book-recommendations

[gray gazelle]

I see, that seems super complicated

[sturdy shore]

yes, you can think of some distributions as graphs which integrate to 1, although that would be a naive way of putting it

[gray gazelle]

it feels like it LOL, can you tell me an intro prob book and I'll skim

[remote sparrow]

Well, it is possible to do probability without a full theory of measure, although it underlies modern probability theory. And you won't be able to unify continuous and discrete probability without measure theory.

[gray jungle]

I 2nd blitzstein and hwang as a lovely probability book

[sturdy shore]

an intro book would be like ross or grimmet stirzaker

[remote sparrow]

blitzstein and hwang is great

[gray gazelle]

when you say measure do you mean measure theory?

[remote sparrow]

Yes

[gray gazelle]

So I don't just need calculus i also need measure??

[remote sparrow]

no, you will be okay with just calculus for now

[sturdy shore]

for an introduction calc 1-3 is sufficient

eventually youd need linear algebra, diff eq for certain topics and definitely measure theory for a graduate level treatment

[crimson leaf]

Some probability introduces some measure like grimmet stirzaker

But they keep it self contained

[gray gazelle]

You really underestimate how much math there is and how difficult it can get if you've never seen beyond highschool stuff

I really thought probability was just flipping coins and basic bayes stuff

[sturdy shore]

probability is notoriously difficult I'd say

at least to me

[willow pecan]

Flipping coins continues to be important throughout all of probability

[crimson leaf]

I don't know much about higher level probability but my friend seemed to get stuck in his probability theory course mainly on the counting stuff

[sturdy shore]

not only is it built on advanced analysis, it has its unique difficulties

[gray gazelle]

Is stats and prob considered pure math?

[willow pecan]

Stats is stats

[gray gazelle]

counting?

[willow pecan]

Probability can be considered pure or applied

[remote sparrow]

Combinatorics is also very deep. I'd venture there are some hard counting problems in discrete probability.

[willow pecan]

Depending on who you ask

[sturdy shore]

probability can be considered both depending on your specific area

stats is definitely not pure math, some consider it applied math and some consider it its own thing

but it definitely uses a lot of math

specifically probability

[crimson leaf]

probability and combinatorics are very interesting to me random walks on lattices, random recursive trees, percolation, etc

[remote sparrow]

There is an entire field of math dedicated to sophisticated counting techniques called combinatorics.

[crimson leaf]

It is very beautiful and has connections to other math you wouldn't even imagine

You don't need calculus to start but it becomes very useful towards the end of an introductory course (at least understanding sequences and series)

[gray gazelle]

Ah so when kids think you are good at counting because you study math in university they think you are a combinatorics professional?

[gray gazelle]

You don't need calculus to start
Tell me more

[crimson leaf]

Lol you'll still need it relatively soon as you get into things that require power series and you'll start seeing derivatives

https://www.whitman.edu/mathematics/cgt_online/book/chapter01.html

I enjoyed this book as a quick introduction it's not particularly hard or anything though you may want to know proofs

Book of proof chapter 3 is also good

[gray gazelle]

By the way where do you learn about power series? My calculus book has integrations of power series and taylor series in later chapter but not the normal infinite series

[elfin marsh]

Calc bc

[crimson leaf]

Which book do you use

[gray gazelle]

Thank you 😊 I'm using Velleman's calculus

[crimson leaf]

The last chapter most likely

10.6 "Power Series"

[grave thorn]

even the cantor set can be represented by coin flipping

[remote sparrow]

I heard these two books are good and only require algebra of the non-abstract variety:
Mathematics of Choice: Or, How to Count Without Counting by Ivan Niven

Introduction to Graph Theory (Dover Books) by Trudeau

[crimson leaf]

Yeah Introduction to Graph Theory is very basic

[remote sparrow]

If you want to wait until you've finished calculus, A Walk Through Combinatorics by Miklos Bona seems like a very good book. The main exercises all have solutions in the book.

[crimson leaf]

It's good, hard exercises though imo

I would chapter 2 then 1 though

[gray gazelle]

This looks great it's only €12 I might order it

[gray gazelle]

Yeah I'm not going to be done until late 2023 or 2024 cause I'm slow at understanding so I'll do another topic meanwhile

[remote sparrow]

Do note combinatorics is a very broad subject, so combinatorialists don't only do graph theory. But graph theory is a good setting to learn some nice ways to count.

[gray gazelle]

When you say count do you mean literally addition and subtraction?

[crimson leaf]

Not exactly

Those are 2 of the principles

Once you read more you'll see

[gray gazelle]

What is the difference between Book of Proof and How to Prove it: A structured approach ?

[remote sparrow]

they are very similar to each other. try one and if you don't like it, try the other. or maybe you can read both, referring to one or the other back and forth.

https://www.maa.org/press/maa-reviews/probability-an-introduction

review of grimmett and welsh

[willow pecan]

[crimson leaf]

If like to explain which one you didn't like and why I'd be interested

[orchid mortar]

Stirzaker is amazing reference. Not too sure as a textbook, but could be good as that as well.

It's not too deep into the (measure) theoretical woods as well, at least for me

[remote sparrow]

grimmett/stirzaker has the companion book one thousand exercises in probability

[crimson leaf]

I know who to ask @grave thorn, you're the probability lover right? What's your thoughts

[grave thorn]

for measure theoretic probability?

[crimson leaf]

Grimmett Stirzaker or something similar

[grave thorn]

I personally like Jacod and Protter

it is short

but gets all the theorems in

if you want a reference book, Shiryaev's GTM is the best

[crimson leaf]

Just looking for something good to read alongside analysis right now

[grave thorn]

then (imo) jacod and protter

is your best bet

[remote sparrow]

isn't grimmett an intro calc-based book?

[crimson leaf]

Welsh yes

Stirzaker they also say is an undergrad intro book but uses measure

They just try to limit the amount of measure required

[left cloud]

hiiii so i just skimmed through his algebra book

i think it could be a good read if someone was interested in it

i only skimmed it so i don't really want to criticize anything 😭 but i think there could have been more emphasis on functions

[floral cairn]

[remote sparrow]

i think that would be in his functions book

https://www.amazon.com/Functions-Graphs-Dover-Books-Mathematics/dp/0486425649

[left cloud]

but i think it's nice as a pre-university book that's both mathematically correct (as far as i could see and just based on the author's reputation) and digestible

[left cloud]

hey that would make sense haha

[remote sparrow]

https://www.amazon.com/Elementary-Mathematics-Higher-Standpoint-Arithmetic/dp/366249440X

there's this three-volume series for math teachers with advanced math training that focuses on how one can synthesize their mathematically sophisticated training with teaching pre-college math

it's an advanced book so it's not meant to be used in a high school setting

[left cloud]

wowww interesting

[valid kiln]

Hey is the book The World According To Physics a good one?

[terse arrow]

Can anyone suggest me a good Additional Maths Book for Grade 8-10

[twin fox]

How is the book Calculus With Analytic Geometry by George Simmons compared to Stewart's Calculus ??

Do they cover same topics, which is good for self studying ?

[gray gazelle]

which text/book has the best treatment on the inverse function theorem and implicit function theorem of multivariable calculus/analysis in your view?

[tough zealot]

I only know a very good brazilian one
Tao has a cool post on the intricacies of the implicit FT, which Id recommend emphasizing more
that theorem is hard

[gray gazelle]

@grave thorn Privault's notes?

what do you think about them

[sturdy shore]

can you link the post? I couldn't find it

[tough zealot]

oops
got confused
Tao weakens the hypothesis of the inverse FT

I replaced it with something else in my head

still, the implicit FT is definitely the more elaborate one

[sudden kindle]

I read FT as fourier transform and was very confused

[remote sparrow]

#book-recommendations message

layla recommended hung hsi-wu's books

you might be interested in some of gelfand's lower-level books

like his books on algebra, geometry, functions, etc.

[cinder trellis]

Does anyone have any good recommendations for a book on functional analysis? Preferably something less intense than Stein and Shakarchi.

[grave thorn]

I havent looked at them

[gray gazelle]

I cannot compare it to any of the books by Stein and Shakarchi because I haven't read any of them, but Pedersen's Analysis Now is a fantastic book on the subject.

[cinder trellis]

Thank you, I will give this a look.

