book-recommendations

[gray gazelle]

Yes, I took a college course and I liked it.

Passed so figured I would try it.

[fierce hedge]

Yeah but it was probably Dami and his dislike for how Axler treats determinants in the 3rd edition. 4th one improves in this regard so it's definitely better

[past flame]

So what’s the consensus

[fierce hedge]

Since the 4th edition is recent, probably no one has read it yet but I think it is slightly better than FIS at least for me, FIS is more handholdy and does things a bit slowly.

If you want ever more speed then try H&K

[past flame]

This makes FIS sound good to me haha

[fierce hedge]

Personal advice is that don't quit the book in between. I paused it and it was a bit daunting to get back to where I was

[vague wren]

hello all. I know how to solve some quadratic equations, some stuff about functions and how to graph them, some geometry and very little trigonometry. What book should I take to learn more about mathematics?

[molten mason]

Basic Mathematics by Lang is on Amazon for $41, great book

[vague wren]

nvm, scrolled a bit, thanks

[thorn elbow]

I wish everyone a good evening, I am a high school student and I want to improve my skills in math and physics, of course I understand that math is not the same as physics. However, I wanted to ask you if you have any book recommendations or author recommendations. This is very important to me because I really want to get better at math and physics. I would really appreciate and value your response !
Thank you in advance !!

[finite gale]

What kind of topics are interested in learning about

[marsh ingot]

Rudin

[thorn elbow]

Calc and trigonometry

[marsh ingot]

I have one but in spanish

Even have an introduction to Linear algebra

[trail hemlock]

ive heard good things about "Conceptual Physics: The High School Physics Program"

[marsh ingot]

@thorn elbow "calculus" james stewart, try this

[timber ermine]

Hello good people. Currently attempting to complete Analysis I by Terence Tao. Could you recommend me a good pace?

[dusk wind]

100 pages a day

[slim anvil]

hi, for anybody who’s taken a course on combinatorics, what was the assigned textbook/does anybody have recommendations otherwise?

[wraith sandal]

What is the book called?

I have one and is algebra de baldor

great book it has challenging problems

[remote sparrow]

A Walk Through Combinatorics by miklos bona

[slim anvil]

ty

[fleet solstice]

What're some good cheap Algebra books for intermediate level?

[past shoal]

Good books for self studying physics?

[wicked thunder]

Just read it at your own pace. Some concepts you will get faster some concepts you will get slower.

[vital bane]

Don't worry about pacing, just focus on learning analysis and doing as much math as your can everyday (with breaks in between of course)

[dusk wind]

don't worry, eventually we'll be able to install it via a drive augmentation

at that point rpm wont matter

[marsh ingot]

Calculus by Apostol

[remote folio]

It is better dive in. You can think of there being different levels. The intuitive stage, very minimal mathematics, understanding stage(advance math is required). A good course for getting started is Jose Portilla on Udemy.

[sick river]

Id like to go deeper into stochastic analysis, any recommendations for a book after having gone through Cinlars Probability and Stochastics?

[wraith sandal]

wow, didnt know there was a spanish version

[marsh ingot]

I think during the degree my teachers recommend us

[marsh ingot]

Book for introduction to PDEs? I had a subject of PDEs during the degree but uhhhh it was only doing exercises to the end and few theory. No demostration of results

I would like advanced one because Sobolev spaces have my interest

[marsh ingot]

It was a surprise for me too

[remote sparrow]

evans

[marsh ingot]

Pde evans right?

I found it fast lol

[remote sparrow]

not aware of many others

[marsh ingot]

Over 600 pages damn

[sage python]

If you think that's long check out Taylor

[halcyon wasp]

What book should I learn representation theory with?

[brave glacier]

Hello, I'm a 2nd year undergrad, I'm trying to learn abstract algebra, for now I'm self-studying Jacobson and I'm planning too try some category theory in parallel, I'm taking Jacobson mainly because (at least according to pinned messages) it covers uncommon topics, which I feel is best when I already vaguely know some of the content I'm reading (like I already have some undergrad algebra courses, but it feels a bit lacking as we don't cover some things I feel like are fondamental/important results, like Cayley's and Sylow's theorems).

My question is:
My goal being to not get bored while studying subjects I already partially covered, is it best to:

• keep studying Jacobson (or some other, maybe Artin would be more fun as I would need to do more active reading?) and try some category theory aside (if so, which book are recommended, I heard McLane is good but since its a graduate text, I fear he takes examples a grad student would know and I wouldn't)
• or is it best to learn a bit of both at the same time, with Aluffi's Algebra 0 for instance (or Lang, but again, its a graduate text + he has the reputation of disliking category theory), keeping myself entertained with new definitions of the stuff I covered (differently) in class.

[signal forge]

Please what’s the best book to learn Abstract algebra and Numerical analysis efficiently?

[sage python]

I got Jacobson when I was thinking of using it to go over stuff for quals.

One thing I like is that he feels more conceptual in his explanations. For example, normality is often presented as "Oh we wanna multiply cosets because... We do, I promise. But oh look see there's a hiccup. But if we're normal... :0"

Jacobson, on the other hand, talks about congruences as equivalence relations where multiplication descends to equivalence classes (in fact this is done, along with other things, at the level of generality of monoids, which is good if only because it makes ring theory more convenient later). Then he shows that the equivalence class of the identity ends up being a normal subgroup H, and the relation is G/H. Also, he first presents modules in terms of ring actions on abelian groups, rather than just a map RxM->M satisfying blah blah blah.

As for the nonstandard topics, I would say the content up to chapter 4 is fairly standard, but then he does stuff like real closed fields, classical groups, k-algebras, etc.

Volume 2 starts with category theory, and only needs chapters 1-4. You therefore wouldn't need Aluffi, and if you want more category theory afterward you could use Maclane or Riehl or smth

[gray gazelle]

any book recommendations to study recurrence relations?

[analog roost]

Hello Guys,

I am a Bachelor of CS, I learned Linear Algebra 1,2, one DE course, one LA course and one Statistics. It wasn't hard the school was normal level.
Now I want to have a deep understanding especially on DE and LA
Can I have some books?

I want to be ready to understand advanced ML and DL

[sage python]

What kind?

[analog roost]

I have a problem with some authors that they skip steps implicitely (as if its common sense)

[halcyon wasp]

I don't really know, I just heard about representation theory in my grad algebra class.

[sage python]

Serre is good for finite groups. Fulton-Harris goes finite groups -> Lie theory, very example driven though I've heard of complaints about organization. A lot of stuff on Lie groups/algebras. Etingof is more broad overview

[brave glacier]

Thanks

[halcyon wasp]

Ah, thank you!

Hm, should I learn more about finite group when the classification is finished there

A review on the Serre's representation:

If you don't have an expert to chat with, this will be a waste of your time

[normal ruin]

50 shades of grey

I read it yesterday, was good

[storm fossil]

Anyone know of a very fast, simple introduction to set theory? Pretty much just a "get up to speed notationally, some examples, etc." kind of book. A lot of books obviously use the basics of set theory, but none of the ones I currently use go beyond notation.

Just something slightly more in depth than "here are the definitions of each symbol."

Otherwise I could just look up the symbols and be fine.

[normal ruin]

Introduction to set theory from Henry Carlton is a good one

[storm fossil]

I'll take a look at it, thanks

[upbeat vine]

You are better off picking an intro book for a specific field as the relevant set theory will usually be developed, for example if you pick an intro book for analysis, algebra or topology.

[storm fossil]

I've found that the books that do introduce set theory at the beginning (Apostol's Calc for example) do give you the tools you need for the book, but it kind just rushes through it because it's assumed you're familiar with it.

But I found a pretty decent YouTube video that goes over it relatively quickly and gets you up to speed on the terminology.

Is Set Theory still being actively developed or is it mostly a done deal?

[stray veldt]

its an active area of research

albeit largely disconnected from most other areas of mathematics

[chrome tide]

Guys I am having a mental breakdown deciding between larsons calculus and stewarts calculus. Larsons seems more promising and organized but stewarts seems more "complete and comprehensive" I am self studing university physics so what do u guys think can someone help with that choice.

[stray veldt]

it doesnt really matter

you can also just work through say the first chapter of both and then decide

[chrome tide]

I worked through the first one and I liked larsons way more but I am afraid that I am missing out on some lessons because stewarts have more pages. (If that doesn't matter and both are the same in term of content then I am 100% choosing larsons)

[stray veldt]

well, i cant promise that they have the same content (though pagecount is a really bad measure for this, just look at the table of content instead)

but having 100% content is just not as important as you think

[chrome tide]

Thanks for telling me you'r amazing 😊👍😎

I was wondering what do you prefer

[analog roost]

............

[oak sable]

Are there any books which explain continued fractions at a really elementary level? Going back far enough, I found one by Euler (maybe went way too far back), but I think it’s an analysis paper.

Are there any books that treat continued fractions assuming only really basic knowledge, for example high school algebra?

Not just an explanation of them, but transformations and other cool things with them.

[chilly bobcat]

I participated in a compition called seamo.does any1 know a good book to prepare from for paper E as its course is diff from o levels and is not taught in it

[novel hound]

Many of the elementary number theory books have a chapter on continued fractions: Rosen, Burton, Niven, etc. Usually leading upto Pell's equation.

[oak sable]

Any of them particularly approachable for someone with just a high school algebra background? Or will I need to read some other texts before?

