book-recommendations

[shadow crown]

not Isaac asimov

that was just the authors name

how dumb I was

but though

is asimov on numbers a good book

[quaint wraith]

Thoughts on Artin’s Algebra?

[fierce hedge]

I am assuming you're gonna use for algebra. It is recommended route if you wanna do abstract algebra+linear algebra. For first course in abstract algebra it might not be for you then try Pinter or Gallian

[remote sparrow]

chartrand covers more topics than velleman in the ebook, and he also has some pages online specifically dedicated to real analysis. but really either book is fine. you just need to pick up a real analysis book after working your way through either of those books. i also liked hammack, which is pretty similar to velleman. i also really enjoyed sibley's Foundations of Mathematics and Proof and the Art of Mathematics by joel david hamkins (though I read hamkins' book well after my transition to proofs class).

[zinc jewel]

thoughts on A survey in modern algebra

[gray gazelle]

Thank you! I'll pick Velleman (it's cheaper and more compact) and after it start Abbott's Understanding Analysis. I think I need to revise/re-read Spivak's Calculus again as I haven't touched analysis/calculus for a long time.

Unfortunately Foundations of Mathematics and Proof and the Art of Mathematics are very expensive. I'll check my Uni library or get a pdf ;)

[remote sparrow]

Just checked hamkins' price, it's pretty comparable to velleman in price atm, unless you're looking somewhere i don't know about.

In fact it's cheaper than velleman for me on amazon

You don't have to get his other extensions book, it's a solutions manual basically

[marble solar]

AHERM

Knot Knotes by Justin Roberts on his website is free

There's also some good youtube videos out there

You'll have to pick up some algebraic topology and differential topology at some pt or another

If you're learning 3-manifold topology as well, there's no truly good source

Schulten's 3 manifold topology book is a beast to learn from

There's also Bill Thurston's book

[forest sleet]

Ooh that reminds me there is a cool YouTube video called Not Knot

Old video made by a geometry center

That has a lot of visualizations

And intro to at/knot theory stuff

[remote ginkgo]

gnot gnotes

gnot ptheorists

[gray gazelle]

What are the prerequisites for "A course on convex geometry" by hug and weil

[remote ginkgo]

a zeroth course in convex geometry

[hidden apex]

any good book for particle physics?. Easy to understand for high schoolers/beginners

[desert tusk]

I found this in my school library, is this a book that would be accessible/comprehensible for someone that just finished calculus

[fluid bay]

in general, don't learn from really old stuff like this ^

it probably won't be "accessible/comprehensible" and old books use a lot of antiquated concepts/notation that no one will recognize or be able to help you with these days

[desert tusk]

Is the material itself outdated or is the problem mostly the notation

I know math moves a lot but since this is an “introduction” I thought it would be fine

[fluid bay]

im just talking about notation/presentation

[restive falcon]

both will possibly be problems

[lone ingot]

bro I tried reading that book

it's painful

im on like chapter 2

[restive falcon]

the number theory that was important many years ago will be different to the number theory that is important nowadays

[lone ingot]

I disagree

[fluid bay]

ehh

[lone ingot]

the book covers some really important stuff

even in modern nt

[restive falcon]

ok fair enough

[lone ingot]

like elliptic curves

[fluid bay]

at the introductory level, i expect it covers most of the same stuff

[lone ingot]

tbh it isn't outdated at all

it's just really difficult to understand

[restive falcon]

but it'll be hard to get help

[fluid bay]

im just saying that old books are not a good pedagogical tool. not saying that they contain outdated info, or aren't good books or anything like that

you just won't have a good time trying to learn the material

[tepid prairie]

Outdated maths. 🧐

[lone ingot]

I think that applies to new books just as much

[restive falcon]

well new books will have recognisable notation

[lone ingot]

hardy wright has good notation

well

they do use (m,n) to mean gcd(m.n)

but still

not that bad

[fluid bay]

new books have differences in style/exposition that makes them better/worse than others, sure. But clearly this is different

[lone ingot]

I think hardy wright is wayyyyy to rigorous

[fluid bay]

that's not even uncommon notation

[lone ingot]

so don't use it if you aren't already familiar with nt

[restive falcon]

hardy

[fluid bay]

idk, maybe it is an okay book, but there are many fine options in pinned which are more standard learning resources in the 21st century and a lot of people are familiar with

[lone ingot]

yeah if you want an actual intro to nt then use silverman's friendly introduction to number theory

or something like that

[tepid prairie]

That book looks ghetto even to me lol.

