book-recommendations

[forest sleet]

Reading a lot of well written math also helps you get better at writing math

[gray gazelle]

thank you so much

[timber mesa]

analysis and LA, I don't think there's a single "standard" book (as is the case for most things other than the usual calc sequence)

[night prism]

That’s the best question I’ve seen asked in here since I joined

👌

[timber mesa]

try Hirsch-Smale-Devaney

Strogatz is more of an overview for non-math stem people

I also like Robinson's dynamics book

[gray gazelle]

the struggle is real

[gray jungle]

ile give it a look
ty for suggestions

[twin ridge]

Hi everyone 🙂
I was looking for survival analysis books. Do you have any recommendation? I'm primarily interested in applications.

[late plinth]

anyone good recs for prob theory or graph theory books, would also like a rec on book on compelx analysis. heard the first two classes are p hard at my school so would ideally like to get head start in summer so i dont die when i take in fall

[glad prairie]

#book-recommendations message for complex analysis recs

[late plinth]

based

[gray gazelle]

Good abstract algebra book if artin’s not available

[hallow oriole]

artin is free online?

[gray gazelle]

Yea but I prefer physical math textbooks

Thx still

[hallow oriole]

np, sorry i have nothing

[foggy relic]

DF

I've only used it as a reference though, not sure how it would be for learning

[night prism]

Lang

Intro one though

Also Fraleigh

[runic hatch]

Jacobson is cool too

[blissful pike]

Anyone got good books for GRE prep looking for stuff on Real Analysis, Linear and Abstract Algebra

[night prism]

I didn’t know Jacobson has two volumes

Seems pretty extensive and well written

[night prism]

As far as I know the GRE doesn’t include any of those topics

[fluid bay]

the math gre does

[night prism]

Ah yes I forgot there are subject exams

[hollow valley]

Do you guys recommend the art of problem solving as a good way to self study and learn math?

[blazing canopy]

I used the original book back when I was a kid. It does teach you math, but as you might expect it emphasizes problem solving methods. But you do learn some truly interesting mathematical concepts (at least, compared to what is learned in school).

[hollow valley]

does it make your math level higher than what schools normally teach you?

[blazing canopy]

For some definition of math level, definitely yes. It has an emphasis on solving difficult problems rather than solving problems that require advanced math knowledge.

[hollow valley]

Thanks.

[weak solstice]

What's a good textbook for learning real analysis?

[blazing canopy]

I can only speak from experience. I thought Carothers' Real Analysis was good. Abbott's Understanding Analysis was also quite nice. I think Rudin's Principles of Mathematical Analysis was not great.

[night prism]

Carothers is underrated; Bloch is good too; Tao is left out a lot but I initially learned from that

[fluid bay]

+1 for carothers

[weak solstice]

Is it ok to learn from if I have 0 experience in real analysis

[fluid bay]

do you have experience reading/writing proofs?

[weak solstice]

A bit

[fluid bay]

maybe start with abbott then

[runic hatch]

you can always try starting a book and see how you progress

[night prism]

I was going to say

[fluid bay]

carothers is good, but probably not without any analysis experience whatsoever

[night prism]

Are you at a university?

Go sit in the analysis section and read the first 5 pages of a bunch of books; you’ll know right away

[weak solstice]

I just left

[night prism]

Permanently or tonight?

[weak solstice]

Tonight

[night prism]

When you have 2 hours go to QA300

Sit and read through a few that have “introductory” or “elementary” in the title

Don’t ask how I know the reference numbers

[patent swallow]

hello everyone I'll be starting a physics degree in the fall and want to develop my math skills and intuition. I am unsure if I should try the AoPS books as I'm not really a remarkable math student. I currently have stewart's precalculus mathematics for calculus and thought of going through the exercises and brush up on my weaknesses. My first math subject will be elementary analysis. What's the best way to prepare? is it better to build myself from the ground up with aops or just focus on precalc and some analysis

[gray gazelle]

@patent swallow you can use gelfand's books for precalc

They're very good

That's what I've heard and read at least

[patent swallow]

I see that they are divided up? how many books are there and what are the titles?

[junior merlin]

probably practicing proofs is the best way to prepare for analysis, actually, analysis is the best way to prepare for analysis

[desert thorn]

I'm a first year econometrics student and the lit we're using is a poorly written reader and Bain & Engelhardt, which was seemingly last printed in the 1980's

Can anyone recommend a probability theory & statistics book that is actually decently readable and good in terms of content?

[hearty steppe]

you would need to work through the terseness of Casella and Berger at some point to have a strong rigorous grasp of the subject. That is not an easy book.

honestly I am finding out for now, it is better to spend most of my time in abstract algebra land and analysis land to really focus on developing the rigor but I don't think many people have the patience to develop a mathematician's focus on a subject.

[proper lotus]

Casella and Berger is not an undergraduate book.
If you're looking for a first book I suggest something more standard on probability theory.
Also there's probabilitycourse.com

[unkempt glade]

What is an undergraduate?

[gray gazelle]

If i wanted to learn from the beginning of high school all the way to the end what books should I read to get the entire curriculum. for math of course.

[gray gazelle]

It means early university

[unkempt glade]

Tomorrow I’ll look more into math books

[desert thorn]

yeah i'm looking at Casella and Berger right now, and i can understand it in broad terms, but this is definitely a step above what we're doing right now

[unkempt glade]

Rn is sleep time so for now, peace

[proper lotus]

What do you think about probabilitycourse?

[desert thorn]

i've seen this site before i think, this looks in line with the level we're at

[misty wyvern]

Casella and Berger is absolutely doable by a math undergrad

It's only MS-level for stats students

literally all you need is ugrad probability, a strong linear algebra course, and some baby analysis

[gray gazelle]

Not sure what you'd call it, but maybe someone can recommend a book to help me with this. I've been working through hundreds of problems in this College Algebra book, and I find that the majority of my mistakes are because I make a typo, not necessarily the calculations I make; missing negative sign, missing coefficient, placing something in the wrong context of the bar, etc. Does anyone have a book recommendation for managing these kinds of common errors?

I should note that my error rare is about 1/10, and it's almost always because I've made a typo somewhere in some long expression

[stiff lodge]

Generally what are the prerequisites for john m lee intro smooth manifold? I'm going to participate in the course sequence "smooth manifold+riemannian geometry" both of them uses john's book

[fluid bay]

linear algebra, basic point set topology (for example the contents of hatchers notes on point-set topology), and multivariable calculus which you can find in the appendix of Lee's ISM.

[zenith plume]

Hello, I am sixteen, and very stupid at maths, I would like to be smarter at it, I only know primary school maths (which is embarassing), please can someone reccomend me a book?

[hallow oriole]

i dont think a book would help you

i suggest going to https://khanacademy.org

it's free, has amazing lessons, and tests and benchmarks to see where you are

this should work for you until college

[grand thistle]

how is hatcher’s notes on point set topology compared to a standard text like munkres or mendelson?

i’m thinking of using it since it’s very concise

but i’m afraid it doesn’t cover enough detail

or something

[zenith plume]

Thanks bro

[night prism]

I wonder if there would be this many textbook questions if libgen didn’t exist

[grand thistle]

i also use zlibrary

[orchid silo]

CAN SOMEONE SUGGEST A BOOK FOR GRAPH THEORY IN DISCRETE MATHEMATICS

[pseudo forge]

NO

[marble solar]

Schaum's outline discrete math

[flint bay]

Ah yes what textbook should I use for this very standardized undergrad class

[blazing canopy]

I think people here are too married to "using" a particular book. In the past when books were harder to find (e.g. expensive physical copies only) it might make sense to invest in the "right" book for you, but nowadays with online resources, free lecture notes, etc, I feel it is actually better to use multiple resources in order to synthesise multiple viewpoints and presentation styles

[night prism]

I entirely agree with you in using different resources for different coverage as well as different approaches and perspectives to the same topics. However, I’m quite annoyed by the echo chamber this place seems to be becoming; it’s evident by the ridiculousness of the comments. So much lately it seems along the lines of “I’m just starting linear algebra but I’m thinking I’ll dive into Rudin over the summer and tackle Lang’s Algebra afterward so I’m ready for functional analysis by Fall

Not to mention, I’m sure it’s entirely discouraging for any serious students who have invested time, energy, and money and are actually working in the trenches to understand these things who may feel behind or inadequate seeing those kinds of things.

[sage python]

I think that's a different problem from textbooks in particular tbh

That's just a matter of people being ballsy, either correctly or incorrectly

So even if e.g. Rudin was the only relevant book on analysis and Lang on algebra

You'd hear some people "talking about their plans" just to brag, and other people who are doing so more genuinely

[night prism]

No doubt, for sure. Hopefully my comment helps even the keel

Or one Can hope 🤣

[sage python]

Unfortunately with the volume of the server I imagine it'll get lost fairly soon. But yea

[night prism]

At least I know I’m not the only one sensing it now though; makes me feel a little better

Then again, you guys probably got tired of bothering a long time ago

[sage python]

I guess I haven't particularly sensed this as a huge phenomenon? I feel like for the most part people talk about stuff and in any sufficiently large crowd you'll have braggarts or people who are just so cracked they make everyone else a bit insecure.