[novel hound]

I also have a slim 100 page Dover book titled Continued Fractions by Khinchin. I bought it in high school for competitions but it wasn't much use for them. Check out the ToC in case you see anything interesting in it.

[novel hound]

Burton and Rosen are definitely approachable in high school. Niven less so, although many olympiad kids have been known to do it as well.

[oak sable]

Thank you for the help 🙂

[remote sparrow]

Naive Set Theory by halmos

[remote sparrow]

#foundations

[untold laurel]

I'm gonna try to apply to study applied mathematics next year. Any good book recommendations for that topic for beginners?

Or I might go for something like data science or applied computer science. Either way, any recommendations for anything along these topics are appreciated

[dusk wind]

too broad, it depends on your interests

computers or data?

[gray gazelle]

Discrete Mathematics by Rosen if you apply for CS. Would recommend some literature on statistics if you do DS since it is stats-heavy. As someone currently applying to university to study applied mathematics - it largely depends on the program and country you're applying to.

[heady ember]

You don't need any cutting edge set theory for non-foundations math btw

A page of a grad set theory book, for example, (from Kanamori)

[viscid comet]

What book is this?

Nvm found it

[molten mason]

I have a much older version, it's 4th edition lol But it's a great book, Basically covers Calc I, II, and III. I used it in Middle and High School. Tons of problems and worked out examples.

[untold laurel]

Alright thank you

[heady ember]

Discrete math by Rosen was very boring when I tried it

[dusk wind]

rosen is kinda boring but there not many interesting books on the subject

[undone finch]

i think rosen is ok?

it's just not meant to be read sequentially

most discrete math courses will pick like 5 chapters from it and focus on that

there is knuth's concrete mathematics also but i haven't read it and have no input on the matter

i don't think rosen is the kind of book i'd use for self study, but for a teacher, its a good supporting textbook

[velvet glacier]

I only problem I have is that it contains stuff from derivatives in the chapter called Before calculus

So I have to skip those

[untold laurel]

Alright I'm back home so I'll elaborate more. I'm looking for something more maths focused rather than CS focused. Though I definitely don't mind something not closely related, since I'm just thinking of reading it for my own pleasure for now. Interesting topics to me are discrete math, trigonometry, statistics, game theory, number theory, bit of calculus. Not a fan of geometry, but I can work with it a little too

I have 0 experience in the math books scene, I haven't read any math books other than my high school textbooks, but as I've been getting more into books in general I decided it would be nice to check out some math ones as well

[normal reef]

I'm looking for an introductory problem book on galois theory, any suggestions?

[jolly turret]

Hi everyone. Please can someone advice me a very good book on real analysis ( with series and function) with this concept well explained because I don't understand it at all.
P.S: I am in first year of university computer science

[candid spear]

understanding analysis by abott

but generally its good to have atleast 2 books on analysis

[jolly turret]

Ok thank you.
Did you use it personally? Did it really help you?

[candid spear]

i used it personally, but keep in mind that you need a lot of background in proofs for analysis

do you have that

[jolly turret]

Well, I don't know. What do you mean by that? I'm not sure I understood

[candid spear]

proofs

like in math

like proving things

if you dont know what that is id reccomend reading a proofs book before analysis

otherwise analysis wont make ANY sense

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

@jolly turret or
https://cloudflare-ipfs.com/ipfs/bafykbzacedkghkuaqjoa6fhho25armn7wgouzey2jgv5bdxfsi2h2wrkjdfuq?filename=Jay Cummings - Proofs_ A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)-Independently published (2021).pdf

[jolly turret]

Oh I understand. And that's exactly one of my main problem in real analysis.

[candid spear]

yes you need to read a proofs book before analysis

100%

[jolly turret]

Thank you so much

[vital bane]

this is not true you can pick up proof skills as you go through analysis or algebra

you just gotta pick a good book, like abbott

[candid spear]

yeah but its nice to have some background

you very much can but idk why you would

maybe with linesr algebra or abstract algebra

[graceful moon]

Liebecks concise introduction to pure maths would give you a gentle introduction to proofs while introducing thr basic ideas of analysis and algebra

[candid spear]

thats not the same as analysis in depth tho

[graceful moon]

Well your choices are learn proofs then analysis or learn proofs by learning analysis, you seem to be opposed to the latter

[dusk wind]

You don't need to pick up rosen then. Try more Algebra and stats. Read many different topics that interest you. Tbh imo many discrete math books suck because they are too dry or not interesting enough.

[untold laurel]

I wouldn't know haha

[untold laurel]

Any algebra/statistics books you'd recommend, then?

[dusk wind]

I'll send you a list later

[pliant stream]

depends...

i think there are many statistics books written for people with minimal math background

[untold laurel]

depends on what you classify as minimal

[pliant stream]

perhaps check out regression and other stories by gelman,hill

havent read it personally, but it is about applied stats and I don't think it really discusses math much

[untold laurel]

not suuuure if i'll like it since im looking for something that's math oriented but I'll take a look anyway

[pliant stream]

sure, but you haven't said anything about your math background

in particular, if you don't know any calculus and linear algebra, you basically won't be able to learn stats

i think you might be able to read the first few pages of grimmett and stirzaker, or feller volume 1, however

[untold laurel]

I know some calc, but what's linear algebra exactly, what does it encompass? fyi i'm not from an english speaking country so some things are named/classified different

[pliant stream]

linear algebra is called linear algebra everywhere...as far as i know

but you won't need it until you start doing multivariate probability/statistics (or markov chains)

so you can learn it as you go... but statistics is incredibly useless and boring if you only work in one/two dimensions

[untold laurel]

haha its just that google translate pretty much translates into "algebra of lines"

is it like stuff with vectors basically? from what i understand. i've also got basic knowledge of those, though im not too sure if they're very different in three dimensions rather than just two

[pliant stream]

uh...no

https://www.youtube.com/watch?v=7UJ4CFRGd-U&list=PL221E2BBF13BECF6C

[untold laurel]

basically from just a quick glance of the wikipedia page i can say that im familiar with vector spaces, matrices, and linear systems but not much else

[pliant stream]

in any case, you can learn linear algebra as you learn probabiliy/stats

but i recocmmend grimmett and stirzaker

[untold laurel]

alright ill check those two authors out

are you specifically talking about "Probability and Random Processes: Fourth Edition"?

[pliant stream]

i've never read 4e, i own 3e but i believe the only difference is that 4e has a few hundred added exercises

[untold laurel]

since both authors

[pliant stream]

(so if you prefer a print copy, just get the third edition as it will be cheaper)

[untold laurel]

alright thank you

[fiery hollow]

Are there any good contest preparation books?

[dusk wind]

I don't know what your level of math is, so: Algebra http://wallace.ccfaculty.org/book/book.html alternative https://saylordotorg.github.io/text_intermediate-algebra/ https://www.opentextbookstore.com/precalc Trig https://mecmath.net/trig Stats https://www.stat110.net/ or https://statsthinking21.github.io/statsthinking21-core-site/ as mentioned there are plenty of good stats books at all levels, but you're only worried about their application so any general book or course will do. Strong algebra skills will help in all areas of math but especially in stats, which is very useful. If you still want to look at discrete math, try https://discrete.openmathbooks.org/dmoi3.html, https://www.amazon.com/Discrete-Mathematics-Computing-Peter-Grossman/dp/0230216110 (light), or https://www.amazon.com/Discrete-Mathematics-Applications-Ali-Grami-ebook/dp/B09ZKXCZHL (newer)

after that you can study abstract algebra, booleans, logic, etc

[trail hemlock]

how do u know so many books 😭 holy

[stuck zephyr]

you do research

[marsh ingot]

You get used to it

[oak sable]

My upcoming semester is going to be using Thomas' Calculus. I'm guessing this is the typical engineering kind of textbook? Anyone have experience with it?

I'd like to have an analysis book to go along with it, and I've been looking at several. I know the major ones (Spivak, Apostol), but I also have been looking at Lang's First Course in Calculus. I really liked his book Basic Mathematics and the style works really well with me. Is it a rigorous analysis-type book? I don't imagine he'd be writing applied maths, engineering-type books, but I don't know much about it.

How does it compare to Spivak/Apostol?

Edit: Also, I'm going to be a freshman. I have no issue affording the current edition of Thomas' Calculus, but I also worked in a bookstore and know new editions can just be complete scams. Would I find myself unable to follow along with classwork (problem sets, etc.) if I picked up the 13th edition instead of 14th/15th? Maybe not something you can actually answer. Just based on your experience in college.

[dusk wind]

its called reading lol

[remote sparrow]

lang is intentionally not designed to be analysis-lite

he's written a real analysis book though called Undergraduate Analysis

[cold elbow]

do people just have specific lists for math book links lol

[molten mason]

Oh weird, I don't have a "Before Calculus" chapter in my book. The first 160 pages are effectively that though, it teaches y=mx+b, basic trig, limits, range and domain of functions, polynomials, etc.

The first page about derivatives isn't until page 161

[molten mason]

And I feel like it introduces those topics a lot more formally than a regular highschool class, or even a college pre-calc class, at least in my version, but I feel that's normal in older version math books.

[velvet glacier]

The limits chapter comes first in my edition

After like 90pages

And the trigonometry recap comes at the complete end of the book somehow

But it does have a lot of integrals and derivatives in the first page to quickly check if you need them

Like a table of different integrals, derivatives and their solutions

I don't have experience in later calculus and it seems like Arabic to me

[molten mason]

Yup, Limits are page 106 for me.