[gray jungle]

Peter D lax is legendary

[pseudo forge]

same lol

[fluid bay]

i like the proofs given in the first few pages of nicolaescu's geometry of manifolds

[dark veldt]

Guys what are good textbooks for high school algebra 2 for dumb kids like me

[sage kelp]

Any idea of sequence books on analysis such as Amman and Escher, Garmin, or Jacob and Evans?

[remote sparrow]

amann and escher are probably too difficult for most u.s. students

it has been used successfully in some german universities but i think they have some exposure to rigorous math beforehand too

plus no general eds

[sturdy shore]

seems like you have enough sequences of books in analysis?

if 2 books count as a sequence, there's tao, zorich, duistermaat kolk

though the third one starts from multivar

[sage kelp]

I haven’t read it yet, just skimmed it and not sure if will like their approach. But it is interesting how they cover so many topics across their books.

[sage kelp]

I know it’s quite several books already, I just want to see what other approaches have been taken by other authors. I mean, I think it is thoughtful to have like a clear path to follow in terms of the topics to study

[sturdy shore]

if it counts, there's stein shakarchi but I don't think that's the kind of sequence you have in mind

obviously rudin too

[sage kelp]

I haven’t heard of Stein. But definitely not Rudin at this moment haha. But that actually counts I guess

[sturdy shore]

why definitely not rudin?

idk what you are really going for

if you are looking for a from first principles style, tao zorich and amann escher are the only 3 I know

stein is a 4 book sequence of "topics in analysis" that only assumes single var analysis as prereq

[remote sparrow]

i own zorich, he does not construct the real numbers

he defines them axiomatically

it's not wrong, but maybe not first principles in the loose sense used here

[sturdy shore]

I mean from first principles in the sense that the book doesn't assume any prereqs and goes pretty far by the end of the sequence

I guess I should say, for beginners

[crimson leaf]

Schroder is one book but might as well be several

[remote sparrow]

one of my professors uses an old, out of print book by parzynski and zipse. we have it printed as a course packet.

[hallow oriole]

i could be wrong here but aren't US colleges some of the best in the world

?

[remote sparrow]

amann and escher take an abstract approach that would be inappropriate for most students. the highest math class anyone at one of these top schools has ever taken is going to be calculus. they have never been in contact with a proof in their life.

the most they could handle is rudin

[karmic thorn]

I genuinely think Rudin is worse and more pedagogically challenging

AE is nonstandard in its methods but pedagogically better

[sturdy shore]

better or worse pedagogically, it is way harder

[remote sparrow]

in a european setting, maybe, but the way math progression is set up in the u.s., it just won't pan out.

[sturdy shore]

being a good college has no relation to what kind of 1st years you are working with

yeah, impossible in us

[karmic thorn]

AE is certainly written in a way that it is better suited to a course sequence rather than something you can sample out for a standard course

[remote sparrow]

one or the other is not inherently better, as there are plenty of very skilled american mathematicians that come out of the schooling system, but you can't expect students who only have at most calculus and expect them to do well in A&E

they could pick it up as a nice reference

[steel perch]

Hello, I'm a freshman in high-school. I have a deep love for computer science, mathematics, and physics. I reside in the US but I have lived all over the world from Dubai to Canada. I think the classes are a bit too easy. I've always loved calculus judging by the context of what I hear online. I love how theoretical it is and how abstract its concepts are. I've explored infinite sums in a nutshell and am looking into solving differentials and integrals.

The issue is, I don't know where to start, in the most respectful way possible, I dislike how little stimuli school is giving me and I want to explore but I just don't know where to start. Any good books for someone that's just getting into mathematics? I don't want a baby book, I don't mind if it's challenging, just nothing that's extremely high level, any recommendations?

[remote sparrow]

you can do calculus if you want, and you will spend three quarters or semesters learning calculus, but the bulk of math after that generally has to do with proofs. you can start with intro to proof books. you can also jump into proof-based math books that require very little prior knowledge, like linear algebra, elementary number theory, or combinatorics.

[sturdy shore]

try spivak

[remote sparrow]

apostol is another alternative. spivak is much cheaper as a physical copy, but $100+ is still a hefty price tag

[steel perch]

quick google search, is that micheal spivak?

[sturdy shore]

that is the man

yeah or apostol

[remote sparrow]

velleman's calculus book is also rigorous but it is trying not to be a baby analysis book

[steel perch]

any good specific recommendations that worked for you?

[remote sparrow]

#book-recommendations message

[steel perch]

Thank you, absolute life saver

[remote sparrow]

some people also feel transition to proof books kinda suck (e.g. daniel rubin) because they can give a reader the impression that doing proofs is just learning specific methods of inference without needing to engage with the substance of some mathematical topic, and that instead proofs should be learned sort of through osmosis by imitating proofs in the book, playing around with conditions to get the result you want, sort of experimenting and then cleaning up the proof. i'm not sure what pedagogical research has decided is better but it's an interesting opinion.

certainly that is how i go about doing a proof, but i also absorbed the very formal approach these transition books take well, by just thinking of examples from natural language

i suppose it helped that the critical thinking class i took at community college discussed a bit of deductive logic, modus ponens, modus tollens, what an implication means etc.

[steel perch]

I see

With that information would it be appropriate to assume Proof and the Art of Mathematics by Hamkins is the 'best' book for learning proofs in a mathematical and applied sense?

Since you stated it's "Good to learn from and also interesting to read even if you're advanced, though being organized by mathematical topics rather than proof techniques may make it more difficult to use as a reference for particular proof techniques"

Correct me if I'm wrong but what I'm inferring is that it's more based around mathematical application and not necessarily honed in onto proofs specifically.

[remote sparrow]

just skim through the books and pick what you like. or just read several nonlinearly

[steel perch]

Okay

Once again, thank you. You've helped a lot (:

[remote sparrow]

[fierce hedge]

Can someone recommend some books for quick revision of multivariate calculus? I currently have Schaum's outlines

[indigo solstice]

Hello , can someone recommend book for the SAT?

[remote sparrow]

from what i gather, most transition to proof books focus on the basics of naive set theory, functions, and relations. chartrand has chapters on specific topics like algebra, analysis, and topology but they're not necessary. sibley is similar, though shorter than chartrand and having only algebra, analysis, and a bit of discrete math in part II. i do like his prose. it's not informal per se, but not stultifyingly stiff. he has an interesting chapter giving a brief exposition to metamathematics and philosophy of math.

anyway they're all still different than hamkins

i'd say sibley was my favorite, but i read hammack and the others from time to time

[remote sparrow]

Do some problems from stewart. Math Sorcerer has a workbook rec on his channel.

[sage kelp]

Idk, I was trying to go through it last year. It’s a beautiful book, very elegant proofs but it took me a lot of time

[random hawk]

I'm studying Calculus by James Stewart, I think you can refer that book

The book is quite suitable for beginners

[gray jungle]

Didnt we study through half of tao analysis together last year? or am i mistaking you for someone

If so you should definitely be ready for rudin at this point , unless you were on break

No its definitely you , i remember you asked me about sercoid metric spaces , ok so rudin will take you more time i think thats natural but at this point you should try to push through it , you would be suprised how much progress you can make going through it after some analysis exposure.

Take it from me , last year we were going through the same book by tao , now im studying mt and functional analysis , and rudin level analysis altho took me a heavy amount of time. Was worth the effort all the way.

Just do your best and you'll be fine

I know alternatively people like shroder here too

[rapid lily]

Amann and Escher is a great sequence to follow if you want to cover undergraduate analysis properly.

[tough zealot]

gonna recommend a more advanced book that I consider really nice if you want to have a feel for it. youre not supposed to get right from the start, but in case you want to develop an idea about how math goes after hs

try advanced modern algebra by Rotman
this would be a mid-late undergrad-early grad level book in abstract algebra abd it presents a lot of different topics in the field

[hearty steppe]

@sage kelp I’m going to be going through kreyzig’s functional analysis book at some point.

Do what I did… Jump right into the research arena where you can apply the math you learn. You won’t regret it.

At some point we all have to be less insecure about the rigidity in math we don’t have.

