book-recommendations

[gray gazelle]

Sociology (DAm what does this here?)

according to this, you should check stewart "precalculus" book

and not algebra?

I mean , you should check it too because is good learning new things

But the first in the list is Algebra.

mmmh

Let me ask a friend who gradudated

But What should I ask him?

What kind of algebra he did?

yeah , what were the topics he learnt and notes if he has

then you can answer here according to the topics, and someone will give you a better reccomendation

He have but idk if I will be accepted for Computer Science or I will have to be an Business Administrator...

everything can happen

8.3/10

I am low..

[gray gazelle]

You here?

Gaus Method, Gaus xhordan, Groups, Invert functions? --> Algebra.

[gray gazelle]

Nvm

A book recommendation for this:

Limits and Continuity: Understanding the behavior of functions as they approach specific points or infinity. This often involves manipulating algebraic expressions.

Derivatives: Calculating the rate of change of a function, which requires proficiency in algebraic simplifications and understanding functions.

Integrals: Both definite and indefinite integrals, which are foundational concepts in calculus, relying heavily on algebraic manipulation.

Series and Sequences: Understanding the behavior of infinite sequences and series, which requires algebraic techniques to sum or approximate them.

[tender cobalt]

James Stewart Precalculus for series and sequences

James Stewart Calculus for limits derivatives and integrals

[tender cobalt]

The problems are great and explanations too

you'll be solving limits algebraically

and then looking into the epsilon-delta definition of limit as well

[cedar prairie]

Chat
Im heading to uni in a little bit and hopefully want to try to pick up a topology book
Which one should I grab

[dapper root]

Standard rec is probably Munkres

[tribal crow]

Lee is also a good one

[heady ember]

Willard is also well-liked, I believe

[fresh skiff]

Topology without tears

It's well known and available for free

[heady ember]

What do you mean? Everything is free.

[oblique hatch]

Legally free

[tribal crow]

everything is free if you run fast enough

[fresh skiff]

Nothing is free, everything demands your time

[gray gazelle]

Is time free?

[rich sun]

TwT

[gray gazelle]

time is the true currency

[heady ember]

||BECOME THE TIME||

[foggy quest]

For a beginner I recommend an analysis book that covers metric spaces, as metric spaces are a (the?) major use of topology: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

the one variable book there, to be clear, is good for beginners

[cedar prairie]

I do have the calculus knowledge already (which is a fun bonus of learning everything in the wrong order)

[foggy quest]

If you need point-set topology, e.g. for weak convergence in functional analysis, I like "Real Analysis: Modern Techniques and Their Applications" by G. Folland.

[cedar prairie]

So it covers real analysis and point-set topology?

[foggy quest]

Folland's book requires prerequisite like that one variable analysis book I linked.

[molten gulch]

Abbot or Rudin -> Folland

[foggy quest]

It covers measure theory, point-set topology, functional analysis, Fourier analysis.

[cedar prairie]

Ooo

[cedar prairie]

My learning path has been like
calc 1-4 -> real analysis -> complex analysis -> uh oh I probably shouldve learned about topology, the advanced parts of this aren't going well -> now

[vital bane]

Abbott + 1

[tribal crow]

where’s the linear algebra

[foggy quest]

metric space topology is sufficient for most applications, e.g. in other fields like statistics.

it should be covered in a real analysis class, (IMO)

[vital bane]

Linear Algebra -> Abstract Algebra -> Commutative Algebra -> Algebraic Geometry

happy?

[tribal crow]

[tribal crow]

how about for geometry?

I’m curious

[cedar prairie]

I mean I learned linear algebra like a decade ago

I should clarify this is my recent learning path

[gray gazelle]

wheres algebraic topology

[tribal crow]

a decade ago?

aren’t you basically my age

that’s very impressive

[cedar prairie]

Probably a little less than that but around there

[cedar prairie]

What age are you

[tribal crow]

recently turned 19

[cedar prairie]

Olddd

[tribal crow]

where did you learn LA from?

[cedar prairie]

I grew up on a university campus and had very critical parents

So they just gave me their textbooks to study from and that was my childhood

[vital bane]

Abstract Algebra -> Topology -> Algebraic Topology -> Homological Algebra

[tribal crow]

I see

[gray gazelle]

frr

[tribal crow]

wait, the abstract kind of linear algebra, or the more computational side?

[vital bane]

they are both the same just from different perspectives

[tribal crow]

@cedar prairie I do suggest learning some algebra if your LA is strong btw

[cedar prairie]

For some reason I never remembered calculus

[cedar prairie]

Wdym

[tribal crow]

though I don’t have a book recc

[tribal crow]

wdym wdym

algebra is an important field of math

I’ll be learning some soon too

[vital bane]

???

always the right answer

[cedar prairie]

Ohh abstract algebra

[vital bane]

Best UG algebra book of all time

[tribal crow]

okay but… I have heard very mixed opinions on D&F

[vital bane]

oh you have "heard"

[tribal crow]

mhm, you can pretty much just move straight for it if you know your linear algebra well

[vital bane]

sorry I was about to launch an ICBM to your location

[cedar prairie]

I'm good at the concepts
The formulae on the other hand I can't seem to memorize for the life of me

Or at least not like the matrix multiplication and whatnot

Upside is that uni gets to bully me for the second half of that because I'm taking linear algebra this year

[tribal crow]

I don’t recall that many formulae in LA tbh

I think you’d be fine

[deep nebula]

is it a good idea to do baby rudin after spivak?

or should i do other books to gain mathematical maturity?

[tribal crow]

you’re probably more than ready if you have Spivak tbh

[cedar prairie]

More just the cross product and matrix multiplication

[tribal crow]

the cross product sucks

[deep nebula]

i wanted to skip to papa rudin because i'd rather do something new but a lot of resources online recommend to avoid it

[tribal crow]

luckily I never had to deal with it in my LA class

[tribal crow]

I am not qualified to give an opinion on that, unfortunately

[cedar prairie]

I think the cross product formula is pretty much exclusively the reason behind my high school calc grade dropping 20% halfway thru the course

[tribal crow]

ehh, the cross product is an abomination

I don’t think most linear algebra books or courses care much for it

you just use the determinant instead

[cedar prairie]

Oo

[molten gulch]

the cross product is amazing

[tribal crow]

[tribal crow]

which Axler hates, if you’ve read Axler

[cedar prairie]

I should dig up that book again

I dont know if its axler but its been ages since ive read it

[tribal crow]

his 4th edition was released recently

it’s much better than his 3rd, imo

if you read Axler, use his 4th ed

it’s free on his website

https://linear.axler.net/LADR4e.pdf

[molten mason]

Yeah this sounds like a bad idea.

If baby rudin is easy for you then you'll do it faster but still do it first.

[deep nebula]

alright

[sand lion]

Does anyone know any good introduction textbooks to discrete math

[molten gulch]

Rosen's discrete math

[fresh skiff]

Quite famous one

[sand lion]

Thanks

[foggy quest]

It's enough for most basic Riemannian geometry like differential forms, geodesics, curvature, Gauss Bonnet.

[brazen rivet]

Could someone recommend a textbook that covers properties of Frechet differentiability, with emphasis on infinite dimensional vector spaces?

I need to learn if concepts like, for instance, the gradient is 0 at extrema still hold for infinite dimensions, and whatnot.

[drowsy nacelle]

yeah although i guess i haven't heard "bad" things necessarily just that it has good exercises but the writing style is dry

im doing aluffi rn

[tribal crow]

mhm, that's basically what I heard too

[drowsy nacelle]

i think you should have a good experience with algebra tbh like linear algebra provides a lot of good examples and you seem to have a good handle on it

there was some lecture series i liked i cant remember who gave it

[willow merlin]

I need some book for learning algebra from the groundup

[heady ember]

Continue yapping like D&F.

[heady ember]

I also don't like the cross product, because I can't compute it with my calculator :3

My arithmetic is bad so I always spend a lot of time checking that my cross product isn't wrong

[willow merlin]

can someone recommend me a linear alghebra book from the groundup, for dummies

[orchid pollen]

Linear Algebra Done Wrong is a solid book

[sage python]

To be fair I'd say the same of most linear algebra textbooks

Liquid and gas just doesn't work in textbooks for the most part

[dusk hemlock]

LOL

plasma and BEC would be even worse

[sage python]

True

I'm imagining a book titled "Statistical mechanics with examples"

Example 1: This book

[foggy quest]

There are lots of books, more or less the same in content. I like https://mtaylor.web.unc.edu/notes/linear-algebra-notes/.

