book-recommendations

[crimson leaf]

Most print shops I know won't print copyrighted material

[night prism]

Im not opposed to that, although I much prefer physical copies. My entire comment was prefaced, however. In any case, you could likely still find used copies for less than printing and binding independently.

[runic hatch]

Yeah for some common texts there may be quite a few used copies floating around

Fwiw Jacobson’s Basic Algebra series is also reasonably cheap, even for a new copy

[night prism]

Dover makes some really nice reprints too.

[runic hatch]

Yeah

[gray gazelle]

Has anyone read zorichs mathematical analysis before

If so would you reconnebd it

For self studying

[heady ember]

Look at pinned

[gray gazelle]

thanks!

[sage python]

@gray gazelle you keep asking about different books on the same subject lol

Schroder

I have thought about this extensively

Schroder is the right answer

[gray gazelle]

I like studying with many books

Maybe tgats why

I studied analysis with like 4 books

[runic hatch]

Well ig you can add schroder to the list

[sterile remnant]

Thoughts on Analysis by Browder?

[gray gazelle]

Btw isnt schroder undergraduate analysis?

Im talking about neasure theory analysis here

[heady ember]

Dami loves Schroder

[runic hatch]

There’s a recent pin by Dami on measure theory books

[heady ember]

That's what i was gonna say lol

[gray gazelle]

Oh okay

Maybe i should check that one out

[runic hatch]

Yeah

[gray gazelle]

Btw my review on analysis books that i used

Abbott: friendly introduction but not as easy as it seems recommend it to be used alongside more difficult and sophisgicated books

[sage python]

Schroder does some measure theory actually

[gray gazelle]

Zorich: explanations are gold tier and examples are very good but exercises are quite difficult and had no resources, solutions. Use it for explanations

[sage python]

But it's not dedicated like the others

So it's undergrad analysis and a bit of measure theory, but prob not a ton on e.g. Lp spaces

[gray gazelle]

Lang: used it for problems since it has full solutions manual. If you like langs style i think youll like it

[sage python]

lumi it works better if you write it as one block

[gray gazelle]

Oh okay

Ill write it again later on

[sage python]

Unironically I think it makes almost all analysis books obsolete

[sage python]

Pretty solid

[gray gazelle]

Ive r ecently found a good book by haggarty

Dunno why it isnt more popular

[sage python]

BUt yeah I suggested Schroder to you after you mentioned Amann-Escher because iirc they're at almost the same level

[gray gazelle]

Called fundamentals of mathematical analysid

It also has full solutions

[gray gazelle]

Amann escher had very good explanations

But unfortunately lscked resources

Like solutions or syllabus

I think books like amann and zorich could be used as a book for learning with other problem book alongside

[sage python]

I just meant like

When you were asking about that

I was like

Oh you're asking undergrad analysis

[gray gazelle]

Welp ive taken course in that just last semester

So yeah im not asking about that

But anyways im kinda textbook nerd

I have interest in the industry and various hidde gems

[crimson leaf]

I think I'm gonna Speedrun book of proof then try Tao and Schroeder and see what this Dami hype is about

[sage python]

Lmfao

LosAngeles I c u

[night prism]

🤘

[gray gazelle]

Also I enjoy learning math alone

And from my experience solutions help tremendously for that especially first time learbers

[night prism]

I’m starting to find book recs are an extremely tricky business

[heady ember]

what

[lime sapphire]

@sage python have a look at garling's analysis

[sage python]

Idk it

[gray gazelle]

What are the prerequisites for sipser's intro?

[lime sapphire]

Thats why i said to have a look...

[orchid musk]

what would be a good beginner measure theory book?

[coarse frost]

read pins here

[vital bane]

ah yes, measure theory for preschoolers

[gray gazelle]

although it seems to be a bit obscure

I found out J yeh's book to be good

also one of the biggest advanatage of that book is that it has solutions

[orchid musk]

oh that'd be sick, i'll check it out. thanks

[brittle breach]

Axler, Royden, Rudin
that's three

[gray gazelle]

Wait

I dont think rudin is for beginners

Papa rudin

[runic hatch]

Do you have intro real analysis down?

[brittle breach]

I believe it's the most famous measure theory book, that's why I included it

[balmy flume]

Anyone know of where I could find solutions to Schroder's analysis book?

[gray gazelle]

I don't think it has solutions

unfortunately

[balmy flume]

are there any blogs or websites?

that have some

is there a equivalent schroder book(I really like the pacing), but with solutions?

[sage python]

I'm not too familiar with analysis books with solutions, I feel like the further you go in math the less common that becomes

[gray gazelle]

serge lang's undergradaute analysis

abbot analysis 1st edition

ross analysis(tho its way too easy compared to otherss)

rudin analysis

kaczors problem book in analysis

wade analysis(it is not very good tho)

tell me if there are other analysis books

I really liked Zorichs analysis but it has no solutions whatsoever

I recommend using it for explanations and use other book for problem

[lime sapphire]

Apostols analysis has solutions

[coarse frost]

yess

apostols analysis is great

[gray gazelle]

isnt it in chinese tho

the english version is written by a student I think

[lime sapphire]

Its not though

Apostol is American, no?

[gray gazelle]

yep he is american

but chinese have gathered its own professors

and created their own version of solution

if you have link to official solution guide can you provide it for me

i need it

[lime sapphire]

Not sure about official english solutions

But uhh if there's solutions that are agreed upon they should be fine

[gray gazelle]

oh okay

[mystic orbit]

Rudin got solutions handbook iirc

[quiet forge]

Me and the Lebesgue measure of things.

[mystic orbit]

Not at all

The art and craft of problem solving is significantly harder than AoPS

Hmm

Actually, I might've misread a bit

I meant volume 1 since it was the one I checked out

Yeah

Haven't checked that one yet, sry

I've only seen first chapter and it's pretty good

I've read that it's definitely a good prep

Basically, after finishing it you'll only need to do more problems

Not really

I'm pretty sure the art and craft is all you need

(And, ofc, doing more problems)

[gray gazelle]

btw can I ask which book did you use for complex analysis

[alpine rover]

is Godel Escher Bach worth the read?

[hallow oriole]

ya

[gray gazelle]

Has anyone used books by shirali

Like metric space

And multivariable analysis

[sterile remnant]

What's a good Complex Analysis book? Is Serge Lang's one good? Any others?

[runic hatch]

There’s a list of recommendations in the pinned messages here

[gray gazelle]

It has a full solution manual

which is a good thing

I've heard its one of the better lang books

and I am doing pretty fine with it

though the explanations aren't the easiest

I'd recommend you Freitag's complex anlaysis

its by far the best math textbook i've seen til now

this book also has solutions

[sterile remnant]

Freitag seems more focused in Number Theory am I right? I'm not too interested in number theory

[gray gazelle]

the thing is

first volume does offer examples from number theory

but it is not the amin focus

also the book has very very good explanations

Can somebody recommend me a book with challening math questions

if you are interested in fourier, then I'll recommend Stein& Shakarchi

but it does not have any solutions

theres also dover book by robert ash and it has solutions

[sterile remnant]

I see, noted

thanks!

[unkempt hemlock]

Hey graduate math student here. Do you know any good casualish math books? My graduate textbooks are too dense for me and I feel that I don't learn anything from them. I want something I can "eat" fast and have fun doing it. Anyone knows something like that? Did anyone had feeling like me?

