book-recommendations

[stray veldt]

i assume you want some kind of highschool algebra, so maybe just try khanacademy

[hybrid lake]

I honestly don't know much about discrete math besides truth tables, I checked out a few books but most of them mentioned needing trig / calc so I just put it off for later

[scarlet steeple]

facts lmao

[remote sparrow]

@remote vortex in your opinion, going from abbott to axler's MIRA is okay, right? do you have any opinions for references specifically on metric spaces and function spaces? as far as i know, you need to pick up this material some time.

[remote vortex]

Abbott has a brief overview of metric spaces in section 8.2 of his book which might well be enough for measure theory purposes.

Axler also starts chapter 6 of his book with an overview of metric spaces

[remote sparrow]

when does one really need to know the metric and function space material in-depth, say from rudin or carothers?

[remote vortex]

Rudin's "Principles of mathematical analysis" also has an overview of topology

And having read Abbott first you shouldn't struggle with Rudin

[remote sparrow]

ye ofc

[remote vortex]

You don't need that much topology in measure theory, unless you want to focus very heavily on the L^p spaces, but at this point you're essentially moving into functional analysis

[remote sparrow]

i see, so if you're just gonna do the basics of measure theory, analysis on the real line is sufficient?

[remote vortex]

Yeah

[remote sparrow]

how much of that heavy duty stuff you mentioned comes up in probability?

[remote vortex]

L^p spaces? I don't think they feature much in probability generally, but I'm not a probabilist

[remote sparrow]

if i finish axler, would i understand billingsley

i'm not looking to go deep into stochastic calculus or anything, just want to bring my knowledge of probability to a certain completeness

[remote vortex]

Yeah, probably, and even without Axler.

I quite like Axler's treatment of measure theory, but Billingsley is self contained, and also a good recommendation.

And if your overall goal is probability, Billingsley's book is written with that in mind

Also nothing is stopping you from reading both 😛

[remote vortex]

The first part of Billingsley's book is axiomatic probability theory, which is measure theory, except specifically for probabilistic measures (and with a focus on probabilistic results/interpretations), and then in the second part he discusses general measure theory.

So a lot of the same or very similar results, but in a different language, and taking into account the differences caused by dropping the assumption that the measure of the entire space is 1

I'm not sure if you know that already, but "probability" as understood by the modern axiomatic probability theory, is a measure on the set of events.

[remote sparrow]

cool, thanks

[remote vortex]

So if you learn probability from Billingsley, you're actually already learning measure theory 😄

[remote sparrow]

[remote sparrow]

https://www.amazon.com/Abstract-Algebra-Introduction-Thomas-Hungerford/dp/1111569622

https://www.amazon.com/Concrete-Introduction-Algebra-Undergraduate-Mathematics/dp/1441925619/

[errant heath]

Looking for an advanced calculus book that's more modern.

[dusk wind]

that book is more simple than usual discrete texts, you can probably sample it to check it out since some of the concepts are good to have

[vast jackal]

Hey is Basic Mathematics by Lang a good book to know all the things i needed in for the calculus-based physics?

[tawny copper]

https://old.mccme.ru/ium//postscript/f10/geometry1-lect-6.pdf

I was trying to find the rest of the lecture notes of this course, but I couldn't find them. If you substitute "6" in the link by 5,7, it yields the corresponding notes, but not eg for 1.

[hybrid lake]

I will ty

[dusk wind]

https://www.amazon.com/Algebra-Chelsea-Publishing-Saunders-Lane/dp/0821816462

[remote vortex]

axler

[tribal crow]

Tao and Abbott come to mind

[errant heath]

Aren't those real analysis books

[tribal crow]

eh, does “advanced calculus” not refer to real analysis?

[errant heath]

I honestly don't know anymore

[tribal crow]

what did you mean by “advanced calculus” then?

[mossy flume]

some people use that term for calc 3

or diff eq

or analysis

it's not really a standardized term

[tribal crow]

yeah, but how can one recommend a book without knowing what the OP meant?

[dusk wind]

"modern algebra"

50 years ago

[mossy flume]

considering how old math (and even just abstract algebra) is

50 years is quite modern

[molten mason]

It's a pre-calculus book, it's good to know all things needed before a Calculus textbook

[molten mason]

For Calculus based physics, you need Calculus

[remote sparrow]

advanced calculus is a fairly dated course that's largely been superseded by real analysis

example references would be buck, c. h. edwards, or taylor and mann

generally, it's multivariable theory plus a modest amount of analysis

modern references might be hubbard or shifrin

actually folland has an advanced calculus book too, though it's out of print. however, the pdf is legally free on his website

[errant heath]

It's a course at my class that seems similar to real analysis but apparently they aren't treated the same.

I've even seen books on both so.

[errant heath]

Are there any large differences between the two

[remote sparrow]

between real analysis and advanced calculus?

sometimes schools call introductory real analysis (with a curriculum similar to abbott's contents) advanced calculus

[molten mason]

Dov you have a syllabus or course description?

[molten mason]

Also do you know what textbook your school uses?

[remote sparrow]

there's some overlap between real analysis and advanced calculus

[errant heath]

https://math.sdsu.edu/courses/syllabi_math/math330

[errant heath]

Nope!

[molten mason]

Oh SDSU, yeah they used Advanced Calculus by Fitzpatrick

It's first semester Real Analysis

[molten mason]

If you get the book, the paid version of quizlet has the solutions to the exercises here:
https://quizlet.com/explanations/textbook-solutions/advanced-calculus-2nd-edition-9780821847916

I would recommend double checking from other students that this is still the current recommended textbook. Last I saw it was an optional textbook but recommended.

For me personally, look at the first exercise answer just to see how they do it. Then do the rest on your own before double checking the answer on quizlet to see how far or close you are.

[dusk wind]

looks like axlers precalculus book shares material from his college algebra and trig books

if wiley formatting didn't suck it'd be pretty good to use due to the open solution set

[molten mason]

He does, there's really just a couple differences like IIRC one of them goes over basic prob/stats and the other doesn't.

[gray gazelle]

whats a good book to start learning basics of number theory and proofs

[remote sparrow]

burton or dudley

https://maa.org/press/maa-reviews/introduction-to-proof-through-number-theory

there's also this book i stumbled on in the library last semester

[dusk wind]

Is there a modern physics book or series that isn't filled with clickbait by publishers

[molten mason]

I'm going through Stillwell's Elements of Number Theory currently, I don't know enough about it to be a recommendation but it's another option. It's part of Springer's Undergraduate Texts in Mathematics

That Introduction to Proof Through Number Theory by Chow looks nice though, and it's new.

[molten mason]

No

[molten mason]

Why not just get an older edition of some modern book

[dusk wind]

I went back like 4 editions

at this point I'm just gonna pick up some 80s book

those symbols are too distracting

Halliday book by Wiley is a nightmare

but then if you look at the old physics book there is none there

[novel hound]

Stillwell might need some algebra tho... not a lot and could do it without but probably better with some.

[dusk wind]

Who did this, who thought this would be a good idea

I want my pages completely monotone dammit

[molten mason]

Good thing there's Elements of Algebra

[molten mason]

A Serge Lang of Physics?

[dusk wind]

yeah

[molten mason]

I hate to simp but every book I read of his is just a banger after banger

Monotone writing and straight to the point without any explanation? Say less

[novel hound]

yeah Stillwell hardly has any exercises, which is good and bad. I feel like it's better for a casual read to get a second read on some of the concepts.

[dusk wind]

you could ram it up with this https://archive.org/details/synopsisofelemen00carrrich

[molten mason]

Oh that's interesting, because of that I'm using it as a first read lol To preframe my mind for when I get to a more serious textbook. But I definitely can see the second read vibes.

I'm reading both Elements of Number Theory and Elements of Algebra as my... downtime casual reading such as before bed. Just trying to read it just to read it without doing too many exercises.

[novel hound]

That's probably a good idea too. But, most of the stuff really sinks in on doing exercises, so...

But yeah good books nonetheless and there's a place for them - perfect for casual reading.

[molten mason]

Yeah that's what I'll be doing for my second-read

[molten mason]

That's crazy, I like old math texts like that because it's fascinating to see where we were mathematically in comparison to the time period. For example when that was published, we were in between the American Civil War and the Spanish-American War. The capital of Arizona was just about to be moved to Phoenix. People were using the ballpoint pen for the first time. The stop sign and smoke detector were being invented, and people were starting to eat shredded wheats. Meanwhile in the math world all that was known and happening.

[dusk wind]

its a long history of borrowing and 'acquiring' tech

Academia is so limited

but yea it's interesting how even thousands of years ago math was so sophisticated

Wasn't there a whole war on the ballpoint pen thing too lol

[fluid igloo]

any recommendations for ioqm>

?

[gilded ferry]

Recommendations for mathematical optimization a beginner (with knowledge of analysis and linear algebra)?

[vital bane]

"Convex Optimization" by Stephen Boyd is usually recommended

[elfin finch]

got it right in front of me rn.

[remote sparrow]

check out some linear programming books

anyway mathematical optimization encompasses a lot of things

but the course description at my university says:

Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods and dynamic programming.

[gilded ferry]

Book extract "This book is meant for the researcher, scientist, or engineer who uses mathematical optimization, or more generally, computational mathematics"

I'm just a second year student

in computer science and neuroscience/philosophy

[vital bane]

Lol dont worry, you'll be able to use it perfectly fine, you know analysis and linear algebra, that's enough for it

[tawny copper]

What are nice books/lecture notes on dynamical systems, chaos, fractals, ergodic theory, etc

I know the Strogratz book, but was looking for other books too

[modern ruin]

kentucky theory

[willow basin]

Can someone recommend an ebook on number theory am a beginner

[gray gazelle]

https://www.maths.ed.ac.uk/~v1ranick/papers/borevich.pdf

For your info, it's from The University of Edinburgh

you could find it on google if you write

number theory for beginners pdf

I've never tried it but it seems a big book from a recognised place

[willow basin]

Nah bruh won't understand

[olive cloud]

bruh do you have something thats not 429184921 pages

i need full discrete math book in under 100 pages

any reccomandations

[graceful moon]

It’s hosted my Edinburgh but it’s not used in any courses there, not sure if it’s a good book or not since I’ve never heard of it, but it should be noted it’s not actually used at UoE

[tawny copper]

Bóna's book

the first 100 pages

[dense pumice]

Any recommendations for books on logic & set theory? Ideally something at a late undergrad/early graduate level

[molten mason]

A Russian text from 1964 now thats interesting

[remote sparrow]

https://www.logicmatters.net/tyl/

[dense pumice]

This looks like more-or-less what I'm looking for, thanks!

