book-recommendations

[surreal phoenix]

I get your point, and you're not wrong, but I still think he'd be better off with a book focused on sole computation

[smoky zephyr]

and yes i looked at the solution

[surreal phoenix]

a usual calc 3 course

[quick hornet]

alright i see

youre struggling with parametrizing domains?

[smoky zephyr]

i guess that’s what it would be called here

they didn’t explicitly say it like that

i pretty much understand nothing about the solution explanation if you needed to know

[glad prairie]

Idk if there is a book that does these sorts of problems in a lot of detail.

[smoky zephyr]

oof, guess i’m gonna be stuck for a while

[gray gazelle]

Lang

[manic cape]

I need to grind problems for abstract algebra (mostly group theory). My course textbook doesn’t have very good ones. What book is recommended for practice?

[gusty smelt]

herstien has good problems

but standards like dummit foote/artin/lang etc all have good and by and large the same problems

[twilit crystal]

Thanks

[nocturne sky]

Any recommendations for books that are sorta easy reads? More looking for something interesting but not textbook style with a bunch of problems and stuff

[remote ginkgo]

Raoul Bott, Loring Tu - Differential Forms in Algebraic Topology

Yeah, analysis on manifolds is really bad

The content is equivalent to spivak's calc on manifolds, not calc 3

[nocturne sky]

I’ll look into that. Does it have any hard prereqs? I should have mentioned I’ve only got a background in some calc and a bit of lin alg but no analysis or other higher level math really

[remote ginkgo]

It was joke

[nocturne sky]

:p

I’m a little clueless haha

[remote ginkgo]

I will say

I found milnor's topology from the differentiable viewpoint very good

And it is primarily a picture book sans exercises

[sudden kindle]

Milnors books are so great

[remote ginkgo]

This isn't a, joke

[nocturne sky]

Haha alright I’ll look at that

[remote ginkgo]

Though usually you'll want to have had some advanced calculus exposure beforehand

[nocturne sky]

I was thinking about maybe nonlinear dynamics and chaos by strogatz, seems like a good book but idk if it’ll be too over my head

[uncut zealot]

Any recommendations for free, online introductory complex analysis books? I plan on studying complex analysis over the break with a friend of mine who doesn't like sailing the seven seas, so something available for free from legal sources would be quite nice.

[crimson pagoda]

Huybrechts complex geometry book is my suggestion

[gray gazelle]

introductory

:^)

[crimson pagoda]

oh sorry I misread I ignored the whole message and just read the word complex

[uncut zealot]

Can you get it for free without needing to join the ranks of Jack Rackham, Charles Vane or Edward Teach?

[split pond]

maybe try mit ocw

[dapper root]

Ignore what Gabe said

That was a horrendous recommendation for intro complex analysis

[uncut zealot]

Yeah, I looked it up and it doesn't quite look to be what I'm looking for. I'm thinking more like, the sort of intro complex analysis that's just calculus over the complex numbers but mathematically rigorous.

[broken meadow]

how rigorous do you want tho

[uncut zealot]

I want exercises that are theoretical and proof-based instead of primarily computational.

Like, as rigorous as most advanced undergrad courses tend to be, I suppose?

[gray gazelle]

but contour integrals are the most fun part

my joke recommendation is the complex analysis notes that i typed up a year ago

[uncut zealot]

I mean I'm fine doing some computations, but I don't want a book like a calculus I book where most of the exercises are just computations.

[halcyon hornet]

Is MIT OCW a good resource to learn Calculus, as a supplement or main thing?

[karmic thorn]

Good either way

[halcyon hornet]

Thank you.

[gray gazelle]

honestly for OCW things you are better off trying it yourself and deciding if you're able to understand or not (psets shouldn't be the deciding factor tho)

[hard condor]

anyone got recs for books on combinatorics and graph theory? entry level so i can prepare for olympiads. thanks in advance :)

[karmic thorn]

Miklos Bona, A Walk Through Combinatorics. Maybe better alternatives exist for olympiads, but I like this as a general introduction.

[gray gazelle]

colud you recommend me a book with lots of (difficult) problems on limits, sequences and series? (undergrad)

[karmic thorn]

Kaczor-Nowak, Problems in Mathematical Analysis, Volume 1

[gray crystal]

Titu's problems on the real line

[prime oak]

any recs on books on UG vector calculus?

[karmic thorn]

If you have some linear algebra and first course in analysis/solid calculus, then Spivak's Calculus on Manifolds; otherwise Vector Calculus, Linear Algebra, and Differential Forms by Hubbard/Hubbard

[prime oak]

mm ive done some LA, ig ill get spivak

ty

[gray gazelle]

Concerning spivak's calculus, can I skim the derivatives and Integrals part in favor of infinite Sequences and Infinite Series?

Cause that's how we study it here

[strange osprey]

Well, not really, infinite series is more closely related to integration

since one of the implications of infinite series suggest the Riemann sum which is the definition of the integral

derivatives are more associated with limits

[gray gazelle]

I see

Thank you

[strange osprey]

no problem

[gray gazelle]

What about the polynomials approximates

[strange osprey]

infinite series is a real analysis topic, tends to be after calculus

[strange osprey]

Like polynomial interpolation?

[gray gazelle]

Are they related to integrals?

I think they're called Taylor series in English, I'm not sure

We call them "développement limité"

[strange osprey]

Oh those, yes they are used in approximating integrals

[gray gazelle]

So I can't study them without studying integrals first?

[strange osprey]

No you need not study them first, only derivatives is necessary to grasp the main idea

and basic knowledge of infinite series

[gray gazelle]

Ah OK, thanks again and have a nice day.

[strange osprey]

your welcome, u too

[hard condor]

thanks a lot!

[gray gazelle]

Thanks, Manan. and Noob666!

hopefully those will not be too hard for a beginner.

[leaden prism]

Any good books to learn prob theory and scholastic processes?

[gray gazelle]

scholastic

[drifting wigeon]

scholastic

[leaden prism]

What’s the name?

@gray gazelle @drifting wigeon

[karmic thorn]

You might mean stochastic processes.

[gray gazelle]

for probability Im currently using Shiryaev and it's pretty good imo. I like the approach

[leaden prism]

Ty

[leaden prism]

Yeah typo u have any boooks?

[karmic thorn]

I remember www.probabilitycourse.com being an interactive textbook online that goes into basics of probability and maybe some stochastic stuff too?

I liked it

[leaden prism]

Which version?

[leaden prism]

Sure I’ll check it out

[gray gazelle]

idk

[leaden prism]

Is it called intro to prob, stat,…

[leaden prism]

I have the prob 1 version or grad version?

[gray gazelle]

Im using Probability 1

[karmic thorn]

Yes

[leaden prism]

Gotcha

I’ll check both out thanks guys

If anyone can give me stochastic processes book it’ll be nice as well?

[gray gazelle]

For scholasticism you can start with Feser's Scholastic Metaphysics

[modern stone]

Lol

[atomic stag]

I'm being really confused in number system after watching multiple videos on it..
like interger , whole number, real numbers and their symbol etc
while doing questions of Equivalence relations etc

if you know a good video pls send me link

[leaden prism]

Ty

[karmic thorn]

What you've said so far is very broad. Are you facing difficulty with basic set theory (sets, relations, functions, induction, equivalence relations/classes/partitions, etc.)?