The table of derivatives/integrals at the beginning and the table/appendix of trig review at the end I feel are pretty standard for math textbooks

Not those topics in particular, but whatever the textbook is teaching

[velvet glacier]

But I would need a trig recap before starting calculus

Why would they put it at the end

[deft lark]

Putting prerequisite/review topics in the appendix is typical for textbooks

[molten mason]

@velvet glacier Well knowledge of trigonometry is expected as a prerequisite before calculus, being a calculus textbook and not a trig textbook then this knowledge is assumed. The reference tables and appendices are supposed to be reference sheets to quickly flip to in case you forgot a specific formula, such as the double-angle formulas. My textbook is pre-internet, so this is not something that could have been quickly googled at the time.

Depending on the level of the class and its intended audience, many math textbooks have something similar at the beginning, end, or both. Often times on the inside of the hard-covers themselves. In addition the first chapter of any textbook is supposed to be a refresher of knowledge needed for the course, for example, it could be assumed that you took a pre-Calculus course, went on a 2-3 month summer vacation, then are starting Calc I in the Fall semester. So the first chapter is to help refresh your memory, it's not supposed to be considered a full course in itself.

Before you start Calculus you should have a decent knowledge of elementary algebra, geometry, and trigonometry. Those are taught individually throughout middle and high school in the US and then are combined into a "College Algebra" and/or "Pre-Calc" course at the college level.

If you need help with Trig, this has been linked a few times in this channel and I think it's a good spot to learn. https://mecmath.net/trig/ You can download the pdf onto your phone or computer and go through it. IMO. chapters 1, 3, and 5 of the trig pdf are expected as assumed knowledge prior to starting Calculus.

In general you'll also notice every single author has their own opinion about what their specific textbook should or should not talk about and what is or is not required to know prior to reading.

[dusk wind]

I do at least, or rather I couldn't find what I was looking for so I ended up having to anyway.
Ended up organizing that 'list' and found correlations in what was available

[dusk wind]

also yea it's good to look for several books on the same topics so you get a broader scope, maybe some authors include or leave things out.
Online the mecmath trig link has been used by other professors, so it's pretty much 'the' general trig book, and it is sufficiently short

[cold elbow]

thats cool

[normal reef]

looking for an introductory problem book in galois theory, with solutions

[hollow shore]

I am looking for an easy to follow, example based ODE book/lecture notes

ping if you know any

[graceful moon]

Boyce has a lot of examples in it, it’s not my favourite book but people seem to like it

[velvet glacier]

yes yes I finished Trig, algebra and geometry in school

But I have a question

How did you manage to learn calculus without internet

[untold laurel]

thank you very much. im already familiar with precalc/trig, so I'll check out the harvard one since it seems really interesting.

[hazy elk]

In Dummit Foote, Lang and Ian Stewart's books, most questions have solutions on stack exchange (probably ppl have made solutions manuals too, but these tend to be not so reliable at times)

I think Stewart's book has solutions at the back too, not sure tho, you'd have to check

[oak sable]

How do you feel it compares to other Calc books? From my understanding, Springer (and Lang in general) tend to write pure maths textbooks. Is there some sort of middle ground between something like Stewart and "analysis-lite" books like Spivak?

I've looked at the toc of all of them, but since I have no formal education in calculus, I don't really know what the differences are.

[magic spade]

The middle ground book is "calculus: a rigorous first course" by velleman

[light nacelle]

Which set theory book do you recommend to start with?

[finite gale]

You shouldn't need to read a set theory book to do analysis or calculus imo

[light nacelle]

And a book for analysis or calculos, i want to read a math book but idk what firts

[vital bane]

"Understanding Analysis" by Steven Abbott

such a good book

[oak sable]

If you don't mind me asking, what's the pedagogical differences in the analysis-type, middle ground (velleman) type, and engineering-type?

I know that an analysis-type will have more proofs, but I assume there's a pretty major difference in the overall layout/what material is actually taught.

[vital bane]

the material is pretty much the same

it's just that analysis is about studying the properties of the real line and real functions

Like it's more about the theoretical nature of these objects

[light nacelle]

And for calculus?

[vital bane]

do you know calculus?

[light nacelle]

No much

[finite gale]

strictly you don't need calc for analysis

[graceful moon]

I think it’s probably better to learn plug and chug style calc then analysis, even though you don’t need calc to do analysis.

It’s more practical because you kinda need calc for just about everything, and I think you probably get a better appreciation of analysis if you know some calc. I’d say read Stewart then take your pick of whatever analysis book you can get, I like Tao but they’re basically all good

[vital bane]

yea most intro analysis books are very good

[light nacelle]

So is better start with calc?

[oak sable]

Interesting. I found that when reading some of the common calc books, I got very frustrated. I was able to do everything, but it felt like magic and I didn't like that feeling. I felt like I couldn't explain anything to someone else if they asked "why." The analysis books seemed to be better for my brain.

I was planning on just getting a more analysis-type book to go with my main calc book.

[vital bane]

yes this is part of why I got into pure math

I want to really understand what's going on under the hood

and not just plug and chug

[oak sable]

Plug and chug made me think I hated math in middle/high school

It wasn't until reading some intro analysis books that I realized that there were answers to the questions I was asking in school

[light nacelle]

I think the same

[graceful moon]

That’s kinda why I think it’s best to at least know the basic rules of integration and differentiation first, it motivates it so much better. I also love pure maths and hate calculation based classes but I do think that works better after you’ve had to learn the calculations (at least for a first course)

[oak sable]

They didn't treat questions like "why do fractions work this way. What does it actually mean to add" as dumb questions. It felt very validating. I knew how to count, but the explanations were that it was just ordained by god and I hated that lol

[finite gale]

you could always start with abbott or some intro calc book and then as you go along do some computational problems from stewart or something

[light nacelle]

I could start with the analysis book you told me about.

[finite gale]

instead of like wasting through stewart lol

[oak sable]

Any of you folk have experience with Thomas' Calc?

Compared to say, Stewart, etc.

[graceful moon]

Strang has a calculus book through openstax that you might like if you’re looking for a mix of calculations and still having an ok basis of analysis, from what I remember there’s an ok mix of the 2 in that book

[finite gale]

there are probably many computational calculus books, it just happens (for some reason) that stewart is the one most people are familiar with

[light nacelle]

I will start with the book "Understanding Analysis" by Steven Abbott

And after that I'll see

Thx for all

[oak sable]

I've been meaning to look at that. I didn't like his linear algebra book, but his calc book might be fun.

[graceful moon]

He has 2, there’s the one he wrote on his own that’s a little older which I’ve never read and there’s the newer one on openstax that I’ve skimmed and seems pretty decent, could be worth taking a look. It’s free so there’s no real reason not to

[molten mason]

By going through Anton's Calculus textbook

[oak sable]

Yep, already downloaded it and looking through it. Free books are always nice 🙂

[vital bane]

most people on the math server*

[remote sparrow]

it's more concise and covers the standard single-variable material

as someone else mentioned, velleman is rigorous, but doesn't try to do analysis

[cinder tundra]

Linear Algebra recommendations for someone who just needs a thorough and fast refresher

[remote sparrow]

the suitability will depend on what you've already learned

[woven skiff]

I've worked/struggled through a reasonable chunk of this book

The key is to really memorise/apply/understand the definitions

Intuition wasn't that helpful

[woven skiff]

https://www.reddit.com/r/physicsmemes/comments/ev8xg3/assume_tears_of_joy/

[cinder tundra]

i've done a european undergrad course on it, read about 1/3 of Gelfand's lectures on linear algebra

i want to refresh my linear algebra for use in discrete geometry and differential geometry

[remote sparrow]

i'm not european, what does a european course in linear algebra cover

[cinder tundra]

it covers gauss-jordan elimination, affine functions, multi-linearity and tensors, eigenvalues, eigenvectors, diagonal matrices, jordan normal form, etc, smith normal form would be included but idt its relevant for what i want. there's probably other stuff i forgot

bilinear forms, inner products, gram-schmidt orthogonalisation process as well

[remote sparrow]

hoffman and kunze or axler

[cinder tundra]

thanks

[gray gazelle]

axler is great

newest edition just released (? I think)

adds a chapter on multilinear algebra

[timber mesa]

oh that's interesting

bro being forced to accept the fact that people need to know determinants

oh also new sections on pseudoinverses and QR/Cholesky factorization

that's cool

[shell geyser]

honestly all the mainstream calculus books cover pretty much all the same things, i personally like thomas' writing style a lot more than stewart, but i think its just personal preference. hard to go wrong with calculus

[gray gazelle]

[sage python]

Did you mean to post that here?

[remote sparrow]

oop

[nocturne marsh]

A book for improving my algebraic manipulations skills. Anyone knows one?

Cuz like most of the time, I know how to solve the problem, but an algebra error messes it all up

[vital bane]

literally any high school algebra book

[steel cloud]

I want to start field theory so can someone tell me which book is good for start

[sudden kindle]

Do u know basic ring theory

Like polynomial rings, integral domains, UFDs, PIDs, EDs, gauss's lemma, eisenstein criteria

[fallow cypress]

If you're okay with websites, KhanAcademy is also good for this

[fallow cypress]

I'm fond of Dummit-Foote

[sudden kindle]

I was gonna recomend that but the chapter on field theory does assume ring theory

[fallow cypress]

Yeah that's true. I think it only assumes pretty basic stuff though. Probably linear algebra knowledge is more important.