[white pollen]

Hi, smart people. I come from the land of applied, proofless math. May I ask what y’all think is a good textbook for Real Analysis? Here’s a bit about me for background:

• I am currently taking a proof-based Linear Algebra course, so I don’t need an intro to proofs. Most of the recommendations online are to people who also need an intro to proofs in the text, and while I absolutely don’t mind that, I’ll take a more comprehensive real analysis text without a focus on teaching proofs over a less robust one that walks students through proofs more.
• I have previously taken the three calcs and basic linear algebra and ODEs.
• I’ll probably take discrete math next semester, and try to teach myself real analysis while doing that.
• I don’t mind a dense text. I’d like the book to pretty much be as complete/comprehensive as possible, but would like for my current experience to be enough to fulfill the basic pre-reqs.
• Optional, but it’s a pet peeve of mine when important results are hidden in exercises without an answer key. An answer key or a book that doesn’t have a ton of interesting things mixed in with the exercises is preferable.

[stray veldt]

finding a book with an (official) answer key will be pretty impossible and for good reason

the standard book is rudin's principles of mathematical analysis

personally i like amann-escher

they're both pretty hard books but your background is also pretty strong i'd say

[white pollen]

Large preesh, my friend.

[dense pumice]

I'm a big fan of "Understanding Analysis" by Stephen Abbott

It has very verbose proofs for the explicit purpose of showing you how to do proofs in analysis

[white pollen]

Yes, I can verbosify the proofs myself, for the most part.

I’ll avoid that one.

[dense pumice]

Alright? Its not really a "how to do proofs" text, more just guidelines for you to use in the problems

But if you don't want it, w/e

[white pollen]

I read that as “I’m not a big fan”, lmao.

[finite gale]

I too read "I'm not a big fan"

[white pollen]

I was sitting there like, “Damn, you commented to tell me that you didn’t like this book, must be terrible.”

[dense pumice]

Ahhhhh

Yeah no, I really liked that textbook

I used it to teach myself RA while on an internship

[white pollen]

Oh, you have “not” in your name.

That’s probably where my brain grabbed it.

I’ll keep it on the list.

[molten mason]

The paid premium version of Quizlet has the answer key for Understanding Analysis by Abbot

It's also a very popular book and many people in this server have or are going through it.

[remote vortex]

yeah, I'd definitely recommend Abbott over Rudin to most learners

Rudin is definitely one of the best analysis textbooks for people who already know analysis, though

[tawny copper]

I'm bumping this, although I did find some books

@remote vortex sry to bother, but I have seen you talk about dynamical systems stuff. Do you know any nice book you could recommend?

[remote vortex]

for ergodic theory I'd say Walters, also Einsiedler&Ward, for symbolic dynamics specifically there's a great book by Lind and Marcus. for a brief introduction there's also "Discovering Discrete Dynamical Systems" by Johnson, Madden and Sahin

for topological dynamics I'd need to think, and for differentiable dynamics I have no idea

[tawny copper]

ye I already knew the Ward book. The others I didn't, so I will check them out

[remote vortex]

Walters discusses topological dynamics in his book despite the title

there's lots of interplay between ergodic theory and topological dynamics

[tawny copper]

oki

if it helps to narrow things down, I'm interested in NT and geometric things (like hyperbolic or whatever). Like for example, there are fractals that arise from Schottky groups or something, so I'm interested in that

for NT I guess Ward and Tao's blog are good enough

[remote vortex]

oh, that's definitely outside my area expertise

for NT there's also Furstenberg

https://press.princeton.edu/books/hardcover/9780691642840/recurrence-in-ergodic-theory-and-combinatorial-number-theory

that's where he talks about his structure theorem and multiple recurrence

[tawny copper]

ye I got it when you recommended it some days ago

Thank you

[marsh ingot]

Topological manifolds, Lee

Topology, basic stuff

[vital bane]

Prerequisties for Rudin's analysis book: Analysis

[clever herald]

Which book is best for beginners to learn calculus if he has the knowledge of basic trigonometry and components of calculus?

[daring lake]

Something like Stewart calculus will be very easy

[daring lake]

I read it alongwith Bartle. I felt like it was a wonderful combination.

[marsh ingot]

[alpine rover]

Algebra by Michael Artin

[daring lake]

Atiyah and MacDonald

[cobalt maple]

Hey y'all, what do you think about Dummit and Foote's Abstract Algebra vs Roman's advanced linear algebra for module theory?

[daring lake]

I have only ever used D&F and Atiyah so can't recommend anything else

[molten mason]

Serge Lang's Algebra

[alpine rover]

Ok, Gallian or Pinter or Fraleigh

[vital bane]

@coarse frost

[coarse frost]

that dont mea i will tolerate artin slander smh smh

[vital bane]

[coarse frost]

actually crazy opinion

artin is amazing

i disagree heavily, i havent read herstein, but artin is written very nicely

the lin alg is subpar sure but the group theory part is great man what are you saying

[rigid barn]

I agree that Herstein's great (the group theory chapter is particularly masterful). I have no strong feelings for Artin either way, but I really respect the fact that he presents a very broad algebraic horizon to his readers with minimal prerequisites (knowing what matrices and determinants are, which he recaps). Why do you hate him?

Well he's not so great for pure linalg, the material's too compressed, although it could be reasonably done.

[remote sparrow]

Algebra: Notes from the Underground by aluffi. it's a rings-first book, so it should be helpful for someone struggling with rings.

[rigid barn]

I have a better suggestion @arctic hamlet: Lorenz Algebra 1. It's more fields/Galois theory-oriented, but it covers everything you need to know about rings. Word of warning: it's pretty hardcore. These books are little known I think, so I like to shill for them.

Jacobson Basic Algebra 1 is pretty great too, undisputed master.

You could just learn it from Herstein you know, he covers it well enough.

[remote sparrow]

no

[rigid barn]

All of that's covered in Herstein, no? Those are the basics of ring theory.

Alright, well Lorenz might not be for you then, his presentation's a bit unorthodox. It's probably best if you take Aluffi or any other standard text like Fraleigh and grind the material/problems.

[halcyon lantern]

I'd like to recommend the book "hungry hungry caterpillar"

It is fire

[fossil arch]

Algebraic analysis books?

There's Foundations of Algebraic Analysis by KKK but I can't find a copy

[stiff lagoon]

An Introduction to Sato’s Hyperfunctions by Mitsuo Morimoto

[fossil arch]

[stiff lagoon]

I have a copy but it's extremely difficult to start with.

[stiff lagoon]

This is much better

[fossil arch]

Yeah that's what I've heard too hehe

dw I don't have the background for it anyways

just curious ^_^

Thank you!

[unkempt gorge]

Are the Art of Problem Solving books good for self-learning mathematical concepts?

[remote sparrow]

yes

[unkempt gorge]

Alright. They're a bit pricy but I assume they're worth it. Not sure if I should start with the Prealgebra one if I'm already confident in my Prealgebra knowledge. There could be gaps in my knowledge though which is why I'm still deciding

[remote sparrow]

aops books push you somewhat beyond the standard curriculum

it may be more than what you need to actually advance

[unkempt gorge]

Tbh I like that

[jaunty tapir]

whats a really fat book on homological algebra? I intend to use it for looking things up

[manic cairn]

https://stacks.math.columbia.edu/tag/00ZU

has this as the listed reference:
https://link.springer.com/book/10.1007/978-3-642-62029-4

might be too old for your purposes

but it’s a good 400 pages of homological algebra

[jaunty tapir]

thanks, i'll take a look at it

[sick river]

bro what is that book? 7500 pages of algebra? thats insane

[rigid barn]

It's not that fat, but it's a classic reference https://www.math.stonybrook.edu/~mmovshev/BOOKS/homologicalalgeb033541mbp.pdf.

[trail hemlock]

[stuck zephyr]

https://cdn.discordapp.com/emojis/1196535406930448435.webp?size=48&name=catKing&quality=lossless

[molten mason]

[trail hemlock]

why the emoji is no working 😭😭

[molten mason]

My toxic trait is thinking I can read that entire thing.

[cyan valve]

If anyone here has perused Volume 2 of Gortz and Wedhorn's algebraic geometry books, can you tell me what your impressions are? Are there a ton of errors/typos to keep in mind when reading the book?

[pliant wadi]

How's John Kelly's general topology?

[heady ember]

Then... what's the point of replying...

[alpine rover]

at the risk of an off-topic post, you reminded me of this stand-up moment (explicit): https://youtu.be/UDQr4NbGyNg

[wheat trout]

My first impression when I open the pdf is that why tf it has more pages than Vakil's rising sea, which already has around 800 pages? I skim through some contents, they include a lot of things, some of them are not typically seen in a first year algebraic geometry course but I find them useful. They discuss a bit about algebraic de Rham complex, etale fundamental groups etc.

But again, I feel like it is kind of intimidating.

I didn't catch any errors. Maybe I am reading too fast. Might as well give a good look. My first impression is that it is a good book for someone already learned about Vakil or Hartshorne. I cannot imagine someone learning AG using this book.

[cyan valve]

It is volume 2 though

[wheat trout]

Yeah. It is supposed to be the continuation of volume 1, introducing the sheaf cohomology on schemes and its application. I didn't expect that they would include so much content.

[drifting siren]

what are the best books for statistical math

[glossy zealot]

It varies, depending levels

You might need to include your background or the level of difficulty

[wispy root]

Any recommendation for number theory specifically Congruency topic?

[sturdy dove]

Elementary Number Theory By David Burton.

[jaunty quail]

Opinions on Cohn? I like it. Examples are clear and concise

Cohn Measure Theory

[rigid barn]

It's pretty good. I think Schilling's got more flair and covers more unique stuff beyond an intro, while Cohn's reliable, if unadventurous, and covers more of the standard MT topics that Schilling doesn't.

Also Cohn's first edition cover is cool, I don't know why they switched to the lame no-frills green cover.

[jaunty quail]

Thanks for this. I want to explore different MT uses so Ill definitely check out Schiling

[pure solstice]

a good book with theory and exercises for self-study in number theory?

