book-recommendations

[remote sparrow]

is this the first time you're learning linear algebra? if so, see here: #book-recommendations message

[livid cove]

What do guys think of Lee’s Intro to Smooth Manifolds book?

[kindred sluice]

P good

do u want to know something specific?

[livid cove]

Are you talking to me?

[livid cove]

Is it a standard book? Or would you recommend something else? I am self learning .

[livid cove]

Took me a while to realize that P = Pretty and that you were talking to me lol.

[gray gazelle]

Pretty standard recommendation, yeah

[livid cove]

Ok, thanks 4 info

[gray gazelle]

hmm

[gray gazelle]

Linear algebra book

With lots of solved problems

I need to practice a lot

[remote sparrow]

look at hefferon

he wrote a full solutions manual for his book

[formal apex]

I’m looking to start my book collection. Any good recommendations?

[finite gale]

what kinds of books are you looking for

[fierce hedge]

Dover books are cheap and good quality so they're generally safe to buy

[formal apex]

Stuff that looks cool on a shelf but also has just generally good and interesting info.

[formal apex]

Thanks

[distant bobcat]

any recs on abstract algebra for someone who's learning it on their own?

[hasty turret]

Dummit and Foote

Also pins

.

[fierce hedge]

probably pinter or gallian

ofc check pins

[magic zenith]

I bought Keith Nicholson "Linear Algebra with Applications". To tell you the truth, it was a bit hard at first, but the applications are really nice. PDEs, Markov Chains, etc... Even if you don't have a lot of experience with that, you can still follow through and do the exercises. I was slow and insisted in doing all exercises, so my progress was slow. But i liked it. Let me put it this way. My insistance paid off and rewarded me with a good understanding. I also have Henry Ricardo "A moderm introduction to linear algebra", but i ended up buried a lot more in Keith Nicholson's book. Strang's linear algebra books are recommended too.

[marsh yew]

Book

[foggy relic]

Shilov, has answers to almost all exercises at the end

[sage python]

ngl tho starting with determinants sounds borderline memetic

[marsh yew]

Lol

[foggy relic]

insane motivation

[west cloak]

im in grade 11 and I think I am bit down in algebra. Can someone recommend a book with exercises (better if it small). to find some hard questions thanks

[pseudo coral]

What e book can I start in maths im self learning

[mossy flume]

what math are you looking to learn?

[brittle oak]

Hello, what books are recommended about functions?

[mossy flume]

what about functions?

[brittle oak]

mainly linear and quadratic, how to graph, interpret and everything related to it

[quartz sparrow]

any reference for Set Theory?

[fleet bramble]

Karel Hrbacek has a book called Introduction to Set Theory, or maybe some books related to general topology?

[remote sparrow]

hrbacek, enderton, or goldrei

[strong oyster]

i like jech

[distant bobcat]

is hausdorff good for set theory?

i currently have that but ill look for other options if not

[small lintel]

What's a good book for learning PDE? I'm between Strauss, Farlow and Evans. I don't know if there are others better for self-studying

[slim peak]

PDE at which year/level ?

[small lintel]

undergraduate, just passed Calculus III and introduction to ODE

Which is not really ODE theory, more like solving the different cases

[slim peak]

Calculus III and ODE Intro aren't far from being sufficient to get into ODE/PDE

you need at least additional lecture on normed vector spaces and basic stuff necessary to get into an actual proof of Cauchy-Lipschitz

Once you are there you would expect to be able to start 'undergrad PDEs'

In this case I would tell you to look at Evans.

But to be honest, I'm the kind of person "go wild or go home" and would say go into Brezis which will require you to be near the end of your undergraduates years.

[small lintel]

I'll take a look at evans, thanks.

[thorn cloak]

How is Calculus on Manifolds by Spivak? Is it a good follow up to real anal 1?

[remote sparrow]

what are the contents of real anal 1?

[remote sparrow]

have you had real analysis? what is calculus iii? multivariable and vector calculus from a book like stewart or larson?

[small lintel]

I'm taking real analysis rn, calculus iii is vector calculus and multivariable calculus, yes.

[remote sparrow]

you can read strauss, zachmanoglou, or weinberg after real analysis

evans needs functional analysis and measure theory, although it should be noted that grad pde isn't really a continuation of undergrad pde

ug and grad pde are fairly independent of each other

[small lintel]

so, for ug pde should I just read evans?

[remote sparrow]

evans is graduate

[small lintel]

Strauss?

[remote sparrow]

undergrad

[small lintel]

I think I'm looking at the w- nvm I'm reading strauss so I think I'm good with that book

[thorn cloak]

This but it’s split into two classes so I’d assume some of the later topics are in sem 2

Idk if it would be better to just take analysis 1 self study calc on manifolds and then complex analysis instead of real anal 1 and 2

I believe in previous sems they followed artin

[round geyser]

The Book Thief is a very good book

[remote sparrow]

calc on manifolds covers multivariable analysis up to stokes' theorem

[thorn cloak]

Hmm I see. Is there a book that goes more in depth into vector calc or is that pretty standard?

[small lintel]

There's a super cool book but it's in spanish

[remote sparrow]

zorich mathematical analysis vol. ii chap. 10-15 covers this stuff too i think

also second half of schroder or browder

[thorn cloak]

I’ll check those out then. Ty!

[slim peak]

Not the first chapters

My oint recommending Evans is that first chapters deal with simple concepts and at least Evans aims things near graduate PDEs

Like Evans' to me sounds like "towards graduate PDEs from the undergraduate PDEs perspective", even if I personally don't like it.

[nocturne crane]

Quick question for those of you who have algorithms experience here, how do you understand an algorithm in depth? I feel like I lack the understanding of algorithms to really do well on a project...

[fleet bramble]

try understanding the logic behind it?

[nocturne crane]

Do you have any suggestions for how to understand the logic behind an algorithm? Specifically I get lost on what items I should focus on in the algorithm... should I try to trace one behaviour from scratch?

[fleet bramble]

i think algorithms are like methods for human to teach computers solving problems so maybe u can try computing some simple examples by urself to understand how the algos work

[nocturne crane]

Okay, so for the first step I should try to reason about the behaviours of an algorithm through examples.

Are there any concrete cases that I should consider when creating these examples? Are there logical units that I should decompose examples into? (Also let me know if this conversation is best for another channel)

[fleet bramble]

examples vary by algos i think but i think maybe some examples in lower dimensions or taken fewer steps can help or u can just choose a random example and try computing the frist several steps of the algo personally idk which one helps u most

just computing personally to take a glance of how the algo works is enough i think

[nocturne crane]

I see, so typically try coming up with either smaller examples or going through an arbitrary example should be fine, as long as I try reproducing the arguments by hand to understand how the algorithm works.

Thanks @fleet bramble , that's helpful, I've always felt like there were some problems with my approach so this is good to know.

[fleet bramble]

my pleasure

[crimson leaf]

Is there a good geometry review book for university students something that isn't too long and covers the basics?

[finite gale]

what kind of geometry?

[fleet bramble]

search in the undergrad text of math series?

[crimson leaf]

Euclidean

[abstract walrus]

Complex numbers?

[heady ember]

Sean recommended Morton Curtis to me for linear algebra the other day and it seems cool. But is the book really not missing anything important for a lin alg book? 150 pages seems really succinct. So, if anyone has some experience with it, does it have all the important theorems and stuff?

(Yes I have read Dami's la book review and I know that being fast or short is not necessarily good. To that end, if you have had experience with morton curtis, perhaps you could share what you think with regards to its readability?)

https://www.amazon.com/Abstract-Linear-Algebra-Universitext-Morton/dp/0387972633

I have FIS but it was kinda dry to me while I was reading it (though I didn't read very far, to be fair)

[hollow shore]

Coxeter's Geometry Revisited

[crimson leaf]

This looks exactly like what I want, thank you!

[remote sparrow]

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

you might also be interested in this

it has a solutions manual for the odd exercises to accompany it

[merry sphinx]

does anyone have any good multilinear alg book recommendations?

[remote sparrow]

werner greub multilinear algebra is the only book i've heard of

[gray gazelle]

Any good calculus books to understand the fundemental concepts?

[tender birch]

@gray gazelle the standards probably. Stewart, Thomas or Edwards/Larson/hostetler

[gray gazelle]

I'll check it out, thanks!

