book-recommendations

[smoky zephyr]

it’s only got like 6 topics though

but there’s unlimited questions for those 6 topics

[sharp flame]

@smoky zephyr okay sorry anyway thank you im just trying to prepare for the SAT

[slender dragon]

Yes

[sudden kindle]

One way to prepare for the SAT is to do practice tests. Go to your local library and take out SAT prep books (Princeton review, etc) and time yourself doing the practice exams. Be consistent with the practice and you'll improve.

[slender mortar]

right, so I found myself with around a month of free time. What would be a reasonable ordering for the self-studying of analysis? I have Spivak, Tao, Apostol (I & II), Rudin, and Abbot. I have experience with Math Olympiads, so I'm somewhat comfortable with proof-based math, and have experience with the equivalent of calc 1-3.

[remote ginkgo]

Rudin

[slender mortar]

How much time do you reckon it'd take to go through it thoroughly?

[remote ginkgo]

A few months

But any progress you make at all will benefit you

Particularly chapter 2's intro to metric topology will be helpful

[smoky zephyr]

i’ve already asked this too many times, but this is the last time

what are some linear algebra book recommendations

[smoky osprey]

refer to previous suggestions?

[smoky zephyr]

well i forgot that somehow

[smoky osprey]

use the search feature?

[remote ginkgo]

Shilov, Strang, Shifrin

[smoky zephyr]

no i forgot to do that

i know how to search stuff lol

[empty mortar]

im gonna study

[fervent lava]

Study hard.

[empty mortar]

thats what I told myself a week ago when my probability book arrived. Didn't make it past 20 pages

[misty wyvern]

@main void Foundations of Modern Probability, Kallenberg

It's the bible of mathematical probability theory IMO

[foggy relic]

@smoky zephyr you might also find this helpful https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw

[main void]

oooh this is exactly what i was looking for, thank you

[ornate shuttle]

Imma be real with you chief

reading Rudin is fucking tedious

I would rather read something like Understanding Analysis by Abbot

I think I would enjoy that significantly more

[frosty girder]

[ornate shuttle]

I read through Chapter 2 and understood most of it (except his discussion of the Cantor Set)
But I found most of the exercises extremely dry and tedious

I would rather work in a less abstract metric space

like R with the absolute value metric and nothing else

Can anyone explain why this is true lmao

How does he know "no segment of the form so and so has a point in common with P"?

I don't know if I can understand that

[smoky zephyr]

no clue what that is but this isn’t a question channel

[ornate shuttle]

right, I was just trying to express my frustration from trying to read Rudin

but there's probably a better channel for that particular question

[fluid bay]

the algorithm for obtaining E_{n+1} from E_n is to "cut out the middle third" from each interval in E_n. The segments of the form "so and so" are exactly the middle thirds that were cut out

i agree that rudin could have given more explanation here. I like this level of terseness sometimes because it forces me to engage with the material as I'm reading. When I was first learning proof-based mathematics (like a lot of people getting into rudin), I'm sure I wouldn't have liked this though

[robust mortar]

non-standard analysis all the way down :^)

i find it much more eloquent, if anyone is interested

[surreal phoenix]

A month of freetime + Rudin won't do you much, better start with something like Abbott or Tao if this is your first experience with analysis

You could still get a lot out of it, but I really don't see any reason for someone to put themselves through that tough of a book for a first course. I'd go for Abbott (very well written) and then tackle Rudin as a second look into it, really solidify everything from Abbott and add onto it

[robust mortar]

I second Abbot if you are not intrigued by non-standard analysis

[ornate shuttle]

The segments of the form so and so are not exactly the segments that were cut out
There could hypothetically be segments of that form which do in fact intersect the Cantor Set
I tried to explain this in the LaTaX document
Sorry if it's unintelligible lol

I know this isn't the right channel but I thought it was relevant to the discussion

[fervent lava]

Hey quantum another good linear algebra book is the one called advanced linear algebra by Bruce Cooperstein. I mostly use it as reference for LADW.

[cedar mortar]

hi guys m in 12th grade hs and i REALLYYY loved integration would u pls recommend some books so i can learn more abt it ? hope sm1 ll respond . Thank u !

[analog pollen]

What do you already know?

[cedar mortar]

Well we learned the definition using primitives //areas . Basically high school stuff .but i wanna dive in more ? cuz it really interested me

Also type of problems i need to work on// basically have better understanding abt the whole concept

[analog pollen]

Oh hmm maybe try something like spivak calculus

[cedar mortar]

Kay i ll check it out thanks ! y all have more?

[analog pollen]

P mcuh where you want to start

[cedar mortar]

Analysis ?

[analog pollen]

Its just a calc book afaik but but harder

And you want to know abt integration so i don think a plug and chug book will help you

[surreal phoenix]

It's like halfway between calculus and analysis, it'll help you bridge the gap as well if you're interested in purely doing analysis afterwards

[analog pollen]

And after you want to try some multivariable calc

[surreal phoenix]

Or if you just want to compute more integrals, maybe learn the rest of calculus

Yeah, multivariable and vector calc

[cedar mortar]

So spivak "Calculus" ?

[analog pollen]

Yep

You can always download a pdf and see if you like it

[cedar mortar]

Sure Thanks a lot !!!!!!

[remote ginkgo]

Abbott doesn't even cover anything.

[sinful glade]

Guys i am a highschool freshman and i want to learn calculus rigourously ...btw i already know calculus upto stewarts level and i have covered the differential part of introductory multivariable calculus

Is hardy's course on pure mathematics relevant for me

[analog pollen]

An analysis text is what you want

[sinful glade]

Rudin?

I wanna do that but i feel like it wud be too overwhelming for me

[surreal phoenix]

Not good for a first course, try Abbott, Tao, Apostol, or some of the other you can find above if you scroll up a bit

Way more beginner friendly and can do a better job helping you transition into proof based maths

[broken meadow]

abbott is cool i feel

[frosty girder]

abbott seems nice yeah

[surreal phoenix]

It is cool I feel too

[frosty girder]

apostol feels good as well

[warm glen]

where did y'all learn multilinear algebra

im looking at a text called "linear algebra via exterior products" and it seems cool but idk

[gray gazelle]

from my differential geometry class

nobody actually learns multilinear algebra for its own sake

[warm glen]

oh

multilinear stuff doesn't get used outside DG?

i thought u need tensor products for commutative algebra

[stray veldt]

you do, but commutative algebra books can just introduce them

[warm glen]

alrighty

wait why don't people usually learn multilinear on its own

[stray veldt]

i learned it from linear algebra class and the appendix in eisenbud

[warm glen]

is it harder to motivate without DG or comm alg?

[stray veldt]

you have to fit it into some class

dont think there are enough results to do a whole class of just multilinear algebra

[warm glen]

i see

have u by any chance read the sections on ML stuff in loomis and sternberg's advanced calculus book

it seems they teach some of it in that book to set up analysis on manifolds

[gray gazelle]

Lmfao Apostol.

[frosty girder]

[gray gazelle]

It's my family name. 😀

[frosty girder]

[gray gazelle]

[bleak hornet]

Do you guys have any book recommendation on Differential Geometry and Topology for self-study?