[sudden kindle]

I taught from D&F field theory and galois theory chapters to a class that didn't know ring theory, only group theory

Kinda regret it now

I feel like I couldn't communicate to them the beauty of galois theory :(

[steel cloud]

For field theory module theory necessary?

[sudden kindle]

Not really

[steel cloud]

Okay

And what about Fragile?

[sudden kindle]

[crimson leaf]

A lot of course go straight from polynomial rings to fields and circle back to modules if they have time

[remote sparrow]

any well-reviewed algebra workbook that stands out to you

[steel cloud]

Okay

[molten mason]

Basic Mathematics by Lang, literally the entire book

[vital bane]

wanna get good at algebra? then try "Algebra" by Lang

[hazy elk]

wanna get really good at algebra? then try "Introduction to commutative algebra" by Atiyah

[steel cloud]

Undergraduate Algebra by Lang review?

[glossy depot]

Advanced Modern Algebra by Rotman

[glossy depot]

It's generally ok, surely not what I would choose

[nimble glade]

yooooooooo

im in class 8th

suggest me book pls

[vital bane]

for what?

[manic cairn]

It’s a great way both to learn how to do algebra, and how to write proofs

[steel cloud]

Okay

[torn finch]

Anyone got any discrete math book recommendations? 🙂

[vital bane]

Concrete Mathematics by Donald Knuth, Oren Patashnik, and Ronald Graham

I haven't read the book entirely

I've only skimmed it now and then (never got the time to sit down and go through it)

but it seems like a good book

[silent dome]

Hello

Can anyone recommend a book

For

IMO

[pliant wadi]

Okay, any idea why is J. D. Baum's Book on Topology not that popular?

John D. Baum's Elements of Point set topology

[pliant wadi]

I am talking about this one

[torn finch]

That’s awesome! I’ll take a look into it now thanks 🙂

[fleet bramble]

Are there any books related with or just containing sth about tensor of functions in functional analysis and its applications in operator theory?

[magic spade]

https://link.springer.com/book/10.1007/978-3-031-34093-2

[steel cloud]

Suggestion for Linear algebra

[fleet bramble]

oh tysm i'll check that

[remote sparrow]

never heard of it

maybe that's why it's not popular

[gray gazelle]

any thoughts on the book called 3000 solved linear algebra problems?

i am looking for a problem book for linear algebra, i came accross this one and it seems like its good but can i have any feedback on it before i consider purchasing?

[steel cloud]

What topic include?

[gray gazelle]

in linear?

i am taking an elementary linear algebra course

the topic i must learn are:

Matrices, determinants, vectors, vector spaces, and geometry with lines and planes (distances etc, basically geometry)

vectorial geometry

[steel cloud]

Why you need that book for problems or concepts?

[gray gazelle]

for problems

the problems in my textbook are too easy

[steel cloud]

What your textbook?

[gray gazelle]

Linear Algebra by Howard Anton 10th edition applications version

apparently it is popular

that is the one i use

for my course

the problems are too easy. None of them are challenging

[steel cloud]

What about Paul Halmos finite dimensional vector

[gray gazelle]

what does that do?

[steel cloud]

Good book for linear Algebra

Or Axler?

[gray gazelle]

ye but i am taking elementary linear algebra

not undergrad level

@steel cloud this is the book: https://www.amazon.ca/000-Solved-Problems-Linear-Algebra/dp/0070380236/ref=asc_df_0070380236/?tag=googleshopc0c-20&linkCode=df0&hvadid=292907674762&hvpos=&hvnetw=g&hvrand=8633575672759834978&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9000417&hvtargid=pla-434394963065&psc=1&mcid=bc0ecde4be8232448e660eee19eb84d4

apparently it is good

it solves problems. It's not a theory thing. It's a supplementary book for extra problems

and it covers the topics i am doing

Vector Spaces, Vectorial geometry, Matrices and Determinants

[steel cloud]

Okay

[gray gazelle]

is it good?

[gray gazelle]

id use axler or other stuff but the thing is that it is too advanced for the course

[steel cloud]

Yeah

[steel cloud]

May be I do not know

[gray gazelle]

ok

[fair pawn]

guys

is there any book that can help me prepare for putnam for the next 12 weeks

pls help me cos i might just unalive myself atp

[molten mason]

I mean.. there's 142 reviews to read through

[gray gazelle]

yeah true. But, maybe the problems are too simple

i looked at the table of contents and i just cover 4 of them

1 of which is not even there

geometry is not part of linear algebra. I don't understand why we do anayltic geometry with lines and planes in linear it makes no sense

like, what my school is doing is so dumb. Matrix algebra, determinants are supposed to be so easy, but they literally give the hardest and longest problems to do it's crazy. And we do vectors but it's not even the linear algebra style vectors it's geometry, not vectors. Lines and planes is not linear algebra, it's geometry and my book does not even cover it. I need to find a book on lines and planes and all the possible problems I can get.

the secret to doing good in any STEM subject is very very simple: do as many problems as possible and those problems needs to be very, very difficult (intermediate-difficult). Teachers do it on purpose to give little practice problems because they know that everyone will do if they give like thousands of problems. My textbook only has easy computational questions (unnacceptable tbh). Very little thinking involved, and the fact that i practice only easy problems shows up on the tests!

[sand crescent]

Is there a short and concise resource for understanding volume (integration) of the orthogonal group?

I need a basic understanding for large deviations

[compact copper]

was there a mod ping in here?

[marsh ingot]

Think so, why?

[lean pagoda]

Someone advertised their Discord server but it was taken care of already

[compact copper]

If there was a mod ping, please do not delete them

Even after they have been resolved

It makes it hard for us to determine what is going on

[lean pagoda]

Ah ok, I deleted my mod ping to keep the channel clean. I did not know that it doesn't get rid of the notification, that's annoying

[rustic grove]

This should more than challenge you :)https://www.google.co.uk/books/edition/Linear_Algebra_Problem_Book/SY-_COzW4toC?hl=en&gbpv=0

[gray gazelle]

yeah i heardabout that book. It's good apparently

[rustic grove]

I haven't used it personally, I just use axler and (insel and spence) + some stuff from A algebra books, but ye it's supposedly good

[gray gazelle]

yeah but for me im not doing undergrad linear. It's elementary linear algebra

the problems are easy until I get to the geometry part with lines and planes and distances

which is not in any linear algebra book 🤣

[rustic grove]

What have you done so far?

[gray gazelle]

Did matrices (addition, subtraction , inverses, elementary matrices) determinants, and euclidean vector spaces

i use anton's textbook

[rustic grove]

Well, in that case you have barely scratched the surface and those topics are just easy in general. See how you find some of the later sections of the book. It is a good book that for an introduction.

[gray gazelle]

it's not even a linear algebra course tbh it's more of a geometry course i am taking

with the lines and planes

[rustic grove]

Try Algebra and Geometry by Alan Beardon

[gray gazelle]

ok i will look at tthat

that's the part i struggle with the most

[heady ember]

Look in pinned

[vital bane]

Like intro analysis, almost any linear algebra book is very good

just pick one and get started

[fierce hedge]

Based advice

[gray gazelle]

What is the best book for algebra from basics to complex?

[crimson leaf]

What do you mean by basics and complex

[gray gazelle]

Like from the beginning of algebra like x and then you know complex algebra

[fleet solstice]

When I get a math textbook, how should I read it, to get the best understanding of the chapters?

[crimson leaf]

Probably just do Khan academy for that stuff

[vital bane]

dont read it like a novel, do as many exercises/problems in that book as possible and remember the fact that it's okay to get stuck on certain ideas/problems for a while

[dusk wind]

Read 100 of its pages

Or look at the ToC to find another book

If you get stuck it means the author sucks

There is no reason to get stuck when a youtube clip can explain better

[fleet solstice]

Like do the exercises before reading?

[fleet solstice]

ToC?

[vital bane]

Lol no why would you do that?

[vital bane]

he's trolling lol

[dusk wind]

The table of contents

Actually there are some people that have success with just the exercises

[fleet solstice]

Idk, cause you said you do the exercises, but how do I read the book, before doing the exercises?

[fleet solstice]

Ohh I see I see

[dusk wind]

Prodigies I suppose

Anyway if a books ToC isn't cutting it, maybe another book will

[vital bane]

just read it

[dusk wind]

Some people don't actually read the ToC then get mad when it doesn't have what they want

[vital bane]

they also dont read the preface and get mad when the book requires more prerequisites

[dusk wind]

Nooooo

[fleet solstice]

Bruv

[dusk wind]

Make your own personal library

[fleet solstice]

Alr good you got the msg before I deleted it

I was gon reply to it, but I forgot to click the reply button 💀

And I accidentally copied another msg

[fleet solstice]

But ye, that's what I'm gon start doing

I've been watching this guy that gives suggestions of books to read, depending on what lvl you are in mathematics.

So I might start from there

[dusk wind]

You mean math sorcerer?

[fleet solstice]

💀💀💀

Yeah him

[dusk wind]

If it's him his recommendations are usually clickbait

[fleet solstice]

Wrd

[dusk wind]

But sometimes interesting

[fleet solstice]

Rly?