[proven tapir]

A good textbook for undergraduate year 1 stats in economics, (im in a gap year and would like a little headstart before uni)

[dapper root]

I like that the cohomology is done with the derived category. But it requires a certain level of sophistication to swallow that sort of treatment properly

As for typos, I didn’t read it yet, but the first volume had so many typos. Even after the second edition. So I would assume there’s typos

[trim kayak]

Any book recommendations about algebra, geometry, or stats that are fun and interesting to read but won't make me think too much while reading? I'm looking for something good to read once I get home. At that time, my brain is too tired to think about too much.

[quaint flume]

Does anyone have any links where I can find nice pdf copies of different math types

[cold elbow]

https://realnotcomplex.com

[modern ruin]

cute cover

[cyan valve]

Hopefully there's a good list of erata the authors maintain, right?

[dapper root]

There was for the first volume. I imagine there is for volume 2 as well

[cyan valve]

I do have prior experience with things sheaf cohomology, though not as general as this

In any case, I'd be making my way through a decent chunk of volume 1 before hitting volume 2

What would you say is the minimal amount of content needed from volume 1 before delving into volume 2? I.e. which sections/chapters from vol 1 do you think I should focus on?

[dapper root]

No idea

[cyan valve]

But you know everything

Jk

[tulip moss]

Does Real Analysis by Jay Cummings cover all essential topics or is there a better book?

[remote sparrow]

if you're pre-studying for a specific class, it may not cover all the topics you need

but cummings is good broadly speaking

[tulip moss]

I am self studying

[remote sparrow]

yeah it's good

[tulip moss]

Okay 👍

[queen belfry]

Hi

I need a geometry book

I’m not really god at geometry but I can say that I know the basics

https://www.gutenberg.org/files/21076/21076-pdf.pdf

Is this a good source to start?

[remote sparrow]

from where did you learn the basics? have you already taken a course in plane geometry?

[queen belfry]

Yes, in school

What is plane geometry?

[remote sparrow]

euclid's elements would retread similar material

[queen belfry]

Is it the same with the euclidian?

[remote sparrow]

yeah that's another way to say it

[queen belfry]

I want to refresh my knowledge but I also want to learn some advanced concepts

[remote sparrow]

https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

check this out then

[queen belfry]

Thanks!

[remote sparrow]

there's also a solutions manual to go with it too

[tawny copper]

you should check Coxeter's books

Hilbert also has books on geometry which are nice

and I also like Hartshorne's book

[proven tapir]

.?

[orchid mortar]

Not too sure what you mean by stats in economics.
https://press.princeton.edu/books/hardcover/9780691235899/econometrics
This is more towards a graduate-level, though it won't really push you that hard in earlier chapters.
If really equating stats in economics to econometrics, then https://www.amazon.com/Introductory-Econometrics-Modern-Approach-MindTap-dp-1337558869/dp/1337558869/ is pretty standard to undergraduates, and you should be able to find comparison to/from this book if you want other books

[upbeat vine]

baby rudin

[proven tapir]

I meant more first year undergraduate level

Probably the second book

[proven tapir]

?

[upbeat vine]

Principles of mathematical analysis by Walter Rudin

[orchid mortar]

Just search for books similar to Wooldridge then

[proven tapir]

Tyty

[steel cloud]

Is there a good quality pdf of Basic Algebra by Jacobson?

[remote sparrow]

yeah, but the book is also available rather cheaply if you ever decide you want a hard copy

[steel cloud]

Can you please send that file?

[vital bane]

green is cool too

[heady ember]

Like me

[remote vortex]

it's not easy being green

[gray gazelle]

what are some good books about combinatorics? with like lots of good exercises

[halcyon lantern]

@gray gazelle You want to get better at combinatorics?

[gray gazelle]

yeah i want to mainly learn it cause im not really good with not calculus stuff

[rigid barn]

No it isn't, it's lame as fuck. More maths textbooks should have unique and engaging covers instead of just a colour wall (Springer gets a pass).

[halcyon lantern]

I recommend buying some cocaine, reaally useful when doing combi

[cold elbow]

ouch man

[rigid barn]

Speaking the truth, I can't be stopped.

[halcyon lantern]

All my text books have unique/cool covers

[halcyon lantern]

I think that is a skill issue

[gray gazelle]

what book should i use the paper from to sniff the coke

[rigid barn]

Post examples.

[halcyon lantern]

Buy a copy of berserk, use the pages to sniff the cocaine... you should also buy a maid outfit and start listening to breakcore that's a game changer for combinatorics

[gray gazelle]

awww hell nah i would rather listen to weezer's pinkterton all day 😭

[halcyon lantern]

No image perms

[halcyon lantern]

Fr? I would prefer the maid outfit

[rigid barn]

That's equivalent to wearing a maid outfit, bro

(except Across the Sea, it gets a pass)

[gray gazelle]

yeah but its more mental

[vital bane]

https://tenor.com/view/cat-cope-cursed-gif-25667684

But I do agree they should have unique and engaging covers

Like Spivak

Spivak based

[molten mason]

What about his Calculus cover that just says "Calculus"

[graceful moon]

Seeing that book cover made me read more about spivak, between that cover and Spivak pronouns I’ve decided he is unbelievably based

[tribal crow]

it’s good

I like it

[remote sparrow]

A Walk Through Combinatorics by miklos bona

[gray gazelle]

thanks

[autumn spire]

hey i have been doing number theory for some time

i read 1-2 books but i think i am not really getting the concepts

what should i do

[molten mason]

Number theory seems to be the theme of the week in here.

Which books have you tried so far? What are you understanding and what are you not understanding? Which concepts do you feel that you're having trouble with?

[autumn spire]

so i have tried Zuckerman and Andresccu

tbh it is very different from other branches of maths

and i am not familiar with the topics at all

i understand but i am not able to solve even the basic questions

i was just preparing for olys

[narrow prairie]

try Niven

and maybe Modern Olympiad Number Theory, but it is a bit hard

[autumn spire]

ok

i guess i can try but Zuckerman is also considered a very good book

i think the problem is the way i am doing it

[molten mason]

https://www.math.brown.edu/johsilve/frint.html

Chapters 1-6 are free and available on this link. If you enjoy it, you can find the other chapters on your own

https://wstein.org/ent/

This one is the full textbook and 100% legal/free PDF

Although probably the same level as Zuckerman, so either it'll also be too difficult or maybe you'll be able to understand it from a different writer.

[keen orbit]

its rare to see white grass

[molten mason]

Silverman is a level below in difficulty, so it might be easier.

There's also Elementary Number Theory by Dudley, it's a gentle introduction with hundreds of probelms.

[molten mason]

Some Lecture Notes
https://home.sandiego.edu/~aboocher/writings/NumberTheoryNotes.pdf

[autumn spire]

thank you

[sick holly]

Do anyone have any resource recommendations, books, or otherwise where i can see proofs of simple mathematical statements, done out in the most rigorous and formal way possible? As i have read my discrete mathematics book by rosen it mentions how often in math we do not do so formal proofs. what i want is to see is something like a mathematical proof with the rigor and formality of a proof in say first or predicate logic has, something like every step written out completely in logical notation. If that makes sense. Somebody i spoke to at my uni told me that maybe Principia Mathematica would do. But since it is old and with different notation, and according to some, outdated, i thought i might ask here for something.

[stray veldt]

https://leanprover-community.github.io/100.html#1 or https://madiot.fr/coq100/#1

[stray veldt]

principia mathematica is not written in "modern mathematics"

do not look at the book, except possibly for historical reasons

[sick holly]

yes internet said the same

and 1 look told me that too hehe

[stray veldt]

those are broken down so much that a computer understands them

[sick holly]

Thank you.

[dusk wind]

Spivak's Physics for Mathematicians is of the highest quality

https://www.amazon.com/Short-Calculus-Original-Undergraduate-Mathematics/dp/0387953272 short calculus by lang

[sick holly]

Ill check them out

[molten mason]

Unrelated, @dusk wind I finally made an archive.org account and it's life changing.

[dusk wind]

yea it's some good stuff you can't find anywhere else on there

just remember to get creative though if you want greater access

also, some books are restricted for some reason

can't get them at all, even with an account

[molten mason]

That's interesting

[rigid barn]

Finally, some good fucking food. Although I have no idea how the cover's supposed to relate to the subject, borderline Lynchian.

[rigid barn]

I actually strangely like that one, the bold colour combination and impressive font combine well together.

[dusk wind]

If you need to fix a PDF, try PDFxchange, pretty good for quickly making modifications. Including OCR

[remote sparrow]

there are ways to download certain books that are "borrow-only"

[trail hemlock]

🏴‍☠️

[analog lava]

Yo

I just finished Tu's book,which i believe covers basic smooth manifold theory.

What would you guys advise me to study next? Algebraic Topoogy or the sequel of Tu, differential geometry?

assuming i do not really care which is more fun for now , but rather whats more important for a student to know b4 grad school

[gray gazelle]

Not even with anna’s archive?

[sage python]

You should read the algebraic topology sequel of Tu

Bott-Tu

[analog lava]

differential forms in algebraic topology?

i know no algebraic topology

😄

is that a problem

[sage python]

It's doable without

[dapper fossil]

best books for beginner boolean logic discrete math intro/intermediate

(I have no mathematical maturity/intuition lmao)

[graceful briar]

have someone read "How to solve it" ?

[analog lava]

by polya,yes

[graceful briar]

do you like it?

[finite gale]

i read it in high school when someone suggested it to me; i remember thinking it was a nice read though

[olive bloom]

Is stewart calc a good calculus book?

[finite gale]

it's one of the standard texts for calc yeah

[spring jacinth]

how do people feel about millman and parker's differential geometry textbook

[glad prairie]

Was not a huge fan. Nasty formulas and computations. Imo didn't do a wonderful job motivating everything and giving the "geometer's perspective". It's suitable and standard for a course in curves+surfaces, and covers some very nice theorems, so that's good

But just the process of reading it was kind of painful especially deeper into the surfaces stuff

And iirc it didn't do a great job with things like parallel transport and connections, if it got into those at all

Do carmo is probably better. Though I think it's also not amazing

Diff geo of curves and surfaces is just an inherently bad subject. It probably doesn't matter what book you use

[livid tide]

Can someone suggest an introductory book / short read on set theory?

