when you do fourier analysis on group that one term is reserved for locally compact abelian groups

[remote sparrow]

#book-recommendations message

[gray gazelle]

thanks

[drowsy nacelle]

Does anyone know of good resources to learn about the interplay between logic/set theory and measure theory/topology, like these kinds of correspondences for example

[remote sparrow]

@solemn rover

[drowsy nacelle]

@molten mason bleakkekwing at my curiosity

LMAO

[stoic hamlet]

Measure and category by Oxtoby

[solemn rover]

One book on this is "Stone Spaces" by Johnstone.

Any good text on model theory will treat type spaces

[drowsy nacelle]

thank you i'll check them out

[foggy quest]

Is this a meme

maybe not

[drowsy nacelle]

wait why

lol

[stoic hamlet]

No it’s very obviously a related book…

[drowsy nacelle]

it looks pretty much like what i was asking from the synopsis yeah

[gray jungle]

might not be what you are looking for but you can look into descriptive set theory

[drowsy nacelle]

ill look into it ty

yeah i think it does fall under what i was looking for

[shy silo]

representation theory of finite groups?

[shy silo]

the Fourier Transform is similar to the Peter-Weyl theorem in Harmonic Analysis

[gray gazelle]

I hope this is a joke

[shy silo]

why?

[gray jungle]

i dont think they were asking for harmonic analysis on locally compact groups

[shy silo]

Oh

[gray jungle]

just basic fourier stuff

[gray gazelle]

I will have a course called harmonic analysis soon but don't have info about what it will cover yet

[shy silo]

The Harmonic Analysis I've read was essentially just representation theory

[gray gazelle]

this is confusing now

is there a connection between basic harmonic analysis and representation theory?

[gray jungle]

a massive connection yeah

[gray gazelle]

in the basic theory

[gray jungle]

harmonic analysis grows to the study of unitary representation of certain groups

[shy silo]

Fourier as like a central point was studied in like Analysis and in a class about measure theory and integrals for me

[gray jungle]

but thats beyond basics

for most purposes harmonic analysis is the practical field of fourier transforms and fourier series

as well as there applications

[gray gazelle]

that's interesting actually, what kind of groups are we talking about?

[gray jungle]

locally compact groups

[shy silo]

So for me Fourier in Harmonic Analysis is just Pointgryan duality

[gray jungle]

the topology allows us to actually do integration

essentially measure theory teaches you how you can have a "measure" on your space

and you can use that measure to construct a integral

on R^n that is refered to as lebesgue integration

on groups its called a haar measrue

[shy silo]

@gray gazelle and this integral is unique given the topology (up to scaling)

[gray jungle]

and you can construct a haar measure on locally compact groups

non trivially

[shy silo]

I didn't really know that people consider Fourier Analysis to be Harmonic Analysis but now I guess that makes a lot of sense

[gray gazelle]

this is very interesting, what resources should I use to construct said haar measure on groups?

[shy silo]

I just considered Harmonic Analysis to be the generalization of Fourier Analysis

[gray jungle]

yeah i mean fourier is just gelfand on L^1

[gray gazelle]

before doing harmonic analysis that is

[gray jungle]

you would need to know measure theory first of all

[shy silo]

You can get away with just knowing it exists, for some groups they'll just give you

[gray jungle]

but the tools are the riesz markov representation theory and tychonoff theorem

[trail hemlock]

what gave you the confidence to talk to people helping you like this?

[gray jungle]

you can avoid riesz markov in certain constructions but still needs knowledge of radon measures

[gray gazelle]

is riesz markov different from riesz representation?

[shy silo]

I started studying Harmonic Analysis before measure theory and it was a huge mistake cause I didn't actually know how to integrate

[gray jungle]

its one of riesz representation theorem

ries representation is usually reserved to the duality in hilbert spaces

[shy silo]

Luckily the regular theorems of calculus had analogues so it was still fairly intuitive

[gray gazelle]

this will be me soon if I don't hurry up

[gray jungle]

riesz markov is the duality between certain "nice" measures and positive linear functionals

[shy silo]

oooo

[gray jungle]

the full name is riesz-markov-kakutani representation theorem

[shy silo]

Is that the one which describes signed measures in terms of positive measures?

[gray jungle]

ouf yeah that can be rough

[gray gazelle]

wait what is duality?

[gray jungle]

thats radon-nikodym i think

guessing

[shy silo]

Isn't that called Riesz Representation as well

[gray jungle]

do you know what a dual space is?

[gray gazelle]

the space of linear functionals on X?

(guessing)

[shy silo]

nvm it's just this theorem

[gray jungle]

yeah so the dual of the space of positive linear functionals with compact support is the space of positive radon measures

[gray gazelle]

to some normed vector space like C

[gray gazelle]

I'll have to look up what radon measure is but makes sense

[gray jungle]

if you have a positive linear functional $L : C_{c}^{+} \to \Bbb{R}$ then you can find a "measure" $\mu$ where $L(f)= \int f d\mu$

[shy silo]

man there's this book on measure theory I love

[hasty eagle]

James Banach*-alg

[gray jungle]

so you have a link between this linear functional and the measure

[shy silo]

It's called integral measure and derivative a unified approach

[gray jungle]

again, i would really advise you to sit down and learn measure theory @gray gazelle

[gray gazelle]

makes sense

[gray jungle]

if you want to learn that type of harmonic analysis

[shy silo]

It essentially arrives at a measure theory from an integral theory

[trail hemlock]

perhaps in a reading group ?

