book-recommendations

[hollow shore]

Hello. Are there any video lectures which follows along with Spivak's Calculus textbook?

[lime sapphire]

^^^

[zenith prawn]

thx

[royal bobcat]

in india algebra taught from 6-10.
I dont exactly know the nomenclature.
but, from 11th, we have intensive calculus

[coarse frost]

in 11th u have like limits and basic derivatives lol

also things like equation of line and quadratic formula is done in 9th grades

the syllabus is fairly similar really

11th grade for us is what is called precalc in america

[novel obsidian]

I don't think you cover limits or basic derivatives in precalc afaik

[coarse frost]

yeah thats not there

but we cover them on top of precalc

its like 1 chapter out of 15 or something

[wintry hornet]

anyone have any recs to go along with this list

[gray jungle]

what are the "efficient but not too efficient" books available on measure theory ? ideally something that's not too dense and covers enough of the theory.

basically i have took a introductory course on functional analysis (i loved it) and i want to learn what i need from MT to study more theory of it ,specifically operator theory.
so basically im saying this as a " oh i want to learn topology but not to the point of reading munkres because it covers much more than i need " but for MT.
and i cant really say i have the sufficient knowledge to assess what i need what i don't

( i have read sloths pinned list but it doesn't seem to answer my question)

any recommendations are helpful

[rigid barn]

You could check out Schilling's "Measures, Martingales and Integrals". IIRC it assumes only basic topology knowledge (R^n and metric spaces), starts from the very beginning and covers the basics (including things like change-of-variables, Radon-Nikodym, Riesz representation theorem and so on). It also works with L^p a lot and has a couple of chapters on functional analytic stuff.

[gray jungle]

alright i'll give it a look thank you!

[loud cradle]

recommendations for convex analysis? looking in particular for one that includes convex series, with proofs for example of the following assertions from https://en.wikipedia.org/wiki/Convex_series#Properties

the only relevant citation on that wikipedia page is Zalinescu, Convex Analysis in General Vector Spaces, which looks more hardcore than I was hoping for

[flint forge]

Oops

I read convex as complex

Sorry

[loud cradle]

no problem

it occurs to me that a book on topological vector spaces may also be applicable here, not a subject that i've studied much

[blazing canopy]

To be completely honest, Zalinescu's book looks like the perfect resource. I personally haven't done any convex analysis on topological vector spaces but I'd always wondered about it, and Zalinescu's book is exactly that.

You might also want to read more just about locally convex TVS. There are a variety of books concerning this, such as Rudin's Functional Analysis

OK a colleague also just suggested Convex Analysis by Ekeland and Temam

[loud cradle]

Thanks for the suggestions! I'll take a closer look at Zalinescu to see if it looks digestible, and I found a pdf of Ekeland and Temam which I'll check out as well. It hadn't occurred to me to check Rudin's FA, will look there as well!

[cosmic sphinx]

Does anyone else buy math books they’re probably (not) going to read someday??

I just can’t help when they look too juicy.

[runic hatch]

I have a collection of about 80 pdfs of assorted math books on my “to-read” list if that counts

[gray gazelle]

should i read all of book of proof then start doing real analysis or should i do them in tandem ?

[novel obsidian]

Probably in tandem

It'll take you a year to do book of proof ngl

[river tangle]

Guys any introductory - intermediate book for nt?

[novel obsidian]

It's probably best to just skip it if you can and learn proof writing from just doing the exercises

In your analysis textbook

[gray gazelle]

thanks swiftee

i will do that

maybe 5 pages a day is a realistic goal ?@novel obsidian

on each book ?

[novel obsidian]

Honestly it depends, as long as you feel like you're making progress and you're not spending like a whole day on a page then it's probably fine

But if you feel stuck then I'd probably try looking at another resource or something

[gray gazelle]

i see

well thanks!

may i ask your education level swiftee @novel obsidian

[river tangle]

Guys any introductory - intermediate book for nt?

[crimson leaf]

Dami would say just do Schroeder

[gray gazelle]

i have settled on tao's

i want to know everything!

and tao is real slow

very wordy

[novel obsidian]

Haven't finished hs

[crimson leaf]

Oh you might not even really need book of proof if you're using Tao

[gray gazelle]

i see

[crimson leaf]

Iirc Appendix A should cover all the basics you need

[gray gazelle]

very well

and how well does analysis tie in with probability theory ?

[crimson leaf]

Rest of the stuff is in beginning I believe since he takes like 100+ pages to get to limits

[gray gazelle]

limit of a function is 230pages

but he does series limit first

[river tangle]

Guys anyone?

[gray gazelle]

should i skip book of proof all together and just do discrete maths ?

[glossy nova]

anyone with any good forcing ( set theory ig ) books?

[quick hornet]

this seems like a weird place to ask about chemistry textbooks

i would tell you to check a table of contents, but i cant even find evidence that pauling published a book just titled "chemistry"

in my googling

so finding a ToC would probably be difficult

ah, unless youre referring to peter pauling's book "chemistry"

which i believe was just based on his fatehr's textbook

so i'd imagine they cover the same thing, perhaps peter's edition is more modern.

yes, that book was written by peter and has linus' name because it was based on linus' book

this review might help https://iubmb.onlinelibrary.wiley.com/doi/pdfdirect/10.1016/0307-4412(75)90085-0

i cant comment personally as i found all this info off google

i'm not sure about it, that's just the impression i get from the fact that linus was retired at the time

it's not unheard of for an emeritus to write a textbook, of course

but in any case, it seems quite clearly to be a "retelling" of general chemistry targeted at a slightly broader audience, i.e. with a bit less rigour

based on the review i linked

[quick hornet]

i am not qualified to answer that, and i'd wager very few people, if any, on this server are

[broken meadow]

dont we have a chem server in #old-network

idk if its dead tho lol

[quick hornet]

if the review i linked is to be trusted, "general chemistry" is more comprehensive

take that as you may

[sharp latch]

Thomas Jech “set theory” seems pretty good

[glossy nova]

im familiar ( from the table of contents ) with the part until Constructible Sets
so ill jump right into the second part ( anytime soon )
does the book offers ex? if so, what would you rate their difficulty?
didnt do set\logic in a lot of time

well this seems like a hell of a book

[sharp latch]

I haven’t gone through the whole thing but it looks decently hard if you don’t have a lot of background

[glossy nova]

38 chpaters

[sharp latch]

Yeah it’s super comprehensive

[glossy nova]

where did you got to?

maybe i should revisite some of the earlier chaptre

[gray gazelle]

should i skip book of proof(hammack) all together and just do discrete maths(Scheinerman) ?

[glossy nova]

idk either of those

[gray gazelle]

I need help with a maths question please.

[broken meadow]

#❓how-to-get-help

[near spindle]

can someone recommend me a good limits handout

[hollow shore]

bumping this up again

[brisk ice]

anyone ever read this book are look at it?

Just wondering how much pre-req material one needs to know before reading it

[vivid bridge]

Here is a nice book for functional equations,

Functional Equations Strategies, Olympiads.
https://www.amazon.com/dp/B0B5PS9CBG

[rocky geode]

Nope but I am into rubiks cubes

[brisk ice]

Yeah I was mainly interested if the book was self contained on what it speaks about or not

[proud lantern]

Is there any free book that explains combinatorics, or has tons of practice problems, aimed at first year university maths students? My current book only covers the basics with almost no word-problems

[sharp latch]

Bona combinatorics

[gray gazelle]

Milne ANT

Jansuz Algebraic number fields

[bitter raptor]

any recommendations on books that are more focused on a specific problem and develops tools to solve it or that talks about a more narrow topic and its connections to other fields instead of being more of a general textbook on some field?

[crimson leaf]

https://www.appliedcombinatorics.org/book/app-comb.html

[foggy relic]

I second Bona

[foggy relic]

ch15 😍

[main void]

This might not be exactly what you’re looking for but Multiplicative Number Theory by Davenport could interest you, though I haven’t really looked past page 10 I think the chapters are (I believe) , to a certain extent, logically independent and always aim at proving a particular result.

Otherwise there’s always langs algebra/s

[bitter raptor]

im rather interested in a book that deeply delves into a single problem

rather than a selection of problems

or a single small area

[crimson leaf]

This book is the one that is to my knowledge used by ga tech for their first combinatorics course another good one is Peter Cameron's combinatorics topics techniques and algorithms it's can be a little tough though

[main void]

Ah i dont know any then, sorry

[frigid bramble]

Hi, do you have any recommendations in Analytic Geometry?