If you have time to do more baby rudin then heck take advantage of that. But I think you are a lot like me where Rudin’s approach is way too rigid for our POV but I still appreciate the heck out of that book

[sage kelp]

Did you finish Tao? I stopped in chapter 7/8 I think. I didn’t like it that much by then

[sage kelp]

I’ve heard great reviews, but I want to actually start reading it to see what the book is like

[gray gazelle]

hey

does anyone know a good book to teach myself physics?

i have absolutely no background whatsoever

[gray gazelle]

you know, physics is a huge field

i watched a few videos about quarks and now im really interested in learning more about them

[gray gazelle]

oh yea true

I don't think there's a book titled "physics" (not one that would contain a good chunk of physics in it anyway)

[willow pecan]

Getting to quarks is a very long ways away if you don't know any physics yet

[gray gazelle]

makes sense

so then

what would be a good book to learn like the absolute basics of physics?

[willow pecan]

Do you know multivariable calc

[hollow adder]

Anyone know a good second book in probability

I’ve learned all the basics of normal probability including discrete and continuous random variables

[willow pecan]

With or without measure theory

[hollow adder]

Uh

What’s measure theory?

[willow pecan]

Ok so without measure theory

[hollow adder]

What are the prerequisites to measure theory?!

[willow pecan]

Do you want something like stochastic processes then

Real analysis and topology

If you want to do probability at some point you will need to learn measure theory

[hollow adder]

Yea I’m fine learning measure theory first I guess. Do you need to learn a lot of measure theory to do more advanced probability?

[willow pecan]

Yes

Measure theory is the language of modern probability

[hollow adder]

Oh okay then stochastic processes works for now

Gotcha

[willow pecan]

Grimmett and Stirzaker perhaps

[gray gazelle]

me?

[willow pecan]

Yes you

[gray gazelle]

oh yea

[willow pecan]

You do need to know multivariable calc to do physics

[gray gazelle]

im a bit rusty though

but ive done multivariable calc in the past

plus some real analysis, some abstract algebra and a bit of topology

[willow pecan]

Ok hmmm

Maybe Arnold's classical mechanics is a good place to start

[gray gazelle]

aight

thx!

[willow pecan]

Then for qm, I seem to recall that Landau Lifshitz is a canonical suggestion

[remote ginkgo]

good reccs

[willow pecan]

After qm, you should be able to pick up a book on qft/particle physics

[gray jungle]

I did stop around ch6/7 indeed because tao altho a great "introduction" for my level back then,also didnt have much else to offer and i decided i was ready to commit to learning metric space analysis and metric space topology

It took me a couple difficult months but it was a good investment of time.

[karmic thorn]

I tried learning metric space topology from Tao V2 but it was definitely a big conceptual bridge for me

[fierce hedge]

Why is that?

[karmic thorn]

I'm not sure, maybe in the course of self-learning analysis it just took me a very long time to become comfortable with epsilon-delta arguments

And metric spaces just increased the abstraction a step ahead

[fierce hedge]

I also feel the epsilon-delta arguments a bit off. Like I know what is going on but something about them just feels off

[karmic thorn]

Yeah it definitely took me a long time to get comfortable with it all

But it got better with time

[fierce hedge]

What are you studying these days?

[dapper root]

The blade

🥷

[fierce hedge]

The movie or the series?

Oh wait, that's bladerunner nvm

[karmic thorn]

A bunch of things scattered around 😛 more analysis, dynamical systems, some differential equations based modelling, a little bit of model theory and very recently functional analysis

[sage kelp]

I guess i struggle a little with spending a lot of time breaking my head because I am kind of in a hurry

[sage kelp]

Gonna start real analysis and I want to cover measure theory and functional analysis as well

[remote sparrow]

university physics by young and freedman. pick up an older edition; they're significantly cheaper. or you could pick up a copy of the third edition of physics by halliday and resnick, published in the '70s. they are both calculus-based. many will recommend a mathematically oriented book, but physics is fundamentally about modeling empirical phenomena, and so imparting a strong conceptual foundation is more important than jumping right into mathematical physics. if you insist on something higher level, spivak's Physics for Mathematicians covers some mechanics. it requires differential geometry as a prerequisite, though the first few chapters don't use it.

[gray gazelle]

you could recommend something about measure theory to them

[gray gazelle]

you can learn both if you read Schilling

but then you still will have to grab some probability book to learn what probability is

[hollow adder]

Well I’m taking a probability class rn

[gray gazelle]

since Schilling is really, something more inbetween probability and measure theory

and something purely from probability would be useful

[hollow adder]

Wait so to understand measure theory do u really need to learn that much analysis and topology

[gray gazelle]

kinda

more analysis than topology

I mean, measure theory is fundamental to analysis in some sense, it is analysis you could say

uh

[crimson leaf]

Is Schilling like Dudley?

[hearty steppe]

No not really.

If you want to study it as a mathematician then yes

I thought Billingsley was the book everyone was talking about. Maybe I forgot about Schilling

[sturdy shore]

billingsley is probability proper

schilling is a measure theory book that has like couple sections on martingales

[grave thorn]

you dont need that much analysis and topology to learn measure theory

[forest sleet]

you can start learning it after just a term of intro real analysis that covers metric spaces

[cedar mist]

Any good recommendations for a book about coding and information theory? particularly in algebraic and error-correcting codes

[willow pecan]

<@&268886789983436800>

[karmic thorn]

Such a contempt for coding theory...

[willow pecan]

...

[ruby ingot]

any good resource about linear algebra?

[willow pecan]

Friedberg

[vital bane]

[remote sparrow]

first or second course

[ruby ingot]

from vector spaces, linear transformation, to forward

[remote sparrow]

so you want less emphasis on matrices? are you saying you've already worked with matrices prior or computational aspects prior?

[sage python]

Friedberg is good for that yeah

[ruby ingot]

yes, here is a little bit different

[sage python]

I mean it's clear ish this person wants a proofsy angle which is the only real relevant distinction

[remote sparrow]

yes, friedberg would be fine. i think axler is good too, but it's a controversial recommendation here

[gray gazelle]

For good reason.

[sage python]

You don't need to first go through a primarily computational book

[gray gazelle]

But what if you need to row reduce a matrix 10 years down the line?

[ruby ingot]

why it would be a controversial recommendation lol

[gray gazelle]

Do you know anything about Axler?

Do you know what a determinant is and how Axler feels about them?

[remote sparrow]

some people don't like the way he treats determinants and the characteristic polynomial

[sage python]

I mean a book like Friedberg I'm pretty sure does teach computations along with the rest. Definitely LADW does

[gray gazelle]

Friedberg has a short chapter dedicated to row reduction and whatnot.

It gives the topic exactly the amount of time it deserves.

[sage python]

So the main purpose of a linear algebra book that straight up ignores the theory and focuses on computations is for people in other areas for whom the theory is a distraction

[remote sparrow]

i mean, the reason i asked is that hefferon and meckes are pitched as first courses while still giving plenty of attention to theory

[gray gazelle]

I had a terrible math upbringing. Learnt 1000 formulae by heart and blindly applied it without understanding any of it through school of engineering. Can you recommend a self study math book? Fascinating and simple enough for a smoothbrain like me , but which helps me understand and visualise mathematics?

Background - I have studied set theory, probability, random processes, queuing theory, calculus (regular, multivariate and partial) and the usual trig and other high school math. Knew the formulae, understood none of it. Also Fourier series / transforms / laplace / z transforms but I have no idea what they are and how they’re applied

[sage python]

Perhaps, idk those two in particular but to me books like Friedberg are fine as first books

[thick quarry]

@gray gazelle Idk i've been trying to self-study for a while too, struggling with it. personally i've had to restart with basic stuff like real analysis/set theory, mostly because I need to increase my familiarity with proof techniques

[willow pecan]

Ok grinreaper maybe a good place to restart would be calculus

[thick quarry]

this hasz been helping me? https://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/1108439535/ref=sr_1_1?keywords=how+to+prove+it+a+structured+approach&qid=1668453631&sprefix=how+to+prove+%2Caps%2C135&sr=8-1&ufe=app_do%3Aamzn1.fos.fa474cd8-6dfc-4bad-a280-890f5a4e2f90

[willow pecan]

Velleman's How to Prove It may be useul

Or The Book of Proof

Or whatever it was called

For a calculus book, you may consider Spivak

[thick quarry]

so far I like this book, its helping me actually understand whats going on

[vast obsidian]

Friedberg not good for a first course

[sage python]

It's fine imo, what do you dislike about it?