[rustic tendon]

You know I really like reading "book" as well in pg469 very interesting plot twist

[trail hemlock]

?

[zinc elm]

have you reached p. 420 yet?

[trail hemlock]

[zinc elm]

:3

[vital bane]

Cope

[trail hemlock]

i used to like jacobson but a brief read of artin has converted me

but we stay hating on d&f

[vital bane]

D&F best algebra book of all time, anyone who disagrees is coping

[trail hemlock]

D&F does what melatonin gummies can’t

but it’s a great book no dispute

[molten mason]

[fierce hedge]

Says the person who has barely done the group's part of the book

[granite breach]

this is literally insane to me

[granite breach]

baby rudin isnt too bad tbh

this is coming from someone who sucks at maths

especially if u already have some intuition for analysis from spivak

[brazen viper]

Thoughts about Mr. Gilbert Strang linalg ?

[cedar prairie]

Yea

[gray gazelle]

A book recommendation for this:

Limits and Continuity: Understanding the behavior of functions as they approach specific points or infinity. This often involves manipulating algebraic expressions.

Derivatives: Calculating the rate of change of a function, which requires proficiency in algebraic simplifications and understanding functions.

Integrals: Both definite and indefinite integrals, which are foundational concepts in calculus, relying heavily on algebraic manipulation.

Series and Sequences: Understanding the behavior of infinite sequences and series, which requires algebraic techniques to sum or approximate them.

But not: James Stewart Precalculus for series and sequences
James Stewart Calculus for limits derivatives and integrals

These are 1.1k pages each...

Looking for 100 pages just to be 1 week ahead

[normal crystal]

you want a book that covers calculus but not a book that covers calculus for someone who didn't recognize calculus🤔

[heady ember]

Yeah you're continuing to cope about DnF being good

[heady ember]

Used to like Jacobson? What changed?

Just curious because I have it

[trail hemlock]

i’m being dramatic it’s still good

[heady ember]

Yeah but I'm still curious to know

[trail hemlock]

the explanations and the fact that there’s LA in the start

i mean i learned la but a refresher is nice

mainly his explanations

when he proves smth he will yap a little bit so ur not totally in the dark

[real marsh]

Lang supremacy

[vagrant rose]

thomas calculus uses feet as a measurement of length

i die

[remote vortex]

Why not cubits, like a normal person?

[oblique hatch]

I personally prefer the units “big” and “small”
Now the addition is
big + big = big
small + big = big + small = big
small + small = small (but sometimes big)

Subtraction is
Big - Big = Big (but sometimes small)
Big - Small = Small (but sometimes big)
Small - Big = undefined
Small - Small = Small

[remote vortex]

Surely small-big = -(big - small) = -small (but sometimes -big)

Also this is medium erasure for which I will not stand

[oblique hatch]

There is no -small and no -big

Everything is positive

[rigid osprey]

so would that mean
big x small = big [small>=1]
big x small = small [small<1]

[oblique hatch]

It me!

[oblique hatch]

Big * small = small (but sometimes big)

[gray gazelle]

What is this lol

[thin gale]

Thomas' Calculus in SI Units https://amzn.asia/d/hzqUlrm

[tribal crow]

an excerpt from Schroeder's Thermal Physics, if I recall correctly

[gray gazelle]

I thought it was from some kind of joke article 💀

[tribal crow]

no haha

just thermodynamics things :p

[gray gazelle]

Are they using a nonstandard notion of addition like floating point or just being nonrigorous?

[tribal crow]

nonrigourous, but this is a fairly standard practice in chemistry and thermo, so far as I'm aware

otherwise we'd be keeping hundreds of sig figs

[gray gazelle]

What are sig figs?

[tribal crow]

significant figures/digits

[glad rampart]

higher were you the one to recommend pgte to me a while back?

[tribal crow]

what was pgte?

[glad rampart]

practical guide to evil

[tribal crow]

I was not

[glad rampart]

damn

[tribal crow]

I think that was Xela?

[glad rampart]

no xela recommended something else i think

[tribal crow]

hmm

it might've been valley, from the looks of it

[tribal crow]

the point is that this is really impractical, and you usually don't need this amount of precision anyways

so we just... do this lol

oh wait

Spamakin didn't even include the next part

Very large numbers

[gray gazelle]

I'm glad I don't do physics

[tribal crow]

fair enough

this kind of thing irks me too, to be honest

[brave burrow]

What kind of math is this? Or it is physics 🧐

[gray gazelle]

It is certainly not math. (it is physics)

[brave burrow]

Normal day in physics, I guess

[tribal crow]

#book-recommendations message

it's from Schroeder's Thermal Physics

[vital bane]

shut up grass you haven't even done algebra yet

[remote vortex]

This is entirely fine in a post-rigorous way, although an important thing about being post-rigorous is that you've been rigorous before

[rain hound]

Schroeder is a good book :)

Anyway is this really that bad? This is how floating point actually works lol

statistical physics is all about approximations anyway

[tribal crow]

most physics students at this point have not been rigourous

[tribal crow]

I didn't say it wasn't!

[tribal crow]

no, but it's very funny

[gray gazelle]

I thought so too, but this part contradicted it. In floating point this is equal to 0, not 42.

[rain hound]

Wow the compilers have gotten so good that they can read we’re subtracting it off so just replace it with a 42 rather than carrying on with the significant error.

[vital bane]

Schroeder!!

[tribal crow]

!

[vital bane]

you're missing out

[gray gazelle]

But is Math + what I'm missing out - Math = what I'm missing out?

[vital bane]

[tribal crow]

reminds me of these two

these two books necessarily contain the sum of all human knowledge

[vital bane]

classic

[sturdy solar]

Hello everyone, i am looking for recommendations on books about real analysis that develop everything from scratch. Due to certain mishaps which i cannot mention, i am unable to cover calculus and real analysis independently, and need to develop both side-on-side.

I am not sure what i should do in this scenario, because most books at the very least expect mathematical maturity till single variable calculus.

[heady ember]

No I have done like 3 sections of Jacobson

[vital bane]

sotrue

[vital bane]

I think Bartle would be good for this

[sturdy solar]

How much of real analysis does it cover? How would you compare it to say, abbott's "Understanding Analysis" or terence tao's books on the topic?

[vital bane]

yes

almost every intro real analysis book's topics are the same upto isomorphism

[sturdy solar]

thanks, i will check bartle out.

[gray gazelle]

@cobalt arch what algebra book recommendations do you recommend? till Calculus and stuffs?

[cobalt arch]

Any standard textbook would do, even aops is good

[gray gazelle]

i dont have intermediate algebra solutions manual

but can umm Stewart's algebra and Trigonometry enough?

[cobalt arch]

Yes I guess, they all contain almost the same information

[humble creek]

what parts of evans' does a standard 1 year grad sequence in PDEs cover? all of it?

[molten mason]

There's a reason for that.... At university, learning derivatives take an entire semester to learn, integrals take an additional semester to learn. That's 10 months worth of content. Series is normally a few weeks in the middle of a Calc 2 semester.

Of course you can self-study much faster but I digress.

You can browse these:
https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
https://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx

There's also some great YouTube channels here:
https://www.youtube.com/@blackpenredpen
https://www.youtube.com/@brianmclogan
https://www.youtube.com/@NancyPi
https://www.youtube.com/@ProfessorLeonard

[rain hound]

Tao Analysis I and II. ZFC is given and not even natural numbers are taken for granted.

[cursive orbit]

it varies, but typically if you assume no PDE background then parts I and II, plus half of 3

[gray gazelle]

What books do people recommend for an introduction to smooth manifolds?

I found the book Manifolds, Sheaves, and Cohomology by Wedhorn and the topics seem more interesting than most other introductory books on the subject (like Tu or Lee)

[tribal crow]

alright, who do I gotta ping for this

@modern ruin @wary pier

you two are probably the only two I'm comfortable pinging here :p

[modern ruin]

Tu has an introduction to cohomology, also, from what perspective are you judging “more interesting” if you haven’t read the introductory material yet?

[modern ruin]

you can read about sheaves if you want independently

[gray gazelle]

I just looked at the table of contents and preface

I'm asking the question because I want to learn about this topic

[modern ruin]

is there something that you found interesting in the table of contents of wedhorn that isn’t in the other two?

like specifically

if you are trying to get fundamentals of manifolds Lee’s book is very solid, and i’ll stand by that

[gray gazelle]

Sheaves and abelian categories

[modern ruin]

why bother

you can read about them separately

if the goal is to learn fundamentals about manifolds you don’t need either of those

[gray gazelle]

How does Tu compare to it in your opinion?