[zenith prawn]

what next

[restive falcon]

once you have a solid foundation in algebraic manipulation, a proof book will be helpful

[tawny copper]

nice algebra video lectures? Benedict Gross's are very uncomfortable to watch because of the camera...

[sudden kindle]

Huh

I loved his lectures

Only watched the first few tho

But they were great for me

[tame plaza]

has anyone read Why Math? by R. D. Driver and do you think it's a good book? It is recommended by Susan Rigetti on her website https://www.susanrigetti.com/math

[tawny copper]

I have watched half of them. They sure are good, but the camera is moving all the time and is focusing on a very small part of the board, so that you don't know what's written in the rest of the board... it zooms in and out constantly to single equations, etc. It follows the professor when he walks (lmao). Quite annoying to me tbh.

[tame plaza]

this is a text from Why Math? by R. D. Driver and I answered the 6 questions with the "obvious" answers, do you think it's worth going through or would I be better off taking a course on Khan Academy?

[lime sapphire]

no is the answer from what i've found (and if you mind the lectures being in arabic)

but here are lecture notes that said the main text for their courses was spivak

[calm dirge]

i wish to ask about any place where i can get most if not all of books, it's better if it's a maths oriented library in general but it could be an overall academic (not specific to maths) site as well

[novel solar]

Is it possible to complete spivak in 6 months I have a very basic understanding of differential and integral calculus but I am good with precalculus

[frigid bramble]

b-ok.cc

[flint forge]

Sure

It’ll be a lot of work

Also depends on what you mean by “complete”

[gray gazelle]

complete as in read fully

or something along the lines of that

[heady ember]

Numerous questions can stump you

Many of them took me hours to solve, though sometimes it was just me being blind

Some I couldn't solve after like staring at it for 3-5 hrs

So make of that as you will

(that was with reference to only the first 2 chapter i have done so far)

[blazing canopy]

6 months is my standard amount of time to go through a text, and I would say I'm a fair bit faster than normal

9-12 months is the intended time span I would guess

[primal mica]

Hours spent is probably more useful than months. You should be able to loosely estimate how long a book will take you after a chapter or so through it, past review

[gray gazelle]

Linear Algebra recommendations please

with applications would be nice, and something computer science focused would be even better

[crisp river]

What is felt about Demailly Complex Analuyic and Differential Geometry?

[slate quarry]

Look at pinned messages in this channel, there are good recommendations.

[gray gazelle]

So what do i need to learn for maths

?

LA, Calculus

what else

[quick hornet]

how would we know your needs and goals

[gray gazelle]

math ~ pure math

[quick hornet]

like an undergraduate level education in pure mathematics? those courses are a start, i guess

youve got a lot more to learn beyond that, take a look at the program requirements for a mathematics degree at some universities of your choice

theyll give you an idea of what is typically required

[timber mesa]

LA and Calc is a good start anyhow; any undergrad math program has those in first and second year

might want to learn some elementary number theory (think divisibility, congruences)

I like Burton's elementary NT book

you also might or might not want to read an "intro to proofs" such as http://www.people.vcu.edu/~rhammack/BookOfProof/

[analog lava]

linear algebra , algebra , point-set topology, real analysis,complex analysis, some algebraic geometry or some algebraic topology , number theory

and then add any grad level course something advanced

like precalc

[gray gazelle]

measure theory. Would be nice to have some knowledge of integrals

if you just want to learn math to learn math... well

start learning something, you can get into a lot of subjects very in-depth

[gray jungle]

i think a basic intro to proofs, linear algebra, basic point set topology , real analysis , discrete mathematics (graph theory / number theory) and basic probability/statistics are a good starting point (which will take you a while to get through) before you decide what really interests you in "maths"

this is directed at someone who finished a typical HS level of calculus ofcourse

[analog lava]

definitely learn league of legends

[mystic walrus]

a book about linear algebra?

[glossy nova]

There's the manga book about linear algebra

I don't remember it's name

But if you find it it's pretty funny

[serene reef]

I might have too do that, I am tired of losing.

[serene reef]

#book-recommendations message

[glossy nova]

Play kayn

Kayn is fun

[serene reef]

I don’t see it on the AppStore. Yeah I only play mobile games.

[glossy nova]

Kayn in league of legends

It's a champion

Maybe it's not on wild rift(mobile LoL)

[serene reef]

Oh, I don’t think we have that one yet.

Yeah.

I mostly use Catiyln, lux, Lucian, and jinx. Anything else I suck.

[mystic walrus]

what about Artin?

looks like the best

[gray gazelle]

i want to understand this article, but it has a lot of background that i'm lacking. what should i do?

[lime sapphire]

learn the background you're lacking

[drifting wigeon]

https://cdn.discordapp.com/attachments/795659008735182859/992338503524425728/unknown.png

https://cdn.discordapp.com/attachments/795659008735182859/992338589444735066/unknown.png

there's a whole series of them about oddly specific stuff

[drifting wigeon]

LOL

[foggy relic]

this book is actually very nice

[broken meadow]

ah yes

the linear algebra text

😵‍💫

idk the calculus one is shady and not that good when i remember it

[shell geyser]

Thoughts on Hvidsten's "Exploring Geometry"?

[gray gazelle]

is there a manga about homological algebra

[hearty steppe]

I usually don’t ask for much around this channel but, any good resources on computational irreducibility?

And I guess I would need to learn about intractable integrals a bit in depth but that’s ok

I kinda have surface understanding. I’m already doing stuff like manifolds at this point working through Griffiths QM book and Carroll’s relativity book

[mystic walrus]

Can you share with me its pdf

[foggy relic]

i mean i would buy it as a joke to see the illustrations and stuff but not to learn content from it

[broken meadow]

correct

this was my reasoning too when i bought it

i knew it was not going to be good

[foggy relic]

dm'd you

[blazing canopy]

Isn't that the math encyclopedia? How would it have a workbook?

[summer quiver]

Are you trying to make me jealous because im broke?

And why am i being a bitch all of a sudden

[timber mesa]

it's way closer to an encyclopedia than a textbook you work through, though

it itself describes the way you use it

so I doubt a workbook for it exists -- instead, skim through the sections that interest you and then find a textbook

for each subject

[crimson leaf]

From what I get it's not an encyclopedia only because it's not comprehensive enough

[wicked osprey]

hello, anyone have a recommendation for a writing surface? going back to school and my desk has a full sized mouse pad

so i need a piece of acrylic or something a bit larger then a piece of paper to write on

[timber mesa]

maybe a nice clipboard? a friend in HS had a thick, wooden one

[wicked osprey]

could look around for something like that

[timber mesa]

good if you like writing notes in white paper

[wicked osprey]

gonna need to last years

yeah i retain info much better if i write it

studying chem into pharmacy ive got a lot of years left

[remote nova]

Hey guys. Recently I've been feeling pretty uninspired to do math. I'd like to learn some new math, but I don't want to open some book on like "real analysis" or "algebraic geometry". Is there any sort of fun sort of advanced math book you've got access to that talks about interesting math and introduced the prerequisites early on? A good example would be something like
-elliptic curves
-categories and sheaves
-cohomology of groups
-topology and groupoids

[flint forge]

Whats your background? Some of these topics have hefty prerequisities

[remote nova]

I can follow anything as long as it's not too reliant on (analytic) number theory, partial differential equations, or functional analysis. I also prefer to stay clear of discrete math, so no combinatorics or convex geometry.

[crimson leaf]

I use a deskpad what I do is just stack papers tbh

[wicked osprey]

that work alright? no dmg to the pad?

[crimson leaf]

No I have probably close to 20 sheets between me and the pad so no damage to the paper or pad

[timber mesa]

I quite like the AMS Student Mathematical Library series, sounds like what you'd like https://bookstore.ams.org/STML

basically all of these books are aimed at advanced undergraduates and introduce various topics that aren't usually taught in the undergrad curriculum

sometimes they're lecture notes from REU courses things like that

[remote nova]

This looks fun, thanks

[foggy relic]

Woah the books on that link look extreemly interesting and also very accessible 😍

[timber mesa]

some are pretty good

I've read through Katok's p-adic analysis one

and also skimmed a bit of the matrix groups one I think (it's basically a baby Lie theory text, good for someone who knows like LA and calc)

the ones on fractal geometry, ergodic theory and groups to geometry and back all seem interesting too

I've heard good things about Algebraic Geometry a Problem Solving Approach

[remote nova]

I've got the one on Elliptic Curves and such

lol

[remote nova]

This one caught my eye actually :P

[timber mesa]

it's probably good if you're willing to put in the time into it

since you're walked through most of the important results by doing exercises, that's the idea of the text

[foggy relic]

how is the alg nt one?