[shy silo]

So you don't see measure theory until like the third chapter

[gray jungle]

@gray gazelle yeah you can join our group in #events if you'd like

[gray gazelle]

compact support means they will have finite integral right? and we take that value as its measure

[gray jungle]

it means the function vanishes outside a compact set

[gray gazelle]

so then it will have finite integral

if it's 0 outside

[gray jungle]

$supp f=\overline{{x : f(x)\neq0} }$

[hasty eagle]

James Banach*-alg
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[gray gazelle]

I'd love to bit I think I need to cover it sooner because my classes start in September and I won't have time then

[gray jungle]

if your course is allowing you to join without measure theory

then i suspect its similar to steins book in nature

just reimann integration used

you should ask !

[shy silo]

I love how some theorems in measure theory for like

showing a function is in Lp or something

The way you use it is essentially pretend that they are initially

[gray gazelle]

no it's just a messy situation I don't know what their prerequisites are

[shy silo]

and upper bound the norm

[gray jungle]

you should ask! x2

[gray gazelle]

it's just a messy university I don't know anything but I just enrolled for a masters degree and it will be my first class

I studied CS for my bachelors and I didn't do a lot of math so I need to catch up

I would appreciate it if @gray jungle told me what book to use to cover measure theory in 2 weeks

[gray jungle]

im gonna be honest and tell you that you cant cover measure in 2 weeks

its a full semester course

but folland is a good concise book

[shy silo]

I studied it in 2 weeks but I wouldn't recommend what I did to anyone else

I studied it like it was a full time job

8h a day for 2 weeks cause I missed classes

[gray gazelle]

I mean just a quick overview

[gray gazelle]

isn't measure theory just one chapter in folland?

that's good

[gray gazelle]

isn't it good though?

I'd be happy if I could do that

[gray jungle]

a course in measure theory would be chapter 1-2-3 and 6 of folland

[shy silo]

nop

[gray gazelle]

let's see

[shy silo]

it was basically all I did every day

I had major wrist pain and leg pain

[gray gazelle]

thanks

what about chapter 7?

looks important

chapter 1 is kinda familiar so I can speedrun it in a day

I should challenge myself to cover chapter 2 and 3 in a week

another week for 6 and maybe 7

[loud cradle]

have you actually looked at these chapters?

[gray gazelle]

I was just looking at them

[gray jungle]

those would take a month or two in a course so

you should try to be a bit realistic with your goals

[trail hemlock]

covering 2 chapters of a fairly difficult measure theory book in a week seems dubious at best

[gray gazelle]

makes sense

I will see what I can do

[molten mason]

No no no, let him cook. I want to see this.

Please document your journey.

[gray gazelle]

let's see how it goes, I have no idea how long it's going to take me

[trail hemlock]

scott young?

is that you?

[gray gazelle]

good joke

[molten gulch]

2 chapters of folland in a week is madness

not possible

no matter if you're einstein or tao or whatever

it's just not possible

[gray gazelle]

for clarification this message means I don't know whether those 2 chapters are going to take me a month or two (or more)

not that I might accidentally read it in a millisecond

[gray gazelle]

I think Von Neumann would be able to do it

I think Tao would do it in a day because he already knows what's written there very well (but I get that they meant a version of Tao that doesn't know those topics)

[molten gulch]

yeah

[heady ember]

I can't take you seriously when you have sully in your pfp

[trail hemlock]

mann

sully and I go wayy back

[gray gazelle]

Good luck with your experimentations.

[foggy quest]

and 7 sometimes

[hot gull]

What's the closest book I can get for a quick intro to basic category theory and in-depth discussion of 2-categories?

Looking into higher gauge theory with very little of the required mathematical background so I'm clumsily flailing about.

For the most part, I want to understand the details of gerbes and why they're defined the way they are, if that helps.

[storm tusk]

this obviously isn't books exactly but resources generally so asking here anyway:
any recommendations on active channels like 3b1b? i am familiar w/ lots of youtube channels generally but i particularly like the visual style / aesthetic of his channel. there are lots of channels which use a similar style/aesthetic that have just posted once or twice, likely from his SoME events, but im wondering if there are recs for more active ones?

btw please ping me in replies if you respond b/c i'll likely otherwise miss it among the other messages in this server :P

[hot gull]

Off the top of my head, there's sudgylacmoe, who provides a great introduction to Clifford/geometric algebras (I would recommend not buying into the hype, though), and Physics Duck, who's very QFT-focused.

[covert bane]

sheafification of g and polylog are good

[maiden slate]

What's wrong with the hype

[earnest blade]

Ikr

[torn blade]

vouch for the former

their latest video is so so good

[gray gazelle]

A Guide to Econometrics
Book by Peter Kennedy

[molten gulch]

How is that relevant to the talk of youtube channels currently occuring

[gray gazelle]

very

[molten gulch]

It's not?