[cursive orbit]

this does not have integration on manifolds

[gray gazelle]

I'd like to learn more stuff in the future than just that

[cursive orbit]

I think for self-study, tu provides a concise overview of manifolds, and then after reading tu you can just pick up a book on something else you find more interesting

[modern ruin]

yes, and i’m saying that Lee and Tu are both fine at setting you up for learning later stuff. you can really pick either one. Tu is a bit more friendly and you’ll get through it quicker if you want to learn about sheaves or related algebraic stuff or whatever else quickly, plus there is a nice, friendly treatment of de rham cohomology in Tu

[gray gazelle]

What advantages does Lee have over Tu?

[modern ruin]

i wanna say it just covers more stuff

i liked both books. if you read Tu you probably will end up reading Lee, but not vice versa

@gray gazelle ping (just in case!)

[gray gazelle]

Sounds like if i read Lee i won't need to read Tu

Maybe i'll read Lee then

Thanks for the recommendations

[cursive orbit]

the problem here is that lee is an 800-page or smth behemoth

and tu is like less than 300 pages

[gray gazelle]

any book recommendations for elementary number theory?

[floral lantern]

Rosen is fantastic

you don't need to do every section in the book not even close

but there's a lot of good stuff in it

[gray gazelle]

Then which section do I need to do first?

[gray gazelle]

Thanks for the recommendation, I'll go through it.

[floral lantern]

there's a couple obviously essential ones (mostly through chapter 6), then the rest are sort of optional topics outside of Order and QR which you should probably do

[gray gazelle]

Okay, thanks for the help!

[narrow tide]

random matrix theory books uwu? a friend would like some, I think an intro. so probably an undergrad friendly

[gray jungle]

Not familiar with the field but i know terry tao has a book on it, idk how friendly it is.

[narrow tide]

thank you!

[willow merlin]

best book for beginners learning algebra

?

[gray gazelle]

I will reply to the messages I got on this

#book-recommendations message

#book-recommendations message

#book-recommendations message

#book-recommendations message

[foggy quest]

what do you mean by "algebra"?

[gray gazelle]

Thank you!

#book-recommendations message

[gray gazelle]

may I dm ?

[gray gazelle]

Sure!

[willow merlin]

non-proof based algebra, for engineering,

the college I attend studies algebra in this order more less pre-algebra algebra 1, algebra 2 and linear algebra

but for taking linear algebra you have to pass the requirementsw

its similar to linear algebra I think but non proof based, I am on pre-algebra

Idk how to explain it

something like this is the syllabus

[foggy quest]

This is called linear algebra in the U.S.

[willow merlin]

sure but mines is not proof based

you guys always recommend me proof based books but I dont know any of that

but I am engineering, which algebra books are good from the groundup?

sorry I didnt wanted to sound rude or pretencious or anything, I was just explaining the situation

[foggy quest]

Yeah I recommended https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ and others recommended https://www.math.brown.edu/streil/papers/LADW/LADW.html, but both are proof based and build from the ground up. For books with less proofs, people recommended "Introduction to Linear Algebra" and "Linear Algebra and it's Applications" by G. Strang.

[foggy quest]

All you need to know is the basic notations and conventions of math proofs. The proof based books don't have any prerequisite beyond that.

[willow merlin]

I will try, lets see if I pass this test or not I just want to gather all the algebra info I can tbh

I havent been taught proofs but I will try to follow both

otherwise the other two ones you said I will check them out

[normal crystal]

for the people who ask "I want something that follows THIS course syllabus"
why don't you just use what that course recommended

sincere question

[foggy quest]

You can read https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf to learn proofs.

most american unis have a semester to learn from a book similar to this

[willow merlin]

I need more info aswell, I try to read everything I can but I end up failing anyway

I just want to gather more resources to increase my chances of maybe passing

like more perspectives of the same concept, explained in different ways

[queen fog]

This might be a strange question, but does anyone know of an abstract algebra book that would be considered the most boring abstract algebra book of all time?

Is there on that is like notoriously boring?

[tribal crow]

D&F

[queen fog]

I actually have that book

[gray gazelle]

Every math book is notoriously boring DW :). Just recall memories.

[crimson leaf]

Honestly I found Contemporary Abstract Algebra by Gallian to be very boring

[mossy flume]

D&F agreed

dry as fuck

absolute snoozefest

[crimson leaf]

D&F is weird because I like the examples but the way they put them in is just so mind numbing like having 2 pages of nothing but examples hurts to read for me

[vital bane]

bro wtf?? D&F is so fun to read

ya'll sleepin' on it fr

really good explanations and super fun exercises

[vital bane]

that's a fun book too

I love the biographies of mathematicians at the end of every chapter

and the little quotes everywhere

[remote sparrow]

didn't you have a blue diamond next to your name before?

[crimson leaf]

Lol yes I also had a different user name

[remote sparrow]

o congrats btw!!!

[crimson leaf]

Thank you! I'm not out like professionally cause I'm doing grad school apps now but I'm out everywhere else

[mossy flume]

yea I am sleeping on it

reading that shit puts me to sleep

[broken meadow]

im on team dummit and foote

its nice to read

im no genius or whatever so that might be why

[cursive orbit]

so true

[vital bane]

hell yea metal!

[rain hound]

Fraleigh is definitely the most boring abstract algebra book I’ve read.

Or well, didn’t read all of it cuz it was so boring. I noped out and read other books.

Shoutout to Aluffi for easily being the most exciting algebra book imo.

[weary fox]

Out of Mendelson and Enderton which is better as an introductory logic text? Or rather, what are the big differences? I have taken a very rudimentary class on propositional and first order logic and audited a class on non-classical+modal logics so I'm not a complete beginner but still not that advanced either.

[fierce hedge]

Does anyone know books on analysis of Boolean functions? a book having a section on it is also fine.

Also, need some theoretical cs books other than the textbooks. Nothing particular in mind but it would be nice if it's algebraic.

[vital bane]

need some theoretical cs books other than the textbooks

what does this mean

[queen fog]

this is exactly what i was looking for! something to get me to sleep

[vocal egret]

Looking for an introduction of real analysis book rn so I can get my IB IA done, idk which author to pick or start to read with. Recommend me some books pls, I need it for the essay

[cinder magnet]

https://mathematics.gg/books check over here

[vocal egret]

yo thx bruv

[cinder magnet]

np its there in this channels desc

[jaunty acorn]

Is there any lecture series for based on probability books like degroot and feller

[vocal egret]

Is Terrence Tao's Analysis I and II beginner friendly?

Gonna try out Wade's analysis rn

[slender wasp]

check the 2nd post in pinned messages

[vocal egret]

aight, thx bruv

[gray gazelle]

how does it compare to Artin?

niccolo machiavelli the prince

[vital bane]

Understanding Analysis by Stephen Abbott is the most beginner friendly it literally teaches you how to write proper proofs while teaching analysis

[vital bane]

I'm not sure I haven't read Artin

But I'm sure Artin is a good book too

[trail hemlock]

artin my goat

my pookie woookie

his dad is like one of the founders of modern abstract algebra or smth

[mossy flume]

Artin >> Dummit and Foote

[fresh skiff]

Artin's book seeems like a path towards AG

[oblique hatch]

What’s a good book to learn derived category stuff that isn’t Weibel?

[gray gazelle]

I always thought D&F is more advanced than Artin (haven't read D&F but have skimmed Artin a bit)

but after hearing opinions like "D&F is so slow it practically goes in reverse" I see that it's an undergraduate book

[slender wasp]

It is huge so it covers undergrad and grad stuff. Group theory is 220 pages. Ring theory is 100 pages, Field and Galois is 150 pages. That's all ug stuff but that's only half the book. Another 150 pages modules maybe could also be ug. But then there's still 250 pages seems mostly grad level. Although I'm not sure anybody does that part from DnF or whether they prefer something else by then.

[fierce hedge]

As in, other than the usual stuff say don't recommend clrs or sipser

[gray gazelle]

where do you guys buy used books for cheap. Thriftbooks often scams me

[rain hound]

Sad as it is to say this, very often I find cheap used books on Amazon.

But honestly the best source of physical books for truly cheap is a university library if you have one available, can’t beat free. Yes you don’t own the book, but do you need to? You don’t use a book forever.

[cursive orbit]

O'Donnell's analysis of Boolean functions

[fierce hedge]

Ah, he even has videos on this. Thanks!

[fierce hedge]

Just get them printed from somewhere.

[gray gazelle]

options vary depending on where you live and what languages you speak

[gray gazelle]

how much usually

[somber cloud]

Does anyone have begginer friendly book suggestions on olympiad level problems?