A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z

[wheat cargo]

serre's "a course in arithmetic" is quite good from what ive heard but i havent looked at it much

not sure how relevant it is

[gray gazelle]

Does anyone know whether the AoPS series is good? I'd be using it to supplement Khan Academy.

[naive plank]

Hi I'm going through Strang's Intro to Linear Algebra (4th ed), but am currently stuck at understanding the chapter on 'Independence, Basis, Dimension', especially with regards to 'vectors' that are other forms such as matrices/functions. I feel that the text gave little detailed explanation into this portion, and was wondering if anyone could share another text that does a better explanation on this? Much appreciated 🙏

[tardy walrus]

Sorry, what exactly are you struggling with?

You want a book which views vectors as more abstract and not as like column vectors?

[naive plank]

apologies for the poor phrasing of the qn, my knowledge of linear algebra is still very basic

but basically a more detailed explanation into this section of the book

[quick hornet]

the reason strang is kind of vague is that he avoids defining vector spaces in generality

as doing so takes a lot of work

(for students who haven't seen definition-based mathematics, at least)

any linear algebra textbook that defines a vector space (which is most of them) will have a "better" treatment, in the sense of more clear/detailed

but that's all kind of orthogonal to strang's point here

strang is trying to say that linear independence/bases are determined by abstract algebraic behaviour more than anything

he gives examples of things that dont "look like" traditional vectors but do "act like" them

at least wrt addition and scalar multiplication

his example of 2x2 matrices, for example, is just if you rewrote 4x1 column vectors to be 2x2 instead

obviously this changes their multiplicative behaviour, but they still "add" the same way

the point is that, when we're looking at bases/spanning/linear independence in some space, we're really looking at algebraic properties of that space

the "form" you write stuff in doesnt matter as long as they satisfy the algebraic definitions of spanning & linear independence

if you want something more detailed, again try any formal linear algebra text

lang's linear algebra or whatever

[naive plank]

Thank you so much, this point is especially enlightening for me

I'll check out other texts and see what I can gain from them

[heady ember]

Yeah you can look in pinned

[gray gazelle]

Lang or Dummit and foote for a second time learning of algebra

?

Lang for sure.

[gray gazelle]

is Lang's algebra book actually good?

i've heard mixed reviews about it

[sour pond]

Any reccomendations for books on multilinear algebra(tensors&tensor products, etc.)

[hollow peak]

Greub is really good for vector spaces

If you're looking for tensor products of modules then Keith Conrad has an excellent handout on them, or you could look at a commutative algebra textbook

[hollow peak]

very encyclopedic but that doesn't make it particularly pedagogically sound

[lilac girder]

Hello, which calculus book would you guys reccomend for Calc 1 - 3 and do all the problems

Stewart?

[lime sapphire]

Paul's online math notes

[timber mesa]

I guess it's good if you already have some exposure, maybe for a second course

some of the problems are challenging

I've heard from a prof that some of them were open problems at some point in time (obviously way before Lang wrote the book)

[timber mesa]

Stewart if you're an engi/CS/bio/physics? major, Spivak if you want to do math

basically it depends whether you care about proofs or not

[timber mesa]

this is also a very good resource https://tutorial.math.lamar.edu/

[lilac girder]

im guessing stewart since i suck at proofs lol

ty!

[sharp latch]

looking for a multilinear algebra text i can go through. have taken linear algebra, abstract algebra, and differential geometry, but need some additional resources to understand concepts like tensors etc. going back through an old linalg book and wanted something on multilinear algebra to follow alongside it

[remote nova]

It's a bit intense for me, I think.

[gray gazelle]

so i'm studying descriptive statistics, my university textbook is fine but it's a bit to hard when it comes to proofs, properties (probably because there's a lack of examples). i'd like to refer to some other books as well. any suggestions?

[candid cloud]

Hey bros, any book that covers math history? More specifically, one which covers the history of numbers?

[undone spire]

Any books focusing on trigonometry especially functions?

Or trigo in general

[primal mica]

Why you gotta do my wallet dirty like that?

(Jokes aside, thanks. There are a lot of exciting books in there that seem great for my non-mathematician level)

[earnest gazelle]

has anyone written a good history of 20th century math book?

[manic fox]

Hey I'm looking for an interesting book to pass the time. Something similar to "navier stokes problem in the 21st century". So like something that builds up to a problem or shows off the attempts to solve a problem, something like that. However, that book is way out of my league. So anything else similar to that?

Like something applied ya know

[earnest gazelle]

Maybe you'd like strogotz books? I havnt read them but they are pretty popular and focused on more accessible applied math

[brittle spindle]

Anyone have recommendations for discrete math for self-studying?

[gray gazelle]

Is anyone interested in grouping up to tackle some of Spivak's Calculus between October and February?

[gray gazelle]

https://www.amazon.com.au/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328

I use this and it is very readable. I only covered about a half dozen sections but they significantly improved by mathematical writing, argumentation and reading in calculus.

[gray gazelle]

It also has the "check your understanding" basic exercises before the exercises proper. I don't know why every book doesn't have these. They're really helpful.

[brittle spindle]

thanks

[hollow shore]

yeah I am

[gray gazelle]

Cool 🙂

how to get into Effective Descriptive Set Theory? im just an undergrad idk much math yet

i just know very elementary basics of set theory and logic and topology but not much

[gray gazelle]

<@&286206848099549185>

[heady ember]

Pinging helpers in #book-recommendations

People not reading the stuff on when to use @-Helpers again

[gray gazelle]

oh sorry i understand that i was wrong now

thank you for making me realize it

[gray gazelle]

has anyone ever read a book until the end?

[tepid prairie]

People normally get to the last page and close the book so no.

[lusty briar]

Do you recommend this book for a senior highschooler?

[gray gazelle]

It's considerably more involved than the discrete mathematics we covered in high school but you could use it as a reference and source of proofs/exercises. There will be some topics that are covered (probably in greater depth) e.g. basic counting techniques. I find Epp's writing style and scaffolded exercises easy to understand. For example, I never really understood proof by induction in high school but I grokked it within about 45 minutes of reading her chapter on it, her proofs and doing some exercises. How much you get from it will depend on your background and syllabus. It is commonly used in first year classes in university for discrete mathematics (for mathematics and for CS).

The best answer is to try and find a library copy and try yourself

The first half dozen chapters are on logic. This will be invaluable if you study mathematics at uni. It will also be required for most philosophy courses eventually. If you study humanities and take an introductory (natural language) logic unit that uses a text like Govier's 'A Practical Study of Argument' you could use Epp as a supplement.

[glad prairie]

Singh wrote a book on fermats last theorem like this. It looks accessible but idk if there's any rigor

[lime sapphire]

i'd be down for this if there's nothing like work stopping me

[rare tundra]

Guys, pure and applied mathematics part 3 by Dunfield and Schwartz is an amazing book, highly reccomend

[hearty steppe]

Ok I need book recs and resources on kolmogorov complexity

Now I am not wandering aimlessly in wolframs book since I have a better lead

altho I am also being told, both resources complement eachother

[solemn rover]

"An introduction to kolmogorov complexity with applications" by Li and Vitanye if you have more CS background (easier and more general in its outlook)
If you know more computability theory and are interested in mathematical logic,
"Computability and Randomness" by Nies
"Algorithmic Randomness and Complexity" by Downey and Hirschfeldt
The latter is self-contained if you're decently mathematically mature and know some logic; it can serve as an introduction to computability theory and its techniques (first 100 pages)

[flint forge]

I can second the last book on there

which was used as a textbook for a class i took

(taught by Hirschfeldt)

[hearty steppe]

Yea I have ok mathematical maturity. I don’t shine much of a candle on the honorables here at all but I think I understand the structures I’m working with at a decent enough level

I’ll check out those reads

I’m going thru Carroll’s GR book and Griffiths QM book as well

I’m also going thru A New Kind of Science and I’m about a hundred pages thru it already after just starting it

[earnest gazelle]

I havn't read "A New Kind of Science" but you should know (if you don't already) that it's pretty heavily criticized by scientists.

[woeful estuary]

I'm looking for a really basic introductory source on Galois Theory

Any recommendations?

[hollow peak]

Rotman as usual is a really nice and clear expositor and includes a lot of basic ring theory

If you're looking for a more speedy intro, check out Milne's notes

[woeful estuary]

Thanks a lot

Does it cover field theory too actually?