[night prism]

Very likely

Oh well

Tomorrow’s another day

[sage python]

Tru

[woven forge]

seems like a pretty good book for me

[stiff lodge]

not bad choice he taught analysis in cambridge university for 50 years

[night prism]

That book is an absolute gem

[woven forge]

have you used it?

[night prism]

The really good stuff I buy physically

[woven forge]

oh you use ode by morris too

I really loved taht book

[night prism]

Yes it is! (When it’s your first exposure)

[woven forge]

my uni used boyce

but i ditched it and used morris book instead

[tepid prairie]

The book on the far left is amazing.

[night prism]

I think I bought it for around $12 at the time too

Directly from Dover

[tepid prairie]

Is that the original version? Mine has horizontal text of the authors.

[night prism]

🙏 indeed

[tepid prairie]

I'm on page 421 and would recommend this book to anyone!

[woven forge]

yep I recommend that book strongly too

[night prism]

It says “revised edition,” but there may be different prints

Yeah me too obviously

[tepid prairie]

I tried to find the original out of curiosity but could only find the one I had. I have the book by David V. Widder on Advanced Calculus and that one seems good too but no one seems to know about that book.

[night prism]

Take a look at Dover’s direct site and subscribe to their email

It’s not as fast as Amazon but they routinely send coupons

And that’s where I got mine I recall

[coral narwhal]

is that dummit and foote and if not what book is it? (the one that says abstract algebra)

[night prism]

It indeed is

Have you begun it? Curious how you’re using it; I feel like it could have many places

[woven forge]

no

I'm currently using zorich analysis

was just looking for another textbook

[night prism]

Are you fairly deep into the other text? Are you looking for a complement from Mend of the same coverage or something yours doesn’t contain?

Sorry, unfamiliar with the other you mentioned

[woven forge]

actually i've done the single value part

but the multivariable part is being a bit of a challenge to me

so I was looking for a supplement

[night prism]

Ah ok; in my opinion the biggest strength of that Mendelson book is that you become an active participant of the construction of the reals. The foundational aspects are actually done really well too I’d say, as long as you’re not interested in a deep dive

[woven forge]

i've already done ode by mendelson

i thought you were asking about garling analysis

[cursive orbit]

I'm not too big of a fan of explicitly constructing the reals

[night prism]

You mean number systems?

[woven forge]

no

in general

[night prism]

Oh yeah, I was describing the green Mendelson book you asked about

[woven forge]

oh

maybe i was the one who got confused

sorry

[night prism]

Tedious, but I feel everyone should at least walk through it once

[night prism]

All good, I just walked out but I’m fairly sure there’s nothing multivariate in there however

[woven forge]

oh okay

[night prism]

It does touch some preliminary real analysis though

[woven forge]

maybe gonna look for different book

[night prism]

But you’re far beyond

Yeah; great book…. Unfortunately not for your purposes however 😓

[plain fog]

best stats books?

[woven forge]

https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

a bit late

but this book is pretty good

but its pretty rigorous

if you want introductory book

[plain fog]

I'm looking for what Samulelson is toEconomics, Shreve to Stochastic Calulus, Jurafsky to NLP, Russell to AI, Axler to Linear Algebra, etc

[woven forge]

oh

[plain fog]

THE reference book

[woven forge]

than thats beyond my level

sorry

[plain fog]

thank you for the suggestion anyways. I'm going to look it up nonetheless

[gray gazelle]

I need 3 fancy books about probability and statistics

;-;

[night prism]

If you mean it

Try Savage

May God be with you

[gray gazelle]

No one anwsered my question

If i want to receive the entire highschool math curriculum early what books can i read while not missing anything?

By the way over gr 10

[fervent lava]

Probably lang’s basic mathematics?

[gray gazelle]

Langs?

Does it cover anything

I really do not want to miss anything

[fervent lava]

Yes, most high school math. Except probability and statistics.

[gray gazelle]

OK thanjkk you if it covers the entire highschool

Is it free or paper

[fervent lava]

Not sure if it’s available for free online.

[gray gazelle]

Ok thank you

Also this Lang looks contriversal

[fervent lava]

is that a typo?

contriversal?

Also I forgot one thing, it’s lang’s basic mathematics is proof based

[gray gazelle]

https://www.docdroid.net/K1VENuF/basic-mathematics-serge-lang-pdf#page=15

IS this it

[fervent lava]

Yes.

[gray gazelle]

Can you lookj through it to see if the enitre book is here

So this should cover the entire highschool

Is there anything i need to supplemtn

[fervent lava]

Looks like it’s complete. Everything thing is in there.

[fervent lava]

Not sure, khan’s academy and maybe loch’s intro proof in #proofs-and-logic pins.

[gray gazelle]

I really dislike khan but ok

[plain barn]

anyone knows a good calculus book for self-study?

[pure iris]

@plain barn calculus by howard anton

[shell geyser]

I think Thomas' Calculus is a pretty solid book. I prefer it to Stewart. It does a decent amount of teaching you why things work and has a good amount of proofs, as well as application questions.

[plain barn]

thx

[marble solar]

I also prefer Thomas' calculus, but I've heard somebody say some of the examples in Stewart for surface area and volume by revolution

And some other applied problems are more well put together than Thomas

[polar mango]

does anyone have any really good calc 1 books?

[marble solar]

I have like 5

On my shelf

[sage python]

Somehow I have the impression that most computationally focused calc books are the same

Maybe one has higher quality exposition here, another has better problems there

But the teaching of calc 1 has more or less been established

So probably just go with any reasonable thing that's cheap

[hallow oriole]

^

can confirm, i've looked thru so many calc books

i swear all of them are basically the same with a few exceptions

[median creek]

does anyone have opinions on sutherland's intro to metric and topological spaces as a basic topology text?

got it second hand for £1.50 at a local charity shop and im wondering if it's good

[iron granite]

Is A Walk Through Combinatorics by Miklos Bona hard or am I just not good enough?

[karmic thorn]

Combinatorics is challenging, mostly independent of the textbook you use (placed at the same level of education).

[iron granite]

hm, so I should just keep at it and I'll be fine?

[hearty steppe]

It’s pretty hard. If I were you I’d get a more formal understanding of discrete mathematics first. Matousek is an easier read, I been working through that a little along with Knuth @iron granite

[iron granite]

okay, ill try matousek

[analog dock]

For context, my hs curriculum has calculus up to basic second order DEs and once im done with hs in a couple months I plan on moving onto some form of rigorous calculus
I thought maybe spivaks calculus would do but i feel like I'd be behind while others who finish my hs curriculum usually go straight into analysis. So i wanted to ask whether my prior non-rigorous knowledge of calculus would do to move onto any old analysis book like amann and escher or whether I should just pick up spivak and go from there

[marble solar]

Spivak is almost an analysis book

[night prism]

Please, I am so interested in knowing: what country are you in?

What ticktok channel are high schoolers watching that leads them to believe analysis is sequential to high school?

[runic hatch]

Maybe russia or something?

In any case I’d recommend spivak if you’re in high school and have some basic calc knowledge

Once you get through a decent chunk of spivak reading other analysis texts will probably feel a lot smoother, and you do have time to take your learning more slowly

[gray gazelle]

Ostrowski

[marble solar]

Spivak

Has a complete solutions manual

[gray gazelle]

Courant

[gray gazelle]

If youre not hungarian thats a huge handicap

[hallow oriole]

how so?

i've seen the book recommended to non-hungarians before

is it a translation of some sort?

and does the translation miss a lot?

[karmic thorn]

No

Just that a lot of combinatorists come from that region, plus Hungary does really well on math olympiads.

[tender cedar]

hey guyse

what is a good introductory book on complex dynamics?

discrete complex dynamics

[obtuse tulip]

Has anyone read the book "Elements of differential geometry" by Millman Parker? What do you think about this book

It feels very ancient to me

[terse moth]

Pre-uni maths from Isaac physics

https://onlinesales.admin.cam.ac.uk/product-catalogue/products/schools-faculties-departments-and-institutions/physics/preuniversity-mathematics-for-sciences

[foggy fiber]

Anyone familiar with the Mathematical World volumes from the American Mathematical Society (AMS)? A colleague recommended I take a look at Volumes 7 and 29. The ToC look promising, but looks can be deceiving. Looks like AMS keeps a list of the volumes here: https://www.ams.org/publications/ebooks/mawrld-mon

[fair halo]

Does anyone know any Multivariable Calculus book for self-study?