[loud cradle]

roman's "coding and information theory" is nice for the basics

[vast obsidian]

Assumes you’ve got some experience with matrices, proofs, vectors

[loud cradle]

surely you don't need an entire course in matrices, proofs, vectors in order to proceed with friedberg.. that would be stultifyingly boring

exposure to the basic ideas in high school should be adequate imo

[vast obsidian]

Not an entire course, but he still assumes you know this stuff

[sage python]

Having TAd out of it honestly it feels like you can go into it basically 100% blank slate

[loud cradle]

i guess the authors themselves pitch it as a second course or a strongly theoretical first course, so your comments are fair:

for math students i think it's fine as a first course, maybe not for other disciplines that use LA

[sage python]

Yeah but it's the same way Rudin calls itself graduate level

There feels like this old sentiment that you need to do calc 1, 2, 3, computational linear algebra, differential equations, intro to proofs via discrete math, and only then can you touch Spivak Calc and proof-based linear algebra

And circumventing that will just short circuit undergrads' brains

[loud cradle]

"do 2 years of math for engineers and then you can start real math"

[vast obsidian]

What am I supposed to do then?

[sturdy shore]

ignore the old sentiment

[sage python]

Spivak Calc and proof based LA are kinda doable right from the start imo

You have to take it slower than you would if it's a second pass

But that's just true in life

[vast obsidian]

Right from the start as in blank slate or done at least some proofs like velleman/zhang

[sage python]

Spivak can be an intro to proofs imo

I had a bit of calculus going into Spivak but not much, when I took the placement test at my school I got one quarter of credit lol

[vast obsidian]

lol

I think you are too smart to recommend such approach Dami

[gray jungle]

I'm no padagogical expert but i have a claim that math student could just start studying tao ,ignore calculus books, then jump into metric space real analysis.

[vast obsidian]

Doesn't work for majority of people

[gray jungle]

and just wing what you need from calculus " computational abilities" along the way

[vast obsidian]

Are you being serious?

[gray jungle]

Yes

im confident i might be wrong

just a thought

[vast obsidian]

Did you forget comma

You can use me as guinea pig to prove your theory, cause I don't know calculus :)

[gray jungle]

I mean idk , thats lowkey how it went for me and i definitely had a lot of backfire where i was able to do proofs and understand conceptual ideas well ,but clearly had a lack of computational ability that i always try to improve via practice

so honestly ignore what i said , its a bad idea to skip calculus

well i suppose spivak is sort of a midpoint between calc and analysis which is why people love it here

[vast obsidian]

I think Spivak is too hard for the reputation it's got

[cedar mist]

excellent, thank you

[hallow oriole]

i think it would tho?

js do all the exercises

it might take a while sure but would still work

[vast obsidian]

That's like 1 exercise per week?

[hallow oriole]

not necessarily?

[vast obsidian]

I think you underestimate how hard these are for beginners

[hallow oriole]

there is absolutely no shot this takes more than four hours

but my argument is that they get better as they go

so like they'll go through a lot of other exercises at the start

that's why they gotta do all of em

[vast obsidian]

That is crazy

I guess you are just too smart

[hallow oriole]

cap

im a dumbass

[crimson leaf]

I do not think it is probably the most productive or realistic thing to do every problem in Spivak

[hallow oriole]

for proof you can look at my previous messages

[hallow oriole]

i mean once you get a solid grounding you can start skipping a few

but if you start with spivak

then i think doing all the problems in the start is necessary

you gotta get that sweet sweet mathematical maturity

[vast obsidian]

With no tutor and no exposure to proofs in the past

[hallow oriole]

i believe

okay

here

you know what

i have my little brother right here

ill make him read spivak

[vast obsidian]

do it!!

he will grow up with depression and hate you forever

spivak writes rigorously it's a challenge to even read his explanations cause there's no attempt from him to make it easy to understand

he is full rigor logic robot type theory turing machine writer

[remote sparrow]

lol

that's definitely an exaggeration

he might not be easy but his prose is definitely more relaxed than many other proof-based books

[vast obsidian]

if, then, surely, is, shows, consequently, by definition, thus, suppose

Not a single "Because [explanation]"

Everything is rigorous and robot steps

Page 10 btw

[cedar ridge]

That's coz the start is the deepest/most foundations the book gets

[crimson leaf]

Spivak is worth it if you have the time to spend on it

[vast obsidian]

I got the time but not the brains

[crimson leaf]

Well you do have the brains just maybe not the work ethic

[vast obsidian]

I do read -> try to do exercise -> get stuck -> ask here for help -> I don't understand explanation -> give up

How do you do it?

[crimson leaf]

read -> try exercise -> get stuck -> try again -> get stuck -> ask someone for help -> if I don't understand try to think about it more or ask more questions -> repeat various steps till I understand and get it right

[vast obsidian]

You don't move on until you understand the problem?

[crimson leaf]

I might try other problems in the mean time but I always come back to it

Most problems I'm working on wouldn't take that long to do

[vast obsidian]

Wow

Stop being so admirable

I guess I need to step up

[crimson leaf]

I mean most problems I don't really have a choice I'm getting graded on them

[remote sparrow]

spivak has a solutions manual at least

[vast obsidian]

For like 1/3 of the problems

But they are easy for this server so I can just ask here

[crimson leaf]

Don't use solution manual unless you're convinced you have the right answer and you want to check

[remote ginkgo]

spivak's book sucks

all of his books suck

[crimson leaf]

What do you recommend again Apostol?

[remote ginkgo]

there are plenty of good books on manifolds and multivariable calculus

shifrin has a nice multivar book that covers some basic manifolds & differential forms

if you want single variable calculus

lang's book is fine

it's a little weird though

you could just pick up everything from khan academy real quick then go solve some real problems

then go back and fix up your misconceptions later with rudin or something

[foggy relic]

Browder covers all of this 🙂

[rapid lily]

Why is Spivak bad?

In particular, his calculus book.

[remote ginkgo]

browder is good

[remote ginkgo]

try reading it and see for yourself

[gray gazelle]

"Why is it bad?"
"Just read it."

Do you have an actual argument, or do you just not like it?

[remote ginkgo]

yeah i do

but it is so self evident that the visceral response you have to trying to read it

will outweigh the sense i can try to communicate to you second-hand

[gray gazelle]

It is clearly not self-evident if you're being asked.

[remote ginkgo]

that's not self-evident

[gray gazelle]

I regret asking and no longer want to know.

[rapid lily]

I tried reading a few parts and it looks quite good to me.

So I think you need to specify some parts that you think are not good about it.

[remote ginkgo]

in a vacuum it's fine

[remote sparrow]

zlibrary is back

[hallow oriole]

?

where

if you did find one it's a scam

don't download anything off of there 👍

[zealous light]

(#rules)

[hallow oriole]

ntn here is against the rules

not even toeing the lines tbh

its js a bit off-topic

[elder stratus]

Hiiiii

[remote sparrow]

just looked into it, word is that it's fake

😭

[carmine jungle]

Hi!

[placid monolith]

this is the first chamber and one of the best chapters because it teaches you basic principles

there’s no point picking up a calc book if simple algebra is difficult

[vast obsidian]

why not just libgen?

