book-recommendations

[dusk wind]

all the books are the same and they all carry the same risks

[gray gazelle]

I can say that I’ve learned most of the math I know from books, not classes. I’m not against classes at all, but it’s absolutely possible to self-study math

[dusk wind]

self studying fundamentals is dangerous

a good teacher is like having access to all the cheat codes

[gray gazelle]

Yeah, but there’s a good chance that someone gets stuck with a bad teacher, which is much worse than self-study

[dusk wind]

if theyre doing uni, they cant avoid that

[lusty ermine]

You can try the openstax precalculus and college algebra book from openstax if you actually want basics basics

[stray quarry]

any recommended book about logarithm from the basic to advanced?

[dusk wind]

Khan Academy really seems like a good alternative then

[stray quarry]

that has exercise and its example

[lusty ermine]

There is also solutions in the back not only for even but odd

[steel sable]

Can you guys recommend, any math topics which I should practice in free Time to get ahead.

[ember slate]

What interests you?

[molten mason]

Algebra 1, Geometry, Algebra 2, trig is for teenage learners.

College Algebra is those same topics for adult learners.

Axler has a College Algebra text.

Lang Basic Mathematics covers those + Pre-Calc

Professor Leonard and Brian McLogan for youtube. I don't know the exact spot but I believe they both cover roughly College Algebra through calculus

[steel sable]

Trigonometry but it's too darn hard

[molten mason]

https://mecmath.net/trig/

[steel sable]

What's this bruda??

[molten mason]

Looking at the table of contents, Lang's Basic Mathematics also covers pre-algebra.

Yes "those same topics for adult learners"

I would just go straight into Lang's Basic Mathematics and when the whole textbook is finished then start Calculus

If you feel after the textbook you're lacking in something, for example you feel weak in doing long division of large numbers, then find a youtube video on practice problems.

Yes they're essential for a reason.

[steel sable]

@molten mason let's say if I read this pdf you provided me and practice some of the problems there, would I be able to do all "prove that" questions easily?
Just curious

[molten mason]

There is none, it's just time.

You could theoretical buy 100 kindergarten workbooks and start from there, but if you already know the subject after the first workbook then it's best to move on.

A lot of advanced material uses early material, for example. You can practice single-digit addition many times. 1+1, 2+2 before moving on to double-digit addition, BUT, double digit addition uses single-digit addition, 31 + 42. Triple-digit addition uses both single-digit and double-digit addition and so forth.

Everyone on Earth has the issue of "I don't know what I don't know."

I recommend Basic Mathematics because it's concise and gets you through all of those topics. While using the book, I recommend youtube to help explain topics. You can just youtube "how to complete the square" and thousands of videos will pop up. When the book is finished you will now know what you know, and it'll be much easier to learn more about what you don't know. You no longer need 100 kindergarten workbooks. Maybe you need to review a section on khan academy, maybe you need to look at the trig link I just posted above, maybe you need to watch some more review sections on youtube about calculating volume of a sphere. Etc

For example, it introduces the main bulk of trig you'll need to know, but not all of trig. That trig link I posted is 180 pages of trig with more trig formulas and identitys would be a good thing to read after.

[molten mason]

Those questions you should be able to do, but they're not designed to be "easily" IMO They're to make you think.

[steel sable]

Your help's most appreciated.

[tough egret]

Hello, I'm learning real analysis through the Abbott's Understanding Analysis. I find the book to be quite light proof-wise, although excellent as a first exposure to the topic. I'd like to follow up with The Big Book of Real Analysis by S. Johar as it seems quite exhaustive and rigorous, does anyone here have an opinion on it? Thanks!

[molten mason]

Filling gaps will just take practice, with multiple varied problems designed in different ways, and no single textbook covers everything (mostly), I personally use multiple textbooks, there's nothing wrong with that. You can double check with that book or openstax or anything else just to compare notes.

[molten mason]

You're always welcome to ask and wait but that book looks brand new, I don't know if anyone has used it.

At that level, all the books already mentioned by others above.

Nah

Anything you feel is lacking or needs more explanation you can supplement with YouTube

For example I think the binomial theorem is introduced in chapter 1 or 2, if that one doesn't make sense don't stress out too much, you can move on and then go back to it later.

There are the help channels 24/7 to ask specific questions. There's #prealg-and-algebra #geometry-and-trigonometry channels if you need a concept explained better.

[drowsy drum]

The fundamentals come from books tbh

[storm zinc]

the books come from teachers

[torn rivet]

It’s nice to have good teachers, but we don’t have a society that incentivizes good teachers to teach

[ocean mulch]

bold of you to assume everyone knows how to read those books

[drowsy drum]

Oh, like i guess if the books start from the basics with good explanations then maybe

[ocean mulch]

read a lot, there's no way around it really

Doing math is to suffer. To do it is to find joy in the suffering.

[finite crane]

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
Paul Halmos

[remote sparrow]

never heard of this book. it's pretty new, so i haven't seen any others write a review.

[earnest wolf]

then one should read lecture notes first ig

I'm also a bit biased towards books, because why go to classes if there are so many amazing textbooks?

I mean, what could a lecturer do that a textbook can't?

As far as I know, in Slavic languages (like Polish, Latvian, Ukrainian and so on) the word they use is 'read' as in 'a professor is reading (not teaching) a course'

so why not to directly read it from the source 🤔

[finite crane]

yes abbott is good as first exposure
then read Tao's Analysis I & II for more analysis (emphasis on second volume), then go to Folland's Real Analysis for graduate-level analysis

[earnest wolf]

I should probably say it's just the way I personally like to do it.

And there are certainly lots of amazing lecturers who make the students fall in love with their subject and give lots of intuition

[finite crane]

I mean, what could a lecturer do that a textbook can't?
Easy. Interactive class. Summarize. Ask questions to check understanding. Putting emphasis on something. Examples. Counterexamples.

and especially when you go higher into research phase, for a complicated topic, a lecturer can chart a path for you to learn so you can get to the frontier in a fraction of the time you take to read a whole book

[earnest wolf]

all of that a good textbook does, except for possibly an interactive class

[finite crane]

when you talk to advisors, it's like each week you get handed 6 books and 5 papers to study from

you aren't going to be able to read them all. Then the mentor becomes your guide in that wilderness

what to focus on, what to read

[ocean mulch]

what could a lecturer do that a textbook can't?
the same thing what a pianist do that a music score can't.

In Hilbert by Constance Reed, he told the story of Hilbert when he was at Gottingen. His lectures were not always prepared, messy, and lots of times he would do math on the board without preparation. Klein's lectures were carefully prepared, almost like a play, where he would recite each and every word.

I don't need to say that students loved Hilbert's lectures way more.

It's not every day that you see how a great mathematician works

[finite crane]

interactive is key. you want to save time.

lecturer can spot a problem and fix it in real time

[earnest wolf]

hm, yeah, theoretically

[finite crane]

a good reading course is where you spend 10 hours reading a book then 1 hour with the professor correcting you / lecturing you

for instance I have no clue about some stuff in stochastic PDE I would just ask my mentor whether X is true and I can take it as a blackbox for now

[ocean mulch]

Not all lecturers suck

[earnest wolf]

well, this is a completely different thing!

[earnest wolf]

and this

I absolutely agree that you do need a mentor

but not a lecturer ☠️

[earnest wolf]

(again, my personal preference. not trying to advocate for that)

[ocean mulch]

to each their own, I still like having a lecturer, despite I hate class setting in general

I'm very much biased because I've been in math classes where students have been generally of high level (so no stupid questions) and the profs gloss over the proofs, leave details for us to fill in, and give a lot of intuition. I know not all profs are great.

[finite crane]

the smaller the class, and the more advanced the material, the more effective the math classroom is

sometimes I think there's a reason why nobles in the past hired mathematicians as private tutors

beyond the economics of it, it's also the best way to teach and learn maths

if something is so simple you can just youtube it then there's no point in the class

[earnest wolf]

this depend so much on a lecturer 😦

we have very strong undergrads, and some professors / lecturers do what you just said. but there are guys who mumble it for themselves and on the level they understand it. and there are guys who include so many unnecessary details, that I open a laptop and start studying another subject 💀

so it really depends on the person. even if we talk in terms of one particular institution

[finite crane]

it's a very human industry

[ocean mulch]

but there are guys who mumble it for themselves and on the level they understand it.
yes, that happens to cryptography class this semester in my case, the Wikipedia explains better than the prof. I dropped it, of course

Again, not all profs are great, but not all lecturers suck either

[earnest wolf]

I guess I'm biased then because I have only seen one great lecturer in my life 🥹

[earnest wolf]

but true

[torn rivet]

Good teachers are undervalued

[ocean mulch]

My condolences. Great lecturers will really change your life.

[earnest wolf]

tho as far as I know they are great researchers. like not only on the national level. they are just too bored to teach undergrad classes I guess

[torn rivet]

I wouldn’t know as much math as I do if it wasn’t for great teachers that helped inspire me.

But I also taught myself a lot because of systemic racism, classism, etc

[ocean mulch]

look, they got PhD for their research, not their teaching. Most profs don't have training in giving lectures

[earnest wolf]

yeah, exactly my point

[ocean mulch]

they TA-ed, a lot, and gave seminars, a lot. But that's so little to teach effectively

[torn rivet]

I think academia could benefit from a philosophical overhaul

[finite crane]

philosophical?

[torn rivet]

Mhm yah, like, rethink the way we educate people

Hahaha I have ideas

[ocean mulch]

and also, it's painful to teach these things if you don't like it. I just gave a small lecture this morning on Riemann integration, and boy was I bored.

[finite crane]

was about to have funny images of people reading philosophy books

[torn rivet]

Hahaha I have a funny meme in response to this that I can’t share

lol I could talk a lot about this topic

[earnest wolf]

record the lectures, make the undergrads sit in front of their computers with headphones on, and let the profs do their research 😎😎

[torn rivet]

Hahaha i like that, not so bad.

Wanna hear mine?

[finite crane]

for me at least the most fun part of teaching is asking students to solve / prove things and then seeing someone find the solution

with hints and corrections along the way

[torn rivet]

Abolish private schools.