Not aiming to actually win an olympiad, just self studying for fun because I love these types of problems

[gray gazelle]

Titu Andreescu has a few books of olympiad problems with solutions

[remote sparrow]

Mendelson fleshes out the syntax of propositional logic a lot more than Enderton does, but Enderton includes more modern topics and is a bit more sophisticated. An axiom system for propositional logic is given in Mendelson. The deduction theorem is also stated and proven. Enderton covers the compactness theorem for propositional logic. A proof of unique readability of wffs is given as well. It also covers induction and recursion, which are pretty fundamental techniques in logic.

For first-order logic, Mendelson again goes much more into detail on syntax. While Mendelson and Enderton both give an axiom system for first-order logic, Enderton would probably call Mendelson's approach a "bootstrap" one. Mendelson really emphasizes getting results using mainly syntax, while Enderton permits any correct mathematical reasoning. Honestly, Mendelson's way is a little boring, but it is perfectly serviceable. I honestly prefer the approach given in Enderton, and it has a much more understandable proof of the completeness theorem.

For coverage of the incompleteness theorems, Mendelson, as you might expect, builds towards the incompleteness theorems in a very gory, syntactic fashion. I found it difficult to understand. I prefer the more high-level approach given in Enderton.

Mendelson covers two additional topics: axiomatic set theory (specifically NBG, not ZFC, but NBG is a conservative extension of ZFC. You can read more about the differences between NBG and ZFC at an informal level here) and computability theory. You're probably better off using different books at this point, though. There's also some moderately useful appendices, especially a consistency proof for formal number theory. Mendelson has solutions for some exercises, while Enderton does not include any solutions. Enderton does seem to be the more popular book, though, so there might be more solutions for it on the web.

Besides these texts, I'd recommend A Friendly Introduction to Mathematical Logic by Leary and Kristiansen. It skips propositional logic and dives straight into first-order logic, but that's not a downside. Many other texts do so, too. As a bonus, it's free online.

[slow yoke]

hey can anyone suggest a book about calculus 3. theory as well as practice solving? i have finished calculus 3 and cant get even one book

[weary fox]

Very insightful! Thanks :) Based on what you said I think I'd benefit most from mainly using Enderton and using Mendelson to get a different perspective on some proofs. I am also very interested in learning about NBG, as I have read a good bit of Enderton's set theory, so I'm relatively familiar with ZFC. I will also look into Leary and Kristiansen!

[foggy quest]

The one variable book here is good: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[spark jay]

Where did you study calc 3 from?

[somber cloud]

Thanks! These were not really the kind of problems I was expecting, but they seem good

[south scarab]

need like a pdf on integrating polar

ping me

[molten gulch]

https://tutorial.math.lamar.edu/classes/calciii/dipolarcoords.aspx

https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/ccaae11972cfc4c1987bcceffa660728_MIT18_02SC_notes_24.pdf

[south scarab]

double integral??

😭

[molten gulch]

well integrating in polar is double integrals

[south scarab]

oh

[molten gulch]

if you mean cartesian -> polar coordinate conversions

we got some easier stuff for that

[south scarab]

yeah ngl thats way too confusing

idk what the D under the double integral is

[molten gulch]

that's the region of integration

[south scarab]

[molten gulch]

http://tutorial-math.wip.lamar.edu/Classes/CalcII/PolarCoordinates.aspx
https://tutorial.math.lamar.edu/classes/calcii/PolarArea.aspx

this might be easier

[south scarab]

multivariable calc 😭 🙏

ok

ye the seocnd link seems good

ty

[molten gulch]

yw

[molten gulch]

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/pages/unit-4-techniques-of-integration/part-c-parametric-equations-and-polar-coordinates/session-82-polar-coordinates/

also this

[foggy quest]

One focusing more on theory is https://mtaylor.web.unc.edu/multivariable-calculus/

[gray gazelle]

I would like to read a book

Based of crabs

But like fr they are my favourite creature they’re very intriguing

[south scarab]

crabs are 😋

lobsters too

[keen vale]

what book do i use for intro proof writing?

[remote sparrow]

#book-recommendations message

[stoic sage]

I just got the book Representation Theory of Finite Groups by Burrow, I'm new to RT, any suggestions?

I'm trying to learn how to understand Langland's Program.

I have experience with some Category Theory, much more with Algebra, and much Graph Theory

I'm familure with PS Topology, enough that I'm trying to use it in a proof, I know a little Algebraic Top.

I'm completely new to RT, though I have books that show representations of structures.

My number theory is basic (not basic number theory), so I've heard I should brush up on that.

I have Topology, a Categorical Approach as well, it's on my reading list.

It's been suggested I study "Quivers", so far I like them.

ls

mis tell

Oh, and much of my experience crosses into Computer Science, I'm a developer by trade, but I'm looking to move out of that field and into mathematics. (Something I'm currently working on has connections to NP-hard, and I have something small on Groups, relating to Cryptography) I don't really like Crypt/Compression though.

[vocal egret]

Just checked the book, and the styles for me. Thanks for the reco

[vocal egret]

Yo, the reco's good. The texts are straightforward. Thanks for the reco

[remote sparrow]

#book-recommendations message

[rain hound]

All my friends love Serre Linear Representations of Finite Groups. Here are some lecture notes you may find helpful, https://math.mit.edu/~etingof/representationtheorybook.pdf
https://people.math.ethz.ch/~kowalski/representation-theory.pdf

[foggy quest]

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

[trail hemlock]

when in doubt Michael Taylor prob has some notes on it 🙏

[normal crystal]

he's the Michael Jordan of math notes, and they both are UNC men

[tawdry wigeon]

Any books on tensors/DG in AI/computer sci?

Dg is diff geo

[grave thorn]

"assistant professor"???

[slow yoke]

Professor Leonard

[burnt sorrel]

just so you're keeping your expectations realistic - I think from what you know so far it would take years of self studying before some of the statements in the Langlands programme (and like the basic stuff, none of the modern stuff) even makes sense. For the modern stuff you will definitely need someone to guide you

[fresh skiff]

Any thoughts about using Amann's book for selfstudy? (I mean after covering the first few chapters of Rudin )

[stoic sage]

Thank you for your advice, I've studied math in general for approximately 20 years, and graduate level 6 years. I'm contacting a local college to try to get some guidance as well, do you have any suggestion for finding guidance?

[stray veldt]

do you mean amann & escher?

[fresh skiff]

yes.

[stray veldt]

the books are vastly superior to rudin

the only "problem" is they frontload all the algebra needed for all 3 books in the first book

[fresh skiff]

What about starting from CH2. And if I need any thing related to algebra then I fill that gap by going back to ch1?

[stray veldt]

ye sure

i dont have the english version at hand rn but

1-6 should be known if you want to study real analysis

7 and 8 probably not needed immediately

same is true for 9 probably

10 and 11 are important again i would say

(though could be moved to a later point)

12 will start to be important once you do multivar

this is my review of chapter 1

[molten gulch]

We have the english version on hand

[stray veldt]

starting from chapter 2 its real analysis proper

[molten gulch]

one sec imma get the table of contents

[molten gulch]

For book 1 or book 2?

[stray veldt]

book 1

[molten gulch]

alr

one sec

[stray veldt]

book 2 and 3 go much beyond anything rudin does

[stray veldt]

book 2 could probably be stopped somewhere in chapter 7

[molten gulch]

here's the ToC for the english version

[stray veldt]

yeah, looks identical to the german version

so what i said just applies

[molten gulch]

also, for Amann, does it assume any prerequisites beyond proofwriting or that's all

[fresh skiff]

I see, so which one will be effective way to go though the book either direct starting from ch2 and filling the gaps when needed or covering important sections of ch1 (one you mentioned)

[stray veldt]

this is the standard book for 1st semester real analysis in germany

[molten gulch]

nod

[stray veldt]

its a hard book (so like rudin), but it covers the "proofwriting" prereqs even

[molten gulch]

nod

[stray veldt]

i think if you read the 3 books, its almost equivalent to an entire bachelor in mathematics

[molten gulch]

we'd considered going through some of it if/when we had time because it seems like a very interesting book

[molten gulch]

hot damn

well I'd assume that for algebra and whatnot you'd have separate texts right?