[normal sandal]

Inside Interesting Integrals is always a fun read

[gray gazelle]

is the book measure sintegrals martingales

a measure theory book or probability theory book

[hearty steppe]

Yes I’m so happy that I’m not in a graduate math program yet for those reasons alone 🤣

Some high level stuff I kinda understand but definitely not at the point where I rigorously understand enough stuff rn

You don’t really eat fast, when you get to that level, many Graduate level texts operate at a pace that assumes you covered your foundations rigorously

I remember trying to get through Diestel’s graph theory and peaked at a couple other texts. There may be like a foundational chapter that helps you familiarize with notation and stuff but it’s not much to work with

[robust iron]

is there like a definitive agreed upon calculus book that covers 1-diffeq that is useful and interesting at the same time?

[hearty sluice]

Undergrad?

[robust iron]

yeah

[robust iron]

undergrad mhm

[whole spade]

Could someone recommend me a book on mathematics?

[crimson leaf]

That is very broad what kind of math are you looking for

[whole spade]

Basic math, algebra/equations and formulas

[crimson leaf]

For the basics khan academy is good

[whole spade]

Obrigado

Thanks*

[whole spade]

kkkkk

[gray gazelle]

does anybody know of any precalc book that goes into details and with proofs?

[crimson leaf]

Might be interested in basic mathematics by Serge Lang

[gray gazelle]

ok I will try it, thanks

[runic hatch]

It’s not a book, but I’d recommend Paul’s Online Notes for this

[heady ember]

Spivak's Calculus (if you want it a bit more proof based, as in the exercises)

But yeah for computational problems and learning the ideas of the various theorems, POMN is good

[hearty sluice]

looks like spivak doesnt cover diffeq

based on google and ToC

[crimson leaf]

It's also not for the faint of heart

[heady ember]

Yeah its a calculus book, not a differential eqn book

[heady ember]

Yeah, spending hours on a question is normal

[cedar ridge]

ctrl + f POMN and you're the only guy saying it - what does it mean

[heady ember]

POMN ==> Pauls' Online Math Notes

[gray gazelle]

prax moment

[unkempt hemlock]

What's prax

[gray gazelle]

Not agreed upon, but Differential equations and boundary-value problems (5th edition) by C. Henry Edwards covers everything you'd do in an undergrad ODE course and more

[normal sandal]

[gray gazelle]

so how's life @normal sandal

committing to warwick?

[robust iron]

@heady ember @runic hatch thanks, gonna bookmark pauls online notes and look for spivaks calc online 🙂

@gray gazelle ill check that out aswell

[gray gazelle]

sure thing :D

[gray gazelle]

Anybody read Scheinerman discrete mathematics?

[gray gazelle]

Which books for math for finance

Does not require background on stochastic calculus?

Or should I wait until I learn stoc calc

[cunning crater]

any good books for learning master theorem (determining run time complexity)

[gray gazelle]

Hey, would like a recommendation on discrete math. An introduction that covers the topic extensively. Thanks

[gray gazelle]

use book by rosen

it also has solution manual

[oak pecan]

most of the books on the subject are basically intro to stoch calc. if you want a math book (theorem/lemma/proof) try Oksendal or Shreve. for something more "physics-y" with handwaving and intuition, try Baxter and Rennie

[gray gazelle]

shreve has 2 different books

one is stoc calc for finance

one is brownian motion and stoc calc

which one would be for me

[river tangle]

guys any book for quantum mechanics from beginning ?

[cursive orbit]

clrs has it

[gray gazelle]

?

[cunning crater]

thanks

[oak pecan]

karatzas and shreve is more advanced, and not a book you'll probably want to pick up as an intro to stoch calc if that's the one you meant

[gray gazelle]

oh okay

maybe I should go for finance one

[balmy citrus]

Does anyone have any good resources on interpretability in first order logic? That is, translating one first order language to another. I am reading Enderton’s intro to logic currently and he only briefly touches on it and I would like to know more. I thought it was really cool how you can embed arithmetic in set theory and use the same argument as in arithmetic to deduce the incompleteness of it.

[gleaming pulsar]

,help

[hasty eagle]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[stark kestrel]

Does anybody have a book(s) they would recommend for studying vector calculus?

[heady ember]

You could try Pauls' Online Math Notes, I believe it does cover it. Though yeah it isn't a book

[hearty sluice]

im starting to think you're paul doing some undercover advertising

[runic hatch]

I mean it is a good resource

[hearty sluice]

no doubt

[runic hatch]

I also shill his site a bunch too tbh

[crimson leaf]

I like his notes overall but some parts I'm not a huge fan of

[gray gazelle]

Opinions on Lang's "Introduction to Linear Algebra"? Obviously 'it's Lang'.

[cedar ridge]

@sage python why a "lol" for Roman linear algebra 🧐

[heady ember]

Im not that old

Nor do I have that much mathematical knowledge, like a professor would

[hearty sluice]

That's exactly what undercover Paul would say

[heady ember]

[gray gazelle]

Paul would tell you to go to class. These notes are no substitute!

[gray gazelle]

what are the best books/resources to learn ODEs?

and functional analysis

[finite thorn]

Is "A Classical Introduction to Modern Number Theory" a good introduction to the subject? I see it starts off smoothly but then transitions into more advanced topics.

[manic cairn]

Yeah, I would say so

[finite thorn]

Ight, what are the requirements if ya know that?

The preface doesn't seem to talk much about them

[manic cairn]

Nothing but some basic abstract algebra at first, and later on you may want to know some complex analysis to work with zeta functions

[finite thorn]

Gotcha, thanks

[lime sapphire]

Don't they all?

[finite thorn]

I mean, it goes from defining primes to this in 35 pages so it's a bit sudden lol

[lime sapphire]

Lmao

Fairs

[manic cairn]

Those are just a direct sums and products, which you should learn about in a good abstract algebra course

[finite thorn]

Yeah know the symbols, just that I haven't gotten to that part in my AA book yet

So I'm kinda iffy about starting reading rn

[balmy monolith]

guys any recommendations on classic physics?

[coral narwhal]

it has undergrad algebra as a pre-req

[gray gazelle]

what do you mean by that

if you mean university physics

than I recommend young&freedman

I am currently using it and its very ggood

[gray gazelle]

whats a book with some interesting math problems to try and solve

[coarse frost]

Hartshornes Algebraic geometry

(this is a joke, dont try this book)

[wheat otter]

If you mean classical mechanics, lagrange equations and such: goldstein

[earnest gazelle]

what do people here think of axlers measure theory textbook?

[unkempt hemlock]

Any measure theory book full with exercises? Asking for recommendation.

[gray gazelle]

if you mean pre lagrange equations, kleppner and kolnekow

[crimson leaf]

I think gristle recommended it to me so he might have some words @remote ginkgo

[fringe orchid]

I suck at mathematics even though I love its complexity and would love to be able to fully understand what all these strange symbols means.
Could someone recommend me a book to relearn mathematics from the scratch..? I lost most of my knowledge in mathematics once COVID-19 started.

[unkempt hemlock]

Try looking for books about precalculus

[fringe orchid]

Alright!

[remote ginkgo]

good easy doesnt concern itself with the multi dimensional case

because that case is completely obvious

it's the perfect measure theory text

[earnest gazelle]

4.7/5 on amazon, it must be good

[heady ember]

Look in pinned

[whole mango]

You could use openstax

[faint imp]

I'm self study linear algebra with linear algebra done right; is there anything that I should watch out for, or are there any good supplement materials?

[wanton pilot]

Any great graphic novels about maths/history of maths?