Or is it elementary number theory (congruences, divisibility results, etc.) that bugs you?

[leaden prism]

@gray gazelle are you trolling or being real?

Please guys I need help this is my first time learning the material don’t be mean

[static fog]

I see a lot of people swearing by Analysis 1 by Tao, but I find it extremely difficult to parse and read. It felt extremely rigorous and clunky. The chapters on Set Theory (Vietnam War flashbacks).
Is there a right and wrong way to reading this book? I personally found the opening chapter on constructing the Natural numbers an absolute pleasure to read. It unfortunately went all downhill from there. (I'm currently using Abbott's Analysis)

[quick hornet]

its not trolling, its a joke about you typing "scholastic" instead of "stochastic"

you can ignore it.

[leaden prism]

ITS A TYPOOOOOOOOIO

Is the book legit tho?

I was typing fast is that the only your focused on

[quick hornet]

i mean... its a philosophy textbook lmao

not sure thats what youre after

[leaden prism]

No I want probability

[gray gazelle]

Fesers? Yeah standard intro to scholastic philosophy

[leaden prism]

???

I don’t want a philosophy textbook

Nvm

You don’t get it

Whatever

[gray gazelle]

Lemme see what the stochastic process course in my uni reccomends

[gray gazelle]

Chill and sneed a bit damn

[leaden prism]

Ok

[static fog]

Bumping my question bc spam

[gray gazelle]

Sheldon Ross - Probability (+ intro to Probability models)
Papoulis - Probability, random variables and stochastic processes

[leaden prism]

Alright thanks I’ll check it out

Are they good books?

For quant?

Cuz that’s what I’m aiming for

[gray gazelle]

Its the "mandatory" bibliography in the course

[gray gazelle]

For what?

[leaden prism]

I’m familiar with the first book

You have the 10th edition right?

[gray gazelle]

I havent taken the course yet lol

[leaden prism]

Which edition for the second book?

[leaden prism]

Quant trading interviews

[gray gazelle]

Ok

[gray gazelle]

None but the course links to the 2nd edition

[leaden prism]

Alright

[gray gazelle]

So Ig that one does it

[leaden prism]

Ty

[gray gazelle]

Btw I still think you should take a look at the philosophy book

[atomic stag]

I would say understanding difference between Integers ,Real numbers,whole numbers etc elementary stuff

[brittle breach]

where to learn multi variable analysis

[sage python]

Spivak Calculus on Manifolds probably

[brittle breach]

is there another one, I checked this out before

[cedar ridge]

munkres?

[remote ginkgo]

Shifrin, Multivariable Mathematics

[gray jungle]

differential forms and applications do carmo

[rose rampart]

Can someone recommend good books for reviewing/wrapping up algebra II?

[brittle breach]

thanks for the replies

[rose rampart]

there are some courses on khan academy if you want to see them

[brittle breach]

what they cover

[rose rampart]

idk the basics

not the indepth stuff

[rose rampart]

upvote

[solemn rover]

https://www.wsj.com/articles/succession-drama-grips-scholastic-ceos-sudden-death-an-office-romance-and-a-surprise-will-11627850787

[quick hornet]

okay?

[solemn rover]

sorry i just saw this in the news and thought it was relevant

i think like

it's kinda funny to think of such a powerstruggle unfolding at a company that makes history textbooks for fourth graders

[rose rampart]

nice

i actually thank you for sharing that

that sucks

[atomic stag]

I'm still waiting

[cedar ridge]

got it w/out paywall?

[compact cypress]

recommendations for axiom of choice and its implications?

[stray veldt]

probably unironically wikipedia

[stray veldt]

i think diestel is the standard

prereq is mathematical thinking (intro proofs and logic)

i also like nesetril 'an invitation to discrete mathematics', which has no prereqs

but also covers standard combinatorics stuff (and some other stuff)

[karmic thorn]

Isn't that a GTM?

[stray veldt]

yes

[karmic thorn]

[stray veldt]

but its graph theory

[karmic thorn]

I've seen Bondy-Murty's Graph Theory books (one is Graph Theory With Applications, the other is GTM Graph Theory). Both were slightly intimidating imo. Maybe Diestel is different.

[gray gazelle]

I see

[stray veldt]

yes

[gray gazelle]

right thank you

much appreciated

[jagged spruce]

Can anyone recommend some books for Algebra and geometry for IMO

[still jay]

Herrlich

[uncut zealot]

A textbook written by my favourite supernatural ship

[gray gazelle]

so you'd also recommend it?

[gusty smelt]

i knew u were gonna say it

its a good book i read a bit of it lol

[uncut zealot]

Also just to quickly follow up on this?

[gusty smelt]

doesnt like sailing the seven seas

[uncut zealot]

I haven't read it, I just like Destiel and think the way the show handled it was bullshit.

[gray gazelle]

which show

lmfao

[uncut zealot]

Supernatural

[gray gazelle]

have not seen

[gusty smelt]

good.

[gray gazelle]

how so

is it bad?

[uncut zealot]

Aye, the only thing she has in common with Anne Bonny is her gender.

[gusty smelt]

http://rmi.ge/~giorgadze/G_CA.pdf

is the book i learnt from

[uncut zealot]

Cool thanks for the recommendation.
To cut through all the metaphors, I'm planning on studying with a friend of mine from school and she doesn't like doing piracy, so hopefully this is a legal scan.

[gusty smelt]

https://download.tuxfamily.org/openmathdep/analysis_complex/Complex_Analysis-Gamelin.pdf

better copy

i mean its on google first page

id imagine its legal

[uncut zealot]

Okay cool

[sudden kindle]

I recently learned a proof of Riemann mapping theorem

To find a riemann map (that is a biholomorphic map) from a simply connected proper subdomain of C, to the open unit disk, all you need to do is consider the family of injective holomorphic functions from your domain to the unit disk, that send some fixed point p in the domain to 0, and maximize the absolute value of the derivative at p

You are basically solving an extremal problem

[gray gazelle]

Thank you for the book recommendation

[gray gazelle]

Which NT book would you guys recommend? so far I've been using the one by burton

[uncut zealot]

Ireland and Rosen is good.

[gray gazelle]

I see

tyty

[viscid thorn]

hey. I was looking for pugh's analysis solution manual and couldn't find a single file, But, i managed to find them piece by piece. it took me a lot of time. hope it helps someone.

[gray jungle]

i started using Hardy and Wrights its pretty alright but very old school

[surreal phoenix]

Literally just decided to start it yesterday, thanks a bunch man

[viscid thorn]

happy to help😇

[viscid thorn]

https://github.com/aulchen/pugh
also, i found this on github. credit goes to the author

[digital lion]

Hey does anyone know if there's a website like isthereanydeal for books? I'm trying to find the best deal on this book I want

[timber mesa]

bookfinder

not precisely for deals but it searches for books, both new and used, in various sites

[digital lion]

@timber mesa Thanks!

[split knoll]

Does someone have a good book for advanced number theory?

[quick hornet]

can you be a bit more specific?

number theory is very broad

[short crescent]

"basic" hahahahahahaha

[gray gazelle]

could someone please tell me the order in which i would have to complete the Edexcell books for a level maths and further a level maths?

these are the books i have so far?