😭😭

The vid I watch was his most popular one

[dusk wind]

Yea he has recommended decent books but usually clickbait

We have way better books now than those old classics

[fleet solstice]

Dang, I jus ordered a book that he recommended for College Algebra

The authors name is Blitzer

[dusk wind]

That one is good iirc

[fleet solstice]

Oh yeah I'm kinda trying to avoid older books

But im pretty sure he covers a lot of modern books

[wraith sandal]

Hey, is spivak's calculus great if i know basic proofs but have a little or no background on calc?

[dusk wind]

I only really look for open source books so others can contribute to it and make new 'versions' on their own

The notes are also very helpful

[fleet solstice]

I'm also tryma get another College Algebra book, so if you have any other recommendations lmk pls 🙏🙏

[dusk wind]

Only the free ones I posted

[fleet solstice]

Ohhh I see, where did you post them?

[dusk wind]

Here, somewhere.

[fleet solstice]

Oh wait, on your bio?

[dusk wind]

No

[fleet solstice]

Oh

[fleet solstice]

This?

[dusk wind]

Yea I like that one

Best part is that author has a few other books too

On the various 'college algebra'

Besides that it's probably best to use khan academy or whatever book your school is using for algebra

[fleet solstice]

All the links are from the same author?

[dusk wind]

No. Just that 1

You can check their domain

[fleet solstice]

We don't rly use textbooks until IB Math AA Yr 1, which I should be taking next yr

But im tryna get ahead, which is why I wanna start reading books

[dusk wind]

Maybe exercises and short examples would be fine for you then

[fleet solstice]

And also Mathematics has intrest me a lot, during the last 3 yrs of hs, so I thought this would be a good opportunity, to read more on math.

[dusk wind]

Khan academy and some short book when you get stuck is probably fine

[fleet solstice]

Ohh I see.

[dusk wind]

But most algebra books are very average and not worth reading imo

[fleet solstice]

How so?

[dusk wind]

It will probably mostly be a reintroduction on stuff you already know intuitively

[fleet solstice]

Oh yeah

[dusk wind]

Some are dry or don't have enough detail

[fleet solstice]

Some of the algebra books I've checked out, alrdy had stuff I've learned

I could also just use the syllabus that our teacher gave us, which shows everything we're gon learn throughout the yr

[dusk wind]

Yea that's a good move

[fleet solstice]

Alr then, thank you for the help 🙏🙏

[gray gazelle]

Yea I know lol

[fleet solstice]

I'll jus do this then, and then afterwards read a couple books on Precalc, if that's worth it

[dusk wind]

More algebra 2 and trig or just precalc by itself

[molten mason]

Basic Mathematics by Lang is an old classic but still my favorite for that level of math lol

[dusk wind]

You could probably do some precalc for fun tho

[fleet solstice]

Oh so like, learn more abt the 2 topics?

[dusk wind]

Yea it's good to practice functions

[gray gazelle]

what's like, the definitive topology textbook?

and what kind of prerequisites does it have?

point set, specifically

[vital bane]

there's no definitive textbook for anything

but usually people recommend "topology" by munkres

[graceful moon]

Technically all you really need is like a basic knowledge of set theory, you absolutely can take topology without any real pre reqs and apparently a lot of people do. But there’s definitely more to get from topology after you’ve done some real analysis

[gray gazelle]

yeah I figured, I'm planning to independently study some topology in parallel to real analysis, which should be good

[heady ember]

A lotta people don't particularly like munkres

Apparently it has too much stuff that's unimportant

[gray gazelle]

I couldn't help but notice the 70 page long introduction to set theory and logic

and I usually consider the preliminary set theory section of any undergrad book to be a chore

[trim depot]

could anyone suggest me a book(s) for studying topics including but not limited to functions, complex numbers, matrices and determinants, vector, probability, trigonometry etc and would contain tons of problems(not too easy like plugging values or extremely hard or advanced but somewhere in the middle) to solve?

[graceful moon]

Take a look for an SQA advanced higher maths or further maths A level problem book they should cover all of that at a kinda in the middle level

They’re the like advanced maths courses in UK high schools, they cover introductory linear algebra, complex numbers, proofs etc so it should be pretty similar to what you’re after

[quaint bramble]

I just finished reading Elementary Number Theory by David M. Burton and I want to continue learning about number theory, what topics should I learn now? and what books should i read?

[trim depot]

could you please name some books?

[novel hound]

You can look at Niven Zuckerman Montgomery (still elementary number theory but covers more than Burton, and deeper) or Ireland, Rosen (Classical intro to Modern Number Theory) which requires some Abstract Algebra. Or, you can get into Algebraic Number Theory proper and/or Analytic Number Theory. Also, Borcherds has a youtube playlist off of Niven.

[quaint bramble]

okay, thanks

[proud gazelle]

anyone read: introduction to real analysis bartle and sherbert ?

[molten mason]

I don't have much to say, I only recently started it, but it was recommended a lot on this server.

[hushed garnet]

is concrete mathematics good book for competitive coding?

[orchid sand]

Guys I'm in high school, what r the best books that can make me skip to University level maths📈

[finite gale]

"Skip to"?

[lime vessel]

Study all of your hs curriculum, learn sets and proofs and logic, read Evan Chen's napkin (for brief overview of topics)

Meanwhile continuously get exposure (e.g. this server)

[marsh ingot]

Books about vectorial measures?

[karmic tangle]

Hello, could someone please help me with choosing an introductory book on Analysis?

[ocean mulch]

Rudin?

[karmic tangle]

noooo

[ocean mulch]

But what kind of Analysis first?

[karmic tangle]

sec I will write out more details

[ocean mulch]

you're not the only one, I hate Rudin myself

[karmic tangle]

I've gone through Calculus a few times, first a bit in hs and then a one-semester course in uni (twice lol) where we did one-variable and then two-variable (partial derivatives, integration, some polar coordinates and extrema) and a bit of three-variable integration I guess? then sequences and convergence thereof and some differential equations

[graceful moon]

I quite like Tao, basically all introductory analysis books are good though so just read a chapter of one and see if you like the style

[karmic tangle]

it was super cramped in just one semester and I slacked off hard, so even though I really enjoyed it much my knowledge is still incomplete and spotty (especially the series convergence stuff and diffeqs and in general I guess the computational part lol)

so now I'm not sure where to go next

got Spivak's Calculus from the library and was considering doing that then Analysis on Manifolds by Munkres for the "multivariable part"?

[karmic tangle]

would like to into actual analysis and topology after the 2 books

[ocean mulch]

wdym actual analysis?

[karmic tangle]

my sister brought it home from the library one day and I had a look at the first few pages and knew I didn't like it lol

[ocean mulch]

with measure theory? without measure theory?

multivariable? real? complex?

[ocean mulch]

Yeahhhh, I didn't like Tao either, you're not alone

[karmic tangle]

I'd like to have enough of an elementary analysis base so as to be able to read intro books on all of those

[karmic tangle]

aaah wait wrong message lol

[ocean mulch]

ohhhhhh

[karmic tangle]

meant Rudin

[karmic tangle]

I will take a look thanks, the first reply was meant to go to Ruding

[ocean mulch]

I recommend Princeton's Lectures in Analysis series. It's 4 books, each gives a thorough but quite brief intro into various aspects of Analysis

I like it better than Rudin or any classical textbooks in Analysis

[karmic tangle]

those textbooks seem like the kind I'd be going for after reading my first 1 or 2 books on analysis no?

[ocean mulch]

From there, once you get some grip of it, you can ask for smth more precise, then I can give something more in-depth

[ocean mulch]

It's completely elementary, dw

do read it in sequence tho

[magic moth]

my current besties are apostol and rudin

tom apostol calculus when i get butthurt from rudin

[ocean mulch]

Wait, no, I'm stupid

There's nothing elementary about this

Uhm..., right, gimme a sec and I'll try to find something

[karmic tangle]

I was getting a bit spooked imagining myself reading a fourier analysis book at this point

[karmic tangle]

did you read any other analysis books before that or not?

[magic moth]

bartle and sherbert introduction to real analysis

[ocean mulch]

maybe Cummings?

Real Analysis: A Long-Form Mathematics Textbook

I remember someone said smth about it

[karmic tangle]

oh lol

[karmic tangle]

I was just about to link this and ask about it

it's very cheap also

[ocean mulch]

All math books are free if you know where to look for it

[karmic tangle]

oh I know but I want it in physical book form

[ocean mulch]

I realised I never actually used books for Real Analysis

[karmic tangle]

did you just go by lectures or

[karmic tangle]

will take a look too thanks

[ocean mulch]

yes, and follow the lecture notes

One tip: copy out the lecture notes by hand

you'll find it tedious, but it pays off very quickly

[karmic tangle]

hmm I guess I could do that

[ocean mulch]

especially if you're not familiar with studying math at UG level

[karmic tangle]

they seemed rather dry

like motivation-wise I guess?

[ocean mulch]

they get interesting once you get the foundation right

[dusk wind]

I cant make it past the first page of a math book

[karmic tangle]

I had 3 years in cs math which is where we had the super rushed calculus course and that's it regarding "analysis"

[ocean mulch]

it's like playing chess. A noob would find watching a 5-hour match very dry, but a chess enthusiast would find it very interesting

[dusk wind]

why would a chess match be 5 hours

[ocean mulch]

nahh, that's fast-food math courses for cs majors who need some math, need to fulfil math course requirements, but hate math

real math courses for math majors can be very interesting

[dusk wind]

'real math'

[ocean mulch]

so none of computational linear algebra nonsense

[dusk wind]

do you need to be a math major to do real math

[ocean mulch]

No, but you do need to hate yourself a bit

[dusk wind]

that criteria is very low then

100 pages a day seems accurate

[ocean mulch]

World Chess Championship 2021, Carlsen v Nepomniachtchi, Game 6

The game was played in 7 hours and 45 minutes, finishing after midnight local time, to take Carlsen to a 3½–2½ lead in the best-of-14-game match.