I read logicomix a few years back and absolutely loved it

[slim peak]

https://twitter.com/gro_tsen/status/1539586727878266881

Gro-Tsen (@gro_tsen)

I think this deserves a retweet in English: the Société Mathématique de France is making feely available online all its books published before 2020; later books will be made similarly available when their sales reach a certain threshold. https://t.co/ChoL0F4RtD

Twitter · Jun 22, 2022, 12:30 PM

[foggy relic]

LADR doesn't do determinants

I would rec Linear alg done wrong which is like also proof based and is a good book

[cursive orbit]

it does, at the end

main thing I'd make sure you know how to do is actually compute things

[foggy relic]

I mean it dosent do stuff in terms of determinants

[cursive orbit]

know how to row reduce, how to diagonalize by hand, how to compute characteristic polynomial

[drifting wigeon]

never understood axlers hate against determinants

[marble solar]

Look at the Frenchies; they know they've lost the culture war against the Americans, yet the situation is worse than that -- they lost to the English by proxy. Now they're trying to compensate. SAD

[slim peak]

Haha

True

[compact crypt]

how useful do you think are problem books in analysis

I plan on solving them instead of problems books I use for learning

from

[serene atlas]

Anyone have book recommendations on 11th grade math?

[rich sequoia]

Spivak calc

[faint imp]

thanks! my school actually uses that text book - will check it out!

depends on how fast you work - took me a bit less than a year...

[foggy relic]

Yeah agniv told me lol

[mental flare]

Guys, which is the best pre calculus textbook for self study?

[faint imp]

oh wait didnt know you were here too lmao

not all the problems - I picked the ones I liked

[foggy relic]

I am everywhere.

[mental flare]

Is the "pre calculus for dummies" a good book?

[hallow oriole]

you want Stewart's Precalculus

i think it's pretty expensive for what it is

but it is the best precalc book out there

that said

you could very easily get away with using a free online resource like khan academy

and it might even be better

[mental flare]

Its normal that i'm in 10th grade and i haven't seen functions yet?

[hallow oriole]

like

f(x)?

[mental flare]

Yes

[hallow oriole]

uhhh

can't speak for everyone but i saw those in seventh

i would say no

that's really odd

[mental flare]

Bruh, i started with trig today 💀

[hallow oriole]

its ok u got this

[mental flare]

I know, i'm good at math

But i want to self learn pre calculus

I only wanna have the essentials

I don't want like a bunch of useless things that i'll never see again

And i saw that the "for dummies" book is what i was looking for

[hallow oriole]

in precalc there is nothing useless

[mental flare]

Is this enough?

[hallow oriole]

depends on what you're learning this for

[mental flare]

It's that i also want to learn machine learning

And i need single and multi variable calc, linear algebra and probability & statistics for that

[mental flare]

And as far as i know, i don't need like ultra advanced calc.

I planning to take the MIT OCW courses for that

But i need precalc for that

[karmic crater]

If you want to get past the basics of ML and do research in the field you would probably want to know as much analysis and geometry as possible besides the obvious stats/probability and CS requirements. I do not work in the field but that is my impression from what professor's have said and some articles that I have read

[mental flare]

I want to do research, but for now i only want to know the basics

I'm only 15

I went to the AI discord server and this is what it says with math in resources for beginners

[karmic crater]

I would first start with knowing my single variable calculus very well and get into CS. When you have done that I would move to multivariable calculus and linear algebra and mastering those two. When you have done that you should start looking at probability and stats as well as start looking into analysis

[mental flare]

Wasn't analysis the same as calculus?

[karmic crater]

Calculus has more focus on computations and only covers R^n while analysis has more focus on proofs and works with more general spaces and notions

Real analysis,Complex analysis, Functional analysis, measure theory, PDEs/ODEs and harmonic analysis are some examples of subjects in analysis

[mental flare]

I research about that and i saw that the math is almost the same for an engineer and for a researcher, but the researcher also needs optimization

Is optimization a subject in analysis?

[karmic crater]

Yes

[mental flare]

There's a problem, my school is one of hardest here in my country

And i want to go to MIT

And i want to start learning that now beacause it would also show interest in the topic

And i really want to learn machine and deep learning

[rancid hollow]

Oo give me a reference to that discord server

[mental flare]

#old-network

[stiff quartz]

that’s a good schoo

[cursive orbit]

while getting into MIT is a good goal, it shouldn't be your only focus

[runic hatch]

also at this point I wouldn't be concerned about learning "useless" things

at this point in time pretty much any math you learn will most likely range from useful to very useful for ML

[grand thistle]

for those who've used dummit and foote, it's alright to just do chapters 1-4, 7-11, 13-14 the first time round right?

i'm not sure whether to also look into chapter 5,6 and 12, since i've seen ppl say that they may be unnecessary for just going through the book the first time

for reference, im almost finished chapter 2 rn, im doing around 1 section a day with at least about 12+ exercises per section done

(varying according to the section difficulty and length of course)

depending on time constraints with school starting in august i may have to skip chapters 10 and 11 but i really wanna do them for a review+ more in depth view on linear algebra

[gray gazelle]

ye

atleast for ML researchers

[chrome rock]

hi, does anyone have resource recommendations for complex numbers? I'm using my teacher's notes and having a hard time w it.

[blazing canopy]

I think Khan Academy is pretty much the go-to for any of the basics in high school

[compact crypt]

what are best serge lang textbooks in your opiion

for me it would be basic mathematics, algebra, complex analysis

[scarlet steeple]

I'm looking for good number theory books

[dense pewter]

what level of number theory?

[scarlet steeple]

leve 1?

introductory material

[dense pewter]

so like, modular arithmetic?

have you checked #books-old

[scarlet steeple]

I already know modular arithmetic

number theory isnt just modular arithmetic though lol

[dense pewter]

I know that..... you were the one who said you wanted introductory material

[manic cairn]

Um, what’s your other math background?

If you know some abstract algebra, I’d just use Ireland/Rosen

[random raptor]

Books on... Integrals? :p

Like, I want to do integrals for fun, starting from the basics.

Any recommendations so far as problem books on integrals go?

[broken meadow]

Demidovich

[paper ferry]

Does anyone know abstract algebra books with sections on Semi-Direct products? I’m trying to get an understanding of them

[gusty smelt]

I think something like dummit or foote should have one. I personally learnt algebra from artin but he decided not to include them for some reason??

https://kconrad.math.uconn.edu/blurbs/grouptheory/semidirect-product.pdf

[paper ferry]

Cool, I’ll check it out

[gusty smelt]

this is good too

kieth conrad has good exposition usually

[broken meadow]

thats weird semidirect products seem like they show up in places

like i would imagine knowing more ways to put groups together would be imporatnt

[scarlet steeple]

yeah I do

i just need a well received book by most people, introductory material. it doesnt matter if it has a chapter on modular arithmetic in it i can just skip it and move on to another topic im not aquainted with.

[remote ginkgo]

dummit foote brings up semidirect products mostly in the section on group cohomology, opext, etc

lang's algebra has a really nice explanation of them though

[compact mulch]

idk about other people, but I think the exercises in dummit foote are really good, but i think it lacks in motivation & intuition. i feel like its useful if u want to memorize a bunch of theorems & lemmas quickly

[grand thistle]

the exercises r pretty good imo as well yeah

i also agree in the fact that it lacks in motivation and intuition

i won't lie, it's terribly boring at times

[gray gazelle]

What are the least prerequisites for this book

[stray veldt]

it is stated in the introduction

[hollow talon]

Are openstax math textbooks good ?

[hearty sluice]

good vibe check read for algebraic geometry to see if one likes the subject? maybe some survey?

[sage python]

That's a good question actually

AG is very foundations heavy so that's tricky

I could see either something on curves/surfaces that does good theorems (5 lines determine conic, Bezout, 27 lines on a cubic surface)

Slight complex AG angle

Or something that also talks about connections to NT?

@slim nacelle any ideas?

[slim nacelle]

god yeah there's a lot of directions one could go with this

[sage python]

I almost would say Szamuely but that traumatized Moth

[slim nacelle]

yeah no more Szamuely recommendations

[sage python]

@hearty sluice what sounds cooler to you, topology of manifolds or number theory?