[gray gazelle]

stewart's/serge lang are both good

on that note; can anyone share a book to learn introductory topology? if so, what are the prerequisites for learning about it?

[gray gazelle]

thank you

would you say this would suffice for a beginner such as myself?

[fluid bay]

Have you read/written proofs before?

[gray gazelle]

I have

I know a good portion of axiomatic set theory and logic and I've taken a course in proofs

[fluid bay]

yeah this should be just fine then. There are no actual, like, mathematical prerequisites other than that

[gray gazelle]

ah okay

so it just requires knowledge of induction, contrapositive, contradiction, direct etc.

solid

ty

[fluid bay]

yeah, you just need to be able to understand the proofs and write your own basically using your knowledge of (naive) set theory and functions and things like that

[gray gazelle]

understandable. thanks again

[fluid bay]

[fair halo]

Thanks @gray gazelle

[gray gazelle]

no worries

[inner token]

You guys are feeling Artin for Algebra yes?

[hallow oriole]

that's what most ppl here rec yes

[gray gazelle]

Is Anton good for linear algebra?

[smoky zephyr]

is pugh a good book for analysis? i’ve heard it is, but i’m asking because, for example, the differentiation section in that book is just 15 pages long

[placid pollen]

I got Introduction to topology by Gamelin and Greene myself. Supposedly Munkres is better at motivating definitions and theorems but I wanted this one because it has exercises with solutions (and is cheap)

[fluid bay]

i have gamelin and greene. Its fine, but I think its a bit more obscure than munkres. More people are here are going to recognize questions about munkres than questions about gamelin and greene. But yea, i agree this is another good option.

My only advice about gamelin and greene would be to skip everything in chapter 1 beyond normed vector spaces unless you are interested in analysis.

Another good one i forgot to mention is hatcher's notes: https://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf

@placid pollen @gray gazelle

[gray gazelle]

oh damn, thanks a bunch man!

definitely gonna read this

[fluid bay]

you'll notice that hatchers notes are much shorter. That's because it is kind of the bare-minimum anyone needs to go on to other stuff like algebraic topology. Also, its a bit terse, but it might be doable idk.

Gamelin and greene is nice partly because it starts with metric spaces, which serve as pretty good motivation for the abstract definition of topology

[placid pollen]

reads nice as a quick reference I guess

[rough kite]

it's excellent imo

[fluid bay]

Hatcher's notes aren't much different from chapter 2 of gamelin and greene tbh.

in terms of topics and length anyway

[smoky zephyr]

but i thought it would need more pages to explain that stuff? after all most books make an entire chapter dedicated to it

[rough kite]

eh there's not a ton of stuff to cover in that chapter

i think rudin covers the stuff about as quickly

but less friendly compared to pugh

[smoky zephyr]

well thanks

just needed to make sure

[rough kite]

u can always use a different book for that section if you think u need more exposition

but overall pugh is rly good, especially chapter 2

[smoky zephyr]

yeah that chapter is very long i’ll say

i just don’t like how all the problems are unorganized at the end of the chapter

like in one huge problem set

[inner token]

I like it a lot. Well motivated, contemporary, good images

[blissful pike]

The Math gre does i'm looking for a good review I could just do all of my undergraduate courses again

[night prism]

Yeah I entirely forgot they have subject exams

Weren’t as popular a while back

[pale scarab]

Old exams are probably the best use of your time. The issue I ran into is time management. The questions are not really deep compared to textbook problems but it does cover a lot of stuff and you have to be efficient. I remember a lot of it was calculus heavy. I think even the schaum books could be good prep.

[frosty girder]

use apostol

[marble solar]

Pugh is as good as they come for analysis

[storm yoke]

I'm looking for a self contained crash course/refresher on ODEs and/or PDEs. I haven't studied them since undergrad and I'm starting a PhD soon primarily in stochastics.

a recap of important concepts, methods and results about ODEs/PDEs would be fine. I'm less interested in detailed proofs. tia

[gray gazelle]

Try Evans

[storm yoke]

his book PDEs?

[gray gazelle]

Yes

[storm yoke]

thanks

[dense furnace]

Btw a good starter algebra book is

Also ik its not really a book request but anyone know any online derivatives worksheets?

[grand thistle]

i have stewart's book which has a bunch of exercises if u want

it also has solutions

i can send u the exercises

of the parts

u want

[dense furnace]

Pls do

Im trying to save up for it but dont have that kinda money atm

[grand thistle]

what derivatives do you want to practice?

[dense furnace]

Im just looking for the derivatives practice

[grand thistle]

check dm

[dense furnace]

Ight

[ionic torrent]

borrow textbvook

[brittle breach]

Herstein, Artin or Aluffi

[dense furnace]

Is

This a good one

Just to understand some algebra

[dense furnace]

Thx

[gray jungle]

the cover tells me its not a good one.....but i wont judge on that and ile take a look

[dense furnace]

Its more of the basic kinda book they have other categories and idk ive heard of them and just want the basics to algebra to get ahead of the class since im not going to deep yet because im already doing calculus study

But i want feedback from others

I also can’t afford more of the expensive ones rn

Thats why im resorting to this

[gray jungle]

so i did a small scan over the topics and chapters and this is good if you're in 7th/8th grade and you want to learn math in the most basic way humanly possible ,have a horrible foundation and most likely fail your class
the font seems like its written for kindergarteners the topics are covered incrediblely badly and it seems everywhere the bools treats the reader as a 5 year old, the exercises are extremely bad
i would never recommend this to anyone learning these topics
unless your class is so easy and your teacher gives the most basic exams possible this wont cut it

wish i could say im suprised with a cover like this but I'm not

[gray gazelle]

What's a good book on survey analysis

Is Lumley good

Would be good if I had something to test the knowledge on

[dense furnace]

Dang

[ancient scarab]

Maybe Abbott

Oh wait nvm

I totally misread that question

[gray gazelle]

[steady bobcat]

what's a good math book to read for enjoyment (high school/early college)

[brittle breach]

Polya ,Induction and analogy in mathematics
or another book of his on a similar topic

[steady bobcat]

okay thanks, will look into it 👍

[brittle breach]

"how to solve it" is probably the one

[hearty steppe]

Polya’s book is very similar in approach to Knuth.

When it comes to approaching math mostly by example

[dense furnace]

Any good algebra 1 textbooks?

[dense furnace]

Im trying to decide if there is a better one before i checkout

[gray jungle]

probably aops algebra book

[dense furnace]

Is this one good

?

@gray jungle

Sorry for ping

[gray jungle]

i do not know this book

i use aops to get challenging problems for my young brother and i think its really neat

[dense furnace]

Its almost 5 stars

[steady bobcat]

I thin you will be fine with almost any algebra 1 book

think*

[dense furnace]

Oki thank you

[restive falcon]

"algebra" by michael artin

[smoky zephyr]

cringe yet again

[gray gazelle]

I used this one for algebra 2

Even tho it says precal, units 5-8 are algebra 2 units 1-4 are algebra 1 the rest is precal and intro to calc

It teaches u how to use the graphing calculator a bunch like for making a best fit line and stuff

[dense furnace]

Thx

I’ll probably get that once i understand basic algebra

[gray gazelle]

Yessir, that book assumes very little knowledge, it goes from the basics so its very good, gl with math

[gray jungle]

is simmons book topology and modern analysis good ?

[fervent mist]

Which books do you recommend to learn algorithms?

[blissful pike]

kk thx

[brisk ice]

anyone ever use this book before? It is for math class called "Exploratory Data Analysis", shocker, and was wonder if anyone had some inputs on it

topics for the course:

not really sure what data analysis is all about

the whole description was as follows: Introduction to modern techniques in data analysis, including stem-and-leafs, box plots, resistant lines, smoothing and median polish.

[narrow sonnet]

where is precalculus A-D

[hearty steppe]

It’s not really a book you’ll really learn much from theoretically.

Tukey is the futurist historian type

It’s decent in presentation but don’t expect to be wowed away

Oh wait sorry I’m thinking of someone else but I don’t think Tukey’s EDA book is terse enough to be competent in EDA. You’ll want to go through a book like Casella and Berger at some point for a serious grasp at it

I suppose you can sort of use Tukey to help you go thru it but I mean… I think Tukey is more for the types of people that are probably going the information tech route

[brisk ice]

terse enough to be competent in EDA?

so you are saying the book isn't deep enough?

[hearty steppe]

I feel like you pretty much should study mathematics if your gona do EDA. Not saying don’t read Tukey. Seems well presented but idk if it’s me. I feel like a seriously strong math foundation is the back bone of top class data scientists.

Like people that come out of a rigorous mathematics grad program or something, those are the ones that will make the best of the field because they understand the meta that the regular analytics people don’t

I was thinking of this book @brisk ice earlier https://g.co/kgs/wkqNVA

[blazing canopy]

I haven't read the book, but Tukey is basically one of the founders of the field, I'm sure it'll be a fine book. But it also means that it'll be an old book and thus cover only classical methods.