[dusk wind]

someone must have been stalling

[oak sable]

Classical matches are incredibly long. Many famous matches lasted days. Stalling isn't really a thing that makes sense in classical chess.

[gray jungle]

even tame classical games can easily cross 2 hours unless a draw is forced early , there is so much calculation required at critical moves

[heady ember]

Schroder or Abbott.

[gray gazelle]

is Foundations Of Mathematics: Algebra, Geometry, Trigonometry And Calculus by Phillip Brown a good book for learning about mathematics at a beginner level? if not, does anyone know any better book recommendations?

i’m not trying to rush through anything necessarily

i also hear of the book Basic Mathematics by Serge Lang

[heady ember]

#book-recommendations message
#book-recommendations message

[gray gazelle]

basically looking for a book about basic mathematics yet passed Pre-Algebra

[dusk wind]

Tao seems pretty sane from his notes

I'm sure he's read more than 100 pages

[gray gazelle]

actually is AOPS: Intermediate Algebra good?

im talking from a highschool perspective

i just want to lay the foundation before diversifying my palette of mathematics

but I also want to make sure I have the right tools for school in general

I know aops is generally used for competitions

but i wonder if it can also help with a deeper thinking in mathematics

so yea

[dim sierra]

I think it’d be good

AoPS books are pretty good

[trail hemlock]

if it helps, the way they teach is building intuition and deriving results rather than memorizing, before applying. its a bit "overkill" for Alg1 and Alg2 at the HS level (in terms of getting an "A"), but its really great at building intuition

[gray gazelle]

yeah that’s what I love

i hate when they just give a fact and no proof or applications

i just want to know which book is best

AOPS: intro to algebra is 6-9 grade

so would intermediate algebra be overall good?

for 9-12

[oak sable]

I imagine I'm just missing it, but I can't seem to find English-translated works of Euler. At least, none available online. I've found one translation of Letters to a German Princess, but it uses the archaic "s" character which makes it very hard to read. The only other one I've found translated is Elementary Mathematics.

I keep reading of big translation projects that have gone on, but no actual pdfs of anything.

I'd specifically like to read Letters to a German Princess, but I can't find a modern format.

[oak sable]

I don't think it's necessarily overkill. Lang wrote a 500 page book on high school algebra and treated it with a lot of respect. Euler also wrote a long book called Elements of Algebra. There's a version of this book that's over 600 pages because contributions were also made by Lagrange. Lagrange looked at Elements of Algebra, which is literally just high school algebra, and thought "this needs more."

The reality is that algebra isn't obvious. If it was, we would have had it much sooner. The Greeks were messing around with mathematics very seriously for 1400 years before Al-Jabr comes about. (Yes, there were bits of algebra scattered throughout history, but Al-Jabr is the first true, formal attempt at algebra.)

I think there's two kinds of people who say that high school algebra is easy (I'm not saying that you said it's easy, but just in general): pure mathematicians who have studied much harder things, so they forgot the initial barrier; and the second is people who are incredibly uncurious and never once asked the question "but why" during their math classes, and were happy to do premade algorithms without understanding how those algorithms got there.

[trail hemlock]

i agree, I meant "overkill" as getting an A in the class, but i def agree with this

[oak sable]

But maybe that's off-topic. I've just seen a lot of people treating high school algebra as simple. It's simple compared to Algebraic Topology, but it's not simple compared to 50,000 BC humans counting apples so they don't accidentally starve.

I've heard so, so many professors say "my students are great at the calculus, they just suck at the algebra."

I'm glad books like Basic Mathematics exist.

[oak sable]

And yeah, I figured that's what you meant. I had just seen some other comments about this recently and it made me remember it. Definitely overkill in terms of getting an a.

[trail hemlock]

Calc I and II, to me, is just a bunch oif really interesting observations and algebra haha

[dusk wind]

thats a hot take, writing your own stuff is best

ofc you'll be able to understand what you wrote over what some madman scrawled onto a tome

it depends on how intuitive the math is and how it's taught, you don't necessarily need to be taught algebra, cause it's intuitive, and thats what makes it easy

[oak sable]

Were the mathematicians of Ancient Greece just really dumb?

[dusk wind]

no

they just didn't 'get' it

[oak sable]

Weird. Would you have?

[dusk wind]

who knows

good thing I didnt exist during that time

[gray gazelle]

Is Euler’s Elements of Algebra a good book for high-school algebra as well? I am not JUST trying to do well in school. As I stated before, I want to also lay the foundation (post pre-algebra).

[oak sable]

I do! You would not have.

Because the greatest mathematicians in existence didn't. And unless you're assuming you were much more clever, you would not have. Because it's not obvious. Counting is pretty obvious, we've had that for as long as we've had recorded history.

Geometry can kinda be obvious. As long as we've had structures, we've had geometry.

Algebra? That took a MINUTE for something you claim is intuitive.

[dusk wind]

alright

[oak sable]

It depends. It's a good book because it's somewhat fun. Elements of Algebra was written during a very pragmatic time, and he wrote the book using lots of very applied examples. For example, he uses currency often. Nothing wrong with this, it's really useful for intuition. But Basic Mathematics by Lang is probably the best book for elementary algebra.

[gray gazelle]

alright thanks

By elementary algebra you mean high school algebra?

[oak sable]

But reading Elements of Algebra alongside it would be both fun and probably useful. It's not like recommending Newton's Principia. Anyone reading Principia to learn Calculus is a masochist. Elements of Algebra is legitimately well-written.

[oak sable]

yes

[gray gazelle]

like ALL OF IT?

mb caps

[gray gazelle]

all of what is needed, that is

evidently you can never know enough

but I heard basic mathematics by lang also had geometry and stuff

[oak sable]

I wouldn't say that Elements of Algebra covers "all" of it. Just because the curriculum is very different now. And it has virtually no problem sets, so it's not good as a primary source.

Basic Mathematics has all of it, though. And you can skip the geometry if you don't care about it.

I would recommend doing it though. One, geometry is still high school math (at least Euclidean geometry). And two, algebra has very obvious applications to geometry and his book treats the geometry with algebra in mind.

[gray gazelle]

i care about all of it lol

welp thanks

recently got a bunch of gift cards for this book store

[oak sable]

No problem. I think the book is $41 on Amazon new.

There is no hardback version, but the paperback version is very well made, imo.

[gray gazelle]

which currency

usd?

[oak sable]

Sorry, usd, yes.

[gray gazelle]

i am assuming

yeah ok

ill check it out

thanks a lot

[oak sable]

But there's also websites online that might have it. I wouldn't recommend going to libgen or others since it's illegal. Definitely don't type in Basic Mathematics free pdf. Don't do it. 🙂

[gray gazelle]

i don’t like to use pirated stuff lol

[oak sable]

Me either 😉

[gray gazelle]

much prefer the physical copies

but might for the elements of algebra

unless

is that like

hmm

i’ll look into

thanks again

[oak sable]

No worries. Good luck.

[wicked thunder]

Yes it's too bad that there isn't some device which can print text on the internet into a physical paper form.

[gray gazelle]

Hello! Please recommend books on English grammar to me. I would like to know what textbooks you use in your country.

[marsh ingot]

Book about advanced measure theory

Please

[vital bane]

Bogachev

[marsh ingot]

You scare me

[vital bane]

I learned english grammar by watching movies and TV shows

[marsh ingot]

Same

[vital bane]

I saw you asking about vector measures (this is from bogachev)

"There exists extensive literature on vector measures which we do not consider..."

[marsh ingot]

Yeah since no one answered me I changed the question

The first volume is the unique about measure theory or there is more?

[marsh ingot]

[vital bane]

I do not know I only know this is the most comprehensive work on measure theory

[pliant wadi]

Any linear algebra resource online that goes from Vector spaces, linear transformation then to Dual spaces, Elementary row operations and canonical forms?

I am looking for lecture notes or something like that

I didn't find anything that did it in that order but fair enough

[sage python]

It can make sense

If you introduce linear transformations as the fundamental idea and then introduce matrices as "Linear transformations in bases"

[steel cloud]

Any book for field theory

[gloomy brook]

Can anyone suggest a book for applied mechanics/engineering mechanics?

[pliant wadi]

That's the order in which my prof did it and I was looking for similar motivation because according to the books I was following I couldn't understand why he did it the way he did.

[pliant wadi]

Yes that's exactly how he did it yes.

But I couldn't find any other book that did all of those topics in that order so I was looking for something like that. The books I found were either missing some topics or the approach was wholly different.

I didn't like how I had to jump from one book to another so I was wondering if it was all present in one place.

In a Linear way.

[ember saffron]

Does anyone know any good books about the fundamentals of math

[heady ember]

FIS

literally does all those in the exact order you mentioned

Well, there's stuff in between ofc

e.g. canonical forms is the last chapter

[pliant wadi]

Ooh I'd check it out.

Thanks

[heady ember]

np

Its the book I'm using for LA

Dami has a review pinned here too

[steel cloud]

FIS?