[crimson pagoda]

Probably book 1 then book 2

[gray gazelle]

my plan is to self teach so would like to know what books i need and the order they have to be completed

[lapis sundial]

Usually people learn all the "normal maths" books simultaneously and then move onto further maths i guess

And then year 2 ones

(We had lessons on mechanics, pure and stats going on at the same time)

[gray gazelle]

why are A Level books called Pure Mathematics lmao

[lapis sundial]

Eh to differentiate them from the mech/stats

Even if they aren't very pure lol

[gray gazelle]

weird

[lapis sundial]

Why weird

[gray gazelle]

you guys have stats as a different subject?

[lapis sundial]

Well it's within the same a level

If it were in the same book it'd be in different chapter(s) to other stuff so there's nothing uniqueabout this

[gray gazelle]

when I think of pure mathematics things like Analysis and Topology comes to mind

not precalc lmao

[lapis sundial]

Ye

[gray gazelle]

I used an old pure mathematics text

I think it was Parsonson

[simple lava]

some recommendations of books about linear algebra for statistics ?

[split knoll]

ah, yes.
cohomological class field theory for example.

do you know such a number theory book?

[quick hornet]

i believe neukirch is the usual standard recommendation, although ill admit to not being particularly familiar with the resources in this field personally

theres also the famous primes of the form x² + ny²

which i believe is considered very approachable

[gray gazelle]

Thoughts kn Matej Bresar: undergraduate algebra?

[sudden kindle]

A Gentle Introduction to Local Class Field Theory by Pierre Guillot

It has Galois Cohomology / Group Cohomology stuff

[brittle marsh]

what are some books for someone who wants to study AG but only has experience in algebra and topology?

also I'd like to ask the question, if someone wanted to continue to study AT after hatcher, specifically focusing on homotopy theory, what do you suggest they study?

[urban herald]

Can anyone help me with finding study material?
I am looking for books that start from assuming you know how to find normal derivatives and single integrations. And it teaches you stuff like radius of curvature, partial derivatives and successive differentiation and so on?

[karmic thorn]

Thomas Calculus

[urban herald]

Thanks a lot

[split knoll]

Thank you!

[fluid nebula]

⭐

[wise umbra]

You can look at the book written by David Harari

https://link.springer.com/book/10.1007/978-3-030-43901-9

[split knoll]

Oh yeah, looks also great. Thank you very much!

[urban herald]

Can anyone suggest a book for graph theory, introductory level, with stuff like bellman ford, prom and kruskal's algorithm?(Dijkstra algorithm was taught to us along with bellman ford, so i don't know if it's a separate topic)

[wise umbra]

Algorithms by Cormen etc

[urban herald]

Does it also cover stuff like vertex cover and graph colouring?

And thanks for recommending, I will check it out

[wise umbra]

Yes probably, maybe not everything you said
But it's a big reference in computer science, it's a huge book

[sudden kindle]

Ooh this is an undergraduate text.

[urban herald]

@wise umbra thanks a lot

[wise umbra]

More of a graduate one I'd say x)

[sudden kindle]

Oh i thought UTX stands for Undergraduate Texts

[craggy sapphire]

Use old A-level textbooks. These new textbooks are really bad. Assuming you are aiming for top uni

[gray gazelle]

Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, into very polished texts.

Hi, has anybody heard of Demidovichs Problems in real analysis?

[covert heron]

what book do you recommend to study after calculus?

[iron granite]

Linear algebra?

I think that follows calculus most of the time

Although that's only what I've observed, I haven't done any yet.

[marble solar]

I think there's a few you can go into after Calc: Multivariable is good stuff, linear algebra, differential equations, discrete math (recursion equations)

[iron granite]

Hey moonbears, doesn't multivar require linear algebra?

[smoky zephyr]

<@&268886789983436800>

[lime bison]

bampersand

[smoky zephyr]

beans

[gray bolt]

You guys know a book that explains frobenius method? Advance thanks!!

[analog pollen]

nop

i did lin alg after calc 3

perfectly fine

[brittle marsh]

Any recommendations?

[gray gazelle]

rigorous multivariable calculus does

[sage python]

@brittle marsh hmm, so some follow up directions I'm aware of

Characteristic Classes by Milnor and Stasheff

(Bott-Tu is good for a more differential topology angle on the stuff)

Also Hatcher has stuff on spectral sequences, and vector bunches/k theory

I think there's Davis and Kirk as well for a general "AT 1.5-2"

For homotopy theory in particular

Try Goerss and Jardine

[brittle marsh]

Thanks a lot for all the suggestions!

[slender dragon]

Which book is good for this?

[quick hornet]

ruuuuuuudin

[gray gazelle]

folland's advanced calculus or spivak's calculus on manifolds

there's also munkres' book if you want a wordy alternative to spivak

i dunno any other books off the top of my head

[slender dragon]

👍

[primal summit]

Recs for a book with good exercises for a first course in linalg? By good I mean constructive and not computational exercises that aren't too easy either. Also preferably needs to cover VS and LT before matrices

[surreal phoenix]

Linear Algebra Done Right by Sheldon Axler, that's the standard fitting exactly what you're looking for, as far as I'm aware

[analog pollen]

Friedberg

[primal summit]

I've looked into axler, the exercises in the first few chapters (which is where my students are atm) are mostly computational or not very insightful. Had a few good ones

[surreal phoenix]

Oh, I used the chapters on VS and beyond for it, maybe I did miss some of the earlier ones

Wait it starts off with VS, how'd I miss the computational ones

[primal summit]

nono I mean

the chapters on VS and linear independence basis

just didn't have many good exercises from what I saw

[surreal phoenix]

Ahhhh I see

[primal summit]

most were like 'verify such and such is a basis'

[surreal phoenix]

Yeah, I get what you mean, I remember now

[viscid thorn]

Maybe Linear Algebra and Its Applications by peter lax fit ur requirements

[primal summit]

i'll look into these recs, thanks guys

[analog pollen]

friendberg

[primal summit]

yea I saw

thanks

[analog pollen]

oki

np

[fervent lava]

Adding to what TTera said there also hubbard, and shirifin book.

[fervent lava]

There also Hoffman and kunze LA book and linear algebra done wrong.

[gray gazelle]

axler makes me cry tears

[dapper root]

See Roger Freedman’s response

[frosty girder]

Lmfao old but gold

[analog pollen]

lmfao

what a legend

[frosty girder]

it gets better

[gray gazelle]

any recommendations books for economic calculus?

[crimson pagoda]

Stochastic differential equations by oksendal

[celest glade]

I would like to get into information theory and looking for books on the subject. Any recommendations?

Theoretical CS/languages/computability theory, anything of the sort

[gray gazelle]

#old-network ask the CS server you'll have a better chance of finding a good book

[halcyon scaffold]

Introduction to the theory of computation is a great book on formal languages, computability theory and complexity theory

[celest glade]

thanks

will also as in the cs server as suggested

[magic wasp]

Quick question: I'm a student self studying a textbook for school project and the school requires me to somehow display my work. I've coded a very basic blog where I will post my solutions. Am I allowed to post the textbook questions on the blog too, or is that a copyright violation?