[sinful glade]

Hmm i looked at tao volume 1 and it seems i already know most of what was in the book

[analog pollen]

Lee smooth manifolds, and munkres for topology

[sinful glade]

But is hardys book any good

[surreal phoenix]

The book doesn't teach you calculus computational stuff, it's analysis

The contents page looks the same, but it's completely different from a calculus course

[bleak hornet]

I saw a video by The Math Sorcerer, he highly recommended this and another one

but I couldn't find the latter

[sinful glade]

Oh

[analog pollen]

Which one does he recommend

Munkres?

[surreal phoenix]

Try scrolling through the book a bit and you'll see what I mean

[bleak hornet]

Topology by Gamelin and Greene

[analog pollen]

Oh never heard of that

[bleak hornet]

he said that all the exercises have an answer

[analog pollen]

The go to text is munkres

[bleak hornet]

so it'd help a lot

[bleak hornet]

I got it, will start reading it next weekend

thank you

[analog pollen]

I also saw a vid on self studying mathematics and this guy recommended some lecture notes from the uni of toronto

It has a ton of problems

Wait

[surreal phoenix]

To supplement munkres, I found Hatcher's notes and Snoopy notes (notes written by students of a topology course, looked pretty nice) to help a bunch

Check those out too if you'd like, just search on google

[analog pollen]

https://youtu.be/byNaO_zn2fI

Those lecture notes looked p good

Havent read it yet tho

Lots of problems

@bleak hornet

And lee for diff geo

[bleak hornet]

great, thank you bro

[analog pollen]

I don know abt his topological manifolds book

But the other 2 are pretty good

[bleak hornet]

The thing is I don't really worry about not learning those subjects for now, even though the graduate course is only 4 years if all goes well

I have an entire life to search and read those

hope I have the tools to be able to understand just the basics

[gray gazelle]

tu's "an introduction to manifolds" is a watered down version of lee and a little easier to digest. surprised no one mentioned it so far

that'll teach you the manifold theory you need to go into more geometric stuff

if you want to learn differential topology, guillemin and pollack is the usual recommendation

g&p doesn't require a lot of background compared to lee and tu. lee and tu will require topology beforehand, and i don't think it's wise to start reading either of those if you haven't learned topology at the level of munkres already

[bleak hornet]

thank you ma fren

[fervent lava]

Looking up Lee turns out there also another lee who has a differential geometry book. It called manifolds and differential geometry by Jeffery lee.

Pretty sure I spelled the first name wrong.

[gray gazelle]

everyone means john m lee anyways

sorry jeff

[mortal pond]

Any game theory book recommendations for someone at grad school?

[hollow peak]

has anyone used Riemannian geometry and geometric analysis by Jost? Is it any good?

[amber linden]

anyone know where I can find a cheap (under 40 bucks) copy of Calculus 9th edition by Stewart?

[novel iris]

I've used bits of it as a reference, it's a bit fast but good

author's v much a closeted physicist lol

def don't use it as an introduction to geometry for that reason imo. For eg defines vectors and other bundle sections using transformation laws rather than the more standard geometric definitions (unless you're specifically looking for coordinate-heavy RG books ig)

[fervent lava]

I don’t think that possible unless you buy it off someone. That book is expensive for no reason.

Although you can find a free pdf then use the 40 dollars to buy paper to print it out.

[amber linden]

I'm still looking for a free pdf but no luck :/

[fervent lava]

Try libgen/zlibary.

[amber linden]

I tried libgen, piratebay, zlib and a bunch of other random sketchy sites but no luck

[fervent lava]

I found one in zlibrary

[amber linden]

with this cover? my professor is being super picky for some reason

[fervent lava]

Yeah. Not sure why the professor/school wants the 9th edition. It literally has the same content as previous edition.

Probably webassign stuff they do

[loud cradle]

Stewart's Calculus is expensive for good reason. The Integral House ain't gonna pay for itself. https://www.fastcompany.com/3052267/the-house-that-calculus-built

[fervent lava]

That is funny.

Oh your serious.

[loud cradle]

"Last year alone, he sold 500,000 books, from which he made around $26 million."

(That was 2014, he's dead now.)

[hollow peak]

thank you!

[dapper root]

Has anyone who does not speak French at all ever tried to use a French textbook to learn math before? If so, did you find that it worked out?

I have read papers in French before and read occasional excerpts from French books, but I've never tried to use a French book as a textbook before.

[marble solar]

It's hard to find a good intro Riemannian Geometry book

They're either too low of a level or too high of a level

I'm partial to spivak's first two volumes

Peter Petersen also has a good book on RG, but it's very technical

[novel iris]

Lee's IRM is quite nice I think

[marble solar]

I was never too fond of Lee's approaches

They seem like good books, maybe I'm just a spivak simp

[gray gazelle]

Hello everybody!I found a really nice game that trains your brain!It's called Math Master Riddles and Puzzles😀

[novel iris]

anything in particular that you dislike about them?

[gray gazelle]

Uhhh

If you want to test your skills,really nice

It's something like math riddles from black games:) the old one,but it's more interesting,more questions:)

[broken meadow]

Please don't send advertisements without our permission, thanks.

no

[dapper root]

ok

[restive falcon]

any good nonstandard analysis textbooks?

[modern stone]

As a first introduction i’ve heard the standard choices would be Henle’s “Infinitesimal Calculus” or Keisler’s “Elementary Calculus: an Infinitesimal approach”. If you are confident enough in your mathematical abilities you could try reading Abraham Robinson’s “Non-standard analysis” as he is the one who started it all

[hearty steppe]

@dapper root what is the benefit of learning another language to learn math?

Especially way later in life when you have neurological conditions impeding that ability?

Considering I’m a late bloomer and started learning math for real a little over a year ago

I’m 32 years old with not much expectation of getting into a PhD program in my 40s but I feel like my neurological capacity to benefit from relationships in an industry/trade skill environment leaves me stranded like a child that peaked in social skills before puberty happened.

Like if I stop learning math, I stop learning period for the most part I feel.

I’ve come to the conclusion that learning mathematics is probably the most important thing for my mindset right now and it has made me feel so much more grounded with my life. It makes so much more sense to me than people do the more time I do math.

[dapper root]

Sometimes something you want to read only exists in a certain language so you’re forced to either not read it, or struggle to read it in the language it exists in. That being said, reading mathematics is far easier than reading a novel, I think it depends on the language, but for eg French, I am not afraid to read a paper in French even though I don’t speak the language at all.

Nobody really learns a language for the express purpose to learn math, you just learn how to read math in that language

[wise umbra]

I don't think it will be harder than reading a paper

[hearty steppe]

I wish I could read novels. I can’t. My reading comprehension skills peak when it comes to trying to interpret fiction. It really sucks man. I have a hard time interpreting narratives using vivid imagination

It’s like as if I’m looking at a TV screen full of white noise and static

[wise umbra]

Most textbooks don't use much vocabulary and are really structured, Bourbaki-style

[hearty steppe]

Like I don’t read fiction at all

[dapper root]

I guess my main concern is not being able to understand the prose in the text which explains what the math is actually about, but if all French books are devoid of that, then I guess that’s fine lol

[hearty steppe]

My brain has a hard time interpreting narratives. So even classical philosophy stuff and really old terse writing forget about it. Can’t read it. White noise interpretations of human emotion

Not sure if anyone relates

[gray gazelle]

@hearty steppe maybe you have Aphantasia?

[hearty steppe]

It is not something I wish upon my worst enemies

I am clinically diagnosed with high functioning autism

[gray gazelle]

Ahh

I was gonna sak you about that

But felt it was too personal

[hearty steppe]

I have not heard of aphantasia. I have a hard time with interpreting things

[wise umbra]

really depends of the author, most of them don't have much prose, or at most it's a couple of sentences (like «schemes are a generalisation of classical algebraic varieties»)

[hearty steppe]

I have misophonia tho and that is horrible.