[gray gazelle]

which calculus book i should read

i have a very basic understanding of linear algebra and some highschool math

[loud cradle]

i second the recommendation for Rotman, very clear and efficient book

[hollow peak]

of course!

[vestal root]

hello, I just want to ask a more broad question. I am new to linear algebra and I noticed that there's a lot of proving. I just want to ask if there are any PDFs or resources or books that give me the thought process of proving things. like multiplication of matrices for example?

[karmic thorn]

Any textbooks (or lecture notes) to learn about difference operators and difference equations from scratch? I'm not specifically interested in numerical analysis, so I'll prefer a more general (and introductory) treatment of the subject. Of the two textbooks I could dig up online, Elaydi jumps right into difference equations without ever defining difference operators, while Kelley/Peterson seems fast-paced.

[karmic thorn]

Learning how to prove things can take some time! If you feel uneasy about mathematical notation and the basic structure of proofs, you can go through some book on introduction to proofs. Otherwise (and what I'll insist on) you can stick with a textbook on linear algebra, try to ask yourself why things make sense and attempt the proof for propositions on your own before looking at the given proof, ask questions (on this server or other math platforms) for help or better intuition/understanding, and keep in mind that it will still take some time to get used to it all. Progress will be slow at first, but it'll get better.

[vestal geode]

Hello world

can someone suggest a good and free book abt Analysis 1 and Algebra 1 so I can start my journey in the university
and tnx

dm me with recommendation pls

[analog lava]

analysis 1 :

rudin/abbot/tao

algebra 1:

dummit and foote(a bit harder)/gaillain ( a bit easier)/fraleigh

those are like

at the first level

abbot is easier than rudin

[vestal geode]

tnx man

appreciate ur help

[gray jungle]

rudin is horrible for learning on your own , imma say that
if you never had exposure to proofs before i like tao as a 2 in 1 package which is certainly much slower than books like abott

[vestal geode]

I see

[gray jungle]

and if by algebra you mean abstract algebra i like artin a lot , and you get the extra lectures by Benedict Gross avaliable on youtube to go with it

https://www.youtube.com/watch?v=VdLhQs_y_E8&list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5

[novel obsidian]

Does this follow article?

Artin*

[gray jungle]

yes

[vestal geode]

tnx so much man @gray jungle

[vestal geode]

Idrk cuz I look at my university schudle I saw that Analysis 1 and Algebra 1 are the main modules

so I asked for books

@gray jungle I didnt find the full Tao book

[vestal root]

hey, thank you so much for this. someone sent a pdf in the #math-discussion and I think it's a good starting point. Not a 500-page book... so maybe I'll read that pdf and continue on studying linear algebra

[hearty steppe]

Not so fast mate I’ve been talking to many people. Including Postdocs about Wolframs book and the conclusion is to go through his book and learn about Kolmogorov complexity where they should complement eachother

Wolframs points are about complexity as an amalgamation of processes while Kolmogorov is concerned about the instances of the objects involved

Wolfram’s book is still important to look through* in other words to cross reference the POVs

[gray jungle]

tao has 2 analysis books

[karmic thorn]

Sounds good!

[jade spade]

Whats a good introductory book to topology

[abstract rapids]

Ive been reading through Introduction to Topology by Bert Mendelson and although some parts are a bit unclear i find it easy to follow and read

And related to that i wanted to ask what would be the next logical step to continue on topology after reading that. Ive been advised to read Topology By Munkres but ive taken a look at it and it seems like a big step and pretty difficult (specially the algebraic topology part). Is there anything in the middle?

[novel obsidian]

Has anyone read "A mathematicians apology" by G.H Hardy? Anyone have any thoughts on it?

[dapper root]

Weird

I don’t agree with like any of it, but it’s interesting to see how Hardy thinks about stuff

But it’s interesting to me in a purely academic way, it’s not interesting because I think he makes some really good points or whatever

[novel obsidian]

i guess it's possible that if hardy lived today he'd probably think closer to you? or is it common among academics to think like hardy does in the book?

[hearty steppe]

I like that book from what little I read in the initial chapter.

maybe better than Munkres in some respects

[tepid prairie]

I have this book too, how long did it take you to complete this book?

[gritty nexus]

Do you guys happen to know a book on algebraic NT that gears toward a geometer? I want to learn geometric Langlands :((

[abstract rapids]

ive not completed it yet but im close to do it. Ive been 2 months with it

[thick depot]

Hello Guys, I'm very interested in learning more about Game Theory. And I'm hoping that maybe anyone could suggest a good introductory book or perhaps a lecture series or blog to start with since I can't seem to find one in the #books-old channel. Note- I have basic knowledge of Mathematics of a Senior Secondary School Graduate.

[subtle shore]

Anyone know a good book for applications of differentiation

[mystic orbit]

if all there is to being a mathematician is as Hardy says then I refuse to become a mathematician

based on that essay alone, I think I'd absolutely loath Hardy as a person if I've ever met him

[novel obsidian]

What's his general message? (I'll read it eventually)

[mystic orbit]

that "real" math is a masturbatory activity that serves no purpose than ego boosting

or at least that's the idea I got from reading the essay with no more than a slight exaggeration

[hollow shore]

[mystic orbit]

he also died a virgin, couldn't even bear looking at himself in the mirror and loved cricket

like

how uncool can this person get? lmao

[analog lava]

are you talking about the avg math enjoyer

[novel obsidian]

A sacrifice has to be made to have a few things named after yoy

[sage python]

@gritty nexus probably Neukirch comes closest among those I know?

I haven't read much of it, def the beginning doesn't like, immediately reference Spec and talk about ramification of primes as maps of curves and whatnot

But I think chapter 3 esp has an AG vibe

@slim nacelle would know better

[foggy relic]

whats the prerequisite for Neukirch?

[sage python]

Ordinary algebra tbh

Like he defines integrality in the book

[foggy relic]

oh lol

[dusty badge]

Hey any book recommendations for a like... Umm.. 16 year old kind of beginner. Ik stuff taught at school but I wanna learn more

Can do algebra, graphs, statistics, taxes but what's there further

[quick hornet]

the typical "next course" taken "in sequence" is calculus

[mystic orbit]

literally everything

[quick hornet]

of which there are 10 billion resources out there

but youll probably learn that if you just keep going through school

if you want something a little more niche/interesting, you could look into, say, some elementary number theory or graph theory or somesuch

should be approachable with what you know

(though learning proofs first would be helpful)

[mystic orbit]

yeah, calculus and number theory are good reccs

if you want to go with calculus, 3blue1brown's "essence of calculus" on youtube is a good intro

the series is approachable and quite well produced

and genuinely fun to watch imo

[chilly mango]

Best book on the history of mathematics?

[devout star]

anyone got any cryptography book recommendations?

[remote slate]

What is the difference between linear algebra and vector algebra?

Please recommend me a good book for learning vector algebra

Where's that discussion 1 and discussion 2 channel gone? Or is it my discord which is not showing them?

[heady ember]

What even is vector algebra

Only heard of linear algebra

[primal mica]

It’s the algebra of vectors, so addition of vectors, multiplication, etc etc. sometimes parametric equations and what not.

I’ve seen it covered mostly in the beginning of intro linear algebra books, in calculus books (typically dealing with multivariate functions), and in general physics textbooks

These are all very common places I’d say. If memory serves I used Young and Friedman for my general physics book, but I think my current university uses Resnick? They both go over vector algebra.

Stewart Calculus definitely does as well as Larson (which I used a decade ago)

I think the beginning of Strang’e introduction to linear algebra also covers briefly vector algebra in the first few sections, possibly even retrievable for free on the books website.

[heady ember]

Stewart

[remote slate]

??

[heady ember]

You probably hid them or something lmao

[dapper root]

You have the studying role

Type ,iamnot studying

To remove the role and you’ll see the channels again

[hollow shore]

Hello Chmonkey

[dapper root]

Hello

[remote slate]

Thanx bruv

[jade spade]

Whats a good introductory group theory textbook

[gusty smelt]

artin's algebra is my fav

[analog lava]

rotman group theory

gaillan

artin too yea

[sudden kindle]

Dan Saracino Anstract Algebra

[thick depot]

hey guys, any recommendations for an introductory book on game theory

[rugged seal]

Any recommendations for Fourier Analysis? i doesn't need to be the whole book if its just a chapter its also alright.

[remote slate]

What's the first part of the book
linear algebra done right?

Second course?