Fund education through federal taxes instead of property taxes.

Allocate funding to metropolitan areas by citizen count.

Each metropolitan area uses the funds to build their own boarding schools, meant to cover ages 3-18.

Instead of tiny schools everywhere, make one central “mini university” per metro area.

Schools are managed locally, so no federal “curriculum”, although you do need to demonstrate proficiency in certain subjects to give out a high school degree.

Get rid of K-12 grades. Offer courses based on subject with prerequisites. Passing depends on a capstone class in each core subject, along with any majors you took.

Get rid of A-F grades while you’re at it. Classes can just be there as supplements, like live tutorials. Students show up if they need it.

These educational reforms, at a high level, will reduce the financial and time burden on raising a family.

Having kids isn’t the end of your life anymore, man or woman, rich or poor. You can still have a career and a life and like theoretically 10 kids if you wanted.

The new education structure promotes innovation and initiative, and prepares students for a successful college education.

In this paradigm, a high school education functionally replaces what we think of as a bachelor’s degree. You can use it to get most jobs by building your portfolio. Passing the fundamentals means you know calculus, philosophy, and civics. And your “specialty” is something you care about. This makes teaching fun for teachers too, only kids that want to learn it are there.

College / university is for researchers and advanced study.

PhDs are only given to people that discover something revolutionary, like what we think of as a Nobel prize. Masters degrees are what we think of as PhDs in most fields, you did the research work but didn’t find any breakthroughs. Those are your teachers mostly, phds focus on research.

Lol also, decentralize the peer review process.

phew!

[finite crane]

Get rid of K-12 grades. Offer courses based on subject with prerequisites.
we already have electives and course choices for K-12

[marble solar]

It's that time: people that don't teach give their opinion on how to restructure an entire nation's education system

[torn rivet]

Mhm yah kinda, but what happens if you’re really studious, aka you want to finish high school material by age 12.

How do you do that in our system?

[torn rivet]

ROFL!!!

[finite crane]

yeah when I started teaching and before I started I had a bunch of ideas I wanted to try out as well

[torn rivet]

Hahaha i always wanted to be a teacher, I thought about these reforms with teachers in mind

[finite crane]

everyone has to go through the education system so a lot of people have different ideas about how they could improve it

[marble solar]

By all means become a teacher, you will quickly realize that you had no idea what it means to run a classroom

[torn rivet]

I’ve worked in classrooms before

[marble solar]

I certainly didn't before I was thrown in a room full of 10 year olds

[marble solar]

You were the teacher in charge of lesson planning & teaching?

[torn rivet]

I was responsible for some of that, it was an at risk population so kind of all hands on deck, no budget for textbooks, stuff like that

[marble solar]

It sounds like you weren't the teacher in charge in the classroom, but someone that helped

Which is a valuable role and provides some insight

[torn rivet]

Yep that’s right

[torn rivet]

Hahaha if you’re curious about some of the minutia about my ideas relevant to teachers I could share, I’d be interested in your thoughts on them

[marble solar]

It'd be more appropriate for the math pedagogy channel

#math-pedagogy

[torn rivet]

Mhm okay, well if you’re interested in the discussion I’d be happy to have it, got nothing going on rn

[marble solar]

Feel free to post in the math pedagogy channel

[tawny copper]

Why the hell would you want to "abolish" private schools

[marble solar]

Let's bring this out of the book recommendation chat

#math-discussion could be a place to carry on this interesting conversation

[scenic sequoia]

Would “Basic Mathematics by Lang” and “College Algebra by Blitzer” cover enough of the trig needed to dive into calculus after ?

[molten mason]

More than enough.

[scenic sequoia]

bet

[marble solar]

In general I think people overthink what "book" to use rather than just trying to learn to solve the problems

Something that I'm guilty of myself

[scenic sequoia]

I just want to do calc physics already and started basic mathematics like 4 days ago and just want to rush through it already

[molten mason]

If you've seen it before or you understand it, it's totally fine to rush though.

Physics and calc are both whole new worlds.

For example in calc there's a lot going on with trig that will be completely new but it all takes practice.

[remote sparrow]

after abbott, feel free to look at carothers' Real Analysis, zorich's two volumes on real analysis, or even amann and escher's three volumes on real analysis, which treat real analysis from a very general point of view. you could also look at Metric Spaces by robert magnus or Metric Spaces by micheal o'searcoid. alternatively, you may dive right into measure theory with axler's Measure, Integration, and Real Analysis or schilling's Measures, Integrals, and Martingales.

[narrow mortar]

Hello all, Im looking for a book that specializes in writing proofs. Id like to continue reading some books on real analysis, but Id like to be able to write coherent proofs before I begin

[lusty ermine]

Which books are you using for real analy

[narrow mortar]

Real Analysis by H.L Hoyden 4th Ed

[remote sparrow]

did you mean royden?

that's a graduate reference on measure theory

you should already know some real analysis going into that book

https://maa.org/press/maa-reviews/number-systems-a-path-into-rigorous-mathematics

unrelated book review

[molten mason]

Yes Royden

[remote sparrow]

#book-recommendations message

[narrow mortar]

Yes! Not sure why I read the R as an H

I knew it was a graduate level book going in, and its been a pretty slow read but Ive been learning a bit. I didn't know analysis wasn't the primary focus. Thank you for the heads up🙏🏻

[narrow mortar]

Thank you, Ill take a look at these!

[remote sparrow]

real analysis is the primary focus, just very sophisticated real analysis

[scenic sequoia]

thanks

I don’t want to go crazy I just want solid foundation to start doing calc physics

Alright cool. Thanks

[dusk wind]

this tbh

[novel hound]

Looks like this Springer sale has started. I'm seeing the discounts on the online site. Very limited selection though.

[manic cairn]

i used coupons on the rest to bring it down to 150

[molten mason]

Oh that's today time to browse

[lusty ermine]

what are you guys ordering from springer? axlers ladr and understanding analysis by abbot maybe on someones list?

[molten mason]

So far nothing seems interesting. A lot of nonsense.

The three books I want aren't part of the sale either

[maiden glen]

i really could use some more pdfs

i need more

[lusty ermine]

may I ask, what topic are you looking for?

[maiden glen]

foundational mathematics (including school "algebra" to calculus) to abstract and advanced algebra, (and what comes before studying such topics)

[lusty ermine]

people like recommending here, basic mathematics by lang. maybe somone can recommend something better which emphazises more to your query.

[finite gale]

I can't tell if you're trying to say you're looking for high school foundational math or foundations math

(their history has mentions of looking for "advanced algebra" but not homological or abstract, but it's not so clear as to what they mean by that)

[violet shuttle]

@finite gale this def sounds like high school foundational math to me

[dusk wind]

they want abstract though

this sounds like another book list, in which case https://realnotcomplex.com

[maiden glen]

abstract, and by advanced I mean homological and topology

[finite gale]

ok

what do you know so far

[violet shuttle]

oh, my bad, "school" as in

[dusk wind]

'foundational, basic'

ah yes it was the carrot before the stick

[tough egret]

Schilling's Measures, Integrals & Martingales seems to fit my aims. I'll learn more about real analysis after it, out of curiosity. Thank you!

[remote sparrow]

https://www.amazon.com/Counterexamples-Measure-Integration-René-Schilling/dp/1009001620/

here is a companion volume

http://motapa.de/measures_integrals_and_martingales/index.shtml

here is the book's website

there is a full solutions manual available for free here

[tough egret]

I was eyeing Axler's book on measure theory, but the lack of solutions made me kind of afraid

Thanks for the links!

[dusk wind]

def gonna read their measure theory book

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-030-38219-3

this book is currently on sale

[loud cradle]

the same bogachev of 2-volume "measure theory", it appears

[remote sparrow]

yeah

[loud cradle]

"moscow lectures" series, interesting, i didn't know springer had such a series
preview on amazon has a preface of several pages talking about the series

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-030-79010-3

this book looks like a good supplement to a mathematical logic book

https://www.logicmatters.net/2022/07/28/mathematical-logic-exercises-and-solutions/

https://link.springer.com/book/10.1007/978-3-030-36468-7

@molten mason this book is on sale

[remote sparrow]

@gray jungle newer bogachev in a much smaller package

[tough egret]

I may be a bit ambitious, but would this be a good read after Abbott and Schilling ?

[remote sparrow]

i'd recommend reading a book on metric spaces first or at the same time

[tough egret]

Other than Schilling?

[remote sparrow]

yes, i mentioned a couple earlier

[tough egret]

Okay, thank you!

[remote sparrow]

carothers is also mostly about metric spaces and function spaces.

[sand cargo]

3 days late but this guy is my prof rn and he’s great

[loud cradle]

very cool! i learned grad algebra from his advisor many moons ago, he was also great so i'm not surprised that shahriari is as well

[sand cargo]

ah wow

[glad rampart]

what kind of algebra

[quiet wave]

what's some good mathematical bedtime reading? stuff where I'm too spent from the day to actually read a textbook and do exercises but still wanna see some math and learn a thing or two that's not too involved

but still somehow interesting lol

[marsh ingot]

What level?

[glad rampart]

i used art of problem solving to learn algebra 1 but im not sure itd be the best if you dont have pre-algebra down really well

[marsh ingot]

Mmm unfortunately I dont have a book for that level

[glad rampart]

https://data.artofproblemsolving.com//products/diagnostics/intro-algebra-pretest.pdf they have this thing to test if youre ready for their introductory algebra book, so many try this and if you do well consider it

[rigid sluice]

whats the best book or course or youtube playlist to starting analysis

i have the jay cummings book but its pretty confusing

i was looking at the bright side of math playlist aswell

just not really sure how should i learn it

[remote sparrow]

#book-recommendations message

[rigid sluice]

this is perfect thanks

[dusk wind]

https://beincrypto.com/learn/how-to-mine-cryptocurrency

[tender river]

?

[vale gorge]

Hey, does someone know about CTPCM-Challenge and Thrill of Pre-College Mathematics, an Indian book used for Olympiad preparation.

also Hall and Knight, a algebra book??