[gray gazelle]

sorry

[covert mauve]

does anyone have a book thats mostly self contained and gives me a introduction to linear algebra quickly? i dont really have the time to go through it the formal way.

[foggy quest]

A good book is: https://mtaylor.web.unc.edu/notes/linear-algebra-notes/. Chapters 1,2,3 are linear algebra core. Sections 2.2 - 2.4, 3.7 - 3.8 is skippable for a first pass.

[vital bane]

even he wouldn't be able to do it if he only knew intro real analysis before hand, he too was once a student like us

[regal dome]

I am looking for a book with lots of integrals and/or differential equations

Just in order to do some during the week

[molten gulch]

Any calculus textbook a-la stewart or thomas

[regal dome]

Thank you for your answer but i have already studied calculus and multivariable calculus

I really just want a book with a bunch of integral in it and the same for differential equations

With maybe some methods to solve the problems/exercices

[molten gulch]

Ahhhhh well there's the interesting integrals book and for diffeq there's nagle saff and snider's book

[regal dome]

Okay thank you 🙂

[molten gulch]

Yw :3

[regal dome]

By any chance

[regal dome]

Do you have the exact references for the integral book ?

[cursive orbit]

the "hype" version is usually called "geometric algebra" which a bunch of ppl (usually nonmathematicians) "specialize in" super early and all they do is go posting online to how it should be taught instead of traditional vector calculus

[maiden slate]

Well what's wrong with it tho

I do think bivectors and the wedge product are something that should be taught instead of the cross product

[cursive orbit]

how do you propose teaching wedge product to engineering and biology students who have only had one year of calculus worth of math experience

[molten gulch]

https://www.amazon.com/Interesting-Integrals-Undergraduate-Lecture-Physics-dp-3030437876/dp/3030437876/ref=dp_ob_title_bk
and
https://www.amazon.com/Fundamentals-Differential-Equations-Boundary-Problems/dp/0321977106/ref=pd_lpo_sccl_1/142-5352319-5020651

[regal dome]

Thank you so much

[molten gulch]

you're very welcome

[maiden slate]

You don't need calculus to understand the wedge product

Just motivate it geometrically

Idk what the proper definition is with exterior algebra and all tbh

Just define bivectors as an oriented plane segment

And the wedge product as the plane segment formed by the vectors along their orientation

[cursive orbit]

and how is this easier than just taking the vector perpendicular to two vectors?

[maiden slate]

Idk I always kinda hated how you represent area with a vector

It always felt strange and it took me a while to get used to

Also I can't find this now

But there was some weird integral I did that involved the cross product or curl

[molten gulch]

stokes' theorem?

[maiden slate]

And it stumped one of my classmates but I realized if you saw the cross product ad rhe wedge product it helped me realized their mistake

[maiden slate]

No a specific problem

[molten gulch]

ahhhh

[granite breach]

what is a good book for intro to game theory

and is game theory really maths?

[molten gulch]

yes

[gray gazelle]

i have it for u trust

its called jd william the compleat strategist

it is most simplest I know of

the yale professor that has his classes online recommends a book called thinking strategically

also Gregory Mankiw recommends thinking strategically

but i think jd williams book is easier to understand than thinking strategically

[left depot]

my bad if I'm interrupting something but I'm finishing up abbott's understanding analysis. I love the accessibility and development of intuition in the book. I understand needham's visual complex analysis is somewhat in the same vein, right? And is there a text for something similar for topology?
Bonus points if there's like a big list of approachable books like this for general undergraduate math so I don't have to come back and ask for algebra or something in a year or two

[gray gazelle]

what are the prerequisites for reading understanding analysis

[left depot]

So the prerequisites were basically just calculus, and bonus points for an intro proof course, but it's more or less entirely contained. That's my complaint with it though, I've done proofs for CS theory for a while, so problems like "negate this predicate" are generally skipped. I more just would appreciate a focus on intuition as I find pure symbols dry. I'm kind of looking for highbrow comic books lol

[gray gazelle]

thank you youre very helpful

[left depot]

sure

[gray gazelle]

i also appreciate books that develop intuition

what are some other books you think do a good job on different subjects

"structures and why things dont fall down" is a good intro to mechanics of materials

[left depot]

that's what I'm looking for 😄 I know needham's visual complex analysis is along those lines, but I'd love anything like that for topology, algebra, undergrad number theory, geometry, whatever.

[gray gazelle]

same

[left depot]

there's a book that I love for models of computation though let me grab the name

[gray gazelle]

thank you

[left depot]

@gray gazelle Sipser's "Introduction to the Theory of Computation"

[gray gazelle]

what are prerequisites

[left depot]

discrete mathematics

[gray gazelle]

okay thank you so much

[left depot]

no problem sir

[gray gazelle]

i hate pattern matching memorizing formulas

i only love intuition

and understanding

[left depot]

unfortunately there will always be a bit of that, but intuition is very important

[gray gazelle]

yes

[left depot]

anyway I'd love it if anyone has recs along these lines.