[slow matrix]

it seems to be fair use, I think. I'm not a laywer btw.

[quick hornet]

even if its illegal, i'd be shocked if they care

[novel obsidian]

THIS IS NOT LEGAL ADVICE

[quick hornet]

(and if they do, theyd probably just send a c&d and youd just take it down)

that said, it might be good to rewrite the questions a bit

to use equivalent wording but perhaps more succinct

[stray veldt]

if the questions are "sufficiently creative" they should be protected by copyright

but yeah, they probably will not care

[magic wasp]

thanks everyone, in case this helps the book is Introduction to Modern Cryptography by Katz and Lindell, the book seems to have many questions already posted online but idk if those are illegal and I don't want to get in trouble for copyright stuff

[cunning stirrup]

A mathematician's apology (idk, I saw it in #math-discussion )

[analog pollen]

[quick hornet]

what

is that meant to be funny

whats the joke \

i have never played lol nor do i want to

its just a weirdly clunky insult to use

[cunning stirrup]

Wait, then who's the lol player I remember someone in staff was a lol player

[gray gazelle]

#chill

[junior merlin]

Information Theory, Inference and Learning Algorithms (from https://www.3blue1brown.com/blog/book-recommendations)

[vast onyx]

Hey,
I want to get into applications of calculus into machine learning.
Any suggestions for beginners guide ?

[sharp latch]

Not really a book but Coursera has some great introductory courses for that

Only calc 1 background assumed iirc

[vast onyx]

IIRC meaning ?

[smoky zephyr]

if i recall correctly

[vast onyx]

ohh

[vast onyx]

thanks for the elaboration

I mean like a dummies guide, is there something like that to get introduced from mathematics point of view ?

[vast onyx]

I have done the Andrew Ng's courses for Deep Learning and Machine Learning.
But I feel that some grip of optimization is still missing in me, and I need to revisit the basics and get things rightly done.

For instance, if someone asks me to develop an android app, I know and can visualise it for the opposite person.

I need to visualize it for an opposite person, that this is how it works and this is how the math works.

So i am looking for books or courses, that introduces me as a dummy for math for ML.

[sharp latch]

Ah Yeah that’s fair. In terms of content you’ll probably just need linear algebra and multivariable calculus (which there are a ton of great recommendations for in this channel). But for a specific applied book I do not know, someone else could probably answer better, or you could check the computer science discord

[deep niche]

any recommendations for elementary number theory, my professor mentions burton’s

[junior merlin]

The main application is gradient descent, check out khan academy's videos on the gradient. then watch 3blue1brown's videos on neural networks

that's pretty much the "only" application of calculus in ML. The rest is indirect from probability which uses calc. Integrals are basically never used

[unborn relic]

Is there any good textbook for introductory number theory?

[brittle breach]

Serre ?

[unborn relic]

Already read the basic number theory...

@willow totem

@delicate patrol

[smoky zephyr]

did you just ping two random people with asian usernames

[unborn relic]

There are my friends whom I invited......

[delicate patrol]

hi My name is Luka

[willow totem]

hi

my name is G

[tawny bobcat]

nice

[olive relic]

Use a Korean textbook

[proud lynx]

pretty interesting book

[willow totem]

lt is your homework?

[proud lynx]

no

why?

[willow totem]

I am just curious

[sleek sand]

does anyone know if aops intro series and intermediate series books and volume 1 is good for amc10 prep

[narrow echo]

I have volume 1 and can recommend

only concern would be it might be too dated

[halcyon hornet]

I do.

I have intro algebra, inter algebra, vol 1 and 2.

[storm cipher]

Any good exercice about convexity inequalities ?

[storm cipher]

Thank you !

[fathom elk]

Any good readings for Wavelet Analysis for someone with 2 years of calculus? Well, 4 years, but I only remember 2.

[fathom elk]

http://www-math.mit.edu/~gs/papers/amsci.pdf is a good intro

[shy jolt]

Book suggestions for SAT Math Reading and Writing?

[fervent lava]

iirc khan academy for math has a section for SAT.

[shy jolt]

do you know if its any good

[fervent lava]

Can’t say but since it khan academy it probably good. Also love your Gojo picture.

[shy jolt]

Kk and thanks

[sharp latch]

Princeton review and also this book if you plan to take the act as well (there’s a lot of overlap)
https://www.amazon.com/ACT-36-Just-7-Steps/dp/0071814418/ref=asc_df_0071814418/?tag=hyprod-20&linkCode=df0&hvadid=312106851030&hvpos=&hvnetw=g&hvrand=18314708556399941441&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9029978&hvtargid=pla-569012952413&psc=1

Think about it not only as learning the material but also as learning the mindset

[jade spear]

I am at a high-school level of math (reviewing that is), and I would like to start studying the beginning level of Proofs. Any recommendations for books or online stuff? Is it wise to just stick with pencil and paper in beginning, or use some kind of software right away?

This is because I am learning programming, and an 'introduction to algorithms' book says "You should have some facility with mathematical proofs, and especially proofs by mathematical induction."

[fervent lava]

http://www.math.hawaii.edu/~pavel/Aluffi_notes.pdf

[jade spear]

'advanced mathematics' ?

[fervent lava]

It a intro proof that is concise. It not like 400 pages like other intro proof have.

It the only I liked besides #book-recommendations message

[jade spear]

so it's really intro level, but just written in a highly concentrated and concise style?

[fervent lava]

Yeah

[jade spear]

ok then thanks! I looked at first few paragraphs, seems intro stuff all right

[stray veldt]

even shorter: #proofs-and-logic message

tbf the aluffi notes do a lot of stuff that you probably dont need

(you can probably stop after induction)

[jade spear]

Loch -- is there a difference between your 2020 and 2021 versions? edited/shortened that sort of thing?

[fervent lava]

iirc errors were fixed in 2021. Here the message link #proofs-and-logic message

[jade spear]

got it thanks

My guess is that these documents are not intended to make one an expert in doing proofs, but just to begin by giving a solid understanding of what proofs are and what they look like?

[fervent lava]

Read a math book for that like linear algebra.

[jade spear]

right

Just out of curiosity, when people are doing full courses in proofs nowadays, what software might they be using?

do they program their proofs in programming languages?

or when mathematicians are producing proofs

actually i should have just googled that question, pardon me

[fervent lava]

Discord, stackexchange, and google.

[jade spear]

right

in fact i've already started learning LaTex

[fervent lava]

Tho I heard something similar to what your saying a while back.

[jade spear]

someone in the Python discord said that python was very unsuitable for proofs

[fervent lava]

What does that even mean? I write c++ code and I don’t even know what that means.

[jade spear]

he went into a bit of detail but I'm afraid I didn't undersand

anyway i shouldn't be worrying about such things at this stage

[stray veldt]

virtually nobody "programs" proofs

there are proof assistants but the use is still niche

and unfeasible for lots of mathematics

[gray gazelle]

what is a good book for a proof based multivariable calculus course

the syllabus outline i think is pretty standard, but still can't find a good book: "Functions of several variables. Continuity. Partial derivatives and differentiability. Jacobian matrix and determinant. Differential of a composed mapping. Implicit function theorem and inverse function theorem. Higher order partial derivatives. Taylor's formula. Free and constrained extrema.
Parametric integrals, continuity and differentiability. Fubini's theorem. Classical Fourier series. Fourier transform. Elementary properties. Inverse formula. Plancherel theorem.
Multiple Riemann integral. Properties. Sets with zero volume and measure. Theorem on the existence of integrals. Transformation into a multiple integral. Improper integrals. The use of integrals in geometry and physics."

