book-recommendations

[lunar junco]

i have the tenth edition

[dusk wind]

how do you like it so far

[lunar junco]

pretty solid

ah okay i'll check it out tonight

thanks a lot

[remote sparrow]

yeah, an old edition will work just fine too; you don't have to get the newest edition

old editions sell for a very low cost

[lunar junco]

ye, they just jumble up the questions its just marketing

only very few editions have something actually different

[remote sparrow]

since you said you're an incoming engineering student, you definitely want to get the early transcendentals version

[lunar junco]

ah okay

[remote sparrow]

and be sure it doesn't say something like single-variable calculus or multivariable calculus only

[lunar junco]

i'll just look for a pdf online, not looking to buy a new copy rn pdf works just fine

[lunar junco]

ohk

[dusk wind]

check out antons too

[lunar junco]

have you used thomas' calculus? and if yes is it good?

[lunar junco]

ohk cool will do

[remote sparrow]

some people here have and they liked it

[dusk wind]

actually

[remote sparrow]

i heard newer editions are very similar to books like stewart and larson, though, and that it's lost the charm of significantly older editions

[dusk wind]

maybe you would like abbott

[lunar junco]

interesting

[dusk wind]

personally would only use Courant or Abbott

[lunar junco]

ohhk will check it out thanks for the suggestions guys i think i have plenty of resources to scoure through now lol

i'll let you know which one i find best

[remote sparrow]

courant and abbott are real analysis texts, and they won't necessarily help you do calculus (although they will help you understand calculus)

i don't recommend them if you're not interested in proving things

[lunar junco]

ah, im really not into proving things that much

proving theorems really builds depth in the subject tho so i might give it a look

oh also since you are in engineering, what fields do you recommend? any regrets taking up something in particular?

[remote sparrow]

i'm not an engineering student

i'm a math major

[dusk wind]

isnt that the same thing

[lunar junco]

lmaoo what even

majoring in math is so much more intense compared to engineering from what i've heard

at least in my country

[dusk wind]

maybe from a different perspective

[remote sparrow]

well, at least for me, my degree is pretty flexible

[lunar junco]

true depends on the person really

[remote sparrow]

there are only some core required math classes and the rest are electives, so you can take whatever math course interests you

engineers have lots of required classes

[dusk wind]

feels weird to say you're not a math major when you're taking a bunch of math specific/applied courses...

also feels weird to say you're not an engineering major when you're taking a bunch of physics/engineering ones too

[lunar junco]

yeah i've heard there's a lot of ways you can go from math, like econ and other mainstream stuff as well

[dusk wind]

also yea some people do this anyway so it doesnt really matter

[lunar junco]

what do you major in

[dusk wind]

I'm not a math major or an engineering major

[lunar junco]

mhmm fascinating

bio?

[dusk wind]

no

I'm still forced to take some of those classes though

[lunar junco]

physics?

[dusk wind]

yes but actually no, anyway this is unrelated

[remote sparrow]

it would also benefit you to self-study some linear algebra @lunar junco

[lunar junco]

im so confused

[dusk wind]

you should definitely do that asap

[lunar junco]

up to what level

[remote sparrow]

#book-recommendations message

[dusk wind]

just read tea time linear algebra

[remote sparrow]

meckes and hefferon are a bit more theoretical than average, but since they have full solutions available, they should be doable

they are suitable for any major

[lunar junco]

ah cool will go through them

[earnest wolf]

thank you!
I'll look into it

also, do you have any ideas about the problem books?

[earnest wolf]

I already did and Rosenthal's «A First Look at Rigorous Probability Theory» looks good for my purposes. thanks again!

[remote sparrow]

the books i mentioned have lots of problems

https://www.amazon.com/One-Thousand-Exercises-Probability-Third/dp/0198847610

there's also this book, which is technically a companion to this book

https://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198847599

[earnest wolf]

oh wow. I usually don't expect a theory book to have any computational exercises but those (at least one of them) indeed do, wow

thanks

[remote sparrow]

blitzstein and wackerly are not measure-theoretic books

grimmett/stirzaker as well

[earnest wolf]

I saw this def and thought that blitzstein was semi-rigorous xD, so that's why

[remote sparrow]

no

https://www.stat110.net/

there's a website to go with blitzstein's book

https://statlect.com/

i saw this website but i don't really know how good it is

your mileage may vary

https://www.amazon.com/gp/product/1981369198

it's also available as a hard copy

[trail hemlock]

thanks for the recs yall all this stuff looks pretty interesting

[remote sparrow]

@earnest wolf measure theory does get used

[dusk wind]

might grab some of these

[potent coral]

those look awesome

[molten mason]

Yeah it's kinda great but also annoying. My school is heavily leaned toward the applied side and you can see that reflected even in the required courses.

Linear Algebra and ODE are required courses to graduate with a bachelor's of math at my school.

Abstract Algebra is an optional elective, topology I think is a fringe elective offered every other year.

[graceful moon]

I mean required DEs and LA isn’t that weird

My very much pure maths focused uni also requires both of those, you actually have to so 2 LA classes

[silk sigil]

Recommended books on Nevanlinna theory?

[lusty ermine]

Recommendation readings to learn vector geometry

[floral lantern]

wait lmao this reminds me of a university by me that I used to dual enroll at

[weak nest]

why would linear algebra not be required in any math degree?

[indigo mesa]

I sure hope it is

[molten mason]

It's not weird, its just weird that they're the only ones required (along with Calc 3)

And Real Analysis and Abstract Algebra aren't

And the LA And ODE courses aren't even the proof ones. They're the computational ones that engineer majors take. The proof versions are electives.

[weak nest]

oh, okay, at my uni we have abstract linear algebra as the requirement

http://catalog.illinois.edu/undergraduate/las/mathematics-bslas/#degreerequirementstext

[molten mason]

Yeah it's just wild how we all have the "same" degree but how varying our minimum requirements are lol

[lusty ermine]

Vector analysis, do you guys have any good bachelor recommendations

[molten mason]

Maybe these?
https://link.springer.com/book/10.1007/978-4-431-54571-2
https://link.springer.com/book/10.1007/978-3-319-59800-0

[silk sigil]

The first one doesn't quite look like what I'm looking for as it's multivariable and focused on the link with Diophantine approximation, but the second one looks decent

Any reason why you'd recommend this over any of the classics on the subjects (e.g. Hayman and Goldberg & Ostrovskii)?

[molten mason]

Nope, I just remember seeing them when I was browsing through Springer the other day. I haven't gone through them personally but figured you can take a look if you haven't seen them already and see if they're what you're looking for or not. The second one says the book includes advances since Hayman and is only a few years old, so that might be a benefit.

You can link your school to Springer and access the PDFs for free.

[silk sigil]

Oh yeah thanks that initially didn't work (that's why I was asking instead of looking for myself) but logging in using a different institution I got the PDF now, thanks

[molten mason]

Did you take a look at Anton? What exactly are you looking for?

[molten mason]

Yeah mine didn't work at first too, so weird. No problem if those don't work you can just ask again and maybe someone else will know better.

[tribal crow]

we have a ton of required core math courses, but i would have probably taken most of them even if they were electives anyways

but as a result, there’s not much space for “real” elective courses

[drowsy sable]

i need vid resources to learn calculus

i am in 8th grade andd trigonometry is the closest thing i know to this.

[floral lantern]

if you only know trig why are you trying to learn calc

💀

[drowsy sable]

a person said i need to learn it. and also precalculus

[floral lantern]

what

learn precalculus first

and algebra 2

then learn calculus

[drowsy sable]

what is algebra 2

[floral lantern]

rational numbers, polynomails, logs/exp, some trig,

[drowsy sable]

sounds hard

[floral lantern]

💀

then you're not ready for calc

learn the fundamental spls

[lunar junco]

lolol

this is so funny

Algebra 1
Trigonometry
Algebra 2
Calculus 1

if you try calc first you yourself will realise that you can't do it, try it if you want to no harm

[lunar junco]

dead

[finite gale]

You can honestly probably just follow along the ordering of khan academy

Skip whatever you find easy

[potent coral]

it gets easier with practice honestly

[lunar junco]

everything does

[daring ravine]

hello friends

recommended books/resources on number theory?