[slim nacelle]

also I guess it depends on how much you're willing to read to give a subject a try

[slim nacelle]

Langlands: these are the same picture

[sage python]

Alright so we agree to rec Corvallis?

Oh wait

Eisenbud and Harris might be good

Or does it take too long to get to the meat?

[slim nacelle]

yeah I was maybe going to recommend that

it doesn't take too long

[sage python]

I should write "Algebraic Geometry for non-algebraic geometers: An Introduction to the Langlands Program"

[slim nacelle]

actually yeah my recommendation is Eisenbud-Harris geometry of schemes, skim the first chapter and focus most of your reading on the second examples chapter

if you vibe with the examples and some of the pictures there you'll probably vibe with AG

another recommendation if you want some more classical AG is to go through Harris's first course

[sage python]

Uh

You sure that's a good idea?

I guess if you end up wanting more then yeah

[hearty sluice]

the prior

[wise umbra]

EGA has a lot of details

(but not much pictures)

[slim nacelle]

Harris's first course has a lot of pictures of classical stuff

Harris is kinda annoying if you try to actually structure a course from it but as a vibe check it's good

[sage python]

Fair, I guess I'm worried that it just feels messy as shit. And for vibe checks I like theorems more than I like working out examples in detail

[wise umbra]

There also the book "Invitation to arithmetic geometry"

[flint bay]

How to learn automorphic forms

[wise umbra]

By Lorenzini I think

[sage python]

Cookie that's a longer answer so let's finish with Migillope first

[slim nacelle]

oh yeah Lorenzini's book is good

[wise umbra]

Good way to learn some algebraic number theory and some algebraic geometry

[sage python]

I was thinking that Adrien, and if the answer was "both" to my question I would have said that. But if the desired motivation is more topology than number theory

Then I'm inclined slightly elsewhere

If you're patient, I think Neeman is very good

"Algebraic and Analytic Geometry"

It basically builds up to GAGA

Basically my candidates rn that I'm trying to filter through mentally are Neeman, Miranda, Gathmann, and Arapura

[wise umbra]

I understand why you thought about Szamuely then

[sage python]

Lmfao, yeah it would be the objectively right choice if it were actually good

Basically Neeman is zero to GAGA asap, Miranda is Riemann surfaces cap AG

[wise umbra]

Miranda might be a way to learn some topology
With triangulations/covers

[sage python]

Gathmann kinda is a bit of everything. Has some examples, does varieties "correctly", and has 27 lines on a cubic surface

Arapura is more hardcore AG over C

I probably will default to saying Gathmann

Just because it gets to the point fast

@flint bay sooooooooo

Hmm

[flint bay]

Ok my background btw

[sage python]

Oh that's relevant yea

[flint bay]

I have a full UG curriculum

3 semesters of analysis (2 real 1 complex), 2 semesters of algebra, topology

And some further/graduate level work done in algebra

[sage python]

How's your Fourier/harmonic analysis? Lie theory?

[flint bay]

Tbh my harmonic stuff could be a lot better

Its not zero but its definitely not great

[sage python]

Do you have the group/rep theory pov on the stuff?

[flint bay]

I need to pick up literally everything

I’m quite actually a fresh UG

“Need”

[sage python]

So basically the main inputs to the raw theory of automorphic forms are representation theory/Fourier on groups

If you don't have that, first I'd say it's good to pick that up

But also

Look at stuff by Goldfeld

"Automorphic Representations and L-Functions for the General Linear Group" by Goldfeld and Hundley does GL1 and GL2 stuff pretty explicitly

It has some drawbacks. Namely there's classical theory of automorphic forms on the hyperbolic plane, which has two parts

Modular forms are the holomorphic guys, they're more AGish, and then Maass forms are more spectral theory/hyperbolic geometry

They're sorta united by the notion of a "weight k Maass form" and raising/lowering operators, eventually the representation theory of SL(2,R). This is kinda the "semiclassical angle"

And then there's the modern way through adeles

So with that in mind

[flint bay]

Man this stuff is cursed

[sage python]

• Goldfeld and Hundley speedruns you to the adelic pov on GL1 and GL2, and does a lot of explicit computations. The drawback is that the classical and semiclassical points of view are done badly
• If you want the classical theory, then either you're focusing on modular forms or Maass forms.
  -- Gold standard for modular forms is by Diamond and Shurman
  -- Maass forms there's another book by Goldfeld ("Automorphic Forms and L-Functions for the Group GL(n,R)"), also there's Iwaniec but that makes greater demands on your analysis background iirc. Also Bergeron is good
• Rohrlich does a balance of the holomorphic theory and the adelic. Probably less detailed than either GH or DS. Basically I'd call it Diet Bump with more detail on the holomorphic theory

Depending on which direction you go and how you play things, it's good to also build background in some subset of algebraic NT, representation and Lie theory, hyperbolic geometry, spectral theory, and harmonic analysis

But these recs I don't think need that background except maybe Iwaniec in harmonic analysis

Good luck

[hallow oriole]

dami

how many books have you read

[sage python]

I haven't read all of these lmfao I get impressions easily

I mostly learned from Goldfeld-Hundley

But in general I just consult books on one of bases and get my vibes from there

So like e.g. in my analysis class I looked up inverse functions theorem briefly from Spivak CoM and from Rudin

Because Sally's angle was fucking garbage lol

[hallow oriole]

how do you know if a book is treating something poorly?

and to switch?

[sage python]

Depends you kinda just feel it. When things are clunky and you're not making much progress

Some stuff you only find out in hindsight

[bitter raptor]

I finally decided to give a look at needham’s vca

I’d always dismissed the idea thinking it would be oversimplified or whatever

But holy hell I’ve got to say this might be the most fun I’ve ever had reading a math book

And it’s so easy to read too

[analog lava]

i am done with my cs semeseter and i want to learn more new math

i figured out harmonic analysis seems so nice

especially a textbook called a course on abstract harmonic anlaysis

do i have the right prereqs to reap the benefits?

i know uptill measure theory ( did osme problems in geometric measure theory )

some functional analysis but p sure i forgot everything

and i know algebra

and point-set topology

[sage python]

Depending on what it does it's good to have some idea of rep theory

[analog lava]

i dont

have any

[sage python]

Check the preface to see if they need it or not

[slender umbra]

Next year I’ll start college

Recommend me some books pls

About any area of mathematics I don’t really care

Except geometry

[solar anvil]

Is it reasonable to try and finish Hoffman Kunze in < 2 months, im currently on chapter 4

I usually do problems and read in it for about an hour or two a day

I want to try to finish it before summer ends

but I feel like its taking to long

[heady ember]

Spivak's Calculus, though i do warn staring at a question for hours not knowing the next step is normal

[chilly mango]

Is there a decent way to read about mathematics similarly to reading about philosophy, as in, having a foundation in the chronological start. Akin to the phrase of "starting with the Greeks", perhaps studying Euclid, some other mathematicians, all the way through Newton, and so on. Is there a comprehensible list of significant works to aid this?

I hope I'm putting this in a comprehensible way

[sudden kindle]

Hm

Like whats the mathematical cannon?

[runic hatch]

I’d imagine maybe Euclid first?