Formal set theory that is

[vital bane]

[magic spade]

Use Tapp

https://link.springer.com/book/10.1007/978-3-319-39799-3

[trail hemlock]

use spivak

[gray gazelle]

thank u

[hot gust]

any good books for someone in yr 9 , I already know alot of calc

[trail hemlock]

a book about calc ? probably the spivak or maybe Honors Calculus by Charles R. MacCluer

if u alr have a background

[hot gust]

OK thanks

[remote sparrow]

check out kristopher tapp's book if you care to

[glad prairie]

Cant wait to show that the gauss curvature of an embedded surface is independent of isometry

Can't wait to compute the geodesics on surfaces of revolution

[remote sparrow]

it's not advisable for your introduction to set theory to be formal. it can be an informal axiomatic (non-naive) treatment though. see enderton, goldrei, or hrbacek and jech.

[sick river]

these are facts tho lol, much better to just jump into some smooth manifold theory

[fast pawn]

What algebra book would y’all recommend for self study? I plan on taking it at school next year (they use Artin) but I’d like to come in prepared

[glad prairie]

If you want something chill and friendly, Fraleigh is great. If you want something a bit harder but still very understandable, Gallian is really good.

[fast pawn]

Thank you!! 🙏

[gray gazelle]

Does anyone know of a good undergraduate-level text written in french? I’m looking to work on my mathematical french

[dense loom]

Honestly there are not many good french books I know
You might be interested in reading Rudin PMA in its french translated edition

[gilded ferry]

I have the oportunity of obtaining 'Basic Algebra' by Knapp and 'Algebra' by Dummit and Foote

I'd like to know how Basic Algebra fair (opinion on the book)

PS: I have self-studied algebra for a quarter. So I'm familiar with the basics

[solemn haven]

Are there any analysis or math books that you recommend where the author puts more emphasis on explaining the 'thought processes' that allowed mathematicians to come up with proofs instead of being definition-theorem-proof style? Understanding a proof is very different from understanding how the proof is done, so if there is any, I'd appreciate someone could tell me.

[tribal crow]

Abbott and Tao perhaps come to mind

[steel willow]

hey guys,What topology book is good?

[remote sparrow]

Real Analysis: A Long-Form Textbook by jay cummings

[loud cradle]

there's also "the way of analysis" by strichartz, which does that to the point of being longwinded

[mossy flume]

Munkres is the classical recommendation

[glossy zealot]

He has a section of Axiom of choice in chapter one

Where he spent a page to discuss it

Then conclude it wont be used in the book

Iirc

[loud cradle]

ha, why even bring it up then
tbh, i don't remember the book very well, i skimmed through it some years ago and it seemed fine but quite talkative

[heady ember]

You need choice for a handful of situations though. For instance, to be able to prove the sequence definition of limits is equivalent to that of e-d.

[mossy flume]

one of my favorite quotes is the following: "The Axiom of Choice is obviously true, the Well-Ordering Principle is obviously false, and nobody knows about Zorn's Lemma."

not sure who the quote is attributed to tho

[vital bane]

ah yes e-d, the only thing set theorists have

[heady ember]

What?

[vital bane]

Literally Abbott bro

[heady ember]

Literally Schroder bro

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

[vital bane]

I haven't checked out books like schroder and tao

and cummings

but I am sure they are similar to Abbott

as I've said most intro analysis books are good!

[sly ginkgo]

Any good books on the general history of mathematics from as far back as possibly archived?

[vital bane]

loch recommended one to me but I think it was in german

[heady ember]

Schroder gets to the outer Lebesgue measure at pg 127

[molten mason]

6000 Jahre Mathematik - Hans Wussing

[vital bane]

ah that's the one

[molten mason]

Besides that one, which is in German, you can take a look at:
Mathematics and It's History - John Stillwell
And
Turning Points in the History of Mathematics - Grant and Kleiner

This topic comes in a few times in this channel, you can search for yourself where it's been discussed prior. There's not a lot of history books, or if there are it might be split up. For example a history on ancient math, a history on calculus, etc.

The German book is two volumes with a total of around 1300 pages as an example.

[vital bane]

You can also look up the original papers of Euler, Gauss, Riemann, Cauchy, Hilbert etc.

[remote sparrow]

@daring lake how has your experience been with david cox's Galois Theory?

[molten mason]

Only about 60 pages of Volume 1 are available for preview on Google Books, and I can't find anymore anywhere else. But honestly what I have read it's a great book, super in depth, I think it's about $100 for both.

[vital bane]

huh I see

does "6000 Jahre Mathematik" mean 6000 years of mathematics?

[molten mason]

Yes

[daring lake]

I have read only first section in it so far (which is not really Galois theory per se, just polynomials). It seems to go very gentle so far (with several examples, historical notes, very verbose too). My course only started like a week ago. I will hit you up with a more detailed review in maybe 2 weeks after I study fields and galois groups etc, from it.

[vital bane]

I just assumed the book was 6000 pages long idk why I wasn't thinking

[molten mason]

Yeah $80 to order both volumes, delivers by March 7th

[remote sparrow]

#book-recommendations message
#book-recommendations message
#book-recommendations message
#book-recommendations message

[molten mason]

I'm crying

[daring lake]

My course follows Emil Artin, which is pamphlet sized

[vital bane]

Salagos are you german?

or Swiss like Euler

[molten mason]

No, I just don't have the English- only skill issue

[vital bane]

neither do I I am bilingual as well

so you know german?

so just translate it the book into english I'll give you 8 bucks

[molten mason]

I can read it, but I sound like a 5 year old when speaking.

[molten mason]

1300 pages to translate that would be an endeavor, just whip put those translate AIs

[cobalt badger]

Hey, I was thinking of starting with Dummit and Foote’s Abstract Algebra

If I have roughly 4 days of full-time study that I can devote to the book per week, realistically how much time would it take me to complete everything (that is, proving every Theorem rigorously and solving every single exercise) upto (but not including) Galois Theory?

I know there are lots of factors involved and it’s hard to come up with a number (of months say), but if anyone who’s gone through the book (in D&F or other algebra material) could give an estimate, I’d really appreciate it

I’ve been studying Real Analysis by Abbott and Linear Algebra by Sheldon Axler, and plan on starting with the book when I have some more Linear Algebra under my belt.

(not sure if this is the right channel for a question like this, let me know if that’s the case and I’ll move this over to #math-discussion or some other channel)

[daring lake]

It is a huge book, let me warn you. Assuming if you in average take 20 minute per exercise (some might be trivial, some might take a long time to work out), there are like around 100+ exercises per chapter (each chapter is divided into several sections. 13 chapters till you reaching Galois theory, so that 1300+ exercises which is approximately 433 hours. This is not including sections. Each section is typically 7-8 pages long. Assuming you spent 3 hours on each to throughly understand them, that's another 234 hours approximately. This is considering you are good at understand proofs, writing them, and remembering everything.

If you are like me, multiply all times by 4

I have only read first 9 chapters of D&F but gave up working through it

[remote sparrow]

as alternatives, you could try working through pinter's A Book of Abstract Algebra, judson's Abstract Algebra: Theory and Applications, or aluffi's Algebra: Notes from the Underground

[heady ember]

Detraction: why "notes from the underground" lol

Or try Jacobson's basic algebra I

[daring lake]

I honestly liked reading D&F, but I am not brave enough to work through the long list of problems

[cobalt badger]

Thank you for the incredibly detailed analysis!
And yeah, I’ll probably need to overestimate some of those times myself 😅

[remote sparrow]

i would assume aluffi is a fan of dostoevsky

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

[heady ember]

I see...

[cobalt badger]

I actually went through a bit of Abstract Algebra by Fraleigh, had a bad experience with it, so I’m kind of leaning towards D&F because it’s such a standard resource 😅

Are the notes from the underground lecture notes as opposed to a textbook? That sounds appealing if time becomes an issue

[remote sparrow]

no, it's a rings-first book

[cobalt badger]

I see

[remote sparrow]

#serious-discussion message

@cobalt badger there was a short discussion on supposed advantages of a rings-first approach to abstract algebra

https://www.reddit.com/r/math/comments/1aj8caz/are_there_any_academic_studies_comparing_the/

https://matheducators.stackexchange.com/questions/10478/rings-before-groups-in-abstract-algebra

[cobalt badger]

Will check it out!

[molten mason]

Interesting and made me check my own books... Lang does Groups in Chapter 2 and Rings immediately after in Chapter 3 of Undergraduate Algebra

Stillwell splits it into two books, Groups is in Chapter 7 of 9 chapters in Elements of Algebra and Rings is in Chapter 10 of 12 chapters in Elements of Number Theory, and Stillwell states the books can be read in either order.

There's so many books in every subject because every author has an opinion on what's best, I think it's hard to say what's truly "best" because every learner is different and comes from a different background and knowledge base but got me thinking.

[novel hound]

You can skip some stuff like modules in your first pass. The preface gives such guidance of what you can skip in a first pass. Since it is such a dauntingly large book, I like to think of it in smaller pieces to make it easier psychologically. Group theory upto middle of chapter 5 is 150 pages. Ring theory is 100 pages. And, if you skip modules in first pass, fields and Galois is 150 pages. Still going to be a lot of problems. But, easier to think about it in terms of sub-projects I think...

[cobalt badger]

That’s great! Yeah I should probably map through exactly what I want to know as far as a first course is concerned

[wintry rapids]

Hey, I don't know if this is too much of a specific question for the section, but where could i learn very well p-adics numbers, p-adic norm/valuation, p-adic topology.. in the context of a point-set topology course?

[vital bane]

bro D&F is insane when it comes to exercises

there are like anywhere from 30-50 exercises PER section

Abbott has like 10 per section

[cobalt badger]

jeez, 50 is insane

[vital bane]

even more insane than axler

[cobalt badger]

but i’ve heard mostly good things about it

[vital bane]

he sometimes has like 30 exercises per section

like 3.F for example

[cobalt badger]

Yeah i’ve seen

[cobalt badger]

Yeah lole

[vital bane]

it is pretty cool

[cobalt badger]

Even 2.C is more than you’d expect

[vital bane]

I like it a lot

Lol yea

I think in the 4th edition he has reduced the amount of exercises?

not too sure about that

[cobalt badger]

Axler?

[vital bane]

like throwing out the redundant/not too important ones

ye axler

[cobalt badger]

Not sure

[vital bane]

Also don't look at how much time it takes for you to complete a book

just pick up the book and start doing it

Everyday

or as frequently as you can

[cobalt badger]

It’s just that

[vital bane]

just have fun with it

[cobalt badger]

I’m kind of hoping to prepare for an exam lol

So while I’d really not want to think about the time it takes

[vital bane]

I see

[cobalt badger]

or if the material is relevant

[vital bane]

Compare it with the syllabus and the past question papers

what exam?