Also, by chance do you recommend any non textbook books about math? Just to read for fun

[tropic thorn]

Hi guys, what the best linear algebra book for someone who wants to understand the concepts intuitively ( geometrical représentations etc...)

And not focus mush on computation

[broken meadow]

i liked friedberg

[gusty raft]

any recommendations for learning ode (and afterwards pde)?

[slim peak]

Viorel Barbu's book

[distant solar]

i reccomend da vinci code dan brown ,, its is my fravourite books

[magic raft]

Louis Leithold's "The Calculus"

you can find free PDFs if you google it but unfortunately they are probably all scanned in black and white and butcher the very nicely done diagrams, might be a good way to preview it though

imo he is better than Stewart and Stewart copied a lot of things from him but became more popular for no particular reason : )

[sturdy sail]

Any good references on the representation theory of the poincaré group?

[gray gazelle]

i dont even know why im here

i hate reading, but i still read

i recommend u never ask me

[minor knot]

He got sully bubbled

[maiden halo]

I actually really like Morris Kline's book Calculus: An Intuitive and Physical Approach. It's one of the Dover Books in Mathematics so it's relatively cheap. It's older (I think from the 1960s) but still very good.

[pseudo coral]

What e book can I start in maths im self learning, i want to start from the beginning

[rich sun]

Have you looked into #books-old?

[pseudo coral]

Yes but i want alternatives

[maiden halo]

What do you consider "from the beginning"? What is your current level of maths

[chilly vortex]

For anything below undergrad level khan academy is pretty great

It really falls off though once you get past calc 3 and 4

[graceful dawn]

What kind of maths you need.

[solar junco]

This is not exactly a book recommendation but not sure where this goes. I just wanted to know if anyone else finds it a bit grating that so many math texts use the term/phrase "We will show", "We will prove" instead of just stating the fact they are showing/proving ?

There is a connotation that just kind of irks me when I see that.

[graceful dawn]

Because at that point the math in that book is not sufficient to explain/prove. By the time it explains the concepts, all prerequisite might have been covered.
I found the same issue with 'Tao's first volumn.

[solar junco]

Here's a quote that sparked this: "We will give two definitions of a proposition generated by S"

To be fair, this book was written by 2 authors.... but I've encountered several written by 1 that is constantly dropping the "we" ... "we" has two meanings collective/royal and to me a seems a bit pretentious or something. To reply directly to your comment it's got nothing to do with the math, just the tone.

I was an English major in my last term of studies so I dissect text like this - it just gets my goad a bit! lol

[graceful dawn]

Sorry I am bad in English

[solar junco]

Ahh my bad! what's your first language? You understand pretty well!

[graceful dawn]

Is dissect a short form of diss at these

[solar junco]

dissect: methodically cut up (a body, part, or plant) in order to study its internal parts.

I was using the metaphor of " body of a text "

[sleek python]

"we" is used as a neutral way for the author to say things

Instead of saying "I will show"

Which is pretentious most of the time

[solar junco]

Again just an opinion but stylistically it's a poor choice unless it were an editor writing on behalf of themselves and the author. I will show is actually not pretentious so long as you show the thing you are saying you are going to show.

[crimson leaf]

It's also to include the reader sometimes so my advisor says

[sleek python]

Not really most of the time, "we" doesn't refer to anyone (so it doesn't include the reader) in particular

[solar junco]

True I can see that - maybe I'm just nitpicking here but to me texts are conversations. If I'm in a conversation with one person referring to themselves as "we", I try to end that conversation quickly! lol

The point of the word "we" is to refer to a group of someone

[sleek python]

Not in maths

Well, it doesn't really refer to anyone in particular in maths rather, either a group or a person

Or if you like it refers to everyone

Kinda the same thing

[solar junco]

Haha I think you've arrived at @crimson leaf 's point above - I'm gonna assume they're inferring a conversational group of author and reader and that's who the "we" is!

https://tenor.com/view/the-other-guys-will-ferrell-gator-dont-play-shit-gif-3587568

[sleek python]

It's not exactly Kenshin's point, I don't think it's really to include the reader, it's rather a way to be impersonal imo

Like, I don't think many authors write "we" to mean "You the reader and I can define blablabla"

[restive falcon]

what's a good book on ring theory

[sleek python]

They just use it cause that's something we can use to be impersonal

Alternatively we can say "one can show that" blabla

But sometimes it's a mouthful

[restive falcon]

#serious-discussion this is not the place for discussion

[solar junco]

It's about books!

read above

[restive falcon]

yes this is for book recommendations not discussion on how to write good books in general

[solar junco]

ok well I didn't get to my final point

Can anyone recommend a good Discrete maths book that doesn't use the term "We" when describing concepts?

[gray jungle]

Interesting request

[sage python]

"We recommend the following books..."

[tardy walrus]

Why don't you like "we"?

https://math.stackexchange.com/questions/668645/using-we-have-in-maths-papers

[sullen harbor]

Hello, can you help me to choose a book about geometry theorems at the high school level

[lapis sundial]

So you'd rather have a potentially worse book just to avoid a single word? ^ lol

[hearty steppe]

“We” is more commanding than “I”

[lapis sundial]

huh lol

[sage kelp]

Any books similar to Mathematical Analysis by Canuto and Tabacco? I tried reading the English version, but the translation is bothering way too much

[stoic zealot]

Thy ought

Give me one of them books

[mossy flume]

I say this alot

to the point where I'm probably repetitive

[rich sun]

We say this a lot, to the point where we are probably repetitive

[mossy flume]

Actually speaking of writing

https://faculty.math.illinois.edu/~west/grammar.html
this page is great

And if you're really bored

https://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematical_writing.pdf
along with the lecture series
https://www.youtube.com/watch?v=N6QEgbPWUrg&list=PLOdeqCXq1tXihn5KmyB2YTOqgxaUkcNYG

[desert oriole]

I want to learn trig and was wondering, if someone has read "103 trigonometry problems – titu andreescu " and could recommened it?

[narrow relic]

Hey thanks, that's a great page.

[mossy flume]

I should read through it again

[hallow oriole]

thoughts on reading multiple books on the same topic

not like

all the way through on everys ingle one obv

but say you had like

understanding analysis, baby rudin, and stein/shak

and whenever you got bored of one you just went to a different one

and/or used them for just different perspectives on the same shit

mm, so skip the parts you already know in one

the books i mentioned are all (allegedly) relatively different in content

so that's why i asked

a similar case would be like

ladr and friedman insel spence

hmm

hmmmm

what if learning isn't the point

i got adhd and reading the same book for too long burns me tf out

in that scenario

would u recommend

just getting lots of books

money is probably not an issue

z-lib and printers my beloved

hmm

i was under the impression math was more of like

a

progression thing

hm

actually this sounds like a decent idea

yes sir 🫡

wait

yes ma'am 🫡

sorry 😭 i forget i can check pronouns now

tyty gl to u tooooo have a nice day don't die

wait you didnt say gl

ignore that

oh shit that's what that means? i thought that was new member

OH NEW MEMBER IS THE LEAD

LEAF

facts

[marble karma]

Books to supplement with baby rudin

[deep epoch]

i am partial to pugh's analysis due to the writing style and being a source of many great problems. many of the examples also quite nice
i also like using counterexamples in analysis by gelbaum/olmsted as reference

[hybrid sequoia]

A good book for someone moving to senior high this year?

I have to prepare for competitive exams too, what can I put my hands on?

[rapid lily]

What are you looking for in the book to supplement it? More explanations for the concepts or other material missed in that book? Or something else?

[foggy relic]

Munkres topology

[chrome yacht]

amann escher volume 1

[alpine rover]

Abbott or Tao

[surreal kite]

The Calculus Lifesaver

[hybrid sequoia]

Ok? But the thing is that we'll be studying calculus for the first time
Also i don't think we need to go that deep acc to my syllabus
But anyways thanks, in future I'll def refer to it

Just in case, how would you review IA Maron, Stewart or Thomas and lifesaver? My uncle's saying all of them should be done but bro

[surreal kite]

Actually,this book is quite easy to teach yourself

[hybrid sequoia]

I see

[surreal kite]

errr.I study calculus just for fun.Afraid that i can't give ya further information . 'cause i haven't read IA Maron, Stewart yet.