[sudden kindle]

I can tell u whats the undergrad cannon

Analysis, algebra, topology, complex analysis

[daring reef]

anyone know any good graph theory textbooks that are good if you already have a decent amount of mathematical maturity?

alternatively: what is the best way to quickly develop graph-theoretic intuition for someone who is familiar with a lot of the basic definitions

[quick hornet]

diestel is the gold standard IMO

but it might be too dry for some learners

give it a shot though, pretty sure its legally available online for free?

oh never mind, its 13 euros to get it legally

take that as you may

[crimson leaf]

Bondy Murty has a book that's free online it's an older version though it's called graph theory with applications there's also a newer one but it's not free

[quick hornet]

are you trying to read to learn, or for historical interest?

because this is a terrible way to learn mathematics

mathematics is not philosophy, you do not need to know how Newton phrased his system of calculus or why

if you asked a modern mathematician to define a "fluxion" (the central construction of Newton's work), they would probably say "huh?" or "isnt that that thing from Newton?"

i.e. they would not be able to

because it is useless

and a terrible way to think about calculus

euclid can be somewhat useful if you, for some reason, want to learn euclidean geometry specifically

but that's an exception rather than the rule

if anything, it's the exception that proves the rule, considering how many annotated editions Euclid has had to fix basic logical mistakes

(and yes, if you're going to read euclid, please please please read an annotated edition)

as a general rule of mathematics, it is far easier to read new facts from textbooks than to read them from the primary source

(also, idk how much this is true in philosophy, but in mahtematics, the primary source was very frequently random collections of letters)

(primary-source texts like Newton's principia were very rare)

(hell, even as recently as Grothendieck were major proofs presented as personal correspondences with rough ink scratches lmao)

this is an affix of the famous letter sent by Grothendieck to Serre that proved Grothendieck-Riemann-Roch

trust me, you do not want to read mathematics out of these correspondences

unless you like seeing "Based on that fact we discussed in a conference in Bonn 5 years ago..."

with absolutely no explanation on what that fact is

there's a reason mathematicians read out of textbooks right up until the cutting edge

i genuinely do not think it is possible to learn modern math just by reading "the classics"

or at the very least, it'll be incredibly inefficient

no one things about calculus like newton did, no one thinks about logic like russell did, etc

people do think about euclidean geometry like euclid did, as it happens, but admittedly euclid's elements being the second most published book in human history (after the bible) helps with that

and even then, every student knows that euclid made many mistakes, e.g. in his appeal to "sliding" a shape over another in many proofs

that said, if you want to read these texts for historical merit, that's a little bit more understandable

in that case, though, unfortunately most lack good translations

so you'll probably have to learn latin, french, german, russian at least

maybe italian

most historians of mathematics just focus on the history of one field, which is much more approachable and reasonable in scope

[quick hornet]

(to be clear, though, oftentimes these textbooks are "considered" classics in and of themselves)

(like grothendieck's EGA for example)

(but "most" of EGA isn't original material even if it is presented in an original way from a very at-the-time-uniquely Grothendieckian perspective)

(though certainly a lot of EGA is original work by Grothendieck as well, but again, it's written as a textbook.)

(and even then, most modern students do not learn out of EGA — it's just cited frequently.)

[slender umbra]

what's a nice book with math problems?

[quick hornet]

what sort of problems?

[slender umbra]

i will start college next year

so taht level

about a little bit of verythin if possible

[compact crypt]

https://www.amazon.com/Course-Analysis-Introductory-Calculus-Functions/dp/9814689084

has anyone seen this book

[hasty thistle]

Does anyone know any good math books about proof writing?

[crimson leaf]

Book of Proof

[hasty thistle]

by Richard H. Hammack?

[crimson leaf]

Yes

[hasty thistle]

OK, I'll check it out. Thanks

[keen orbit]

Hello i have a question
Is Stewart calculus a good book for self studying calculus

[quick hornet]

it's fine but typically quite expensive

if you are going to buy it legally

[crimson leaf]

Is it? It's pretty cheap used

[quick hornet]

ive never seen a used copy for less than like, $80 in my region

which is a lot for a used textbook

[keen orbit]

No i got it as a pdf

[quick hornet]

ymmv though

then yeah, its fine

a bit bloated but whatever

[crimson leaf]

Interesting I got it for $5 in the States

[quick hornet]

feel free to skip pages if they dont seem super relevant

(but go back to them if you later realize they are)

[keen orbit]

I am not skipping bc I think that it's better not to skip any ideas

They are all fun in fact

[runic hatch]

Yeah second-hand versions of stewart may be common

although damn 80 for a used copy is a lot

[keen orbit]

Thank you all so much for answering my question

[chilly mango]

A bit of both

[primal mica]

Good non-euclidean geometry book?

[gray gazelle]

where can I find a lot of integrals (derivatives, limits, series) to practice my calculus skills?

preferably of increasing difficulty

[stray veldt]

start with khanacademy probably

[atomic osprey]

does anyone have a reccomendation as to where to read about w lambert function

[rain hound]

Does anyone know any good topology texts that cover the same point set topics as Munkres? I just don’t really like how Munkres explains things.

[hallow oriole]

ya'll rly need to stop posting pirated content lmfao

dm it instead

don't post it on a server

[crimson leaf]

Why is this 2000 pages??

[old elk]

What if you don't look at it?

[hallow oriole]

doesn't matter

pirated content gets servers banned

believe me i pirate all the fuckin time

but posting pirated content on a sever is the quickest way to get it shut down

[old elk]

is it useful to delete the message?

[hallow oriole]

yup

good man

just dm it to whoever you wanted to give it to

[old elk]

I didn't know
I thought it could be useful for someone.

[hallow oriole]

it's okay ❤️

free media is >>>

just that maybe discord isn't the best place to leave it

[unreal copper]

Any good books on game theory?

[winter wraith]

Any good book for differential equation¿¿

[abstract field]

I'm trying to learn differential equations, however, this textbook https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2020/10/diffeq.pdf seems very difficult despite its basic ideas(it's a free textbook uploaded by the creator himself). I'm wondering how I can build the knowledge to tackle this textbook? I already have taken an intro sophomore level diffeq course, however the textbook seems to be quite difficult to comprehend and makes concepts seem very confusing.

[winter wraith]

Just search on YouTube or post it here if u have problem in understanding something

[compact crypt]

are there any good advanced probability books for self study?

preferably with solutions?

it doesn't have to be full one

[random raptor]

How advanced are we talking?

[gray gazelle]

thoughts on "A Problem Book in Real Analysis", anyone? (need to solidify my understanding w questions)

[random raptor]

Ross and Blitzstein have some great problems in undergrad-level probability.

[gray gazelle]

what exactly are you stuck on? what do you want to learn? ODEs? PDEs?

also what did you cover in your intro level diff eq course?

[heady ember]

I don't know that book but here are some general consensus I have heard on RA books here

• Rudin : I mean don't lmao
• Apostol / Abott: Both good
• Browder: Good too
• Schroder: Dami likes it a lot, and I think it seems to be pretty friendly from the first few pages I have seen
  For instance, there's small boxes by the author to explain proofs, and he even summaries a few proof techniques even though if you're doing RA you should know them very well already

[gray gazelle]

awesome, thanks. mainly really looking for problems and the book I mentioned offers exactly that. will 100% check those out, thanks!

[heady ember]

np : )

Happy to help!

[coarse frost]

if u want problems pughs book has a ton of good problems, from what i gather

[runic hatch]

Rudin has some nice problems too if you haven’t already done them

[atomic osprey]

does anyone have a book reccomendetion for complex analysis???

[runic hatch]

Check the pinned messages for a brief review of some standard recommendations

[karmic crater]

Klenke's probability theory

[halcyon garden]

Pugh's book is absolutely poggers, TONS of good exercises and a few chapters have analysis quals questions.

Its a book with soul

I quite like their statement in the suggested readings page : "One thing you will observe about all these books – they use pictures to convey
the mathematical ideas. Beware of books that don’t."