[lime vessel]

Friedberg Insel Spence

[smoky zephyr]

friedberg insel stephen

darn

wait how did amazon show me stephen

[lime vessel]

Stephen Friedberg

[smoky zephyr]

oh

[vital bane]

steven spielberg

[steel cloud]

Anyone read Mac lane book?

[turbid mural]

any book recommendations for Representation theory

[foggy relic]

towards what

[whole cloud]

Is higher algebra by hall and knight good for calculus practice

[gray gazelle]

Hi there folks.

[stuck zephyr]

#discussion or #serious-discussion

[molten mason]

I have that book, 5th edition. +1 to recommendation

[oak sable]

Literally the entire point of this channel is for book recommendations. Basically every question could be answered by "did you try google." People ask questions here because the answers have personal experience with the books or specific math knowledge.

[gray gazelle]

that's an old and outdated book. don't bother with that one.

[whole cloud]

What should I use then

[gray gazelle]

https://courseware.cemc.uwaterloo.ca/11

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

[oak sable]

Is Essential Topology by Crossley any good? It says it's "within reach of a 2nd year undergrad." Usually you don't see topology until 3rd or 4th year. Is it lacking in any way?

Not really sure what the prereqs for topology are in general.

[wraith sandal]

hello, is spivak calc a good book if i know basic proofs but little or no background with single variable calc?

[finite gale]

It should be fine

Though you may want to try doing it along with some computational problems from Stewart or something

[wraith sandal]

But is it possible to learn calculus from spivak and then do computational problems in stewart?

[oak sable]

Could you explain more? Could interpret that question a few different ways. Do you mean set theory, pure maths courses like number theory/algebra, or elementary and high school math?

[dusk wind]

'fundementals of math'

suddenly attacked by a mysterious book coined 'abstract'

ah yes, this is what they taught us in high school

[molten mason]

Yes, there's tons of problems in Spivak, the book is just a little more proof based and has harder questions while Stewart eases into it more. Either is fine but it depends which is easier for you

[molten mason]

Great book, I have it and use it from time to time to refresh or as a reference, I recommend it to everyone. It's $41 USD on Amazon, and in general many math books can be found online in .pdf version legally, not every textbook online is pirated/illegal.

[gray gazelle]

paper getting expensive these days

lol

also uhh

does anyone know any good books about geometry

like

hs geometry again

i heard there was a good one

euclid something

but i forgor so if someoe know tell me pls thx

[dusk wind]

man

our math overlords would be ashamed, 2024 and can't even print free information

maybe the reason math wasn't so intuitive is cause books were too busy being buried and burned

you're telling me I can hold an entire library in my hand?

[molten mason]

My favorite thing is when the author of a textbook has a link to the PDF for free to download

Like on their personal website or whatever

[wraith sandal]

Thanks

[gray gazelle]

i don’t do it for religious purposes

perfect like this

and paper is getting more expensive

and, I have gift cards i got for my birthday at a book store and i wanna spend them (nothing else to do with them imo since there’s like barely any good math books there)

[gray gazelle]

wdym legally? like, published straight from the author?

or like authorized bu the author

[molten mason]

Both

[molten mason]

Like the print version of Linear Algebra Done Right is $50 USD on Amazon

The author, Axler, has the book and his website as free to the world in .pdf

In fact, the pdf of the newest edition is already on his website, but it won't even be available in print until next month

[gray gazelle]

euclidean geometry in mathematical olympiads by evan chen

is that one good

[gray gazelle]

i see

[molten mason]

There's gray zones, The University of Lakki Marwat has the Basic Mathematics pdf on their website, it's up to you personally if you consider that okay or not to download.

[gray gazelle]

i mean, i know

i’ll probably buy the physical copy cause

hey

i guess im helping out the author

[molten mason]

He died in 2005, I actually have no idea where the money goes

He wrote a couple dozen books in math, pretty much covering every topic of undergrad

[kind bloom]

Hey

I am interested in math I want to learn more

I’m a senior in highschool

And to be honest I may be missing some math basics just due to circumstances

I’m really just any average person when it comes to math

I was wondering what are some good entry-level books that are engaging

Maybe something that covers some of the fundamentals, that introduces new things and whatnot

[viral crypt]

I wish I was as proactive as you when I was in highschool, do you know integrals, derivatives etc well?

[molten mason]

Basic Mathematics by Lang

[kind bloom]

Me?

[viral crypt]

yes

[kind bloom]

Thanks I’ll check it out

[kind bloom]

To be all honest I know the names but I don’t remember what it’s all about if I search it up it will come back to me

I’m a special case, I have the interest and the learning capabilities yet I lack the knowledge lol

Math only just became interesting to me a couple months ago

[molten mason]

You would know the words if you knew it well, It's Calculus I, III, and III

[kind bloom]

Yea I don’t know it well

[viral crypt]

wait so you don't know what integrals are? I need to get this straingt

[kind bloom]

Nope I don’t understand what they are

[molten mason]

https://tenor.com/view/maths-gif-26521570

[kind bloom]

See look

I’m sure I do know what an integral is

I just don’t pay attention

I just go through the motions in class

[viral crypt]

Ok, I would strongly advise you to do the problems in "Problem-solving strategies" by Engel, cover to cover, it's somewhat of a math olympiad training book but actually the problems often are versions of real theorems that you will rediscover in your later mathematical career (if you intend to pursue one), with the advantage that nearly all the problems are solvable by basic high school math.

[kind bloom]

This is a habit I’m stopping though

[kind bloom]

I’ll check this out

Does basic math by lang cover this?

[viral crypt]

you'll find it for free with a google search

[molten mason]

High school normally goes something like

Algebra 1 -> Geometry/Trig -> Algebra 2 -> Pre Calc -> Calculus

You would have done an entire semester on derivatives before doing integrals. It's something you definitely would have remembered lol It's a core memory even for people who skip class.

Basic Mathematics covers 5th grade to Pre-Calc all in a few hundred pages

[kind bloom]

Yea I searched it up I remember integrals now

[viral crypt]

haha those fucking things (derivatives) you learn by osmosis

[kind bloom]

I still don’t remember how to do them so I’m gonna need to put in a little work

[kind bloom]

Only reason I survived math

[molten mason]

I still recommend going through that book, at least skimming through it.

Then going through chapters 1, 3, and 5 of the pdf on this website https://mecmath.net/trig/

Most people don't fail Calc because of derivatives and integrals, they fail it because of algebra and trig mistakes

[gray gazelle]

sorry to bother u, just wanna know what portion of Lang’s “Basic Mathematics” covers on this scale

asking you of all people since you read snd havr the book

[kind bloom]

Do they not cover it?

[gray gazelle]

oh lol nvm

just read ur message

so its basic arothmetic (assuming properties) to precalc

so i can do calculus after?!?!??! zamn!!!

[viral crypt]

Has someone read "God created the Integers" ? I want to read the book cover to cover, it would be nice if someone can confirm to me that's a good idea before I do it

[molten mason]

Part I - Algebra
Chapter 1 Numbers
Chapters 2 Linear Equations
Chapter 3 Real Numbers
Chapter 4 Quadratic Equations
Interlude Chapter Logic and Set notation

Part II - Geometry
Chapter 5 Distance and Angles
Chapter 6 Isometries
Chapter 7 Area

Part III - More Geometry
Chapter 8 Coordinates
Chapter 9 Operations on Points
Chapter 10 Segmants, Rays, and Lines
Chapter 11 Trigonometry
Chapter 12 Analytic Geometry

Part IV - Miscellaneous
Chapter 13 Functions
Chapter 14 Mappings
Chapter 15 Complex Numbers
Chapter 16 Induction and Summations
Chapter 17 Determinants

I think the only thing it doesn't cover pre-Calc wise is a stats/probability

[kind bloom]

I’m new to studying math and reading math books and whatnot

I’m assuming the books are gonna be dry?

[molten mason]

Lang wrote Basic Mathematics as a pre-calc book, it's expected to take Calculus I after reading the book.

[gray gazelle]

oh i see

[gray gazelle]

does any sort of category in calculus require statistics?

[molten mason]

The only previous knowledge needed for the book are how to use fractions and decimals, which is normally 4th/5th grade math in the US

[gray gazelle]

i know a good statistic book in a library nearby

[molten mason]

rather, Statistics requires Calculus

[gray gazelle]

now thats actually epic

[gray gazelle]

welp

thx for all the hellp

cya

[molten mason]

That's a personal preference

[kind bloom]

I’ll check it out at my school library

Hopefully they have it

[gray gazelle]

Sadness.

just read this

holy moly i have to pay attention to texts

[oak sable]

The main reason is that it was just really difficult. But book burnings didn't help.

[marsh ingot]

Book about algebraic topology?

Basic stuff

[graceful moon]

Hatcher is the usual go to

[marsh ingot]

Thanks for not ignoring me, I will check it now

[vital bane]

@storm harness

I hope you dont mind the ping

[heady ember]

Some records I saved from people's recs (not mine) here:
*Note: Idk anything about AT

1. Bredon
2. https://people.math.wisc.edu/~lmaxim/topbookf.pdf
   (iirc sloth shared the link to this before so it should be fine)
3. Raoul Bott, Loring W, Tu Differential Forms in Algebraic Topology
4. Rotman
5. Tom Dieck AT

(Not in order of how good they are, its just in lexicographical order I think)

[marsh ingot]

Thanks I will check them later

[pine zenith]

Hello, Everyone!
I need this book, please share me pdf if someone has got it already: Precalculus: Functions and Graphs by by Swokowski(obivously as latest version as possible)
Thank you!