[honest laurel]

Does anyone know what is/are the best books for integral calculus?

[hoary pagoda]

hi im in 9th grade (quite young compared to oder ppl, lol) but i might want sone recommendations for help books

im in india and i have cbse board wud luv if u guys cud give out some recommendations! :)

[karmic thorn]

Would a standard text like "Thomas Calculus" or Paul's Online Math Notes suffice?

[karmic thorn]

Are you looking for recommendations beyond your curriculum, or ones that centre around boards? "Challenge and Thrill of Pre-College Mathematics" is one book that goes beyond and seems popular amongst olympiad students.

For general boards, NCERT Exemplar Problems is the peak. 😵‍💫

[wispy ridge]

If u are asking for board exam then u need to be thorough with NCERT Textbook and NCERT exemplar. thats more than enough

[warped breach]

Does anyone have a book list for middle school/high school level? Around Algebra 1 - Trig/Precalc level

[hybrid sequoia]

K

[hybrid sequoia]

I'd say Rd Sharma is much above exemplar tbh

[graceful dawn]

Do Dinesh and Pradeep still exist?

[timid cosmos]

Can anyone drop good Competitive math books for someone who is seeking to get to the IMO's? I already got these ones

[sturdy sail]

?

[hybrid sequoia]

U sure you can study from PDFs? 💀

[timid cosmos]

Nah bro dw I been doing this shi for a long time now

Just wanted to see if anybody's got more to add on to the collection

[hybrid sequoia]

I see

I can't study at all if I don't have physical copies of the books

[thorn cloak]

I don’t like it as much a physical but those books be too expensive

[hybrid sequoia]

That's true tho

I literally saw aurthur engel books being sold for like 12000 inr which is ig 200 USD

[timid cosmos]

Bro chill 2k for a book is too much

40 - 60 max

[gray gazelle]

Titu Andreescu has more books like the "104 number theory problems" one, in particular "102 combinatorial problems" is an interesting one, with full solutions

[timid cosmos]

Alright let me check it out

Massive thanks btw

[gray gazelle]

np

[timid cosmos]

@gray gazelle seems pretty solid

[sullen harbor]

Hello, can you help me to choose a book about geometry theorems at the high school level

[remote sparrow]

https://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202/

https://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210

[unique yacht]

crazy curves

[blissful drum]

A book for a 6th grader 13yr who is looking to study more!

[thorny spear]

hi to everyone, im looking to learn abstract algebra alone and im not finding anything useful... can any of you suggest me some good abstract algebra book from 0? thank you in advance

[dapper root]

What’s your background with math

Also check the pins, there’s a message by Daminark with recommendations

[thorny spear]

high school math i guess

but i didn't finish euclidean geometry and trig

[dapper root]

Depending on what “from zero” means the proper suggestion is either “learn other math” and go use something like Artin I guess

[thorny spear]

abstract algebra is a lot different to me

i didn't any university math and im trying to get it closer to it

broi

it doesn't work

[desert oriole]

no

[thorny spear]

ur not pinging any

[desert oriole]

<@&268886789983436800>

[thorny spear]

oh

he has perms

[quick hornet]

no he doesnt

[desert oriole]

yea

[quick hornet]

shit lmao that super reacted

fuck off discord

[thorny spear]

thank you

[thorny spear]

is this book alright even if i never studied linear algebra?

[dapper root]

Read Daminark’s pin

[thorny spear]

alr

[dapper root]

I believe that’s the one he recommends for ppl who haven’t done Linear Algebra

[swift dome]

Daminark book suggestions >>

[static delta]

no, its 150 usd

still expensive but not 2k

you can probably get a car with 2k

[heady ember]

Singapore: Are you sure about that

[hybrid sequoia]

Idk man

I'm telling about my country

[static delta]

isnt inr rupees?

[hybrid sequoia]

Yes

[static delta]

indian rupees?

[hybrid sequoia]

Yes

[static delta]

then its 150 usd only....

2k usd is too much

12000/80 is 150

[hybrid sequoia]

Ok I think I made a grave mistake in typing

Yah I wanted to type 200 usd

Sorry bout that 😅

[hybrid sequoia]

I actually took it as 1 usd = 65 inr

Or approax 60

Because generally we're familiar with that value of fluctuation

[sturdy shore]

that still doesn't make it 2000

then it's 200

[hasty turret]

smh quite funnily, abstract algebra is like the only math subject where you will encounter Euclidean geometry

Because Field and Galois Theory

[hybrid sequoia]

Yah sorry bout it i actually mistyped

[hybrid sequoia]

Tbf Euclidean geometry sucks

I hate geometry

Mofos will draw a triangle and ask us to prove it's a triangle 🤡

[hasty turret]

By "Euclidean geometry", I mean "straightedge/ruler and compass constructions and things that follow from those like angle chasing and similarity"

[hybrid sequoia]

By Euclidean geometry I mean plane geometry

[hybrid sequoia]

I'm pretty sure it encompasses that , yah it does

[static delta]

oh ok

[finite crane]

aka stuff nobody cares about nowadays

[hasty turret]

I guess it's like the Sylow of Galois Theory?

[hybrid sequoia]

Shit like similarity, congruency, and theorems like basic proportionality theorem, mid point are all trash nowadays

It sucks

[drowsy thicket]

To people studying mathematics at a German university: which book did your course/your professor use for Topology?

[gray gazelle]

it matters on perspective

cause what maths depends on what yuthink about it

[hybrid sequoia]

I see, but so far I've never seen any relevant use of plane geometry at all

Maybe I'm arrogant but it is what it is

[fierce hedge]

our mod Loch my be able to answer that

[gray gazelle]

you never know when it will help

like a bank account cant help ahomless person now with no money!

[old elk]

I wanted to share with you my first springer book 🥲

[desert oriole]

isnt arthur engel 100$

[hearty steppe]

I think I remember Agarwal being a bit too pedantically terse for me. But it wasn’t a complex analysis text

[gray gazelle]

Gratz

[hybrid sequoia]

Ye

[split basin]

are you looking for a german book on the topic?

[drowsy thicket]

I'm looking for a Topology book that people use in German universities/professors would use at German universities, that could be German but doesn't have to be.

[split basin]

i see, so for topology we used jänich's "Topologie" and for algebraic topology we used bredon's "Topology and Geometry"

[drowsy thicket]

Thank you!

[sullen harbor]

Hello, can you help me to choose an introductory book of Euclidean geometry

[gray gazelle]

Heard Jänich is good

[lusty perch]

what book to read after basic mathematics by serge lang

i want to get into calculus, and do machine learning

not even book, i can even do khanacademy, what suggestions might yall have?

[remote sparrow]

spivak or apostol

[fluid bay]

i like khan academy because it can measure your progress and give you practice problems/feedback

[swift dome]

Spivak is a great choice.

[lusty perch]

okay but

isnt spivak like a terrible book, from what i heard

like iver heard tht the first few chapters r just provin smthn, idk

[crimson leaf]

It's considered a great book just harder cause it does use proofs and actually goes through the theory a bit

[hasty turret]

The first few chapters are the most important because it helps you get into the analysis mindset(I think)

[remote sparrow]

well, considering you completed basic mathematics by lang, i thought you'd be ready

[lusty perch]

no im ready and all

but like,

from what i heard

its like a really "basic" book

the first few chapters are "useless"

according to what i heard

like i heard only bad things about that book

Like the ones that I was told were good calc books were by Jaames Stewart,

but ye ill look into that one

[spiral sequoia]

any good recommendations of real analysis textbooks here?

[remote sparrow]

i don't think proving basic stuff from scratch is useless

[remote sparrow]

#book-recommendations message

[heady ember]

If its so trivial you should be able to prove them as quickly, then.

[heady ember]

Moth would like to have a word with you

[gray gazelle]

Understanding Analysis

Book by Stephen Abbott

is this a good book to learn real analysis ..?

[mellow wren]

yes it's very friendly
It you want something that might go into some things a bit more and is a bit harder I also recommend Pugh's Real Mathematical analysis

[swift dome]

Maybe try Tao analysis.

[rocky nebula]

Book for Vector Calculus?

[alpine rover]

Susan Jane Colley

[fierce hedge]

That's the first time I heard that name. Have you used this book?