Nevermind the PDF just looked terrible. The internet archive copy looks way better.

[desert tusk]

Alright thx for the feedback

[lone ingot]

I have a completely legal pdf of it

[desert tusk]

Can you send it to me? I’ve been wanting to learn nt for a while

[lone ingot]

i dont think i can legally lmao

[desert tusk]

Oh I misunderstood lol

I thought that meant you could share it

[lone ingot]

you could probably find a totally legal copy online

if you catch my drift

[desert tusk]

Oh yeah ofc

Just found my own legal copy thx

[lone ingot]

gj

[remote nova]

Guys I need you to recommend to me (reply and leave ping on, or ping me) some really freaking hard math books based on some really complicated math, maybe complex multiplication, or algebraic number theory, or algebraic surgery theory, homotopy theory, etc...

I don't even care if it costs $105 like just send me something to blow money off of

Also make sure the math is cool really sorry to say this, just personal opinion so no books on combinatorics, analytic number theory, logic, etc...
here's a neat example, but the hope is that there's a decent version on Amazon
https://people.math.rochester.edu/faculty/doug/mybooks/aar-green.pdf

[lone ingot]

harthshorne alg geo is apparently insane

haven't read it

[remote nova]

I've already got it haha

[lone ingot]

damn

idk then

but tbh i doubt it's very difficult to find something like that

[remote nova]

I've got a really good start, as I'm building an Amazon shopping list

parents are gonna browse through it and just choose random crap to buy me

[remote sparrow]

There's a newer edition of this book anyway. Still don't recommend this as a main text since there's no exercises.

[remote sparrow]

Can you spend money for my undergraduate library instead 🥺 👉 👈

[remote sparrow]

Same

[remote nova]

ND LKFDS

[remote sparrow]

I'm kidding...unless?

[remote sparrow]

Idk what that acronym is btw, if it is one

[remote nova]

that is pure keyboard smash

[remote sparrow]

Fanfic website is typing...

[lapis oriole]

hii! I need help, im going back to school soon (I used to be homeschooled) and I need help on finding some math books (for year 10/9th grade) so I can study maths since im REALLYYY bad at maths😭 so can anyone give any book recommendations please? thank you<3

[lapis oriole]

YEAH

[remote nova]

Don't use books

YouTube is going to be your best friend

[remote sparrow]

What are your needs and background? What have you previously studied?

[remote nova]

I highly suggest Professor Leonard for your algebra. But maybe you're going into geometry, in which case... uhhhh get a book lmao and use Khan Academy

[lapis oriole]

LMAO

and I'll use khan academy!

[lapis oriole]

I'm not so sure, I've done so many different things, but there are so many things I'm not that good with, like im not that good w %s of a number, algebra or multiplication

[remote sparrow]

You may want to brush up on some pre-algebra if you're not quite sure what a percent of a number is.

Percents are just numbers from 0-1 multiplied by 100.

[restive falcon]

ravenel - complex cobordism and stable homotopy groups of spheres

said to be the most difficult algtop book ever written

[remote nova]

I happened to discover this book only days ago hence it is on the list haha

Ty tho

[lapis oriole]

ahhh okay

[remote ginkgo]

buy kirill's physics of finance and send me (in some legally permissible way given our respective jurisdictions) a pdf scan of it

alternatively

may i dm you for a list @remote nova

[remote nova]

[sudden kindle]

You're weird

[remote nova]

No I just like my epic algebra and my epic topology and whatever the heck happens when you combine them

[remote ginkgo]

have u tried j p may

@remote nova

[remote nova]

The lovely AG notes?

I want a physical book tho

[remote sparrow]

Based on the preliminary reviews of eugenia chang's The Joy of Abstraction, do y'all think it could become the pinter of category theory?

[manic cape]

what does the pinter of ___ mean?