[vast obsidian]

I have a question about this

[vast obsidian]

It's not the material that's difficult it's the way he explains/writes that's hard to understand

[quick hornet]

it seems pretty explicit to me

dunno how youd make it more clear

[vast obsidian]

Even if it's "simple algebra", when he makes it sound this rigorous and difficult, it's hard to follow and easy to get lost in his jungle

[quick hornet]

i mean, he uses a lot of signpost phrases and whatnot

[vast obsidian]

Instead of saying i.e. "a - b is in collection P" just say "a - b is positive"

[quick hornet]

but this is reasoning from a formal definition

you need to work in the terms of the formal definition

[vast obsidian]

The formality is what makes it hard to understand even if the math is very basic

[quick hornet]

thats kind of the point though?

check your formalism on basic facts to make sure it works

its overkill of course

[vast obsidian]

He could make 1+1 sound like idk super advanced mathto me and I wouldn't be able to conclude it's 2

[quick hornet]

this is far from unique to spivak

its how any book that introduces proofs will look

look into, say, lang's basic mathematics or w/e

[vast obsidian]

No lang is super easy and explains in way less formal way than Spivak lmao

Same with Velleman

And book of proof guy

[steady solstice]

Hey guys, can you tell the best and easiest ways to master calculus i.e., differential equations, continuity and differentiability, integrals, applications of derivations etc

[placid monolith]

i find it pretty understandable

[placid monolith]

khan academy

[vast obsidian]

no shit if you're already familiar with proofs and have some level of math knowledge

[placid monolith]

is really good

[placid monolith]

by level

do you mean someone learning calc who has never even touched maths before

[vast obsidian]

never touched calc yeah

[steady solstice]

Any other recommendations? Khan academy explanations are great and actually I understand calculus pretty easily but I genuinely can't do the sums by myself most of the time and need some sort of external help

[placid monolith]

if you have a good understanding of algebra

you’ll be fine

[quick hornet]

this is how lang introduces positivity in basic mathematics

it seems stylistically similar to me - if anything it explains even less

[placid monolith]

erm let me try think

[placid monolith]

most calc books wouldn’t be helpful i think

[quick hornet]

¯_(ツ)_/¯

[placid monolith]

@steady solstice

what do you find difficult

the concepts or doing the work

[steady solstice]

I find it difficult finding what to do exactly in the first few steps, like which formula to substitute, which trigonometry value to add or which method I must use

The latter steps I can do with ease

So practicing calculus is ez for me but I obviously can't do shit in exam

[vast obsidian]

Much easier to read, less formal wordings, reference to geometry, uses words like "positive/negative" instead of collection. It reads like someone is speaking to you

However reading Spivak it's like reading a programming language

[quick hornet]

i mean idk

i think being able to reason from definitionsr ather than relying on preexisting geometric knowledge is an important skill to learn

at least for the kind of student in spivak's target audience (i.e. a fledgling pure math student)

if you cant substitute the definition in for the term - like if the difference between "is positive" and "is in P" is tripping you up - i genuinely think thats a deficiency that needs to be corrected through practice

[placid monolith]

maybe ur issue is not calculus but trigonometry

this was actually me for a long while in calc

my normal algebra and trigonometry wasn’t that good

[steady solstice]

Even if I put out all the trigonometry formulaes in front of me, I have no idea which to use

[placid monolith]

do you fully understand the concepts of what your trying to do?

[steady solstice]

I could keep on practicing but if I keep on seeing the solution then it's really useless for exams

[placid monolith]

then search up the topic you are in and do some practice questions

it seems like you understand once you see

but like when u do it you don’t

[steady solstice]

I understand concepts

But I don't know the timing and what to apply exactly

[placid monolith]

so find some questions that go from easy to hard

and then work on them

[steady solstice]

I haveclear understanding but I have problem in applying basically

[placid monolith]

for the first few, maybe try seeing a question that is related but different values

and apply it

[steady solstice]

So do step by step slowly?

[vast obsidian]

Yeah this is true, and a major issue at least to me. I couldn't do inequalities for shit when I did Spivak, but then I moved to some other books (Like Lang and Chartrand Zhang, Velleman) and it all was simple, I just find Spivak very hard to follow

[placid monolith]

yeah

and understand what you actually are doing in each step

once you finish the east questions with a step by step help on the side

[steady solstice]

It might possibly work but it's a long method for sure

And I need a proper calculus book to support it

[placid monolith]

then you do more easy questions without help

though if a question is difficult

that is good

don’t spend 5 minutes and think oh i can’t do it let me get answers

take your time, let it sink in your head

try different methods, if it doesn’t work scribble it, try another etc do these values work and do i get this answer which looks right

[steady solstice]

I get what you're trying to say

@placid monolith Is there any other viable method though?

[keen badge]

Hello, which book do you think is the best option to start algebra?

[remote sparrow]

abstract algebra or the one where you solve equations

[quick hornet]

"algebra" meaning...?

[remote sparrow]

what does ms stand for

[gray jungle]

What are some good/classic introductory books to model theory?

[lean pagoda]

For an introductory text, probably Marker

[placid pollen]

is this the poor man's guide to spectral theory
https://m.media-amazon.com/images/I/91ieuKNlloS.jpg

[vast obsidian]

Not a book request, but how do you guys take notes if you even do

[grave thorn]

pen and paper

if needed i type it in latex

[vast obsidian]

Yeah but I meant like, how do you structure your notes

Do you only write down theorems, definitions and proofs or do you try to make some kind of summary/cheat sheet for you to come back to or whatever

[hearty steppe]

interesting twitter publication I am skimming through rn

Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications https://pubs.acs.org/doi/10.1021/acs.jctc.2c00574

[gusty smelt]

i personally dont take notes

i think its counter productive

i would rather pay attention in class and then refer to some resource later

maybe i jot down references sometimes

[sudden kindle]

I take notes , helps me process lectures

[hearty steppe]

I wonder if my baby rudin chapter 1 notes would be helpful to anyone. I mean... I feel like after a while I just can jot a couple things here and there to recall later for something I find very abstract but I need a phrase or statement to connect things.

I don't take notes abrasively. Doesn't work for me. The whole note card thing doesn't work for me either.

i mean trello is technically a digital note card engine so... those kind of notes work for me.

[gray gazelle]

Do you think lectures are boring

[sudden kindle]

No

Not generally

[tidal elm]

anyone want to work through fulton and harris with me?

[cedar flume]

Any book recommendation for topology

[heady ember]

Be more specific

Point set or general topology

[cedar flume]

General topology

I'm looking at a book by James Munkres

[willow pecan]

Pretty classic recommendation

[gentle arrow]

i have been told that munkres is too slow

and based on #point-set-topology pins

[willow pecan]

You can always go faster

[cedar flume]

What do you mean ?

[heady ember]

I have heard some people say that murkres spends too much time on stuff that isn't too important

[heady ember]

Also, I have heard that Lee's Intro to topological manifolds is a good book on general topology. So perhaps, you can flip through a couple pages and see if you like it, I guess

[cedar flume]

Ok I'll try thank you

[heady ember]

If not you can always find another one you like

[cedar flume]

I was trying to find something that will touch some basics & slowly get into topology

[tidal elm]

Lee is nice

munkres isnt bad

[sturdy shore]

do these two not mean the same thing

[fierce hedge]

Another efficient point set recommendations are - Hatcher's notes on point set topology and 1st chapter of Brendon

[grave thorn]

for pointset you could use Hatchers notes

[heady ember]

Wait really? Isn't 'general topology' done later than point set topology?

[grave thorn]

"general topology" is the same things as "point set topology"

[sturdy shore]

I'm curious what you thought they meant content wise

[heady ember]

Well, Im still quite a bit far off from doing topology so my original intent was to just make the question clearer to anyone who might be answering. Don't really know too much content wise about either topic for now.

[cedar flume]

I gave some rough reading, wasn't hard to understand Lee, thanks

[glacial crypt]

Yes so you are using dnf?

I mean everyone learns in different ways so if you're self studying you can just try it I suppose

Yep

I find it pretty good

Why though

I mean it's a textbook and I find things are explained well

Isn't the whole point of self studying so that you can study in a way that works for you?

If you find your current book inadequately challenging you can pull exercises from other books

[sturdy shore]

I don't think D&F is easier than Artin?

in fact I'd say it's slightly more difficult from what I've skimmed, but definitely not easier

[glacial crypt]

Yeah just find exercises from other books, no need to switch over unless they have like entire theorems missing (why?)

w a t

[heady ember]

Np! Glad I could help!

[orchid mortar]

Does anyone here have opinions on the Knill's Linear Algebra/Multivariable notes?

[gray gazelle]

it's not a intro to general topology

[gray gazelle]

Dugundji

the book by Kuratowski and Engelking is also good

and I don't mean Engelking's General topology because that's too hard for you

[hazy elk]

How terse is Dugunji ? (Compared to (say) Rudin or Hungerford)

[fierce hedge]

Is it Introduction to Set Theory and Topology or (just) Topology?

[heady ember]

Oh...