[alpine rover]

had a skim

got it from math sorcerer: https://youtu.be/tBj2bgrlGp8

[strange vector]

Hi, I'm reading michael spivak's and Tom M. Apostol's calculus books but having trouble understanding limit/differentiation proofs using delta-epsilon definition. Any recommended book that explains these concepts clearly?

[west heath]

Not sure if I should ask this here or in one of the analysis channels. I was introduced to the idea of lower-semicontinuous metrics. That is, given a topological space (X, tau), having a metric d which is lower-semicontinuous as a function with respect to the product topology of tau (but does not generate tau). But I can't seem to find any sources about this, only papers that use them without citing anywhere about their properties. Does anyone know of such a source?

I should clarify, I have found lots of sources on lower-semicontinuous functions, but nothing on lower-semicontinuous metrics.

[civic python]

I believe it is mostly a matter of proof technique. Setting out to do epsilon delta proofs, you do proof “scratch work” to find delta given epsilon. Then in the actual proof, you’d probably just say “hey, given epsilon here’s the delta, if you do not believe me check it yourself”.

[remote sparrow]

one of the professors at my college used it as an upper-division multivariable calculus book

you know, something around hubbard and hubbard's level

[undone pine]

Yo could someone suggest a book on linear programming following theorem/definition structure please?

[finite crane]

I would be hesitant to recommend any obscure book from math sorcerer

he only goes over superficial things, while to understand a textbook quality it often takes a generation of learners

it is much better to go with consensus of the tried and true, until you get to a level where you can make independent judgments

[gray gazelle]

Any books on differentiable equations or Riemann surfaces?

[proud gazelle]

do you guys know a good book about elementary algebra for someone who has little knowledge about algebra and wants to revisit it with some rigour

things other than khan academy

[crimson leaf]

Based on this I'll assume you mean high school algebra, for this I would recommend Lang's Basic Mathematics

[fierce hedge]

I see, how does this book or H&H compare to Shiffrin?

[narrow relic]

You might check out the explanation in Introduction to Real Analysis 4th Edition by Donald R. Sherbert and Robert G. Bartle.

[hybrid sequoia]

I was going through calculus lifesaver book but might I mention that i have not seen exercises in it so far ..........
How's that gonna help considering I have to prepare for competitive exams?

[delicate hemlock]

Agreed

[undone pine]

f

[weak lake]

hello I need book on proofs before I read this real analysis book does anyone have suggestions

[hollow shore]

first 2 chapters of rosen's discrete mathematics and its applications

[weak lake]

oh my god is that the real Thom yorke

[balmy isle]

do you guys know what book this is?

[quick hornet]

A quick google brings up "calculus for business and economics" by comandante

Might be wrong tho

@balmy isle

Specifically googling the chapter title in quotes: https://www.google.com/search?q="maxima+and+minima+involving+algebraic+functions"

[narrow relic]

http://logic.stanford.edu/intrologic/public/chapters.php Chapters 1-10

[finite crane]

#discussion message
Read this. Just 20 pages.
Then start reading Tao's analysis 1

[crimson leaf]

What do you like about Tao analysis 1, just curious

[finite crane]

The remarks

You read Tao and Eli Stein for their chat

It may not be immediately obvious at lower levels but when you read his higher level notes like in Epsilon of room or his course notes, they tell you the way to think as an analyst

[crimson leaf]

That makes sense, I could never get into it because the first 3 chapters felt like they dragged on so long, also no metric spaces was a bit disappointing

[finite crane]

Skip whatever you have already seen

The book starts from scratch literally

If you're already at metric that's in 2nd volume

[crimson leaf]

I just meant in contrast Rudin who does them very early I'm still in ch.2 of Rudin

[finite crane]

Rudin gave bad / ugly proofs for theorems such as inverse function theorem

Tao gives the proof that one would naturally think of

If you skip the proofs themselves Rudin is a nice reference like a shopping list

[fierce hedge]

Tao's only issue is how slow it goes especially compared to something like Rudin. Plus, it leaves a lot of things to the reader making it a slog

That said the first 5 chapters are impeccable and there's nothing quite like it

[finite crane]

Leaving things to the reader is how it should be done. A lot of people unfortunately just read proofs from Rudin book and never learn to become an analyst

Even when one reads Rudin one should try ignoring the proofs

The process of picking your brain to solve exercises is how one learns the connections between the concepts

Another benefit is that once you get used to Tao's style you can later on read his graduate level course notes. Which I still refer to in my research. They are filled with epic exercises and stuff you have to fill in yourself

[fierce hedge]

Which particular ones are you referring to?

[finite crane]

Fluid mechanics. Ergodic theory.

[fierce hedge]

He has notes on fluid mechanics

[finite crane]

Fair warning that you need to be fairly proficient as an analyst to trek through it

[fierce hedge]

Okay, I should revisit Tao after Rudin

[finite crane]

A common feature of his grad notes is that they seem very calculation heavy. Certainly at first I felt intimidated and it was hard to see how anyone could like the tedious subject. But the more proficient you get as an analyst the easier it is to ignore the calculation details to focus on the higher level picture.

When you get to near his altitude you understand why his notes leave gaps for readers to fill. As only the biggest picture matters

And when you finally revisit them after your PhD the notes make even more sense

As now you stop caring about proofs

[fierce hedge]

Tbh Tao leaves much simpler gaps compared to Rudin and the gap is also very reasonable. I just felt some things were repeated and he gives equivalent definitions. For example he defines things in terms of each other where a simple definition could suffice. It's definitely more of a nitpick though.

[finite crane]

We are talking about different things. I'm referring to his grad notes

But oh well you'll see

[fierce hedge]

Yeah, I was talking about this book. I'll see the notes after going through the book once

I think he has some good notes on measure theory idk how advance they are

[finite crane]

I believe his measure theory notes are like intro before you get to his Epsilon of room notes

They combine to be roughly like Folland

But Tao will go further and cover Fourier transform on locally compact groups

And pontryagin duality

Because that's his main job: harmonic analysis and Fourier

[crimson leaf]

How do his books compare to S&S real analysis

[finite crane]

I think Epsilon of Room should be read after Folland if that is any indication of its level

The Pontryagin viewpoint is worth it

Before you fully jump into harmonic analysis which is what adults use for PDEs

[coral prawn]

Speaking of introductory analysis books, I was a bit confused over what I should do- there's tao, Abbott, and Rudin, all 3 which sound pretty great- but going through all 3 is definitely not an optimal choice. How should I pick which one(s) to use?

[finite crane]

Once you understand harmonic analysis you will see how all of Tao's accomplishments, from number theory to combinatorics and dispersive PDEs and fluid, come from knowing that one hammer

Which Eli Stein taught him

[coral prawn]

Hammer?

[finite crane]

Harmonic analysis

[coral prawn]

Ahhh

[safe lintel]

Hey, I am looking for a good book about Calculus. I am pretty comfortable with the basics (Calculus 1-2 and parts of 3) and am good with the algebra needed for it. I'd like to go deeper and also learn about multi-variable calculus, could anyone recommend me a good intermediate book?

[sturdy shore]

shifrin - multivariable mathematics

[slender hawk]

Anyone have a good abstract algebra or elementary set theory pdf? I'm self studying and those are the next things on my list (the elementary set theory more to make sure my personal understanding isn't missing anything before doing axiomatic set theory)

[coral prawn]

For AA, dummit and foote is a classic. And for set theory, a possible consideration would be Enderton

[slender hawk]

I'm really strapped for cash so I've been using free PDFs for both number theory and linear algebra. It'd be convenient if I could continue the trend.

[coral prawn]

Yep

Some websites include libgen, pdfdrive.com

[slender hawk]

So if I were to absolutely not pirate things, those would be places to avoid? Cool

[coral prawn]

What book did u use for LA BTW?

[coral prawn]

Yep, absolutely!

[slender hawk]

Oh, shoot, I'll have to find it again. It had lots of sample problems and solutions in a separate pdf so you could just plough through it

It's on my laptop

[coral prawn]

[safe lintel]

Thanks

[coral prawn]

Just as a side note- he also has a 100 hour long playlist of lectures, where he teaches his own material

U may wanna check that out too

[safe lintel]

I’ll check it out, thanks for the recommendation

[sturdy shore]

he is an amazing teacher for sure

[safe lintel]

Looking at the description and comments, it seems a little too advanced for me atm. do you by any chance know something a bit simpler?