[tired lake]

Hello

[fleet isle]

Hi guys I'm new at maths, i want to learn more, can you recommend me some beginner books?

[tired lake]

what are your thots about the book series maths for self study by JE Thompson

?

[vale gorge]

hey, can u tell which level u at??

[fleet isle]

Middle high school level😂😂😂

[vale gorge]

which grade??

[fleet isle]

I think like 8th/9th grade

[tired lake]

Can someone tell me too

[vale gorge]

this is a detailed discussion on likes and dislikes, so can we talk in DM

[vale gorge]

sorry bro, not familiar with it

[tired lake]

OHk 🥹

[fluid violet]

Try khan academy

Its not a book but it is quite decent

[fleet isle]

Ok, thanks but i prefer books👍😎

[fluid violet]

What about reading through whatever book your school provides?

[fleet isle]

I'm not studying now

[vale gorge]

Try mathematical circles, take your time with it. solve what you can

[tired lake]

Idk but from the books' content maths for self study takes from arithmetic to calculus i believe it covers basics then further you can switch to other books. I am planning to start from this.

[fleet isle]

What do you mean with "mathematical circles?

[vale gorge]

its a book

name of the book

[fleet isle]

Ok, thank you very much

[vale gorge]

but fairwaring, it can be hard

as it is an Olympiad book

[fleet isle]

Don't worry i will try to give the best of me

[fleet isle]

Do you have the pdf?

[tired lake]

Send it to me too!

If you have that is

[fleet isle]

Are you beginner too?

[vale gorge]

where is the file button

there is no file button

[fleet isle]

You can send dm

[tired lake]

No i would say but i have gaps in my knowledge

[vale gorge]

did u get it

[vale gorge]

and wbu?

[tired lake]

In what context

[vale gorge]

did u get the pdf?

[fleet isle]

Yes

[tired lake]

No

[vale gorge]

Ask @fleet isle

He can share with you

[buoyant void]

Hello, does anyone here know any books on combinatorics that are good for beginners?

[hallow oriole]

enum by stanley and walk by bona

enumerative combinatorics and a walk through combinatorics ^

[maiden glen]

I'm trying to strengthen my foundation in foundational mathematics, but I'm scared that I'll miss something I really need or want to know, so I want to know as much as I can about a topic

I feel as though I really need that to progress.

Which is why I haven't yet approached calculus or anything further.

but I can never seem to figure out where to look for my aspired knowledge. essentially, I want my knowledge to be "perfectly" structured

[tired lake]

@fleet isle pls

[vale gorge]

did u not get it yet?

[tired lake]

No

[buoyant void]

Ok, I appreciate it.

[earnest wolf]

wind back a bit — I asked about it recently and there were amazing recommendations given

starting from here #book-recommendations message

[buoyant void]

okoko

[oblique dove]

what are some good abstract algebra books that give a good exposition for galois theory that is necessary for algebraic number theory?

[molten mason]

Have you already done abstract algebra or will this be your first time?

[oblique dove]

ive done group theory and have been introduced to fields and rings

in group theory we covered homomorphisms, isomorphisms, classification of finite abelian groups (but not finite simple groups), and quotient groups

[molten mason]

Abstract Algebra: The Basic Graduate Year Chapter 6 covers Galois Theory, has solutions in the back. Go through Chapter 3 before you go through Chapter 6. Anything else you need to review would be in the other Chapters 1-5. To me it's a soft graduate book: It's written in a readable/conversational way but puts rigor in when needed. That would be a good book to get into Galois theory but have right next to you anything in abstract algebra you need to review.

If you're ready to dive into a graduate level Galois theory book, there's Galois Theory by Steven Weintraub

Weintraub = written perfect for algebraic number theory

[oblique dove]

Thank you so much, are there any pre-requisites? I’m not entirely familiar with linear algebra unfortunately

[molten mason]

Third book would be Algebra by Serge Lang, Chapter VI

As in after Weintraub

[molten mason]

Also Chapter 7 of Abstract Algebra: The Basic Graduate Year is Algebraic Number Theory

I mean you technically you can look up LA stuff as you go along, but I feel like you should learn LA anyway no matter what, and sooner the better.

Linear Algebra by Friedberg, Insel, and Spence is a good option

like Weintraub required linear algebra

[oblique dove]

i know basic linear algebra but i haven’t taken a course in it :/ covered transformations duality inner products eigens vector spaces

[remote sparrow]

https://maa.org/press/maa-reviews/galois-theory-4

[maiden glen]

can someone please respond

[slender cargo]

I feel like you shouldn't be too concerned about learning in exactly the "right" way. Just right enough. You're going to be constantly relearning foundational topics as you advance further and gain more tools and insights

I'm not that far along either but that's clear enough to me with the courses I'm taking

I have learned about continuity over the real line in my Real Analysis class, and as I understand it I will learn about how to recast the definition of continuity when I take Topology later. It's not necessarily better to learn the most general definition on your first exposure. Just pick some proof-based book on a subject that's reasonably at your level and you will likely be fine

You haven't approached Calculus yet, you said. Go pick up Spivak's Calculus if you want a proof-based approach to Calculus. Don't start with something like Rudin as your first exposure to Calculus

If you find that you're missing something later on, you'll be mathematically mature enough to fill in the gap.

[glad rampart]

what are your thoughts on using spivak to get deeper knowledge about calc after using a different book to get the basics down

[slender cargo]

My personal opinion: just go for a Real Analysis book

Spivak's Calculus was written for people learning the subject the first time

[torn rivet]

Like Tao?

[glad rampart]

itll be a while till i actually learn calc so i'll decide then i guess

[maiden glen]

thank you @slender cargo

[slender cargo]

Yeah like Tao

[maiden glen]

are there any PDFs you may recommend for fundamental topics?

[slender cargo]

You say you have not taken Calculus yet? Will you be taking it through a course eventually?

[maiden glen]

I'm self tutoring

[slender cargo]

Ah okay. Try Spivak's Calculus then

[maiden glen]

thank you

[glad rampart]

ill probably be using both AoPS's calc book and spivak to learn calc when i get there i think

[slender cargo]

If Spivak's Calculus becomes tough, I'd say look at a proof book also. I know there are some good free ones online, though I'm not sure what they are

@remote sparrow

[slender cargo]

Yeah, imo better to think about calculus when you actually take the course. Better to work on something like Number Theory in the meanwhile

[lusty ermine]

does someone have any opinions on J Stewart for pre calculus?

[glad rampart]

thats actually exactly what im doing lol

reading AoPS's number theory book

[slender cargo]

Nice!

[glad rampart]

and im not actually gonna be taking any courses, im self taught lol

[slender cargo]

oh gotcha

[slender cargo]

as in, you will learn Calculus when you decide to?

[glad rampart]

i have a path im planning to learn the stuff leading up to calc in

[slender cargo]

I see

[slender cargo]

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

^ look at the above book also alongside Spivak's Calculus. Maybe go through the above book first

[maiden glen]

may you send a PDF of Michael Spivak's calculus please?

[maiden glen]

okay

nevermind

I've found one

[lusty ermine]

anyone has a review for Essential Linear algebra with applications by andreescu

[remote sparrow]

#book-recommendations message

[slender cargo]

@maiden glen ^ there's a good list. People at universities usually go through an Introduction to Proofs course after going through a Calculus class (at a lower level than Spivak's Calculus)

[minor shoal]

Are there any good books that survey the developments and results in Hyperkähler Geometry from an Algebra Geometric perspective? There are several good articles online, but im looking for a more comprehensive reference

[earnest wolf]

why do so many people like Fraleigh's algebra book?

when I tried it, it seemed too childish ig? like the examples were too elementary, the progress is incredibly slow and so on

and warning: I read only some chapters, since I used another textbook as my main

[novel hound]

If you have anoher textbook it doesn't make sense to do Fraleigh. I look at it as good for a quick intro, to get one familiar with the terms and definitions. And then follow it up with a second course/book which goes deeper. I don't get how childish = slow progress? Yes it is basic (or childish if you prefer) compared to other books, but that is why it can be used as a quick intro with a better follow up.

[earnest wolf]

tbh I don't remember what made me think it was slow to read — it was a long time ago

maybe just because it included too many unnecessary details

[novel hound]

Imo, if you are doing a course, you should do it from a better book and Fraleigh/Gallian etc are not worthwhile (except maybe selectively as reference for easier explanation). If you are self-studying (where the main issue is burn-out or the book being too hard so you give up), it is decent and it should be done in 2-3 months max. With the understanding that you can skip some non-essential stuff and follow it up with a better book.

[earnest wolf]

better book
like dummit? ☠️

[novel hound]

Depends on the uni, course. etc. Standard alternatives are Artin/Herstein etc. if you are self-studying then it's different.

Obviously ymmv...

[heady ember]

Some like Jacobson

[heady ember]

3 months seems ridiculously fast to me

Or I just have a skill issue

[novel hound]

Well I meant like if you are only self-studying one book xD. A standard undergrad course is 4 months. And, that's usually 4 courses. So, it's not unreasonable. 😛 And, you can skip some stuff, stop before Galois theory, etc. to make it like a one semester intro course.

[heady ember]

That'll probably take me a year

[novel hound]

well, it's not a race so it doesn't matter. But my point is... if are going to spend one year on AA (which is perfectly standard with 2 courses on intro AA in some unis), then do it with a better book than Fraleigh.

Optionally, do Fraleigh 3 months and Artin 9 months or something like that 😛

[heady ember]

Yeah its not like I can magically speed up, and since I have no particular time pressure, I don't usually stress myself over being slower.

Yeah I'll be using Jacobson when I get to learning algebra

[lusty ermine]

which graph theory books are the most recommended ones, if possible with lots of problems?