[lunar junco]

oh lord your bio T_T im dead

[daring ravine]

took the course 2ish years back but wasn't taking it seriously so I'd like to re-learn

[lunar junco]

i think aops has a pretty decent book on it, haven't used it personally tho

might be more inclined towards olympiad solving but idk maybe its useful

[narrow prairie]

Niven

for elementary number theory

[floral lantern]

it's all olympiad stuff

aops is great and all but it's not rigorous by any means

[molten mason]

#book-recommendations message

[daring ravine]

Based and helpful pilled

Ty

[gray gazelle]

Is it unethical to download pdf of mathematics books? I plan to buy them in the future when I get a job

one textbook costs about 4 weeks of groceries

[graceful moon]

ToS says that we’re not allowed to comment. An interesting unrelated fact though is that authors don’t see much of the money from the purchase

[molten mason]

Especially when a lot of them are dead

[potent coral]

NO ONE IS ALLOWED TO MENTION MY BIO

NEW RULE

GOD DAMNIT

[left cloud]

oh lord your bio T_T im dead

[potent coral]

WOWZA!!!! LOOK AT YOUR BANNER!!!! OOGA BOOGA!!!

[graceful moon]

I assumed that lavender was your alt, apparently there’s just 2 now

[left cloud]

some people still think she is

[potent coral]

what the fuck

maybe im ur alt and i dont even know it

[potent coral]

whos the author of the commutative ring theory book

the older books are always better

[left cloud]

matsumura

[potent coral]

thank u

[left cloud]

i’ve never read it but chmonkey says that’s the one he likes

[potent coral]

who is chmonkey

is that your alt

[tender river]

hang around in #algebraic-geometry geometry for a while

[potent coral]

i appreciate your assumption that im smart enough to do that

[finite gale]

there are plenty of people (too many) that stumble in there for a couple posts that don't belong there and pointed elsewhere

[crimson leaf]

How does Matsumura compare to A&M

[crimson leaf]

Additional question is it legal to print like Matsumura's Commutative Algebra if it's the Texromancers version

[left cloud]

the man of my dreams

[potent coral]

thats awesome

omg math lovers

[novel obsidian]

Does anyone have any recommendations for an algebra book to supplement Jacobson? I tried reading artin already and didn't really like it

Pls ping if any ideas 🙂

[gray gazelle]

Brešar; Undergraduate algebra

[novel obsidian]

Looks quite interesting. Thanks

[gray gazelle]

It's great cause it covers all the algebraic structures at once and really highlights the central ideas and similarities

[novel obsidian]

Yeah it definitely looks good. The 'applications' section also looks good. I'll download a pdf later and give it a quick look.

[remote sparrow]

Advanced Modern Algebra by rotman

note that the third edition is split into two books and is a substantial revision of the second edition

compare the editions and see which you prefer

[novel obsidian]

Hm. This looks a little advanced for what I need atm I think

[remote vortex]

The spirit of Mrs Slocombe lives on

[remote sparrow]

https://www.math.stonybrook.edu/~aknapp/

[novel obsidian]

This also looks good, thanks!

[lusty ermine]

I liked it but I would prefer something more specific towards anton's chapter 3 and chapter 4 , from his Elementary Linear Algebra with Applications book, possibly something more formal with definitions theorem and corollaries with vector geometry visualizations would be fine

[earnest wolf]

strange request: could you please recommend any semi-fiction math books about math (not history of math or mathematicians)

something to read in bed after a long day, but with some mathematical content

maybe something like 'an Eternal Golden Braid', but on a different topic: I didn't really seem to enjoy the contents, since I've heard here and there about the main results before reading the book. so that broke all the fun

~~or recommend just anything. idk what to read when I'm bored lol.

this is book-recommendations after all, not math-book-[...] 😆~~

[dusk wind]

Cyberpunk 2077

[trail hemlock]

that sounds so interesting lmk if u find smth

[molten mason]

More formal would be Linear Algebra by Friedberg, Insel, and Spence

[lavish radish]

linear algebra done left

[remote sparrow]

https://www.reddit.com/r/math/comments/1avrkef/just_found_this_cool_interactive_complex_analysis/

https://complex-analysis.com/content/table_of_contents.html

[tribal crow]

what the heck this is so cool

[molten mason]

That top comment by reedef lmao

That is pretty cool

[remote sparrow]

is reedef someone i should know?

[molten mason]

Nope just thought it was funny

[gray gazelle]

is there any introductory statistics textbook that have an emphasis on psychology? accessible to someone who's taken say a class in statistics and in psychology? also do textbooks come with data to mess with or where would i rather data to do experiments for self study?

sorry if this vague, idrk anything about statistics progression or psychology, but I just think they're cool

[remote sparrow]

google "statistics for psychology book" or "statistics for social sciences book". there are tons of options for you to consider

these courses are somewhat common, and many people have written textbooks for them

[gray gazelle]

woah cool!!!!!

for some reason i thought stats and psychology would be a niche combination, but now that you word it like that it makes perfect sense

[hardy folio]

Hey guys

[gray gazelle]

waddup

[hardy folio]

"Fundamentos de Matemática elementar" is good?

[remote sparrow]

who is the author?

also, i'd wager most of us do not speak spanish

[hardy folio]

Gelson Iezzi

[hardy folio]

The book is in portuguese language

[remote sparrow]

probably even fewer then

[gray gazelle]

😬

[remote sparrow]

is this an algebra textbook?

[hardy folio]

Is like 1 version complete of mathematical content

[remote sparrow]

let's see, portuguese has lots of english cognates, so looking at the table of contents shouldn't be too difficult

[hardy folio]

yes

I have one "fundamentos de Matemática elementar vol-4"

Is too god

[remote sparrow]

seems fine to me.

[hardy folio]

ok

[gray gazelle]

Any book recommendations for multivariable calculus?

And book recommendation Calculus (1,2,3).
I know calculus 1 and some of calculus 2. But with time I forgot small points like (what is critical point, inflection point, how to find global max. Etc).

I don't like physical problems. Is there any good calculus book for review? (That doesn't contain physical problems like thomas, james Swartz etc)

[floral lantern]

Stewart’s is fine for a regular multivariable calculus class

Just skip the physical problems

There’s also Apostol but that’s more proof based

[tribal crow]

what's wrong with physical problems

[molten mason]

There’s also Apostol but that’s more proof based

[floral lantern]

Valid

[gray gazelle]

Okay. I shall try this. Thank you

[molten mason]

All of the answers, even and odd, are on premium Quizlet.
https://quizlet.com/explanations/textbook-solutions/calculus-early-transcendentals-9th-edition-9781337613927

[gray gazelle]

Idk why but physical problems irritate me.
I am studying math and for physical problems I have to recall formulas from physics.

[tribal crow]

fair enough

[gray gazelle]

I have heard about it. Kinda famous like spivik

[molten mason]

Yeah all 3 of my calc classes had me do ONE problem each on Work/Force, memorize all that nonsense, then never seen again the rest of the semester except when they wanted to throw it in the final exam. Useless

[molten mason]

Very famous

[gray gazelle]

I didn't understand this

[molten mason]

It was meant for marlins, but it's a good book.

[gray gazelle]

Yes exactly. This is kinda irritating and annoying.

[gray gazelle]

Oh okay.
Rn I am taking a look at both Stewart's and apostol.

Thank you for the recommendations.

[floral lantern]

Oh wait lol

Yeah I don’t have the time to pursue Apostol rn whcih is sad

we’re using agodawful Pearson textbook

But it’s serviceable and braindead

[molten mason]

Apostol is better, but I don't think there are solutions or not very many.

Stewart still works, and if you pay for Quizlet it doesn't just show you the answer, but it goes through the steps and walks through every single problem. All of the problems.

[gray gazelle]

Wait. I just saw rn, apostle has solutions at the end of the book.

Stewart, apostle and lang (calculus of several variables).

These three books look interesting.
Now I am thinking which one I should study (according to my background). I know calculus 1 and some of calculus 2. Also I know about proof writing (because currently studying Velleman's book too)

[molten mason]

WOW maybe I'm blind, I don't remember those being there lmfao That's good to know.

Also I simp for Lang but that's actually one book I haven't looked at. It looks like he also has answers in the back, that's good. One thing with Lang is that his books tend to be proofy and dry. Which is fine but some people get fustrated with it.

[loud cradle]

the lang "several variables" book is pretty good actually, not proofy or dry, but more to the point and less full of fluff than stewart etc

[molten mason]

Interesting, good to know.