[sturdy shore]

I don't, but if you are "pretty comfortable with calc 1-2" as you said then shifrin is just the natural progression after that, so idk what you are looking for

[chrome yacht]

maybe combine abbott with amann escher vol 1 which is a really good textbook as an alternative for rudin for self study, both have sizeable problem sets

[safe lintel]

„for those of you who are not familiar with Shifrin's books or style of writing I would not recommend this book to any beginner of linear algebra and/or multivariate calculus“.
I am not the best with linear algebra and haven’t done anything with multi-variable calculus yet

[slender hawk]

Linear Algebra by Jim Hefferon, 4th ed.

[coral prawn]

[sturdy shore]

so you are taking some random's word essentially? the book is for sure difficult without any background beyond calc 2 but it is explicitly the intended audience (picture is from the preface). If you don't want a challenge then use some other book I guess

I guess this part is as important

[safe lintel]

I see, thanks. I’ll go for it

[remote sparrow]

they're both supposed to be comparable to shiffrin

[lapis sundial]

Any feel-good novels that anyone can recommend

[desert oriole]

recommendations for an introductionary abstract algebra book?
Im not planning on learning everything, I just want to understand some basic stuff about groups, rings, fields

should i just go with dummits book?

[finite crane]

what is your current level

[desert oriole]

not high

idk

[finite crane]

Rotman Advanced modern algebra

[desert oriole]

ok

ty

huh

advanced

[remote sparrow]

pinter or judson

[desert oriole]

ty

[finite crane]

it starts from scratch

[desert oriole]

oh ok

[finite crane]

4 first chapters are simple then they will revisit those topics later

[desert oriole]

the only requirements are lin alg and discrete math right?

[finite crane]

from scratch

[desert oriole]

ah ok ty

[finite crane]

not even lin alg

[desert oriole]

oh ok ty

[finite crane]

Rotman is basically Serge Lang but written in a gentle and pedagogical way

Dummit pales in comparison

[remote sparrow]

do you recommend the second or third edition

the book got split up and changed substantially in the third edition

[finite crane]

I think I grew up with the one-volume version

it was enough for me so meh.....

[remote sparrow]

https://www.maa.org/press/maa-reviews/advanced-modern-algebra-0

https://www.maa.org/press/maa-reviews/advanced-modern-algebrathird-edition-part-1

[finite crane]

I'm not sure what he added in the 3rd edition. if it's just bloat maybe we can do without it

[remote sparrow]

The third edition of this book is very different from the previous ones. As the reviews of the first and second editions indicate, Rotman is a very good writer. Those editions were masterful reference works presenting most of graduate-level algebra. Indeed, the second edition served as one of my go-to books as I was writing my Guide to Groups, Rings, and Fields. I often found that Rotman presented the material better than his competitors.

Clearly, however, the author has felt some restlessness about his book. Between the first and second editions, there was a change in publisher and also various additions, but there was also a significant “I changed my mind” move: instead of including a review of basic abstract algebra, Rotman decided to point to his undergraduate textbook. The additions made the second edition quite big (“elephantine”, he says in the preface to the third edition), so it is not surprising that the third edition comes in two volumes. More surprising, however, is the radical reorganization.

Where the second edition is clearly a reference book, an encyclopedic account of modern algebra to which one might turn to recall a theorem or learn a particular topic, the third edition is clearly intended as a textbook. It is divided into two parts labeled “Course I” and “Course II”, which apparently correspond to the first and second graduate courses in algebra at the University of Illinois at Urbana-Champaign.

[desert oriole]

this the right one?

[finite crane]

yes

don't bother with any chapters marked as "II"

if it's just intro

[desert oriole]

ok

ill just start from chapter 1

[coral prawn]

Better than dummit?

Wow

[finite crane]

yes rotman is one of the best expositors

[coral prawn]

Icic

Will give him a look

By modern algebra... its algebra in general, like AA, commutative algebra?

[finite crane]

just stare at the contents

[coral prawn]

Ah, right, mb XD

[desert oriole]

i think modern algebra is just a synonym for abstract algebra (thats what ive heard)

[red river]

I find Artin a great resource. A lot of personality, a little bit of everything, and great exercises.

[thorn cloak]

Yeah I asked before about my modern algebra class at my uni and I was told it’s just abstract algebra

[finite crane]

the fact that Rotman's book separates group theory / ring theory into "I" and "II" is absolutely great. sometimes people just need to get to the meat first. Leave the advanced stuff for later.

[thorn cloak]

I was planning to use contemporary abstract algebra but it doesn’t seem to be very well regarded here

[desert oriole]

i just googled stackexchange abstract algebnra book, and ever reply recommened a different book, so i wasnt sure which one to pick

[thorn cloak]

Yeah I feel that haha

[coral prawn]

Hmm, he does have books on topology too....

[crimson leaf]

I like this so far

[red river]

Honestly, do you know what you want to study it for/ what style books do you tend to prefer?

[gray jungle]

I 2nd recommend artin as a good book

[crimson leaf]

A lot of the stuff about groups we've learned so far just feels kind of crammed in there

[sage python]

I have a list of books in the pinned messages if you wanna hear my thoughts

[red river]

That sounds like a solid choice. Showing the similarities and trying to do both at once feels very much like Lang and not a style I've appreciated.

[sage python]

I don't know Rotman's algebra book tbf but I liked his group theory book

He has this "Introduction to the Theory of Groups" which I spedrun in second year a bit since I was considering taking a class called "Algorithms in Finite Groups"

[coral prawn]

How an i only noticing it now 💀

[cursive orbit]

rotman has so many books it's insane

[coral prawn]

Aren't AA and grp theory kinda interlinked

[sage python]

Group theory is a subset of algebra

[red river]

Artin is great if you have a linear algebra background. He uses it often as an example for things. He also really likes to put in occasional geometry. It's really a very colorful treatment.

[crimson leaf]

Yeah abstract algebra starts with groups usually

[red river]

Often groups are the first topic presented in AA.

[sage python]

Artin includes the linear algebra he uses

[coral prawn]

Ahh

[sage python]

So you don't even need that background

[red river]

True. That's like his ch1 IIRC

[coral prawn]

So artin does both LA and AA?

Wha

[red river]

His treatment of linear is very brief. It's kind of more of a refresher imo.

[sage python]

Linear algebra is also a subset of algebra

[red river]

He does more like advanced topics of LA sprinkled throughout.

I really found the book to be a delight.

[sage python]

Is it? Feels like it's probably not Strang but that it's on par difficulty-wise with e.g. Hoffman-Kunze or whatnot

[red river]

Strang is better on youtube than in print imo

[red river]

Idk, it's p subjective tbh.

[sage python]

I'm not endorsing it, fwiw I don't think books at that level are useful for math majors

I just mean Strang is my mental model of like, the computational/engineering style linear algebra class

[gray jungle]

Another book I've came across is
"The theory of finite groups" by Hans Kurzweil
But its a bit less introductory, overall liked his treatment of group theory.

[red river]

Fair. He says he prefers teaching engineers. He kind of slips in theory underneath, forcing them to eat their veggies.

[red river]

I thought of that as like a second book on group theory.

[gray jungle]

Any good books on lagrangian mechanics?

[gray jungle]

Yeah it felt that way , but its a decent option.

[remote sparrow]

probably landau lifshitz

[coral prawn]

Recs for number theory? Nothing too in depth tho

[fierce hedge]

Check pins

[coral prawn]

[steep badger]

el psy…?

[coral prawn]

Hm?