[tawny copper]

Found a very nice book about Borel sets which I'm skimming. It's of the highest quality, it includes many exercises interpersed in the explanations. It can also serve as an introduction to set theory and topology (if you focus on metric spaces at least), it's pretty cool. Chapters 4 and 5 seem to be slightly more specialized tho. https://link.springer.com/book/10.1007/b98956

[lusty ermine]

not for me I pressume

[tawny copper]

no, just sharing in case anyone is interested. I always wanted to learn about Borel sets, but never found a nice entry point

[tawny copper]

Go to Soberon's book chapter 4

[tawny copper]

You can also try this problem: There is an integer $n>1$. There are $n^2$ stations on a slope of a mountain, all at different altitudes. Each of two cable car companies, $A$ and $B$, operates $k$ cable cars; each cable car provides a transfer from one of the stations to a higher one (with no intermediate stops). The $k$ cable cars of $A$ have $k$ different starting points and $k$ different finishing points, and a cable car which starts higher also finishes higher. The same condition hold for $B$. We say that two stations are linked by a company if one can start from the lower station and reach the higher one by using one or more cars of that company (no other movemenets between stations are allowed). Determine the smallest positive integer $k$ for which one can guarantee that there are two stations that are linked by both companies.

[hasty eagle]

croqueta3385

[lusty ermine]

problem solving methods in combinatorics, soberon?

[tawny copper]

yes

Pranav Sriram's book also has a chapter on Graph theory

[lusty ermine]

thanks, will use this.

for now.

[violet shuttle]

there's the GTM

https://link.springer.com/book/10.1007/978-3-662-53622-3

[lusty ermine]

reinhard distel

its because its less expensive due to springer sales?

[violet shuttle]

I think it's useful to think about what affects speed of learning. For me, I've found it useful to:

1. Sleep more
2. Know where I'm going. That is, read ahead, skim first, figure out what these theorems are used for, what the general program is, before delving into the details.
3. work at night, with no people around

[fast bone]

sleep more + work at night = insomniac

[violet shuttle]

i think you mean "nocturnal"

[fast bone]

good catch on the linguistical mistake there, thank you

[heady ember]

Yeah sleep is 💯 important. I like it. For 2, I use a bulldozer approach and I don't really skim, but maybe I should (I tend to avoid that to have more suprises). People isn't really a problem for me since I have no social life

[violet shuttle]

It's not about having a social life

I am including people you don't know and don't talk to.

I like my approach because it helps me know what's important, it helps me tackle things like important definitions and concepts before needing to use them heavily, it lets me learn the subject in parallel, it lets me decide what path to take first (like with differential geometry, where my path was "generalized stokes speed run any%")

[heady ember]

So, if you think a certain section (for instance) is detractionary to your goals, you'd place less emphasis on it, I suppose?

[lusty ermine]

what is the easiest book on discrete math with lots of problems for undergrad?

[dusk wind]

wouldn't it be easy if there were few problems

its probably not a good idea to use an easy book for it either

[gray gazelle]

What about if you can't avoid people and nose most of the day?

[violet shuttle]

My life would have to be very different for that to be the case

[violet shuttle]

Yep!

Wouldn't say "detractionary", it's not like it's negative

[gray gazelle]

Oh ok got it.
Actually I mean if you have single free room in house and your siblings listen songs there and make other noise etc.

[dusk wind]

really good noise suppression

[violet shuttle]

Then try a building

[dusk wind]

headphones exist, go somewhere else

[gray gazelle]

Building?

[tribal crow]

random remark: i've never wore headphones before

[dusk wind]

thats a massive L on your part then

[modern ruin]

i have seen some really really good headphones

literally no noise comes through fr

[dusk wind]

a good pair should make your studying somewhat enjoyable

[modern ruin]

i am a bit of an audiophile

[violet shuttle]

Libraries! Places in a college! Coffee Shops! The outdoors! The park! Etc!

[modern ruin]

i love headphones sm

[gray gazelle]

That's the problem. I don't listen songs so don't use headphones. Also there is no other place near to where I can go like Library near to me. So only option remains is that room

[violet shuttle]

I just use my earbuds

[dusk wind]

still recommend going out to study

[violet shuttle]

there's nowhere near you that's good for studying? really?

[tribal crow]

idk i've functioned all my life without headphones/earbuds

[lusty ermine]

I really like listening to white noise btw

[dusk wind]

you become hyperaware/productive in a library for some reason

[tribal crow]

it's been alright

[dusk wind]

I cant study without music personally

[violet shuttle]

music used to be more helpful to mr

[gray gazelle]

Unfortunately yes there is no such place. (Its kinda village type) my college and other libraries, coffee shops etc are in different cities away from me

[modern ruin]

i wish my campus had more "beautiful" spots that were productive

like had tables

etc

[violet shuttle]

what is near you?

[dusk wind]

surely theres an open quiet space by you

even a hole is fine

[violet shuttle]

big fan of math holes

[scenic sequoia]

headphones are a must. I live in nyc and even the libraries are too loud without headphones

[dusk wind]

dr.dre's headphones should be part of your standard issue survival kit

[gray gazelle]

Houses and local shops.
But I think I can go to the roof of my house. Although I only can sit on stairs and can do math.
Not till late night because of lighting issue there

[lusty ermine]

you can study home, or wherever you are without active noise cancellation headphones, white noise will isolate that with 5 dollars earphones, or the ones that come with your phone

[scenic sequoia]

brown noise is good too

[violet shuttle]

what's your favorite sequence of homology groups to study in?

[scenic sequoia]

or ambient music

[violet shuttle]

for some reason music stopped working for me

[gray gazelle]

Sounds good. I shall try

[dusk wind]

you probably became numb to it

[violet shuttle]

i don't think so?

[dusk wind]

you need to listen to more obscene stuff then

[violet shuttle]

it doesn't put me in the focus state anymore

[dusk wind]

DMX will help with that

get kicked out of the library

[violet shuttle]

unzip that acronym please

i use earbuds i'm not subjecting others to my music like an asshole

[dusk wind]

thats the problem right there

music should be heard

[violet shuttle]

nada

[dusk wind]

you're music too tho

[scenic sequoia]

I been roughly listening to the same songs for like 2 years which sucks

[violet shuttle]

no, i'm discordant chaos

[tribal crow]

i guess having earbuds would let be listen to music while working, but i guess i got too used to working w/o it

[heady ember]

Right, I meant detractionary as in sidetracking (not necessarily in a bad way, but perhaps just not what you need).

[violet shuttle]

i am a sidetrack

[heady ember]

lmao

For me, it seems I'm still quite uncomfortable with skipping stuff

[modern ruin]

i skip everywhere i go

[violet shuttle]

a skip in your step?

[alpine bison]

what are good undergrad books with good and difficult problems, particularly on calculus, geometry and algebra?( I've passed jee for reference)

[modern ruin]

[dusk wind]

@lusty ermine easy https://www.amazon.com/Discrete-Mathematics-Computing-Peter-Grossman/dp/0230216110
new https://www.amazon.com/Discrete-Mathematics-Applications-Ali-Grami-ebook/dp/B09ZKXCZHL
free https://discretemath.org/

just found this too https://www.amazon.com/Discrete-Mathematics-Graph-Theory-Undergraduate/dp/3030611140

[modern ruin]

i literally don’t know how to respond because passing the jee doesn’t tell me anything about you or your goals

[dusk wind]

give em a book trio series

[modern ruin]

just check the pins

[dusk wind]

the nonexistent ones

[lusty ermine]

thanks renji, 🐐

[dusk wind]

when you feel up to it check out art of computer programming too

[lusty ermine]

by knuth.

?

[dusk wind]

yea

[violet shuttle]

...?? what level

we talking Galois theory or we talking quadratic formula?

[tribal crow]

always defer to this book when we dont know

[violet shuttle]

we talking lines and circles in R^2, or we talking lines and circles in a riemannian manifold?

we talking integration by parts or we talking PDE theory (aka integration by parts)

(@alpine bison)

[crimson leaf]

There are 3 I recommend: 1. Graph Theory by Diestel 2. Graph Theory by Bondy and Murty, these two are the main ones I see referenced and used in courses. 3. Introduction to Graph Theory by Doug West this book is large but good and coherent.

[tawny crater]

im looking for a calculus textbook which starts by developing sequences fully before starting functions, since that's how we do it in my course

spivak, apostol, etc, dives straight into functions and continuity

my course when discussing uniform continuity mentioned that they preserve the convergence of sequences for example while most textbooks don't care about that

[violet shuttle]

most textbooks do,

[lunar sparrow]

does anyone have good book recommendations for ODEs and PDEs

[glad rampart]

what are those

[tribal crow]

ordinary/partial differential equations

[remote sparrow]

#book-recommendations message

#book-recommendations message

[lunar sparrow]

thanks Sour Drop will check them out

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4939-2651-0

i don't know how good this book is but i saw it on the title list for the yellow sale

although traditionally a real analysis textbook structures itself similarly to a calculus textbook (doing a bit of material on sequences, then jumping into limits of functions and holding off on further discussion of sequences and series until after integration), some do offer flexibility. see schroeder as one example.

[remote sparrow]

i believe cummings mentions this fact

[alpine bison]

basically I want to venture into more advanced mathematics but I know just integration by parts..
with algebraic geometry and multivariable calculus.. and develop more on it

[alpine bison]

galois theory

[alpine bison]

thanks

sorry for replying late, had an unexpected lecture

[slender wasp]

Apostol Calc I (or better Spivak if you want something in-between calc and analysis, or Abbott if you are done with calculus and want to start with analysis), Apostol Calc II for Linear Algebra and Multivariable Calculus.

If you are in engg (considering you said something about jee) then Kreyszig Advanced Engineering Maths.

[alpine bison]

okay👍🏿

can you also suggest some books for geometry

[alpine bison]

thanks for the details

[slender wasp]

I'm gonna have to defer on geometry, no idea 😛

btw, you can also look at the math courses on the iit websites.. they usually list the books, etc they use.

[remote sparrow]

hubbard and shifrin are good for multivariable calculus

[alpine bison]

okay

[remote sparrow]

#book-recommendations message

these are good for linear algebra

[alpine bison]

thankss

[remote sparrow]

#book-recommendations message

some algebra recommendations

you can also check pins for other real analysis, linear algebra, and abstract algebra recommendations

[alpine bison]

lol I do relate, even as a beginner calc looks like something u can't get out of

thanks again @remote sparrow :))

[remote sparrow]

[alpine bison]

excited to dig deeper and solve complex probs in maths :))

[ocean mulch]

it's always like that. Ppl would say "geometry", "algebra", "arithemtics", or "calculus" and then expect us to know what they mean.