[gray gazelle]

I don't have any experience with Lang's books. I just saw his book, and have some overview. That look me good. Also there are solutions at the end.

[gray gazelle]

I think as compared to other lang's books (except basic mathematics) this is less proofy.

[earnest wolf]

i mean, GEB an ethereal golden braid is very interesting. i just don't like logic so much

but it's probably at the edge of what u can read in bed without taking some notes

[trail hemlock]

idk enough math to do that tbh

hmm i’ll take a look

[earnest wolf]

it's aimed to somewhat mathematically mature audience i think

so there are basically no prerequisites: he says everything as needed

[silk apex]

Has anyone read Leil Lowndes "How to Talk to Anyone"

[storm zinc]

Any suggestions for an intro to Information Theory?

[fierce hedge]

Lemme know if you liked that book, I have a pdf of it but never tried it

[novel obsidian]

I think I'm gonna use knapp. Bresar is a bit slow ithink and doesn't cover too much ground in terms of pure algebra

[thorn cloak]

2 questions! 1) I'm looking for a good first book in diffeq. I have been putting of that class for a while now, and need to eventually go back for it. I have taken two semesters of analysis if that matters. 2) any books on modular arithmetic/number theory tricks? Not necessarily a full course on number theory but I like solving puzzles and many of them use tricks that I feel like I could never derive on my own

[thorn hinge]

I'm looking for this book "JACOBSON, N. - Lectures in Abstract Álgebra, Vol. I, Van Nostrand, New York, 1951.". I search online and there are many Lectures in Algebra from Jacobson

Is this one https://link.springer.com/book/10.1007/978-1-4684-7301-8?

[stuck elk]

Journey into Geometries by Sved, Coxeter, and Stillwell. It's like a fan sequel to Alice in wonderland

[gray gazelle]

hey

ve been wanting to study "low level math" for a while

of you know what im talking about

stuff like abstract algebra, group theory

building stuff from scratch from axioms

2= {{∅}, ∅} kinda stuff

are there any go-to books?

[thorn hinge]

Naive set theory?

[thorn hinge]

He has a chapter on peano axioms and natural numbers

[gray gazelle]

Hey there, I started a calculus 2 course in university a week ago, and the professor is really bad, if someone could help me finding videos or books or anything that explain the contents I'd be really grateful
Here are the contents
Hyperbolic and inverse hyperbolic functions
Integration methods
Tyler expansion and Maclaurin expansion
Litzen's theory
Rolle's theorem and mean value theorem
Lobital rule
Integration applications (areas and volumes)
Dysfunctional integration
Functions in two variables

[novel obsidian]

https://www.youtube.com/@ProfessorLeonard you may find this channel useful

[gray gazelle]

Thank you

[gray jungle]

@gray gazelle old professor notes from my freshman years, i think they are pretty good (these are publicly available, no piracy)

[gray gazelle]

Thank you so mucchh

• Oh my
  He's Arab :3

[remote sparrow]

this book has a new edition FYI

it's called Basic Algebra I and Basic Algebra II

the books are available as dover editions

[remote sparrow]

not low level

you might be interested in logic and set theory

[remote sparrow]

#book-recommendations message

[gray gazelle]

Math Gene is such a good book

[violet shuttle]

"Dysfunctional integration"

[fierce hedge]

I see

[remote sparrow]

so how did the knapp study group end up

[fierce hedge]

It was put on indefinite hiatus, tbh it probably died cause almost everyone there was either already at uni or joined uni soon. So as soon as the summer holidays were over, none has time.
Also, after the LA part we switched to Rotman for abstract algebra cause people weren't liking Knapp that much.

[molten mason]

There's always next summer lol

What was wrong with Knapp

[fierce hedge]

It was pretty fast, almost Rudin level fast at times and the notation was unusual. It's not that bad once you get used to it but it has some non standard notation at least for the LA part. I think the biggest issue was matrix with respect to ordered bases had wak notation.

[molten mason]

Ah interesting, good to know.

[remote sparrow]

i see. i ordered a copy of the first edition on amazon today since a vendor was selling it for an absolute steal of a price

[heady ember]

FIS notation is some of the best, according to tera iirc.
Its notation for that is [T]_b^g

[tribal crow]

absolutely

[gray gazelle]

can anyone recommend a beginner friendly set theory book with exercises?

lecture notes work too

[remote sparrow]

enderton or goldrei

[gray gazelle]

is there smth more modern?

[tribal crow]

just straight up set theory with nothing else?

[remote sparrow]

why does it need to be more modern?

[gray gazelle]

they tend to be better and more relevant to the current research

[gray gazelle]

yes

[remote sparrow]

but you are only learning the basics

besides, goldrei was written in the 90s...

[gray gazelle]

ig ill give those two a shot

do you know of any lecture series that accompanies either of the books?

I feel like studying smth this abstract requires watching some lectures

[remote sparrow]

https://www.youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf

this playlist follows enderton

[gray gazelle]

thank you sour drop :)

[fierce hedge]

Oh, is the second edition similar to the first one or is there a significant difference?

[remote sparrow]

similar. you can check the preface to the second edition to see what major changes were made.

[heady ember]

How beginner friendly are we talking about

Kunen's foundations of mathematics covers most of what Enderton does in like 100 pages

Look at Clerk's recs too

Baby jech is well liked, if you have some mathematical maturity.

[gray gazelle]

to give you an analogy, it must be the same to set theory as what gallian/pinter is to abstract algebra

[heady ember]

Enderton, then. In my exp it has been good, idk about the 'moderness' though

[gray gazelle]

gotcha

[dapper inlet]

is there a good calc book for self teaching

[silk sigil]

What is Litzen's theory?

[gray gazelle]

Leibniz' theory

[dapper inlet]

lol thanks for the subtle nudge

holy moly this guys hot

[gray gazelle]

Any one please recommend me the university when has real analysis course (Homeworks, notes) on online page. Which follows Abbott's book

And if possible recommend other resources related with Abbott's book

As someone who has read the book, any introductory real analysis lecture notes online should suffice imo

You might be able to find some uni that follows Abbott though

[remote sparrow]

#book-recommendations message

[gray gazelle]

Yes. James Stewart.

[gray gazelle]

Oh yes. I was searching for this.

How quickly did you find it?

[remote sparrow]

fast

btw did jay cummings ever reply to you if you emailed him

[gray gazelle]

I mean how? Is there any option so that I can save or pin useful messages?

[remote sparrow]

use your memory

[gray gazelle]

I emailed him that day. But unfortunately he didn't reply to me.

[hallow oriole]

i have a separate private server i store links in

[gray gazelle]

Ah

[remote sparrow]

you can just copy down my message somewhere

[gray gazelle]

That's a great idea.

[gray gazelle]

Okay. Btw thank you.

[dusk wind]

using memory is too hard

[small perch]

no, they doesn't

There's really nothing more, except imo they do not include useless theorems and topics that better to learn if you specifically need it

in beginner set theory

[gray gazelle]

https://www.cmi.ac.in/~vijayr/analysis_2017fall/index.html

[floral agate]

Any suggestions on books for linear algebra and multivariable calc, ideally with a lot of practice questions with solutions to go alongside my uni course

[gray gazelle]

We don’t know what goes along with your uni program

[modern ruin]

he probably just meant "as a supplement to"

[floral agate]

Yeh, I think it’s just a normal linear algebra and mv calc course (I can work out what lines up and what doesn’t) but they don’t give us many practice questions so I was after a book w more examples if one exists

[thorn hinge]

THis is on the bibliografy of my course. But i'll also download the new edition

[brazen rivet]

Could someone recommend a good introductory textbook on the geometry of stratified spaces? One that avoids category theory in particular.

[gray gazelle]

Oh wow. Thank you so much

[north thunder]

I want to pick up some maths to help me reason about some maths when programming or atleast have a base to learn more. I found a book called Programmer’s Introduction to Mathematics by Jeremy Kun. What do you guys think about this book?

[gray gazelle]

anyone know any good introductory books for combinatorics?

prefer more rigor

[tawny copper]

Please, look old messages in this channel.

[remote sparrow]

A Walk Through Combinatorics by miklos bona

[cosmic gulch]

Which books would you recommend to get a 5 on AP Calc BC, given I'm entirely self-studying? Thanks

[alpine rover]

I used Barron's AP Calculus

[gusty orbit]

I need a book recommendation - set theory and topology?

[lusty ermine]

any recommendations to learn euclidian geometry, with hard problems?