[remote sparrow]

As in like pinter's A Book of Abstract Algebra

[fickle whale]

Fun book

[remote nova]

Fair opinion

[remote sparrow]

https://www.cambridge.org/core/books/joy-of-abstraction/00D9AFD3046A406CB85D1AFF5450E657

here's what i'm talking about

[remote nova]

Logic, categories, and sets

Sounds like a wonderful book

[grave thorn]

To me sounds like the opposite of an enjoyable book

[remote nova]

Well look at your nickname

I don't think that's the book's fault

[grave thorn]

Neither finance nor physics has much to do with logic/categories 🤷‍♂️

[remote nova]

Not what I was getting at

[grave thorn]

Then what were you getting at

[remote nova]

Unbased opinion regarding math-related interests implies an Unbased opinion regarding math-related interests

[grave thorn]

"math finance" (aka a branch of math) > "physics" (not a branch of math) is a very based take

[remote nova]

Wrong

[grave thorn]

Justify

[remote nova]

Proof is trivial and left as an exercise

[grave thorn]

Counterexample: math anything > physics

[remote nova]

Counter example: physics > probability

[grave thorn]

[remote nova]

Physics > combinatorics

[grave thorn]

Physics does use probability a lot

[remote nova]

Still cooler than the probability

[grave thorn]

Combinatorics is used extensively in statistical mechanics

[primal mica]

Physics uses most fields of math a lot :)

[remote nova]

Statistical mechanics is for nerfs

Nerds

[primal mica]

And physical systems motivate answers and new mathematics :)

[remote nova]

Based

[grave thorn]

Probably the coolest book I have on any topic

[remote nova]

Have you tried quantum field theory

Or uhhhh string theory or uhhhhhh

Yhhhh

[grave thorn]

As does finance

[remote nova]

Conformal field theory

[grave thorn]

QFT is just the study of Gaussian measures on S'(Rd)

[remote nova]

Yeah that's a lot more based thst combinatorics

[grave thorn]

But tbf I could def be better at Gaussian measure theory

(Gaussian measure theory is a branch of probability)

[remote nova]

How does QFT contain less interesting math when it's just better QM

[grave thorn]

QM is just noncommutative probability theory

[remote nova]

Diff eqs is probability theory

[grave thorn]

QM is not the study of PDEs lol

[remote nova]

Wot

[grave thorn]

I'm talking about the basis of the theory

Its noncommutative probability theory

[primal mica]

The basis of the theory is physical measurements

[remote nova]

The basis of abstract algebra is pretty boring but algebra itself is really based

[primal mica]

Math is just a tool to relate the physical measurements and make predictions

[grave thorn]

But the underlying theory heavily relies on noncommutative probability; note that a wave function is a probability amplitude

[primal mica]

Once again, just a mathematical descriptor, not the basis of the theory, which is still a topic of speculation.

It’s possible quantum mechanics is entirely non probabilistic

[grave thorn]

in order to postulate anything about the world you have to make several assumptions

[primal mica]

Indeed, is the same true for math?

[fickle whale]

it is true for everything

[grave thorn]

Many statements in ZFC dont hold in ZF for instance

[grave thorn]

String theory 🤮

[remote nova]

This is a lot of work to defend the faulty notion that any sort of finance anywhere can be cooler than physics

[grave thorn]

More generally I could write mathematical economics

[remote nova]

That only worsens your case

[grave thorn]

But why is physics "more cool"?

[primal mica]

Thermodynamics

[grave thorn]

aka statistical mechanics aka combinatorics

[primal mica]

Ah yes, combinatorics, the reason there is temperature

How could I be so foolish

[remote nova]

Suppose that one could define the "silly chain" given by
Biology < Chemistry < Physics < Mathematics. Then it can be trivially shown that if E is any field of economics, mathematical or not, that E < X for all X in the silly chain.

Thus physics is cooler objectively

[grave thorn]

Mathematical economics is a branch of math

Not economics

[remote nova]

However it is a study of economics and hence it is a branch of economics

[grave thorn]

No. It is math motivated by economic problems. Same thing with mathematical physics: it is a branch of math motivated by physical problems.

[primal mica]

It’s a weird argument you’re making :“physics is just math so it’s dumb. Economics is just math so it’s better”

[remote nova]

If mathematical economics did not produce useful or meaningful results to an economist, it would not be called mathematical economics. Economics regards all things that have to do with economics, thus mathematical economics is a subset of economics. Rather, it is an intersection of mathematics and economics.