[alpine bison]

i did mention above jee level

[gray gazelle]

Jee indian exam?

[alpine bison]

yeah

[clever kindle]

Yo anyone got any book recommendations, gonna start bs first year in maths

[marsh ingot]

Jk

Spivak or Apostol, but if its your first year. Take it easy before grab a book. Maybe one of your teachers explain pretty well the subject

[sage kelp]

Some book, lecture notes or something to study an practice about planes and hyperplanes?

[graceful moon]

The metric spaces book I just finished recommends both Rudin texts, then goes on to mention another text that he notes people find difficult and dry

The fact that there’s a harder, less interesting analysis book out there, than Rudin, terrifies me

[tender river]

dieudonne lol

[supple folio]

Ayoooo. Do you guys have book suggestions for abstract/ modern algebra? Those that are legally free to access online coz yo hooman right here is broke

[gray gazelle]

I think you can get a pdf of most of the famous books.

[violet shuttle]

Lang

some like Dummit and Foote

[graceful moon]

Dummit and Foote and Artin are both easily available. I quite like Artin, D&F isn’t bad but it’s extremely dry. It’s good for a reference or for problems, because it’s got loads of problems, but it’s far from an interesting book to read

I’ve never personally used lang, I know some like it but I’ve also seen it referred to as,

[tribal crow]

what book did this cover originally come from? Grillet?

[graceful moon]

Afaik it was a random meme, there’s loads of different ones, there’s a watermark at the bottom of the website that posted loads of them

[tribal crow]

yeah I’ve seen a lot of those memes lmao

Looks like it came from here though

[graceful moon]

Oh you mean the actual image on the cover? From a quick google yeah it is, I’ve never heard of that book before though

[potent trout]

Hi guys does anyone have books / pdfs recommendations for learning about connections on principal bundles?

Doesn’t have to be super deep I just want to know the basics like connection and the associated 1-forms, paralllel transport and curvature

[molten mason]

I cry laughing every time I see this image. It will never not be funny.

Also I'm personally going through Lang rn

[molten mason]

If you're a university student, Springer textbooks are free via PDF.

If you're not I'm sure there's other ways, I get all my PDFs legally.

[earnest wolf]

lmao. so what was it?

[gray gazelle]

How’s that going?

[molten mason]

https://tenor.com/view/hold-on-animals-ouch-gif-10490381

[gray gazelle]

Lmao, what chapter are you on?

[tribal crow]

LMAO

[gray gazelle]

You can go to springerlink and log in via institution

[molten mason]

Chapter 2

It's not my main priority so I'm going through it slow amyway, but everytime I go into it I immediately need to load up a second window like wikipedia or something lmao

Somewhere on the website, maybe desktop view, when you look at a book near the PDF it should say via institution.s

It'll then ask you your school and have you login.

[violet shuttle]

I read the part on groups, the too small part on rings, half of the part on polynomials, skipped modules, then the Galois theory part up to Abel Ruffini

[molten mason]

Yeah I've popped into galois theory and the linear algebra section a couple times

Even with everything said I'm liking it a lot

[urban lily]

whats a good book for self studying complex analysis?

[gray gazelle]

#book-recommendations message

[urban lily]

TY

[sage python]

Lol my book reviews are my best contribution to the server

[snow flower]

If you're still looking for a book like this then check out Surreal Numbers by Donald Knuth. I haven't read it myself, but it's the closest I can think of to what you asked for.

[gray gazelle]

Is there any representation theory book that actually motivates the subject?

[earnest wolf]

oh, wow. thank you! I will definetly check it out!

[karmic thorn]

Have you looked at Etingof's book?

It's called Introduction to Representation Theory

[gray gazelle]

no but i like that it talks about quivers and abelian categories

[upbeat vine]

Complex Made Simple is a really good book, there are good reviews of the book if you search for it's name. For my own thoughts, check this #book-recommendations message

[earnest wolf]

if you don't have any specific preferences, here's my list of books and lecture notes (I will have complex analysis course this semester) not in any particular order

I definitely don't intend to read all of them tho 🙂 Real analysis course showed that it's critical to have lots of resources. So ig I will eventually find one-two books that I like the most (n' which coincide with my uni's syllabus) and choose them to be my main ones. And the other ones will be just for occasional reading, in case one particular book didn't explain concept well enough or whatever

[molten mason]

When does semester start for you? I've heard not so good things about Conway. I'm probably going to go through Lang and Freitag

[earnest wolf]

it kind of started already, but the lecturer basically goes over elementary stuff for now, like proving BW for complexes etc. So I just allocate my time for other subjects for now

they said it's because in the previous year the pace was too high for a reasonable amount of people to catch up

[earnest wolf]

I heard conway was like dummit but for complexes — incredibly boring but awesome as a reference

[molten mason]

Yeah I guess that tracks similar to what I've heard.

[molten mason]

Sweet let us know your own reviews and how your class goes and what your recommendations end up being.

[left cloud]

nah it’s your jokes

[sage python]

That too tru

[marble solar]

I'm using Conway for Complex Analysis right now, and its approach has merit. The problems are standard, yet the material is dry

He has a neat proof of the Cauchy integral formula, and his formulation of the Riemann Mapping theorem is exceptionally clear

[molten mason]

If you can make her giggle, you can make her... nvm

[molten mason]

Is that as a first course or a second course though?

[marble solar]

It's a standard first year graduate sequence

It's my third or fourth? time taking complex

[molten mason]

Goals

What books have you used for them all?

[marble solar]

No, it's a waste of time to take it this many times. The first time I didn't understand anything. The second time it was the grad sequence and I felt like I learned a lot

I did complex-adjacent things during my MS program

And now I'm in my phd and have to take it again

Back to the books: stein and shakarchi complex, ahlfors, rudin real & complex analysis, marshall complex analysis, and Terry Tao's lecture notes for 246C in spring 2018

Now we're using Conway's Complex Analysis

When I did analytic NT we used Stein and Shakarchi Fourier & Complex. Fourier part for Dirichlet's Theorem on Arithmetic Progression, Complex Analysis for Proof of the Prime Number Theorem

[molten mason]

Did you do masters and PhD at different schools, is that why?

[marble solar]

Yes

[molten mason]

My school uses Ahlfors I believe. I keep going back and forth on various volumes of S&S for the fourier analysis mixed in, but I was thinking of going through Freitag and then picking a specific book on fourier analysis later.

[marble solar]

Yeah, Ahlfors is a great book, but I think it's a little dated

I'm partial to Marshall's text, but I'm becoming a fan of Conway even though it is very dry

[molten mason]

Thanks!

[violet shuttle]

I like Conway!

[violet shuttle]

excuse you

I've read the first half.

I didn't find it dry at all.

The approach to integration was neat and easy if you have mathematical maturity and understand Riemann integration, I found the proof of the Cauchy integral theorem easy, I liked the handling throughout the rest of the first half

I remember really liking one specific problem

It's also been a while

that was back when I was writing on the windows of my highschool

[molten mason]

This is why I like asking multiple opinions

[sage python]

He heard it from me lmfao

[violet shuttle]

to be fair, I haven't looked at any other canal book

[true leaf]

can anyone recommend some good books/pdf/online resources on bernstein polynomials?

[marble solar]

Conway often gets bogged down in technical details, the font sucks, and is overly pedantic on many definitions or points

[violet shuttle]

The font?

[marble solar]

I rarely feel that I'm challenged or gain greater insight from the book

[violet shuttle]

tbf I read it when I was a bit less mathematically mature

so the technical details and pedantry were helpful to me

[marble solar]

It's a good book for a lot of reasons, especially if you're reading on your own

I just think that the others convey the spirit of complex analysis a bit better

Especially Stein & Shakarchi

[trail hemlock]

thoughts on Analysis On Manifolds by Munrkes?

[fleet solstice]

Any good Precalc books anyone recommends?

[trail hemlock]

Aops precalc is good, so is axler's "precalculus a prelude to calculus"
but "precalculus" is not broadly standard, so if u wanna prep for precalc the class, use whateber textbook is standard in your state, for example Texas and TEKS Precalculus.

[lusty ermine]

Which linear algebra book has hard non-proof problems? For undergrad.

[trail hemlock]

my local community college uses
"Elementary Linear Algebra Applications Version, Anton, Rorres, 2010, Wiley, Inc., Tenth Edition. "

[lusty ermine]

Anton's.

Thx.

[lusty escarp]

There is some book on functional analysis by some authors from epfl. I am not able to recall it right now. Can someone tell what is the name of the book or authors?

[dusk wind]

you might like one of these #book-recommendations message

[whole coral]

Any book rec for algebra 1 and 2 with trig?

[gray gazelle]

The term "mathematical maturity" is kinda confusing. Specially when the author says the only prerequisites is mathematical maturity.

[west cosmos]

Is schaums outline for calculus a good book?

or stewart calculus 10th ed

[daring lake]

Yes to stewart calc if its your first introduction to calculus.

Idk about Schaums outline

[slim ridge]

I've been wanting to start Linear Algebra and I would want to ask if Schaum's is a good book to start with

[tough egret]

I can’t speak about this one, but I learned LinAlg from Johnston’s two books and they are amazing. I can only recommend them if you’re a self-learner.

[earnest wolf]

I recently learned there is a definition https://en.m.wikipedia.org/wiki/Mathematical_maturity

[gray gazelle]

Wow. This is amazing.
The way of defining mathematical maturity as ability to "Fill in missing details" seems me more reasonable than others.

[earnest wolf]

well, I think all the other parts of the definition are as important

[gray gazelle]

This seems to me somehow better. But yes, no doubt all other parts are important. All looks reasonable.

[violet shuttle]

well, for example, logically speaking one needs only basic set theory and the definition of ℤ and arithmetic on ℤ to read Lang's Algebra

[violet shuttle]

ah, okay, sorry, i had assumed you had gotten the wiki page

[gray gazelle]

Do you mean Lang's Algebra?