Frequencies that make you feel like your in pain

Noises*

I don’t have a problem visualizing things. I have a problem interpreting things

[gray gazelle]

I see

[hearty steppe]

Yea math books are fun to read when you have to go through at least half a dozen reference/supplementary texts to use with the standard text(s) sometimes

That’s my experience of using standard math texts tho. At first I didn’t get the hype but trust me. Make sure you work through the standard texts mentioned here. There’s a certain way to interpret the information that you gotta figure out for yourself to make it click but when it clicks, it’s a great feeling

[wise umbra]

(what do you want to read ?)

[dapper root]

Simpliciale methodes en algebre homologie et commutatives (or something like that, it’s by Michael André)

And Homologie Des Algebres Commutatives by André as well

Or at least I am considering it

[gray gazelle]

@dapper root they used different words

[hearty steppe]

@dapper root have you considered that there is potentially some cross over with other topics? Like from category theory or commutative algebra texts?

[dapper root]

What?

[hearty steppe]

Regarding the French texts your looking for that is?

Maybe you haven’t searched for something more niche in English

Or less niche

[dapper root]

I mean possibly, the latter one sort of exists in the form of a paper by Quillen

But the paper by quillen is way more dense and less friendly

And I want to read these books specifically because I want to read these books

[hearty steppe]

Oh ok interesting.

[wise umbra]

I'd say, try it, you'll see pretty quick if you can read it or not

[dapper root]

Also idk what you mean here lol

[gray gazelle]

@dapper root you know span right in LA?

[dapper root]

Yeah Adrien, I realized we have the books in my school library

[wise umbra]

maybe you'll have some troubles with the introduction and it we'll be easier after

[dapper root]

Yes I do Halwa

[hearty steppe]

There also an ocean of linear algebra texts it’s somewhat overwhelming to think of sometimes

So much to learn from so many texts

[wise umbra]

(it's probably «Méthodes simpliciales …»)

[dapper root]

Probably

I was running off of memory

[hearty steppe]

I feel like you can learn linear algebra for a lifetime haha

So many books

[wise umbra]

much of them have the same content

[hearty steppe]

Well it varies a bit

[wise umbra]

at least elementary ones

[hearty steppe]

I didn’t realize how many linear algebra texts I found compared to most other math books. Even analysis texts

[wise umbra]

seems like the first page

[gray gazelle]

@dapper root if you have trouble understanding something in french you can ask me

[hearty steppe]

@dapper root so you are focused on studying homological algebra?

MaxJ goes off the face of the earth at the best times doesn’t he? I’d imagine he know a lot about this stuff

[cinder steeple]

Anyone here who has read six of crows?

can i just read six of crows and not crooked kingdom or does six of crows have a cliff hanger ending that will make me want to go for the sequel?

and 2nd question:

IS a man called ove book slow paced/ slow developing?

[mellow bison]

If I remember six of crows u can read by urself

I forgot the ending tho and didn’t read the sequel

also is steward's calculus book for beginners or for more experienced people?

[sinful glade]

Stewart?

Thats introductory

[analog pollen]

#book-recommendations message

This is 9E

[cinder steeple]

Ook ty

[mystic orbit]

Yes it does

[paper stratus]

intro

it's the standard intro calc book for ap calc and calc 1

if you do want a challenge, you can checkout apostol calc or spivak

[mellow bison]

whats the specific book by spivak

im not sure i found it

[fervent lava]

It called calculus by micheal spivak.

Not the calculus on manifolds one.

[mellow bison]

ohk thanks

[serene falcon]

does anyone have any experience with fluid dynamics by gk batchelor? how mathematically intensive is it?

[cinder steeple]

Ook tu

Ty*

[gray gazelle]

What do you guys think of Tao's Analysis I?

[restive falcon]

very slow
good if you want lots of detail before you even get to the reals

[marble solar]

If you haven't done rigorous calculus, it's better to do spivak's calculus

Do some linear algebra, and a good calc 3 class

Spivak's Calculus on Manifolds

[gray gazelle]

Ah.

[dapper root]

@marble solar you said you used Spivak's diff geo book?

the first 2 volumes?

[marble solar]

Yeah

I read the first two

[dapper root]

did you read any of Lee?

[marble solar]

I tried

Didn't like the style

[dapper root]

how was Spivak different

[marble solar]

Spivak gives a lot of time to motivate things

and has funny little one liners

That keep me going

[dapper root]

lol

is it as verbose?

I feel like Lee is...

Idk, he says a lot but then doesn't say muchg

[marble solar]

Spivak says a lot, and it ties in real well

Sometimes I get tired and try to skip to the point

but then I go back and see I missed something important

he does a lot of back and forth between a "classical" viewpoint, and a more modern research point of view

Trying to motivate where it came from, why we have it, and how we deal with it

[restive falcon]

I'm currently doing abbott for analysis

[dapper root]

do you remember roughly how many pages the two are combined?

I'm thinking I'll probably spend a lot of the gap year I plan to take learning diff geo and maybe analysis?

[marble solar]

The first one is like 700

[dapper root]

Just like, round myself out, get ready for quals courses

[marble solar]

But it'll go by quicker than you think

Especially if you have background in diff. geom.

[dapper root]

I am undecided if I want to just use a really terse book that doesn't have much intuition and motivation

or go really heavy on that

since really I want to learn it to have more intuition for algebraic geometry lol

[marble solar]

What I started doing is just latexing solutions to problem sets

and I'd make casual notes in the book in pencil as I read

[dapper root]

yeh

that's what I do too

were the exercises good?

[marble solar]

only the first volume has exercises

There are a lot

[dapper root]

ah okay

[marble solar]

and they are very good

[dapper root]

do you think it's worth doing a lot of them?

or are there skippable ones

[marble solar]

There are certainly skippable ones

I made a rule to try 2/3rds, and solve somewhere between 1/3rd to 1/2

[dapper root]

okay that seems maybe like a D&F level of good exercises

it kinda depends on the book you know

Hartshorne is a you have to do every one book

D&F is definitely not lol

[marble solar]

I'd put spivak in that category

You certainly don't have to do every single one, but they are good practice

Some of them are very easy, some of them are very difficult

[dapper root]

cool cool

I'll see if our library has a copy to see how I vibe with it

it does RG too right?

the second volume?

[marble solar]

Yeah, it gets there

[dapper root]

cool cool

[marble solar]

I have volume 2 on PDF

lemme pop'er open

Yeah volume 2 certainly gets into RG

And also explains classical DG, and how it leads naturally to RG concepts

[dapper root]

naisu

I'm looking through Columbia's modern geo course topics

and there's quite a bit, way more than UW covers

But I think overall it covers a lot of the material here?