[cobalt badger]

i just think this is a sacrifice i have to make if the potential reward is admission into a masters degree

[cobalt badger]

ISI M.Math (I remember you said you were from India so you might recognize this)

[vital bane]

ISI based

You should join this server, it has a few ISI people

[cobalt badger]

And thinking of appearing for CMI too (but that’s completely hopeless

[cobalt badger]

Dudeeee

I was just thinking like an hour ago

How nice it’d be if there was a disc server for that

Insane

[vital bane]

Noooo do the CMI one as well

[cobalt badger]

For CMI I’d need to do Complex Analysis and Topology ON TOP OF algebra (abstract and linear) and real analysis

completely unrealistic for 3 months

[cobalt badger]

But yeah I’ll still appear for it

[vital bane]

it's based af

[cobalt badger]

Yeah

Would really like to go there

[vital bane]

Nah you got this bro

[cobalt badger]

Man I’d need to do Abbott, Axler, D&F anyway for ISI

Munkres and a complex analysis book on top of that (Stein and Shakarchi maybe) would actually kill me lol

(I also have a job which is why the 4 days a week and not 7 unfortunately)

[vital bane]

I've dmed you the link to that server

[cobalt badger]

Since I’m already working through Abbott and Axler, if I really push through I might be able to cover some of the required D&F to maybe do well on the ISI this year, but seems kinda bleak lol

[vital bane]

But still there are only two possibilites, you either have enough time or you dont have enough time

so worrying about how much time you need is not too fruitful in both cases

just start doing it!

[remote sparrow]

why do you want to complete this test this year?

[vital bane]

You can only take it once a year

[remote sparrow]

yeah but whatever that test is, it seems inadvisable to try to rush through all the necessary material

@sudden kindle next time you have an opportunity to teach galois theory, consider using Galois Theory by david cox

https://www.thepsmiths.com/p/review-galois-theory-by-david-cox

[vital bane]

what is that cover

is that Galois getting killed in the duel?

[remote sparrow]

i assume so

https://maa.org/press/maa-reviews/galois-theory-2

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

here's a couple other reviews

[cobalt badger]

Fair! But I wonder if I should utilize the 3 months more effectively than diving straight into D&F

[vital bane]

That's a reasonable thing to think about

a few months of work can save you a few hours of planning

[cobalt badger]

Because I’d much rather be involved in Math now than suffer through another year at my software job lole

[vital bane]

Perhaps you should find a graphics programming job it's super fun

[cobalt badger]

Did you mean the opposite? Or am I missing something xD

[vital bane]

opposite of course lol

[heady ember]

CMI=Cannot Make It in Singaporean slang

[cobalt badger]

Hmm, I was honestly thinking about maybe try for a research intern instead of continuing with my current job if I don’t get in this year. Don’t know how doable that is, but I talked to a Graph Theory prof from my college who went to CMI for masters. He suggested I can try for a more applied math internship, something in probability and stats or maybe in Theoretical Comp. Sci.

[vital bane]

ooh

[cobalt badger]

Yeah that is my concern

[livid tide]

I've checked elements of set theory out, and it seems like a nice read. Easy enough that I can go through it without worrying about my other subjects.

I feel like set theory is something that is just kind of assumed that we'll kind of learn intuitively

but its such an interesting topic

historically too

[sly ginkgo]

Copied and saved thank you

[sly ginkgo]

Copied and saved thank you :)

[unkempt gorge]

Hello, has anyone here read books from the Art of Problem Solving (AoPS) series?

I want to buy their Introduction-level (Prealgebra, Introduction to Algebra, Introduction to Counting & Probability, Introduction to Geometry and Introduction to Number Theory) & their Intermediate-level books (Intermediate Algebra, Intermediate Counting & Probability, Precalculus and Calculus) to prepare for University.

I'm not 100% certain I'll buy all of their books, but I am definitely at least interested in their Prealgebra and Intro to Algebra books and was on the verge of buying them today. However, it has come to my attention that AoPS books are apparently only good if you want to do Competition Mathematics, is this true? I have no interest, at least not now, in Mathematics Competitions but seek to deepen my mathematical understanding, problem solving and just learn math in general.

Would the books not serve me well? They're very expensive so I would rather not waste a lot of money on something that would not be beneficial to me.

I appreciate any advice, and please ping me when responding to me

[finite gale]

I don't think aops books are worth it, especially if you're not interested in comp math

If you just want to learn high school math, just use khan academy or something

And also if you do decide to buy some books, it's not really realistic to plan to go through 8 texts lol

[unkempt gorge]

I already use Khan Academy, videos and even another book series.

However, I've noticed the books only impart decent but ultimately superficial knowledge, barely explain and also have genuine mathematical mistakes so I want to replace them. And I don't know why but I guess I prefer physical mediums like books as opposed to online tools, though Khan Academy and videos great and I'll be using them for other subjects apart from Math, but for Math I want to buy a solid book series. I also prefer the satisfaction of going through a textbook as opposed Khan Academy or videos. I recently finished my first math textbook and was super hyped, but when I hit 1m points on Khan Academy I felt almost nothing besides a small amount of satisfaction.

And I don't plan to go through 8 books in a short amount of time either.

[remote sparrow]

the majority of people use regular, non-aops books and succeed, even in top universities

something you want to keep in mind

[unkempt gorge]

Of course, but I heard AoPS books go beyond the regular curriculum I liked the exerpts from them

I'm just asking if they'd let me succeed outside of math competitions. In general academic/university context.

[heady ember]

Yes, Enderton was my first math book and I liked it a lot.

It's nice

[heady ember]

What is considered formal set theory?

Just curious

[remote sparrow]

set theory formalized in first-order logic

e.g. kunen or big jech

[heady ember]

I see

But for the overlapping coverage of, say Enderton, and big Jech, this difference doesn't metter too much right?

At least in my random peaks at kunen/big jech. In fact, Enderton sometimes seems to provide more 'formalisation'. Feel free to correct me though! That's my point of asking.

[unkempt gorge]

[spring jacinth]

LOL ty

[spring jacinth]

ty for the rec

another book q: how do people feel about bak and newman's complex analysis?

[tulip moss]

They mostly revolve around competition all math

And there are better books too imo

Particularly, I would recommend Elementary Number Theory by David M. Burton

But what’s your goal, really?

[remote sparrow]

well, it's interesting in that it begins with power series

lots of solutions are included in the back, which is nice

[unkempt gorge]

I want to thoroughly understand mathematics, be able to apply mathematical concepts to real life, have strong problem solving ability and study mathematics or computer science at university

I’m also self studying right now and have been for a little over a year now

I’ll definitely check out the book by Burton

[tulip moss]

If you want stronger problem solving skills then you should definitely check out mathematical Olympiads, they are specifically to develop problem solving skills and develop intuition

[unkempt gorge]

I did check those out. I tried one of the past worksheets, I got humbled real quick cause I've never seen those problem types before. I do want to get good enough to solve them though

Do you think AoPS would be good for me then?

[tulip moss]

I don’t think it’s worth that much

To get “good enough” to solve them, the most important thing you need is practice

These type of questions would be new for you, so it can be hard to develop intuition on how to solve them

And honestly, the most important think you can do it practice, yeah

[unkempt gorge]

Well, of course. But I'm not talking about the Competition Prep books from AoPS, I'm talking about the Introductory and Intermediate books

[tulip moss]

It’s not worth to spend money on a book at the beginner level

Atleast, I didn’t buy any

[sudden kindle]

Thanks

[remote sparrow]

not sure. you definitely need to know some elementary model theory some time down the line in either

[heady ember]

Yeah I know basic logic is a necessity for grad set theory

[vital bane]

I think humans come pre-installed with basic logic

[heady ember]

Counterexample: Humans took so long to come up with Godel's Incompleteness Theorem

[warm cedar]

AFAIK the standard way to learn calculus is to do it intially with no rigor and then learn the proofs and stuff later in Real Analysis. But I don't like studying things non-rigorously. Should I do things the standard way or skip straight to analysis?

[warm cedar]

I recommend the Everaise handouts, they're like AoPS but better.

[vital bane]

I don't think it matters

you can take either approach

[warm cedar]

What are the advantages and disadvantages of both?

[slender cargo]

Are you in high school or college?

[warm cedar]

High school

[cobalt badger]

If the computational aspects of Calculus are important to you (if you want to use mathematics as a tool for example, in physics or other sciences), then it’s worth studying the mechanical aspects of calculus

[slender cargo]

I would just follow the standard curriculum and do well in the calculus course. If you want to do proof-related stuff, do something on the side like Elementary Number Theory

[warm cedar]

I am mostly learning it for fun

[slender cargo]

After finishing Calculus, then choose one of the books for learning it rigorously, like Abbott's Understanding Analysis

[warm cedar]

I am already doing number theory on the side

[cobalt badger]

If you’re primarily interested in why calculus works, and the rigor is important to you, and you feel comfortable with at least some level of formal proof-writing, you can start with real analysis

[cobalt badger]

If you can handle the proofs there, I don’t see why you shouldn’t give analysis a shot

[unkempt gorge]

I'll check them out, but how are they "better"?

[warm cedar]

AoPS books are too bloated

they are unnecessarily long

the problems are of very poor quality

here are the pdfs:
Handout #1: https://drive.google.com/file/d/1B-gJJQUtcOKAaHeNGzRL1assWxEwtu0j/view
Handout #2: https://drive.google.com/file/d/1MSfgZqRZghfVRn8csvcLMZYGIRaYHV1o/view

(don't worry they are publicly available, this is not privacy)

[unkempt gorge]

What do you mean bloated? And how are they poor quality? I've seen some excerpts and I find them very interesting and difficult

[warm cedar]

What do you mean bloated?
I mean that both the Everaise handouts are about 500 pages in total, and they cover almost everything that all the AoPS intro and intermediate books do in just as much, if not more, depth.
And how are they poor quality?
The exercises can get pretty repetitive.

[gray gazelle]

hello does anyone have any good book recommendations
for mathematics till calculus?
I feel weak in my school mathematics and want to focus on making my foundation better.

[molten mason]

I think I've seen a couple universities combine it into the same class. IMO there's no real benefit or disadvantage either way. You can learn Analysis before Calculus, you can learn them together (probably preferred) or do Calculus before Analysis. It's up to how you learn best and what you can understand.

[molten mason]

Basic Mathematics by Serge Lang

[violet hearth]

Diff geometry by serge lang is also a good book to start diff geo ?