[finite crane]

geek card revoked

[rich sun]

kongroo

[sage python]

Artin + Aluffi is redundant, Munkres is excessive, and Rudin is good but at this point suboptimal

Browder I think is a better Rudin. Schroder is also a good analysis book but its organization is a bit different

Some here like Tao's books

For topology, I don't see a point in Munkres at all. Read either chapter 1 of Bredon's Topology and Geometry or the topology chapter in some measure theory book

As for which algebra book, Aluffi probably does more, categorical take early is good as long as you don't obsess over it too much right away, problems I felt were eh, and it was a bit slow but that's good

Artin's gonna be more about connecting algebra to other areas of math

[hallow oriole]

for future reference i believe the proper term is 'speedran' because grammar

normally i wouldn't correct that but 'spedrun' has negative connotations towards a certain group of ppl

oh shit sry for ping 😭

lwk still not used to not having quotes

[sage python]

It's been so long lol

Like still putting 2022 as the year all the way in November 2023

Also for public record, seems that "sped" is occasionally used as a term for special ed but I don't think it's common, nor is it avoidable in other contexts ("sped up"), so probably I'm gonna classify it as, ordinary term that can be co-opted badly. As for raw grammar... idk in my mouth "spedrun" sounds best somehow

[foggy relic]

+1 for landau-lifshitz

@gray gazelle aluffi exercises are like writing stuff out

a good idea is reading aluffi and doing exercises from Lang

(Lang is a bit terse maybe, but it is still possible to read it directly)

[hot ice]

Which one of these is best to buy? I need to learn all of Calculus 1 and Calculus 2

These are the only options available

Any help appreciated

[heady ember]

Can't you print one out at a local print shop?

That way you can use any book you want + probably making it cheaper for you as well

[hot ice]

Its just more convenient to get one from this list while im in a city that has a book store

I just need one that covers Calculus 2

I cant exactly check each option because theyre wrapped; so i was hoping somebody here knows one of them and says its good and includes calculus 2

Anybody?

[coral prawn]

Stewart calc seems to be the best from all of the above

[hot ice]

Thank you, i was also somewhat inclined to that option but didnt want to make a quick judgement

Which one of these do I get?

[coral prawn]

ODEs and PDEs..... it really depends on Yr current level tbh

As well as what field u aspire to be in

And.... frankly speaking, you could find books with much more reputation for free online

[hot ice]

Alright, do you have any recommendations for reading up online?

[coral prawn]

What's Yr current level of study?

[orchid mortar]

https://tutorial.math.lamar.edu/
does everything

[coral prawn]

Ah yes Paul's online notes

[hot ice]

Well, I have completed calculus 1 and am generally looking into trying to understand differential equations (mostly ODE’s), as i have never done them before

[orchid mortar]

DEs are also on Paul's notes

[coral prawn]

Idk if its recommended to jump into DEs with only calc 1

[hot ice]

Well yeah thats why i plan to do Calc 2 before i try differential equations; hence why i asked about the calc books

My usual home city doesn’t have a book store, so i was thinking abt buying a differential equation book while im in a larger city as i may not have the opportunity to come back later

Tho I suppose i can just read it online

Anywho, thanks for the help

I’ll be getting the stewart calculus book

[lime sapphire]

gl

[graceful dawn]

I will get first 6 books on the top left side

[grizzled heath]

Hello, I wrote a book on linear algebra for machine learning, where I have taken a different approach from a textbook. The book is structured like a story where it starts with the vector and ends with the principal components analysis. between there is a lot of mathematics deduced and real-life examples

you can find it here if you are interested https://mldepot.co.uk/ - there is a pdf version on the site as well as a paperback on amazon.

[river glacier]

Hii everyone!

I need suggestion for a test preparation
Actually they didn't provide any kind of outlines. They just mentioned that test will be conduct from general mathematics. Anyone can tell me what does it mean by general mathematics?

[cedar flume]

Can I have a book recommendation on Tensor Calculas from basics pls

[fiery geode]

any1 got any book recommendations to just understand and learn about the deeper meaning of maths or any suggestions related to calculus

[small lantern]

spivak calculus for theory

james stewart calculus for applications

[fiery geode]

thnx

[marble solar]

I learned from Spivak's Calculus on Manifolds. I learned Tensors from the Schaum's outline

Seems to have done a decent job given that I took it 7 years ago, and when I took grad Riemannian Geometry it was fine

[cedar flume]

Ok I'll check it out, thank you

[gray gazelle]

what's the standard text for differential topology at the upper undergraduate level/graduate level?

covering up to De Rham's cohomology and integration on manifolds

[broken harness]

out of context question, but is derek holton - A First Step to Mathematical Olympiad Problems: Mathematical Olympiad Series — Vol. 1 a good book to start competition math?

[cursive orbit]

I liked Tu (Introduction to Manifolds)

[umbral plank]

hello! what books would you recommended for someone in their final years in secondary school (irish highschool, doesnt make a difference)

[inner token]

What do you want to do?

[umbral plank]

Well I'm not really sure at the moment, maybe expand my word problem since i suck at them or the logical stuff. Maybe some algebra and trig too would be nice

[inner token]

Hm I'm not so knowledgeable about good books at that level. There is a YouTube channel called "math sorcerer " or something and I think he reviews books at that level a lot. There's also a book called "Basic Mathematics " by Serge Lang who is a famous author of math books. I've never looked at it but I think it's interesting he wrote something at that level. Maybe give that a try. As far as word problems, physics problems would probably be great practice for that

[graceful dawn]

Are you preparing for some competitive exam?
If not, then school text books are sufficient I guess

[marble solar]

I liked Milnor because it was short & sweet, but I used that after I read spivak Calc on manifolds

You can try G. & Pollack's book

[umbral plank]

We don't have competitve exams here from what I know, but i would like to expand my knowledge for fun

[umbral plank]

thank you so much will look into it

[gray gazelle]

Lang's Basic Mathematics is very good, particularly if you're just getting started with thinking about and writing your own proofs. It's also a good way to cover material from high school (in the U.S.) mathematics

I have less experience with Spivak's Calculus, in terms of problems solved and pages read, but it's extremely well-written and a classic in its own right. Would be curious if anyone here who knows physics could comment on his last book, Physics for Mathematicians.

[inner token]

@umbral plank see above

[gray gazelle]

@umbral plank , this is an oddball suggestion on my part, but a short book you might be interested in is Edmund Landau's Foundations of Analysis. It constructs the real and complex numbers from the Peano axioms. It's not an exciting read in the way that Spivak's text is -- it's buttoned-up and formal (this style is called "Landau style" after the author) -- but some analysis texts refer to the fact that you can build the requisite systems axiomatically, but don't show in detail how you do it. Landau shows how you do it.

Landau's book is also available in German, so if you know the language or want to get started on reading some math in a language other than English, it may be a good fit for that reason too

[remote sparrow]

a more modern book like Number Systems and the Foundations of Analysis by elliott mendelson would be better suited to that purpose

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

landau has no exercises iirc

[crimson leaf]

Tao also builds analysis from scratch if that's what you want

Peano axioms included

[gray gazelle]

Yes, that's right.

[gray gazelle]

Is that his two-volume set on Analysis?

[crimson leaf]

Yes

[gray gazelle]

Ahhh, neat

[umbral plank]

oh interesting, i will definitely look into it

yeah this will be my first time buying a maths book that isn't like a school book

its just the maths we do in our books is too easy for me so usually in class im crocheting or drawing

[gray gazelle]

high school?

there's a book called basic mathematics by lang that does everything up to calculus, but in an advanced way

might be worth checking out

(lang, not strang)

[umbral plank]

pretty sure somebody also recommended that book, might get that one. seems to cover everything but as you said in more of an advance way which seems super fun

[gray gazelle]

oh didn't spot that.
keep track of the lessons though, if you're working ahead.