[cosmic bridge]

Hello
I need some recommendations for D-Modul and Galois theory of differential equation books

[remote sparrow]

i recommend using needham's book as a supplement rather than a main text

you can use gamelin's book instead

#book-recommendations message

[shy silo]

this is how I understood what the exterior algebra was

constructive definitions for me are more intuitive

I could not understand it before

[left depot]

awesome! I will certainly be doing that.
Is Munkres the main go-to for topology, or is there another "Needham" supplement for that?

[remote sparrow]

i'm not aware of anything like that for munkres

[left depot]

cool, thank you

[granite breach]

but is it a math textbook or just kinda a reading book?

[wheat remnant]

need book recc's for optimization mathematics

[hollow drum]

Can anybody suggest a reading material for symplectic topology or symplectic geometry?

[tribal crow]

perhaps @modern ruin?

[gray gazelle]

What parts of game theory do you want to have the math in

Thinking strategically doesn’t have calculus in it

[modern ruin]

mcduff-salamon is the standard reference

also da silva's notes

https://people.math.ethz.ch/~acannas/Papers/lsg.pdf

[hollow drum]

Do you know some active topics in symplectic geometry? I saw some stuff about pseudo holomorphic curves. Maybe a lot of research is related to specific topics in physics?

[modern ruin]

mcduff has a whole book on this

https://link.springer.com/book/10.1007/978-3-030-80979-9

it's fairly recent as well

i have not read it myself, but mcduff was pretty based, and was (is) friends with the person who taught me symplectic geometry lol

[hollow drum]

This is perfect thank you so much! And nice

[rough umbra]

sorry for year later ping lol, what by him?

[willow merlin]

best book for algebra

??????

I want to be able to solve this

[vital bane]

this is a linear algebra problem

[willow merlin]

is called algebra here I guess

linear algebra is proof based course

[marsh ingot]

Its linear algebra

[vital bane]

Well if by algebra you mean abstract algebra then yes that does include linear algebra in a sense

but for a linear algebra book take a look at this

#book-recommendations message

[willow merlin]

thanks i will check lang

Hopefully covers orthogonality and direct sum of subspaces

[vital bane]

that is covered in every LA book lol

it's a fundamental topic

I would recommend Friedberg, Insel, and Spence or LADR by Axler (4th ed)

[willow merlin]

what would be the easiest one to learn with?

this lang book is for graduate people

[vital bane]

Friedberg

or LADR

or LADW

[willow merlin]

all of this books is proof based but im engineering is there a simpler version?

[vital bane]

Ohhh

you should've said that sooner

yea of course Gilbert Strang is a great book for that

Gilbert Strang's "Linear Algebra And It's Applications"

though in that book direct sum is introduced in passing in an exercise in the appendix

[burnt sorrel]

a lot of modern symplectic topology is about various forms of Floer theory

I think a good start would be McDuff-Salamon's book on holomorphic curves

(start with the one from the 90s, not the modern version)

so yes this is mostly about pseudoholomorphic curves, Gromov-Witten theory and Hamiltonian Floer theory

in some sense Hamiltonian Floer theory is "global", and there's also a "relative" version called Lagrangian Floer theory

(in general Lagrangians are very important in SG)

so if you're interested in foundational aspects, then there's still loads of work to be done to make the above all work

which is usually either fairly analytic, or some of the more recent stuff is more homotopy-theoretic iirc?

Also, a lot of people are motivated by homological mirror symmetry

which (roughly) says that for each CY-manifold X, you have a dual Y, and you have equivalences between Fuk(X) and DCoh(Y), and DCoh(X) and Fuk(Y)

where Fuk(X) is the Fukaya category of X

[sudden kindle]

His complex analysis book

[burnt sorrel]

lots of handwaving here btw, the Fukaya category isn't actually a category, and you want something like an equivalence of triangulated categories or smth like that?

so this side of symplectic topology is very "algebraic", so there's invariants which are built topologically, but you also need loads of homological algebra and category theory

[burnt sorrel]

actually step -1 would be to learn Morse theory, cuz Floer theory is like morse theory on the free loop space, so knowing the finite dimensional version is pretty useful for motivation

there's also lots of interesting stuff going on with contact geometry, and also with dynamical systems, but I don't know anything about it (and I'm not sure they would call themselves a symplectic topologist)

[burnt sorrel]

There's two good survey articles if you want to get the vibes of this area, there's one by Denis Auroux and one by Ivan Smith

in general though, imo a lot of modern symplectic topology is extremely technical, and so it's very easy to get lost if you don't have someone guiding you

as far as I can tell, maybe apart from Seidel's book, everything in the area from like the 90s to now aren't really in any book, mostly just in various papers

(warning: I haven't read the mirror symmetry books, so idk what they contain)

[burnt sorrel]

actually what I've just written is basically the complement of what this book contains lol

so the union covers a decent chunk of modern SG research

[deft thistle]

does anyone know what subjects aops algebra book covers? I am thinking about start to read but idk if it is below my level

[gray gazelle]

any book recommandation for perosnal statement?