What it means?

[quick hornet]

literally a second course

it's intended to be a slightly more advanced look for students already familiar with the basics of linear algebra

if you're confident, you COULD use it for a first course, but it's not the easiest text for that

[remote slate]

Is there first course book for linear algebra by the same series?

[quick hornet]

no.

[remote slate]

So students are supposed to use some other books for the first course for linear algebra?

What book should I use for the first course?

[halcyon garden]

I think you can use it as a first course and get by, it was my first exposure to proofs, it is not super hard... you just need to take it slow. However, if you want something more computational, this isnt the book for you

[remote slate]

I am finding it a bit challenging...

Any recommendation for first course on linear algebra?

[heady ember]

Friedberg perhaps?

Look in pinned

(if you haven't already)

[shell geyser]

I'm pretty sure Friedberg is also usually used for a second course. I guess a first course book would probably be a standard computation book like Anton, Strang or Lay.

[tulip blade]

Friedberg basically covers the same material at the same level as axler lol

[heady ember]

Oh lol oops

[grave thorn]

am i the only one who thinks kolmogorov and fomin > rudin?

[sage python]

They're kinda different

[analog lava]

no ur not @grave thorn

but too much on the set theory chapter tho

haha

[slender dragon]

Hmm. The first five chapters of Hoffman Kunze are good I'd say

[hearty steppe]

It’s a tough book to work through but I kinda like it in some respects

I think I went thru the first chapter and a half maybe?

I am a sucker for Janich’s linear algebra book. I really like the explanations

[runic hatch]

yeah I'm not sure H&K is the best first book either; maybe if you're pretty comfy with proofs and stuff already

[grand osprey]

I think Janich is pretty underrated. His LA and topology text are written really really well, although his topology text lacks exercises or problems.

[gray jungle]

i love H&K but absolute not a good 1st exposure unless you're comfortable with abstract math already

https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/pages/syllabus/ you should check this out @remote slate

[junior mantle]

Thoughts on this book?

[remote slate]

This one?

Anton's?

[gray gazelle]

whats a good functional analysis book

[analog lava]

rudin

kolomogrov

conway

i learnt from a textbook called intro to topology and modern analysis

[analog lava]

p cool

by simmons

[forest sleet]

There's also brezis if you want functional analysis+pde or reed-simon functional analysis for math physics

[gray gazelle]

ill go with kolmogorov then

just because it sounds the coolest

[gray jungle]

there is also Kreyszig if you dont have a measure theory background or just want something very introductory.

[gray jungle]

im also using this book for general topology and its pretty cool , looking forward to go over the functional part

[analog lava]

good luck and enjoy

[blissful gust]

Hello guys, is there anyone who has Discrete Mathematics and Its Applications - (with connect) or know where to buy it for cheap? 😄

[dapper root]

Unbelievably based

[gray gazelle]

thats how ive been picking my books

[shell geyser]

That is the book I first used yes. I'd say this is more accessible as a first course in linear algebra. It's not very rigorous, i.e. it doesn't cover that many proofs, but it should allow you to become more familiar with linear algebra, and then you might be able to do in something like Friedberg. I find Friedberg hard to use with no prior experience. That being said you probably won't need the applications chapter of this book if you do use it.

You might also want to consider Gilbert Strang's book, since that has accompanying video lectures from MIT.

[languid galleon]

Hi

I am not looking for a book recommendation but more of a paper-recommendation

I am looking for a detailed paper on the Laplace Transform, it properties both discrete (z-transform) and continuous.

Essentially, I am looking for a "Fourier analysis" but for the Laplace transform. If anyone has any good reads on the transform.

Please do tag me in the message or DM me if you have a recommendation. Thanks in advance!

[pure solstice]

why a paper specifically?

[languid galleon]

Doesn't need to be a paper, it can be a book if that's better. I am just looking for something detailed in explanation specific to Laplace transforms but doesn't have "padding." Good papers usually achieve that type of explanations. Books esp most textbooks are usually filled with the "padding" where you have to skip around and filter out everything else to focus on the theory you wanted to see.

Like this is the Fourier analysis I always keep as reference : https://www.roe.ac.uk/japwww/teaching/fourier/fourier1415.pdf.
It provides detailed information about the Fourier analysis with some talk about application but the author still keeps the information short and sweet.
It seems like the professor's lecture notes but it was still a lot better than most things I found.

[gray gazelle]

can someone recommend me a good book for learning practical statistics and bayesian statistics theory for application in Python

[earnest gazelle]

http://dec41.user.srcf.net/notes/ Anyone read through these notes? I started through some of them, they seem great

[gray gazelle]

really liking "Basic Algebra 1" by nathan jacobson

good for abstract, linear and even some lie and jordan algebra

[tropic dune]

Does anyone recognise these questions? Im trying to find the book which i got these questions from for my revision. Pls help

[heady ember]

I highly doubt a random person who happens to see your message at the correct time who just so happens to know this book so well they can rather instantaneously spot it and identify it to you. Especially given that it seems like a rather random book.

Seems like hs algebra, which they are an wide assortment of resources for

You can consider using those other resources too.

E.g.: Khan Academy

[tropic dune]

Okay thanks

[heady ember]

np : )

[tender cedar]

is there a place I can find the solutions for Serge Lang's Linear Algebra book for free?

[tribal bolt]

Hi, I'm looking for textbook recommendations for trig, 2D Geometry, and 3D geometry. For 2D Geometry I really like Geometry the Easy Way by Lawrence S. Leff. Unfortunately the book does not include a bibliography.

[lime seal]

Yes

[tender cedar]

legally?

🙂

[lime seal]

Solutions Manual for Lang’s Linear Algebra

192 Pages · 1996 · 2.94 MB · English

by Rami Shakarchi (auth.)

It's on pdfdrive. com
idk if it is legal or not

[lime seal]

Yeah

[dusty badge]

Hey guys! I am interested in a book for algebra... I am just 15 so i guess more on the beginners side, Thanks!

[gray gazelle]

I'm assuming college algebra?

If so, you might not need a book, Khan academy and other channels have good playlists for most math up to calculus.

[dusty badge]

umm... college or?? high school

i guess age 15 is high school right?

[sterile harness]

yes it is

[gray gazelle]

Yes, sorry; when I say college algebra I usually also refer to what is being taught in high school. Mainly finding roots of polynomials, exponentials etc.

[dusty badge]

then why college lol?

[dusty badge]

ohh right

[gray gazelle]

I believe that's just the general term for any algebra that isn't linear or abstract.

[dusty badge]

so no books for that? In terms of math i prefer books over tech. The rest of the time visuals over books

[gray gazelle]

I mean there are a lot of books for elementary algebra, probably any you'll find in your local library will do. Otherwise, like I said, khan academy has good videos explaining it.

[dusty badge]

what if I want to master my level of maths and go beyond it as well. I know I am asking too many questions but sorry lol 😁

[gray gazelle]

So what do to after elementary algebra?

[dusty badge]

what exactly does elementary algebra include?

[flint forge]

There’s sort of an issue here where like

Before higher level stuff

Most of the books in math are indistinguishable vaguely corporate messes

So it’s hard to recommend one

You could really go to any library (or Amazon) and buy any level appropriate book

And you’d be fine

[dusty badge]

right, I understand that partially

[flint forge]

Plus most of the users here probably haven’t studied that kind of math in a long time haha

[dusty badge]

yeah, Most of the help channels have questions that go beyond my understanding

[flint forge]

Nothing wrong w that were just old

Anyway; if you really want to use a textbook maybe openstax is a good suggestion

They have tons of free books online and the physical copies are as cheap as possible basically

[dusty badge]

right

[flint forge]

So you can skim the book before you buy it if you want

[dusty badge]

got it

[gray gazelle]

https://youtu.be/LwCRRUa8yTU this might be what you're looking for

I'm assuming you already have some amount of understanding of variables and functions.

[dusty badge]

i.. don't

[dusty badge]

https://openstax.org/details/books/college-algebra i found this one kinda appropriate. It begins from the part where i have left and goes beyond

[gray gazelle]

https://www.khanacademy.org/math/algebra This should be what you're looking for.