[marble solar]

yeah

There are some topics you might have to look elsewhere

[dapper root]

Yeah, I mean I'll take the course eventually probably

[marble solar]

but as far as giving you a grounded sense of what's going on in computational problems and theoretical exercises

[dapper root]

Maybe I'll try to pass one more on arrival, but I am not gonna be able to pass them all on arrival unless I go crazy hard

[marble solar]

I've been happy with Spivak

[dapper root]

yeah that's what I'd like

Best way to do well in a hard course is to know what's gonna happen going in lol

[marble solar]

Yeah, if I get into Irvine, I can pass real & complex on arrival w/ summer prep

But the algebra one is gonna be brutal for me

I never took galois

[dapper root]

Columbia doesn't even have an algebra grad course lmao

they just have comm alg & AG / NT

[marble solar]

Honestly, I'd prefer that

[dapper root]

It just really says that like

they're in a different tier than most schools lol

you pretty much need to have a grad algebra backgroudn going in or you're fucked

unless you just avoid every algebra related course lol, but idk if that's even possible

[marble solar]

yeah, my friends say at princeton you don't really take courses

It's more seminar style

[dapper root]

yeah lmao

[marble solar]

Friend ended up going to MIT, where they make you take 8 classes

[dapper root]

wtf

like 4 a semester?

[marble solar]

no, you have 5 years

To get all 8 classes in

[dapper root]

oh

year long courses?

[marble solar]

Nope, just one semester courses

[dapper root]

ah okay

[marble solar]

But they're not seminar courses

[dapper root]

that's more reasonable

[marble solar]

They have to have some form of problem set, final, or presentation/write up

[dapper root]

I know my friend at Utah they have like

6 prelims?

But it's like

1 for each semester

[marble solar]

Same thing at UIUC and UT Austin, 1 semester exams

Yeah

[dapper root]

and they're pretty easy

from what I hear at least

I really need to pass the AG qual on arrival

if I go to columbia

[marble solar]

UC Riverside has 4 quals you have to pass

[dapper root]

I mean I'm not worried, but if I don't I am so fucked

[marble solar]

They're each 1 year long sequence

[dapper root]

jesus

I think it's kind of funny that Princeton famously "doesn't have quals"

but they have that oral exam at the end of the first year lol

[marble solar]

That just destroys most people

[dapper root]

I think most ppl pass but

it's very stressful it seems

and everyone is super fucking nervous

and forgets simple stuff lol

and on the AG side

[rugged maple]

just how highly would you guys reccomend pugh's analysis?

would it be the self-study analysis book?

[rugged maple]

wow, pugh is a rlly good book

i might drop kenneth's book lol

my god, it reads so well, i can basically read it like a novel

[halcyon hornet]

Hey. Any book recommendations for Mathematical proofs?

Especially those with relatively less prerequisites(HS Mathematics mostly and some basic Calculus).

[karmic thorn]

Proof and the Art of Mathematics by Hamkins

[dapper root]

I’m of the opinion that you can get by with a linear algebra textbook. I think you can follow how proofs are done because the stuff is quite intuitive

[halcyon hornet]

I see, never heard of that one lol.

[halcyon hornet]

Hmmm.

[karmic thorn]

There's a newer version with examples and extensions

[dapper root]

This isn’t the best advice for everyone arguably

[halcyon hornet]

Mainly heard of Polya's book lol.

[karmic thorn]

I think lin alg would make more sense to Senku after probably 2 or so years, when he has dealt with a fair bit of linear equations in more than one variable.

[halcyon hornet]

Proofs come up everywhere and 1 day I will have to do them, so I guess I will start with them soon.

There is no avoiding them.

[karmic thorn]

Sure

[halcyon hornet]

Hmmm?

Is not Linear Algebra just on the level of Calculus?

[karmic thorn]

Have you dealt with solutions of linear equations in 2 or more variables?

[halcyon hornet]

I am starting with Stewart's Calculus, got the book and will resume after exams.

[halcyon hornet]

Yes.

Of course.

It is basic 9th-10th stuff lol.

[karmic thorn]

Then linear algebra is fine as well

[halcyon hornet]

Systems of equations.

[karmic thorn]

But I'd still insist on checking out Hamkin's book

Just to get a feel for abstract math first

[halcyon hornet]

I see.

Thank You!

[surreal phoenix]

Does Apostol's Analytic number theory skip a lot of the stuff you'd find in an elementary NT course? Or does it cover most of that too?

[stray veldt]

depends on your elementary NT course

apostol probably assumes the content of an elementary NT course

it proves quadratic reciprocity, which is often done towards the end of an introduction to NT i think

it also covers primitive roots from the looks of it but probably assumes the related theorems

nvm, it proves the theorems

(but if you take a good elementary NT course, it will study quadratic number fields)

(also does not cover pythagorean triples/geometry of numbers and pell equation stuff, which is probably pretty standard in elementary NT)

[fervent lava]

I used Loch intro proof when I was starting, then use other intro proofs books as reference. Here it is, #proofs-and-logic message.

[halcyon hornet]

YEsh ik.

I looked at it.

[fervent lava]

Ok.

[serene falcon]

a journey

@rugged maple

[smoky zephyr]

they couldn’t get an answer so they did it themselves

amazing

[hollow dome]

https://tenor.com/view/thanos-infinity-gauntlet-ill-do-it-myself-marvel-villain-gif-16087834

[mystic orbit]

https://tenor.com/view/improvise-adapt-overcome-bear-grylls-gif-10468556

[sage kelp]

I used Velleman How To Prove It, and found it really helpful. Have heard good things of Book of Proof by Hammack

[ember hearth]

any real analysis book from scratch and good for self study?

[karmic thorn]

Understanding Analysis by Abbott

[ember hearth]

i will check it out thanks

[karmic thorn]

[brittle latch]

ive been trying to use baby rudin for this

it is not going well

[ember hearth]

just read a few pages, i am already loving it, cya in maybe a month or two,asking for another

[frosty girder]

[ember hearth]

maybe i would learn some topology after that

[frosty girder]

[brittle latch]

yall know anywhere to buy books like this, besides amazon and B&N

[frosty girder]

does abbott cover topology?

[ember hearth]

no ig

[frosty girder]

like a little bit of it, thats useful in calc?

[frosty girder]

search the book for metric spaces

[ember hearth]

btw, i have just started reading the textbooks because like, i only used to watch some open lectures on yt

and i thought

learning it from a textbook alongside would be better

[frosty girder]

that would be nice, yeah

[ember hearth]

just for fun tbh, its a hobby now

[karmic thorn]

You essentially learn by solving problems

[frosty girder]

i myself just started analysis myself

[frosty girder]

[ember hearth]

exactly, thats why i wanted a textbook

[ember hearth]

thats cool

[restive falcon]

abbott is the real analysis textbook

[lapis sundial]

cries in rudin

[fervent lava]

Yes, chapter 3. It just topology in R.

I can’t wait till I get too it.

[frosty girder]

noice

topology stuff is a bunch of definitions

but its fun

intuitive, visual

beautiful

[analog pollen]

iirc it also does some at the end

[frosty girder]

[analog pollen]

Are metric spaces a part of topology tho

I thought so

And prob something else

Also at the end

[frosty girder]

yeah

[analog pollen]

Ok then yea it discusses some of it at the end

[frosty girder]

nice

[atomic stag]

which book is best to understand calc 1 integration?

[analog pollen]

Stewart

[atomic stag]

I want to understand 3 concepts

1/integration by trig identies
2/partial integration
2/int by substitution

[analog pollen]

Partial integration? Do you mean by partial fractions?

Stewart is still good for those

[atomic stag]

thanks

[marble solar]

Spivak's calculus

But that depends on your definition of understand

[restive falcon]

integration by parts is also key

[tawny copper]

Terence Tao's

The exercises are very good

[marble solar]

Unironically wrong

[hardy junco]

any books for mathematics behind graphics programming?