[grave thorn]

Mathematical economics rarely produces interesting results to an economist (same thing with mathematical physics: physics people don't care about it)

It has made breakthroughs in math (eg BSDEs, positive operator theory, etc)

[remote nova]

I can make breakthroughs in mathematics and still be unbased

[grave thorn]

In fact in pretty much every field theorists are disliked

[remote nova]

Oh and pro tip

If you are a physicist and you don't care about mathematical physics, then all I can say is that you smell like beef

[manic cape]

[forest sleet]

i originally read this as no one likes field theorists lol

[remote nova]

same actually

[wild harness]

does anyone have Differential equations short formula pdf?

[sand ingot]

Hello! I need a book reference for complex variables.Can anyone suggest me?
Actually I found a book called Complex Analysis by Serge Lang (4th edition) in the library. If anyone knows about the book please let me know about it.
I am a BSc Maths 1st year

[solemn rover]

Ahlfors is a classic. Stein and Shakarchi is very readable

[sand ingot]

Thank You

[lone wren]

Is this a good buy? I have my math finals in spring and thought some extra calc practice would be good

[spiral portal]

just use the internet version if there is

u can always copy the problems on a piece of paper

And check solutions online

[heady ember]

If you want challenging exercises you can try Spivak. However, they are more proof based. If you need to practice manual derivations and calculations you could try Pauls' Online Math Notes, Khan Academy, Steward.

[spiral portal]

true I shoulda said that

[gray gazelle]

Check out Visual Complex Analysis by Tristan Needham. It's not super rigorous but is the best complex analysis book I know of when it comes to the presentation of the fundamental ideas

The best combo would be to do Needham's book and read it alongside something more classical like Ahlfors

[gray gazelle]

Yes, I checked it in my local academic store, expensive but trusted (and helps small businesses/bookstore rather than Amazon)

It's cheaper than Velleman on Amazon for me as well but the seller has low ratings. The one I prefer unfortunately isn't selling it.

[daring rampart]

who got coursehero

[stable dagger]

what are good books about calculating the fundamental group with many examples?

[proud gazelle]

is there a good book about complex numbers?
I don't want a book that states that a complex number is of the form a+bi and starts listing properties and proving theorems
I also don't want a book to define a complex number to be a R×R where addition is such and such and multiplication is such and such so that (0,1) = i and i^2 is (1,0) which we is equivalent to 1
I want some motivation behind the rules and the intuition of extending the numbers not by filling numbers in the numbers line (like the extension to the rationals or to the reals) but by going up a whole new axis and geometric intuition and consequences behind this extension and so on

[wise crater]

what do you think the complex numbers are exactly?

[proud gazelle]

ordered pairs of real numbers where (a,b) + (c,d) is (a+c, b+d) and (a,b) . (c,d) is (a.c - b.d, a.d + b.c) ?

[wise crater]

if that was the case then you would be happy with any of the things you don't want a book of

maybe learn about the theory of fields in algebra and see why the complex numbers are special there if you're expecting much more than that

[proud gazelle]

just because I know what something is doesn't I mean understand where does it from and what are its consequences and how was it discovered

[shy compass]

do you know what an algebraic closure is?

[proud gazelle]

closure as in closure under addition and such ?

[shy compass]

among other reasons, C is very useful and important because it's the algebraic closure of R

I suggest looking this up

[wise crater]

then yes, take the second thing about learning the theory of fields and specifically field extensions

complex numbers were probably motivated from that sort of thing first before any of the other things we use em for now

[proud gazelle]

I know about this, we C we gain closure for all the operations

I don't want the advanced stuff

I want to motivation and the intuition behind its extension

[shy compass]

what are "all the operations"

[proud gazelle]

just because something is presented in a certain order in a book doesn't mean that was the correct order it was discovered with/thought of

[proud gazelle]

roots? mainly that you can solve any polynomials and you gain the fundamental theorem of algebra ?

[wise crater]

go build yourself a time machine and figure that out then

[proud gazelle]

have you ever heard of math history ?

[wise crater]

math history is mostly just talking about peoples names and the problems that were discussed at the time, as an interpretation of some other dude born in the future

[proud gazelle]

you probably learned history the wrong way

[sick river]

Just pick up some complex analysis book and go ham

[proud gazelle]

an example about this is chapter 18 of calculus by spivak where he explores the exp function, how he starts the motivation by finding a function that can define 10^x where x is a real number, he goes over the properties that we expect from exponentials and then the rule that f(x+y) = f(x) . f(y), then how if we want to find such function we tackle a harder problem which is to find its derivative and arrive to the logarithm and its properties then define the exp as the inverse of log and find its properties mainly exp'(x) = exp(x) and other properties and then find its taylor series and so on, this is contrary to other books which start by defining exp(x) as the taylor series and derives other properties such as exp(a+b) = exp(a) . exp(b) and so on, which is totally true and logical but extremely dry

[vital bane]

wdym not super rigrorous?