[molten mason]

I personally haven't gone through it, but I've heard it's fine from others

[violet hearth]

I mean its 500 pages

[slender cargo]

imo if the person is going to take Calculus in high school anyways, it's more productive to study a different subject rigorously and save Real Analysis for after Calculus

[violet hearth]

I woulndnt consider reading it if its just fine x), there is a lot of very good books that are more worth to spend time one

[slender cargo]

Number Theory, Combinatorics, Linear Algebra... there are other options

[violet hearth]

What would you suggest for a beginner in diff geo

[molten mason]

Yeah I agree if that's going to take too much time, they're delaying that much more practice and understanding of Calculus. They seem mature for high school and "learning it for fun." Who knows if they're taking Calculus already or not for another couple years, which then begs my next question is if they're this far advanced for that age in math, why aren't they in Calculus already.

[slender cargo]

Yeah, that would be my next question. Just get Calculus over with already

Take it over the summer or something like that

[gray gazelle]

thank you! and what should i use for some good questions?

[molten mason]

It has tons of problems in the text, what do you mean by good questions?

[gray gazelle]

im thinking of something like a website which has some interesting questions beyond the book [ yeah ik that i havnt even started wih the book and i am thinking far too ahead but i just wanna make a note of it ]

[molten mason]

Website? Everyone recommends Khan Academy.

If you have specific things you want to work on, YouTube. There's thousands and thousands of problems, walkthroughs, and explanations on YouTube.

[gray gazelle]

okay, thanks

[violet hearth]

Still looking for a book guys i have no idea on which one i have to start with

[modern ruin]

what's your background in topology

[violet hearth]

I got the basics i guess , i'm starting algebraic topology

[modern ruin]

also do you want like, riemannian geometry or just like something about differential forms?

[violet hearth]

I just want to learn the basics so i know what would be interresting for me

[modern ruin]

okay just read like Tu Intro to Manifolds then lol, you can decide later if you want a different flavor/difficulty

[violet hearth]

Like both are good, it doesnt matter if the book is long as long as its good and im note spending hundred of hours for nothing

[modern ruin]

I am thinking about writing a list of beginner differential topology and beginner differential geometry of curves and surfaces books like the pinned algebra list that daminark has

[violet hearth]

What's the diff between diff geo and diff topo

[modern ruin]

well it depends on who you ask

[violet hearth]

Damn

[graceful moon]

I’d recommend Kobyashi’s curves and surfaces book for that, I took a class last semester which vaguely followed that book and it was amazing

[violet hearth]

Math not mathing

[violet hearth]

I'll look for it ty both of u !

[graceful moon]

If you’re doing algtop that book might not be enough for you, but it’s definitely enjoyable and I found it quite challenging to start with

[violet hearth]

Im asking you then x)

[modern ruin]

here is (part of) my understanding of the "difference" (though I might get beheaded and it's incredibly poorly worded, and also the difference doesn't matter that much) it just has to do with what kind of structure that you put on your spaces. Suppose you have some topological space $X$, then if you make considerations only about $X$, then you're doing something like "pure" topology. If you know that $X$ happens to be a manifold, and you specify some atlas $(U_\alpha, x_\alpha: U_\alpha \to \mathbb{R}^n)$ with smooth transition functions, and then require that homeomorphisms are smooth with respect to the given atlases, then you're doing something like differential topology, and there are a lot of things that are interesting in their own right in this setting (both objects of study and classification problems), for example, with these smooth manifolds, it's natural to think about tangent vectors and differential forms and what they say about the space. Sometimes, though, we will go further and equip our spaces with even more structure, for example a metric (or a connection) which gives us now a notion of parallel transport and lengths of curves, where before we were not able to talk about these kinds of things, and at this more "rigid" level you can talk about more "purely local" invariants like curvature, where you couldn't find any before

[hasty eagle]

almost complex smaycture

[violet hearth]

Wow lemme read

So the diff geo is attached to the metric part when u give more structure than just the basic topology settings right ?

[modern ruin]

yeah, metrics/connections make manifolds much more rigid than they would be without one

you can talk about physics-y things with rigid structures like that

[violet hearth]

Okk so diff topology is more "pure" but have less freedom in a sens

[modern ruin]

they're all pure in a sense

i don't really like the distinction between pure and applied math that much tbh

[violet hearth]

I dont see why it would be applied math here since we are discussing about shapes

Like physics could be interrested in that but its still pure math (imo)

[modern ruin]

okay sure then they're both sort of pure then, they have interesting questions that you can ask and be interested in that are independent of any other field of study

[violet hearth]

Okk tyvm for your answers !

[crude sage]

How do Spivak's Calculus on Manifolds and Tu's Intro to Manifolds differ?

[distant void]

Anybody read Palem/Weichsel's "A First Course in Abstract Algebra"? It was the cheapest used algebra book I could find

Or if there's another abstract algebra book someone would recommend, I've got a pdf of Dummit/Foote but a physical copy would be 50 bucks at least

[marsh ingot]

Tu has more theory about manifolds indeed

[gray gazelle]

Basic Algebra I by Jacobson has a dover edition

[marsh ingot]

Btw you say this Spivak?

[distant void]

I'll check it out, thanks 👍

[crude sage]

I see

[crude sage]

Yes, this book and not his Calculus/intro real analysis book

[gray gazelle]

there is one discrete math book I am thinking of, i came across it a while ago, it has so many practice examples, I just forgot the name, could someone give me the name of a few popular discrete textbooks?

[marsh ingot]

Then yeah Tu has more theory than Spivak about manifolds. Spivak is like a approach for students who didnt take diff geo before

Also Tu is like ~500 pages

[crude sage]

Somehow I got the impression that they both had the same prerequisites

What kind of diff geo do you need to have taken to read Tu? I thought it was "diff geo" 🤣

[icy forge]

what are the best popsci math books

[tribal crow]

not sure if this counts, but i've always heard people recommend Godel, Escher, Bach

i have not read it myself though, so dont take my word for it

[rough umbra]

whats a good book to learn enough abt field extensions to be prepared for an intro to commutative algebra course?

[modern ruin]

good book

[dusk wind]

Get 1 good Algebra book, and 1 good geometry book, and a stats one optionally. Probably not necessary to buy so many books from 1 publisher or use AoPS or even khan academy for those subjects. Maybe what you want is something more interactive? Perhaps take more of an applicative based approach. Actually, these handouts @warm cedar are okay for problem sets but not for learning, would still recommend books for learning

If you do pick any alternatives to AoPS, learn from an author that also actively teaches, chances are it may be easier to learn from them

[pseudo heart]

anyone have any good book recommendations for learning number theory?

[trail hemlock]

ctrl + f

[pseudo heart]

ty!

[candid cipher]

I use David burton's elementary number Theory all the time, no background knowledge really needed

pretty cheap too

[crimson leaf]

I would not give this book to someone who has not completed a course in groups, rings, and fields

[trail hemlock]

ok my bad

[trail hemlock]

no ignore that apparnetly its not good unless you have completed a course in groups, rings, and fields mb

[crimson leaf]

Or probably analysis as by page 26 they're talking about convergence in the field of p-adics

[pseudo heart]

oh real, thanks yall :D

[crimson leaf]

Here's a review of the book if anyone is curious

[molten mason]

at a level of difficulty considerably above that of Hardy and Wright

[rough umbra]

Bump

[unkempt gorge]

I actually had a pretty decent learning method until now:

• A book series (two books, one Prealgebra & one Algebra 1)
• Khan Academy (Supplementary Resource)
• Videos (Namely The Organic Chemistry Tutor & Professor Leonard, also Supplementary Resource)

However I came to realize that the books I had kind of sucked midway through the Prealgebra one. I finished it nonetheless, but here is my opinion:
It had many, many genuine mistakes, and it barely bestowed superficial knowledge. The worst was the introduction to functions chapter. Overall a 6/10 experience.

In fact I did the "Are you ready?" diagnostic for the Introduction to Algebra AoPS book. And I meticulously studied and explored the previous Prealgebra book I had so I should've scored well within ~80%. I didn't. I got like 40% simply due to so many gaps I had in knowledge that the previous book I had should've introduced me to, but didn't.

And I like how Khan Academy works, especially how interactive it is. But I struggle viewing it, and the channels, as more than supplementary resources.
Not because it's bad or anything whatsoever. It's moreso a personal preference. I prefer having a physical book > anything online like courses etc.
And this is coming from someone with over 1,000,000 points on Khan Academy, lol!
Still, I'm using and will continue using it as a supplementary resource for mathematics, and possibly main resource for other subjects as it is simply amazing.

I decided to treat myself today, kind of like investing in my future, and buy the Prealgebra AoPS book.
I paid over 100.- USD due to the international shipping, but I know future me will appreciate this decision.

[dusk wind]

Which book were you using primarily? If you have all those resources (especially using organic chemistry tutor videos) you might even be overprepared, I'm not sure if AoPS is a good metric in general, in the future you will still run into the same discovery of needing to find alternative materials. The pacing of AoPS might be a bit much in exchange for solid fundementals or the enjoyment of them.

At the Pre-Algebra+ levels, any book should suffice if the explanations are clear (moreso than in a video or even khan academy).

I do advise to always leisurely consider alternatives, as your enjoyment of the material is paramount. Curiously, what was it that prior books were lacked in particular? Authors also have decent to varying quality books released online, while not as difficult, perhaps they have a better vision than the books you read before.

[dusk wind]

Someone linked this https://www.ppstest2.com/PreAlgebraBook.pdf but you could use Algebra by Yoshiwara or Wallace. With some searching, I found these @unkempt gorge

[unkempt gorge]

I used the Mathematics series from Workman Publishing. I bought the Prealgebra and Algebra 1 books, but only worked through the Prealgebra one. Wasn't impressed.

It was nicely structured, but only superficial knowledge and wasn't anywhere near rigorous. It also left me with some holes in knowledge that I realized during the AoPS diagnostic test. It’s order of content was also quite strange

I’m not overprepared, I can attest that. I’m not using Khan Academy or videos that often, as I said they’re supplementary resources for when the book wasn’t enough.

I checked the AoPS books and their overall content and structure was very appealing to me. Regarding the AoPS books I’d say I’m quite informed and I’m satisfied with essentially everything bar their price. Though it’s kinda given since it’s a textbook and those tend to get pricey. Especially at college level. And spending ~100$ once every few months isn’t that bad of a deal, especially when you’re investing in your future.