[quick hornet]

Might have better luck asking in a CS server

[gray gazelle]

keep at it, you can do it !!!

[gray gazelle]

https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.html

try this maybe

[brittle latch]

isnt tao like super dense

[smoky zephyr]

this seems interesting, thanks

[tulip blade]

I think its the opposite

[tawny copper]

Why

Just the fact that he doesnt prove many of the important results is a good thing

Most books I've found arent like that, though I don't have a lot of experience

[marble solar]

Big picture gets shrouded by obscure details or technicalities

I think Pugh is a better intro to real analysis

[tawny copper]

You are correct actually

[marble solar]

I know, I worked through his analysis volumes extensively

[tawny copper]

But that doesnt mean the exercises are not good

It's a matter of exposition of the topic

[marble solar]

The exercises have to be put in context of the material shown

You don't put graduate algebra problem sets in a high school algebra book

[tawny copper]

And it does that very good

[marble solar]

So the question then becomes are the exercises good in context of the material of the book

And I'd say no

Because Terry isn't that great at exposition in his analysis volumes

Also, I think there's too few exercises

This becomes apparent in comparison to books like Spivak's Calculus or Pugh's Real

[halcyon hornet]

[slender dragon]

I like Steps into Analysis. It's a Inquiry Base Learning book

[gray gazelle]

you need linear algebra, calculus, analytical and vector geometry, numerical analysis and some signal processing

there's no one book that is going to cover all of it

you will find these in any standard engineering math book

[atomic stag]

i already have book for practice but i want under diffrent techniques

i want get "experiance"

[foggy relic]

what do you mean by experience

since you said you have a book for practice, do you mean you know how to do the computaions?

if thats the case, spivak will probably be really good for you

it proves why all those computations work

[frosty girder]

spivak does?

damn it i should have actually read that book properly

[foggy relic]

at least so far

i havent finished it yet, but it has so far i think

idk if illl ever finish it

why tf are there like so many problems

it takes like a few hours just to do those

[frosty girder]

spivak is halfway between an analysis book and a calc book right?

[foggy relic]

yeah i think so

it dosent really have the traditional analysis topics

[frosty girder]

hence the halfway between an actual analysis book

[foggy relic]

yeah

[pulsar geode]

does anyone have any stochastic calc book recs? generally looking for good writing quality and exercises, mostly regardless of applications vs theoretical focus

[near spindle]

all in one math book

[atomic stag]

experience means getting to know how to solve questions.
edit: Stewart's book got the thing I needed

[full linden]

anyone working with fourier analysis?

[novel mica]

does anyone have a recommended, fairly "light" book on algebraic geometry? i'm trying to gauge my interest in the field but i wont have much time this semester for dedicated self-study

background is intermediate-advanced undergrad algebra

[marble solar]

Fulton's introduction to algebraic curves

[novel mica]

ty.

[gleaming nova]

@azure stratus ey bro are you still offering the OneNote notebook on intro to materials science and ode's?

[azure stratus]

Sorry, I'm probably not going to share them with those who don't go to my college

It feels like sharing them with strangers doesn't feel super appropriate for me right now, sorry

[gleaming nova]

ah no worries

[azure stratus]

Sorry about that

But if you got individual questions - I can try answering them

And sending individual tidbits of it

[gleaming nova]

hmmm

do you have a good recommendation for a book for material science?

the one i'm using kinda sucks

[pale scarab]

If your able to do the majority of problems you won't have any issues with any typical undergrad analysis class. Most struggle in that class because they learned calculus from an engineering calculus book like Stewart

[frosty girder]

I am kinda "struggling with analysis" but thats just the proofs part, but i see what u mean

i should do spivak some day

[halcyon hornet]

😔

[gray gazelle]

just do the questions

[frosty girder]

i cant do them right now, but yeah i will

[gray gazelle]

what multivariable calculus books would u recommend?

"advanced calculus" by folland

[near spindle]

mathematical analysis rudin or abott

[surreal phoenix]

Abbott if it's a first course in analysis

maybe consider Rudin after that

[near spindle]

what if its for a high schooler friend

[surreal phoenix]

Abbott for sure then

[near spindle]

ic

so rudin is more complex?

[surreal phoenix]

Not complex, it's just a lot harder to read because he skips a lot of details and expects you go he able to fill them in on your own

[near spindle]

https://www.youtube.com/watch?v=KH-8lZBa76E&t=86s

[near spindle]

oh ic

no then

[surreal phoenix]

Yeah, Abbott is much better for an introduction

[near spindle]

ok thanks

[surreal phoenix]

Np

[gray gazelle]

Any book that deals specifically with integrals and Taylor series?

[shut lily]

Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares by Boyd and Vandenberghe - has anyone studied this and if so would they recommend it?
https://web.stanford.edu/~boyd/vmls/vmls.pdf

[subtle siren]

No clue about that book but Boyd and Vandenberghe's Convex Opti book is a classic

I'm looking through the table of contents and it does feel like it has a stronger applied math or just straight up optimisation vibe to it

[shut lily]

thats what I've heard too. What would the prerequisites be for working through this?

[subtle siren]

It's very introductory so hopefully nothing? Perhaps the usual high school/pre-high school math

The book covers less mathematics than a typical text on applied linear algebra. ...

Note this if you want to substitute it for actually learning LinAlg, although tbh if you're into applications, theoretical LinAlg won't come back until possibly grad school

[shut lily]

sounds good, i was hoping to study it because ive heard its good for ML (which I would like to pursue professionally)

[subtle siren]

If you'd like to go into ML, the book is a starting point but very insufficient

[shut lily]

i see

[halcyon hornet]

Any Resources/Books which make me go "Aha" over Mathematics? Been missing that for some time 😔.

[smoky zephyr]

the information about sets in book of proof is pretty easy to understand and cool to me

you could try that

[halcyon hornet]

Is it "Aha-ey"?

[smoky zephyr]

no clue i just found it cool

[halcyon hornet]

xD.

[ember hearth]

Have you read what is mathematics by courant and ian stewart?

Its quite nice

[still saddle]

Indra's Perals by Mumford et al

[halcyon hornet]

Nope.

[halcyon hornet]

Which is on?

[gray gazelle]

Posamentier's Challenging Problems in Geoemetry is quite a rewarding read.

[sage kelp]

I found the opinion about Tao interesting, because I agree with you. Most of the exercises are not in context with the exposed material. I was wondering if you could share your opinion on this matter when comparing Baby Rudin and Pugh

[foggy relic]

maybe do pugh

[frosty girder]

apostol ftw

[sage kelp]

Why Pugh instead of Rudin?

[foggy relic]

its easier to read, better writing style, has good problems

[halcyon hornet]

Oooo!

[near spindle]

bro any one

[frosty girder]

?

[near spindle]

any one author

abott, apostol, rudin, pugh

[frosty girder]

all of those are pretty good in their own right

im using apostol myself

[gray gazelle]

read all, see which one fits you.

[sage kelp]

I’m currently reading Rudin, but might change my mind to Pugh

Theory in Rudin is amazing, but not sure how I feel with the exercises

[near spindle]

ic

[sage kelp]

Plus, Abbott is not at the same level as Rudin or Pugh, so you might want to check that

[marble solar]

Baby Rudin and Pugh are basically the same, except Pugh actually explains more steps and has more varying exercises

[icy knot]

Finally got Pinter’s book on Algebra. Such a fun read.