[dusty badge]

that looks apt, yes

thanks, I think I have found my resource

[gray gazelle]

👍

[mighty sequoia]

Anyone know a good book on discrete calculus

[lapis sundial]

How is Bott-Tu? Seems people have mixed opinions about how good it is to learn from

I imagine it could be rough if you've never done alg top before or smth so maybe that's why

[hollow peak]

BOTT TU

I have spent a lot of time reading that mf

It's lots of incredibly interesting and very concrete geometric applications of algebraic topology

Basically, you can learn from it in a vacuum if you've got some exposure with smooth manifolds and commutative algebra-y linear algebra, and it'll be difficult but very rewarding in terms of learning how to think about algebraic topology if that makes sense

It's even more rewarding if you've seen singular homology and fundamental group stuff before, but you technically are not required to have seen it

I'm like 1/2 through so far and the exercises can be a little brutal or just rehashing a proof that was just done

[dapper root]

BOTT AND TU MORE LIKE ROTTEN POO

Jk I heard it’s pretty good

[unreal token]

are there any books about math that are less formatted like a textbook and more about just general exploration of topics?

its hard to casually read many of them without a pen and paper to follow along with

[pliant stream]

@unreal token try What is Mathematics by Richard Courant

[misty wyvern]

What about those Princeton Companion books

There's one for pure math and another for applied math.

[gray gazelle]

what are the differences in these two books:
A Concrete Introduction to Higher Algebra
An Introduction to the Theory of Numbers

[lime sapphire]

one is a book on algebra which first teaches you a bit of basic number theory to then learn groups, rings, field etc.

the other is just a number theory book

[gray gazelle]

hmm

[lapis sundial]

Ye that's how I'm finding it :)

So far it's mostly made me review/learn more analysis lol

[rugged seal]

Any recommendations for Fourier Analysis? i doesn't need to be the whole book if its just a chapter its also alright.

[sage python]

@rugged seal what angle on the material?

/What's your background in analysis?

(Also algebra)

[rugged seal]

ive done Real and complex analysis also measure theory

[rugged seal]

i have done algebra a bit but it should be an analysis angle

i need to learn fourier transformation and series (dini etc.), also convolution and a bit distributions

if that helps

[sage python]

Muscalu-Schlag then

[rugged seal]

classical and multilinear Harmonic analysis?

[sage python]

Yup

[rugged seal]

alright thank you!

[sage python]

I haven't read it myself, I'm taking a class in the fall that (at least loosely) follows it

But my friend who used it swears it's the best math book in existence

And knowing Schlag myself i can't say I'm surprised

[rugged seal]

damn that gets me excited reading it

[vital bane]

what's multilinear harmonic analysis?

[slim peak]

C.Hao's online book

Way more readable

[slim peak]

Multilinear Harmonic analysis is about Multilinear Operators from Harmonic Analysis like convolution of more than 2 functions

[vital bane]

[slim peak]

Check out bilinear Hilbert Transform

as an example

[vital bane]

so like instead of an integral transform taking in 1 function it's taking in multiple functions

[slim peak]

That's the generic idea

[vital bane]

like you study fourier transforms on more general spaces in harmonic analysis but in this multilinear flavor it's a "multilinear" fourier transform?

[slim peak]

not really

[vital bane]

you dont study that in harmonic analysis?

[slim peak]

Multilinear Fourier/Harmonic Analysis is not that standard

[vital bane]

oh it's a niche subject?

[slim peak]

Somewhat

[sage python]

Anatole undercutting my recs 😦

[slim peak]

Its a good book but that starts too general to go into too niche stuff imo

(Muscalu was the PhD Advisor of the professor that thought me Harmonic Analysis, its books were in recs of the given lecture)

The pfp is me

as an anime character

In fact it is easier and we can read book way more quickly when you are already familiar with some topics

And I didn't count

depends on the topic, the book and my goal

Most of the time I'm not indeed

generally I read half of a book

Again it depends

But for standard Harmonic/Functional Analysis books it is like 50-50

generally its due to the necessary amount impregnation of notations/concepts and math style to get the proofs

[rugged seal]

alright i will check it out aswell thank you

[rugged seal]

which one exactly? i have "Algorithms for Discrete Fourier Transform and Convolution" is thatrright?

[rugged seal]

thanks!

[slim peak]

200-300 pages is about 50h depending on prerequisites

how familiar I am with various topics

There are 30 pages long papers that took me months to understand

This means nothing really relevant

Again it depends hugely on how familiar I(you) am(are) with covered topics

Generally the book I read do not contains problems

Yes, mainly

Research

[rugged seal]

if you think about it a lecture with 3 lectures a week for 12 weeks is about the same

[slim peak]

When books have exercises/problems I generally try to solve a part of them

The only one I really tried are books about Interpolation theory : Bergh and Lofstrom 1976, Alessandra Lundari (1999-2009-2019, 1st, 2nd, 3rd Ed)

[rugged seal]

sure the lecture example I think is a lower bound for how much to do if you first encounter a topic

i think its far better to not read the book one time carefully but read it multiple times with increasing intensity

you dont have to get everything on your first read

[slim peak]

depends on the book, and the way it is written, but I heavily agree

[rugged seal]

yeah i think first time should give you a rough idea and if you kinda get what its about you are also much better at recognising whats really important

also a second reading where you understand many things much faster is much more fun then the first one

i would try to read everything and where i stumble i would maybe think a few minutes about it. If i am not getting it by then write it down and be sure to understand it on your second read

yes

[hushed saddle]

Hi I am trying to learn statistics for data science. Could you recommend me any book or course Please? Thank You

[rugged seal]

sometimes there is stuff which is dont really necessary for moving on, but on a new topic reading for the first time its not possible to make this out, thats why a second read can be much more fruitful because to me its easier to see whats important and what not

[pliant stream]

what's your math background?

I mean the obvious answer is just to read casella and berger

[hushed saddle]

Well I am CS undergrad but not a great student so ik stats but i don't really know it cause i just read it for the exams.

[pliant stream]

But for a resource specifically tailored to data science (and less thorough and comprehensive) try https://www.google.com/url?sa=t&source=web&rct=j&url=https://cims.nyu.edu/~cfgranda/pages/stuff/probability_stats_for_DS.pdf&ved=2ahUKEwilxvjT8aH5AhUFjYkEHVgbBiMQFnoECAkQAQ&usg=AOvVaw1sLTtlgOf6Mhx3J4a-bwQz

these notes are for an intro probability/stats class for the data science masters program at nyu(for people who didn't take it in undergrad)

[hushed saddle]

oh that might really help

the issue is i see people are able to get much out of data than me and they are able to get there with stats and all like eda

so i am trying to address this issue

[pliant stream]

You can also try introduction to stat learning

but if you dont have any stats knowledge, it will be opaque, since the authors just give you formulas

[hushed saddle]

should i jump into it directly cause like i said my stat concepts aren't that great

so what do i do?

[pliant stream]

how much math do you know

[hushed saddle]

i am good linear algebra and basic calculus

in stats its tough to gauze

[pliant stream]

well basic calculus as in

multivariable?

[hushed saddle]

yep

[pliant stream]

well you definitely need to learn some basic probability first

before you can understand stats

[hushed saddle]

i know basic probab too

[pliant stream]

like at the level of an undergrad probability class?

[hushed saddle]

but the problem is i've learnt it in a non intuitive way

[pliant stream]

including calculus*

[hushed saddle]

sorry?

[pliant stream]

like you've taken an undergrad probability class with calculus as a prereq?

or something similar

[hushed saddle]

yes

no no

wait i never used probab and calculus together

[pliant stream]

because if not, the first thing you need to do is that

[hushed saddle]

oh

so i need to learn probab and calculus together before statistics ?

[pliant stream]

yes

[hushed saddle]

damn oh well any suggestions for that?

[pliant stream]

the notes I linked are very brief and don't even include problems, and I don't know how much use you'll get out of them

But they do cover a bit

[hushed saddle]

np i'll read em

[pliant stream]

The standard text used in colleges is ross a first course in probability

I don't really like it though

I learned more or less through grimmett and stirzaker

[hushed saddle]

brother or sister you are killing me

[pliant stream]

Though it's a much much harder book, and I definitely didn't understand most of the things, but it was still a good read

the first ~5 chapters of casella and berger are also great

[hushed saddle]

i am ready to work but you are taking me to a whole new level like i was just browsing how much a data analyst or science undergrad should know

stats? and it was just desc stat and inferential stat

[pliant stream]

well I don't know about other schools, but at nyu the math courses a data science undergrad is required to take is super minimal

[hushed saddle]

f bro i need to level up my game
are you in data science ?

[pliant stream]

im trying to break in right now

[hushed saddle]

if so could you like tell me how they intro'd you all math and data science pls

[hushed saddle]

?