[daring lake]

Munkres Topology is the standard recommendation. The first chapter also treats sets.

[molten mason]

@heady ember @dusk wind @remote sparrow any of you three interested in a reading group of this textbook starting in May, led by @torn crypt

https://link.springer.com/book/10.1007/978-3-319-60231-8

[torn crypt]

(Or anyone else who happens to be reading, idk any particular chapter numbers I’d wanna cover in it or the pace atm though)

[hardy folio]

169,99 USD

I will sell my mother to buy this

[torn crypt]

Definitely want to see some of the forcing at least, and chapters 4, 11, and 14

[molten mason]

PDF is free for university students.

[gusty orbit]

Can you help me with the link? Where can I find? Do you have a physique too?

[hardy folio]

Where is the pdf?

Im newba

[molten mason]

On the link. If you sign in through your university authentication system, the "eBook" will change from "buy" to "download"

[gusty orbit]

Does anyone have set theory?

[daring lake]

Just search online

[floral lantern]

aops geometry

if you want high school level but difficult olympiad style geo

for hard problems there's always just EGMO

[hardy folio]

EGMO is for girls

[floral lantern]

the book

💀

https://web.evanchen.cc/geombook.html

[hardy folio]

My honest reaction
https://loja.sbm.org.br/geometria-euclidiana-plana.html

[viral breach]

Animal Farm

[heady ember]

My concern would be my lack of foundational knowledge, like basic measure theory and (non-metric space) topology

[dusk wind]

yea, same issue as grass, although I might join in anyway

[molten mason]

I mean same, but with our powers combined...

I'm hoping more advanced people become interested in joining and provide balance, otherwise it probably won't be a go (sage has other topics he also wants to explore)

[torn crypt]

Measure is probably not a point, topology might have some relevance

But yes, there’s other things I was considering

[heady ember]

Hm, well, I would love to learn some more set theory. But, simultaneously I don't wanna put the cart before the horse

[exotic belfry]

What resources can I use to learn basic integration?

[tawny copper]

Usual calculus books should suffice. First try to do the integrals yourself, if you have put some effort but didn't succeed, then look at the methods

Find antiderivatives of the usual elementary functions. Specially of arcsin, arccos, arctan which are a bit trickier

If you wanted something more, let me know

[stone sandal]

@everyone i hate math

[modern ruin]

lol

[steel cloud]

Has anyone comments on Visual group theory by Nathan Carter?

[zinc bronze]

Does anyone have the solution manual to Barnard and Child's Higher algebra? Or a book that has solutions to similar problems, especially the number theory section

[remote sparrow]

https://maa.org/press/maa-reviews/visual-group-theory

[stuck apex]

Can you guys help me find a book in linear algebra especially in topics like vector spaces where I can find hard exercises on spanning set and basis and linear independence

[chrome yacht]

try this https://linear.axler.net/

[gusty orbit]

Does anyone have a catalog of mathematical books?

[tribal crow]

like, just a ton of books?

[gusty orbit]

yes

[tribal crow]

do pdfs count

[gusty orbit]

yes

[tribal crow]

@molten mason has like, most of Springer's UTM/GTM series

[gusty orbit]

OK

[tribal crow]

why do you need so many though?

[gusty orbit]

It would make my understanding easier and when I find them

I'm terrible at finding introductory books

[tribal crow]

if you're searching for book recommendations, you can always ask in this channel you know

[gusty orbit]

Ok

[tribal crow]

i'm sure someone here will be able to assist with that

[gusty orbit]

Right

[tribal crow]

if you're looking for books on a specific topic at the moment, you can just ask here right now

and wait for someone to give you recommendations

[gusty orbit]

Of course, I'm interested in set theory and abstract algebra

I'm looking for good books

[pliant wadi]

Howz Rotman for homology?

[last bloom]

Anyone has recommendations for introductory game theory textbooks that include actual formal math?

[gray gazelle]

Halmos for set theory, there’s a pinned message for good algebra books

[hallow oriole]

if you don't like halmos give enderton a shot

artin is highly recommended by a lot of ppl for alg

[molten mason]

The mad lad

[molten mason]

A lot of people have said good things, I'm going through it right now to check it out. He builds up on things as he teaches and holds your hand through it all.

[molten mason]

You can look up Springer's Undergraduate Texts in Mathematics and also check out out https://raw.githubusercontent.com/TalalAlrawajfeh/mathematics-roadmap/master/mathematics-roadmap.jpg

[lusty ermine]

its in portoguese brasilinho, is it worth the read?

[molten mason]

There's dozens of categories in math, each with dozens of different textbooks. I have a personal list with exactly 2400 math textbooks in it and it's still missing a ton of texts.

It's much easier to ask in here than consult a list lol.

You said introductory text to set theory and abstract algebra. How introductory? Undergraduate or graduate? Do you have background in those topics at all from another text or class?

[lusty ermine]

👀

[molten mason]

I might have something actually let me take a look...

[molten mason]

Check out Lectures on Euclidean Geometry 1 and 2 by Pamfilos

Combined they have 1000 pages.

I think combined they have a couple thousand problems, and a few thousand figures. The target audience is university-level math major

[lusty ermine]

thanks

[hasty eagle]

Removed the studying! role from you.

[gusty orbit]

Postgraduate, books that can help me now

[hallow oriole]

if you have postgrad you should know at least the fields of math you want books in, no?

oh, wait, misread

[gusty orbit]

Yes, but I think something is missing

Honestly, and as incredible as it may seem, I still have difficulty with this.

[potent coral]

ooo coexeters geometry would be perfect for you https://www.cimat.mx/~gil/docencia/2021/geometria2021/[Coxeter]Introduction to Geometry,2ndEd(1969).pdf

[potent coral]

anyway you could share that list????? that would be the most insane resource to have

[feral zenith]

Any books to learn about calculas 3

[tribal crow]

2400....

i have about 100, and i consider that a lot

[plush inlet]

Looking for something Number Theory that has a very introductory overview of Sieves with necessary background if anyone has any good recs

[remote sparrow]

#book-recommendations message

[remote sparrow]

Set Theory:
Set Theory: A First Course by Cunningham
Elements of Set Theory by Enderton
Classic Set Theory by Goldrei
Introduction to Set Theory by Hrbacek and Jech

Abstract Algebra:
Algebra: Notes from the Underground by Aluffi
Abstract Algebra by Beachy and Blair (has a website with supplementary materials)
Abstract Algebra: Theory and Applications by Judson
Discovering Abstract Algebra by Osoinach (if you're the type that enjoys proving everything themselves in a guided fashion)
A Book of Abstract Algebra by Pinter
Abstract Algebra: A First Course by Saracino
Algebra in Action by Shahriar Shahriari

[finite gale]

there's an abstract alg book thing in pins

[last bloom]

thanks

[molten mason]

a majority of them are books I'll never look at, but when someone says they're working on problem a in chapter b book of book c, I can normally quickly look it up. Some are duplicates I e. Edition 2, edition 3

[lusty ermine]

any good recomendations for learning Analytic Geometry?

what is the goto, for this?

[remote sparrow]

https://www.reddit.com/r/math/comments/1ay2got/what_would_you_consider_some_of_the_most/

[stuck apex]

Hey guys I hope you doing well, so I want to learn how to do hard proof by induction for university level does anyone of you know a book who could help me with that.

[gusty orbit]

Thank

[finite gale]

If this is about a specific problem, it's probably better to go to the help channels; if you mean in general, you can probably just read up on how induction works in any number of resources

[torn crypt]

Not sure how much I agree with some parts of this

[torn crypt]

Either way, I might end up doing something non-set theory regardless since a couple months out

[heady ember]

I was interested in Princeton University Press' 75% off sale, til I saw the comical shipping costs.

[lusty ermine]

[heady ember]

The delivery cost is 3.86 times of the on-sale price

[modern ruin]

lol

[molten mason]

I didn't see any textbooks on the sale, just random books 🤔 S&S is still $105 on Princeton Press (only $89 on Amazon though)

[heady ember]

Saeed Zakeri's CA book.

[molten mason]

Thank God I live in a low-shipping rate country.

That book looks so familiar....