@everyone

[molten gulch]

Why are you trying to do an everyone ping on a server with 200k people. Wouldn't you expect that the mods would have disabled that functionality?

[gray gazelle]

i was jk lol

[molten gulch]

beyond that, there's no books on writing a personal statement, it's meant to be unique and represent you and who you are

[molten gulch]

Don't. Do. That.

[gray gazelle]

can u suggest me a book that contains cool mathematical thoeries?

[molten gulch]

by mathsmaticla do you mean "mathematical"

[gray gazelle]

yes. thanks for the correcting my error

[molten gulch]

Well I can't think of a book of theorems but there's Aigner and Ziegler's "Proofs from THE BOOK" if you want something to go over some cool theorems and proofs

[gray gazelle]

hmm ok i will have a look at that

ty for the recommendation

[foggy quest]

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

[gray gazelle]

there is a book called influence by robert cialdini and a book called how to win friends by dale carnegie

will teach how to effectively communicate in a good way

https://scottadamsblog.tumblr.com/post/129784168866/the-persuasion-reading-list

scott adams blog on books he recommends for persuasion

[rain hound]

Influence is a really good book.

[gray gazelle]

yeah it is really good

[gray gazelle]

do you think it helps on a personal statement

i dont know much about those

[rain hound]

For feedback on personal statements I trust my advisor and a friend who’s a really good writer.

[gray gazelle]

nice

[gray gazelle]

thanks

thats much more efficient than reading 10 books on persuasion

even though i believe its a skill worthy of developing in life

[gray gazelle]

woah okkk :)) if u have any more.. plz share :))

i think those are it

i learn persuasion and i dont know anymore good books besides those on the blog

i think sales and marketing is fake so i discount those type of books

[rain hound]

In general I think a book on scientific writing is good. My class used Hofmann Scientific Writing and Communication: Papers, Proposals and Presentations

[gray gazelle]

any book reccomendations for 7th and 8th grade math?

[mossy flume]

personal statements for graduate school?

If so do what armadillo said

ask your letter writers / people you trust for feedback

[trail hemlock]

yes the aops calculus book was specifically made for comps

[torn blade]

does anyone have good lecture notes or books on representation theory?

[hollow peak]

Humphreys, Fulton-Harris are both great rep theory books

Fulton Harris in particular is huge, I think it's considered a standard reference

[torn blade]

are these decently beginner friendly? like is a good understanding of group theory and linear algebra enough

[hollow peak]

I would say you could get by if your understanding is good

[river rock]

"representing finite groups: a semisimple introduction" by sengupta

[foggy quest]

Try https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/

[keen vale]

what book is recommended for calc 3? bonus point if it also includes a refresher on calc 2

[cursive orbit]

when I TAed calc 3 we used Stewart, which also includes 1 and 2

[dapper root]

The class I just taught was outta Stewart

Calc 3

[keen vale]

i see. is it suitable for self-studying? i am prepping for uni, and according to my syllabus i would have calc 3 on year 2 as a cs major, so i wanted to get a headstart

my calc course during hs missed out on some stuff like series and sequences, improper integrals and taylor

[trail hemlock]

stewart is very gentle

really good for self stidy

[keen vale]

alright thanks!

[cursive orbit]

it's pretty suitable

[crude belfry]

Spivak

[trail hemlock]

🫵 ew

its you

[crude belfry]

Bros shocked to see I exist outside of post-ap-math 😭

[trail hemlock]

rattled me to my very core in fact

[junior isle]

Is it feasible to go through lee's book on topological manifolds with real analysis and linear algebra only as a background?

Supplementing where needed on algebra

[tribal crow]

yes

this is what I am doing rn

[junior isle]

Is it worth it?

[tribal crow]

depends on your goals

[junior isle]

The content seems cool

[junior isle]

Learn topology and manifolds

[cursive orbit]

I mean I thikn the content in there is pretty important no matter who you are

[tribal crow]

then it is a great book lol

[tribal crow]

yes, but if you have no interest in, say, manifold theory, then there are better topology books

I do have interests in manifolds, so that's why I'm reading it

[cursive orbit]

I mean even if you are trying to do algebraic topology or algebraic geometry you need to know about manifolds

[tribal crow]

I meant the people who want to do say, descriptive set theory

I probably wouldn't recommend ITM to somebody who's not interested in anything geometry/topology

[mossy flume]

haven't heard of that book

but that's a BANGER of a title

[trail hemlock]

you know its gon be hard when the author doesnt trivialize the entire subject in the title

"semisimple" instead of "a brief introduction" 😨 😱

[rough umbra]

What can I read to learn about hopf algebras?

o nvm, W, ty

[gusty smelt]

lol nice, btw if ur into this stuff, mike brannan my advisor is an expert on this

[rough umbra]

Is this also good for someone not super interested in the physics applications of them?

[gusty smelt]

and he takes a lot of UG students

yeah

[rough umbra]

Lmao coincedence ill dm u

[gray gazelle]

Hi i like manifolds how do i study starting from pre algebra

also real analysis (just figured i have no talent in Physics)

[trail hemlock]

that’s a pretty big leap

pre algbeta to manifolds

[stray veldt]

how would you even know what a manifold is...

probably finish khan academy first, then come back and ask again

[trail hemlock]

look at dani’s recs in the pins

i like rudin but abbott and tao are good choices

[gray gazelle]

what the fuck do i finish in Khan Academy

[gray gazelle]

who's dani?