[fervent lava]

Everything you described there is in folland advanced calculus.

[gray gazelle]

thank you. is it a hard read or does it have good explanations? is there any other book with this material you know so i could compare?

[dull pasture]

Does anyone have any recommendations on Linear Algebra books which are question heavy with solutions provided? I'm trying to tackle a problem, but none of the books I've looked at have similar examples. I've tried Linear Algebra and Its Applications & Elementary Linear Algebra

[fervent lava]

I haven’t read it, I went through the pdf of it after someone was talking about it here. I think that person was TTera, you ask her/him/etc.

The table of content has everything you described that why I mentioned it.

Here a free pdf online of it for you to form you own opinion. http://site.iugaza.edu.ps/mashker/files/Gerald_B._Folland-Advanced_Calculus-Pearson_2001_1.pdf

[gray gazelle]

ok thank you a lot @fervent lava

[dapper root]

yooooo

Advanced Calculus is awesome

Folland gang

[analog pollen]

schaum's outline of linear algebra

its more rigourous than lin alg and its applications

and has alot of worked examples/proofs

[gray gazelle]

Dont tell me you fell for some kind of ML meme

[gray gazelle]

could someone suggest me a problem book on polynomials in one variable? first year undergrad

[remote nova]

Like... solving polynomials?

Numerical analysis type stuff?

[gray gazelle]

Polynomials in one variable. Quadratic function. Theorem on null-polynomial. Divisibility of polynomials. Horner method. The greatest common divisor of polynomials. Roots of polynomials and algebraic equations (especially cubic and quartic algebraic equations). Trigonometric form of complex number. Fundamental theorem of algebra. Interpolation polynomial. Integer and rational roots of algebraic equations. Complex roots of algebraic equations. Reduciblity and irreducibility of polynomials over the fields C and R. Viete formulas. Fractional rational functions. Polynomials in several variables. Polynomials in two and three variables. Ring of polynomials in two variables. Symmetric polynomials. Fundamental theorem on symmetric polynomials. Symmetric equations.

*************I need a problem book on these topics, if there is any. Thanks!

[smoky zephyr]

from quadratic functions to rings and fields huh

[gray gazelle]

not really, polynomials are enough.

:)

[marble grotto]

Polynomials by Edward Barbeau does a lot of stuff from what I remember

[sacred pond]

read "vedic mathematics"

and "the elements of logic"

[halcyon hornet]

Wow what the literal fxck.

[halcyon hornet]

Exactly.

[halcyon hornet]

Oh boy. Oh ho ho ho ho ho boy.

[iron granite]

Vedic mathematics is weird, because there is no mention of it in Vedas (our religious texts).

[halcyon hornet]

I learnt 2/3 of it.

Like there are 3 courses in it, I did 2.

Forgot most of it.

Boring.

Just use a calculator lol.

[jovial bison]

some dude wrote it a 100 years ago , he claims to have derived the formulas from the vedas

[iron granite]

I know, apparently, it's only found in his copy of the Vedas.

[jovial bison]

you have read the vedas ?

[iron granite]

I haven't.

It's what he said when someone questioned him

[gray gazelle]

what topics does it cover?

[dapper root]

It's like, real analysis

it won't cover measure theory, but it does multivariable analysis, differentiation, integration, series crap, and then some fourier analysis

the only thing it's kinda weak in is like R^n -> R^m stuff

I used it my freshman year

[gray gazelle]

so no lebegusususes integrals?

[dapper root]

nope

it develops the Darboux integral

[gray gazelle]

imma check it out

[dapper root]

well like you do pseudo measure theory

for the darboux integral

[gray gazelle]

seems kinda cool

[gray gazelle]

i see

[dapper root]

The first chapter is just topology type stuff

Idk I like the book

¯_(ツ)_/¯

[gray gazelle]

[gray gazelle]

thank you, @marble grotto

[gray gazelle]

Is anyone familiar with Functions of Several Real Variables (by Moskowitz and Paliogiannis) and how does it compare to Advanced Calculus (by Folland) ?

[marble solar]

The best book of that order is Calculus on Manifolds by Spivak

[sterile gazelle]

I recommand checking out Homo Deus: A Brief History of Tomorrow. It's really good and interesting.

[rapid merlin]

Though not particularly helpful for real variables 😝

[agile jay]

Hey uh I would like a book on basic analysis

Any suggestions?

[dapper root]

Like

How basic

I think Pugh is one of the easier analysis books

If you just want to see calculus but with proofs there’s Spivak

[agile jay]

Like end of secondary school basic with knowing what an integral and derivative is and power rule and that's about it

[dapper root]

Oh

That’s not really in the realm we call it analysis

This is just calculus

So like

Some ppl would torch me for this but

I think the best book is just whatever intro calculus book you can get your hands on

If you have options, just see which one you like the writing the best

Some ppl are gonna say DO SPIVAK so it’s all super #rigorous

But IMO you just want to be good at computation and see the calculus concepts, then you can do it rigorously on a second pass in an analysis class

[agile jay]

Yeah makes sense I'll just find some intro book and pray I can understand it lol

[dapper root]

As long as

You are comfy with algebra and symbolic manipulation

And then know some trigonometry you should be fine

I personally view calculus mainly as algebra new game plus

You just add a couple new operations, and the rest is mainly just doing a bunch of algebra

[agile jay]

Yeah I do pretty well

Okay I can see why I was told to say analysis

Anyway

[dapper root]

Like honestly

Ppl shit on it but Stewart isn’t bad

Lol

It’s just expensive, find a cheaper alternative

Pretty much every intro book covers the same stuff

[agile jay]

I've found an interesting one

[dapper root]

Make sure it does differentiation, integrals, and infinite series

If it does multi variable calculus, even better

[dapper root]

Lmfao

[agile jay]

Yes or no

[dapper root]

Uhhh…

I dunno

[agile jay]

Hm

Ig I'll try this

[dapper root]

¯_(ツ)_/¯ hope it goes well

Check the reviews I guess haha

[agile jay]

Good point

[dapper root]

Only 3 reviews

[agile jay]

Yeah I see

What in god's name

[surreal phoenix]

It has Apostol's name on it

so there you go, that's why

[glossy bison]

Niche topic but any good book on the math and physics of bridges, stress on objects or such? I did a really cool question about the stress on a beam modeled with a DE and I'd like to read further into it.

[oak arch]

best books for algebra and precalculus?

For precalculus I found this two

[analog pollen]

precalc is just bs

go for normal calc

[oak arch]

requires precalc

[analog pollen]

nah

i learnt calc without knowing trig

only some algebra

[oak arch]

yeah I mean in terms of classes

HS

[analog pollen]

trust me

you can do normal calc just fine

if you know some basic algebra

like 10th grade algebra is fine

[oak arch]

^

Though I might be able to skip precalc if I can demonstrate knowledge

Looks real scary lol

Stewart's precalculus

Is it not too hard to learn?