[earnest wolf]

omg, is that how he writes his books? 🙈

I have only read some of his undergrad textbooks and they seemed very readable

[violet shuttle]

Why shouldn't that be true?

Wouldn't that be true of most abstract algebra books?

[gray gazelle]

Yes. I have got some ideas about mathematical maturity

[gray gazelle]

For real?
Ig you are reading "function of several variables book" of lang right

[earnest wolf]

Yeah, some chapters of it

[violet shuttle]

what is so unreasonable about an abstract algebra book not logically needing much prerequisite

[slim ridge]

Is the author Nathaniel Johnston?

[tough egret]

Yes

His books are very good at both presenting the concepts in an articulate way and developing the mathematical intuition of the reader

In both volumes, there are plenty of computational as well as proof-writing exercices, and answers to a lot of them

[dusk wind]

they have videos on youtube as well

[stray quarry]

Can you guys recommend me any math basic logarithm books?

[gray gazelle]

Oh. Wow.

[gray gazelle]

Logarithm is just a topic in basic maths. However you will find it in the beginners Calculus book.

[gray gazelle]

Oh. I am excited to see this when I will start abstract algebra

[violet shuttle]

@gray gazelle A topology book is also like this, see Munkres who doesn't even assume basic set theory

[earnest wolf]

sorry for not replying: I was in a hurry. Well, it's perfectly reasonable. It's just the way you said it I thought he had his book written in "ZFC" style \

like, instead of saying: for any group, there's exactly 1 neutral element he'd write
$$
\forall G , \forall e_1, e_2 \in G [\forall x \in G ,, e_1 + x = e_2 + x = x] \implies e_1=e_2
$$

[hasty eagle]

Sweet Tea 🧋

[violet shuttle]

no

[gray gazelle]

Oh yes exactly.
But he assumes mathematical maturity right.
I almost have heard that before taking munkers topology you should be familiar with first course in real analysis

[swift dome]

want some recommendation for number theory book that will cover from basic to advance topics + another book only for problem solving in number theory

[gray gazelle]

Hi.. Am new here
Can anyone suggest me some tough maths books as am in high school and wish to prepare for math olympiad

Some really tough books for high school

[violet shuttle]

toughness is not the criteria to optimize for

[gilded notch]

singular criterion

[gray gazelle]

True but I like that

[violet shuttle]

my point is that if you just wanted something hard, you could try, say, that book published that explains the proof of the Poincaré conjecture

but, if you actually wanted to learn, it makes sense to start at a different place

[gray gazelle]

Ofc what I mean is,
A book that clears the concepts and has good set of problems

[normal beacon]

anybody got a book that will help me understand calculus in its whole and its easy to comprehend? like easy enough for a dummy like me to understand...

[lusty ermine]

Discrete mathematics book for learning combinatorics and graph theory, with lots of exercises?

[tawny crater]

thanks drop !

[fresh nova]

Hello folks,
I am a computer engineering student in his second year, and I didn't really work really hard in high school. Now I am suffering the consequences and maths related things are making me struggle in university. I kinda like maths to be honest, but I really never strove to understand them.

**I'm looking for books that teach from a beginner level to a university one of Calculus, Discrete Mathematics and Algebra. **
If someone has some good recommendations it would be greatly appreciated.

[reef escarp]

What would you all consider the most rigorous yet still theory/practice complete book on high school mathematics (by practice I mean it has a problem set that is difficult to solve and varies, rather than being easy and repetitive)?

[dense loom]

Depends on how beginner friendly you want the book, but if ur really starting from ground level "Everything you need to ace math in a one big fat book" is good

[lime hawk]

I'm a big fan of Papula but I don't think that exists in English, unfortunately

[scenic sequoia]

Annoying question but would you guys recommend Halliday and Resnik or Young for Introductory Physics ? I really want to just jump into Taylor and Landau while learning calc but from what I heard it’s not ideal without a strong hold on it.

[remote sparrow]

https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877

[remote sparrow]

it doesn't matter whether you pick halliday/resnick or young/freedman

personally i enjoy the informal tone of young/freedman a bit more but content-wise they're basically identical

[scenic sequoia]

alright cool

[gray gazelle]

Serge lang Basic maths and stewart's precalculus and calculus. Is it all thats needed for self learning math and computer science. Or is there a better alternative for self learning

[dusk wind]

well those are math, they aren't CS

[gray gazelle]

What I meant is if thats all needed for that field

Apologies for the misunderstanding

[reef escarp]

How theory complete would you consider this book? and are there any pre requisites or books you would recommend i read before/along with this?

[trail hemlock]

https://artofproblemsolving.com/wiki/index.php/Math_books
wow guys look at this

[gray gazelle]

AoPS books are the best

[trail hemlock]

😍

[remote sparrow]

more theory than most

there are no hard prerequisites besides a familiarity with numbers. however, the book was intended as a remedial course in algebra and analytic geometry, so modest familiarity with the basics of algebra and geometry would be helpful.

[fleet solstice]

How good are Barron's books for self teaching?

[karmic thorn]

Has anyone read Sharpe's Differential Geometry? Would you recommend it as a first introduction to manifolds and related topics?

[marsh ingot]

I would recommend Lee or Tu

[final swallow]

What books do would you recommend for a beginning proof-based linear algebra book, presented in an intuitive manner?

[remote sparrow]

#book-recommendations message

[molten mason]

Is Jech's Third Millennium big Jech?

[remote sparrow]

yes

[covert bane]

I'm doing some work on homotopy type theory next year, but I haven't worked much on type theory before -- only structural set theory at most -- and my supervisor has recommended that I read up on some martin lof type theory beforehand

does anyone have any gentle introductions to that?

[heady ember]

When did Sharp switch from foundations to DG?

[remote sparrow]

https://www.logicmatters.net/resources/pdfs/LogicStudyGuide.pdf

also check pins

there is a logic reading list

[covert bane]

tyty

[remote sparrow]

i would say Lectures on the Curry-Howard Isomorphism by sorenson and urzyczyn seems good

http://www.lix.polytechnique.fr/Labo/Samuel.Mimram/publications/

@covert bane ctrl + f "PROGRAM = PROOF"

https://www.reddit.com/r/math/comments/1apneml/what_are_good_textbooks_to_learn_proof_theory/

Proofs and Types by girard should give a broad overview of proof theory and type theory and their connection to each other

almost no exercises though

https://www.paultaylor.eu/stable/prot.pdf

[swift dome]

i need book recs for number theory that will cover from basic to advance topics. also a book with bunch of problems from where i can solve after learning after learning one concept

[remote sparrow]

#book-recommendations message

[swift dome]

ty

[karmic thorn]

1980s

[lusty ermine]

any book that has solved problems for cramers rule? undergrad.

[uncut salmon]

Any book with an ultra-shit ton of linear algebra exercises (difficult ones too)?

[ocean mulch]

Should be in #discussion but ok

[tough egret]

Personally, I take handwritten notes as I read about a subject, then type them, and go back to them whenever I work on something related to it

Also try to create an explanation that you would give to to someone that has a knowledge of math just below yours

Or even a complete neophyte, although this clearly cannot be done with advanced subjects

[ocean mulch]

it's always like that. If you ask nicely, ppl will respond.

Tbh we are all bored and procrastinating on doing math so we will respond to anything

[remote sparrow]

https://www.amazon.com/Linear-Algebra-Challenging-Problems-Mathematical-dp-0801891264/dp/0801891264/

[uncut salmon]

Thanks thats what I needed

[tough egret]

I'll answer you in #discussion

[molten mason]

#discussion is for everything that's not homework help. If it's too busy and off-topic then #serious-discussion is slower and more serious.

[thorn hinge]

Is Singularities of Differentiable Maps good?

For an introduction on the topic

[magic spade]

What is your math background? For a really intro book you should look at Curves and Singularities by Bruce and Giblin

But the book you are looking at is great too

[empty mirage]

Sup guys! Book Recommendations about diff equations and applications

[lusty ermine]

how do I get introduced to Number Theory? if possible with multiple hard exercises (proofs)

[lusty ermine]

undergraduate level.

[graceful moon]

If applications appeal to you you’d probably like Boyce DiPrima and Meade

[graceful moon]

#book-recommendations message

[lusty ermine]

thank you sir.

[molten mason]

#book-recommendations message

[gray gazelle]

Do you guys have any books that teach complex numbers but more rigorously?

Like from a more abstract algebra standpoint

Maybe an algebra or analysis book with a more in depth section about them

Thanks in advance

[hallow oriole]

im searching for textbooks that teach math differently from other textbooks about the same subject yk??

famous examples would be LADR (which to an extent eschews determinants) and aluffi (which involves some category theory). i would like more books in this vein, that either teach differently than other books written on the same subject, or books that present proofs, theorems, and methods which are also not commonly taught in other textbooks. tyyy!

[cobalt maple]

Anyone got any recommendations for books presenting more research-related problems and topics or modern developments in regards to algebraic topology and or 3-manifold theory?

[tame sphinx]

Is there a book on fourier transform that defines the fourier transform on a measure?

[remote sparrow]

are you interested in the construction of the complex numbers or something?

[novel sluice]

Same here.

[remote sparrow]

what does studying complex numbers from a "more abstract algebra standpoint" mean to you exactly

are you interested in its properties as a field?

[upbeat vine]

Grafakos Classical Fourier analysis

[lusty ermine]

in which book can I find lots of exercises for matrix transpose, and linear transformations

if possible with proofing

or whichever is useful actually. please let me know.