[lime vessel]

Try continue with Aluffi

It has bits of cats and hom alg early so going into alg top/alg from might be smoother

[vital bane]

"mathematical analysis" by tom apostol has some stuff on that

Multiple riemann integrals

[mossy shell]

I can get you it later if you havent already

[gray gazelle]

anyone know any good geometry books about euclidean geometry (high-school 9-12)

well

actuslly

its not only euclidean geometry mb

so i guess a wider category is high school geometry

actually

not necessarily a wider

but yeah

does anyone have any good geometry books about euclidean geometry high school geometry (euclidean, analytic, etc.)

[crimson leaf]

For comm algebra the standard is Atiyah Macdonald, for Rings you can check out a first course in rings and ideals by Burton but I have never read so I can't gurantee its good

[nova breach]

I'm curious if something like this exists. I'm looking for a non-technical, relaxing math book, but one that has serious substance. A bit hard to describe. Think of something more in the respect of GEB (minus some of the pretty uninteresting philosophy stuff), Euclid's Elements (to some extent), Flatland, or some of the original Greek/Arabic math books like the original Balancing algebra book.

I would say that Euclid's Elements is the closest to what I mean. It's readable, but still mathematical. It requires too much involvement to be considered relaxing though.

Something I can reread, keep on my nightstand forever. In the same way that a philosophy major might have Meditations, Plato's Republic, etc. on theirs. A Christian has their bible, a Muslim their Qu'ran, a physicist the Feynman Lectures.

In fact, I'd say the Feynman Lectures are very close to what I want. There's real science, real physics, but it's not pop-science. It's not just a history book. It's not sensationalist. It's not "a cute history of pi." It's readable while being serious.

Is there anything in the history of math that might fit?

Sorry for the long ask, but I've been wanting to find something like this for years.

[remote sparrow]

see kiselev's two volumes on geometry and lang's high school geometry book

[woeful ravine]

The Princeton Companion is probably the closest thing to what your asking for in terms of a book that you would keep on your nightstand. If you haven't already read them, I would also recommend looking at Fearless Symmetry and Elliptic Tales by Ash & Avner. If you're familiar with undergraduate abstract algebra and number theory, they are a casual, but still interesting read

[gray gazelle]

Hello, someone here knows any beginners physics books, but with calculus?

[woeful ravine]

Like purely mathematical physics? Or just a physic textbook that uses a lot of math

Because essentially all physics textbooks are going to use a ton of calculus

[gray gazelle]

Hm

I think both options are great

[woeful ravine]

If you want some super introductory stuff, there are a some great youtube videos that go over the physics of basic pendulum motion

where you can learn about newtonian, lagrangian, and hamiltonian approaches

[gray gazelle]

🤔

[woeful ravine]

It doesn't require anything beyond calc 1/2

Otherwise it kind of just sounds like you want a physics textbook

[gray gazelle]

yeah

thx

[pine zenith]

No, I have got the book using tor from darkweb. Thanks by the way.

[hidden fractal]

Do you have any channel recommendations

[woeful ravine]

This (https://youtu.be/0DHNGtsmmH8?si=E_0MbehsZ6kAkOLg) is the video I was directly referring to. There are many great Physics channels out there, I would also recommend looking for college lectures that have been posted on youtube based on your specific interests, because there are a lot out there

[mighty surge]

Yall know any fun books about cool math concepts? looking for a book that isnt super duper mathy and that anyone can understand uhh math concpets like ig golden ratio or number e would be cool

[woven imp]

Hey, I wanted to start learning maths for machine learning. Does anyone have any recommendations?

[magic spade]

What's your background?

[woven imp]

Very minimal, not much experience with linear algebra and related stuff

[candid spear]

do yk calculus

[molten mason]

Get Linear Algebra by Friedberg, Insel, and Spence to start you off.

[vital bane]

check out Paul J. Nahin's books

[vital bane]

For maching learning? then I'm assuming you're not looking for a pure math book

maybe you'd like Gilbert Strang's "Linear Algebra and it's applications"

[marsh ingot]

I think I know one but in spanish

[woven imp]

Alright thanks , will refer to these books

[remote sparrow]

https://www.amazon.com/Primer-Mathematical-Writing-Disquisition-Appreciated/dp/1470436582/

seems neat

https://maa.org/press/maa-reviews/real-analysis-and-foundations

this book is in its 5th edition as well

according to the book's author, it's strongly inspired by rudin, but written in a more gentle fashion

[remote sparrow]

#book-recommendations message

[median saffron]

sour drop is a confirmed bookworm

[stark minnow]

Can someone suggest for me some textbooks for real analysis

[graceful moon]

You’d be hard pressed to find a bad real analysis book, I’d say just read a chapter of a few and pick what you like.

Im personally a fan of Tao, some people aren’t. I think there’s some fans of baby Rudin on here. I’ve heard Abbot is good, but again really anything should be fine

[magic spade]

Can you be more specific about kind of analysis book you are looking for and your background? I could probably think of like 40 analysis books depending on what content and difficulty you want

Most common recommendations will be Tao and Abbott like Nope mentioned

[mighty surge]

idk spanish

[gray gazelle]

Jay Cummings real analysis

Great book for a first real analysis passthrough

[storm fossil]

Not sure if this exists. But are there any really old mathematical philosophy books? Ancient Greek/Islamic/Latin works? Maybe some sort of treatise explaining the purpose of studying math.

Meaning, I know there is an old anecdote that ends with Euclid saying that math is worth studying for its own sake. I'm curious if anyone ever wrote a book/series of letters explaining the philosophy of why they choose to do math.

I don't mean the modern philosophy of math genre.

[plain barn]

anyone has any textbook recommendations of abstract algebra? (group theory and stuff)

besides herstein's book

[graceful moon]

Artin or dummit and Foote are the go to’s

[plain barn]

ty

[graceful moon]

I’d personally say artin though, dummit and foote is good as a reference but it’s so slow to try to work through

[plain barn]

ty

[marsh ingot]

Its depending what you need in the end

[plain barn]

I need happyness

tbh I'm not sure on my objectives I just want to learn abstract algebra

[marsh ingot]

Me too.... me too

[plain barn]

one objective would be understanding galois theory maybe, that's something I'm curious about

but I like the concept of abstract algebra in general I just want to learn stuff in it

[marsh ingot]

Galois is cool for what I remember. Is not my main, Im from analysis

[plain barn]

I was already doing herstein's book by a teacher recommendation, wondering if there is a better book

not that I don't like it it's just that I've never searched any other ones

[marsh ingot]

Its very useful tbh when you deepen more about one branch you will eventually need abs alg

[plain barn]

if I go read artin's and know LA should I skip the parts with LA?

[marsh ingot]

Whats LA?

[plain barn]

las vegas

linear algebra

[marsh ingot]

Lol

If you already know LA then just read that part more fast

[plain barn]

by the preface it seems like it has a cool philosophy

like showing examples before concepts

[plain barn]

makes sense

maybe I just read it without doing exercises

or do one or two

[marsh ingot]

Yeah thats good

By reading it again you can check how well you know the theory fron LA

[plain barn]

ye

and maybe recontextualize

what I already know

which is one of the best things in math tbh

artin's really attractive ngl

[marsh ingot]

[plain barn]

not the person I don't know how he looks like

the book

I mean text

math

[marsh ingot]

Hahaha

Yeah

[marsh ingot]

Indeed, I wanna read measure theory from another author

[plain barn]

also just realized I already had this book downloaded lol

[marsh ingot]

Rudin was....

[marsh ingot]

Happend to me with an alg topology book lol. Downloaded from September like I didnt remember when

[plain barn]

I think I'll give a read on artin's second chapter and see if I get good vibes

I donwnload a bunch of random ass books about stuff lmao

[marsh ingot]

Thats good, for collecting. You dont know when you will need one

[plain barn]

also it has galois theory at the end

[plain barn]

yes yes

[marsh ingot]

With just one god damn exercise about convexity I downloaded like 3-4 books/notes

I wont touch convexity again

[plain barn]

damn

[marsh ingot]

Btw how is called that Artin's book you mentioned?

[plain barn]

algebra

apparently

[marsh ingot]

Found it quickly yay

Thanks

[plain barn]

artin has way less exercises than herstein lmao

artin has some exercises at the end of the chapter herstein has a bajillion exercise at the end of each small section

and they're hard

even the so called easy ones

unless I'm stupid idk

[marsh ingot]

Never tried exercises from math books

Look scary

Maybe after my post degree I will try to do some

[plain barn]

It's my favourite part tbh

[marsh ingot]

I think the principal exercise is understand the content

And how some authors put "yeah from there is easy to prove the statement" then is like 3-4 paragraphs

Flashbacks from my thesis degree are comming

[plain barn]

I generally understand stuff very easily

and interestingly I've never had this experience of seeing a "is easy to prove the statement" without it being actually easy

I'm getting good at doing proofs Ig

[marsh ingot]

Sometimes it take me a bit to understand some arguments even more if Im studying a new stuff

Like "why are you using that?" Then after an hour realize why

[plain barn]

oh yeah

I mean there's types of understanding

how it works
where does it come from
why it is important
why should I care
why would someone do that...

understanding all that does take more time

sometimes I do that while doing exercises lol

I think that's a bad thing actually, I don't take the time to experience the reading

should do that more

I'm too exercise obsessed