[odd spade]

pinter is good

i really like gallian's contemporary abstract algebra

[tulip blade]

Dummit and foote>

[slender dragon]

The best book

[terse anchor]

Book recommendations for discrete math?

[glad prairie]

i used rosen's book and i liked it.

knuth's concrete math is a harder book and doesnt cover everything a discrete math class covers, but it's tremendously high quality.

there's also this

[smoky zephyr]

is that a serious book

like does it actually teach you stuff

[marsh skiff]

does anybody know where I could buy a solutions manual for "Understanding Analysis" by Stephen Abbott. I want the second edition, not the first.

[dapper root]

Yea

[smoky zephyr]

wow

[tulip blade]

Concrete math is epic

[near spindle]

do you guys know a book in which there is everything from algebra to calculus

[tulip blade]

No

That would be a lot of information for one book.

[near spindle]

yes

[tulip blade]

Calculus books tend to be pretty big on their own. Adding a ton of algebra would make it extremely thick.

[near spindle]

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

something like this

even without calculus is fine

[gray gazelle]

that book is only results of a particularly difficult exam

it contains no explanation whatsoever

[tulip blade]

Ya you wont learn much from a book like that

Dont try to be Ramanujan

[near spindle]

lol

i thought it would be nice if i had a big book which had everything

[tulip blade]

There are plenty of genuinely good resources available.

[near spindle]

since i won't be able to use the internet because of unknown reasons

[tulip blade]

Just buy many small books then.

And download pdfs

[near spindle]

No computers too

suffering

[tulip blade]

Just buy the princeton companion to math then

[gray gazelle]

you don't need computers/internet. get a few pdfs and print them

[near spindle]

Ic

[near spindle]

its a big book

[tulip blade]

Seriously though what are you going to do w a large book containing high school algebra and calculus?

[near spindle]

does it have everything in it

[tulip blade]

Just buy a calculus book and algebra book separately

[tulip blade]

It summarizes a lot of ~modern math~.

[near spindle]

i have higher algebra by hall and knight

[gray gazelle]

that will do for algebra

[near spindle]

and calculus made easy by silvanus p thompson

[gray gazelle]

you can do the questions at the back of hall's book for difficult problems

[near spindle]

okay

why does the princeton companion book cost 102 USD

[tulip blade]

Its huge. And textbooks (books) tend to be expensive

[gray gazelle]

you are trying to learn math for high school right ?

[near spindle]

no

i'm trying to learn math because it is fun

not for school

[gray gazelle]

ah welp

[near spindle]

ig i'll go step by step

it'll take me long enough to finish hall and knight

do you think its a bad idea to go beyond school syllabus @gray gazelle

[gray gazelle]

no

but learn school stuff first since there is no point in compromising scores for the sake of it i guess

[near spindle]

school stuff is easy

all of school's stuff is like the first page of every chapter in hall's book

[gray gazelle]

well if you are done with school subjects, then sure move ahead

[near spindle]

nice

[gray gazelle]

(have you done questions by the way ?)

[near spindle]

only in the chapters i read

arithmetic progressions and logarithms (first section)

[gray gazelle]

uh

[sage python]

What is this book

It's so chaotic

[near spindle]

https://www.google.co.in/books/edition/The_Princeton_Companion_to_Mathematics/ZOfUsvemJDMC?hl=en&gbpv=1&printsec=frontcover

[brittle breach]

might be a good first math book

[gray gazelle]

recommendations for peak fiction?

and a somewhat honest review?

[misty wyvern]

Princeton Companion is actually good. So is its ugly sister, Companion to Applied Math.

I wish other fields would get their own Princeton Companion

legit I would kill for a Princeton Companion to Mechanical Engineering or something

[shadow tusk]

it's really that good huh

[misty wyvern]

no

i just think mechanical engineering is just a big collection of random techniques and needs some core structure

[shadow tusk]

it doesn't?

wow

learning mechanical engineering by yourself would be a nightmare then

[misty wyvern]

I think the average mechanical engineer basically learns Goldstein and tensor calculus, and that's all they retain. They specialize after that.

There's too much.

[shadow tusk]

actually, I think learning any field of engineering by yourself would be a nightmare

[gray gazelle]

Any advice on approaching Spivak for the first time?

calculus or calculus on manifolds?

[karmic thorn]

The mathematician.

[gray gazelle]

lmao

[marble prawn]

can anyone recommend a good book for number theory?

[gray gazelle]

elementary ? algebraic ? analytic ?

[marble prawn]

idk

like in decent depth but not university level

for olympiads

[gray gazelle]

oh

Try Modern Olympiad Number Theory by Aditya Khurmi

or Titu Andreescu's Structures and Examples in Number theory

if both of those seem difficult, try Burton

[marble prawn]

do i get pdfs online?

[gray gazelle]

upto you

modern olympiad number theory is free to download by the way

[gray gazelle]

Calculus.

[halcyon hornet]

Which book?

[karmic thorn]

Book of Proof by Hammack

[halcyon hornet]

Sure that is the spelling?

[still saddle]

i am sorry i was out

[still saddle]

Indra's Pearls my bad

[wintry current]

Hello guys, I recently got interested into algebraic geometry and wanted to go deeper into it. I have a large knowledge about algebra and linear algebra and some middle level geometry. I am seeking for a book that is more theory oriented and goes gradually from the basics of the topic to it's advanced level. Thanks !

[regal wasp]

Hartshorne is very beginner friendly!

Jokes aside, these (https://www.jmilne.org/math/CourseNotes/ag.html) are probably the only way to get introduced to AG w/ your prereqs

Assuming by algebra you mean abstract algebra up to commutative algebra

[wintry current]

Yes totally

Okay thanks a lot

I’ll go check it up

[shadow tusk]

not a book but what's your favorite pdf viewer?

[maiden slate]

I just use Firefox

[gray gazelle]

Okular is nice

[shy compass]

edge

[analog pollen]

I use google

[shadow tusk]

chrome?

[analog pollen]

Yes

[shadow tusk]

are you using linux?

[gray gazelle]

Nope

It's available in the Microsoft store

[shadow tusk]

damn it supports epub as well

[foggy relic]

xodo

https://www.microsoft.com/en-us/p/xodo-pdf-view-edit-and-annotate/9wzdncrdjxp4?activetab=pivot:overviewtab

[subtle siren]

I use
https://github.com/sumatrapdfreader/sumatrapdf

[foggy relic]

sumatra is ok

[mellow bison]

What about MacBook preview

[shadow tusk]

I'm not on mac

[shadow tusk]

damn it's beautiful

[gray gazelle]

is there a first order logic book/lectures(notes if also possible) targeted towards computer scientists ?

i mean first year

[solemn rover]

Hartshorne is very beginner friendly!

hahaha. it's not bad but i found it challenging the first time ir ead it

[quick hornet]

Hartshorne is beginner friendly relative to other texts that existed at the time it was written

"other texts" here means like

Lecture notes from students who took grothendiecks classes

So of course it's beginner friendly in comparison

Nowadays better sources exist

[sage python]

The guy who said it's beginner friendly seems to have been joking given the followup message

[quick hornet]

I'm aware

Im just saying there's historical truth to it

So you might still see some stackexchange users or whatever say that

Since they were raised in a time when it was legitimately the best option pedagogically

"the dark ages"

[marble solar]

You could always just read EGA

[sudden kindle]

For some reason I dont like Milne's books

[sage python]

His NT book I def don't like as much as Neukirch

[foggy fiber]

What is a good textbook based on the mathematical parts of Formal Verification? The stuff I'm finding is focused on the actual verification of hardware. None of the books really explore the mathematical side of the subject.