@sudden kindle does your strong recomendación for Zakeri still stand? Have you or others you know compared it to the CA pin by Dami? (I already saw you bhate Ahlford)

[maiden glen]

May anyone suggest any pure/applied math oriented, basic-advanced (advanced, as not in homological, abstract algebra, etc. But rather the intrinsic English definition of "advanced"; a more refined, perhaps obscure way of thinking and mathematical modeling and providing alternative, but effective methods to problems of all difficulty.) algebra books which can satisfy the layman of the amateur of readers (or the adept of experts) looking to improve their foundation in algebra before approaching more intricate fields of mathematics.

[sudden kindle]

Truth be told I havnt read Zakeri, I just really liked him as a prof and liked his selection of topics as we went through and followed about half the book.

I read parts of Ahlfors and hated it

Idk abt other CA books

But I will still say Zakeri is the best

[molten mason]

When I get home I'll see if I have any notes about it on my computer otherwise I'll just spend an hour looking at up. The cover and name are fa iliar to me but I don't remember why or from where

[crimson leaf]

S&S being at full price made me sad

[pliant stream]

the functional anal one is discount

[molten mason]

I love myself some fun anal

It's funny that they selected which ones on discount instead of putting all of them

Yeah Volume IV is the only one on discount

[molten mason]

Same

[maiden glen]

response please

[crimson leaf]

What exactly are you looking for a first or second course in algebra?

[maiden glen]

I am not familiar with "first course" or "second course".

i'm self tutoring

[crimson leaf]

Nevermind I thought you were looking for a like first course in modern algebra book

[maiden glen]

any other responses?

[sturdy shore]

I ordered this, hope it's good

I went thru a fair bit of complex made simple (it's great) but I'm really looking for another perspective aimed at the same level

[heady ember]

You can ask Yamin about it if you want. Their prof for their CA course was the author, who provided them with pdfs of the draft

[daring lake]

Even that is not available for my country

Cries while studying from Rudin

[sturdy shore]

well, I already ordered it so
I'm gonna ask myself instead once it arrives lol

[heady ember]

Sure

[sturdy shore]

the ToC looked promising

[maiden glen]

someone give me something please 🥺

[molten mason]

First course = your very first textbook in abstract algebra
second course = something more advanced than that, normally upper undergraduate or first-year graduate level.

[maiden glen]

thank you

[molten mason]

One Reddit post says Zakeri is too fast paced for first time, and would be good after S&S

[lusty ermine]

Any good recommendations on proofing

How to write them

Contradiction, Inductive step, by cases

How to understand proofs and write them

[lusty ermine]

Rca by papa rudin?

Is it any good?

[tribal crow]

How to Prove It by Daniel J. Velleman is a good one

some like Book of Proof by Richard Hammack

alternatively, you could just choose a book on whatever subject you intend to study and pick up proof-writing on the fly by examining how the authors write theirs

[lusty ermine]

you like the math sorcerer very much?

I think this are classic recommendations from that guy

[tribal crow]

i think they are just classic recommendations in general lmao

i haven't seen too much of the math sorcerer

only a bit

[tribal crow]

these were what i was recommended

so i'm just passing them along

[heady ember]

Practice

and ask for feedback

[lusty ermine]

which books have good introductory proof writing exercises?

[tribal crow]

...how to prove it would still be my go to lol

for general proof writing

its literally designed to teach you the basics of proofs + some discrete math stuff

[maiden glen]

any book or pdf file recommendations for differential Geometry?

[heady ember]

• Linear algebra by Friedberg, Insel, Spence
• Schroder's a concise introduction to mathematical analysis
• Abbott
  These are well liked for getting straight into things + learning proofs simultaneously

[molten mason]

~~Algebra by Lang ~~

[tribal crow]

i see FIS mentioned, i like

[molten mason]

+1 to FIS

[heady ember]

Personally I read Enderton's elements of set theory first, because I wanted to learn set theory.

I still wanna leaen more set theory. First, I need to get the prerequisites though

[tribal crow]

still, i guess it depends on what subject you're trying to learn

do you just want the basics of proofs? or is there a subject you'd like to learn simultaneously?

[lusty ermine]

nah just basic proofs

I still havent learn any algebra so I prefer starting with proving odd or even numbers and what not

[tribal crow]

my first two recommendations probably get as about as close as you'd like to an introduction then

[heady ember]

Words of wisdom by Schroder.

[lusty ermine]

what would be the following book after Enderton's elements of set theory?

[molten mason]

That's literally the begining exercises of How to Prove It by Velleman

[heady ember]

Enderton has an overkill amount of set theory if you're not interested in set theory, fyi.

But if you have read Enderton and know some

1. Analysis
2. Algebra
3. Topology
4. Mathematical logic
   you'd probably be set to learn more set theory. E.g. Kunen's Set Theory or big Jech.
   (Not all those are strictly necessary to know before learning more set theory, but nice to have from what I've heard)

My plan is to learn those stuff before getting back into set theory.

I would have built up years of anticipation by that point lol

[molten mason]

edging yourself on set theory

[heady ember]

Wdym edging

[molten mason]

I'm not allowed to answer that publicly without

[lusty ermine]

I will take a look at it. thx.

[molten mason]

But it basically means built up anticipation

[heady ember]

I see

but uh what's the intent behind that remark

just curious

[molten mason]

None

[lusty ermine]

what would be good introduction material to functional analysis, is it a prereq knowing the in and outs of algebra/linalg?

[tribal crow]

knowing linear algebra very well is basically a prereq to like, 90% of mathematics

[molten mason]

topology, measure theory, linear algebra, and very strong with proofs. I'm currently working my way up to functional analysis and hope to do it in a year or two

[lusty ermine]

do you solve many exercises daily or something?

apparently topology is a prereq for any mathematics whatsoever

I need to learn that.

[molten mason]

Actually I do, but on some days it might literally just be 5-10 minutes worth of work because I don't have time.

[tribal crow]

i gotta learn some topology soon too

[tribal crow]

some days i solve quite a few, some days i solve 0 lmao

[molten mason]

I have days of "What the hell even is this" with tears forming followed by "Oh wait, this makes sense, I think* then I flip to the next page and repeat

[final goblet]

hi guys

i'm from australia and i need help to understand algebra and simulataneous equations

[tribal crow]

@gray gazelle i want to know your recommendations for this actually, since i'm interested too

(sorry for the ping)

[lusty ermine]

did you take a look at antons?

[final goblet]

No what are antons? and i'm year 10 at a Australian high school

[gray gazelle]

you're allowed to ping me

my quick answer is the following (im gonna sleep real soon so i can't write a detailed one)

basics of smooth manifold theory: tu's book supplemented by lee's ISM (ISM has better exercises and material on stuff tu lacks)

differential topology: guillemin and pollack if you're okay with a conversational style book, and milnor's 50 pager

differential geometry: lee's IRM for riemannian geometry, also maybe tu's other book

[tribal crow]

how is lee's ITM?

i was planning to read some of it over the summer

[gray gazelle]

never really read it, but it's probably good

[tribal crow]

to study topology from it, would i need to supplement it with something else

oh actually, i guess you havent read it too much

so this question isnt useful

my bad

[gray gazelle]

mat327 used it once, if that means anything

one of the summer offerings of the course

[tribal crow]

i see

thanks for answering

[daring lake]

I haven't read it entirely, only the first 6 chapters but I really liked what I have read so far. Much better written than PMA.

[novel sluice]

If only our uni knew this everything seems rushed and I am dying over years at this point

And I know this is true because whatever I have learnt and actually retained is due to me struggling weeks with a single problem

[novel sluice]

The entire book is an exercise

[dusty stirrup]

Any good book on mathematics of AI field?

[lusty ermine]

How to get started with lambda calculus, any recommendations?

[lusty ermine]

I see, thx.

[hallow oriole]

oh when i was in my logic type shit phase there's a canonical reference for this

bandelberg?

brandenburg?

something like that?

you'll know what i mean if you look it up

[lusty ermine]

Barendregt

[tame sphinx]

i'm ordering a book on real analysis, are they any prerequisites I should be aware of?

[stray veldt]

depends on the book

check if the introduction mentions anything

[tame sphinx]

ok

[finite gale]

you could also say which book you are considering if you want a more directed response

[molten mason]

What book

[tame sphinx]

https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116

[molten mason]

Should just be 3 semesters of Calculus

[tame sphinx]

As in Calculus I, II, and III?

[finite gale]

so like single variable differentiation, integration, and some multi, i guess

[tame sphinx]

Or just A school year of calculus?