[gray gazelle]

The proofs mainly consist of an outline of the "correct" ideas. Many technicalities are left out because that's not the focus of the book

[vital bane]

what is the focus of the book?

[gray gazelle]

Intuition

[vital bane]

damn I wish it's focus was both intuition and technicalities

[gray gazelle]

That's why you read Needham alongside something like Ahlfors

[vital bane]

what's a good book to go through after VCA to get all the technicalities?

[vital bane]

i see

[gray gazelle]

Read them at the same time

[vital bane]

[gray gazelle]

I personally read half of Ahlfors first then a couple years later discovered Needham's book and read it

Were I to study complex analysis again I'd read them concurrently

[vital bane]

"Complex Analysis: An Introduction to The Theory of Analytic Functions of One Complex Variable" by lars ahlfors?

[gray gazelle]

That's the one

Ahlfors is a super famous book in maths

[vital bane]

wow nice

VCA was like the only complex analysis book i knew of

[gray gazelle]

Where did you hear about it?

[vital bane]

I don't remember, must've been in some youtube video or this server

[gray gazelle]

Right, I had a youtube video in my recommended feed about maths book for self study

[vital bane]

complex analysis seems fun, but I have to learn intro real analysis for now

[gray gazelle]

I think I was bored and clicked it because all the recommeneded books were mainly BSc level and I'm already doing my masters

Glad I was bored that day

[vital bane]

what are you doing your masters in?

[gray gazelle]

Complex is more algebraic in nature, algebraic in the sense how people in algebra tend to think

[gray gazelle]

Diff geo

[vital bane]

niceee! lol diff geo is my favorite

I don't know much about it though

[gray gazelle]

I have a love hate relationship with diff geo

[vital bane]

Lol why?

[gray gazelle]

Super messy at times

[indigo mesa]

Diff geo kicks your ass regularly

[gray gazelle]

Is there a field of maths that doesn't

[indigo mesa]

It has such nice motivations and ideas and then often the details are just

[vital bane]

[vital bane]

as in notation?

[indigo mesa]

Fair

But in different ways

[gray gazelle]

The details are a 4 page tensor calculation

[vital bane]

lmao

[indigo mesa]

Wait i have something for you

[gray gazelle]

Notation, calculations, the objects themselves. It's like you're parsing through a lot of data and suck at book keeping

[vital bane]

hm I think I might've heard of this, like when you hear "differentiable manifold" you have to remember that it comes with charts and atlases and transition maps and stuff

not sure if that's the kind of stuff you're referring to

[gray gazelle]

That's the beginning of it

[vital bane]

[vital bane]

yes

[indigo mesa]

Put it in discussion 2

[vital bane]

lol I have the perma-study role I can't see discussion 2

[indigo mesa]

https://cdn.discordapp.com/attachments/991827364352892938/1001565441744969928/unknown.png

[vital bane]

it is pretty messy but to me it also looks super cool

holy crap it's super messy, subscript upon subscript

[vital bane]

so what is it?

[gray gazelle]

Why didn't they just give varphi j+1 pj a name

Call it qj or sth

[vital bane]

that's what I would've done

[gray gazelle]

Half of maths is exposition

[indigo mesa]

It’s from a proof around orientations

That closed curves preserving orientation is an equivalent condition something something

[gray gazelle]

Is an equivalent condition to what?

And what's a closed curve preserving orientation?

[indigo mesa]

I didn’t go in depth with this on purpose

Here if you’re curious

This is the equivalence I meant

[vital bane]

[restive falcon]

could anyone recommend a book on semiring theory?