I’m open to alternatives though, so I appreciate your efforts. Although I already bought the AoPS Prealgebra, for Algebra+ I’ll definitely check them out. Thanks!

I’m not home rn though so I’ll look at those links later

[wicked coral]

hey yall i got a question, what's the best math book to algebra 1 and some pre algebra, im in community college rn but i want to refresh my math skills since the pandemic messed them up horribly, what book would you guys recommend to relearn math?

[crimson leaf]

You should just be able to pick your favorite graduate algebra book. There should be reviews in the pins

[wet sand]

I wanna get into cal or pre cal any recommendations???

[sturdy flame]

Can anyone recommend book for linear algebra in proof ways.

[thin kernel]

Sheldon Axler, Linear Algebra Done Right

[gray gazelle]

hi guys

dyk how i can find a specific math book bc my teacher uses the same book but ss the specific qs and i cant find it on google

[tribal crow]

Alternatively to Axler, Linear Algebra by Friedberg, Insel, Spence

[rough umbra]

Cool thanks

[daring lake]

just ask the... teacher?

[magic zinc]

@remote scaffold

finding resources?

[remote scaffold]

Yeah for calculas!

https://discrete.openmathbooks.org/dmoi3/dmoi.html
If something like i appericate!

[magic zinc]

okay

You can ask about books or resources in this channel to people

I am sorry but I am very early for calculus and cannot help but surely go for Classic Text Series for questions from Arihant.

helpful for algebra atleast

for me

[remote scaffold]

I am looking for a resources that explain basic and advance of calculas
I am looking for a website other than book

[gray jungle]

https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

[remote scaffold]

Thanks man!

And any resources for cordinate geometry

@gray jungle

[gray jungle]

not that i know of (and please dont ping me randomly 😄 )

[remote scaffold]

Ok!

[round pelican]

I’m trying to self study real analysis but I’m not sure which direction to take. I bought Introduction to Real Analysis by S.K. Mapa. It covers a lot of material. One thing it doesn’t cover is Metric Spaces. I’ve taken an intro to analysis class where we covered up to uniform continuity and the intermediate value theorem. I want to get a good foundation and prepare myself for grad school because my school doesn’t have a class that follows the intro to real analysis class. I’ve read that many people use Rudin to get a solid foundation in the material. Should I follow Rudin and use my other book when Rudin gets confusing? Or what have you all done to learn this subject? Thank you!

[rugged maple]

#book-recommendations message

[graceful moon]

I wouldn’t self study Rudin, I’d use Tao or Abbot to self study personally. You can also get a book on specifically metric spaces by Magnus (I really like that book) or Sutherland (never read it but I’ve heard it’s good)

[dusk wind]

Use Abbot

[dusk wind]

https://www.amazon.com/Math-You-Need-Comprehensive-Undergraduate/dp/0262546329 sample is blurry

[sudden kindle]

Naive Lie Theory by John Stillwell is a nice undergrad book

[ocean mulch]

I asked in #advanced-number-theory but it seems quiet there. Does anyone have any literature recommendations for (infinite) exponential sums?

I know it's a central topic in anal NT and there's a lot of work done about it, but I'm an outsider and finding an entry point is tricky

[dusk wind]

interesting way to put it

[ocean mulch]

pun unintended

[molten mason]

Linear Algebra by Friedberg, Insel, and Spence

[heady ember]

That's not a lie, is it?

[dim sierra]

Axiomatic Lie Theory would be better (and definitely wouldn’t be a lie)

[hallow pivot]

Hi. Opinions about Zermansky and Sears pls? Not sure if it's me but the book feels pretty much 'dry', it looks like written in prose. Also, is it me or the book starts explaining particular exercises to then give the general concept? Like, maybe it would be easier to understand the general concepts before giving examples? (because those examples are just specific cases of the most general stufff??? idk what I just said)

okay, I know this is a math server but anyways

now that I think about it, calculus by Stewart and some discrete math books are "verbose". What are advantages and disadvantages of these books?

[dusk wind]

historic account on number theory https://archive.org/details/numbertheoryappr0000weil

[molten mason]

I'm currently going through two of his books and he's growing on me as an author. What would you say is a needed background for that book? I know some Lie texts can require a huge background.

[earnest wolf]

hi 🙂

what can I study after Abbott's understanding analysis?

like measure theory/Labegue's integral straight away or there should be something in between?

[remote sparrow]

you can read axler's Measure, Integration, and Real Analysis if you want

you can also read more about metric spaces and function spaces with carothers

[earnest wolf]

hm, when I looked at it a while ago it seemed a bit too advanced

going by the contents at least: didn't dive into the details

[remote sparrow]

you only need to know single variable analysis

[slender cargo]

Axler himself said that Abbott is fine

[remote sparrow]

a crash course on the definition of a metric space and some examples should be fine later in the book

he also gives a quick review in the text

[earnest wolf]

then i probably confused that book with some other

[slender cargo]

From what I've seen of schools, there's a lot of options for after Single Variable Analysis. Some schools will suggest you study Rudin, others would suggest going straight to Measure Theory (which imo would be less boring). You could also study Analysis on R^n

[loud cradle]

you could always take a side trip into complex analysis as well

[remote sparrow]

#book-recommendations message

you can also look into Metric Spaces by magnus or Metric Spaces by o'searcoid

o'searcoid has solutions in the back, and also a full solutions manual

[quasi isle]

Hey i wanted to ask if james’s stewart’s single variable calculus is like a good book for someone currently doing precalc. My father used it way back when and i wanted to ask if it still holds up

[molten mason]

Which book does this message pertain to? Yeh?

[remote sparrow]

it's a graduate textbook

[molten mason]

Stewart is still pretty common for Calculus around colleges in the US.

All of the exercises (including even problems) have not just the answers, but a full worked out explanation on the paid version of Quizlet.

[remote sparrow]

about the same level as folland

but it has an accompanying complete solutions manual

[molten mason]

Yeah I read the MAA page about it. I was wondering if that's what the person in the statistics server recommended.

[remote sparrow]

yeah

[molten mason]

THAT is amazing. The only thing I dislike about Lang is there really aren't any solutions online for a lot of his books lol

[molten mason]

I'll add it to my list, thanks

[quasi isle]

Right, thank you.

[molten mason]

I wonder how Yeh compares to Bass 🤔

But if Yeh has a solutions manual and Bass doesn't (idk I haven't checked), then Yeh automatically wins

[loud cradle]

yeh is very detailed but it's dry as dust to read

[molten mason]

I actually don't mind that

[loud cradle]

aside from that it seems fine, proofs give every last detail for the most part so it's kind of the anti-rudin in that respect (that's why it's such a thick book), and with solution manual i imagine it would be good for self-study

[molten mason]

Perfect!

[sudden kindle]

He claims his book can be read with only lin alg and calculus background

[molten mason]

Interesting

[molten mason]

I skimmed it briefly on archive.org, actually very interesting, very self-contained. Thanks for the rec!

[remote scaffold]

Any website article for limit and differentability and differentability based on trignometry?

[fierce hedge]

What would be a good book for ug complex analysis which can cover the following topics within around 3 months -

Holomorphic functions, Cauchy-Riemann equations, integration, zeroes of analytic functions, Cauchy
formulas, maximum modulus theorem, open mapping theorem, Louville’s theorem, poles and sin-
gularities, residues and contour integration, conformal maps, Rouche’s theorem, Morera’s theorem

I currently have physical copies of Krantz and SS, I don't have much idea of should they suffice or should I get something additional

[upbeat vine]

Complex Made Simply by David Ullrich

[remote sparrow]

gamelin

[fierce hedge]

Like as a primary book or as secondary reference?

[upbeat vine]

Primary primary

[fierce hedge]

Alrighty thanks

[upbeat vine]

#book-recommendations message
#book-recommendations message

[remote sparrow]

also bak and newman

[fierce hedge]

Hmm, I'll check both of them. Both are intended as primary books right?

[remote sparrow]

yeah

[fierce hedge]

Thanks 🙏

[remote sparrow]

i wasn't aware strang had a complex analysis book btw

@fierce hedge

[fierce hedge]

Oh shit, I meant Krantz my bad

I meant this book @remote sparrow

[remote sparrow]

ye i heard that book was okay

[marsh ingot]

Krantz?

[fierce hedge]

Bad experience with this book?

[marsh ingot]

Im reading the several complex variables one

Literally this

[fierce hedge]

Lmaoo

[pliant wadi]

What's that one famous and thick book on history of topology?

I can't remember its name

[quick hornet]

i m james?

https://www.sciencedirect.com/book/9780444823755/history-of-topology

[haughty dagger]

how hard is the black book for JEE

[pliant wadi]

Yea I think so

Thanks

This is for after poincare, any recs for the history before him

[gray gazelle]

recommend a good book about calculus

[vital bane]

Gamelin

[fierce hedge]

Hey would you happen to have a decent copy of that book, all I could find was okish djvu copies. Also, it's pretty expensive to actually have a physical copy.

[upbeat vine]

I think I just did a djvu2pdf and created my own table of contents, if you want I can give you the "software" in dm

Actually no, I think I downloaded the book from my university library, and it contains the university reference. But yes, the above strategy will work

[fierce hedge]

I have that software too but it basically just changes the container from djvu to pdf right. Like can you highlight stuff in that pdf?

[upbeat vine]

Lemme check

It probably depends on the software you end up using, I will check if mine retains most properties

[vital bane]

just take a printout of it

also are you writing CMI/ISI?

[upbeat vine]

Yep, you can highlight and everything: I use a python package called djvu2pdf to convert

[fierce hedge]

Oh sweet, can you dm the converted copy please

[fierce hedge]

CMI definitely, ISI I am not sure

[upbeat vine]

Messaged.

[dark berry]

Hey guys any recommendation book about probalitity and statistic ?

[vital bane]

Why are you not sure??

ISI is based

well not all of them but ISI-K is based

and are you not applying for grad schools outside India

[fierce hedge]

As in not sure if I want to apply for Maths or CS. Neko has been convincing me to apply for CS

[fierce hedge]

Nope, although it is strictly an lor issue

[vital bane]

that is simply a skill issue

just email all your past profs and ask for an LOR

anyway we should talk about this in some other channel

[covert mauve]

any books that cover basic algebra and (geo/trigno)metry? except khan academy and serge lang's basic mathematics.

[gray gazelle]

how do you create your own table of contents?

can you tell me which software do you use for that?