[gray gazelle]

I have a question guys

[finite gale]

but typically multi is a later problem

so a school year of calc is probably fine

[modern ruin]

yes

[finite gale]

abbott is not too bad to read though i think

[tame sphinx]

oof, I'm in Pre-Calculus, so that's a long way to go...

[gray gazelle]

Does anyone have a list of books for each subject of math where there's 3 or 4 good textbooks for every subject arranged in an order that makes sense to learn?

[gray jungle]

more important prerequisites is basic logic and proof writing

[modern ruin]

yes uh someone posted it just recently

[tame sphinx]

any book recommendations for those topics?

[gray gazelle]

Yo can I see it?

[modern ruin]

#book-recommendations message

found it

[gray gazelle]

thx bro

[finite gale]

i think the best way to learn basic logic and proof writing is either through an intro analysis class or discrete

[modern ruin]

sharp says he disagrees with some parts of it and i have not read about it to verify

but

seems fine for the most part

[gray jungle]

The appendix of tao analysis I is enough, the pinned summary in #proofs-and-logic by loch is nice too.

[finite gale]

you can learn it just to learn it but it's probably more effective/efficient if you learn it as you go through some class

[glacial crypt]

oh you bought abbott lol

you'd probably need calc1 at least

maybe 2

to make sense of the concepts

[tame sphinx]

I didn't get it yet

[glacial crypt]

strictly it's not FULLY necessary

[finite gale]

alternatively you could just go in without any calc

[tame sphinx]

someone said it was really good for analysis

functional analysis

[glacial crypt]

like I didn't know anything about sequences and serieses when I read this book

[modern ruin]

it's okay, one thing at a time. You will realize that there is "always a bigger fish", and what you have to remember is that math is sort of a walk in a neverending woods, and if you're just focused on the fact that there's more woods ahead of you instead of stopping to see the trees and the leaves, and admire the bits of sun that poke through the canopy, you're going to have a much worse time than if you just stop and appreciate what you're doing now

[glacial crypt]

I dont' think it does any of these lol

[finite gale]

and just use stewart to do some computations as you go along to make sure you can actually compute things

functional analysis is a while down the road

[glacial crypt]

it introduces pointwise, uniform convergence of functions but that's not really functional analysis (?)

[gray jungle]

a WHILE

[tame sphinx]

Ok, I'll just take my time and wait till I finish Calculus 😄

[finite gale]

don't worry about what is down the road

[glacial crypt]

I mean the first few chapters probably do not require calc

[finite gale]

you'll get there when you get there

[glacial crypt]

it just helps to contextualize it

[tame sphinx]

ok, I'm just really facinated by advanced mathematics

[finite gale]

i mean strictly speaking, you don't need calc for analysis

[lusty ermine]

how do I get my head around planes, normal vectors, parallel vectors, orthogonal vectors, and lines in 3D space vector mathematics?

[finite gale]

just like you don't need analysis for topology

[molten mason]

I also disagree with it, and there needs to be an updated and improved version, but there isn't. That's the closest we got for now. Someone looking through that map shouldn't follow it blindly, just let it guide them then come back in here to ask more questions.

[glacial crypt]

chapter 1 in particular is mostly discussing some proof techniques and getting you more comfortable with proof techniques

[tame sphinx]

I just want to be comfortable with proofs and logic

[modern ruin]

agree

[glacial crypt]

strictly speaking you only need some basic set theory and logic to learn category theory
~ riehl

[modern ruin]

this is something that you can build up. I think precalculus is the first time I actually learned how to prove anything (we had a section on induction)

[molten mason]

Functional analysis is a few more classes past real analysis

[tame sphinx]

we dealt with proofs in geometry, but I haven't done proofs since Algebra II

[tame sphinx]

oooooh

[glacial crypt]

it's fine though I know high schoolers who have finished the whole book

[finite gale]

strictly speaking, you don't need intuition to learn anything

[glacial crypt]

just manipulate symbols sotrue

[molten mason]

We all do

[finite gale]

you can become chatgpt, barely know definitions then get asked a question and start cranking

[tame sphinx]

eh, I'll figure it out...

[modern ruin]

that's what half our math majors do

[tame sphinx]

I want to major in Physics,

[modern ruin]

i love physics ❤️

[tame sphinx]

so I need to be comfortable with LA, Diff-Eq and such

[tame sphinx]

me too

[molten mason]

I went through a youtube category theory lecture series before I went through abstract algebra lmao Was interesting.

[glacial crypt]

tbh I've never been able to actually learn anything properly from youtube

I have to do exercises anyway

[modern ruin]

wow it's just as though you worked through Algebra: Chapter 0 by Paolo Aluffi

[finite gale]

youtube is only in place of lectures

[modern ruin]

i love aluffi

[glacial crypt]

category theory examples do require some stuff

[finite gale]

obviously you cannot replace actually working through problems with youtube

[molten mason]

blackpenredpen

[glacial crypt]

@mystic orbit isn't your first algebra book aluffi lol

[tribal crow]

you'll probably need a bit more than that depending on where you want to head in physics

but those are definitely needed

[finite gale]

well you gotta start somewhere

[modern ruin]

who knows, maybe you'll find the math more interesting, and then head into differential geometry instead

[tame sphinx]

oh, yeah totally

[tribal crow]

this might actually be me

[tame sphinx]

I might do a double major in theoretical physics and pure mathematics

[modern ruin]

lol me too

[tribal crow]

oof, i wish you the best of luck with that

thats quite hard

[tame sphinx]

that's why I want to do it

[molten mason]

Blud wants to do a 5 year undergrad

[tame sphinx]

the what-ifs are what led to groundbreaking discovery

[tribal crow]

i've seen people do it in 4

[molten mason]

That's disgusting lol

[tribal crow]

cs + math + physics

3 majors

4 years

i dont know how they do it

that guy is at MIT now though

doing high energy physics research

[tame sphinx]

that is so cool

[tribal crow]

i dont think he was a human though

[tame sphinx]

my standardized testing score isn't enough for MIT

but it would be cool if I got in

so I am stick in In-state

if I don' t get a full ride or scholarships

[tribal crow]

being ambitious is good, but it's important to take things one step at a time

[mystic orbit]

no

my first was artin

[tribal crow]

not everything will work out as intended

[glacial crypt]

darq owns 0 undergraduate books

[molten mason]

Anyway, either the Physics or the Math route, you have, let's say 15 classes in front of you, some can be taken together, some have a very linear progression. It's going to take time and patience is key, as you take more classes though you will unlock more and more classes you can take.

Pre-Calc -> Calc and Linear Algebra, the rest will fall in from there. Set goals but don't stress yourself out or get too far ahead.

[tame sphinx]

yeah I know, that's why I am lowering my expectations as much as possible

[mystic orbit]

[tame sphinx]

Ah, thank you! this really puts it into perspective.

[molten mason]

Why waste time in the introductory when you can go straight to the real stuff

[tame sphinx]

right now I am working on Trigonometry

in this section we are going over Inverse Circular functions

if you don't memorize the unit circle, things get very confusing very fast

[gray gazelle]

Lang’s Algebra is self-contained 👍

[tribal crow]

i dont hear good things about Lang's books usually

is there a reason for that

[molten mason]

Just memorize it

Also https://mecmath.net/trig/

[molten mason]

Skill issue

[tribal crow]

to this day i cant memorize the unit circle lol

[gray gazelle]

Some of his books are lacking in polish

[tribal crow]

i just draw triangles every time

i see

[tame sphinx]

isn't it a bunch of patterns?

and reflections

[tribal crow]

yeah

and i have a skill issue with it

[tame sphinx]

ah ok

too bad

[molten mason]

Just memorize Quadrant I

[tribal crow]

bold of you to assume i was able to do that

[tame sphinx]

lol

[tribal crow]

(yes im aware only quad 1 is needed to know the rest)

[tribal crow]

but i have to do this everytime for Q1

[molten mason]

Skill issue

[molten mason]

The long answer is yes, his books lack polish, some of his books aren't even real expert books, they're just his notes from learning the subject for the first time himself, and he organized the notes into a textbook. He assumes certain things on the reader, and it's the textbook equivalent of an instructor plowing through the lecture without taking any questions from students. Either you understand it, or you can go somewhere else. He doesn't need to add in 100 examples and graphs and pictures about how this formula is used in biology and car manufacturing and whatever else. This is the formula, take it or leave it, now we're moving on.