[umbral plank]

yeah i am dont worry! we're doing currently trig proofs which i already learnt and know pretty well. i spend most of my free time doing math bcs numbers go brrrrrr but i need more

[gray gazelle]

trig proofs?

numbers go brrrrrr
agree with the sentiment that it's the only useful thing you'll get out of high school

[umbral plank]

well sorry its under the trig heading but its sine rule and cosine rules and etc

[umbral plank]

every time i do maths, i look at it and say "no way somebody came up with this", and then keep on doing it

[gray gazelle]

those are not proofs. they're just formulas, and possibly their derivation

[umbral plank]

oh interesting we have it labelled as 'proofs' but yeah it is derivation but here we label it as proofs

don't know why

[gray gazelle]

proofs mean something else, you'll learn later

[umbral plank]

i'll ask my teacher then

since that is quite odd

[gray gazelle]

pretty satisfying, right? like a skill tree

[umbral plank]

thats why i love it honestly, its the same with chemistry the more you know the more it explains itself

god i wish i had more people to talk about math to

every time i do to my friends they just say autistim moment and laugh

[gray gazelle]

like a map that's interconnected.
something to look forward to is calculus, if you're into functions and graphs

[gray gazelle]

it should be your own journey. make sense of it how you will

[umbral plank]

i still don't really get graphs, like i know how to do the questions and so on but like when people graph sine for example im like why

my teacher did explain it but i still dont really get it

[gray gazelle]

the unit circle tells you how to think of sine in the context of a function

https://tenor.com/view/math-curve-circle-sine-cosine-gif-4839795

[umbral plank]

yeah i did not study or look at that at all, i was sick that entire time maybe thats the issue

[gray gazelle]

build some intuition

[umbral plank]

oh wow what the

why is that so cool

[gray gazelle]

khan academy is a good resource for that

[umbral plank]

okay and what about tan then? since it spikes up and repeats it self then right?

but it doesnt end right so how do you know when it starts

[gray gazelle]

not to clog the chat too much.
but in short, think of tan = sin/cos. and how cosine in the denominator creates asymptotes

[umbral plank]

yeah im aware of that its just the way it looks yk?

[umbral plank]

ah, and yes we should probably stop lmao

[gray gazelle]

me neither. i just think of asymptotes created

[umbral plank]

anyways thank you for giving me recommendations and explaining some stuff :))

[slate pond]

anyone aware of good audiobooks or anything with audio(like videos) that actually go into rigorous proofs, like a textbook might

[marble karma]

Abstract algebra book not like gallian, rigorous, First introduction?

[chrome yacht]

Hungerford maybe

[coral prawn]

Rotman

Advanced modern algebra

[fierce hedge]

For gt only I'd recommend Herstein. For intro graduate textbook with answers try Robert B. Ash - Basic Abstract Algebra

[broken meadow]

was gonna suggest dummit and foote but u wanted concise Kekw

[finite gale]

might want to take look at dami's book reviews in pins also

[marble karma]

Concise compared to gallian

[heady ember]

Have a look at Dami's AA recs in pinned if you haven't done so :)

[marble karma]

How do you guys differentiate between what exercise is worth doing and what's not? There are so many exercises in these books , one can't solve em all

[dapper root]

It’s a skill

For theory based one’s I tend to try and do them all unless they seem really dumb and useless which requires knowing a bit about the subject anyway

For examples or computation you try to do enough so you feel reasonably confident you can do the others

And can form a pretty good idea on how to solve them

And then sometimes you just look at a problem and it looks so horrible you say nope

[stoic nova]

You develop an intuition for what you have solved and what you can solve. In most cases, you would have a clear path to get the answer. If not, then maybe you don't know it well enough.

[gray gazelle]

How can you recommend a book when you’ve never studied algebra

[glacial crypt]

If you recommend a book ya should read a few chapters first at least

[coral prawn]

Mb, Yr right lmao. I'll keep that in mind

[coral prawn]

Anw, any recommended texts on descrete maths?

[chrome yacht]

rosen

[coral prawn]

thanks!

[gray gazelle]

based book

[heady ember]

Rosen bored me out of it a couple dozen pages in personally

[chrome yacht]

what would you recommend then?

[gray gazelle]

Any books on proving inequalities? I found the book "The Cauchy-Schwarz Master Class" but is there any alternatives? Maybe some books that are more general rather than focusing solely on the Cauchy-Schwarz inequality.

[sage kelp]

Inequalities A Mathematical Olympiad Approach. Maybe you can check it out

[gray gazelle]

seems interesting, actually im preparing for a contest as well

[sturdy shore]

how much have you read of the cauchy schwarz master class? because I am pretty sure that book does not solely focus on cauchy schwarz

[storm fjord]

Hello Guys!!

I just read the Alchemist

[finite gale]

Check out dami's book review in pinned messages

[finite crane]

Stein complex is probably nice as an introduction without assuming too much real analysis. Later on you will probably revisit the topic anyway

[remote sparrow]

gamelin also does not assume any real analysis

not sure about bak and newman's prerequisites but it seems good too

[silk fiber]

Does anyone know any good books for learning Real Analysis? Have some time to burn over the summer and want to learn the subject on my own

[sage python]

What's your background rn?

[gray jungle]

If you have no proof background, you can consider tao analysis.

[silk fiber]

Multivariable Cal, Discrete Math, and Intro to proofs

[sage python]

Hmm, so you know some stuff already

Have you seen delta-epsilon calculus?

Or just normal Stewart-style computational stuff?

[silk fiber]

I've seen delta-epsilon before but never really took the time to understand it fully

[hearty steppe]

anyone else gone through the feynman lectures? Are they really that insightful?

[gray gazelle]

i havent read a single page of it but you are right. i just skimmed the contents and it actually covers more than just the cauchy inequality, my bad for judging the book from its title.

[elder stratus]

I’m interested in reading two of stein’s books: 1. singular integrals 2. Harmonic analysis. What are the prerequisites to get started on reading those books?

[thorn cloak]

<@&268886789983436800>

[silk fiber]

I've heard good things about this book. Apparently its very well written

[remote sparrow]

idk, but i think minimum measure theory

[loud cradle]

have you read his "introduction to fourier analysis on euclidean spaces"? it's not technically a prerequisite but it would probably make sense to read it as well (or something equivalent) if you haven't already done so.. Here's what he says in the preface to the singular integrals book:

[elder stratus]

I haven’t read that, I suppose I’ll start there. Thank you!!

[loud cradle]

if you find that one to be tough going, a well regarded, somewhat easier intro would be katznelson's "harmonic analysis", which is quite nice (the parts I've read, at least)

[elder stratus]

i’ll take a look at that as well, thanks!

[lapis heart]

Is a set of lecture notes more effective than a book to relearn for you? Material that you were once familiar with. Eg. undergrad analysis

[tulip saffron]

Do you think Fichtenholz or Zorich's books are worth reading?

[hallow oriole]

looking for good dynamical systems books and prereqs necessary

ping me please

<3

[silk fiber]

My calc 3 prof actually recommended that book to me. I think it does a basic intro to proofs section at the start of the book

[subtle mango]

we used strogatz's nonlinear dynamics and chaos

pretty good book, targeted towards more applications and less math theory

prereqs is basic ODE's, lin alg, calculus

[remote sparrow]

hirsch, smale, devaney

just need real analysis and linear algebra

[gray gazelle]

does anyone here have a good guide/textbook I can use to learn about highschool level probability

things like permutations and combinations, geometric probability, dependent and independent events and such

[finite gale]

there is an art of problem solving book on probability that was pretty nice as i recall

[unborn copper]

can some one tell any good youtube channel for learning advanced mathematics from basic level

[rich sun]

I think this is a good channel for that: https://youtube.com/@brightsideofmaths

[unborn copper]

thanks

[rich sun]

Note that it's not a substitute for actual math courses and textbooks with regular exercises.

But I find the videos very motivating and helpful.

[analog lava]

what are the prereqs for brezis functional analysis

[chrome yacht]

in the preface it says "It is intended for students who have a good background in real analysis (as
expounded, for instance, in the textbooks of" ... folland, royden, knapp etc

[analog lava]

do i need to know about differential equations?

[chrome yacht]

i am not qualified to answer that 😓 never did brezis myself

[graceful dawn]

I need a few good math book for layman.

Not too easy and not too difficult.

[gray gazelle]

I need a trigonometry book for self study that is only focused on trigonometry (not like the algebra and trig books like stewarts) and will teach trig to me as a beginner; and will take me to a good point on knowlendge of trig.

[hollow shore]

http://mecmath.net/trig/

[teal dove]

can someone suggest any resources for learning calculus as a beginner?

[red river]

Khanacademy

[coral prawn]

If yr looking for a book, stewart's calculus would do fine. My personal favourite is Spivak, but others may not like him as he does a bit of analysis in his book too

[gray gazelle]

did anyone here read basic real analysis by Houshang H. Sohrab and if you did what is your thoughts about it?

[finite crane]

if you know Folland that is enough

but be warned that Stein's books are rather old by this point

in particular littlewood-paley theory is no longer done the way he does it

Tao cites Singular integrals as his biggest influence

but unironically if you want to see how L-P is done today in PDEs and research, read Tao

[elder stratus]

Ok thank you! I’ll check out his lecture notes assuming that’s what you mean!