[keen mountain]

is there a math book with easy syllabus and review of main points in math?

i need to get back to uni level maths but i don't remember much

[wheat tendon]

Martin J. Osborne, an introduction to game theory seemed nice

[remote ginkgo]

von Neumann and Morgenstern have the classic. But it is a little wordy so you should follow up with Game Theory by Maschler, Solan, Zamir

these are the basic/most complete texts

[abstract field]

Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
John Hubbard, Barbara Burke Hubbard a good book for self studying calculus?

[unkempt plank]

Any good books about congruence modulo m?

[remote ginkgo]

gauss' number theory book

or kenneth rosen discrete mathematics

[remote ginkgo]

it's good at what it does. but it's not a calc 1 book

it's part of calc 3

[timber mesa]

I like Burton's Elementary Number Theory

only the first few chapters are about the integers, divisibility and congruence modulo an integer

but if you're interested in number theory you can read the following chapters on quadratic reciprocity, some diophantine equations etc.

[timber mesa]

I think it's very pedagogic and it has a ton of exercises, some of them with solutions or hints iirc

[abstract field]

Ah gotcha

[sick sonnet]

What are some good books on Toric Varieties?

[broken meadow]

i should know like a couple resources but

uhm

[sick sonnet]

Username checks out

:)

[broken meadow]

Cox little schenck

[sick sonnet]

What are the prereqs for that book? Is it scheme theoretic?

Ill have a look, thanks!

[broken meadow]

it requires very little AG

but has content for scheme theoretic stuff later

[crimson leaf]

I'd probably suggest looking at Khan Academy or a copy of basic mathematics by Lang (I would recommend this if you plan on taking calculus right away)

[broken meadow]

i am learning out of this book having not taken a class on AG which is

a mess

but this is how REUs go

Also see https://arxiv.org/abs/1708.01842v1

[sick sonnet]

Yar, I was hoping toric varieties would be especially accessible to people without an extended background in ag

Our group is organising a workshop on them for that reason, but... I dont know much about them myself

[broken meadow]

yeah i think you should be fine

its just that the cox little schenck book is Dense so some lectres to go with them would be better

[sick sonnet]

Sure, should be fine

Thanks, Ill have a look at those

[broken meadow]

np

You will also want to have a text for polyhedral geometry stuff for reference just in case

so see Ziegler

for polytopes

[keen mountain]

Thanks a lot, I'll definitely check it out

[sage python]

@broken meadow the nice thing about dense books is finishing them

You get a lot of closure

[broken meadow]

i see

One day i hope to

[sage python]

@broken meadow you missed the pun

Dense

Closure

[broken meadow]

oh

bruh

ok this is now much much better

🧠

[sage python]

Nobody sees me coming even though they know I'm liable to go for puns at all times

Hiding in plain sight

[broken meadow]

😵‍💫

yea was not expecting it

but here we are

[crimson leaf]

I had a dream so I gotta ask how's Artin for learning Linear Algebra?

[sage python]

P good

[crimson leaf]

So it basically aims to teach Abstract Algebra and Linear Algebra at the same time?

[sage python]

Sorry was out but yea

[crimson leaf]

Cool thank you Dami, I'll give that a shot at some point then see if I can pick up both at once

[onyx oar]

currently working through euclid's elements. does anyone have a recommendation for a next good book?

anything is welcome of course but im hoping to find an older text like elements that feels like discovery the math all over again

well... full disclosure, it has been a decade + since school. i now do a lot of computer security work and for that I have always found that reading an exploit proof and then "rediscovering" it myself is what builds the understanding. So im looking for an algebra book with proofs so that I can fill in any gaps that I have and develop a deeper understanding for the math so that i can move on to more advanced topics. I have taken a few calc classes before but want to go all the way back.

if that makes any sense. i have a hard time explaining myself lol

basically i want to read the proofs myself, but i have no idea where to start. 😦 my math history is poor

oh great 🙂

this looks good too

this was my idea... ya

so schroder analysis looks good

https://www.target.com/p/mathematical-analysis-by-bernd-s-w-schr-der-hardcover/-/A-86805352

is this the book you're referring too? or did i miss it lol

[karmic thorn]

Looks like it

[onyx oar]

nice... thanks guys 🙂

[foggy relic]

Principia arithmetica

[onyx oar]

niceeeee

Invictus comes in with a win 🙂

thanks man!

[runic hatch]

Is this for historical reasons or learning math?

In general super old books like those aren’t that good for actually learning math tbh

[lime sapphire]

Galois theory by Harold edwards sounds like what you're looking for

[muted oyster]

Are there any good books for analysis that have similar contents when compare to Principles of Mathematical Analysis but with softer/friendlier approach?

[heady ember]

General recs frm what i have heard from the time i have been around here

[muted oyster]

My professor recommended me Ken Ross's Elementary Analysis but the book doesn't seem to have some cotents from PMA.

[runic hatch]

Apostol's book feels pretty close to what you're describing; I'd probably describe it as PMA but with more explanations and exposition added in

is there a reason you want something similar to PMA specifically (e.g. for a specific future analysis course)?

[muted oyster]

I am planning on taking course of analysis next semester which uses the book of Rudin.

But I find Rudin to be very time consuming and inefficient.

[runic hatch]

I see, yeah that makes sense

[muted oyster]

Especially during summer vacation where I have to work.

[runic hatch]

Apostol's book should be good then

[muted oyster]

Okay, gonna check it out.

Thanks for recommendations.

[runic hatch]

np

[heady ember]

Dami likes Schröder a ton too

[runic hatch]

yeah I can see why; the topic selection for Schroder seems really nice

fwiw I would recommend Schroder over Apostol for general study, although if you want something that sticks closely to your course I can understand that

[muted oyster]

Also, I know that this is kind of dumb thing to ask at this level but I would prefer some problem sets/books that has solutions too.

Since I have to do everything alone.

[gray gazelle]

is this your first proof based class ?

[heady ember]

At this level there isn't an exercise book normally

At least an official one

[muted oyster]

Yes.

[gray gazelle]

why not learn how to do proof

s

[heady ember]

If its your first proof based topic in math

[muted oyster]

This may sound dumb but our school does not provide course on that and I didn't know its existence until today.

[gray gazelle]

well

you have to know proofs for like a lot of math

[heady ember]

It will quite difficult to learn RA and there'll be a steep learning curve

[gray gazelle]

unless it's computational

[runic hatch]

personally I think it's doable enough

but it will have quite a bit of toughness involved yeah

[muted oyster]

I'll have to bear with it though to accomplish my goal.

Anyways I'll go with Apostol.

Thanks for recommendations.

[runic hatch]

many of these books will have some solution sets online, but I do think it's best to just try to go at it alone first, even if it may take a long time for some problems

if you get stuck feel free to ask questions in #real-complex-analysis first before searching for solution sets

[muted oyster]

Thanks for spending time answering!

[prime oak]

opinions on lang undergraduate algebra?

[coarse frost]

based ab

[gray gazelle]

Hello

What time of math books should I read if I just completed the IGCSE

or if I'm soon starting IB AA HL

I just want to expand my knowledge on maths do exercises and make it a habit

[gray gazelle]

does anybody have any book recomendations to self study linear algebra for engineers

[foggy relic]

strang

[crimson leaf]

Strang also has video lectures, exams, etc through MIT OCW

[gray gazelle]

Book recommendations for someone planning to apply for undergraduate study for Maths & Stats?

[remote ginkgo]

shilov, strang

[gray gazelle]

not shilov

[tepid prairie]

Don't say that, I just bought that book lol.

[timber mesa]

not exactly a LA book I'd rec for engineers lol

can't go wrong with strang though, and he has some nice lectures at MIT OCW I think

[random raptor]

Hwang and Blitzstein is the best introductory probability textbook.

[sage python]

Ballsy claims

I like it

[remote ginkgo]

better than kostrikin manin

[muted oyster]

How are Lang textbooks in general?