[wicked osprey]

never heard if the semiring theory, interesting

[remote ginkgo]

rng

[fallow cypress]

I personally like stein-shakarchi's complex analysis book

Neamesis ^

[remote ginkgo]

ahlfors maximalism

[dapper root]

I used Gamelin

For my first course

[broken meadow]

using conway rn

[jagged zealot]

I asked this in #probability-statistics but maybe better suited here: I wonder if anyone can point me at a rigorous epistemic theory in the (introductory!) philosophy literature for frequentism. Like, Bayesian epistemology I have a good intuition for. But the frequentist idea of treating aleatoric and epistemic uncertainty differently is new to me. It has a certain appeal but I don't know how to describe it beyond that.

[remote sparrow]

there are several introductory anthologies on the philosophy of probability. you can google around or ask on r/askphilosophy

https://philosophy.stackexchange.com/questions/89433/books-and-papers-on-the-philosophy-of-probability

https://www.reddit.com/r/askphilosophy/comments/c78y27/any_good_books_on_the_philosophy_of/

these may be helpful jumping off points

you are likely (no pun or circular reasoning intended) familiar with the basic questions of philosophy of probability, but it also can't hurt to revisit those basic ideas in the following two videos:

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

https://www.youtube.com/watch?v=9ApjAYTRilo

[remote nova]

I think I've asked this before, but does anyone know of some solid and brief (self-contained) introductions to number theory? Specifically either for a student who hasn't learned abstract algebra, or one who is willing to learn it within the pages of the book teaching the NT?

I'm talking brief as in sub 150 pages, but also good for getting a grip on the basics.

There is also plan to move on to alg nt or cft

[remote ginkgo]

manin

[grave thorn]

cft meaning?

[remote sparrow]

burton, dudley, or rosen give completely elementary treatments

[remote nova]

class field theory

[crimson leaf]

What's a good algebra book for someone who doesn't have LA but is (hopefully) going to be learning it at the same time

[remote nova]

How much algebra do you plan/want to learn?

Like, are you planning to (immediately) go beyond the elementary content (e.g. representation theory, homological algebra, etc...)

[dapper root]

#book-recommendations message

It sounds like Artin may be a good choice

[crimson leaf]

Yeah I thought about Artin the class I'm hoping to join is using Friedberg for LA so I was worried about overlap. I sat in today and nothing seem too hard to follow

[dapper root]

I think overlap is a good thing

Like if you learn a concept that you need in order to work through an abstract algebra concept

You can’t really progress until you learn it

¯_(ツ)_/¯

[crimson leaf]

Fair enough

[warm glen]

has anyone read the book "topology: a categorical approach" that's in books protoype channel

and if so would u recommend it

looking for something to supplement my course notes with, prof suggested munkres but it's boring imo

[woven glacier]

any recommendations for books after calculus by gilbert strang

[remote sparrow]

I guess intro to proof books if you want to do more math

[remote nova]

especially the one by Zhang

and the others

A Transition to Advanced Mathematics

[woven glacier]

what are some good books for maths olympiad grade 12

[gray gazelle]

watch flammable maths and blackpenredpen

the tricks you need to solve those problems

otherwise:
The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books) by Shklarsky, Chentzov, and Yaglom

[remote sparrow]

#book-recommendations message

discrete math books could also work

[gray gazelle]

I got a big selection I need to read a book for school assignment I already tried one and didn't like it was as you like it a play I didn't like needing to look on different page to understand I'm giving list of books I can read
Anna Karenina
Atonement
Beloved
The blind assassin
The Bonesetters daughter
The Burgess boys
Catch22
The color purple
Crime and Punishment
The crucible
A doll house
Extremely loud and incredibly close
In the lake of the woods
Invisible man
Jane eyre
Jude the obscure
The kite runner
M.butterfly
Madame bovary
The memory keepers daughter
Middlesex
Much ado about nothing
Never let me go
Oryx and crake
Othello
The picture of Dorian gray
The portrait of a lady
Pride and prejudice
Snow flower and the secret fan
Twelfth night
Who's afraid of Virginia woolf
The women of Brewster place
Wuthering heights
A yellow raft in blue water

What would yall say are the best I should look out for

[remote sparrow]

what do you like in a book?

i liked catch-22 and crime and punishment when i read it

the crucible was alright when i had it as an assigned reading

[gray gazelle]

Idk I don't read but I want to

[remote sparrow]

i tried pride and prejudice and got bored of it, but in fairness i was in junior high then

[gray gazelle]

What is catch 22 and crime and Punishment about

[remote sparrow]

well, you could just google their synopses

[gray gazelle]

OK thanks for the recommendations

[remote sparrow]

since you're doing this for a homework assignment, i don't really want to be an incidental sparknotes for you

[marble solar]

Anna Karenina was great; Crime and Punishment is good depending on the translation, the Crucible is kind of boring

[gray gazelle]

Can someone plug me with a good overview of analysis?