[signal mountain]

pre-alg, alg, precalc, calc

[gray gazelle]

can i do aops volume 1?

[marsh ingot]

To know the basics before manifolds, since is a long path from pre algebra to manifolds

A very long path

[trail hemlock]

dami. sorry

[cobalt arch]

I think they are looking for a roadmap from pre algebra to manifolds. That isn't a strange request at all. First learn pre-algebra -> algebra and trigonometry -> single variable calculus (differential and integral calculus) -> multivariable calculus -> linear algebra -> real analysis and abstract algebra -> point-set topology -> classical differential geometry -> differential topology (manifolds)

[marsh ingot]

Yep but it will take so long

[gray gazelle]

for learning the Algebra can i do the Aops volume 1 by aops?

[cobalt arch]

I don't know if it covers the standard material but most probably it does so yes, do you have a good foundation in pre-algebra?

[gray gazelle]

yes

[cobalt arch]

Okay then read that book, use Khan academy as well, it a good resource up to calculus

[gray gazelle]

oh ok

why cant i send pics

[cobalt arch]

I think you can't send pictures in this chat

I don't know why

[gray gazelle]

Chapter 1: Problem Solving
1.1 What is Problem Solving?
1.2 Working with Numbers
1.3 Algebra: Setting Up Equations
1.4 Using Inequalities
1.5 Induction
1.6 Special Tactics
Chapter 2: Exponents and Logarithms
2.1 Exponents
2.2 Logarithms
Chapter 3: Numbers and Operations
3.1 Numbers and Number Systems
3.2 Divisibility
3.3 Bases
3.4 Fractions
3.5 Operations on Fractions
3.6 Modular Arithmetic
Chapter 4: Algebra
4.1 Factoring
4.2 Expanding
4.3 Equations
4.4 Quadratic Equations
4.5 Complex Numbers
4.6 Polynomials
4.7 Special Tactics in Algebra
Chapter 5: Counting
5.1 Counting Techniques
5.2 Permutations and Combinations
5.3 Binomial Theorem
Chapter 6: Probability
6.1 Basic Probability
6.2 Advanced Probability
Chapter 7: Number Theory
7.1 Primes and Divisibility
7.2 Greatest Common Divisors
7.3 Diophantine Equations
7.4 Euler's Theorem
7.5 The Chinese Remainder Theorem
Chapter 8: Inequalities
8.1 Linear Inequalities
8.2 Quadratic Inequalities
8.3 Absolute Value Inequalities
Chapter 9: Geometry
9.1 Points, Lines, and Angles
9.2 Triangles
9.3 Quadrilaterals
9.4 Circles
9.5 Polygons
9.6 Area and Perimeter
9.7 Volume and Surface Area
9.8 Coordinate Geometry
9.9 Trigonometry
Chapter 10: Trigonometry
10.1 Trigonometric Functions
10.2 Trigonometric Identities
10.3 The Law of Sines and Cosines
Chapter 11: Functions
11.1 Basic Functions
11.2 Compositions of Functions
11.3 Inverse Functions
11.4 Graphing Functions
Chapter 12: Sequences and Series
12.1 Arithmetic Sequences
12.2 Geometric Sequences
12.3 Series and Sums
Chapter 13: Intermediate Topics
13.1 Vieta's Formulas
13.2 Complex Numbers in Polar Form
13.3 De Moivre's Theorem
13.4 Miscellaneous Topics
Chapter 14: Competitions
14.1 Math Competitions and Preparation
14.2 Selected Problems and Solutions

this was the volume 1

[cobalt arch]

It covers some extra material like combinatorics (counting), probability and number theory. You can skip these if you want

[gray gazelle]

oh ok

[cobalt arch]

Also I don't know about the geometry chapter but it might be good to know some geometry

I think it will be good so read that

Then there are many standard books for learning calculus properly, I think you will need another book which covers up to multivariable calculus like Stewart if I am not mistaken. You can skip parts of Stewart if you have covered them already in the AOPS book

For linear algebra Friedberg, Insel, Spence is a good mix between applied and abstract linear algebra

[cobalt arch]

For real analysis maybe do Spivak's Calculus first if you are not that good with proofs and then elementary real analysis and real analysis by bruckner, bruckner and thomson is good and comprehensive and then for a more compact presentation try Rudin's Principles of mathematical analysis and/or Browder's Mathematical Analysis. For abstract algebra try pinter and then Artin and/or Dummit and Foote. For point-set topology munkres is the standard text (it also covers algebraic topology which might be good to learn). For classical differential geometry pressley is good and lastly for differential topology maybe try Milnor's Topology from a Differentiable Viewpoint, and then An Introduction to Manifolds by Tu and then Lee's Introduction to Smooth Manifolds

You can skip some chapters of a text or texts if you have already covered them previously

Maybe William Fulton's Algebraic Curves, An Introduction to Algebraic Geometry?