[fresh current]

The Princeton Companion to Mathematics https://g.co/kgs/kkrV2g

Has anyone read this book?
How is it?

[kindred laurel]

Could anyone recommend a probability and statistics book from an information theory prospective?

[gray gazelle]

You can try the book of blitzen and Hwang

Or u can also take help from #books-old section too

If u were looking for something specifically

[kindred laurel]

I didn't see any relevant books in #books-old :(

[gray gazelle]

Okay u can try The book which I mentioned before

It's really a good book

[patent mango]

Does anyone know of any good books filled with questions of Floor and Ceiling functions??

[main void]

any resource with good exercises for real analysis (ie. measurable sets/functions through Lp spaces)? I've gone through the exercises in stein and the exercises in Tao are kind of meh

[gray jungle]

is kreyszig book good for intro functional anal ?

[daring oasis]

https://reddit.com/r/math/comments/u0cdw7/giving_away_dover_math_books/

[tardy walrus]

Dayum

[daring oasis]

mhm

Don’t ask for the multivar calc book >.>

it’s minereee

[tardy walrus]

Kek

Imagine doing multivar

Ewww

[daring oasis]

shut, there was no linalg left

[tardy walrus]

HAHA LAMO

[daring oasis]

i would’ve taken it i sweat

stfu lamo boy ur options are numerical analysis or logic

[daring oasis]

everything’s gone btw

rip

[timber mesa]

dover cheap tho

[hallow oriole]

free is free ¯_(ツ)_/¯

[hallow oriole]

shifrin's multivariable mathematics

[marble solar]

spivak calculus on manifolds

[grand thistle]

isn't that really dense

[marble solar]

density = mass/volume? Rocks r denser

[fringe kraken]

outlier

steps tto success

[timber mesa]

and it has a bunch of typos and errors

Munkres' Analysis on Manifolds is supposed to be the same but better, haven't actually read it though

instead I suffered through CoM

[old elk]

logic and set theory
for beginners?

[quick hornet]

logic and set theory in the "i need it for other courses" sense or the "i already know the bare basics and want to study it for its own sake" sense?

i.e. do you need a book that defines "union" and "countable" for you

[old elk]

I need it to study on my own
because the teacher is garbage at explaining
so yes
I need it to learn on my own and
for the course

1. Syntax
2. Formal deduction
3. Derivative rule
4. Semantics
5. Equivalence
6. Symbolization
7. Relationships
8. Functions
9. Families
10. Equivalence and order

[quick hornet]

alright, just making sure since "logic and set theory for beginners" can mean different things for different people

a lot of books cover this and i dont really think there's a "best option"; the first few chapters of how to prove it do so with the intention of you eventually being able to, well, prove things

although it seems your syllabus is just a bit more formal than the style of how to prove it

[old elk]

These are the topics
The teacher explains as if he already
and does "logical" exercises of low level and "logical" exercises of low level.
and in the workshops they are quite difficult

[old elk]

Quite intuitive

If you have any suggestions, let me know
I would appreciate it
I will keep reading my notes

❤️

[grand thistle]

munkres looks really good, i look forward to using it for multivariable analysis

[runic hatch]

It’s like a more detailed version of spivak, and doesn’t seem to have the same number of major typos

The exercises though feel a lot easier, to the point where you might want to supplement them with a few from Spivak

[night prism]

Goñldrei

Goldrei*

[scarlet pumice]

What textbook should i look at for high school statistics?

[proper lotus]

try probabilitycourse.com ? a bit closer to undergraduate, but I think the exposure will help rather than hurt

[edgy cradle]

https://www.amazon.com/Principles-Techniques-Combinatorics-KHEE-MENG-KOH/dp/9810211392

hi

is this book good for beginners?

like i've only taken basic probability course

[gray gazelle]

Did anyone get the new CLRS?

If so, do you recommend it?

[edgy cradle]

wait new edition was released?

[gray gazelle]

Yes

[gray gazelle]

4th one

[edgy cradle]

gotta check it out

not now

but I plan to apply for double major

next semester

thats why im studying combinatorics btw

thanks

i've already taken a semester of discrete math

by rosen

but tbh i don't think its really enough

https://www.amazon.com/Discrete-Mathematics-Its-Applications-Seventh/dp/0073383090

you mean this?

yes we did use this book

but we didn't get to cover many parts of it

okay gonna check it out

also ive heard taht solutions are provided for free

to be honest most 'new editions' doesn't really matter I think

especially to general physics and chemistry books

what is prereq for that book?

okay

gonna check it out anyways

[analog oxide]

Hey bois!

I needed some help.

I want some good reference book for Engineering Mathematics. On Calculus(Vector and complex).

I use a few already but the content is so so. Gives you the formulae and not the motivation behind what made the analysis to be carried out in the first place and how the concept developed and its applications.

I want something that tells how and why instead if something that tells this is it, learn and get lost.

[eager mural]

Same ngl

[fervent lava]

Maybe something like spivak calculus for single variable and shurman Calculus and analysis in Euclidean space for multivariable stuff.

Also apostle has two book for single and multivariable calculus. Which I have been told is rigorous.

[umbral lantern]

i also need some text for calculus, because the way they teach us here is "look this is a type, here's how to solve this type. you'll need this formula. good, now memorise all of this"
but the problem is that when you can't classify a problem into a type you sort of get lost as to how to solve it
so i need something with a lot of questions and with like an intuitive feel for basic diffn and integral calculus and their applications, like tangents, normals, and areas

even like a good selection of problems would help a lot!

[gray gazelle]

piskunov

both volumes

you can get both for 18 bucks, very cheap

[gray gazelle]

what's the best book for learning basic topology from scratch (no need for advanced stuff, just the basics)

munkres had a good book on topology

Topology; a first course

[gray gazelle]

thx

[gray gazelle]

no but i'm obsessed with soviet scientific literature so i might as well be

[gray gazelle]

introduction to symbolic logic by carnap

the first 60 pages will cover you for symbolic logic

given that your only concern will be with extensional languages

[umbral lantern]

thank you!

[ivory grotto]

Are there any good books on linear algebra that focusses on algebra meeting geometry?

[brittle breach]

https://personal.math.ubc.ca/~carrell/NB.pdf

[ivory grotto]

kk

lol

ty

[ivory grotto]

any prerequistes?

[edgy cradle]

topology without tears and munkres

use both books togethre

also for problmes use schaums outlines

it is best of the series

[gray gazelle]

thx

[edgy cradle]

are there any good books to supplement d&f for algebra beginners?

[frosty girder]

artin is good and i will shill it all the time

[thorny latch]

anyone got any book recommendations relating to maths and computer science?

[crude pike]

Why should we real books instead of reading pdf/other format available on the screen?
Is this better to read a physical book because one can feel the page, smell the book? Does these help your brain to focus?
I spend most of my time reading pdf file. I haven't touch a book for a years now and read a physical book.
I am lately loosing focus and so thinking to switch to physical book.
Does physical book really help focusing and understanding things better??

*** feel free to ping me on this because I really wanna read your reply***

[stray veldt]

there are some issues with reading pdfs on a conventional screen

1. the screen refresh rate has a tiring effect on your eyes, this can be prevented by instead using an ereader, which is closer to a normal book
2. usually the device attached to the screen can be distracting. if you have access to games/discord/internet/wtv on the same machine, it is easy for your brain to think of that instead of the content

[crude pike]

yeah I read on laptop and where I have access to all of it.

the feel of touching a physical book can help understanding the material better???

i think I need to switch to physical books

[hollow shore]

if you have a printer you can print out specific chapters and read them on paper

[stray veldt]

probably the feel has some impact

but the main thing i think is that digital devices provide many distractions

using an ereader would have roughly the same positive effect than using books

(if your ereader doesnt have games or social media...)

[timid vector]

its also nice when writing things up to not have to alt-tab constantly from your latex editor to your pdf

[crude pike]

yeah I am thinking about this for a long time now. why not print all these pdf pages and read. But unfortunately i don't have a printer. And I could print in a shop but not enough money even to buy the book. I collect all those pdf from the internet. The books are Mathematics, computer programming and physics books

[crude pike]

truth is I don't a own e reader.

[hollow shore]

invest in a good inktank printer

it's def worth it

[crude pike]

yeah

it's like i have a small library in my computer.

[stray veldt]

im just saying its not necessarily a book that is required

[crude pike]

i read a lot

[stray veldt]

i shill ereaders all the time because it was a great investment for me

[crude pike]

i agree

Even though i don't give attention to other apps and focus on reading and try to understand but still it gets hard. Maybe it's because of the frame rate of my screen

I have spend tremendous time reading pdf but i feel like learning less than I learned with a physical book. and also realized that it take longer time to figure out something with a pdf on the screen than from a book. which slows down my leaning.