As I posted that, I came across one text Formal Verification of Floating-Point Hardware: A Mathematical Approach that focus on more of the math; however, the book is very hardware centric (not so much software).

[quick hornet]

@molten wave maybe you have relevant recs?

(though my informal outsider impression is that this particular subniche is often learned in githubs and weird chatroom communities rather than a formal book)

[gray gazelle]

a calculus book which is not abstract (mostly for engineering & computer science) and has something like application based questions or just applications and has problems/excercises which are harder than stewarts?

I dont like Schuam's outline because its structured in a weird manner and most of the excercises are straight forward with most of them having solutions just after the excercise, I dont like Stewarts & Thomas because the excercises are too easy, and also abundant which makes it difficult to utilize the book without spending 90% of your time doing plug and chug questions

@gray gazelle are lectures OK?

[gray gazelle]

its god level, i used heavy pdf readers earlier but switched to sumatra yesterday and its been awesome ngl

[gray gazelle]

uh, i kinda dont have a lot of time in a day

It's a full course from MIT

i know about ocw

books help me to consume more content than lectures

pauls notes also has very straight forward excercises, so does khan academy

Spivak and stuff is like hard but for a but wont be helpful in my cs work at all

The problem is that it's hard to find a book with solutions included/solutions manual

I will find the manuals, dw

what book were you going to recommend?

One second

@gray gazelle I forgot it's name, sorry

well

was it hughes-hallet?

or adam & essex?

No

alright those are all the books i know of in calc

[gray gazelle]

learn concepts from pauls online notes, do questions from spivak

both fit your requirements

[next olive]

hey im looking for a text book that can help me with math, im currently in 10th grade highschool we are currently learning about higher than 2 degree polynomials, and i wanted to learn a bit more on my own so i downloaded mathmatical methods for physics and engineering textbook, but its doesnt really explain very well so im looking for a different book anyone have any suggestions?

[pale scarab]

Which do you recommend? I know the rising sea is popular

[gray gazelle]

@gray gazelle Tried Anton? Iirc exercises harder than Stewart and Thomas but it's still in the same category IMO. Are you checking out the 'Applications and Theory' exercises in Thomas?

Try Lang's calculus too.

Thomas with Analytic Geometry (3rd ed) gets recommended a lot - difficult to find a physical edition though

I have Lang's a First Course in Calculus (2nd ed). It's short (~310 pages). It's very, very concise. It covers a lot of ground but not every topic you will find in Calc 1-2. The exercises are good. Did I say it's concise? Such a difference compared to Anton or even Thomas. It is, however, Lang which might be an acquired taste.

However, it's much closer to typical calculus books than Basic Mathematics is to a typical high school algebra/pre-calculus book.

[gray gazelle]

Have a look at College Algebra. It's free. If you want it, you can get it through their printer. https://www.stitz-zeager.com/

[gray gazelle]

Any advice for transitioning to Spivak? Waiting for my copy to arrive :x

[foggy relic]

AoPS Introduction to Algebra

[halcyon hornet]

Also Intermediate algebra.

[gray gazelle]

No lemme have a look at it, as for applications and theory excericses they are pretty easy too you just lay out the information and then its just straightforward then

[gray gazelle]

couldnt find a decent pdf so I just decided to not do Lang, will try that after anton

[gray gazelle]

I did start Langs Linear Algebra course on OCW and so far I've been liking it

[gray gazelle]

since the topic your mentioned is very specific, and you are in 10th grade you are better off googling the topic you like, you will find pretty nice explanations

[quick hornet]

i will confess that i dont really have much experience with other books besides knowing that they tend to be better than hartshorne

i personally learned out of hartshorne as an undergrad and "turned out fine" fwiw

i have also heard good things about rising sea

so thats probably a safe enough bet

[sinful glade]

Try apostol or courant courant especially is suited fr physics and engineering

[sinful glade]

If u want a classic go wit higher algebra by hall ans knight but its in the general style of a textbook

More of a set of results proved and pondered upon

[south salmon]

I’m going to ask here, but the Helgason Diffgeo book was recommended after buying evans PDEs, I’m wondering how the book is?

[gray gazelle]

Never heard of it

[sage python]

I've read a shorter thing by Helgason and overall it's not bad

I have the book but haven't read it much. If you diffgeo with a leaning toward like, Lie theory and analysis on symmetric spaces

It's worth checking out

[foggy relic]

Thats probably too hard \

[gray gazelle]

You mean Strang?

I think if you find Theory and Applications type questions are easy, it's worth considering whether it's worth the time to go "deeper" into Calculus 1-2 without actually making the move to Spivak or Apostol or other type of 'Honors Calculus' treatments? If you don't need to treat calculus like a math major does, will you get more mileage from studying a new topic or moving onto new chapters?

What math classes do you need to take in the future?

Have you taken a discrete math class? Have you been introduced to proof writing? Set Theory? Difference between injective, surjective and bijective functions? Etc.

[hollow drum]

Is Lang the best algebra book fo grad students?

[gray gazelle]

oh yes confused the names

[gray gazelle]

yeah I have done all this stuff

[gray gazelle]

i will have to self study all this, mostly because I want to do ML stuff and presently I wont be able to do "real" ML (and already know most of the non-math pre requisites), although math is not a pre-requisite, I will be learning (self-studying) topics from ML like Linear Algebra, Probability & Distributions, Continuous Optimization & Vector Calculus over the course of 2 years

I have 2 options at this point

1. Learn essential calculus (till integration) by just learning it, and move on to the other math I need
2. Or grind on spivak and then move on to other math

what would you suggest at this point?

i've already started adams & essex

[dull bluff]

Anyone have any book recommendations for calculus?

[wheat cargo]

how rigorous? apostol's book or spivaks book are rigorous and nice, spivak is more difficult than apostol generally though

[dull bluff]

I'd prefer less rigorous, but still a little bit?
Sorry that that is such a bad answer

But, do both of the two cover curriculum from calc 1-3?

[wheat cargo]

no

if u want that, then try

one sec

[smoky zephyr]

i’ve never read it but people seem to praise stewarts calculus

[wheat cargo]

yeah its very standard

i dont like it though

https://www.whitman.edu/mathematics/multivariable/multivariable.pdf

this one is nice

@dull bluff look through it

[dull bluff]

hmm

Does it have 1-3?

Sorry, i see multivariable

[smoky zephyr]

it’s got some odes too

[dull bluff]

Wait, Nvm it has everything I think

[gray gazelle]

Use your campus library to loan out Stewart, Anton and Thomas. Try them each for a few weeks. They're probably going to service what you need.

But it depends on the class.

Anton introduces epsilon delta early which is nice.

[dull bluff]

If you know, would a public library serve well enough? I'm not at a college

[gray gazelle]

Yeah these are standard a public library should have them. Maybe not Anton, it's not as common here.

Any year edition is fine.

[dull bluff]

thank you so much

[gray gazelle]

What's your goal? Do you need to learn proofs?

[dull bluff]

One more question, Stewart being james setwart and thomas being george calculus?

[dull bluff]

Trying to self teach calculus

I would be able to do some dual enrollment sooner, and it looks good on a college application

[gray gazelle]

James Stewart and George Thomas, yeah. I prefer Thomas to Stewart and Anton.

https://www.goodreads.com/book/show/818077.Thomas_Calculus

If your library has old editions of Thomas 'Calculus and Analytic Geometry', check those out. They're well regarded. Obviously, more emphasis on analytic geometry

What major are you intending?