[pliant stream]

i'm trying to enter the field and hopefully get into a phd program

[hushed saddle]

oh dude that's like a waaaay high level. i thought u would say masters at least

[pliant stream]

yeah i mean the notes i posted are for a class you'd take as a first semester masters student at nyu in data science

[hushed saddle]

tbh i am trying to get in nyu

i have my gre in 2 days

[pliant stream]

oooh

good luck

[hushed saddle]

lol this is a crazy coincidence lol
anyway i'll do the probab ross book first

[hushed saddle]

i really need it man

thanks!!

[pliant stream]

i wouldnt though if your goal is to learn

the material quickly

like that book is way too long imo

youll probably learn a lot if you go through it but it's just a very long read

[hushed saddle]

brother pls help me i want to learn things quickly

[hushed saddle]

not like i am trying to skip things but i want to be efficient

cause if i get in a data science program and i am not able to keep up with the courses then its useless

[pliant stream]

you can try this: https://ocw.mit.edu/courses/18-600-probability-and-random-variables-fall-2019/

but ross moves at a pretty slow pace

[dusky spire]

Can anyone recommend me a book on differential geometry that has a lot of general relativity applications?

[pliant stream]

I mean you can get into a ds program and not know probability right

[hushed saddle]

tbh yes

[pliant stream]

that's why they have a prob/stats class for masters students

[hushed saddle]

it has more emphasis on stats and statistical learning espiceally in r

[pliant stream]

yes, but it's not like stats just comes from nowhere

[hushed saddle]

yes that's the issue if go a little deeper it gets intiutive and all the other things i don't know

[pliant stream]

like the fact that $\bar X \to^d N(\mu,\sigma^2/n)$ if $\mathbb E X = \mu$ and $\mathrm{Var} X = \sigma^2 < \infty$ is from probability

[hasty eagle]

Andrew071

[pliant stream]

and grimmett and stirzaker proves this

[hushed saddle]

Sir @pliant stream after looking at your post i realize i am uneducated

[pliant stream]

it's just the weakest form of the central limit theorem

[hushed saddle]

i'll go back to your very first suggestion and take corusera

[hushed saddle]

oh yeah lol

still

[pliant stream]

or like why the sample variance is typically defined with n-1 instead of n

it's all basic things you should know

[hushed saddle]

yeah exactly what my prof asked my while scolding me

any way thanks @pliant stream i got a direction to go now

[pliant stream]

yeah if you don't know then it's just because you never took prob/stats

it's not a big deal

just need to learn it

[hushed saddle]

yessir

[pliant stream]

and i'd recomend if you read ross to go along with mit 18.600

the psets are really good

[hushed saddle]

i will give it a go thx

[forest sleet]

O'Neill semiriemannian geometry w applications to relativity

[dusky spire]

Thank you a lot

[sage python]

Feels inefficient

To actually do Riemannian geometry you need to read this book twice

[gray gazelle]

what free book could I pick to start self-learning calc?

[pliant stream]

i would just watch like say mit 18.01

if you really want a book, then the book they use? Or stewart which is the standard text for calc.1 classes at least in us colleges

[gray gazelle]

uhh thanks I guess

[flint forge]

Open Stax also works

[gray gazelle]

Lookong for recommendations for fun math pronlem books

rhinking of getting presh talwakars math problems

[modern stone]

You could also try Paul’s Online Notes

[novel obsidian]

What do you guys think of algebra: chapter 0 by aluff?

[dapper root]

I like it 👍

[novel obsidian]

Do you thinks its possible as a first dive into aa? And also do you think that it's more modern categorical approach lends itself better to learning ag and at later down the line?

The math se post I read on it said it was fine as a first book but I figured I'd reask

[dapper root]

Thats how I did it

If it’s your first foray with proof based math maybe it’s a little abstract, but you’re gonna get pwned on your first time learning proof based math anyway

The category theory isn’t very heavy until the last two chapters anyway

I just think introducing terminology early is good, and sometimes things just need time for you to stew on it

[novel obsidian]

The god chmonkey has spoken

I'm considering buying a copy because my next paycheck will be pretty big

[dapper root]

Maybe just get a pdf for the first chapter

If you vibe with it, go and buy it

[novel obsidian]

Okie, tysm

[lilac girder]

Hello

I wanted to know if there was a curriculum or book series to start from basic math to complex

Currently doing all the questions of James Stewart Calculus and build myself up

[hearty steppe]

Just go through a general relativity book like Carroll?

Like just jump into it that’s what I’m doing at this point.

[dusky spire]

Why is that

[foggy relic]

@novel obsidian i would recommend doing some of the aa excercises from a different book though

[pliant stream]

basically whatever ur interested in

what's your goal of learning math?

and then go from there

[dusky spire]

Ok thank you so much! Which book would you recommend

[pliant stream]

like if your goal is to ml research, then you probably don't need to do any algebra

[foggy relic]

aluffi excercises are not very good imo; i would recommend doing the category theory excercises in aluffi and then aa excercises from something like Artin or Dummit Fotte

[pliant stream]

but if your goal is to do algebra then yeah you'd do algebra lol

[lilac girder]

I want to self learn math to accomplish the goal of doing higher math like topology or real analysis

[foggy relic]

but aluffis exposition was very very good when i read it

[dusky spire]

So like the basics

[lilac girder]

Currently doing linear alg, discrete, and cal

yes

yup

ive done humanities all my left; wanted to try this

[foggy relic]

after those three you will be able to do real analysis

[lilac girder]

https://www.youtube.com/watch?v=pTnEG_WGd2Q

I'm using this as a curriculum

[pliant stream]

if you want to do analysis then try learning calculus then linear algebra then start doing analysis

although you can do linear algebra concurrently with analysis, since you don't need linear algebra until multiple dimensions

[lilac girder]

is there anything i need to supplement this?

is it fine to do stewart and move to spivak after finishing?

[pliant stream]

idk if you would need to move to spivak

there's no reason I'd think to do spivak over an analysis text

unless you're referring to calculus on manifolds

[novel obsidian]

mhm, any suggestions?

[foggy relic]

@novel obsidian

[novel obsidian]

Oh lol, I missed that, ty

Are the topic covered in both similar,

?

[foggy relic]

somewhat

artin does more linear algebra, aluffi does categories and basic homological algebra

[novel obsidian]

D&f?

[foggy relic]

dummit fotte

oh youre asking how that content compares

uhh

content covered is decently similar? i dont think df does categories but he does do some basic homo alg and also some rep theory

[novel obsidian]

Gotcha, thanks :)

[gray gazelle]

Introductory category theory textbook recommendation?

[flint forge]

Riehl

[sage python]

It's a joke, "semi Riemannian"

[dusky spire]

Lol

[gray gazelle]

best textbooks for number theory?

[hollow shore]

check the pins

[gray gazelle]

Just start with analysis

[heady ember]

[fallen palm]

I just want to recommend two really enlightening books that helped me self teaching proof-writing and basic set theory/logics:
A book of set theory by Charles C. Pinter, and
Mathematical Logic by H. -D. Ebbinghaus.
I compared them to a lot of other books on similar topics, and they are a lot more coherent and readable than most texts.

[earnest gazelle]

Are you actually planning on reading all of those books from cover to cover? If you want an entire math degree+masters worth of notes, this site is prob what your looking for. http://dec41.user.srcf.net/notes/. Reading all of those books is gona take a long time and it may kill your motivation. I'm not sure if it's the most efficient way to learn math either. That said it's worth choosing 1 of them to start with and seeing where you go from there. I began with Tao's analysis 1 and 2.

[timber mesa]

don't read books cover to cover lol

[earnest gazelle]

Yeah

Esp not Dummit and Foote!

[lilac girder]

Thank you!

[gray gazelle]

Is there a abstract algebra book that does linear algebra

Excluding Artin

[cursive orbit]

Knapp basic algebra

[gray gazelle]

Book for conic sections

I need a book that will help me master conic sections completely

I was reading SL Loney and its conic sections becomes way too formulaic and messy to handle with high school geometry

Which branch of mathematics will help me deal with hard conics problems involving poles -polars ,locuses , diameters , envelopes etc etc and analyse equations effectively

Because standard algebraic methods are becoming too long and unintuitive

I need a book/mathematical branch that helps to intuitively attack conics, i am talking about hard locus problems from SL Loney coordinate geometry

[night prism]

Interesting

[rose cargo]

Hello!

I am looking for a book(s?) with some pre-university math basics explained from scratch, but in a very detailed manner. Possibly with historical notes (for example, take a function. Why exactly this notation is used, where it came from, what other forms of notation are there, and so on).