[edgy cradle]

I go to local print shop

they are a bit shady but still they print out libgen materials for me

I recommend doing that because of eye health+navigating through books using computer/ipad is tedious especially ones with no ocr featuresw

[gray gazelle]

books that cover grade 9 - 12(high school grade 1 - 4) maths ( can be multiple, many books )
can be more books just suggest anything that is useful please

[karmic thorn]

Lang's Basic Mathematics covers a lot of stuff, essentially everything you'd need to get started with calculus (assuming you understand middle school math).

[gray gazelle]

perfect, thank you
also do you have any more books to recommend to learn the topics within that book more in depth

kind of like books that can be used as a supplement to that book

[karmic thorn]

There's a book series by Gelfand that I'm aware of, and also Precalculus by OpenStax Project. AoPS books can serve as a good supplement for challenging, olympiad-like problems.

[brittle breach]

https://personal.math.ubc.ca/~carrell/NB.pdf

[gray gazelle]

Thanks!!

[rose bridge]

any good books on stochastic calculus that review some of the necessary measure-theoretic probability prerequisites?

[primal mica]

Gilbert Strang's Introduction to Linear Algebra (5th edition is the one I've used) does a lot with diagrams to build some geometric intuition, while still being very introductory and holds your hand quite heavily. I found it very easy to self study from and just blast through chapters.

If memory serves none of it required calculus, but there is the rare example from calculus (or other fields of math) where knowledge thereof would be useful for understanding the problem. However in the same sense, it does introduce some concepts from things like algebraic graph theory in a way that I found very easy to understand and very motivating to learn.

Even moderate ability in high school level algebra should be able to find your way through the book, but with more experience with math you can fly through it :)

Additionally Linear Algebra and Group Theory for Physicists and Engineers had a lot of good diagrams and explained things that I really always understood how to use but never really understood what exactly they were, like the dot product, providing some more physical intuition behind the math.

[night prism]

You’re aware studies have been done on this?

I was just discussing this with someone a couple weeks ago, actually

[hallow oriole]

oooh losangeles i've heard that too but dyu have a source? it'd go a long way to convince my parents to get me physical books

also anyone got any math-oriented cryptography books?

[loud cradle]

physical books have fewer distractions, also I find the bookmarking and general browsing experience far better. but electronic versions are searchable, which can be hugely useful

[gray gazelle]

I am going into spivaks now as an introductory calculus course (i did proofs already and I prefer this rigor.) But I seem to notice that many chapters for the average calculus i and II course (differential equations as one) are skipped. Is there any other book to supplement this gap or would I simply have to switch back to apostol

Rigorous proofs

@gray gazelle ^

Alright

[night prism]

Yeah hang on

@hallow oriole

https://www.nature.com/articles/s41598-022-05605-0

[hallow oriole]

tyyyyyyyy

citing sources is a <3

[night prism]

It’s Nature

Doesn’t get much better than that

I could also see the value of physical books skyrocket in the next 15-20 years

With resource availability dwindling and space becoming more scarce i wouldn’t be surprised if books were hundreds of dollars by then

[tame plaza]

fyuhh

glad I read my books on pc

[blazing canopy]

I don't know if I mind reading on a screen, but one thing I notice is that a lot of people read their screens (esp. mobile devices) far too close to their face

my understanding is that this contributes to eye strain and worse eyesight

[runic hatch]

yeah I think that's part of it

maybe I should swap back to physical books soon

[fervent lava]

I respect people who go through a online books for math. Everything I try going through books online it’s always a pain.

[lapis heart]

Ctrl+F

[fervent lava]

Meant online books.

[tame plaza]

ctrl + f goes brrr

[night prism]

I just love physical books too

The smell, the pages to flip, being able to carry just a book and a spiral and chill anywhere and read it

Probably have over $5k in math/science books alone from over the years

[mellow bison]

its been too long since i read a physical book for fun in general, and now im been amassing a collection of pdfs for when i wanna study math

[fervent lava]

I have the tendency to give out my physical books. I gave out a copy of spivak calculus to the library for some dumb reason.

[tame plaza]

wow

[night prism]

😳

Better storm back and get it lol

[fervent lava]

It’s been a couple months.

[forest sleet]

we have a free book pile in the math dept that fills up at the end of the year when people move out

I got some fun books

[night prism]

Oh siick

[forest sleet]

and will be dumping a whole ton back on the free table when i graduate

[fervent lava]

What good books do you guys have?

I currently have rudin and Hoffman and kunze.

[night prism]

Hit me up if you remember, I’ll pay for your time

[forest sleet]

ironically most of the books I own are not books I actually use

[night prism]

Lol

[forest sleet]

the pile of library books that I keep renewing so I don't have to return them is more useful

[night prism]

Technically that’s always true for n-1 books at any given time though

Ah yeah, the library pile

[forest sleet]

I think of math books I've own I have rarely opened one in the last year

[night prism]

I had a whole table dedicated for that

[forest sleet]

but maybe if you count pdf versions

then I have opened a pdf of a physical book I own

i also have the pile of library books i checked out and never open

[night prism]

The ones on the bottom usually unless you have a really good reason to fetch them

[fervent lava]

My college library is closed for the moment, I wanna check what type of books they have.

[forest sleet]

and the two library books i keep checked out for putting my laptop on

[night prism]

🤣

[forest sleet]

one time i panicked when I thought I had lost 2 library books, and I was thinking wow how did I loose the two most useless books that I never use

[night prism]

Right under your nose

[forest sleet]

yep

[mellow bison]

also which book is better, ladw or ladr

[fervent lava]

I like ladw.

[blazing canopy]

on the other hand, electronic books in latex can take advantage of some useful features

the notes/book I'm writing tries to use hyperlinks everywhere, text highlighting to make things more readable, etc

[night prism]

I think the subject matter of the text could also be a factor

E.g. if I’m reading material I intend to use for computer-reared applications, I’d prefer reading it on the computer to streamline

But if I’m reading on the theory of integral equations, I don’t want/need my laptop and to switch between looking at the screen and my legal pad

[blazing canopy]

hmmm, I don't know if I see that. Regardless of what object I'm reading on, the device I'm doing my actual work on (notebook, scratch paper, computer, etc) will still be a different object

[night prism]

Best that all the options are available I suppose

Don’t get me wrong, I’ll whip out a book on my phone if I’m, for instance, waiting on someone somewhere obscure and am otherwise bored; but when I have the choice I always prefer physical

[runic hatch]

the one advantage of pdfs I have found is that you can keep a bunch of tabs open to keep some important results at hand

[ivory grotto]

Thanks.. I will go thru it along with going thru another math textbook.. Precalculus for maths by J Stewart and company

[junior mantle]

Thats also the book Im starting lol

[hasty turret]

I hate being force fed geometric intuition,which is probably why I hate Strang's Linear Algebra book

I want content not your intuition

[junior mantle]

Isnt that content in some way?

[hasty turret]

Ok, What if I draw 2 diagrams and say "I explained the algorithm"

That would be bullshit because it's just 2 diagrams

I want a thorough exposition of what the algorithm is supposed to do,how the algorithm works, what motivates the algorithm etc.

Strang doesn't do that

https://math.stackexchange.com/a/320226

For example, This is a better intuitive explanation of SVD than Strang's lecture

https://www.reddit.com/r/learnmath/comments/g8sc5k/serious_why_is_gilbert_strangs_linear_algebra/

[gray gazelle]

What’s the best book to learn geometry European style?

[hasty turret]

Highschool Geometry or real Geometry?

[tame plaza]

european style?

what does that mean?

[sudden kindle]

European style

😎

[gray gazelle]

Real geometry

[gray gazelle]

Rigorous, actual proofs, etc.

[sudden kindle]

I didnt know thats what made it European

[heady ember]

[sudden kindle]

I used the book "Geomerty: An Introduction" by Gunther Ewald

[heady ember]

Geomerty

[edgy cradle]

https://www.amazon.com/Mathematical-Analysis-Universitext-V-Zorich/dp/366248790X

is this good book for beginners of analysis?

[gray gazelle]

Thank u

[restive falcon]

never heard of this one
I'd recommend andrew browder - mathematical analysis: an introduction
or if you want something lighter than that there's also abbott's book

[junior mantle]

Lol

[cursive orbit]

I want spoonfeed

[tame plaza]

since people say Spivak's calculus is intro analysis, what's the equivalent book for intro calculus

[shell geyser]

That's because Spivak is a more rigorous introduction to calculus. An ordinary introduction to calculus book would be basically any mainstream calculus book.