[stray veldt]

the books cover most important things from linear algebra (though not in depth enough probably)

and some other algebra stuff too

[molten gulch]

yeah

[fresh skiff]

He has presented a lot of material. But its interesting, Amann and eascher don't let his reader to feel bored cuz almost every page contains something new and interesting

[molten gulch]

hence weasked that

[mossy flume]

Never heard of this book

maybe I'll check it out

[charred thistle]

I don't think I have to defend myself, but I will still reply. My colleagues and I are currently writing our own book on introductory algebraic topology. I wanted to see what types of books people prefer in various contexts (rigor, language, etc.), so I was looking for recommendations. I've done something similar for real analysis in a different channel at a different time. I asked about books because I wanted to understand the types of literature undergraduates prefer. If you want to see more, please go to this message: #「graduate-lounge」 message

An addition: I asked about real analysis books in this very channel.

[fresh skiff]

Analysis (amman and eschar)?

[burnt sorrel]

Fundamentally I don't think you can have a book which fits all types of UGs. I'm pretty sure any low dimensional or geometric topologist would like Hatcher, whereas homotopy theorists probably dislike Hatcher. So like imo it makes the most sense to write a book with a "second course" in mind

e.g. Hatcher leads pretty naturally onto a topology of manifolds course, or knot theory, differential topology etc

The rigour and style will then depend on the area which you choose

[vital bane]

I have heard criticism about the lack of category theory in Hatcher when it's used a lot in algebraic topology

[burnt sorrel]

Right

But like geometric/low dimensional topology is a lot less categorical

[vital bane]

ooh I see

that makes sense

what do you think of Bott Tu's "Differential forms in Algebraic Topology"?

[burnt sorrel]

Very nice book

not necessarily a substitute

[vital bane]

well it has differential in the name so I'd assume it would be similar to Hatcher in the sense of leading into a topology of manifolds course

[burnt sorrel]

Yeah

I think a good (aka ambitious) course could cover a bit from both

[vital bane]

Since I'm interested in Differential Geometry Hatcher actually sounds nice

[burnt sorrel]

like ch2 and 3 of Hatcher

then do characteristic classes from Bott-Tu

and de Rham's theorem from uhh idk where lol

[vital bane]

both

[burnt sorrel]

Lee has a good description in terms of smooth simplices

Griffiths-Harris has an abstract nonsense proof

which might be in Bott-Tu?

[burnt sorrel]

Yeah I mean I'm a differential geometer lol

[vital bane]

the best kind of mathematician

[burnt sorrel]

also normal bundles, tubular neighbourhood and stuff like that

[vital bane]

What do you work in?

[fresh skiff]

[vital bane]

symplectic geometry?

[burnt sorrel]

my PhD will be on complex differential geometry

but I do have quite a bit of background in symplectic topology

[vital bane]

Woahh niceee, did you see Lee's book on complex geometry

[burnt sorrel]

My masters thesis was about Gromov-Witten theory

[burnt sorrel]

yeah tbh not convinced

[vital bane]

why so?

[burnt sorrel]

I'm not sure what it provides which the current books don't

[vagrant sedge]

Hi! I'd like book recommendation for the teaching of calculus and/or linear algebra for new undergrads. Any tips?
Just to give more info, I'm not looking for books teaching calculus/linear algebra. I'm looking for books talking about the practice of teaching these subjects, showcasing examples, talking about common doubts students have and how to deal with them, etc. It'd be a book to expose to teachers some ideas on teaching calculus and/or linear algebra.
If you all happen to know books like this, but for other subjects (e.g. maybe you know something like this, but for polynomials, for group theory, precalculus, ODEs, etc), I'd appreciate the recommendation as well. Same if you know video courses, recorded courses, podcasts, etc.
Thanks!

[vital bane]

different/better exposition maybe?

more choices are always good

[burnt sorrel]

maybe

[vital bane]

it might be good to ask this question in #math-pedagogy as well

[burnt sorrel]

but like unless you want to do purely analytic things you do kind of need some AG (ish) input

[vital bane]

oh nvm you did

[vagrant sedge]

@vital bane Just came from there 🙂

[burnt sorrel]

and Lee's book seems to stick with just the DG side

[vital bane]

you know I've had this question, DG is filled with curvature, that's the major thing you talk about, but in AG you never see curvature, is it just hard to capture curvature of a manifold/variety algebraically?

[burnt sorrel]

Baaically yeah

but also a lot of the most interesting work is connecting curvature on the DG side to stability conditions on the AG side

[vital bane]

what are stability conditions?

[burnt sorrel]

okay just had a look at the table of contents again: basically same content as ch0, 1 of Griffiths-Harris, or in Huybrechts, G-H has a bunch of other stuff and Huybrechts has a bunch of appendices

[burnt sorrel]

so like it's a concept from moduli theory basically. One of the simplest things in AG is vector bundles over curves, and like we'd like to form a moduli space of them. The issue is that if we include all vector bundles, then we don't get a very nice space. So the solution is to throw out the "bad" ones. A stability condition is basically a function which tells us whether a vector bundle is "bad" or not

[vital bane]

is this related to the "ample"-ness of a line bundle?

[burnt sorrel]

mhm

not really

ampleness is to do with embeddings into projective space

(I mean it might be, I haven't actually started my PhD yet lol)

So the simplest stability condition is called slope stability, which is that if we define m(E) = deg(E)/rank(E), then we want m(F) < m(E) for any proper subbundle F of E

on the DG side this corresponds to hermitian yang-mills connections

(also called Hermite-Einstein)

[vital bane]

wow

[burnt sorrel]

which is related to stuff like (A)SD instantons, donaldson theory etc

[vital bane]

is stuff like this done using category theory?

[burnt sorrel]

not really

until recently I think categorical input in this kind of area is pretty minimal

[vital bane]

I see, I would've assumed this sort of stuff where you make connections between related but different fields of math is where cat theory would shine the most

[burnt sorrel]

like the main difficulty tends to be analytic

[vital bane]

do you do mathphys as well?

[burnt sorrel]

I mean there's a general principle, which is that "stable objects in AG correspond to extremal objects in DG", which is sort of a generalisation of Kempf-Ness, but nothing which is rigorous

[burnt sorrel]

not really

at my UG where was a pretty strong pure vs applied split

and so I took a dynamics and SR course, and an intro course to QM but that's it

but I think a lot of stuff which I'll be doing is somewhat motivated by mirror symmetry

and so transitively, by string theory

[molten gulch]

https://tutorial.math.lamar.edu/classes/calcII/calcII.aspx

[peak hawk]

Thank you

[molten gulch]

whatever calc textbook your uni uses

and

do all the homework

[peak hawk]

Can I have a book or a resource that relates all the calc to real life examples

[molten gulch]

https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-

[peak hawk]

Noted it !

[peak hawk]

Sure

[molten gulch]

we don't have any off the top of our head, we kinda live in abstract-land for 3/4 of the day so we don't have any good answers to this; maybe try doing integrals and whatnot in context of physics

many popular physics textbooks a-la halliday and resnick have many problems that require integrals for solutions AFAIK

[peak hawk]

https://www.youtube.com/watch?v=dgm4-3-Iv3s

I heard this can help too

[peak hawk]

Sure, Noted.

[molten gulch]

Well this is just a video of him doing lots of integrals, try to solve them yourself first, and definitely not all at once as some are quite difficult when first starting out

[peak hawk]

Sure then thanks !

[molten gulch]

blackpenredpen's channel can be quite good, we agree

[tawny solstice]

Was there any debate about him?

[remote sparrow]

https://link.springer.com/book/10.1007/978-0-8176-8283-5

@fickle whale have you heard of this book before?

i was looking through a professor's past courses and he assigned this book before

[fickle whale]

Heard of it, seen it recommended, not personally read much of it

Homie threw me off by using degrees and even worse, using ^0 for the degree symbol

[remote sparrow]

[fickle whale]

But he does this cool thing where he marks optional chapters

[remote sparrow]

[fickle whale]

And he takes several historical detours which are nice for perspective

The last part I remember reading was some exercises about symmetry groups of polyhedra

Fairly early in the book

I would hesitantly recommend it

It's not garbage but I didn't see anything that spoke out to me, does seem to be one of the only real references on the topic

Tentative 6.7/10

[grave thorn]

As a fellow assistant professor from massachusetts, i understand

[trail hemlock]

hi yall this mighr be a dumb question, but what are teh prereqs for Spivak's Physics for Mathematicians?

[halcyon wasp]

Are there happen to be concise book for (insert anything here)

[gray gazelle]

A cup of coffee and lots of spare time.