[upbeat vine]

PDF Outliner

[gray gazelle]

it's a paid app

:(

plus it is mac exclusive

is there a free windows alternative?

[gray jungle]

nitro pro has 14 days trials iirc , you can abuse it with temporary emails when you need a bookmark

[ocean mulch]

think of it this way: it's easier to jump from Math to CS than from CS to Math

not everyone likes Math tho, that's why we have jobs, so do think about if you're ready to suffer

[fierce hedge]

I think pdftk should do the job although you might have to search a bit on how to actually do it

[vernal eagle]

hello, i need resources to study markov chains.

introductory texts, or notes. anything would do the job.

[dusk wind]

https://www.pdf-xchange.com/product/downloads many free features

[gray gazelle]

Any book recomendations for Number theory. assuming a high school level of maths. I have a proof book that I probably won't finish in two years but I think I can self study proof and number theory side by side and would like to do that now.

preferably not too expensive

and available in europe

[autumn spire]

Zuckerman

also Dudley can be used if you just want to get the basics

[fervent wave]

Here is one from the open textbook initiative https://aimath.org/textbooks/approved-textbooks/shoup/ that has a low floor for prereqs.

Although the level is directed toward senior year UG/intro Grad

[finite gale]

If you have calculus, you can maybe read some of apostol for analytic nt

[karmic tangle]

Hello

I've heard people say that one could do with having gone through a "computational" linear algebra course before going with Axler's LADR, how far should one go in the former ideally?

I've gone through 1 which was pretty much a proof-less speedrun in 1 semester and another one which was with proofs but just one semester so not that much stuff was covered (matrix stuff, vector spaces and subspaces, linear maps, bases and dimensions, determinants and then affine subspaces but those weren't needed so I don't know anything about them really)

my question is if I can go for Axler's book now provided that I also had an abstract algebra course

[magic spade]

Yeah go for it. You should be fine

[karmic tangle]

Thank you

For a second-ish pass at abstract algebra, should I go with Aluffi's Algebra:Notes from the Underground or Algebra: Chapter 0?

[molten mason]

Introduction to Proof Through Number Theory by Chow

Stein is available free and legally.
https://wstein.org/ent/

[molten mason]

https://mecmath.net/trig/

[dusk wind]

also consider 'Precalculus Made Difficult'

[remote sparrow]

how much did you learn in your first pass with abstract algebra

[karmic tangle]

a tiny bit of semigroups/monoids, lagrange's and group homomorphism theorems, some stuff about rings and ideals and factorization, integral domains, fields, rings of polynomials over fields and some things related to them, field extensions, and I'm reading a short book right now that should expose me briefly to the sylow theorems and a tiny bit of galois theory apparently (visual group theory)

[gray gazelle]

Thanks

[remote sparrow]

you can read aluffi's Algebra: Chapter 0 if you want

aluffi's Algebra: Notes from the Underground has a rings-first treatment and a pretty gentle treatment of modules though

although it won't push you much further beyond your groups, rings, and fields class

Galois Theory by david cox is a very well-motivated introduction to galois theory

dummit and foote is a standard reference, and it has tons of exercises. it can be used for a groups, rings, and fields class, but it has graduate material too

[karmic tangle]

ah interesting

I haven't encountered modules at all really

I've heard some kinda polarizing things about dummit and foote

[remote sparrow]

the exercises are good if nothing else

and it's one of the most comprehensive books

[karmic tangle]

I'd like to pick up that or lang's algebra afterwards as a reference text but I fear it might not sit well with me as a "learning" book

and I like that chapter 0 should supposedly introduce me to some category theory basics too

(xd)

[remote sparrow]

you can try hungerford as an alternative to lang, though it's missing coverage of group actions

jacobson is available for a very low cost

[karmic tangle]

those you mean as reference texts?

[remote sparrow]

people do learn from hungerford and jacobson. you can thumb through their pdfs to see if they're right for you

i mean, they're probably a bit more accessible now that you've had one algebra class under your belt

[karmic tangle]

we've Jacobson's lectures in abstract algebra in our uni library and dummit and foote and aluffi's chapter 0 too

so I think I could take a look and see which one feels right

[remote sparrow]

https://www.amazon.com/Basic-Algebra-Second-Dover-Mathematics/dp/0486471896

the dover edition is substantially revised

notably, jacobson no longer covers linear algebra, since he now assumes students have been taught linear algebra

the typesetting of Lectures is kinda ugly tbh

[karmic tangle]

I also have Pinter's "A Book of Abstract Algebra"

bought it because I found it cheap but then ended up not having even opened it, do you think that could prove useful if I've already encountered the topics once?

[remote sparrow]

it's probably too simple for you to bother working through in-depth, but pinter motivates the subject well

maybe consider it "bedtime" reading

[karmic tangle]

wow that is also cheap yeah, bless Dover Books

[remote sparrow]

i still love recommending pinter for beginners

[karmic tangle]

xd I guess I'll gift it to someone

[remote sparrow]

although i would also recommend they pick up judson or aluffi's notes from the underground in addition since pinter relegates a good amount of core material to the exercises

[karmic tangle]

I've heard as much, but many people praised that

[remote sparrow]

pinter does not make a good reference

which is why i tell people to pick up judson and pinter

[karmic tangle]

ah

[remote sparrow]

http://abstract.ups.edu/

[karmic tangle]

I think I will go with chapter 0, I still really like the allure of the categorical presentation, seems hard to resist

[karmic tangle]

I think I have this opened in some tab from maybe 9 months ago? haha

[remote sparrow]

https://www.math.fsu.edu/~aluffi/algebraerrata.2016/Errata.html

be aware of the errata

it's pretty long

[karmic tangle]

oh wow

I saw that mentioned in some comments/reviews but didn't actually see the thing

[gray gazelle]

I would instead recommend Lax: Linear Algebra and its Applications

[gray gazelle]

Casella, Berger: Statistical Inference

[remote sparrow]

don't be put off by the word applications, boyard, it's a pretty hardcore book

doesn't get into module theory for obvious reasons

[dark berry]

Thanks dude

[covert mauve]

when I say basic, I dont mean that basic. also no precalculus books, they tend to skip a lot of important details. like half the ones I have seen don't cover irrational number properties or prove them.

I don't want to pick a book and feel like there are major gaps in my basics after I am done with it.

[remote sparrow]

you were considering buying serge lang's Basic Mathematics before but decided not to because of its expense

wait until the next springer sale if you can

that's really your best option

alternatively, work through a regular precalculus book, a book that teaches you how to write proofs (e.g. Book of Proof by hammack), and Number Systems and the Foundations of Analysis by mendelson

[covert mauve]

will try that

[gray gazelle]

Have ya'll ever tried Algebra 1 by Stevenhagen?

Thrilling book

[molten mason]

That's a topic normally in Number Theory, and there's some irrational numbers/properties that are still open problems. I could be wrong, but I don't think I know of anything pre-Calculus that really says too much more than stating a few facts about them e.g. cannot be expressed as a fraction or has a non-terminating decimal.

What exactly do you mean about important details and properties/proving them.

and what is your end goal after all of this?

[covert mauve]

my goal is pretty simple: have enough math knowledge that I can pass my classes and start basic calculus / linear algebra.

I am not against covering things from other resources if a book doesn't cover them (like say, irrational number operations or plotting), but its way more sane if I can just learn from a single source.

[slender cargo]

Any standard pre calculus book will get you there

I hear khans academy is good also

Many of the topics in pre calculus are not covered more rigorously until later courses

[covert mauve]

makes sense

[molten mason]

The goal of a pre-calculus textbook is to prepare you for calculus. You're asking for advice here from those who have already been there and done that and we're letting you know all these textbooks are perfectly fine and shouldn't have any major gaps. To try to figure out every little detail is a bit pedantic. At the end of the day, trig books cover trig, geometry books cover geometry, algebra books cover algebra, pre-calculus books cover what you need for pre-calculus. At this level there's not too many differences between books. Some books might be more problem heavy or set up for Olympiad competitions. Lang is more proof-oriented. It's all the same. I think in all 3 semesters of calculus the only geometry and trigonometry I needed was the following: https://mathsux.org/wp-content/uploads/2022/05/Geometry-Cheat-Sheet.pdf Anything not in that pdf was introduced in the textbook/class. If you want to be extra and really get an understanding of trig/geometry and get some practice in there's this one: https://mecmath.net/trig/ which is a free pdf and I think the physical text is $11. Linear Algebra, depending on the level, requires about the same or less. Again a Pre-Calculus textbook, any textbook, will be enough as a background for Linear Algebra.

Don't think/study too hard at the current level you're at. Everything you need to know will be covered and explained more and more, and most importantly, as you learn and study more advanced topics, you will always be practicing the basics and discovering more about them.

[covert mauve]

thanks, will do it.

[molten mason]

Also Calculus is the same; literally any book will do.

For Linear Algebra, here's this.

#book-recommendations message

For textbooks past LA and Calculus, that's a whole different story and depends on different things.

[dusk wind]

theres not much in a basic high school course, precalculus will take you there, plenty of alternative texts that do the same thing, like axlers precalculus book

[trail hemlock]

you can also try TEKS Texas Precalculus, just because all the problems have solutions worked out on quizlet:
https://quizlet.com/explanations/textbook-solutions/teks-texas-precalculus-1st-edition-9780021402502

[covert mauve]

all the resources are very helpful, thank ya all so much!

[remote sparrow]

PSA: if you can help it, don't buy spivak's calculus new. ever since his death in 2020 and subsequent takeover by the hindustan publishing agency, the binding of the book is worse

[left falcon]

is apostol's mathematical analysis better at explanation than rudin's pma?

because only studying from pma is making my head explode

and I am considering changing book

[graceful moon]

I think speaking to a wall would have better explanations than PMA

[left falcon]

i mean I am not in positino to judge a textbook

but even so PMA sucks at 'teaching'

it feels like a list

of theorems and definition

[gray jungle]

rudin is only good as a reference or for a tutors usage, i would recommend a more padagogical book to use with it

ideally you have lecture notes somewhere

[left falcon]

maybe I should search for these in internet

also one more question: does apostol assume you have knowledge of his own calculus books? or is stewart's calculus fine?

[rain wren]

look into abbott!

it's a book but it's very well written and quite beginner friendly

[daring lake]

He doesn't

Its a good book but more or less redundant if you followed Rudin. Both are more or less on same level imo. I felt like i was reading off-style rudin while going through Apostol. Keep in mind, Apostol covers way more than Rudin.