[rotund osprey]

Hey everyone I wanna deep dive into random problems in geometry anyone gonnna suggest me some good books

[gray jungle]

does anyone know the book by simmons topology and modern analysis ? im considering using it for some general topology
because munkres seems a bit too "Detailed" and lee seems to be aimed at a certain type of people who are interested in algebraic topology at least thats what he said in the preface , while i dont hate the idea im still unsure what "Exactly" im interested in aside wanting to learn dynamics at some point so i kinda just want to get some solid topology going on without spending too much time on it (as i already took a detailed course on topology on metric spaces)
if you guys have any nice suggestions or advice im open to hear them
i heard hatcher has some nice notes as well

this is the content for the section on topology for reference

[rotund osprey]

You wanna Deep dive

Aur just random basic

[gray jungle]

im not sure i understand what you mean by "random basis"

[rotund osprey]

Sorry it's basics

Typoerror

[gray jungle]

i want to learn enough to be able to do advanced-analysis without worrying too much about my topology background

that can include functional /mt/operator algebras and especially dynamical systems

[gray gazelle]

Looks like a good amount of topology to me

[gray gazelle]

I think this is good amount of topology to do just that

[rotund osprey]

I would recommend you two books one you mentioned about Hatcher's algebraic topology and another is countarexample in topology by Arthur Steen

Second book can be considered as library of example

[gray gazelle]

What for

[rotund osprey]

Sorry

[rotund osprey]

I didn't get you

[gray gazelle]

He's not looking to learn algebraic topology

[rotund osprey]

And ya do go through random online stuffs

[gray gazelle]

And counter-examples in topology is neat but not necessary

What he has already is good

[gray jungle]

alright that is good to hear i will stick to this one then
thanks for the help

[rotund osprey]

Ha ha I think you know him personally is it so

@gray gazelle I am new here lol

[gray gazelle]

Enjoy yourself

[rotund osprey]

Thanku bro

@gray jungle any recommendations for geometry book

[frosty girder]

[frosty girder]

do hartshorne

[smoky zephyr]

cringe

[frosty girder]

damn it not what i was looking for

[smoky zephyr]

read loring tu instead

[frosty girder]

loring tu?

oh tus book?

wait quantum are u already doing AG?

[smoky zephyr]

no lol

[tame plaza]

I'd assume those are Thomas' and Stewart's

[smoky zephyr]

why would you think that

[frosty girder]

idk

[rotund osprey]

Thanks buddy actually I had completed it I want book much more in collection of questions and ya don't hesitate to ping 😂

[frosty girder]

you have completed hartshorne?

[rotund osprey]

Ha bhai

[rotund osprey]

Sorry yeah

[stray veldt]

there is "open problems in arithmetic algebraic geometry"

[frosty girder]

sahi hai

[rotund osprey]

Again no ping

😂

[gray gazelle]

Are you guys speaking some kind of common lamguage

[rotund osprey]

Yeah lol we indian

[rotund osprey]

Yeah

[gray gazelle]

There's a lot of languages in India

[frosty girder]

hindi

[rotund osprey]

Yeah and never go to the official data of Indian government they sucks

😂

[gray gazelle]

Well I started reading a book about statistics by Rao recently

Speaking about data

[rotund osprey]

I can bet it is masterpiece

[gray gazelle]

It's a chill book so far, nothing too concrete

[rotund osprey]

That's why I am saying it 😂

[fickle granite]

how do people feel about Tao's Analysis books? I plan on tackling them after going through Spivak's Calculus, wanted to know if that was a good plan for getting involved in analysis

[gusty smelt]

recommendations for algebraic groups?

[brittle breach]

I don't like it , go with abbot or rudin

[gusty smelt]

finished a lie groups book

[hearty steppe]

I go with both. I’m plowing through LA right now though

[night prism]

Hey, if so, you mind helping me out with something in #math-discussion please?

[frosty girder]

TLDR version from me, dont read taos book by itself, it has tons of flaws (not as in things are just wrong)
Use apostol or abbot or something like that

[blazing canopy]

Having browsed through each of them, I feel that Tao's book is more like a complete tutorial on how to start thinking like an analyst, starting from scratch. Most of the criticisms I've heard of Tao's book have to do with his choices of conventions, or slightly unusual way of defining things, or order in which he presents things. I feel that from an educational standpoint Tao has put a lot more effort than some of the classic books into making a text that is made to be used like a learning course, as opposed to some high-level concise reference where everything is presented carefully and exactly on the first run-through. I think Abbott's analysis book does this well too, that being said.

[karmic thorn]

Completely agree with the assessment about pedagogy but it's the absence of problems about analysis that strikes me the most. The book will have two pages of exercises on equivalent formulations of axiom of choice but almost none on actually computing the limit of a series or sequence.

If Tao ever presents a reworked edition with more problems, I'd rank it the best book for self-learning analysis in a breath.

[blazing canopy]

Fair enough. I guess I generally do not feel this is a problem because most courses can assign exercises from somewhere else. And otherwise you can always find exercises online to handle.

[karmic thorn]

Yeah, but this is usually a textbook's job. Textbooks for the layperson are generally written in a way that the need for external references should be nominal.

[blazing canopy]

As I've mentioned before, I think there is too much emphasis here on studying from a specific book, and using that book as a template for a how a subject should be learned. I usually used a book's exposition to try to understand a topic better.

[karmic thorn]

If I have to end up using a textbook just to complement a textbook, then I might as well stop using the first one, especially so when it uses some non-standard conventions that do not correspond to any other resource I use immediately.

[blazing canopy]

I think there's some false assumption of having to have a "main" textbook. I learned most subjects by just browsing around in libraries, looking at online lecture notes, mixing and matching when necessary

[karmic thorn]

I learnt analysis from Analysis 1, and I do admit it helped me understand a lot of ideas much more easily, compared to almost all analysis textbooks placed at the same level.

[blazing canopy]

and of course going to my lectures (but often I was sleeping)

[karmic thorn]

True, but without adequate guidance, especially as a beginner, it's easy to get drowned in a pool of different presentation of the same ideas. Of course, if it's to support an ongoing class, then freely browsing references sounds good.

Tao's text is barely a reference though, it's written in a very tightly-knit, result-to-the-next manner.

[blazing canopy]

Yeah, it's hard to jump into the middle of it.

[karmic thorn]

Exactly

Not to mention most core theorems are left as exercises.

[blazing canopy]

Haha, I feel that is quite typical of many authors. However, Tao often leads up to those theorems with a lot of lemmas so that you're not left proving it from scratch.

[karmic thorn]

Definitely, this is one of the reasons why I could keep up with the text.

He gave necessary building blocks wherever necessary and then just asked you to assemble them for a big result.

[blazing canopy]

Regardless, I think I'm just mostly disturbed by some nearly dogmatic following of certain textbooks around here, I don't feel that in my education I ever really learned "from" a book entirely

when self-studying I just browsed some random online sites 😛

[frosty girder]

@lunasong

[karmic thorn]

I was originally very hardwired into working through a "main" textbook linearly as well but I'm becoming more liberal now.

Now I read chapter 1 from 10 books and finish none of them. 😎

[frosty girder]

a bit too liberal dont you think

[blazing canopy]

I also feel that most books actually go in too detailed on the first run-through, compared with how I think it is best to learn a difficult subject

I would probably spend the first 1/3 of my time trying to survey the whole field and get intuition for the broad ideas, without any details at all whatsoever

and once the big picture is established on all the main bullet points, then you'd revisit each topic and actually prove everything

however, textbooks almost never do this because they don't like to repeat themselves

but I think learning is best done by revisiting topics a few times

[runic hatch]

For me it’s also a matter of time

I would love to follow through multiple texts on a topic but if I’m just crunching for my studies it’s hard to pull out all the time that’d be needed

It’s fine, this place is public anyways so anyone can talk; to answer your question you should at least keep going through khan

[blazing canopy]

oh yes, absolutely 🙂 I think for university studies where you have exams and have to keep up with the pace of scheduled lectures, tutorials, etc, it's a whole different strategy then

[karmic thorn]

Agreed

[soft zenith]

I really like Humphreys "Linear Algebraic Groups". Very accessible since it doesn't use schemes (just classical varieties) and develops all the necessary ag in the first chapter , which I think is a plus if you're just starting in the subject

[sudden kindle]

I also wanna read That book

[ebon dust]

Hi are there any good books related to Mathematics olympiad

[night prism]

This is such a vital point! Im surprised no one else remarked on it

A fantastic example is Enderton’s Intro to set theory

He essentially outlines what the constructions of set theory will “look like” in section one somewhat informally just to give a “lay of the land”

Im 100% with you. Makes you feel way less as though you’re on a leash

[gray gazelle]

hey so I recently started doing this reasoning test and I'm so impressed with it that I want more of it, so I'm trying to find a book which would help me develop my logical thinking, numerical analysis & verbal communication, doesn't have to be a book per say I just want to do more questions like the ones I'm going to attach

everything is a polynomial, it just depends on how polynomial you are before polynomialing polynomials polynomially

[stray veldt]

this isn't mathematics, but those are standard IQ test questions, so you can look for a book covering those (or just look at random IQ tests)

[gray gazelle]

Thank you, I think I might have stumbled upon some good books on that by Philip Carter

[gloomy halo]

With L'Hopitall rule

[tardy walrus]

No real need for lhopital

Anyway this isn’t the right place

[blazing canopy]

I thought users are required to read the rules before joining this server, is that not true?

if not maybe taht should be instituted ( I know some other discord servers do it) it might save some hassle

[tardy walrus]

It is true

Obviously.