[willow merlin]

what are the pre reqs to linear algebra

[umbral field]

high school algebra and mathematical maturity

[heady ember]

I don't think you need much mathematical maturity for lin alg

[trail hemlock]

my fav

[somber prairie]

Any suggestions for linear algebra and analysis books for someone who has a good bit of experience in both, but wants a more thorough understanding beyond the basics

• numerical analysis

I kinda know a good bit about all 3 topics but there’s a lot of holes in my knowledge

[heady ember]

Try some exercises from baby Rudin, perhaps, for solidifying your knowledge on intro analysis. I wouldn't necessarily recommend it for a first pass, but it might fit your needs well.

[molten gulch]

Analysis: Assuming you've finished a first course and/or have knowledge equivalent to the first 7-8 chapters of Baby Rudin then you can try folland's real analysis, Axler's Measure Theory, or Cohn's measure theory
Linear Algebra: Axler's LADR, Roman's Advanced Linear

[somber prairie]

Thank you very much for that info

May I ask approximately what would be taught in the first 8 chapters of rudin?

Bc I don’t have the book

[fresh skiff]

Almost all the usual topics that are covered in real analysis courses

[molten gulch]

Here's the ToC

• Real and Complex Numbers
• Basic Topology
• Numerical Sequences and Series
• Continuity
• Differentiation
• The Riemann-Stieltjes Integral
• Sequences and Series of Functions
• Some Special Functions

[fresh skiff]

Don't forget Axler's measure theory book. I love it

[fresh skiff]

Btw you can check three volumes of analysis too by Amman and Escher

See this
#book-recommendations message

Some overall review

[molten gulch]

OOH yeah Amann is very good

[fresh skiff]

Yes. I am thinking to study it

[molten gulch]

Also idk if we said this yesterday, but we really don't see this as a problem

[fresh skiff]

[molten gulch]

sadly no answer key AFAIK

so you'll have to be confident in your solutions

[fresh skiff]

Ch1 is kind of time consuming. There is a bunch of material (linear and abstract algebra, set theory and many more)

[fresh skiff]

Shit. I hope i will find solutions on MSE and for some problems maybe I didn't need solutions (sometimes own proofs makes a lot of sense)

[molten gulch]

oh yeah true

[molten gulch]

also mathcord might be able to help

[fresh skiff]

Also we have complex and real analysis channel which I really love

[fresh skiff]

Yes yes, exactly

[molten gulch]

[chrome wasp]

Did you do point-set topology, differentiation/integration in R^n?

[blazing canopy]

What have you already learned in this area? Numerical analysis is a pretty vast subject. Do you want to know more about the theory, or practice?

[formal parcel]

Anyone reccomend any textbooks for pre algebra? I saw miller, o Niel, and Hyde’s pre algebra book but I wanted to make sure it covers everything. Would anyone possibly know?

[blazing canopy]

When referring to "pre-algebra", approximately what age bracket of math level in school do you mean?

[formal parcel]

Like around middle school. I’m a lot older and I wouldn’t mind a more advanced book that tackles those topics but I don’t mind a regular textbook too.

I also just want to use what is popular and recommended and that textbook I found was mentioned in a google search and looks good but I wanted to ask here to make sure.

[foggy quest]

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

[foggy quest]

analysis + multivariable calculus and differential geometry: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[formal parcel]

Also is this a good textbook for pre algebra? I just want to make sure it covers everything I need to know https://textbookequity.org/Textbooks/Prealgebra.pdf

Idk which is better

[somber prairie]

I’ve done multivariable calc if that’s what you mean, no point set topology

[rose hazel]

Greetings, fellow comrades. I will be doing real analysis soon, and i have always struggled quite a bit with mathematical logic and proofs, and as much as i would love to pick up a large book on the topic, it does get fairly demotivating to read hundred of pages on a singular topic. Therefore, i would appreciate if anyone could recommend a concise book on this. (or maybe, even an real analysis book that's friendly!)

[somber prairie]

The practice.
I’ve learned about RK, including adaptive step size, although I don’t know how to efficiently solve the algebraic equations for implicit methods. I don’t know any more advanced methods

[remote sparrow]

#book-recommendations message

[rose hazel]

Which is the friendliest in your eyes? I'd rather something that's gentle at the start.

[remote sparrow]

probably cummings, but i like abbott the most

[molten mason]

Cummings also has a separate proofs book which is nice. I don't know how much overlap is between the proofs and real analysis books, but it could be beneficial to have the extra practice and by the same author.

[rough umbra]

What’re some textbooks a first graduate course/sequence in algebra might use?

[blazing canopy]

There are two very popular books: Finite Difference Methods for Ordinary and Partial Differential Equations by Leveque, and Numerical Linear Algebra by Trefethen and Bau. Those are more practical-algorithm oriented. For more low-level topics, consider "Accuracy and Stability of Numerical Algorithms" by Higham.

[remote sparrow]

aluffi, dummit/foote, hungerford, jacobson, knapp, rotman, lang

check pins

[rough umbra]

Oh, I did, I didn’t realize those were considered grad level

D&F/Aluffi I thought were ug

Preface to Jacobson says it’s for a first course in algebra after linalg hrmm, guess I’ll go with lang 🫡

(Another book I’m trying to read says prereq is a first grad course in algebra and I have gaps for some stuff like tensors of modules/algebras so I wasn’t sure what a standard book to try would be)

[formal parcel]

anyone able to answer my question?

[remote sparrow]

jacobson is an old book for yale students

it's plenty challenging

[heady ember]

Are answer keys really that helpful? I have never really cared for readily available solutions, since that doesn't necessarily help me ensure the validity of my proofs.

[cursive orbit]

I think aluffi is pretty good

[heady ember]

Hi Alphyte

[cursive orbit]

since being able to think categorically is pretty helpful

hello

[normal crystal]

pre-algebra US textbooks will be pretty standardized, similar material in similar order
you can just pick whichever suits your fancy

[foggy quest]

The one variable real analysis book here is friendly,: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/. It is a bit less friendly than Abbott (which is also decent), but much more friendly than Rudin.

[willow merlin]

best calculus book? or kind ish real anal typo beat

?

[trail hemlock]

spivak's calc

[manic token]

Hey

[fading wave]

does anyone have a good book on ODE (maybe containing PDE as well) that focuses on theory rather than techniques?

for an undergrad

[crude belfry]

Anyone here know of a good book on numerical methods? Preferably something with content that I can easily implement in C++ or Python, but it doesn’t have to involve programming.

[cursive orbit]

pde theory rigorously is kind of hard to do with just undergrad analysis

for ode, there is perkos differential dynamical systems

[karmic thorn]

A couple of other recommendations are Teschl's "Ordinary Differential Equations and Dynamical Systems" (available on the author's webpage) and Coddington's "Ordinary Differential Equations"

[vital bane]

I think once you get to grad level algebra isn't taught like a single subject right? it splits off into rep theory, homological algebra, module theory etc.

[foggy quest]

For ODE, this is good: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/. For PDE there is "
Introduction to Partial Differential Equations" by Folland and "Partial Differential Equations I/II/III" by M. Taylor; though these PDE books are for advanced undergrads or graduate students.

[heady ember]

Iirc you need to know some diff geo and fun analysis for that right?

[molten gulch]

dg mentioned

[vital bane]

dg mentioned

[foggy quest]

For Folland's book you need functional analysis; he covers some in his book, but I don't know if it is enough. For Taylor's books you also need some diff geo; he covers some diff geo, but it's a very terse treatment, mostly a refresher.

[willow merlin]

Which book covers orthogonal projection for dummies

[molten gulch]

I think any book on linear algebra would

[willow merlin]

Do they all present it in a geometric intuitive way

Sorry for the ping

[molten gulch]

I'm not too sure

[willow merlin]

What do you recommend

[vital bane]

Gilbert Strang

[gray gazelle]

What books do people suggest for introductory model theory?

[remote sparrow]

chang and keisler or hodges' A Shorter Model Theory for pre-stability theory material. for coverage of stability theory (though pre-stability theory material is also included), marker (note: contains many typos) or tent and ziegler.

[barren turret]

I agree that Cummings proof book is good. I purchased it and felt satisfied with it.

[tawny solstice]

What’s a good book on the Riemann Hypothesis?

[glad rampart]

i dont think there will be a whole book on one conjecture

[molten gulch]

what types of books would cover it (in context)

[glad rampart]

maybe like a complex analysis textbook or smth?

[cobalt arch]

There is The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike

What classical number theory book is considered the most comprehensive? The one by Hardy?

[oblique hatch]

What’s a good way to learn about Symplectic geometry?