[analog pollen]

nah

as i said

i learnt normal calculus with only some algebra

[gray gazelle]

looks trivial tbh

[smoky zephyr]

please learn some trig before learning calculus

[analog pollen]

nah not rlly needed

[dapper root]

The fuq

???

[smoky zephyr]

good luck understanding the derivation of the sin and cos derivatives

[analog pollen]

i learned trig by learning calc

but sin and cos is not necesarilly trig

[smoky zephyr]

so you’re saying that you literally need no trig to learn calculus

[analog pollen]

only like radians maybe, and sin cos

but most of the time there are appendices at the back of a calc book

i literally learned it like this

[smoky zephyr]

that’s still learning trig before calculus but ok

[analog pollen]

so ur saying radians is trig

[smoky zephyr]

lol

no

[analog pollen]

yea exactly

[surreal phoenix]

They are one hundred billion percent trig

[brisk ice]

adding to this, you said you didn't need it but you looked in the back of the book

So essentially you just learned the basics of trig to get by when you came across you needed it?

[analog pollen]

i never learned these in a trig class

[analog pollen]

i didnt look in the back of the book, im just saying you can

[brisk ice]

Sure but in some way that is still learning about it?

[analog pollen]

only thing was, i kinda knew what a radian was, not rlly tho

[analog pollen]

ye but you dont need a whole course on it before lol

[halcyon scaffold]

Can anyone recommend some textbooks for self studying order theory and lattice theory?

[still jay]

The one I’ve been planning to use is Introduction to Lattices and Orders by Davey and Priestly. I haven’t worked through it yet so I can’t attest to its quality, though at a glance it looks nice

[gray gazelle]

is "mathematical analysis" by Tom Apostol a good book?

[misty wyvern]

It's not Rudin so no

[frosty girder]

i would say so
tho im still reading through it

[frosty girder]

[gray gazelle]

how far have you gotten into it?

[frosty girder]

i am at the 3rd chapter currently

been there for sometime

(coz of exams, not coz i am actually stuck there lol)

[brisk ice]

how many chapters are there and when did you start?

[gray gazelle]

there are like 15 chapters

i think

16 lol

[frosty girder]

There are 16

i started in Early november

but didnt do much coz of other exams and stuff

[gray gazelle]

yeah exams are stupid, I could learn so much more stuff if it wasn't for skool

[frosty girder]

True

and then i have a college entrance 18 days after my current exams end

[dapper root]

This is apostol?

[frosty girder]

yup

[dapper root]

Huh

[gray gazelle]

hey boss, i just delivered 10 tons of our drugs

[dapper root]

Thank you

That’s quite a lot

You must be tired

[gray gazelle]

I am very tired, because I'm not a chmonkey

[dapper root]

Take the weekend off

[gray gazelle]

how do I become a chmonkey?

[gray gazelle]

thanks :D

[dapper root]

You don’t choose to become a chmonkey

It just happens

[gray gazelle]

the chmonkey chooses you?

[gray gazelle]

damn

how do I increase my chances of that happening?

should I return to monke?

[dapper root]

¯_(ツ)_/¯

I didn’t return to monke

I just, became monke

When I became Chmonkey

[gray gazelle]

[brisk ice]

Take out the Chmonkey 😼

[dapper root]

I think it’s best to find something you want to become for yourself tho

[gray gazelle]

:O

[dapper root]

If it isn’t Chmonkey, it isn’t Chmonkey

[gray gazelle]

I wanna become happy

[dapper root]

Me too

[gray gazelle]

mathematics makes me happy :D

[brisk ice]

I thought dealing drugs in some mafias was considered bad

Are we not a drug free gang?

[gray gazelle]

bad = good

problem solved

[brisk ice]

is there any enthic or geolocation that relates to this gang?

[gray gazelle]

planet earth

[brisk ice]

https://www.youtube.com/watch?v=DyKr8NhxGnE

[gray gazelle]

we're soon exapanding to mars

[brisk ice]

oh kangaroo

lol

nvm

[gray gazelle]

Lol

[modern stone]

What are some of the advantages and disadvantages of Apostol’s Calculus?

[prisma snow]

Advantage: You're not using Stewart.

Disadvantage: You're not using Spivak.

[quick hornet]

im not sure spivaks approach is objectively better

integrals first is weird but i see the argument for it

and spivak has a proclivity for going on weird tangents

[gray gazelle]

https://tenor.com/view/whyareyougay-uganda-gay-gif-14399349

[prisma snow]

[flat kiln]

hello there, does anyone have any good on discrete calculus and finite differences?

good book*

[marble solar]

I think the main point in spivak's favor is the lighter exercises

Or at least the vastness of the exercises

It used to be books were torn between teaching differentiation first, and integration first

[halcyon hornet]

Does 3B1B's Essence of Calculus cover most Calculus theory and material except problems and exercises?

[smoky zephyr]

his videos are like 20 minutes long and there’s only like 15 of them

so definitely not

[maiden slate]

i definitely wouldn't say it's enough. like they're good for conceptual help not for learning calc on their own

[smoky zephyr]

calculus takes at least a few months to learn

[maiden slate]

it took me 2 years technically lol

[smoky zephyr]

it took me like 5 months when i was really into it

[maiden slate]

i had an on off relationship with calc

[smoky zephyr]

i tried to learn it when i was 15 or 16, but really tried at 17

[halcyon hornet]

I see.

[maiden slate]

yeah same

[halcyon hornet]

But it has all the intuition for Calculus?

[maiden slate]

ehhh, idk about all

but it has a lot

the way he explains the chain and product rule is soo good

[halcyon hornet]

Is the derivative of s(t) = t^3 =
3(t)^2?

[coral narwhal]

@halcyon hornet if you want a book that talks about intuition in calculus I have a recommendation

[halcyon hornet]

Sure!!!!

[smoky zephyr]

@halcyon hornet you wrote a minus sign instead of an equal sign but yes

also unnecessary parentheses

[halcyon hornet]

Yeah yeah.

[gray gazelle]

same it took me a few months

[smoky zephyr]

i probably could have gotten it done in 3 honestly

[coral narwhal]

Infinitesimal Calculus by James M. Henle, Eugene M. Kleinberg

[halcyon hornet]

Sure let me check it out.

[smoky zephyr]

no

[gray gazelle]

oh wait sorry this is the book recommentations channel, I thought it was disscussions or chill

[halcyon hornet]

Guys.

[coral narwhal]

and I always recommend this book because I used it
Keisler Infinitesimal Calculus

[halcyon hornet]

Do we derive the derivative of every, I quote every, graph, by the derivative formula?

[smoky zephyr]

no

[halcyon hornet]

What no?

[smoky zephyr]

after a certain point you no longer use the limit definition

i might not have understood your question

[halcyon hornet]

See.

To find the derivative of every graph, do we use only the derivative formula?

[maiden slate]

derivative isn't a property of a graph it's a property of a function

the derivative is defined using the derivative formula

so yeah you have to use that

[halcyon hornet]

I see I see.

Thank You!

[analog pollen]

+multivariable??