[gray gazelle]

any good topology book will teach you basic set theory

even better if it does some more, with ordinals and cardinals

[fierce hedge]

I meant that Kuratowski has written two different books - "Introduction to Set Theory and Topology" and "Topology" which one was it
Anyway, I read both of them and I'd stick to dugunji or willard

[fierce hedge]

Is there any other book except dugunji that does ordinals and cardinals? Except ofc proper a set theory book

[gray gazelle]

Kuratowski and Engelking

I don't know Kuratowski's topology book, but it does sound interesting

[fierce hedge]

Can you tell me the name of the book, it's mildly confusing

[fierce hedge]

I found separate topology books by Kuratowski and another book Engelking

[gray gazelle]

Introduction to set theory and topology by Engelking and Kuratowski

I didn't mean the monograph by Kuratowski, nor the monograph by Engelking, which are another two topology books

The one by Engelking is a famous reference text and it shouldn't be read to learn topology

[fierce hedge]

Not sure about monograph but there's, Topology by Kuratowski and General Topology by Engelking

Ah, got it

[gray gazelle]

I think they satisfy the definition of a monograph

but I'm not sure, I'm not even from an English speaking country

[fierce hedge]

In all honesty I don't even know what a monograph is

[gray gazelle]

Oh, I see where the confusion is.
Introduction to set theory and topology is actually formally a book by Kuratowski, with a supplement from Engelking about algebraic topology

[fierce hedge]

Yes, I was about to say that. Also, it is a monograph whatever that means

[gray gazelle]

monograph means more or less a book by one author

[orchid cobalt]

so I'm planning to buy one of three books
Infinite Powers by Steven Strogatz
Unknown Quantity by John Derbyshire
Journey Through Genius by William Dunham
cuz these are the cheaper books I could find

[sullen raptor]

Good calculus 3 books?

Preferably for self teaching

And also, for the love of god please make it have answers

[gray gazelle]

are there any good calculus 1 books

[sullen raptor]

Spivak's book on calculus

lol

[remote sparrow]

if you like spivak, you might like hubbard and hubbard

[sullen raptor]

boi it’s 117.81 on amazon

But looks perfect

Vector calculus and linear algebra

And I don’t know what are differential forms

[gray gazelle]

You pay for books?

[sturdy shore]

you arent supposed to

book teaches it

I think shifrin better tho

[sullen raptor]

A ok, I just have some background in vector calculus and linear algebra and want a more rigorous understanding

[sullen raptor]

some yes, so I don’t stare at my computer

[gray gazelle]

Understandable.

Eye strain is hell.

[sullen raptor]

Yeah

[sullen raptor]

This one has manifolds, interesting

Does it teach manifolds at the end?

[sturdy shore]

yes at an elementary level

to be clear so does hubbard hubbard

they cover roughly the same stuff I just prefer shifrin because he has his own lectures up on yt and doesnt have every proof at the appendix

[remote sparrow]

it's cheaper if you buy it directly from their website

google matrix editions

[sullen raptor]

That’s cool, lectures are the best

[sullen raptor]

aight

[sullen raptor]

right now

[remote sparrow]

if u want?

[sullen raptor]

They ship only to US

But yeah way cheaper

[remote sparrow]

the official PDF edition gets occasional updates fixing errata, but they'll email you a list of errata when it does update

[remote sparrow]

they should have separate pricing for international

[sullen raptor]

It’s 63

Better but still pricey

[sullen raptor]

sounds good, I will keep that in mind

[remote sparrow]

i feel ur pain, tho i have a hard copy. trying to build a small library

[sturdy shore]

isnt 63 fairly acceptable price for a book like hubbard hubbard

that thing is massive

[sullen raptor]

How massive is massive?

[remote sparrow]

the binding's really good too

[sturdy shore]

900 pages or sth

[sullen raptor]

alright then it’s pretty good for that price

[sullen raptor]

Out of curiosity, what’s one of your favorite books in your library?

[remote sparrow]

understanding analysis by stephen abbott

[sullen raptor]

I’ve seen this one before, springer has the best stuff

[remote sparrow]

sometimes, yes

[gray gazelle]

never had a problem

Good for you!

I'm sleeping well, lowest brightness, no blue light.

same for phone

never was a problem

I am glad that these work for you.

I've been experimenting with these things and they help, but I still get some strain. I think I'm spending too much time on screens.

The extremely bright rooms at my university do not help.

maybe, I sit near pc almost all the time

but I do prefer reading in slightly darker places, not too dark, but not too bright

like when a lady at my institution always turns on light for me and says it's too dark, but it was actually ideal for me

but I'm agreeable so I don't complain

[sullen raptor]

The no blue light helps a lot

Feels way better for my eyes

[sturdy schooner]

yo who has a good kids chapter book

im trying to get my son to like reading

[remote sparrow]

flat stanley?

um those treehouse books

if you asked maybe a decade ago harry potter 🤢

cornelia funke's ink books or whatever

[willow pecan]

How old is your son

[remote sparrow]

i'd say eragon but the end to that series was super underwhelming

[willow pecan]

PJO perhaps

[remote sparrow]

what's pjo

[willow pecan]

Percy Jackson and the Olympians

[remote sparrow]

figured

never read that tbh

was hype with other people when i was little tho

warrior cats maybe

[willow pecan]

I mean if your want your kid to be a furry...

[remote sparrow]

nah that would be redwall

those books were so good

[cedar ridge]

i liked it

[misty wyvern]

How did people here learn complex geometry and Hodge theory as topics (if at all)?

[foggy relic]

amazing book

[pine cloak]

yh the series is quite good

but let's not talk about the graphic novels & movies...

[gray gazelle]

People recommend Voisin’s Hodge Theory and Complex… Geometry book

[grand thistle]

any books on interesting series/integration techniques that cover stuff like generating functions, recurrences, special integration techniques like leibniz's formula, differentiation under the integral sign, cool substitutions like normalization onto [0, infinity) and other tips and tricks?

[crimson leaf]

For generating functions I can recommend you two books I like generatingfunctionology and analytic combinatorics both are free online

[grand thistle]

is there any book that covers the intersections of these topics? i find things like solving hard integrals using series expansions and the binomial theorem, etc. very satisfying

[gray gazelle]

Anyone have a book recommendations for graph theory?

An introduction.

[polar phoenix]

https://twitter.com/LodhSpringer/status/1592878811388911617 Sounds neat

Rémi Lodh (@LodhSpringer)

"a great resource that provides an excellent overview of some recent mathematics without requiring the reader be an expert"
Nice review of Bogdan Grechuk's book
Landscape of 21st Century Mathematics
in the December issue of the Notices of the AMS
Link: https://t.co/9DfhJmrAGE

Likes

460

Twitter · Nov 16, 2022, 1:54 PM

[gray gazelle]

it does

[gray gazelle]

I’ll read this, this week

[zealous light]

The content is interesting, no Wasserstein stuff though </3

I briefly skimmed it with my uni’s springer subscription

[gray gazelle]

you're an optimal transport person?

[zealous light]

Yeah

I guess it’s shifting more towards gradient flows as a whole now, but yeah

[gray gazelle]

I'm a nothing person

[fierce hedge]

I am curious about optimal transport. What's the central question being asked there? And what tools do we use to study that?

[gray gazelle]

Read the first 20 pages of this, probably about 1st to 2nd year undergrad level to understand it so far

[grand thistle]

woah thanks for this this looks really cool

[gray gazelle]

jojo

[gray gazelle]

Measure theory

[fierce hedge]

if optimal transport is what I think it is then I feel weird that it uses measure theory

[zealous light]

The literal question being asked is “what is the best way to move stuff around”

I’m going to move this to #advanced-lounge

[fierce hedge]

Understandable

[orchid cobalt]

what should I consider before buying a book?

i want to buy books not to pass exam or anything, just want to know more about math

and I'm in highschool

[willow pecan]

Whether or not you can get the book for free

[orchid cobalt]

well I have my eyes on one

it's got a free pdf online

or I can buy it as a collection

[placid pollen]

I get it, I understand everything now <--- read grandpa Rudin in undergrad (me)

[placid pollen]

Yo should buy books that will help you synthesize or digest past or current courses

And a bit for the future, but less so

[gray gazelle]

1. Your net worth
2. Your ability to get it for free
3. Your ability to find a PDF
4. Your comfort with PDFs.
5. How much you care about aesthetics
6. Importance to your career

[gray gazelle]

How much math is required until you can do all the interesting looking math like Topology, alg geo, knots, cat theory, homotopy etc

[quick hornet]

answers may vary

[stray veldt]

with the exception of topology and knots those are probably grad classes

in like a standard degree

[quick hornet]

you can start doing topology as soon as you learn how to prove things

but it wont get interesting for a while

[gray jungle]

You only need some analysis and "maturity" to do topology

[quick hornet]

unless youre one of those freaks who really likes point set

topology is most interesting when given algebraic or analytic context

or data analytic

Anyway in practice most of those are upper undergrad level at least

You can beeline to them if you try though

I was doing algebraic topology in second year undergrad

[stray veldt]

[quick hornet]

and i wasn't a particularly strong student

(as in like, i was probably one of the best students in my undergrad program, but my program wasnt particularly strong)

(and didnt have super accelerated material or anything)

[paper ice]

what would be the appropriate order of books to self-study linear algebra as an undergraduate from basic to advanced ?