[earnest wolf]

(this isn't for the sake of getting a book recommendation – I just dk where else to ask)

Does anyone know of any good alternative to Apple Books? The main things I'm looking for
• Good support for both mac and ios
• And by «support» I mean at least the following:
• Being able to either add bookmarks (especially on ios) or the feature of remembering where you stopped last time
• Decent pdf viewer (especially on ios, since on mac the built-in Preview app is more than enough – it supports both bookmarks and remembers where you stopped)

I mean, it may not necesserily be some kind of 'book app'. Maybe just a cloud service provider (my icloud is almost full xd)

The reason why google drive and for example Mega don't work is that they don't remember where you stopped :((

[gray gazelle]

Kindle

[manic cairn]

hot take: imslp ios app

[dusk wind]

root your apple or find a better web app use linux lol

[earnest wolf]

:))
I used to be a linux user for many years. Like arch, gentoo and whatever. But when you get a mac you don't typically try to make your life harder [by installing something other than macos] xD

And also, web apps don't work with ios well unfortunately

[earnest wolf]

thank you both @gray gazelle and @manic cairn – I will check those out

[gray gazelle]

Arch Linux is truly based 🗿

[manic cairn]

i use arch linux, but my biggest problem with it is the linking of haskell packages, which is pretty bad

the haskell toolchain on arch is harder than it needs to be

[dusk wind]

you could sandbox a better OS

maybe theres readera for it

[earnest wolf]

nope. on retina display [very high res] it's very hard to run a vm

[gray gazelle]

I found it way better than Ubuntu and debian

Also very flexible and lightweight

[dusk wind]

yea its really lightweight

[earnest wolf]

this is becoming off-topic, but I wouldn't argue macos is a bad os
like it's unix-like and parts of it I think are borrowed from bsd(?)

[manic cairn]

i was going to give a tty workaround, but then i realized that would totally constitute "very hard to run a vm"

[gray gazelle]

MacOS is best for beginners

And those who wanna learn programming

Should shift to Linux later

[spring solstice]

i have Pindows 11

it is developed by a Chinese company

[gray gazelle]

Great

But where's the funny part

[earnest wolf]

and also for ppl who just want it to work and don't want to spend a good portion of their time doing sys admin stuff when you could have spend it on something else (I'm one of those)

[gray gazelle]

Exactly

Tho it's getting off topic now

#computing-software

[soft egret]

Hey, I’m doing IB and my extended essay is about tessellation and cryptography systems, do any one of you have a good book that covers extensively the topic of tessellations and patterns?

[fierce hedge]

Why not use Manjaro or something similar which is built on top of Arch

[hallow oriole]

not sure of exactly how cryptographic it is but conway has a book on symmetries and tessellations called "the symmetries of things"

[soft egret]

Hey, thanks a lot! I was just looking for something to get deeper into tessellation, I will take care of the other part later

So that books fits perfectly

[gray gazelle]

yes, that

[soft egret]

Any more books on tessellation and patterns? I’m trying to get as much information as possible as this is a mostly new field for me, also, it’s really interesting so I’m open to reading lots of books about it

[pine widget]

Hi,
i am planning on participating in maths olympiad, can anyone suggest some really "tough" books for preps...?
thanks in adv.

[glad rampart]

AoPS volume 1 and 2?

[earnest wolf]

also, I just found (actually I had the pdf for a very long time — just was not bored enough to give it a try) the princeton companion to mathematics

I only read one article in it but it was just amazing

And I thought it was in wiki-style, but hell no!

I won't probably read all the articles — just the ones I'm interested it, but imo it's a great bedtime read for anyone else interested

[pine widget]

by richard rusezyk?

[glad rampart]

yeah ive heard theyre good for competition prep

im going through their main cirriculum and its good

[pine widget]

will it cover every corner ?

or anything closer?

[narrow prairie]

Aops books mostly cover more computational contests like AMC and AIME

[pine widget]

olympiads?

[narrow prairie]

Check out Euclidean geometry in mathematical olympiads for geo and Modern Olympiad number theory for NT

Afaik there aren't any combinatorics or algebra books in the same style as those

But you should be fine with just online handouts and maybe one of titu andreescu's books

[remote sparrow]

https://www.amazon.com/Number-Systems-Foundations-Analysis-Mathematics/dp/0486457923

https://www.amazon.com/Number-Systems-Path-Rigorous-Mathematics/dp/0367180650/

[earnest wolf]

perfect description i think

[gray gazelle]

Thanks

[gray gazelle]

Books I got were gelfand algebra and trigonometry, stewart precalculus and calculus, serge lang basic math, number theory by andrews, graph theory by trudeau, rosen discrete math and code by charles pretzoid. Hope thats all I need for self learning and rebuilding a foundation for coding and computer science.

Or am I missing something else?

[uncut salmon]

OTIS-Excerpts is extremely tough but very good

Also, specifically for number theory there is MONT and for geometry there is EGMO

You should find the pdf online for free

[dark tulip]

Could someone recommend a decent book on inequalities for Math Olympiads covering the standard ineqalities like AM-GM-HM, Cauchy-Schwarz, Muirhead, Jensen, Weighted Power mean, Holder, Karamata etc. ? I tried reading Cauchy-Schwarz MasterClass but it was a bit too hard

[glacial coyote]

Do you guys know any good books about functions?

[gray gazelle]

where can i find a good book on combinatorics

[trail hemlock]

https://artofproblemsolving.com/wiki/index.php/Olympiad_books

look under algebra theres a section for inequalities

i thought cauchy-shwarz masterclass was good ngl

[remote sparrow]

where can you find a good book on combinatorics? this channel

what is a good book on combinatorics? A Walk Through Combinatorics by miklos bona

[hallow oriole]

or enumerative combinatorics by stanley

[gray gazelle]

ok

will check it out thanks

[lusty ermine]

Introduction to math olympiad reading please

[languid bloom]

got "algebra" by Serge Lang for really cheap can anyone share any insight into that specific book?

[violet shuttle]

It's something.

I find he doesn't do a good job at actually explaining things at a broader level.

It works for me, despite that.

[steep slate]

so like, i might need to withdraw from calc, bc it aint going so well for me. Its a combo of minimal time, teaching style, and the fact i havent taken math in so long so ive forgotten a lot of trig; but ive decided if i have to take it again in the fall i am going to prepare this summer so its a breeze in the fall. does anyone have any recommendations for calc prep; whether it be a physical tutoring institution or one online. I am aware of khan academy, but i would like other suggestions as well.

[dusk wind]

try a book that has many exercises in it with not many artifacts from publishers

Maybe Leithold TC7

[languid bloom]

The Math Sorcerer does a decent job with his udemy courses if you want a similar style to khan academy just a bit more polished. I enjoy his video format a lot and they are very cheap courses. For calc I also enjoyed the book "Calculus Made Easy" by Silvanus P. Thompson and Martin Gardner on top of those courses

[steep slate]

joel been typing for a min

[languid bloom]

Thanks! I don't need help with the subject necessarily I just enjoy reading many books on the subjects I enjoy and was hoping it was a good read since I've heard a few good things about it here and there 😁

[languid bloom]

sorry I didn't finish my sentence for a minute haha

[steep slate]

had me waiting lmao

[languid bloom]

my bad 🫡

[languid bloom]

but anyways there are also some "assignments" that come along with those udemy courses which I enjoy so it feels more like a class (even though some people may dislike that)

[steep slate]

im fine with thaT

[languid bloom]

they are optional of course but worth going through if you need the extra polishing

[manic cairn]

make sure you know a little abstract algebra beforehand, and do the problems in the given chapter as soon as you can

but that's kind of a given

whenever a sentence is said, justify it yourself and see if it makes sense.

or rather, make sure that it does

i like lang because he is concise and not talky, and much of the technique comes from studying the examples and the proofs of the given theorems.

[languid bloom]

nice that's the type of book I was looking for so hopefully it meets expectations but if not im not too worried since I got it for about $10 haha 😁

[manic cairn]

oh, that's epic

the third edition?

[languid bloom]

yeah third edition

[manic cairn]

i first used it with this: https://math.berkeley.edu/~gbergman/.C.to.L/

i have nostalgic memories of the mental hospital printing out companion to lang's algebra in high school

[pearl nimbus]

does anyone know a good book where I can self study calculus? I know the basics, approx calc 1. I know about derivatives, some basic integrals, IBP, u substitution. I haven't learned implicit differentiation/trig sub/practice many integrals. I'd like a book that can explain all the way from calculus 1, up to multivariable calculus, or maybe a bit further. The more rigorous the proofs are, the better. I'm aware a lot of calculus concepts can't be rigorously proved untill real analysis, but I'd still like to learn the formal proofs of as many concepts as possible. Thanks!

[graceful moon]

Stewart could work for that, it covers an insane amount of stuff with loads of exercises. Afaik the proofs are decent too

[pearl nimbus]

what's the full name?

[graceful moon]

James Stewart - Calculus, Early Transandentals, I believe

[stray quarry]

can you recommend any number theory books? its quite hard for me to find this kind of book

[graceful moon]

#book-recommendations message

Rosen has 2 books, it’s the one he authored himself you want not Ireland & Rosen, that’s a bit more advanced

[slender wasp]

Apostol or Spivak.

For single variable Spivak is better than Apostol but problems are hard. For multivariable, Apostol Calc II is good for an intro. If you wanna do differential forms and get into multivariable a bit more than Apostol's intro then do Shifrin or Hubbard instead.

[remote sparrow]

Some calculus books:

Mainstream texts
Calculus or Calculus: Early Transcendentals Stewart, Clegg, and Watson (formerly only Stewart)
Calculus or Calculus: Early Transcendental Functions by Larson and Edwards
Thomas' Calculus or Thomas' Calculus: Early Transcendentals (formerly known as Calculus and Analytic Geometry until the 10th edition onwards, when it was renamed to Thomas' Calculus) by Hass, Heil, and Weir

Most other calculus books are similar to these market leaders. Old editions are often available at much lower prices than the newest edition. Stewart does have rigorous proofs of some results, though not always the most general case (which is not intended as a criticism of the book). I think newer editions of Larson have relegated some proofs to the book's website.

Rigorous calculus textbooks
Calculus (Two-volume set) by Apostol
Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubbard (if you wish to buy their book, buy from their website as it is cheaper)
Calculus of One Variable by Kitchen
Multivariable Mathematics by Shifrin
Calculus by Spivak

Apostol covers single-variable calculus and linear algebra in the first volume. In the second volume, he covers linear algebra and multivariable calculus. Spivak and Kitchen only cover single-variable calculus. Hubbard and Shifrin cover linear algebra and multivariable calculus.

"Half" rigorous calculus textbooks
The following books can be described as an interpolation of mainstream texts and rigorous calculus texts (which are pretty much analysis-lite sans topology). They omit proofs and concepts that the authors feel more properly belong to a real analysis course but give definitions and proofs of the essential ideas.