[dull bluff]

I've got no clue, I'm too young for that

[gray gazelle]

Velleman's "Calculus: A rigorous first course" fits the bill

[dull bluff]

I'm a freshman

[dull bluff]

Thank you so much

[gray gazelle]

I'd say any of those books + prof leonard + pauls notes + khan academy are fine for self learning. But you might want to clarify rigor.

The transition into Honours calculus / intro analysis is a bumpy road (I'm on it now), and requires multiple references imo

[dull bluff]

Good luck!

[gray gazelle]

You too

Stewart and the likes are more of an engineering books and has lots of redundant and repetitive problems. A way around it would to follow a course schedule which uses Stewart. But ig you would fare better if you pick up books such as Velleman, Spivak, Courant and the likes.

Whoa Velleman posts on SE

https://math.stackexchange.com/questions/2483650/in-the-conventional-less-than-rigorous-calculus-course-is-vellemans-new-notati/2489293

For many students the investment in a more rigorous calculus course or reading might not be worth it. If they're going into math or physics or econometrics than yeah - CS maybe? Jumping straight into rigorous calculus from plug and chug high school math is challenging because it's a different ballgame.

[gray gazelle]

Some additional reading: 'How to think about analysis' & 'How to Study for a Mathematics degree' by Lara Alcock are fantastic for helping you understand how to study university level math. They're written conversationally. Totally changed my approach. Richard Hammack 'Book of Proof' or Vellemans 'How to Prove It' supplemented by something like Epp discrete math (chapters pn relations, functions and sets) might help you transition to the more rigorous texts or classes.

[dull bluff]

These books, would I read them after being somewhat proficient in calculus beforehand? Or would I read them straight out of the gate?

[gray gazelle]

Alcock: straight out of the gate imo. You can read them in an afternoon and refer back to them as needed.

Hammack, Velleman, and discrete math: if you need it.

Math majors love to recommend Apostol and Spivak to first time learners of calculus for some reason but I'd encourage you to get a basic proficiency in calculus first, with an eye to proofs, definitions, theorems before trying to build calculus from the real numbers first.

No point obsessing about epsilon delta or how to correctly reason about a supremum if you can't use chain rule or integration by parts

[dull bluff]

That makes sense

I'll start with the more basic stuff for now

but I will save these lists because they look really helpful

[gray gazelle]

Sure, one suggestion you can get into with the basic stuff: keep a notebook for definitions, theorems and proofs.

[dull bluff]

or just basic rules for stuff

I will get on that

[gray gazelle]

Yes, those properties for rules. If you can, note the proofs used for them because getting into the habit of deriving relationships for yourself is really good.

It will help when you can't remember something

Get the Alcock from a library IMO. They're not technical. They will help you approach your learning with more wisdom.

[dull bluff]

Should I write the step by step proof, or just a vague way to describe how to derive it?

[gray gazelle]

Good question. I'm not an expert, I'm also a beginner learner but here's what I've noticed. In early calculus, proofs tend to rely one one trick. So if you can remember the beginning and end of the proof, you can probably remember the middle. If you want to study calculus seriously (not even as a mathematician, let's say in engineering) than knowing the definitions cold is helpful (I memorize them with Anki).

I keep a notebook where I copy a proof line by line, and explain in a different colour pen what is happening.

[dull bluff]

I'm not running low on notebooks or on pens

Ill take a swing at both

[gray gazelle]

Sure. There are also many different ways to skin a cat. A text like Stewart might prove something with the use of a property from a table. It looks almost trivial.

In university math, generally, your teacher will start from some axioms and definitions at the start of semester and then every property will be proved. So the proofs will be more involved and usually come back to the definition of the derivative and of continuity.

Nb not really true for engineering math classes - they cover more techniques in a shorter period so you can start your analog circuits or mechanics classes faster

[dull bluff]

you've been such a help

I've got to go to bed

because, its 1 am where i'm at

once again

Thank you

i've got all of the resources I need from here out

hopefully

[gray gazelle]

This is why it's relevant whether you intend to major on math vs engineering btw - different approaches for different curriculums

Good luck

[dull bluff]

well, I've got time to figure out which one

good luck to you too

[abstract walrus]

Polynomials

[sick wigeon]

Is this book a good place to start learning number theory?

I haven't read a lot of number theory
I just know a few results like Euler's totient theorem, Wilson's theorem etc with proof

[smoky zephyr]

considering that it says elementary i’d say yes

[sick wigeon]

These are the table of contents

(Taken from the preview available in Google)

[sick wigeon]

The table of contents don't seem elementary beyond the third chapter right?

[dapper root]

Bad answer

[smoky zephyr]

oops i guess

[dapper root]

You can never trust a math book’s title for saying elementary or basic or something

[smoky zephyr]

well i didn’t know that

[dapper root]

That’s why this sticker exists, unironically

[smoky zephyr]

not my fault, seems intentionally misleading

[dapper root]

I’m just saying that as a like, general warning

[sick wigeon]

So not so elementary then?

[dapper root]

I am not sure, I don’t know number theory sadly

The first three are definitely elementary topics, but the treatment of them could be far from elementary if they chose

[sick wigeon]

Three chapters you mean?

[dapper root]

Yeah

Do you know any abstract algebra?

[sick wigeon]

I am studying group theory from galian

I have done the very basics

[dapper root]

I see, this book uses abstract algebra, but I don’t know if it introduces the concepts or assumes you know it

[gray gazelle]

I'd say a standard like david burton might be good if you are just getting started with nt

[dapper root]

I think this probably isn’t a good book if you want super duper like, eleementsry number theory

[sick wigeon]

Nah

[dapper root]

The kinds done pre 20th century

[sick wigeon]

Not so elementary...

[gray gazelle]

yeah the title is Graduate texts in mathematics, so it assumes you know UG math or smth

[sick wigeon]

Just an undergrad level intro

[dapper root]

Yeah that’s what I mean by very elementary

[sick wigeon]

Is what I want

[gray gazelle]

you are good with burton in my opinion if ug level intro is what you want

[sick wigeon]

I see
It's fully rigourously written right?

[gray gazelle]

its a bit casual, not very rigorous

[sick wigeon]

Hmm

[gray gazelle]

True.

[sick wigeon]

So like it assumes abstract algebra and analysis i think

Right?

[dapper root]

Probably

[gray gazelle]

you can open one of the chapters and go through it, the first one i mean

[sick wigeon]

Yeah that one seems elementary only

The very first one

[gray gazelle]

I just know UG NT and Combi so I dont know if it is suited to a UG person

[sick wigeon]

Oh i see

Alright i will just keep reading this one till i get stuck

[gray gazelle]

yeah

[gray gazelle]

any thoughts on müger's Topology for the working mathematician?

[grand thistle]

just started "How to prove it" by velleman, and gotta say it's as good as they say

so easy to read and well written

[manic cape]

[halcyon hornet]

Oohh.

Even I plan to start it soon.

[halcyon hornet]

Daym that is great!

[grand thistle]

yeah u should

[halcyon hornet]

Hmmm.

How much have you read?

[grand thistle]

im going through it because ive done very little proof writing and actual rigorous math so i felt like i should have some kinda introduction to it before i progress further through calculus and linear algebra after