This straight shooter, no-nonsense approach is what makes it polarizing. To those used to normal human textbooks, he's vile and grotesque. To those who hate normal human textbooks and just want it told straight, he's a godsend.

[hot dagger]

Is Spivak Calc good book? Im 1st year undergrad learning analysis/calculus

[molten mason]

100% yes

[hot dagger]

I dont really know why but course is called Analysis although its mostly stuff done in calculus (sequences, series, functions, limits, derivatives, integrals) with lots of proofs and advanced stuff

I also have Abbott understanding analysis and Keneth Ross Real Analysis on side

although im not native english speaker

[molten mason]

Different countries and even different universities in the same country combine Analysis and Calculus.

[molten mason]

Both good books too, Abbot has a lot of resources online and in this Discord server.

[hot dagger]

alright thanks! I will be having English course this semester (mostly translating scientific articles) and in domain of math, do you maybe have some book recommendations for that? Correct, strict math expressions

[molten mason]

Nope, sorry

[tribal crow]

is fine imo

spivak is a good writer

[hot dagger]

alright ill give my best to go through the book

although its 600 pages

[tribal crow]

(his exercises give me terminal cancer though)

[molten mason]

1. That's short
2. His book covers 2 semesters of content.

[hot dagger]

bruh yeah I found another book that has nearly 1k pages

but written in espana ahhh

[molten mason]

Spivak en español?

[hot dagger]

Yes hahaha

[violet shuttle]

Hot take: it's more important than Calc 2, about as if not more important than Calc 1.

[violet shuttle]

The mnemonic I learned: sine goes sqrt(1)/2, sqrt(2)/2, sqrt(3)/2. that is, 1,2,3.

You can get all the rest from that

[tribal crow]

i agree actually

i didnt say that LA was more important than calc

just that it is very important

[violet shuttle]

i didn't say you said that

[tribal crow]

.

ig thats my bad too then lol

[molten mason]

Yeah 1, 2 3 - 3, 2, 1 - sqrt them all then divide all by 2

[tribal crow]

actually, now that i'm reading this again, i wonder if this is a hot take at all

[hallow oriole]

i think it's a pretty hot take on the grounds that calc 1 and 2 are fundamental

tf would you do in life without series

or derivatives

i'd be down to say c1/c2/la are abt equal in importance

[violet shuttle]

tf would you do in life without linearity

[gray gazelle]

Anyone have course hero and can help me?

[violet shuttle]

valid

Where I'm at, people tend to do calc3, diffyq, and only then linear algebra

[hallow oriole]

that seems odd

im in the camp that the best order is c1 --> c2 --> la --> c3 --> anything else

[molten mason]

That's potentially against the rules of this server.

[hallow oriole]

unsure how one gets a proper understanding of c3 without linalg

[violet shuttle]

Diffyq before LA is the weirdest part to me.

[tribal crow]

i still think LA and C1/C2 should be taught simulataneously

[violet shuttle]

Shit involves students who don't understand linearity trying to reason about linear operators.

[hallow oriole]

that seems unwise pedagogically for there to be two different courses that are individually c1/c2 and la taught at the same time

think of it like before this you're doing like precalc shit

and now you're being slam dunked w so many diff concepts

i think a single course that represents a unification of the three while somehow not losing material would be good

[violet shuttle]

my place has an honors class that does calc3+la+diffyq

[hallow oriole]

obviously for a more advanced student this isn't an issue but i'm talking about the median

[tribal crow]

fair enough

[violet shuttle]

So... I'm a weird person, but, what does the average person get from precalc? All I got was the definition of an inverse, trig, and then a long review of algebra 2.

(from the US)

this experience makes me feel like precalc is useless.

[molten mason]

At my school Linear Algebra is a prerequisite before you can take differential equations

[hallow oriole]

that's the thing

calculus is actually very easy

the issue is

[violet shuttle]

Now, I do think the problem people have is algebra.

[hallow oriole]

tons of people think calc is hard

but they're just being skill checked by algebra

[molten mason]

It really is

[hallow oriole]

precalc reinforces algebra knowledge and is taken as a chance to teach trig on the side

[violet shuttle]

Literally everytime I help someone with math it's algebra stuff.

[molten mason]

Yeah it all just felt like reinforcement.

[hallow oriole]

for more advanced students this is completely unnecessary as they'll already know this all

but again for the median this is super helpful

of course this could be fixed by teaching algebra better

but there's issues there too

[violet shuttle]

I think it makes sense to start algebra earlier.

And take it all slower.

[hallow oriole]

i think what would make the most sense would be to start with geometry and slowly transition this into an algebraic framework so kids will always have intuition

[tribal crow]

i still dont quite know what i got from it

[hallow oriole]

but wdik

[violet shuttle]

Gut polynomial long division.

[tribal crow]

i guess logs/exp, trig, polynomial division, function composition, ...?

[violet shuttle]

Teach logarithms properly.

[hallow oriole]

ehhh

what is there to learn abt logs

[violet shuttle]

They are the inverse of exponentiation.

[hallow oriole]

teach exponentials better, really

the issue is that i think ppl consider exponentials/logs pre calc material when a full understanding of them really requires calculus

[violet shuttle]

People, including myself, keep failing to learn this from their algebra classes.

[tribal crow]

eh, there's two inverses of exponents are there not? roots/logs

[hallow oriole]

i think the point of teaching exponentials and logs in precalc and such is so you're not lost asf when you see them in calc

[tribal crow]

one of them is for when the unknown is an exponent, while the other is for when the unknown is the base

[hallow oriole]

exponentials --> a^x exponents --> x^a

[violet shuttle]

i mean the inverse of a^x as opposed to x^n.

[tribal crow]

okay

makes sense

[violet shuttle]

I think you can get a lot of proper understanding without the rigorous definition.

[hallow oriole]

can you really

[violet shuttle]

Start with the rational case, hand wave about extending to the reals by saying "connect the dots".

[tribal crow]

are you guys proponents of early transcendentals or late transcendentals

[hallow oriole]

like let me ask you a question

what do you think the most important property of an exponential is

[hallow oriole]

idk what this means

[violet shuttle]

ok fair
(the derivative is itself (with maybe a constant factor))

[hallow oriole]

yep!

[violet shuttle]

one can still have students understand what exponential growth looks like on a graph, the idea of doubling/halving, the idea of inverting it with a log, the ideas of turning multiplication into addition.

[hallow oriole]

sure!

but i'm pretty sure all that is already taught

[tribal crow]

probably a bit to read, but i couldnt explain it otherwise lol

[violet shuttle]

that is, one can still teach the algebra of them so that students don't get lost in calculus or in subjects that use them but don't yet introduce calculus.

[hallow oriole]

i like using both tbh

define it all using early and then after integration prove the ln stuff

[violet shuttle]

Honestly my favorite definition to introduce to those that don't know is still going to be defining b^x via a limiting process with rational numbers, even if my personal favorite definition is the series for e^x.

Reason being that there's less prerequisite and that it's easier to intuitively explain.

[hallow oriole]

i think the repeated multiplication for integer x is better pedagogically bc u can start them rly early on it

[violet shuttle]

Oh, I meant after making sure the student understood that!

That is, either in a calculus course or in like precalc.

[hallow oriole]

oh sure

[violet shuttle]

I think one of the biggest crimes of math education is failing to convey the concept of a function as a machine that takes input and spits out output.

But I'm not the first here to note that

[hallow oriole]

i think the biggest crime of math education is geometry proofs 🙂 horrific

no wonder kids dont like math

[tribal crow]

how else would you introduce them

[violet shuttle]

As like a formula.

[tribal crow]

i recall learning about "input-output machines" as far back as grade 8

[violet shuttle]

It took coding and learning advanced mathematics to understand that properly.

Most, including past me, wouldn't recognize f(x) = 1 if x is rational, 0 otherwise as a function.

Or the function from {a,b,c} to {1,2,3} that sends a to 1, b to 2, c to 3.

Or the function that outputs the first digit past the decimal point.

Etc.

[tribal crow]

thats a bit of a pity

huh.

i didnt realize a lot of places taught like that

[violet shuttle]

Are you in the US?

[tribal crow]

no

[violet shuttle]

This may be a US thing.

[tribal crow]

i'm from Canada

which i'd imagine isnt so different

[violet shuttle]

I've heard a European (I don't remember which place in Europe...but, the entire continent of Eurasia is basically all the same, right?) tell me that she learned about sets in elementary school.