[analog lava]

do i need to knwo about PDEs beforehand to do brezis

like would i lose alot of the motivation

the textbook is literally titled with pdes

[remote sparrow]

do you know calculus

[gray gazelle]

not yet

we're not taking that

[forest sleet]

No brezis is intro to pde

[analog lava]

cool

tysm

[glad prairie]

BASED

I rarely click this channel but I do by accident and the first thing I see is the most based textbook

HSD >>>> Strogatz

[hallow oriole]

hmmm looks like im getting strogatz then

jkjk ly ryc

why hsd over strogatz tho

what does it do better

SHIT SORRY FOR PING

[glad prairie]

it just has good vibes

smale best mathematician

[astral linden]

Anyone know books about the mathematicians and their lives themselves? Particularly Cantor

[glad prairie]

This isn't exactly cantor but he's in it, the graphic novel Logicomix is super good and is all about russell

and his life and struggles with foundations in math

cantor shows up among many other logicians

[astral linden]

Thank you! That sounds lovely and perfect

[subtle mango]

cantor's life just kept falling apart so he made it into a math concept and called it cantor set

[astral linden]

oh dear lord lmao

[zinc rain]

wattpad

is scary

@torpid cargo

oop soz not u

@zinc rain

[red river]

yessss

i like the scene depicting frege losing his damn mind

[gray gazelle]

Is there any book that teaches you calculus in a theoretical manner like focussing on the concepts

?

[rich sun]

...any real analysis book?

[coral prawn]

Spivak

or perhaps a real analysis book, but that requires more mathematical maturity

[safe lintel]

Has anyone heard of / read this book https://www.mecmath.net/trig ? If so, can you recommend it?

[marble karma]

Linear algebra book recommendation? Give me a list

[gray jungle]

@marble karma

[trail yarrow]

Spivak doesn't?

[coral prawn]

Spivak doesn't what?

[trail yarrow]

require mathematical maturity..

[coral prawn]

It does, but not as much as analysis

[trail yarrow]

which spivak? the 100 pager?

[coral prawn]

700

[trail yarrow]

ahh... i was thinking calculus on manifolds

[gray gazelle]

damn

LMAO

how many members xD

[sleek python]

[gray gazelle]

OH

is it an april fools joke??

[trail yarrow]

server got hacked

[gray gazelle]

I looked up fools and apparently

it is an april fools joke

[trail yarrow]

i see

[gray gazelle]

oh wait

maybe not.

rip server

[trail yarrow]

WAIT

IT COULD BE APRIL FOOLS!!!!!!!!!!

YOU ARE RIGHT!!!!!!!!!!!!!!

totally forgot april is tomorrow

[gray gazelle]

LMAO

[trail yarrow]

maybe this is a brilliant hackers april fools joke

[gray gazelle]

But someone said that they thought it was an april fools done too early

indicating that they were wrong

[trail yarrow]

what happened to the channel name

[flat lantern]

hacked

[rich sun]

pirated

[brisk ice]

what you think of that #groups-rings-fields name?

[gray gazelle]

torn to pieces

[trail yarrow]

op its back

[smoky zephyr]

based channel name

[torpid turret]

Channel Topic (for specific): Book Recommendation

[ruby sparrow]

there's no way ppl think it isn't hacked

[delicate trail]

I really don’t get it I thought it s hacked and then I get here and see people saying it s April fools

[pine cloak]

it's very likely april fools

[lapis heart]

🏴‍☠️

[pine cloak]

many of the other public servers have changed their names and stuff

so like 🤷‍♂️. And the coincidence that it's april fools and the server gets hacked is too sus

lol but the channel names are hilarious

[rich sun]

#totally-not-pricey-here

[teal crater]

They've outdone themselves for april 1st

[subtle mango]

this is a very good gag

[trail yarrow]

can always count on math server to be the GOAT

[elfin shard]

#book-recommendations ?

[subtle mango]

yeah

[grizzled rover]

wow a piracy channel

I mean totally not

[teal atlas]

I thought it was totally no privacy here lmao

[compact sandal]

Anyone measure theory book from a set theoretic perspective?

[edgy heath]

Happy aprilfools day

[solar echo]

rip hacked

[normal forum]

this is a good april fools

rip people with legit book questions

[gray gazelle]

bro channel name

[alpine rover]

stein and shakarchi real analysis?

[hybrid patrol]

lol

[stuck frost]

Hi, I was looking for a recommendation on any landlubber advice on piracy? I seem to have found five seas, but I'm having a lot of trouble locating all seven on the globe.

[teal atlas]

Underground ocean maybe

[charred pagoda]

My friend just asked me to tell them where the algebra 1 channel was even though it was the only unmuted channel on their Discord 🤦‍♀️

[cedar ridge]

where the goated book lists at

[heady ember]

LMAO the channel name

[coral prawn]

[past gazelle]

lmao

the server pic got me

[unique quartz]

Lmao

[hardy oak]

what is happening to the server pfp

its going crazy

[jagged ether]

It's having a seizure

[hardy oak]

LMAO

what happened to the channel

[scenic tendon]

I'm only human after all

[inner token]

Don't put the blame on me

Guess what

I got a free copy of Casella and Berger "Statistical Inference " today

[loud cradle]

totally no piracy there? 😁

[inner token]

No actually! The math department had a box of free books and they were actually good

[sleek python]

[remote sparrow]

now i just need people to give me free books

[foggy relic]

Hi

[loud cradle]

nice! seems like a good book, at least the parts i've read. has some tricky exercises

[inner token]

It was recommended reading in my stat class and now I actually have a copy. Looks great

[charred pagoda]

Damn that's a lot of notifications

[gray gazelle]

whats happening with the server

[chilly crown]

april fool's i guess

[gray gazelle]

I

OK

MAKES SENSE NOW

[sturdy shore]

I would recommend it, I've read it up to section 5 and I'm really liking it

[gray gazelle]

Wait the server profile is caution???

[tulip bane]

Don't put the blame on me

[balmy quartz]

What is happening to this server

[unique lichen]

Too many notifications

[errant tartan]

there no piracy

[charred pagoda]

I think this server needs even more notifications

[young slate]

Hey guys

Why’s wrong with the avatar??

[obsidian valley]

no one can figure it out.

[noble prawn]

Anyone here used khan academy for linear algebra? Is it good or should I get a book for self study?

[coral prawn]

Well, 1st thing to consider is yr preference

it's not bad at all tbh

but personally I prefer books over KA

if yr looking for books, the pins has a list of LA books u could give a shot at

[noble prawn]

Thanks!

[noble prawn]

damn... books are expensive

time to do what I have to do 🙂

duck... I forgot I have two library cards for a reason

I almost committed some crimes

😮‍💨

[coral prawn]

Well

certain websites exist yknow

[heavy moon]

April Fool

[coral prawn]

remember

totally no pirating yeah

[noble prawn]

I am an honest and law-abiding citizen; I have no idea what you are talking about

[coral prawn]

ah, of course not, my bad to assume as such. Just in case, though, one of them would be a certain website by the name of "libgen". Disgusting.

[rotund flint]

I pirate stuff all the time

And skip taxes

[noble prawn]

eww... what is that? I should look more into it so that the future generation can avoid it 🤨

[rotund flint]

I'm above the law.

[noble prawn]

I heard I get a portion of the tax if I report a tax evader 🙂

[rotund flint]

Good luck catching me

No one ever catches Chuck

[paper plover]

anyone want john wick 4 ?

just kidding NO PIRACY

[rotund flint]

Holy shit real Johnathan candle stick 4

[paper plover]

stop it u unlawful citizens

[noble prawn]

Exactly!!!

[rotund flint]

Guys as a moderator I will have to ban anyone who mentions piracy

[noble prawn]

Thank you for your service, sir! but please pay your taxes by the deadline.

[rotund flint]

Fucking make me

Telling a moderator what he/she should do?

Well I'll be damned

That's bannable

[noble prawn]

Oh, I didn't know that. But since a mod is saying it, I should believe it.

[fierce hedge]

You just mentioned it you, fake chuck

[rotund flint]

Wdym fake Chuck

I am the real Chuck

[fierce hedge]

Real chuck would definitely pay his taxes

[rotund flint]

No