[gray gazelle]

knots? I kinda disagree, to properly do knots you need at least some algebraic topology knowledge

[gray jungle]

I would start with gilbert strange introduction to linear algebra as you will have access to some very neat lectures and assigments via youtube and mit ocw , then as a 2nd pass you have a variety of options when you are ready to tackle proof based La , my favorite option is hoffman/kunze but it could be just a bit "technical" , which is why many people here recommend friedberg insel spence as a more modern version of the book.

some people also recommend axler but you would need a reference to study determinants from what i have heard.

[hearty turret]

is discrete math by johnsonbaugh good? I heard it's pretty intense on the problem sets

[sage python]

@paper ice relevant question: what is your desired angle on linear algebra?

[paper ice]

what do you mean

[gray gazelle]

In my opinion, you can learn Point-Set Topology with some notions of Calculus, and you can learn Homtopy with some Topology and #groups-rings-fields background. Category Theory requires no background per day, but you should do after you’ve faced the dilemma of transforming/mapping objects into other objects. Algebraic Geometry is done after 1 year of Abstract Algebra, including Comm Alg.

[thin hollow]

hey do u guys know an advanced math discord

[gray gazelle]

Some people will also have a ton of other prerequisites, but some people do these stuff with no background, so I think this straightforward path is the best of both worlds.

[sage python]

For example, compsci folk care a lot about linear algebra over finite fields, physics folk not so much

Some people care about numerical stuff, others not so much

[gray gazelle]

The AT, AG, TAU Discords are fairly advanced, at least relative to this one.

[sage python]

If you're more pure math inclined you'll want a more theoretical treatment, other areas less so

So that's what I mean, what's your general vibe mathematically? @paper ice

[thin hollow]

can u send me link

[paper ice]

ye im looking for pure mathematical linear algebra books since im interested in it but we didn't cover almost any of it since im in mechanical engineering

[sage python]

Dam darkwarrior we can be advanced too!

Some folk here do good stuff

Incrio: then look at Friedberg-Insel-Spence

[gray gazelle]

You can google them

[thin hollow]

ok

[gray gazelle]

Note: AG and AT discord is no-nonsense postgraduate works for high-achieving grad students or post-graduates. You might not be able to meaningfully contribute to them yet, but TAU is more welcoming for undergraduates and new maths folks.

[rich sun]

What does TAU stand for?

[willow pecan]

The affinoid union

[rich sun]

Thanks

[vast obsidian]

Ironic I'm studying logic (elementary) but am illogical 🤪

Does Hammock's Book of Proof have all solutions available? Currently reading Velleman's HTPI but it has solutions only available to like 2/20 exercises

As I'm self-studying and newbie it's not fun having to come here all the time to verify answer ))

[gray gazelle]

Alg geo doesn't require differential or normal geometry?

[gray gazelle]

iirc, there are two versions of AG, the classical one and the modern one
The modern one uses functors extensively, so you need to learn category theory for it
as well as, I think, commutative algebra

[remote sparrow]

hamkins' Proof and the Art of Mathematics has a companion volume that's basically a solutions manual

[gray gazelle]

there's no need for differential geometry although I heard there are some analogies

[remote sparrow]

not hammack

has anyone read eugenia cheng's new book on category theory?

https://www.amazon.com/Joy-Abstraction-Exploration-Category-Theory/dp/1108477224

[vast obsidian]

is it for me?

[vast obsidian]

what

I'm talking about Book of Proof

[remote sparrow]

no

[remote sparrow]

idk

[tawny copper]

1. Friedberg, Insel and Spence. 2. Steven Roman, that's all

[dapper root]

Incel

[willow pecan]

Insel lol

[tawny copper]

If you want you can read other books as supplement, sure. But really, Roman should be the second/third stop in your linear algebra trip

if that makes sense

xD My bad.

[gray jungle]

do you really need a roman level pass on linear algebra tho , 2 passes are enough

im curious, who exactly is the audience that would want to read most of roman?

[tawny copper]

Roman is divided into two parts, first part is in standard undergrad curriculum

second part is not meant to be read linearly, you can choose topics. But looking at the contents it seems stuff that shows up in math lol

I have not read that tho, but billinear forms, tensors, metric spaces, Hilbert spaces are all important topics I think

The last chapter on umbral calculus seems something Roman himself made up xD, but I think it is related to Bernoulli numbers somehow

[gray jungle]

yes, but , do you really want to learn metric spaces and hilbert spaces from roman? there is so much better alternatives

like i havent read roman actually so maybe they are amazing

[tawny copper]

No idea, since I haven't read those chapters

[gray jungle]

but im skeptic as to whether its wise to use a linear algebra book for that

[tawny copper]

I have only read almost everything in the first part, and I really liked it

If you just want to learn "pure" linear algebra, just skip those chapters

[paper ice]

no linear algebra done right ?

[tawny copper]

Well, linear algebra done right is at the level of Friedberg, Insel and Spence, so you can read both at the same time

But I would be against of doing something like first reading Friedberg, then Axler, and then something else, because Friedberg and Axler are roughly at the same level

Though, Friedberg covers more material actually

you can look at the exercises from Axler too if you want

[vast obsidian]

Friedberg a lot harder

[tawny copper]

Didnt know. I only read some of the first chapters of Axler while I was reading Friedberg

If Incrio thinks Friedberg is too hard, he can start with somethibg else

[obsidian dock]

Hey! I'm in high-school but I'd love to get into a bit more advanced mathematics. Got any book recommendations? 🙂

[willow pecan]

You'll need to be more specific

What math do you know

What math do you want to learn

[tawny copper]

But Friedberg, or something equivalent, is way enough background (of linear algebra) for starting Roman

[willow pecan]

Do you have experience with proofs

[obsidian dock]

I'm not quite sure yet. I know very basic algebra, geometry and calculus

[gray gazelle]

Algebra by Serge Lang

Don't read that book I just mentioned

[obsidian dock]

How come?

[remote sparrow]

#book-recommendations message

^ above are recommendations for first courses

[gray jungle]

fair enough , i could possibly do a skim over the 2nd part in the future since im familiar with the topics and ile give you a feedback on how its written, ive only read bilinear forms from roman and it was pretty ok actually.

[obsidian dock]

I'm not very familiar with linear algebra. Do I need any prerequisite knowledge of it before reading?

[tawny copper]

I do plan on reading tensors, metric spaces and Hilbert spaces from Roman in the future

[remote sparrow]

#book-recommendations message

[willow pecan]

You need to know proofs before linear algebra

Probably start with a proof book

[remote sparrow]

hefferon and meckes are designed to be usable for people with no background in proofs

[gray gazelle]

Try Topology of metric spaces by Kumaresan

[pine cloak]

best books for Lin Alg?

[willow pecan]

Consider reading the immediately preceding conversation

[misty wyvern]

I never learned to read, what's the best book for lin alg?

[vast obsidian]

Serge lang's linear algebra of course

[misty wyvern]

https://www.math.brown.edu/streil/papers/LADW/LADW.html

This is the best way to learn lin alg

[vast obsidian]

nooo

[gray gazelle]

im trying to read baby rudin by following a video lecture + mit 18.100C format

how do interperet this?

i read pages 3 to and 24 - 30?

[willow pecan]

Sure

[gray gazelle]

and then pages 5 to 11?

[willow pecan]

Sure

[gray gazelle]

sure?

[willow pecan]

Sure

[gray gazelle]

so i read basic topology in the first reading?

[loud cradle]

haha, what happened to pages 1-2?