[tardy walrus]

No one actually ever reads the rules. Most people just react with the checkmark or whatever. It’s not fool-proof

[blazing canopy]

a few other servers I'm in, the "react to get access" instruction is a little more nuanced, almost like a multiple choice question

[gloomy halo]

I'm new that's why i don't know where should I send it my bad and i will read the rules too

[gray gazelle]

what books are yall going through this summer ?

s&z

1632

this is a physics book ?

the best around, and nothin's gonna ever keep me down

[willow oriole]

Any good sat books?

Oooh ok

[dawn venture]

I want to start learning R to an advanced level and I'm a beginner. Are there any books, YouTube videos or courses people would recommend? I want to try and learn in a structured manner.

[flint pagoda]

hey guys, does anyone have any book recommendations for learning multivariate calculus and matrix calculus? I used Stewart for single variable calculus but not sure where to go from there. I know Stewart also has a multivariate calc book but any other suggestions are welcome as well

[fervent lava]

Paul's online math notes have a multivariable calculus course.

[gray gazelle]

I don't know R myself, but I'm a pretty seasoned programmer

If you're educated on programming more generally, your best bet is usually going to be the official docs https://cran.r-project.org/manuals.html

[gray gazelle]

Additionally -- again I don't know R, but JuPytR is a tool you should probably look into, since i suspect the official manual won't mention it

jupyter

[flint pagoda]

thanks. i'll have a look at those. any suggestions for vector and matrix calculus? or is that type of stuff covered in multivariate calc?

[civic star]

the communist manifesto

shits fire

[night prism]

What are you using matrix calculus for?

[flint pagoda]

machine learning, but also would just like to keep learning more about different areas of calculus

@night prism

[night prism]

Ah yeah; I just came across them a couple months ago for a neural network application

[flint pagoda]

yea for neural networks

do you have any resources for that?

[night prism]

This one got me started as to what I need to look into more specifically:

https://arxiv.org/abs/1802.01528

[flint pagoda]

thanks

[night prism]

I found the topics I was rusty on or never learned in standalone texts or other resources

[flint pagoda]

yea i see, i was still hoping there was like a nice book on this stuff that pulls it all together but i guess I can just work with various resources

[glad arch]

Hello, can someone help me? I need some books to study for IMO and MAT admission test from Oxford pleaseee

[hasty turret]

IMO and an admission test are 2 wildly different goals

IMO is like practically impossible to crack unless you are really good in which case you won't be asking this question

Also MAT doesn't seem that hard,atleast in comparison to IMO

[glad arch]

Oh okay, but what recommendation for IMO would you make?

[hasty turret]

Arthur Engels problem solving strategies

Although,first qualify for your national time(pass the equivalent of USAMO or something)

Your coach will guide you then

[glad arch]

I won't gonna do IMO, I'm just studying to get a strong base at Olympiad math, I don't a coach :(

My friends talk about IMO and I wanted to study to know a little too

[hasty turret]

Arthur Engel's book is good even if you don't want to do Olympiad

[glad arch]

Okay, thank you!

[shell geyser]

As someone who has done the MAT, I don't think you need a book to study for MAT. All the math you need is already taught at high school. I'd suggest just doing as many past papers as possible in timed conditions.

You might also find the STEP support program useful. STEP is the Cambridge admissions test, which is considerably harder than MAT, but it is a good source of problems that require the same kind of problem-solving skills as the MAT. Though beware that there are far more topics in STEP than MAT, so make sure you do the topics that are actually in MAT.

[hasty turret]

Is time the big problem in MAT?

[shell geyser]

Not really, it's just that you should be prepared to get stuck on certain parts for very long, so you need to manage your time well and know when to skip when you get stuck.

You have 2½ hours to do 10 MCQs and 4 long questions, so it's not the tightest timewise, but do be prepared to get stuck.

[thorny latch]

im interested in computer science but i have very little knowledge on it. Does anyone have any computer science book recommendations?

[proper lotus]

Need to ask here but I need background in Generalized Linear Models, as I am grading them (Well, students use models as told mostly, and I am essentially grading code rather than theory) and honestly not understanding what is going on.

If anyone has any other book for recommendation other than this
https://link.springer.com/book/10.1007/978-1-4939-2818-7
Please let me know. Perhaps relevant chapters from sufficiently advanced books (or simple as necessary) as well

[proper lotus]

I don't know any generic CS book, but I recommend CLRS as it is a standard topic in CS and it is so standard a book everyone in CS knows it.

[thorny latch]

oh ok

[gray gazelle]

CLRS focuses mostly on study of algorithms and data structures

[cursive orbit]

I really liked Introduction to the Theory of Computation by Sipser

[thorny latch]

oh ok

because im trying to read books so that i can learn a bit before i start going into uni

im only 17

[wispy garden]

Hi guys does someone have any books to recommend to learn machine learning. I don’t have an strong math background or coding.

[gray gazelle]

then get a strong math background first

[wispy garden]

Which math course should I take?

And do you have books for it

[gray gazelle]

multi-variable calculus, linear algebra, probability, statistics

at the minimum

[mystic orbit]

does several sloths have analysis books review?

[swift dagger]

hey y'all I'm going to have a lot of free time in the future with no internet connection. Does anyone have any recommendations for a stand alone book I could use to teach myself multivariable calculus?

[atomic hound]

Please, Book on everything on arithrmtic!

[wheat cargo]

how theoretical do you want it and what do u already know?

https://www.whitman.edu/mathematics/multivariable/multivariable.pdf

this could be nice

although it is online

which defeats what u said

try Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds

[sacred delta]

Anyone got some good books for computational techniques in Galois theory?

I'm following van der Waerden's "Modern Algebra I" which outlines an algorithm for computing Galois groups by studying their decomposition groups, but I'd like to learn more about this topic (other algorithms, complexity analysis etc)

[swift dagger]

In the field i want to go into, geospatial statistics is really important. The golden grail book that keeps being recommended to me has a blurb at the start mentioning how you should already know a bunch a of things including multivariable calculus. So i wanted to read up on it before diving into advanced statistics. first link you sent looks really promising, ill still have screen time so i can just download the PDF thank you

[wheat cargo]

what field is this

[swift dagger]

survey engineering

[gray gazelle]

What books continues Tom Apostol’s Calculus Rigor? For these subjects: differential topology, differential geometry, differential equations, vector calculus, a more in-depth linear algebra, and pdes

[junior merlin]

https://intuitiveexplanations.com/assets/CalculusIntuitiveExplanations.pdf

is also good

[gray gazelle]

Is there any recommended mathematical reading books? Especially statistics/analysis

[swift dagger]

ooooh thank you i gave it a download

[crimson pagoda]

gabe

[night prism]

Yooo gabe

[marble solar]

You're gonna wanna head on in to Spivak's Calculus on Manifolds before diving into Diff. Top/Diff. Geom. For ODEs there's not a whole lot, most of it is pretty cook-book. For in-depth linear algebra I like Sergei Treil's Linear Algebra Done Wrong

For PDEs, I think the best intro is actually Stein and Shakarchi's Fourier Analysis, then once you've done some manifold & measure/integration you can jump into the intro PDE texts. I'm partial to Evans PDEs, as I think it's a very clean and neatly done reference

More advanced PDE books might require more fcnl or complex analysis under your belt

I'd say take it slow with the Manifolds & Topology stuff. Computational ODEs/PDE stuff can be gone through very quickly if you want

Some neat tricks

[hearty steppe]

You probably want to go the topological data analysis route

Which is mostly what I’m trying to kinda do

[uncut zealot]

Does anyone know of any good intro fourier/harmonic analysis books? I know the very, absolute basics (what a fourier series is, fourier's theorem, parseval's theorem), but that's about it

[slim peak]

Oh,

for bFourier Series/Parsecal etc.

[uncut zealot]

Like, I read chapter 5 of Analysis II by Tao, is what I'm up to

[slim peak]

Stein & Sharkachi's book should be okay

I just opened it few times without carefully reading it, but almost everyone agree about it : it's a good book

[uncut zealot]

This one?: https://www.amazon.com/Fourier-Analysis-Introduction-Princeton-Lectures-ebook/dp/B09HDVXSQC

[slim peak]

They seem similar, but no, I was talking about this one : https://www.amazon.com/Fourier-Analysis-Introduction-Princeton-Lectures-ebook/dp/B003V4BQ46/ref=sr_1_1?crid=NSD6V5IR14Q1&keywords=Fourier+Analysis%3A+An+Introduction&qid=1650116038&s=digital-text&sprefix=fourier+analysis+an+introduction%2Cdigital-text%2C171&sr=1-1

[uncut zealot]

Thanks

[heady ember]

Lmao I said Zorn's Lemon last time as a joke lol

[hearty steppe]

Oh yea zorns lemma that is basically another way to show upper bound

[grand thistle]

isn’t it equivalent to AC

[hearty steppe]

It’s not as generalized

[earnest drum]

May I know which online course I can follow for advanced statistics and probability?