[hallow oriole]

i learned functions as input/output things too and im in us

[violet shuttle]

fuck. I went to a damn expensive private school that wasn't worth the money, and yet they couldn't get that across to me.

As in, even after taking a precalc course, I didn't understand that fact.

[hallow oriole]

rip 💀 tbf my public school was best for education in the state

so could be that

[violet shuttle]

here, students could take calc 3, diffyq, and the not-proof-based linear algebra class without knowing what a set was.

And most wouldn't, methinks.

[tribal crow]

how do you teach those courses without sets though

[violet shuttle]

At least, most that go through calc3&diffyq don't.

[molten mason]

Functions were explained to me in this way in 6th or 7th grade, I'm in the uS

[violet shuttle]

This just seems so normal to me that I don't get what you don't get 🙂

[tribal crow]

e.g how do you explain the null space without any notion of a set

[molten mason]

A lot of elementary algebra didn't truly click until I started learning how to code

[violet shuttle]

How about "If x is such that Ax=0, we say x is in the kernel"?

(or maybe they don't explain the kernel)

I'll try to find someone that's taken the not-proof-based LA class and see what they know. It'll be easier for me to find those that've taken or are taking the diffyq class though.

[tribal crow]

i mean at that point you could also call it the null space and not explain it either ig

my question would be: do the professors do this intentionally?

like, they obviously know all of this stuff

so why not teach it properly lol

[violet shuttle]

Well, the classes like the topology class start with a part about sets.

[tribal crow]

why topology

thats so late

for an intro to sets, that is

[violet shuttle]

I agree with you. One could start explaining the concept before someone even knows what numbers are.

[tribal crow]

agreed

[violet shuttle]

One could even do that with functions.

[tribal crow]

at your place, do you take intro analysis before topology or?

[tribal crow]

also agreed

[violet shuttle]

I don't know. I think neither are prereqs for the other?

(i skipped a bunch of classes)

[tribal crow]

huh. i would imagine it's not easy to motivate topology without analysis though?

[violet shuttle]

I agree?

I kinda agree.

No, I agree.

[tribal crow]

the computational ones?

or also some proof-based ones?

[violet shuttle]

Both, yes.

I'm an autodidact at heart.

[tribal crow]

self-learning gang

[molten mason]

Topology isn't even required at my school, it's a senior-level elective

[tribal crow]

i think thats somewhat common

you reminded me of this passage from the preface of Lee's ITM actually

i wonder if it's a US specific thing? my guess is likely not

[molten mason]

Actually, technically, Real Analysis isn't required at my school either

[tribal crow]

what is required of math majors?

[molten mason]

For my school...

Calc III, Proof Writing, Linear Algebra, Differential Equations

[tribal crow]

so theres a lot of room for elective choices then

[molten mason]

On one hand, it's choose your own adventure, on the other hand, there's no standardization among graduates with the same degree.

[tribal crow]

is it like, you must take 1 course from this selection, 1 from that selection, etc?

or undergrads can do whatever they want

[molten mason]

Yes... but a few of those don't have analysis or algebra

[violet shuttle]

Calc 1,2,3, DiffyQ, an abstract algebra class (choice between the less mathy version), linear algebra (choice between the less mathy version), analysis (choice between the less mathy version), A certain amount of extra math classes of a sufficient level, a programming class, a stats class (choice between the less mathy version)

[tribal crow]

maybe i'm wrong, but the way i see it is that a math degree that does not incorporate at least analysis/algebra is no math degree at all

[tribal crow]

ah, programming/stats

i probably should take a stats class tbh

i'm quite fearful of knowing nothing about it

[violet shuttle]

The applied math majors need discrete math and numerical analysis. They still need an algebra and analysis course, they also need a PDE course

[molten mason]

Like the route I'm going I need to take real analysis, probability, statistics, and then pick ONE ( stochastic Processes OR Advanced Linear Algebra) and then one class of my choosing.

The Math Education doesn't have their own degree, so they technically get a bachelor's in Math, but all their coursework is education related like history of math, math literacy, etc

The applied math people again, don't have their own degree, it's just a bachelor's in math, but all their classes are applied math nonsense.

etc etc

[tribal crow]

i see

[violet shuttle]

The sample math curriculum is hilarious.

It has linear algebra in the last semester, after abstract algebra, topology, number theory, diffyq, complex analysis and analysis (or maybe "advanced calculus" has concepts from differential geometry).

[molten mason]

Yeah the applied math focus for us is...

Math analysis for Engineers, ODE, PDE, Modeling, and an elective

[tribal crow]

how does this even function

[molten mason]

Again, just awarded a bachelor's of math, no abstract algebra or analysis

[violet shuttle]

I don't think people actually do the sample curriculum.

At least, they better not be.

[tribal crow]

ig this curriculum isnt bad though

at least you cover most (all?) of the main areas of math

[violet shuttle]

The order is bad

I agree that the classes present in the sample curriculum are good.

[molten mason]

Yeah I want to go to graduate school, so I'm planning on taking both semesters of abstract algebra, both semesters of real analysis, and a semester of complex analysis and a semester of topology. Plus my stats and prob classes

[violet shuttle]

lol the physics sample thing has them taking linear algebra sophomore year, much more reasonable, concurrently with diffyq

[tribal crow]

but you can choose to take the courses in any order you like, yes? (provided you have the proper prereqs)

[violet shuttle]

For the sample, you can definitely do a different order. I'm too lazy to do the prereqs, but I am sure that if physics majors fulfill the prereqs for linear algebra by sophomore year, that the math majors would too

[tribal crow]

i see

[violet shuttle]

I personally took the written anal qualy and passed, which made it easy to convince the math department to let me take graduate courses.

[tribal crow]

the physics program here is a bit rough in the sense that the math courses are taught at the appropriate times

[violet shuttle]

tbf the written anal qualy here is easier than other places seem to have

[tribal crow]

e.g we have to do E&M without having learnt vector calc beforehand

[molten mason]

My school works similarly, what did you do to study?

[tribal crow]

the graduate analysis courses are open to undergrads here, so i luckily would not have to do this

[violet shuttle]

I read Baby Rudin, then got measure theory from "Real Analysis for Graduate Students" then basic complex analysis from Conway's book (there was an integral by complex analysis on there)

[violet shuttle]

I think this is the eternal problem all undergrad physics departments have to figure out.

Unfortunately the physics department wasn't so willing to let me skip classes.

[tribal crow]

they dont allow it much here either

but neither does the math dept

[violet shuttle]

But, hey, this is working out well enough, so, I'll take a win and a meh.

[molten mason]

Bass?

[violet shuttle]

...I think so?

[tribal crow]

here, you can only take the algebra course in your second year if you get a 4.0 in the linear algebra courses from the first year

[violet shuttle]

I remember emailing him a correction and feeling the sense of accomplishment about getting a response.

It was very minor :p

[tribal crow]

what do you study now Xela?

you're in grad school, right?

[molten mason]

I'm going through Lang then Yeh and Bass for the next 18-24 months self-study and hoping that should be enough.

[violet shuttle]

Currently taking a differential geometry class that imo should be called Riemannian geometry.

I'm an undergrad.

[tribal crow]

i see

[violet shuttle]

I just take grad math classes.

[tribal crow]

fair enough

i gotta learn some DG

[violet shuttle]

I also finally got some of the algebra I missed, like wtf a Galois group is.

[molten mason]

Pick up Tu and you can start today

[tribal crow]

junior/senior?

[tribal crow]

i gotta learn topology first

and some multivariate calculus

[violet shuttle]

next up on algebra that I really should know - modules.

Oh, and I'm learning representation theory with a prof through one of those things that many universities have.

[molten mason]

Learn as you go

[violet shuttle]

(Fulton and Harris feels so nice compared to Lang)

[tribal crow]

i'm gonna read Lee's ITM over the summer (well, at least the first few chapters)

[molten mason]

For rep theory?

[violet shuttle]

so, what's ITM?

[tribal crow]

probably some parts from Spivak too

[tribal crow]

Introduction to Topological Manifolds (by John Lee)

[violet shuttle]

yes, but I'm comparing to Lang's Algebra.

[violet shuttle]

Oh, I skipped that because I wanted to beeline to Stokes theorem.

and then wanted to beeline to General Relativity.

[molten mason]

Anything feels nice compared to that tome

[tribal crow]

thats what Spivak is for

[tribal crow]

same!