[smoky zephyr]

yes

i got calculus 3 done in like a month, although i skipped surface integrals

[marble solar]

I think that's a bit too fast to really put calculus 3 into long term memory

Unless you're brain is just on another level

[smoky zephyr]

i probably just mildly speedran it

[marble solar]

your*

I've done that a few times, then like a year later I forgot everything

[smoky zephyr]

yeah i definitely didn’t memorize a lot of it

[marble solar]

It's fine to practice picking things up quickly, getting it done, then moving on

But if it's something you plan on using a lot, it's worth putting into long term memory

[smoky zephyr]

well i at least memorized the important stuff

aka the stuff i’ll use a lot

[maiden slate]

best way to practice calc is to learn physics

[marble solar]

I think the best way to get good at calc 3 is to do differential geometry & PDEs

[smoky zephyr]

[marble solar]

Which, depending upon your point of view, is the same thing as learning physics

[flat kiln]

is anyone familiar with discrete calculus?

[brittle breach]

What is a good book to learn differential geometry

[gray gazelle]

manifolds, or curve and surface geometry?

for curve and surface geometry, do carmo's "differential geometry of curves and surfaces" is the popular option. i don't know many books that do this stuff

for manifold theory, there's lee's "introduction to smooth manifolds" and tu's "an introduction to manifolds." both books cover abstract manifold theory, not quite differential geometry but they prepare you to do so

for differential topology, g&p

for differential geometry on manifolds (riemannian geometry), lee's "introduction to riemannian manifolds" or do carmo's "riemannian geometry" are both good books

there's also tu's differential geometry book

people i trust have said good things about petersen's riemannian geometry book as well

[brittle breach]

I am looking at Tu manifolds now for an intro/overview
I found Lee good but too chatty at times

[analog pollen]

can someone pin this message plz?

the differential geo stuff

[gray gazelle]

tu covers the same core manifolds content that lee's book does

it's definitely less chatty than lee

[brittle breach]

What would be good after Tu

[gray gazelle]

any of the riemannian geometry books i guess

that's what people usually do after smooth manifold theory

[brittle breach]

Not necessarily diff geo

[gray gazelle]

[brittle breach]

Any recommendation

[gray gazelle]

after differential geometry, take a nice vacation at a beach with someone you love

[analog pollen]

the large scale structure of spacetime by steven hawking

[marble solar]

Just do all 5 volumes of a comprehensive introduction to differential geometry

[slim peak]

J.Jost's book to conquer the world

[brittle breach]

Would Dieudonne 9 volumes on analysis pair well with these

[analog pollen]

jesus.. 9 volumes??

[dapper root]

Don’t do Dieudonne…

Lmfao

Oh this is in response to a meme answe

You should do the full like 20 volumes instead then

[sage kelp]

Opinions on Metric Spaces by Searcoid? Like, why choosing this over a General Topology book, what is the advantage of studying this book, and whether this an appropriate choice for sutdying some function analysis afterwards

[tender egret]

Hi,
I was wondering if Pugh's Real Mathematical Analysis is a suitable substitute for Spivak's Calculus on Manifolds?
Thanks

[quick hornet]

no

pugh is an intro-to-analysis text (ie mainly works in ℝ or ℝ^n), spivak's CoM is an analysis-on-manifolds text

its like the difference between odes and pdes

kinda

not in terms of content but in the sense that one necessarily comes after the other, and despite one technically being a subset, they have different feels

[marble solar]

I think Pugh's later chapters do a good job of covering some of the same things that Spivak's Calculus on Manifold does

Especially things like Fubini's theorem

[quick hornet]

yeah but not fully

[marble solar]

It's not a replacement, but more like

A good resource

[quick hornet]

it could serve as a partial substitute

but not a replacement

[marble solar]

Yeah, I ta'd a class on it 3 times

and two of the times I recommended students to read parts of pugh

Students found it helpful

[quick hornet]

fair

[tender egret]

Could you suggest any good replacements for CoM?

[gray gazelle]

none

there are none

[tender egret]

noted.
Thanks :DDD

[dapper root]

[marble solar]

A few have tried like Munkres Analysis on Manifolds

Or Ted Shifrin's Multivariable Mathematics & Linear Algebra

[remote ginkgo]

i hate this one

[remote ginkgo]

this one good

[sage python]

Damn we got some passion here I like it

[gray gazelle]

lmao that's like 2500 pages

that'll take at least 3 years

[rapid merlin]

Really? I quite liked it tbh

[remote ginkgo]

i literally threw it out the window of my car (while driving through a recycling plant, of course) i hated it so much

[foggy relic]

can anyone reccomend a text on intro to number theory such as reciprocity, forms, elliptic curves

i need to learn more nt

[brittle latch]

sierpinski has a book full of problems too if ur into that

[gray crystal]

I find Zorich's book pretty nice, though I think contents are a bit different from COM

[rugged maple]

pugh vs rudin on real analysis?

[quick hornet]

pugh is a good deal more pedagogically approachable

and doesnt really lose out on depth unless you NEED to learn about metric spaces ASAP

but i dont think it hurts to have rudin on the side

[surreal phoenix]

I thought Pugh covered metric spaces pretty early, it doesn't?

[quick hornet]

it does but not as early

rudin works with them immediately

[frosty girder]

[quick hornet]

chapter 1 (of rudin) is sets and supremums and shit, chapter 2 is metric space topology

[surreal phoenix]

Ohhh I see

[frosty girder]

Thats very quick
Apostol takes a chapter more, first chapter is Real numbers, their properties, inequalities, complex numbers and a lot of stuff about them
second chapter is sets and sups, 3rd is topology

[cunning stirrup]

Industrial Society and its Future

[rugged maple]

u'd recc apostol?

is it any good? as compared to pugh, for example

[frosty girder]

i havent done pugh

i am doing apostol

and im liking it

[rugged maple]

alright

i will keep that in my mind

[foggy relic]

.

[stray veldt]

i wouldnt call elliptic curves intro number theory, but silverman has two excellent books on it

rational points on elliptic curves is the easy one, the arithmetic of elliptic curves is more advanced

more generally i like "a classical introduction to modern number theory"

[foggy relic]

@stray veldt what are the prereqs of the books you mentioned

Prereq to Ireland Rosen

[stray veldt]

some abstract algebra

knowing what a ring and a group is basically

then later a bit more (some galois theory)

i think it technically introduces everything but its not enough if you have never seen it before

[foggy relic]

I know introductory group theory

Thanks

[modern stone]

From what I’ve read I’ve got the impression that Pugh is a good alternative to Rudin as an intro to real analysis. Am I right?

[quick hornet]

this might be enough honestly, the prerequisite ring theory is just definitions

you could google search unique factorization domain or whatever

and get the gist

maybe spending like, a couple days doing exercises involving ideals of a ring would help

[foggy relic]

I know like up to/including sylow

[foggy relic]

aight, thanks for the advice

[smoky zephyr]

[odd spade]

for a while you just need a decent grasp on elementary algebra

being okay with a group in the abstract is good, cause you are introduced to a pretty interesting group structure

to get into the actual theory beyond that you end up needing more algebra, and also algebraic geometry, but it's a huge topic with lots of levels

you could spend a long time just studying computational/crypto results with just some piecemeal understanding of stuff

[foggy relic]

algebraic geometry

i wish i was smart enough for it 😩

[odd spade]

yeah i mean you dont gotta know a lot of all that to do a bunch of stuff with ECs

to get anywhere near all the big spooky stuff you do tho

[foggy relic]

what are ECs?