[hearty steppe]

AC is like basically everytime you use arbitrary elements of a set to prove your point

It’s also not really AC I would say

But it uses AC

[grand thistle]

isn’t it where u can pick out exactly 1 element from any number of sets

idk what it is, only read some brief mse post about it

[hearty steppe]

The fact your picking out an element always implies choice

[grand thistle]

why is it so controversial tho

[hearty steppe]

Uh cuz you need to be more specific when you get deeper in math holes

[grand thistle]

some people say they’re ‘against’ it? how can one be against an axiom

or do people not say that

[hearty steppe]

An axiom is something we take for granted to make a theorem come together and is consistent for other theorems that build on it

You start with axioms to get to theorems

Same thing happens in physics but they call it something else and they are mostly interested in algebras

[grand thistle]

oh

so like some people don’t like how we take AC for granted?

[hearty steppe]

No you do take it for granted, it’s how you use it

You use it in physics too with observers

[grand thistle]

oh so people don’t like how we use the axiom of choice, not the fact that we take it for granted

i see

[hearty steppe]

If you use it wrong then we don’t like how you use it, I guess

If I choose to assign objects in physical contextual space/time then I use the axiom of choice to construct my model

Since this is now an instance of an experiment, we now have an observation, or an observer point of inference now

But we can construct many instances of the model from different perspective parametric angles

So we can construct many observer point of inferences, which I would deem as observers.

So things get interesting in quantum land, where you have the de Broglie Bohm double slit experiment

You have different trajectories to consider now when the photons go through the slits.

Anyway getting more into it will end up getting over my head since I don’t really study physics. I study math

I just have some foundation in physics to work with

[dense furnace]

Anyone know any good online textbooks that teach polynomials good

[swift dagger]

Any recommendations on books to get me started on topological data analysis?

[dense furnace]

?

[hearty steppe]

Probably ask MaxJ

I am not even at the point in my mathematical studies yet. I only been actually studying math rigorously for about 2.5 years now.

Going on 3 by the end of the year

[shy compass]

it is

some people don't like AC/zorn because it leads to weird stuff like nonmeasurable sets

there's probably weirder consequences that I can't think of right now

[hearty steppe]

Well I mean your gona have uncountable sets and countable sets

[rain hound]

Looking for a book all about functional derivatives and functional integrals. Preferably from a more calculation based perspective, but I’d also be happy with something that goes off the deep end of pure theory.

[hearty steppe]

Zorns lemma works when we have bounds

But it’s still kinda generalized in most cases so you have to be specific

Like you need to make an association between the type of objects your using and the case of using Zorns lemma using strong induction (if possible)

[quiet forge]

Thank you for remembering that people like me exist. 😄

[timber mesa]

something like Cartan's Differential Calculus on Normed Spaces? (I haven't actually read it though)

[shy compass]

np, have fun not believing that the product of nonempty sets is nonempty :)

[quiet forge]

I accept countable choice.

[rain hound]

Thank you for the suggestions, but just eyeballing it, it looks to be the usual topics of functional analysis, which despite the name, is not about arbitrary functionals, just linear functionals. I'd like to consider the calculus on more arbitrary functionals, not necessarily linear. In the same way vector calculus considers more arbitrary functions of vectors.

[sage python]

You're thinking like, calculus on Banach spaces?

[rain hound]

Yes, but not just using linear operators, specifically focusing on functional derivatives, variations, functional integrals, distributions, and whatever else is relevant for this kind of stuff.

[swift dagger]

sounds too advanced for my needs, think im gonna just get an understanding of multivariable calculus and move onto geospatial statistics for now

[flint forge]

Idek if there are TDA textbooks

The field might be too young

Oh there are several

I have no idea if they are any good

[gray gazelle]

Hall and Stevens.

A School Geometry is the name of the book.

[hearty steppe]

Probably just do what I’m doing and go through books like Casella and Berger and find a way to be able to get to the stochastic processes based texts and measure theoretic based texts. That’s a long road even for me cuz I’m still working through Casella and Berger

You’ll also have to go through topology text like munkres at least

Which I pretty much just started at beginning of the year

[sturdy sail]

Are there any introductory references to stable homotopy theory suitable for those interested in the applications to differential topology (say via cobordism theory and surgery theory)?

[gray gazelle]

What book of Irodov? c:
I'm going to study his Mechanics!

[slim peak]

I've seen a book once dealing with cobordism with the Sobolev spaces framework

PTSDs came in just opening the book

[sage python]

What

That's nuts

[rich sun]

Which one?

[slim peak]

I don't remember, it was years ago when I was a rookie

[iron granite]

Is Topology through Enquiry a good book?

[gray gazelle]

Really struggling with factoring, esp. in the context of college algebra (mainly difference/sum of two or three squares ). Is there a book I can use alongside my textbook that I can practice with? I'm using Kaufmann's College Algebra

[rain hound]

It’s not a book, but I found a great deal of help with beginner university math from khan academy and blackpenredpen on YouTube.

And khan academy has problems you can work through too :)

[gray gazelle]

I'll check out blackpenredpen, thanks

RE Khan Academy, I've often found they don't give enoguh problems?

I need to work a kind of problem at least 200 times before I start feeling comfortable with it

[sturdy sail]

I wonder what's the connection tho.

[primal mica]

Has anyone heard of Vladimir Ivancevic and Tijana Ivancevic? I grabbed one of their books for pretty cheap and it sounds like nonsense but on closer inspection seems pretty legit

I started looking into their other books and they look very complex, typically focusing on biomechanics

[hearty steppe]

Any kind of domain specific focus book is generally a reference book outside of theoretical texts

Either you lean more toward math or the physical representation of applying math. You may be better off asking physics server if math is not an all in focus for you for the most part

They’re probably gona recommend you work through a book like Landau first

You could work through Young and Freedman first but I think it lacks the rigor you need to build on from an aspect of getting to biomechanics

[edgy cradle]

I love young freedman physics book

[hearty steppe]

Yea but it’s for people who want first honest exposure to physics

That isn’t too much to handle

[edgy cradle]

welp i'm not a physics major

so that was pretty good for me

best part was that it didn't require high school physics

[hearty steppe]

Yea I don’t really study physics either. I mean I somewhat dabble cuz I have to but I will say spend as much time as you can developing some kind of foundation getting just past the fluid mechanics chapter

I think that’s about 11 chapters in that specific text

[primal mica]

Oh I'm a grad student in physics and I'm doing some computational biophysics for my research (Although not at all related to mechanics (doing molecular dynamics junk for proteins))

Just glancing at some of their stuff and table of contents for their books seems a little hokey at a glance, so I didn't know if anyone had any exposure to say so or otherwise.

[edgy cradle]

which book did you use for multivariable calculus?

[hearty steppe]

So here is the thing about biophysics, yea it’s gona require a chemistry background. Seems like your there with that kind of?

Tbh man, I would have a hard time recommending books because I am going the mathematics route with biology while your going the physics route. I would totally recommend going to physics server and asking what rigorous books would help. You may need to hop on chemistry server too.

Well also there is a biophysics server that physics server partnered with a year ago thanks to yours truly

You will always work with proteins.

I would recommend a dynamical systems text like Brin and Stuck but that’s math and not physics so, that’s why I suggest going to physics server and asking. You seem to already have developed a focus in that area anyway but seems like your dabbling more into math.

[tame plaza]

learn from their videos, do the problems from books in libgen

[flint forge]

Fwiw the physics server might have more to say at that level

Not a ton of people well versed in grad level physics around here

[edgy cradle]

is hubbard's vector calculus, linear algebra and differential forms good book for beginners of multivariable calculus?

[gray gazelle]

is this for math books or books to chill with

[grand thistle]

i heard that one is really good

im pretty sure 3b1b recommended it

but idk i havent used it

[iron granite]

Books on Computational Complexity. Really math heavy ones.

[sage python]

@edgy cradle it's very awkward imo, I prefer "Multivariable Mathematics" by Shifrin

[tulip blade]

Modern complexity theory by barak and arora.

[iron granite]

What a coincidence, I was thinking of buying the same.

[tulip blade]

Its basically THE book on complexity theory.

[mossy flume]

I should pick that up

Since I wanna learn more about algebraic complexity theory

[tulip blade]

Its a great book.