[tribal crow]

@modern ruin ping again

TTeppa left so I can't ping him for this stuff anymore

[trail hemlock]

why did he leave 😔

[modern ruin]

da silva's notes are introductory https://people.math.ethz.ch/~acannas/Papers/lsg.pdf
also try mcduff salamon introduction to symplectic topology.
also, https://arxiv.org/pdf/1011.1690 is one way to do gromov nonsqueezing which is one of the fun classical theorems
also, maybe look for semi-introductory things by hutchings (but not before the first items on this list). i have not read all of https://arxiv.org/pdf/1303.5789, but i want to at some point.
maybe also find a symplectic geometer near you.

[oblique hatch]

Thank you!

[foggy quest]

Try "Partial Differential Equations I" by M. Taylor, which has a few chapters on symplectic geometry. The second volume also has a few chapters dealing with symplectic geometry.

[trail hemlock]

any recs for introductory physics book with calculus

it would be nice if it covered a superset of the ap physics 1 curriculum

like spivak's physics book is prob not the best choice lmao

halliday resnick maybe?

[cursive orbit]

university physics by young is the standard it seems

but for more advanced there'd kleppner/kolenkow and morin

[trail hemlock]

hmm i was dissuaded from using morin as an introductory text

what like maturity would you need?

hopefully nothing higher than analysis or a bit of abs alg

[remote sparrow]

ap physics 1 is algebra-based no?

you mean ap physics C?

[trail hemlock]

no i jus wanna learn physics

lol

oh yes, ap physics 1 is alg-based

[zinc thistle]

morin has no analysis or algebra 💀

[marble solar]

Heck and Wreck is a good book to learn physics from

It contains a lot of good insight, non-trivial examples/problems

[trail hemlock]

o_o

[zinc thistle]

i do recommend morin over K&K though

for an intro to classical mechanics

[remote sparrow]

what about taylor

[trail hemlock]

yeah idk the next thing aby physics i jus wanna learn smth interesting over the algebra based app 1 cirriculm

[zinc thistle]

taylor is better for a 2nd course in mechanics, even then i'd say it's slightly outdated and would recommend Helliwell & Sahakian's "Modern Classical Mechanics"

[marble solar]

I used Heck and Wreck for my mechanics class my freshman year. For E&M/Modern physics I switched to university physics. I felt University Physics was written for someone that can't fill in any details themselves

[trail hemlock]

ok whats the title of heck & wreck

[marble solar]

Halliday & Resnick

[remote sparrow]

you can use halliday/resnick/krane if you can find a copy

or like third edition of halliday/resnick

[trail hemlock]

yeah i saw your rec of this when i searched it up

just wanted clarity

thanks yall

[trail hemlock]

wait theres a 12th edition why use the 3rd one?

[remote sparrow]

newer doesn't necessarily mean better

[trail hemlock]

o_o

perfect i found the 3rd edition

thanks again

[remote sparrow]

[remote sparrow]

only minor downside is the derivation of the wave equation of a string isn't shown in the text? it might be in the back, not 100% sure

you can easily google that though

[trail hemlock]

good lord

1368 pages

[remote sparrow]

it's supposed to cover three semesters worth of physics...

it's like, you know, a calculus book?

[trail hemlock]

my computer is crying

sumatrapdf being pushed to its limits rn

[floral lantern]

who told you to not use morin as an introductory text??

[trail hemlock]

good lord

here we go

[floral lantern]

halliday resnick and krane is fine

[trail hemlock]

who tf is krane

[floral lantern]

but I oppose the notion that morin isn't fine as an introductory text for someone suitably mathematically advanced

[remote sparrow]

krane was a pretty short-lived coauthor

i think he only worked on the fourth edition

[trail hemlock]

mine says Halliday Resnick with the help of John Merill

[willow merlin]

Best intro to higher math?

[molten gulch]

What have you studied so far, what do you wish to study

[willow merlin]

I want to stop sucking at set theo and combi

Maybe the foundations of nt

Pidgeonhole príncipe, idk I just want am intro to math

[molten gulch]

Discrete mathematics by rosen

[molten gulch]

Ireland and Rosen

[floral lantern]

this is not an introductory NT book 💀 for someone looking for an intro to higher math

Rosen's "Elementary Number Theory" book might be at the right level, but I doubt it's what this user is looking for since it looks like they're looking for "intro to proofs + mathematical formalism"

[molten gulch]

okay fair

[forest temple]

are there any legally free textbooks on higher math? (referral from disc)

[floral lantern]

https://sites.math.washington.edu/~conroy/m300-general/ConroyTaggartIMR.pdf

[forest temple]

anything more advanced in the same category?

[cursive orbit]

there are many free legal "lecture notes" online that can easily replace a textbook

you'd have to get more specific for actual recommendations tho

[forest temple]

true, but I've mostly found slideshows that are incohesive without context

[forest temple]

something on proofs after a basic intro course ig

[floral lantern]

after that, you'll want to study an actual subject like algebra or analysis

[forest temple]

what does "algebra" mean in the context of higher math?

[floral lantern]

a theory-focused book in linear algebra (the gold standard is Axler) or abstract algebra (i.e Dummit and Foote, Artin, etc)

[willow merlin]

What are the preqs to Ljnear algebra

[floral lantern]

high school algebra

[cursive orbit]

after learning the basics of proofs, maybe you should study discrete structures. This site has a set of notes you can use to do that, along with exercises: https://www.eecs70.org

[willow merlin]

Thanks

[trail hemlock]

there is also Hardy's A Course of Pure Mathematics (public domain in the United States)

[tribal crow]

higher!

math

[molten mason]

My uni uses University Physics

[trail hemlock]

a uni using that

would make sense

[normal crystal]

give your Sully a black beard
same logic

[fresh skiff]

Today our TA was teaching us about functions of bounded variations in the course of Real analysis 2

When asked for reference she said that she has studied it from YouTube

I wonder, why I haven't seen this topic (function of bounded variations) in any real analysis text yet

Neither in rudin iirc, nor abbot nor bertal

Is there some good reference to study it?

[rough umbra]

yeah idk the book im reading just said a first grad course in algebra

[charred roost]

I’ve seen it talked about in “Kreyszig introductory functional analysis”, the space is a Banach space under a natural norm and appears in the Riesz rep. theorem for functionals on C[a,b]. Maybe check the Wikipedia for more, seems like it’s an interesting enough space of functions

[chrome wasp]

An introduction to analysis, W. Wade

[buoyant saddle]

did anyone read dune?

[fresh skiff]

Thank you so much I will check it

[fresh skiff]

I have a copy of it. But forgot to check in this book
Lemme check. Thank you!

[vital bane]

An Introduction to The Theory of Numbers by Niven, Zuckerman and Montgomery

good book but you do need some analysis and algebra knowledge before hand

though it is an elementary number theory, starts off with divisibility and GCD in Z

[gilded olive]

rudin introduces functions of bounded variation in the integration chapter (ch6?)

[fresh skiff]

I see, he did not mention the name

[vital bane]

Abbott also introduces that in the integration chapter

[gilded olive]

i cant post images on this channel for some reason but the physical copy i have has a full section for functions of bounded variatoin

i checked the PDF version and seems like it doesnt have that section

between integration of vector valued functions and rectifiable curves, the book has two more sections: functions of bounded variation and further theorems on integration

[gilded olive]

@fresh skiff can dm the pages on that if you want

[fresh skiff]

are you talking about baby rudin?

or papa/big rudin?

[fresh skiff]

yeah sure.

I found it in big rudin

But I am not that much able to understand it

[vital bane]

maybe check it out in Abbott Afzal

[remote vortex]

Yeah, it's not an easy notion (although surprisingly a function of bounded variation is always a difference of two nondecreasing functions, which is not a very intuitive description, but not hard to work with)

[teal tendon]

any suggestions
I am looking for free videos to practise for IMO

[gilded olive]

Baby

[fresh skiff]

I guess Abbott doesn't introduce it

[gray jungle]

so one way to think about the total variation on a compact interval is that its measuring how much a function "oscillates", and functions of bounded variation are the ones that "oscillate too much"

[gray gazelle]

You mean that don't "oscillate too much", I believe

[gray jungle]

yeah

it would be quite catastrophic if it was the other way around lol

[fresh skiff]

I see, i think I should spend some time on the topic to understand the visualization

[pliant wadi]

What's y'all's opinion on Artin's book for Galois theory?

How complete would you call the treatment?

[vital bane]

he does lol

look at exercise 7.5.9

[fresh skiff]

what

[vital bane]

well it's a passing mention of the concept I suppose

[fresh skiff]

omg I was blind. I read that section too and did problems too but I did not focused

[vital bane]

[fresh skiff]

my bad

[vital bane]

imagine if Abbott writes a measure theory and functional analysis book

[remote vortex]

Axler's Measure Theory book pretty much fills that niche.