Like I have searched through math textbooks yesterday and found a bunch of them.

[hardy citrus]

hello

[timber mesa]

decent as references, not sure if I'd recommend them as a first introduction to the subject

I'm thinking of his alg book and his undergraduate analysis one

[loud cradle]

lang's algebra is classic, i also like both his undergraduate analysis and "real and functional analysis" although I would use them as supplements.. same with his complex analysis and linear algebra

his calculus of several variables book is actually really good

his undergraduate algebra is really underwhelming

those are the only ones i'm familiar with

[slender umbra]

what's a good book with math problems?

i havent started college yet

[random raptor]

Really depends on what topic you want problems on.

[muted oyster]

Have you looked at the multivariable part of Lang's Analysis? If so, what are your opinions regarding it?

[main void]

Any nice book about Fourier Analysis with applications to PDE's? I'm mostly looking for exercises.
I know about Stein's series

[frail sail]

any good abstract algebra book I can pick up that goes into great depth but is also not TOOOO difficult to get through

[mystic orbit]

Artin is beginner friendly afaik

You can also see dami's review

.

[novel solar]

Are there books on application based calculus problems?

[mystic orbit]

.

[frail sail]

hi I would like to read the dummit and foote one but I dont have much background in this field apart from very basic set theory

[muted oyster]

I've seen people recommending Hersteins Topics in Algebra.

It also has a solution manual unlike Dummit and Foote making it more accesible

[mystic orbit]

well, that's why this server exists, doesn't it?

just pick it up

and you can ask questions here whenever you get stuck

[mystic orbit]

that's not really true

having the ability to stare at solved problems doesn't make a book accessible much

it merely makes it easier to fall into the delusion of understanding

[foggy relic]

but the ability to know if your solution is right makes it easier to avoid misconceptions

esp in group theory its easy to make false proofs

[mystic orbit]

you build a sense of knowing when you're proof is correct with experience

and the sooner you develop that skill the better

[foggy relic]

yes but 1111z likely dosent have much

[mystic orbit]

besides, the pros of that are marginal at best and definitely don't outweigh the cons

having a friend or a prof or this server to check your work and show you where you went wrong is far more optimal

[tepid prairie]

Trying to get help on problems in harder books is usually very difficult.

[mystic orbit]

that's a fair point but it doesn't apply to 1111z

[runic hatch]

yeah for most undergrad texts people here should be able to help

or on math.stackexchange

sometimes trying to assemble everything to ask your question can also make you see the answer too in the process

[tepid prairie]

I tend to find that if I need help the problem disappears into the ether. 😆

[fallow cypress]

I think dummit and foote gives the necessary mathematical background in the first chapter or two

Is there anything in particular that you're struggling to follow

[desert herald]

I want to get better in discrete mathematics, because I want to study more theoretical computer science, so can any of you recommend me some books or courses for self studying it? I am already familiar with introductory proofs, logic, sets, relations, recurrences and functions because I've taken a short course in discrete mathematics but I want to further my knowledge about the subject.

[gray gazelle]

knuth's concrete math?

i haven't read it tho

so i can't say my opinion

[desert herald]

Yeah, I've heard of the book but is it appropriate for self study?

[crimson leaf]

You might be interested in this course from MIT https://ocw.mit.edu/courses/6-080-great-ideas-in-theoretical-computer-science-spring-2008/pages/syllabus/ on this page are some books and you can read through the prereqs and stuff but if you don't feel ready I second concrete math

[gray gazelle]

i am also looking for a discrete math book for computer science, but i havent done any proofs or anything like that (i have basic programming knowledge).

[primal mica]

In response to this I went and did a glance at Knapp's both basic and advanced algebra and it looks pretty good. Have you looked into it more since then to say whether or not it's a good grab?

I was coincidentally going to ask for a good progression to get into Clifford algebra/geometric algebra in general.

[tardy walrus]

PAPA KNUTH

[gray gazelle]

did you read it slurp

[tardy walrus]

No

[sage python]

I haven't looked into it much tbh. I don't really read many in depth tbh

[hallow oriole]

[latent magnet]

I've recently figured out I'm almost perfectly fit curve to Brouwer's Intuitionist formulations.

I'm looking for two book recommendations, if they exist.

1. Any modern treatments or surveys of Intuitionism and modern pure mathematics.
2. Any intersections of Intuitionism with Logic since Gödel or modern physics since the denunciations of space-time as a fundamental property have become less fringe.

[sage python]

Call me out on something specific then bitch

Lol

[tepid prairie]

Book review requests. 🙂

[sage python]

I mean if I know that someone who I trust moderately well has a strong negative opinion about the book it's reasonable to include. And I make it clear it's second hand

[primal mica]

I worked through Hungerford but no other algebra books, however I don't really felt like it went as in depth as I would have preferred, looking at other indices

However I think it's intended as an undergrad algebra book, as opposed to D&F which I've heard is typically used in the grad courses.

But I'm just a dumb physics man so what do I know.

[sudden kindle]

Old people who died

[slim peak]

Not gonna lie, in their first mind set it was initially just about publishing complete and definite foundation of Maths

[sage python]

Wasn't there something about creating a maximally efficient path for the next Riemann to just learn everything fast?

[crimson pagoda]

People should stop learning math

[night prism]

Yooooo!

Whatup bro, hope you’re well

[heady ember]

Hi

[ember ridge]

I want a book for precalculus which is short for 15 days?

Please ping me

[heady ember]

Not a book but Khan Academy

[ember ridge]

Thanks

[river tangle]

Guys any good book for differential calc for beginners?

[muted oyster]

What is your major.

And do you plan on studying math further?

[river tangle]

Well yes

[muted oyster]

Then I'll recommend Spivak's Calculus to you

[heady ember]

Be warned that you'll will have to often spend hours on a qns but still have no idea ono how to proceed

[muted oyster]

Yes that is true.

But if you want to proceed further in math you'll have to get used to it anyways.

[heady ember]

For starting to learn calc Paul's Online Math Notes and Khan Academy can also be good choices

And when you want to learn things more rigorously you can try Spivak's Calculus or even like Schroder's Analysis

[coarse frost]

damn they were making something for me? How sweet of them

[muted oyster]

https://www.amazon.com/Course-Analysis-Introductory-Calculus-Functions/dp/9814689084

Does anyone know this series?

[sage python]

Yeah and you disappointed them

[wise umbra]

No I don't think so
Initially it got started by André Weil, who was not satisfied with the few textbooks on integration/differential calculus around.
So he gathered a few mathematicians in order to write a textbook which would be standard for the next decades.
Then they decided that they should first write about basics things, and that's how the series of volume started

[coarse frost]

i didnt!

they didnt finish the material!

not my fault

[runic hatch]

should've just wrote the next volume

I am curious though, when would bourbaki become useful

like is it after 2-3 years of graduate study, or would you need even more

[brisk ice]

Anyone know a book that has a section on the topic of infinite sets with regards to the topics of set theory and ideas about subsets, cardinality, etc (basically I understand the principles in the finite cases but don't really understand it when you extend to infinite sets)

Like stuff like the set of even natural numbers is a subset of the natural numbers and that they share the same cardality

I am reading the wiki about it but want to get a bit more knowledge on the the topic

I can see how E could be a subset but it also feels strange if we are saying they do have the same cardinality (if you have a bijective mapping from the sets).

[hallow oriole]

honestly i would just throw out your intuition in this case and go solely based of of definitions. E is a proper subset of N because N obviously contains E but also contains 1, which is not in E. they have the same cardinality because you can construct a bijection between them.

nothing more and nothing less

but if you want a good set theory book have you tried Hammack's Book of Proof?