[marble isle]

Hello! i have just completed Hung-Hsi Wu's book "Algebra and Geometry", and would like to start calculus. Any recommendations? (I find Hung-Hsi Wu's texts quite dry, so i do not plan to read his text on calculus)

[molten gulch]

Stewart's Calculus
Thomas' Calculus
Strang's Calculus

Spivak's Calculus (A bit advanced and dry)
Apostol's Calculus (also a bit dry AFAIK)

[marble isle]

I hear the first three dont cover any proofs, or at the very least, dont include any in their questions. i would prefer to not go that way. Do you have any recommendations that are relatively rigorous yet not awfully dry?

[molten gulch]

You could try an analysis textbook but I fear a bit that unless you've had experience with doing proofs and a bit of set theory you would struggle

Abbott's Understanding Analysis
Rudin's Principles of Mathematical Analysis
Tao's Analysis I and II

[signal mountain]

there's also tao which is quite gentle

but spivak or apostol is probably most appropriate

[marble isle]

i think i have had some exp with proofs, hung-hsi wu's book is pretty proof-focused, and i can solve most questions in serge lang's basic math

i have not checked out any analysis books, mostly under the fear of them being too hard and ruining any motivation i have.

[molten gulch]

yeah this book does have some proofs, but we'd recommend still keeping something like Hammack's book of proof (freely and legally available online) beside you and maybe going through an analysis textbook

[marble isle]

which one would you recommend for someone who has never been introduced to calculus, though? would rather not get a book thats just "introduce 500 lemmas; prove 500 lemmas; solve questions"

[molten gulch]

that's how most advanced texts go

as you go up the math ladder this is how it goes

we can only really think of computational books for ODE's, Calculus, and Linear Algebra

if you want to see the machinery, you'll see all of it

[marble isle]

well, i meant in relative terms, which would be the best?

[normal crystal]

that book is primarily meant for the education of HS teachers, probably part of why you felt that way

[marble isle]

figured, thankfully the author isnt too focused on the teacher aspect, so i could still read it and solve the problems.

[worldly nimbus]

What is a good pre calculus and calculus book

[sand path]

Currently using Lang & Axler for PC self study. Both are good

[worldly nimbus]

Really just acing everything

[molten gulch]

That's not possible

there's too much to learn for one lifetime

[worldly nimbus]

I mean getting really good at math

[molten gulch]

name the specific fields you want to work in

[worldly nimbus]

Idk

Yes I’m 16

Misclick

I mean 16

I clicked with the wrong finger

I’m on mobile

Almost

[molten gulch]

Then just go through calculus

don't worry about other fields yet

[worldly nimbus]

The university books would be great

[gray gazelle]

Idk if this is the right spot to ask, it is about free (quality) courses eventually including certificates - which is recommended?

[gray gazelle]

coursera and edx offer free courses in many subjects from large universities

to get the certificate you have to pay like $60 each time

[gray gazelle]

is SL Loney good for decent trigonometry

[left spade]

https://prnt.sc/d8VLk1n3sEXg

what is the book in this meme?

[molten mason]

States of Matter by Goodstein

[left spade]

thank you!

[sand lion]

Does anyone know any good college algebra textbook I could get as a PDF online?

[molten gulch]

The only one I have in my folder that's legal to acquire is Stitz and Zieger's Precalculus

[sand lion]

Does that cover college algebra? And is it a excellent book?

[molten gulch]

I'm not very familiar with the quality, we'd assume it's pretty okay; college algebra is a subset of precalculus mainly

[sand lion]

Where could I take a look at it? If you don't mind

[molten gulch]

https://www.stitz-zeager.com/szprecalculus07042013.pdf

[sand lion]

Thank you

[molten gulch]

there's also the openstax project and khanacademy for videos and problems

[gray gazelle]

what is a good graduate textbook in set theory?
including interesting problems , open problems and so on.
(especially a book which some material is left as exercise)

[gray gazelle]

Jech?

[molten gulch]

We thought jech was late undergrad

[gray gazelle]

no way..

[remote sparrow]

jech and kunen

[woeful rock]

It worth to read the Euclide's Elements to study formal maths, or there are better modern books to study Euclidian Geometry (no Analitical)?

[glad rampart]

there are better books

[woeful rock]

For example, David Hilbert's Foundations of Geometry it could be a better way to start? Or it is to advance for a first study of Euclidian Geometry?

[floral lantern]

Has anyone read Quantum Theory, Groups, and Representations by Peter Woit?

Doing an independent study this year on it and wanted to know thoughts

[molten gulch]

much better

[remote sparrow]

@glad rampart have you read the webfiction i recommended to you?

[glad rampart]

which one was it

[remote sparrow]

https://www.royalroad.com/fiction/72771/depthless-hunger-underdog-strong-to-stronger

[glad rampart]

i havent

i have read pgte twice though im not sure who recommended that one to me

i should reread wtc

[willow merlin]

Can i ask for lots of algebra booka

Books

From algebra to linear algebra

I have failed two times this linear algebra course and I'm not planning on failing again

Recommend me material and i will read

Its undergrad level with very few proofs other than basic

So if you can recommend me engineering linear algebra i would be happy

A deep explanation on subspaces aswell as manipulating them would be useful

[winged bluff]

post syllabus

[night prism]

Hey does anyone have a physical or digital copy of Apostol’s calculus?