Calculus with Applications by Lax and Terrell
Multivariable Calculus with Applications by Lax and Terrell
Calculus: A Rigorous First Course by Velleman

the early transcendentals label just means the transcendental functions are used freely before we have the tools to properly define them (not a criticism, and possibly even a benefit as you probably want students to get lots of practice with these functions)

if mods may indulge me, can this get pinned

[dusk wind]

pins dont exist you know this already

[short violet]

are there any books on axiomatic definitions and how naturals/integers/rationals/reals were constructed

[earnest wolf]

as for reals open (almost) any analysis textbook

and for nat, int, rat any zfc textbook will do

[vital bane]

but especially tao is notable for that

[vital bane]

Tao spends the first 5 chapters on that

[earnest wolf]

abbott also has an appendix constructing r from q

[earnest wolf]

'jech intro to set theory' is a good one

[remote sparrow]

Number Systems and the Foundations of Analysis by Mendelson
Number Systems: A Path into Rigorous Mathematics by Kay
Number Systems: An Introduction to Algebra and Analysis by Ovchinnikov

This material is also discussed in Elements of Set Theory by Enderton and Classic Set Theory by Goldrei

[short violet]

Tao ?

[short violet]

really?

[short violet]

damn , which one is good ?

[remote sparrow]

mendelson is the most detailed

[short violet]

have u read that?

[remote sparrow]

good is up to you

[remote sparrow]

bits and parts of it

i have a copy at home

mendelson is by far the cheapest choice if you want a hard copy btw

https://tenor.com/view/i-saw-what-you-deleted-cat-gif-25407007

[short violet]

lol i thought it was wrong URL

[short violet]

not really looking for a cheap rather quality book

[remote sparrow]

dover books are good in general

high quality books for bargain prices

[short violet]

dover is the company's name ?

[remote sparrow]

the publishing company yeah

[short violet]

really focuses on set theory first

[remote sparrow]

no

[short violet]

damn i can't send image

[short violet]

the first chapter is basic facts and set theory ?

[remote sparrow]

yeah but it's the simple naive way that you learn in most math books

it's not really a thorough introduction to axiomatic set theory

[short violet]

oh really

is there any good book or a website where i can practice questions of nearly every topic out there?

[earnest meadow]

How does OpenStax compare to paid textbooks? Mostly interested in Algebra + Trig right now, and might not mind spending some money to help learning

[glad rampart]

theyre ok for a free resource, theres a lot better out there that are paid though imo

[vital bane]

Terrance Tao's Analysis I

[vital bane]

I'm stealing this gif

[gray gazelle]

What about barrons books?

There were a few math sorcerer recommended but heard a lot of mixed reviews

[remote sparrow]

@daring lake thoughts on david cox's Galois Theory?

[vocal schooner]

hi, can i have some topology intro book recommendations that are good for someone whos bad at math

[dusk tapir]

I started reading intro to topological manifolds from John M. Lee.
Imo the exposition is nice and not too dense.
I picked the book because it has been referenced as a good recommendation on this server a couple of times.

[remote ginkgo]

Ronald Brown, Topology and Groupoids

cleanest intro anywhere tbh

[vital bane]

Have you studied real analysis?

[chrome yacht]

give https://www.topologywithouttears.net/ a try

[sullen raptor]

anyone got a solid introduction to topology. So rigorous would be nice yes however idk what rigor means in topology.
I am familiar with fourier analysis and abstract linear algebra.

[dim sierra]

I think Leinster’s notes are great, they present the material very clearly

But it doesn’t do the weird point set stuff, it’s just the different topologies + compactness + connectedness

[gray gazelle]

can you guys suggest a gentle introduction to number theory?

[novel hound]

#book-recommendations message

Burton, Silverman and Rosen are good one's to start with. NZM is the "best" but a bit harder.

[gray gazelle]

silverman looks good

[narrow oyster]

need a good resource for fractional calculus

would strongly prefer something physics agnostic

[wild flare]

Best entry-level book for linear algebra?

[finite gale]

https://discordapp.com/channels/268882317391429632/716264872018706443/959370522938974228 if you're looking for lots of computation, idk, try searching through this channel

[wild flare]

Thanks

[remote sparrow]

gamelin/greene, munkres, and willard are good

[lusty ermine]

which books has complicated exercises con lagrange multipliers and optimization topics, if possible calc 3 undergrad with lots of exercises

?

[remote ginkgo]

frfr check out brown u will love it

[pliant wadi]

Okay so I am solving Spivak's Calculus on Manifolds and the book doesn't contain anything on Taylor's polynomial, any suggestions on where to read about it from? Any expository articles or books as recs?

[remote ginkgo]

apostol

there is also ahlfors complex analysis which spends a little while talking about one-variable taylor series expansions

[pliant wadi]

Oh nice

I'll check that out

[gray gazelle]

any1 around here owns a new edition of spivak differential geometry book 1?

[torn crypt]

Mfw “yeah dawg just have f^n(x) be o(1/n)” mfw wrong channel open

[violet shuttle]

rudin

[gray jungle]

any calculus book, but if you want the most general treatment, you can checkout henri cartan "Differential calculus"

[gray gazelle]

also hubbard

[tawny copper]

Do you mean this one? https://maa.org/press/maa-reviews/differential-forms

[gray jungle]

https://www.amazon.com/Differential-Calculus-Normed-Spaces-Analysis/dp/154874932X
(i mean most general minus jets ofcourse )

in the setting of a banach space with frechet derivative

[gray gazelle]

is this 100 page book even good for an undergrad?

[tawny copper]

Google didn't show me this when I googled idk why

[tawny solstice]

What are some good books for self studying set theory, logic, and proofs? I have my eye on “Set Theory and Logic” by Robert R. Stoll and “Journey into Mathematics: an Introduction to Proofs” by Joseph J. Rotman

[hallow oriole]

enderton elements of set theory

i like halmos a lot more for the record

but most people would recommend enderton

[tawny solstice]

“Naive Set Theory” Halmos?

[hallow oriole]

yep

[heady ember]

Uh

Depends on what you're looking for

[tawny solstice]

Got it, I’ll get that one then, as “Elements of Set Theory” is a bit expensive

[tawny solstice]

Books that can give me enough of a background to look into number theory and abstract algebra without too much difficulty

[hallow oriole]

they mentioned they were looking into an intro to proofs book so naive set theory is def good enough

[heady ember]

Enderton is a good intro to axiomatic set theory for people with little to no mathematical maturity, like I was.

Halmos is for naive set theory

[hallow oriole]

wait

u dont need

set theory

[tawny solstice]

I don’t?

[hallow oriole]

there are self contained nt and abstract algebra books

[heady ember]

Why did you rec enderton then

[tawny solstice]

Do I not need set theory, logic, and proofs to learn those two though?

[hallow oriole]

enderton is fine too for "self studying set theory"

[hallow oriole]

you can pick that up as you go tbh

but if you want to learn ahead of time then

book of proof by hammack

it's free and legal online

[heady ember]

If you have some basic naive understanding about logic you're fine

[hallow oriole]

probably the best proof introduction book out there

[heady ember]

E.g. universal and existential quantifiers

[tawny solstice]

I’ve looked into it, but I don’t like the way he teaches about proofs, just not my style

[hallow oriole]

ah

well

[tawny solstice]

“There exists” and “for all”?

[hallow oriole]

you'll probably be fine jumping in to something like artin

are you okay with calc?

[tawny solstice]

Haven’t taken it yet but I do know how to calculate basic limits, derivatives, and integrals. I plan to either take Analytic Geometry & Calc 1 and 2 or AP Calculus AB next year

[hallow oriole]

not sure what analytic geometry is so it's probably skippable

you'll want artin's algebra imo

take calc ab

it's not bad

[tawny solstice]

Geometry on the Cartesian Plane, to my knowledge

[hallow oriole]

mm it could be okay to build intuition for later

but if you learn calc the right way you'll be building up plenty of geometric intuition

[hallow oriole]

but yeah this

it also treats linalg iirc

[tawny solstice]

Found one for $19 by Pearson on Amazon, thank you

[hallow oriole]

yeah ofc good luck man you got this

[tawny solstice]

Thank you, I’m trying. Picked up Hardy’s book “A Course of Pure Mathematics”, but was lost around page 10

[remote sparrow]

a used copy of Classic Set Theory by goldrei in good condition is going for $27.30 with a $3.99 shipping fee on amazon. a used copy of Elements of Set Theory by enderton in good condition is going for $43.71 on amazon.

[remote sparrow]

#book-recommendations message

[remote sparrow]

the international edition is missing the chapter on galois theory

it is also missing the index

[tawny solstice]

Is that a big problem?

[gray gazelle]

https://bookstore.ams.org/view?ProductCode=TEXT/72 I found this neat little book which I am gonna use

[tawny solstice]

Bit expensive, is it not?

[remote sparrow]

up to you, i just wanted to inform you

it is a bargain price for having the majority of the content

paper and print quality may be subpar however

[tawny solstice]

Got it, I found lecture notes on Galois Theory from a different Artin

[gray gazelle]

well you can get a pdf for free

[tawny solstice]

As long as it is readable, I don’t care. I own a stats book from the 50s, I believe

[remote sparrow]

maybe they want a hard copy

[gray gazelle]

I see

[tawny solstice]

Physical > pdf

[gray gazelle]

tbh I have gotten used to digital copies by this point

[tawny solstice]

I look at enough pdfs in AP Lang, I don’t want to look at any in my free time

[gray gazelle]

fair

in my country there is a pdf printing service

you can get it printed and bounded for very cheap

[tawny solstice]

I own a printer, but not a three-hole punch to fit it into a binder

[gray gazelle]

well you can print relevant chapters as you go along

[tawny solstice]

Is it in the United States?

[tawny solstice]

Fair enough

[gray gazelle]

no

you guys have lulu I think

[gray gazelle]

you can buy folders to store them too

having a printer is a great advantage

[remote sparrow]

https://www.lulu.com/

try uploading the pdf here