[odd spade]

elliptic curves, or are we just talking number theory?

[foggy relic]

ah i see

just didnt come to mind lol

[odd spade]

oh yeah

[foggy relic]

i just want to get a good understanding of all the elementary nt stuff, reciprocity and very elementary ECs basically

[odd spade]

that's doable

[quick hornet]

yeah eventually elliptic curves stuff really goes off the deep end

but at a basic level its just group theory

[odd spade]

lol yeah it made me realize i like CS-y math more cause i didnt wanna do all the geometry

[quick hornet]

• a bit of geometry that can easily be explained on the fly

[odd spade]

but to just get it isnt so bad

[dapper root]

Showing multiplication on elliptic curves is associative by hand

[quick hornet]

yeah thats what i mean byy

you want a bit of geometry

but that can be explained on the fly

if you have absolutely 0 pictures you will drown yourself expressing obvious facts

[odd spade]

it's actually a cool way to get a feeling for projective stuff

[dapper root]

You should take it for granted IMO. If you eventually go super hard on elliptic curves you can like show the multiplication is induced by something else to get associativity for free

[quick hornet]

i dont like that

[slim peak]

Show it drawing a picture

[quick hornet]

i think you should at least convince yourself

[slim peak]

0-line proof

[quick hornet]

to get intuition for how they work

writing up an algebraic proof, maybe not

but draw a picture

[slim peak]

lines and aweful geometric construction everywhere

[sage python]

Is it somehting you can visualize?

[slim peak]

yeay

[sage python]

Like within reason?

(Associativity in particular)

[dapper root]

You could draw a few examples

But like, I struggle to see that you can prove it for all of them

[sage python]

Yeah

[dapper root]

Just with a picture

Certainly draw a few so you see it works

[sage python]

I feel like you should define the group law geometrically, say it's some binary operatoin

[dapper root]

You can…

[sage python]

And use Riemann Roch for associativity

[dapper root]

You draw a line and then reflect

[quick hornet]

https://math.stackexchange.com/questions/76813/geometric-reason-why-elliptic-curve-group-law-is-associative

[sage python]

Yeah I know that Chmonkey

[slim peak]

Introduce the right morphism and prove that it preserve the group structure

this will give you the group structure

[sage python]

I'm saying the correct thing to do is to define the group law geometrically but only call it a binary operation

[dapper root]

What a hurb

[sage python]

Then prove that it's associative by relating to Riemann Roch

[quick hornet]

jeez i thought i was algebraistbrained

[sage python]

I have multiple hats

And I alternate which one I wear

[quick hornet]

is this really so scary

its way less scary than riemann roch

(screenshots are from milne)

(https://www.jmilne.org/math/Books/ectext6.pdf p27 of the text, 35 of the pdf)

[sage python]

When he wrote "general position" I was like ohhhhhhh nooooooooo

Until he specified

[odd spade]

algebrapilled and based

idk how yall can look at these runes all day

[gray gazelle]

so how is axler's linear algebra done right for an undergrad student ?

[marble solar]

I've now been informed that it's correct

but you should do linear algebra incorrectly

Linear Algebra Done Wrong by Sergei Treil

[gray gazelle]

i want a book that starts from with vector spaces

[coral narwhal]

both books mentioned and most UG linear algebra books will start from vector spaces

[gray gazelle]

i see

thank you both

[sage python]

I will push back against Axler as I often do

[marble solar]

Sergei Treil fan over here?

[sage python]

Because he makes you think about stuff in the vein of char/min poly and determinants like a moron

I graded for LA recently and it used Friedberg-Insel-Spence which seemed good

Treil I've heard good things about

[gray gazelle]

axler uses some weird notation that i can't find in other books like the term "list", doesnt define fields well and defines vector space functions like this

https://math.stackexchange.com/questions/1694865/help-understanding-a-paragraph-from-linear-algebra-done-right this is the answer i got up when i googled it

[whole rain]

what's the problem with the defn of vs fonctions ?

[gray gazelle]

well i couldn't understand it until it was explained in the last link that i sent

@whole rain

@marble solar sergei treil's book seems good

I might be wrong but the book used by Gilbert strang in the course that he teaches in the MIT course is not Linear Algebra and its Applications but is Introduction to Linear Algebra

so in the books channel it should be changed to avoid confusion

[cunning stirrup]

Industrial Society and its Future

[sage kelp]

Linear Algebra by Singh and Nair

[sharp solar]

Recommended resource for learning trigonometry really well?

I learned the very basics of using trigonometry in school of course (sin, cos, tan,...) but didn't gain an intuitive sense as to why things are so.

[brittle latch]

math department moving = free books lets gooooo

[fervent lava]

Khan academy.

[sharp solar]

Thank you.

[fluid bay]

Treil gang

[marble solar]

if I ever meet him, I'll get him to sign my copy

[smoky zephyr]

is linear algebra done wrong a good book for learning linear algebra

i’ve only read a few pages but honestly so far it seems perfect

[marble solar]

It's pretty good

And it's written by a guy who knows what he's doing

[smoky zephyr]

nice, looks like i know what i’m gonna use

it’s not super long either

[marble solar]

https://sites.google.com/a/brown.edu/sergei-treil-homepage/home

Here's his homepage

"Hi, I am Sergei Treil.

When I am not kayaking or scuba diving, I pretend to be a professor at Math Department of Brown University. "

[novel obsidian]

from these 2 lines, you can already tell this man is fucking awesome

[smoky zephyr]

yeah i already love this guy lol

[novel obsidian]

Is treil a good book for a first look into lin alg?

[marble solar]

I wouldn't say so

[novel obsidian]

What is a good book for a first look into linear algebra then?

[smoky zephyr]

linear algebra done wrong apparently

[marble solar]

Hrm, I guess anything that does some computation

So that you learn the basics

[novel obsidian]

for example?

[gray gazelle]

Anton

[fervent lava]

Maybe Gilbert strang book.

[foggy relic]

its nice because of all the OCW content it has, vid lectures and stuff, but i find the writing style is kind of different

you should probably delete that lmao

[brittle breach]

What's a good Algebraic Topology book besides Hatcher

[fluid bay]

tom dieck

[spice sentinel]

Do you guys know any good sources for the history of linear algebra?

I know that the determinant was first discovered 2 centuries before matrices were developed as well as that Gaussian elimination was basically developed in Ancient China, and it would be really interesting to see how the contributions of these great mathematicians lead to what we have today

If not then any books that discuss the history of any field of maths in a technical level

[sage kelp]

Opinions on Metric Spaces by Searcoid? Like, why choosing this over a General Topology book, what is the advantage of studying this book, and whether this an appropriate choice for sutdying some function analysis afterwards

[peak dragon]

Opinions on Introduction to Mathematical Cryptography (by Hoffstein, Pipher, and Silverman) or Introduction to Modern Cryptography (by Katz, and Lindell)?

[gray gazelle]

whos an author i should investigate

[gray gazelle]

I want that

[gray gazelle]

Any good books recommended for a class 9 std for Calculus

I know most of the basics