[prime oak]

imo the cover page is the hardest part of rudin

i sometimes see it in my nightmares

[loud cradle]

even though chapter 2 "basic topology" starts on page 24, in fact the topology content doesn't start until 2.15 on page 30 (metric spaces), the stuff before that is just some basic set theory

[heady ember]

~~Does Enderton's Elements of Set Theory like me ~~
(Jk don't.)

[gray gazelle]

ah i see i peeked at it and it was just defininf functions/mappings and such

[remote sparrow]

https://www.youtube.com/watch?v=VPVirZTfcz0

[sterile harness]

how so

[gray gazelle]

He isn’t a sellout I’d say, but he’s certainly a little different from what I would watch for math advice.

[remote ginkgo]

do you know why bourbaki stopped writing books?

because they found out serge lang was one person

[sudden dock]

Recommend a Physics book (Mechanic Specifically) for a first year high school student (no calculus please)

[jaunty bison]

Hey guys
do you have any book recommendations on calculus? Not academic book(textbook)

[tepid prairie]

Integral and Differential Calculus by Richard Courant.

[remote sparrow]

That is definitely a textbook

It sounds like they want an informal book that might be something like The Manga Guide to Calculus or whatever

[vast obsidian]

Fr

And he looks like eulers cousin

[cedar ridge]

who would you watch

[heady ember]

Ryc

[cedar ridge]

who?

[heady ember]

Chalk

[rich sun]

Ran Yakumo's

[cedar ridge]

this brother is not happy

aint watched him recently but seems like he's spiraling mentally 1/3 of the time 💀

[heady ember]

Chalk's only video I know of is his latex workshop in #events

How is ryc "spiraling mentally" lol

[remote ginkgo]

complex conjugate eigenvalues

[willow pecan]

Off to #discussion everyone, this is no longer about book recommendations

[tawny copper]

Some texts on inequalities, focused on problem solving ? Thanks

[heady ember]

Perhaps Khan Academy?

[swift dome]

Any books for practice algebra from basic to advance problems

[willow pecan]

Khan academy

[tawny copper]

I don't like Khan academy, and I don't think they have what I'm asking for

[vital bane]

I'm pretty sure they have everything you'd learning from grade 1 to grade 12 and even first year uni

it's just sometimes you need to actively look for them

idk they're like hidden behind some other set of lessons

[tawny copper]

What Im looking for is not something standard in high schools lol

[sturdy shore]

the cauchy schwarz master class

[regal wasp]

Reading about Kan complexes and kan extension and stuff of a similar flavor

[vast obsidian]

Spivak's calculus has good inequalities problems

[tawny copper]

I'm looking for something more specialized

[tawny copper]

Thanks! that one looks pretty good

[undone sleet]

can someone suggest a book that focuses on probability distributions and how to sample and approximate different processes and is a bit hands-on with exercises?
The reason I am asking is I am studying about machine learning and their probabilistic interpretation, the way it is done, is a bit confusing. I think doing practicing with some hands-on learning would help me.

[hollow adder]

Anyone ever read this?

It seems too easy

Is this book like not at a normal first algebra class level

[dapper root]

I think it’s like one of the most intro-level books that are commonly used

If you’re enjoying it, I don’t think there’s issue in just continuing if you’re self-studying or something. If you end up taking a class on it you’ll already be familiar with the stuff

[prime oak]

set theory/logic intro recs?

[dapper root]

If this is your only algebra class and you’re trying to go to grad school or something, you probably should work through a harder book later or concurrently with your current class

[prime oak]

uhh new domain prolly

[dapper root]

No it got seized because it’s piracy lmao

And government entities are supposed to like, do stuff about piracy

[willow pecan]

Best not to talk about this, against Discord ToS

[dapper root]

I don’t see why talking about it is a violation of TOS

Nobody is providing a link or saying you should go do anything

[willow pecan]

Oh is that what it says

[prime oak]

college students trying not to paying $300 per book, biggest problem the govt decided to tackle 🙏🏾

[dapper root]

I’m not gonna comment on my thoughts about it because of TOS, but the reason it got seized is obvious

Like it was without a doubt illegal, and so the govt moved on it

[rich sun]

Now the FBI's coming for all trying to access the website

[tardy walrus]

Bunch of killjoys

[gray gazelle]

Serge Lang is a terrible author

Well, that’s false, his Number Theory book is classical, but everything else is of poor quality

[gray gazelle]

Enderton then Jech

[prime oak]

is it though

lang alg

any better recs then

[gray gazelle]

Artin if you want to refresh Linear Algebra & smoother intro. Dummit & Foote if you want an encyclopedic book with plenty of examples.

You can get a Lang “Algebra” PDF AFTER you’ve studied Abstract Algebra for his Homological Algebra chapter.

[gray gazelle]

Well, it is certainly more like a community-college level Algebraic Structures, and most Algebra courses I’ve seen use what is considered “graduate” for their Algebra course.

I recommended some books above 👆

[hollow adder]

Thanks that makes sense

I do really like the book though

I’ll probably read it and then move to an advanced one

[remote ginkgo]

do you just go around trying to be wrong or is it accidental

[vast obsidian]

his calculus of several variables, abstract algebra, linear algebra are good also

[winged gust]

Does anyone know of any other books like "A Friendly Introduction to Number Theory by Joseph H Silverman" or "A Book of Abstract Algebra by Charles C Pinter"? Specifically, I'm looking for other books that have short chapters that introduce one idea at a time and has exercises around that idea that allow me to explore the concepts myself.

[remote ginkgo]

strogatz nonlinear dynamics and chaos

[cinder trellis]

Wait is the FBI shutting down other sites too?

Or is z-lib the only one that’s down

[regal wasp]

Sally’s introduction to analysis is basically you writing the book through exercises

Covers analysis 101, measure theory, multivariable, some field theory, some abstract algebra, and fourier analysis

[prime oak]

some library genesis mirrors

thats all i know

[cinder trellis]

Ugh that’s so annoying

[prime oak]

i mean

dm?

[sage python]

Ohhhhhh nooooooooooooo

God that fucking book

[regal wasp]

Lets hear your take

[sage python]

Did you... Does the name Souganidis ring a bell to you at all?

[cinder trellis]

Nah nah it’s ok, I have other ways it’s all good

Still sucks though, probably hit a lot of people harder

[regal wasp]

Yes actually

[prime oak]

yes

[cinder trellis]

The FBI just bought the domain name since it expired, so I don’t think it’s that scary tbh

[sage python]

Yeah sounds about right. When did you take that class?

[prime oak]

i have a lot of friends in uni who cant afford the absurd prices here and dont know other sources to get some of the important books

[prime oak]

the organisers of the sites got arrested

[cinder trellis]

Oh wait really?????

Wow that’s absurd

[prime oak]

z-lib organisers are in argentina or something rn and getting extradited by the US

[cinder trellis]

Yeah it’s internationally based, most shadow libraries are so it’s weird the FBI was involved

[prime oak]

ugh
US moment

[sage python]

But yeah so there's a class in UChicago called honors analysis. It... changes a lot year to year depending on instructor proclivity

But it was created by a guy named Paul Sally

And he wrote that book basically based on his approach to the material

[winged gust]

no, not really... though at first I thought this was a setup for a "deez nutz" kind of joke, lol...

[regal wasp]

I used it to review analysis

[sage python]

Oh

Yeah so for me it was like, I took that class well after Sally died, and the emphasis kinda changed since then. But our instructor discovered that book and liked it kinda? So he partially used it

Along with Rudin and this trash fire called "Advanced Calculus" by Buck

And Hoffman-Kunze

[winged gust]

sounds like an IBL kind of approach (inquiry based learning)

[sage python]

Sally was very team IBL I think yeah

[winged gust]

Which I actually like, though I'd prefer a solutions manual in case I get stuck

[regal wasp]

I think every honors analysis course in the country is IBL

[misty wyvern]

Tbh I think Rudin's series is actually good even though people think it's actually bad when other people say it's good.

[sage python]

Well by the time I took that class it was very not IBL

[prime oak]

who says rudin is bad??

[misty wyvern]

Of all the analysis books I return to, it's 90% one of Rudin's.

There's a bunch of people who claim Rudin is too terse or obtuse or something.

[prime oak]

i read rudin before going to sleep so i feel safe

[misty wyvern]

Rudin is basically the only analysis reference I return to though, so it stands the test of time.