I have a background in non-functional programming, so it would also be useful if the book covers something on functional programming too (or some examples of historical math applications in computers, or something), but it is not necessary 🙂

[karmic scaffold]

I was in a used bookstore and found this. Does anyone know if it might be a good introduction to set theory, or if I should just look for something more recent?

[rare star]

anyone knows about a good book for differential equations

[crimson leaf]

If you want a good foundation lang basic mathematics would be good

[rose cargo]

Serge Lang?

[crimson leaf]

Yes

[civic surge]

Hey guys! A couple of months ago I've watched a video of 3b1b where he recommended two books: "generatingfunctionology" which I bought cause it seemed ok to learn about generating functions and "102 combinatorial problems". I have some doubts with the latter, I'm looking for a book with problems related to all kind of discrete math which has problems on combinatorics but also basic set theory (relations, counting over functions), basic number theory (divisibility, modular arithmetic), complex numbers (roots of unity, algebra over the set of complex) and also has some theoretical exercises that involves proof writing (using induction and the properties of different sets) and not only the mechanical part of this topics. Is this the right book for me? Can I combine it with some other to achieve what I want? Maybe I'm asking for a lot, but recently a took course that had all this topics and I want to keep my algebra fresh at the same time I get better in this topics.

Also I want to know how hard it is, cause I want something challenging that help me build my intuition, but I don't have much time to spend on it so probably what I'm looking is for something mid level that goes progressively up. Challenging enough to keep me oiled and maybe get something new from some of the exercises but not too hard to have to spend days with every prompt. Does it make sense??

[queen beacon]

any great resources to learn Markov chains?

[pliant stream]

Is that strand?

[karmic scaffold]

Are you referring to the author or the store?

[pliant stream]

Store

[gray gazelle]

You can't stop me

[karmic scaffold]

Nah, it’s a different one but I’d rather not doxx myself

[timber mesa]

time certainly will

I don't need to beat common sense into anyone

[gray gazelle]

How are you supposed to then

I need a good and quick analysis 1 book (preferably with solutions)

quick in the sense that it doesn't dive into other topics too much

any suggestions would be appreciated

[blazing canopy]

Understanding Analysis by Abbott is reasonably short and has lots of exercises, there are no official solutions but it is a very standard book so there are solutions written by others that are posted online

[gray gazelle]

I get it. But this is what I enjoy

[timber mesa]

just read the chapters that interest you. in the case of a book like D&F algebra, this won't be all of them -- some topics are best studied in other references, you might already know basic stuff, etc.

and you don't need to do all exercises either

I usually just do the ones that don't seem easy or seem interesting

time is a precious resource

[regal violet]

what is a good abstract algebra book?

[fierce hedge]

You should check the pinned post. TL;DR - Start with Artin.
.

Is there any analysis book or series which starts as usual but then also properly covers metric spaces and stuff. I have been reading Zorich but it diverges in very different topics in Volume 2. Tao's A2 covers these topics but then he leaves gaps in theorems to be filled by the reader (or so I have heard) OR should I go a different book for Analysis 2 ie metric spaces.

[brittle breach]

baby Rudin

[gray gazelle]

I see, what do you think about using course syllabus for selecting exercises for a book

Since beginners can’t decide which exercises to chosen/focus on

[runic hatch]

That seems like a decent idea imo

I’d trust most profs to know how to select good exercises for the most part

[vital bane]

what's a good book that teaches you analysis in R^n and general metric spaces?

like a comprehensive book that has a lot of info in it and one that is good for self study (like yk has lots of examples and problems and good explanations and stuff)

[pliant stream]

Rudin, Zorich, Abott, Apostol

Literally any analysis book intended for a first course in undergrad analysis

But those 4 are pretty well known

[vital bane]

do they discuss analysis in R^n and in metric spaces in detail?

[pliant stream]

Yes?

I mean I'm pretty sure most books do not put much time into riemann integral in Rn, like rudin for example

I know apostol discusses integration in Rn

Because generally, a first course in analysis goes like

Talk a bit about topology, continuity, differentiation, riemann (stiejtles) integral, sequences and series of functions, and other select topics time permitting

[vital bane]

i wasn't asking for a first course in anaylsis

like something after apostol

that discusses general topics in detail

[pliant stream]

The coverage of Rn analysis in apostol is not enough?

[vital bane]

isn't there more?

nevermind I should finish apostol first

[pliant stream]

I mean logically, the next book would be something like royden

[vital bane]

the next step would be measure theory and stuff?

[pliant stream]

I'm not really sure what else you would expect, like differentiation you have inverse function and implicit function theorems, and some optimization. Integration you have lebesgue theorem/criterion for riemann integrability, fubini, integrating over arbitrary sets, change of variables

[vital bane]

[pliant stream]

so yeah royden

I'm reading kolmogorov intro real analysis right now, it's pretty good I guess

Under 10 bucks for a hardcopy version too!

[neon tiger]

Some book recommendations for pure geometry?

[heady ember]

What geometry

Diff geo, alg geo, etc?

[primal mica]

pure geometry

[heady ember]

[primal mica]

I find if you zone out hard enough all books are geometry. Your eyes blur and letters become just little shapes

[vital bane]

lol I think they mean euclidean geometry, yk high school stuff and math olympiad stuff

[heady ember]

Oh

Well they did put "pure geometry"

[vital bane]

Lol grass about to throw a diff geo book at a high school student

[heady ember]

I was just trying to make his qns more specific so ppl answering will have an easier time haha

but the first thing i thought of when i saw pure geo was Lee, not gonna lie. But yeah i know nothing about diff geo for now

[vital bane]

Lol same, but soon we will learn diff geo!!

[heady ember]

I still have to learn a ton more prerequisites haha

[vital bane]

i think all you need is real analysis, some basic topology and some linear algebra

[runic hatch]

Yeah that should suffice

[foggy relic]

That's for diff geo on manifolds

Diffgeo on curves and surfaces has less prerequisites, only calculus and linear algebra

[coarse frost]

Apostols book does this
and so does pugh, schroeder and all

[coarse frost]

dont u dare.

[vital bane]

don't worry I'll only start it after jee

[coarse frost]

i dont trust you

[vital bane]

stupid ass jee

[coarse frost]

its our only hope at getting into a uni

stop crying, start grinding

[vital bane]

[halcyon garden]

SCB channel exists

[coarse frost]

yeah thats no option for me anymore
I have bombed that exam

[halcyon garden]

Damn

[coarse frost]

😭

life is sad

[halcyon garden]

Time to hit the books then

[coarse frost]

i am hitting the books

the most of my marks lost in scb were coz i wasnt reading properly

and they also made tons of mistakes that they didnt fix this year

😭

[halcyon garden]

My condolences

[coarse frost]

hows uni going for u

[halcyon garden]

Summer break

[coarse frost]

Oo, i thought the semester would begin from the first of august?

[halcyon garden]

What's a resource with a lot of fun recreational math problems. Something that freshmen can attempt and will find challenging.

Not too challenging tho

Bonus points if it involves implicitly thinking about more advanced math

[hollow shore]

"Mathematical Circles" might be the book you are looking for

[halcyon garden]

Looks like it fits the bill. Thanks

Actually is there something a little more advanced and still engaging.. I feel like most of the questions are too easy for freshmen

Something like Simon Marais but easier because It should take lesser time to solve

[night knot]

I'm self studying out of D&F, any ideas what chapters I ought to cover to be at the knowledge level needed for something like Eisenbud's Commutative Algebra?

[dapper root]

You should cover the ring theory stuff, homological algebra

And field theory, you probably don’t strictly need the Galois theory, but it’s probably good to for general development

D&F also has basic commutative algebra and algebraic geometry, I don’t think that’s necessary since eisenbud starts from a pretty elementary place IIRC

[hearty steppe]

Is anyone familiar with this book https://www.amazon.com/Computers-Intractability-NP-Completeness-Mathematical-Sciences/dp/0716710455

[orchid mortar]

I am not familiar, but Garey Johnson is considered a classic

It is routinely cited for problems with known complexity

[outer olive]

Any recommended special relativity books?

[gray gazelle]

Beautiful maths problems

[coarse frost]

....

why.... 😭

[gray gazelle]

Lmao

[coarse frost]

[gray gazelle]

Why u crying lol

[coarse frost]

coz of jee

[gray gazelle]

Bruh

I am preparing for jee

Lmao

[gray gazelle]

Why tho

[coarse frost]

coz i have to give it

😭

[gray gazelle]

In?