[brisk ice]

I have not

[hallow oriole]

i would give that a shot

https://www.people.vcu.edu/~rhammack/BookOfProof/

legally free online

[brisk ice]

yeah I suppose if you just follow the definitions then it will follow but I just don't have any experience with working with infinite sets in regards to stating their relative cardinalities or what is a subset of another (beyond just the naturals, rationals, etc...)

[hallow oriole]

hm

yeah i get wym

book of proof seems like the best fit for you

feel free to skip any sections you think you already know

[runic hatch]

Naive Set Theory by Halmos is also nice, but it may be a bit advanced

[runic hatch]

For the time being though this should work

[runic hatch]

For the most part I dont think you really need anything more sophisticated than this for most undergrad math

I’ve gotten by with a very shaky understanding of cardinality (not much more beyond hurr durr bijection stuff)

[gray gazelle]

I wish I was smart enough to understand math, it's really hard for me but I'm willing to get better at because I love physics, and physics is just maths with application, so gotta learn it. Can someone recommend a book so I can clear my basics

(I basically know nothing)

[hallow oriole]

i would start at khanacademy

[river tangle]

Guys what book do you recommend for a beginner in calc?Btw plz include integration if possible

[grand thistle]

pov calc without integration

[fallow cypress]

have you tried khanacademy

[river tangle]

Yeah but still it needs a bit too much of time and I am more used to reading books than visual learning

[sage python]

Ah so it turns out what I was thinking of was Dieudonne's idea that most work in math in general was about setting the stage for the next Riemann to blast through

Not sure if that played into his vision for Bourbaki but yeah

[onyx oar]

Just sayin thanks! I checked this book out, very much what i was hoping to find.

[primal mica]

anyone know a textbook that goes over Riccati equations? I’m tutoring someone in ODEs and I haven’t seen them before

[timber mesa]

they're usually left as exercises since there's not much to say about them, really

even the wiki article about them is a good enough explanation of how to solve them https://en.wikipedia.org/wiki/Riccati_equation

[timber copper]

LQR in shambles

[timber mesa]

that said, I think Simmons' Differential Equations with Applications and Historical Notes has some exercises about them

and some applications

[timber copper]

Viorel Barbu's Differential Equations goes over them a bit, mainly as exercises like derivada said

[primal mica]

Okey dokey. Thank you, kindly, both.

[gray gazelle]

Hello.

I'm looking for a good text on ODEs and PDEs.
Ideally something someone in the senior year of their undegrad could handle ( undergrad analysis and linear algebra, etc )
But ideally something that isn't like in the usual cookie-cutter format of other approaches to DE.

[slim peak]

Viorel Barbu's Differential Equations for ODEs

there is no real undergrad book for PDE, generally people recommend first part of Evans.

[placid pollen]

What about the Dover book for ODEs? by Tenenbaum

[slim peak]

I just heard of it, but never open

[gray gazelle]

Thank you.

[placid pollen]

What about these? The Sawyer book feels very intuitive from the Amazon preview but I can't find a scan online. They are about the same topic

[slim peak]

I completely omit Numerical Analysis aspects

since one asked me for a Differential Equations book

I don't like to mix Numerical and pure functional analytic aspect of PDEs

it is personal tastes

[placid pollen]

I had a Numerical Analysis course with Burden, seems like many methods are related with a bigger structure that isn't studied in the book. The iterative methods seem related but the proofs of each method is different with its own details, seems a bit wild

[slim peak]

and personnal experience showed me that it is better to focus on one topic first give better results for students.

[placid pollen]

I was about to ask in the Dynamical Systems channel, if a solution to a problem is usually transforming a problem to a form that is known to be solvable numerically? Mainly with PDEs

[gray gazelle]

does anybody have book recomendations for discrete math but with computer science focus

[crimson leaf]

Concrete Mathematics

[placid pollen]

so does anyone have an opinion of these books

[tepid prairie]

It's really good but the chapters between the methods chapters about application takes ages to compete.

[narrow relic]

I recommend this: https://openlibrary.org/books/OL3565500M/Discrete_and_combinatorial_mathematics

[blazing canopy]

A solid advanced undergraduate text that covers a lot of the qualitative and more physics-oriented aspects of differential equations is Zauderer's Partial Differential Equations of Applied Mathematics. While its focus is on how PDE pertains to applied mathematics, it is still mainly about analytical, rather than numerical, topics.

[hasty turret]

Any recommendations on Markov Chains?

[sage python]

So I haven't read this myself

But Greg Lawler has a book called "Introduction to Stochastic Processes"

And knowing Greg Lawler being very good at exposition it's probably a solid book. So I'll throw that out there but say to prioritize more informed suggestions

I would like to learn Markov chains at some point tho tbh

[gray gazelle]

thoughts on Gallian for Abstract Algebra?

[karmic thorn]

Good for someone new to writing proofs and algebra, too slow otherwise. In case you plan to go through it, avoid the temptation to be a "perfectionist" and do each and every exercise (there's just too many, and the return becomes increasingly marginal).

If you are already comfortable with writing proofs, something like Artin or Judson might be much better.

[gray gazelle]

hey there

I just finished the igcse math course

and wanted to learn some math during the summer

what would you guys recommend

[gray gazelle]

normal or add math

normal

i'mm going to do IB Math HL AA

Basically I did accelerated maths which is normal maths but 2x faster

[gray gazelle]

I see, does it cover as much content as Michael Artin or Dummit, though?

[shell geyser]

Pretty sure I've seen IB math textbooks floating around online if you want to get a head start.

[gray gazelle]

nice, me too next year

[gray gazelle]

what do these acronyms mean

[gray gazelle]

yeah that'd be sick I'm just not sure where to start because I'm technically starting in 2 years

[gray gazelle]

International Baccalaurete Math Higher Level Analysis and Approaches

I see

[gray gazelle]

it's like AP for US folks or A levels for British, except this program is everywhere

HL just means higher level

[gray gazelle]

it's the equivalent to Calculus AP BC apparently

[gray gazelle]

nah

in terms of rigor probably more

[shell geyser]

Not allowed to talk about obtaining books in non-legal ways here but surely you can find some if you look on Google.

[gray gazelle]

but in terms of content for the calculus portion it's less

[shell geyser]

If you've already finished iGCSE you should be able to start doing IB. Probably just follow the textbook order.

[gray gazelle]

nah it's not hard

trust me

I can give you some advice since I self studied it

[gray gazelle]

not necessarily but compared to A levels probably yes

[shell geyser]

Meh IB Math HL is definitely not the hardest math course in the world. Don't worry. Also probably not the right channel to discuss it. Maybe move to #math-discussion.

[gray gazelle]

A level FM is harder yeah

they do second order des and some elementary linear algebra as opposed to ib

Ah I see, can I consult you in DMs for advice since we're off-topic

yes, u can

[runic hatch]

Some popular IB texts are those published by Oxford, Cambridge and for math in particular, Haese and Harris

Khan Academy is good as an extra supplement too, as is Paul’s online notes for calculus @gray gazelle

[gray gazelle]

sick thanks

[hallow oriole]

not equiv

they cover slightly different material than we do

[gray gazelle]

yeah

[hallow oriole]

alsao

*also

no point in getting separate IB texts

they're a scam

just go with Stewart's Calc

or something similar

khan academy is good too

lol

[heady ember]

Just use Spivak's Calculus (jk)

[delicate hemlock]

what book do you guys like for representation theory of groups? I tried Fulton and Harris but wasn't a huge fan of the big focus on symmetric groups and I found it a little wordy. Serre on the other hand was a bit too terse

[karmic thorn]

No, it falls way short of either. It does however have a few chapters on applications (an introduction to coding theory, for example).