Looking for a screenshot of a page

[willow merlin]

Me in spanish

Physical

[night prism]

Works

I just need an exercise

[night prism]

Page 20 please (if first edition)

Oh wait

That’s the second volume

Do you have volume 1?

[willow merlin]

I only have volume 1

Lmao

My bad i didn't specified which apóstol

[willow merlin]

Just vector spaces, linear transformations complex numbers and polynomials and diagonalization

I don't see any syllabus posted anywhere so that's what i can say

[night prism]

I think you mean volume 2

[willow merlin]

I am not passing algebra any time soon

[night prism]

Those are covered in vol 2

But, thank you!

[winged bluff]

during exams, do they ask you to prove stuff, or just calculations?

[night prism]

Weird!

[willow merlin]

Computations but hard

[night prism]

Does it have concepts of integral calculus, etc..?

[willow merlin]

Yeah

Volume 1 first page starts with integrals

[night prism]

Oh, then maybe it is the same

Is that first or second edition?

[willow merlin]

Doesn't say

Its in Spanish

I guess first

[night prism]

Then it’s first

Perfect

Can you send section 1.15 please?

[willow merlin]

This?

About the existence of square roots for non positive real numbers

This is the back of the page of you still need it

[winged bluff]

This looks kind of hard. But one can reduce the problem significantly through RREF. I TA'd two years linear algebra classes, and at this level you can do almost everything with RREF. For example, you RREF T to get that T is actually spanned by 2 vectors. For S, S is the kernel of a linear transformation and you find it by RREF too. So basically you have to get really good at RREF.

[willow merlin]

Yeah exactly

Dimension of T is 2

After rref yeah

But i still fail

I need more theory

Otherwise you don't know when to rref

But yeah

Idk of S is kernel of linear transformationim not sure about that

But if u TA i trust yo ass

[night prism]

Thanks!!

[willow merlin]

I want to be ta aswell but I suck at algebra

Maybe if i manage to pass it

Lmaoo

[winged bluff]

https://yutsumura.com/linear-algebra/

[winged bluff]

The best thing you can do I think is see lots of problems with solutions from previous years of the course at your university. If you can't find those, see lots of problems and solutions like in here:

[willow merlin]

We have lots of problem but no solutions

I will give that website a try and overall do more solution search

Ah you said kernel because both equations are homogeneous

For S

I don't want to derail but its just something that came to my mind

[winged bluff]

By kernel I mean null space

[willow merlin]

Yeah i was confused

Since kernel is dim of nullspace

[winged bluff]

https://en.wikipedia.org/wiki/Kernel_(linear_algebra)

[willow merlin]

Oh no its not

Kernel and nullspace are equivalent dimension of nullspace is nullity

Im blaffing I'm sorry i think we derailed because of my fault

Anyways i will give that website a try

With a little bit of luck maybe i pass algebra this semester

[winged bluff]

Good luck. If you see a bunch of ugly vectors, ask yourself "Should I use RREF on this?" and the answer will most likely be yes.

[rough umbra]

@gusty smelt Bell said to to read Hopf Algebras and Their Actions on Rings by Montgomery

we were talking abt an algebraic perspective last night

thought youd be interested maybe

[gusty smelt]

i see, thanks i might check it out

[gray gazelle]

Is linear algebra a good algebra book for university**?** Preparing in a didactic away**?**

linear algebra is not a book , is a branch of math
i guess you are asking for university algebra

I am sorry my brain dead my mom was talking.

I have linear algebra book I want Algebra

and maybe, but better is to begin by a university algebra book, rather than only linear algebra

I have linear algebra and its aplications..

[gray gazelle]

oh nice book

[stuck zephyr]

linear algebra is different

[gray gazelle]

But after I have been toold that I need algebra for the first semester

yeah

I just realised I wasted 1 month

200 page

Now I am studying Computer Science...

[stuck zephyr]

algebra like 1?

[gray gazelle]

but sometimes algebra is called for a lot of introductory topics, rather than just linear algebra

Idk 😭

But for Semester 1 what do i need?

In my curricula it says only algebra...#

[stuck zephyr]

there's abstract algebra if that's what you want

[gray gazelle]

what degree?

[gray gazelle]

Computer Science

lol, can be the two

well mmmh

still depends if the university is like more pure or more applied

😦

what comes after in the curricula

[gray gazelle]

pls let me search it again and send it

Stay here.

ok

[gray gazelle]

Cant post photos...

Can I dm?

mmh, but any ways there are two options, and in both cases is good to follow a path

ok wait look

first , there is this sort of precalculus which is taken as algebra

Algeber

Informatic

Entry on programming

Science

Entry on Economy

I recommed you

Civilisation History

oooohhh

Academic Letter

I think I know that type of algebra is

Digital logic

and probably is not linear algebra

Tecnic English

it is probably pre-calculus

Discrete math#

Programming on C++