Admittedly I don't know of any gentle introduction to FA

Let's write one

[vital bane]

I mean is it really meant to be gentle

it is a graduate level subject after all

[vital bane]

let's go

Open source textbook

[remote vortex]

It's as gentle as an introduction to measure theory can get.

[vital bane]

But you said FA

[remote vortex]

Ah yes, I thought your "is it really meant to be gentle" was referring to Axler.

[cursive orbit]

kreyzig

[rain hound]

I feel axler’s sections on it are quite gentle. I also think some of Brian Hall’s work is gentle.

In general though, yeah absolutely not. It is a cracked subject afterall.

[gray gazelle]

Calculus book recommendations anyone?

[tribal crow]

how rigourous of a treatment are you looking for?

[gray gazelle]

beginner friendly ig

But informative

[tribal crow]

hmm, the standard non-rigourous books people recommend here are Stewart and Thomas

[remote sparrow]

#book-recommendations message

[tribal crow]

but most calculus books are approximately the same

[gray gazelle]

Ah ok

[remote sparrow]

there are a number of undergraduate level treatments

[gray gazelle]

Thanks

[tribal crow]

if you want smth a bit more rigourous, you can try Spivak

[gray gazelle]

i see

[remote sparrow]

@remote vortex

[foggy quest]

Folland's book

in the context of measure theory

[marble solar]

I found Folland to be a little dry on the meaning of Bounded Variation and Total Variation. While good, the point of view is abstract. I like Stein & Shakarchi Real Analysis treatment of it in chapter 3

[rain hound]

Assuming you’re asking for singlevariable calculus. I like Calculus Made Easy by Silvanus Thompson. It’s free (legally!) on project gutenberg.

Blackpenredpen (youtube channel) and khan academy are also really helpful imo.

[rain wren]

stein and shakarchi is really really good

I used it myself just a couple weeks ago for a review

[gray gazelle]

Any recommendations for a discrete math textbook?

[molten gulch]

rosen's discrete math

[gray gazelle]

Thank you. Will check it out.

[molten gulch]

it's no problem :3

[gray gazelle]

Tysm

[sterile horizon]

anyone here like any Justin cronin novels?

its not a math text book, but he is a good author in my opinio

n

[covert mauve]

his sci fi novels were on my radar for a while, but at that point, i had read too many novels and eventually grew sick of the genre.

[pale hearth]

"there is a bomb at -45.29044,140.89544."

[remote ginkgo]

i already defused it dw

[rose hazel]

Greetings, i was unable to find any help yesterday, so i am looking for once again. Does anyone have a good high-quality lecture series on Introductory real analysis? (preferably ones in line with tao's analysis)

I am quite new to mathematical logic and intuition, and don't have the strongest calculus foundation, therefore it would be nice if the lectures could accommodate for that.

Any lectures series, yes. Doesent just have to be on youtube.

[remote sparrow]

#book-recommendations message

the videos follow abbott

good lectures for rudin

only downside is it ends on differentiation

or about chapter 5 of rudin

if he did all the way up to chapter 7 or 8 it'd be perfect imo

also the video quality is quite low

but i don't think i've had an issue inferring what was on the board

[rose hazel]

sometimes i wonder if i should just switch to abbott since there are very few resources available for tao, but tao's writing feels so much more friendly.

[cursive orbit]

because tao isn't really a standard book

[rose hazel]

I understand, but its still a pretty hard switch for me because i like the writing more. it feels more gentle, almost defines everything from scratch and sort of focuses on the general thinking a student might have with his proofs. (and mentions when they are informal!)

[molten gulch]

by whom

isn't kolmogorov's book a measure theory book

[gray gazelle]

it also has a pretty cheap dover edition

[regal wasp]

Whats a good reference for Lie Theory and Rep theory? I tried Humphries and it was too dry and I tried Harris and Fulton but it was quite thick

I’m in a real Goldilocks situation

[molten mason]

@sage python

[sage python]

Try Kirillov

[regal wasp]

Thank u

[wanton oxide]

Good morning! (or afternoon, or evening) Does anyone have a recommendation for an SAT math reviewer? Do they come in pdfs? Thanks.

[tribal juniper]

its actually goodnight

[fresh skiff]

I will check

[fresh skiff]

I haven't read Folland yet, but if I joined James group for measure theory then definitely I will use it.
Maybe Stein and axlers as reference

[fresh skiff]

I will check in stein.

Thank you guys

[molten mason]

Join

[foggy quest]

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

[fresh skiff]

yeah, I am working on the review sheet

[rigid flint]

Are there any good resources to learning jacobian matrices?

Or calc 3 in general.

[rain wren]

it will be our main reference so

you better

I think stein and axler wouldn't be sufficient

since they only do lebesgue measure on R^n?

[fresh skiff]

It seems like, going though Folland requires HUGE efforts

[ebon cedar]

im looking for math textbooks that are relevant in 2024, im a highschool student so hs math and introductory college math would be appriciated

also any textbooks that people use in hs/college 2024 in ANY subjects

[livid lintel]

Campbell Biology 12th edition

Chemistry The Central Science 14th Edition

[rain wren]

it's doable

I think if you can do rudin you'd have no issue with folland

[remote vortex]

I'd rate Folland as a bit less inaccessiblle than Rudin

[fierce hedge]

You mean baby Rudin right? I can't believe Papa Rudin is more accessible than Folland

[remote vortex]

I said Folland is less inaccessible

I.e. more accessible

[fierce hedge]

Double negatives smh 😭

[marsh ingot]

Double negation cofuses me

[gray gazelle]

Double negation doesn't not confuse me

[marsh ingot]

[brave burrow]

Double negation in English is so confusing but I have negative times negative = positive

[fresh skiff]

I am not totally comfortable with rudin, but not totally uncomfortable too.

(double negation again)

[marsh ingot]

If you already know about the contents of Rudin imo you can go for it

[fresh skiff]

I see

I hope first 7 or 8 chapter of rudin will be enough

[rain wren]

dude no one reads further than that

[fresh skiff]

Damn.

Oh wait I think Eric explained this in some server

[soft dagger]

so the order is basically pre-algebra, algebra, geometry, precalculus, calculus, as far as academic curriculums are concerned? (may vary per country/education system)

[fresh skiff]

Like Rudin'a treatment in later chapters isn't really good as compared to other books

[gray gazelle]

In music there are well known technique books (like Pischna books or czerny books for piano)
What could be analogous books in mathematics? (famous books that are classics for technique)
(probably technique in piano is like problem solving to mathematics)

[echo acorn]

practising études in maths is writing proofs to solved problems

[gray gazelle]

what type of solved problems?, I think I know what you mean, but just for being sure

[echo acorn]

more basic stuff, going "okay I know how the IVT works, but how do I show it?"

or I guess like the isomorphism theorems for algebra

[gray gazelle]

I had tought in that before, but I was thinking about some textbook or something
just as czerny etc
but for math

[echo acorn]

I'm probably not the best to ask then, I find going through a whole book a bit numbing, whether its Spivak or Schule der Geläufigkeit

[gray gazelle]

yeah , but a good example is Schule der Geläufigkeit , after practicing that book I noticed I improved a lot
so I was wondering if there was a similar textbook in math, which is similary trusted

[echo acorn]

It probably is Spivak or Rudin for analysis

not really sure for algebra

[gray gazelle]

but wouldn't spivak be an analogy to repertoire?

since is not like a general technique book

[echo acorn]

these are good questions, but I'm not sure I've actually read enough textbooks to answer them, sorry

there's always Bourbaki if you want something a little bit old fashioned, like I suppose Czerny is

but they do do things a little bit non-standard

[gray gazelle]

well , It is not like a direct analogy to specific czerny, or hannon or whatever, Just , classic problem solving book that is seriously trusted

since there are a lot of books, going for a classic is a good idea

[echo acorn]

I can't think of anything really that general beyond the high-school/olympiad level

[thin swan]

Dark Brilliance is good intro in Medieval-modern day history

[primal token]

any weel applied while including the proofs book for probability?

[rose hazel]

Any recommendations for proof books i could pair with real analysis books? (it should be a short reference, not a 500 page book for a entire course in logic)

[molten gulch]

Hammack's book of proof

[rose hazel]

To be honest, my friend had a copy, and I went through the first few chapters, and it felt way too grindish. The chapters about set theory have millions of repetitive questions which tire you out, and considering how big it is, it definitely doesn't fit my need.

[molten gulch]

Most set theiry and proof books have lots of problems on purpose

[rose hazel]

I am looking something that gets my hands dirty quick and early