Also, what are some alternatives to Axler?

[zealous coyote]

I have a two-word overview of analysis

reaw numbners

Also do you mean Axler's linear algebra?

[west sand]

Anyone know any resources for Fourier series and Similarity Solutions?

[median stump]

Anybody know any good text to help improve calculation and accuracy in math?

[past linden]

wdym

[median stump]

Any book that has exercises and tricks so that you get much better at calculations in mathematics

Or a book with exercises and strategies to help analyse a problem

[past linden]

calculations such as?

[past linden]

what kind of problems?

[median stump]

Math problems.So hopefully the book explains how to approach to a problem in geometry or algebra.In general, how you should analyse the problem and go about solving it.

[past linden]

what kind of math problems?

[median stump]

Olympiad level

[sudden dock]

Problem Solving Strategies by Arthur Engel is a famous book among students preparing for olympiad, however I haven't read it myself

Another one maybe the Art of Problem Solving vol .1

[sudden dock]

if you don't mind, I may ask which class are you studying?

[median stump]

Eleventh grade

[median stump]

Okay thank you I’ll have a look at them

[sudden dock]

How you have prepared for olympiad till now

I mean which books have you read

[obtuse ridge]

Are you preparing for IMO

[median stump]

Some Evan Chen, intro to number theory by oyestine ore, some geometry revisited, hall and knight, and I was doing polynomials by barbeau

And handouts

[median stump]

Yes

[obtuse ridge]

2023

the one which will be held in Japan

nice

i am also trying

but i wont even be able to pass my country first round lol

[median stump]

Best of luck to you then.

[obtuse ridge]

ik very little stuff and its gonna be hard to study lots of them before First qualifier round

[obtuse ridge]

same 2 u

[sudden dock]

hmmm Did you attempted to solve complete book or few chapters here and there

[median stump]

Not the whole books in geometry

But I completed the other books

[sudden dock]

thanks for your time

[median stump]

Thanks for the recommendations.

[alpine quarry]

can somebody provide a book reference for these topics ?

The prescribed book is Elementary Number theory by Thomas Koshy

i'm looking for book where author speaks to the reader a bit while on the explanation ( hope you get what i mean)

[karmic thorn]

@alpine quarry You can look into Elementary Number Theory by Burton

Any standard text on elementary number theory would do the work here, pick one that suits you

[fallow cypress]

anna karenina <3333

also this is such a random selection of books what lol

they have like no relation to each other

[ornate sedge]

Any recommendations for calculus 1 (analyse 1) preferably in french if possible

[remote sparrow]

fr*nch 🤬 🤢

[remote sparrow]

https://www.amazon.com/Calcul-différentiel/dp/289650558X

there's a fr*nch edition of stewart's calculus book

not sure about anything else

try looking for whether common english language calculus textbooks are translated to french

[remote sparrow]

btw, forgot to mention this, but you could totally do ordinary differential equations right after calculus if you wanted to

[slim peak]

Depends if you want to buy it, or just study with it

If you can borrow one from your Uni's Library

Mathématiques License 1 Pearson, or Mathématiques MPSI-PCSI Cap Prépa Pearson should be okay

And if the thing is really only about computing weird integrals without any justification

There are thousands of exercises on the internet

[muted torrent]

hello everyone is there a good book for learning linear algebra?

on my own

[sage python]

@muted torrent are you more about proofs or nah?

[muted torrent]

i dont rlly need proofs i was just lookign for a book to like learn the concepts or whatever ;-;

or a resource im not sure

[sage python]

People seem to like books/lectures by Gilbert Strang

[muted torrent]

i found https://math.mit.edu/~gs/linearalgebra/ online, i'll look at it maybe

:)

dang this guy likes linear algebra a lot

[remote sparrow]

https://www.amazon.com/Linear-Algebra-Theory-Intuition-Code/dp/9083136604

this looks promising and cheap

no calculus required at all

[fallow cypress]

There shouldn't be any calculus required in any linear algebra book lol

[remote sparrow]

let me rephrase that, does not mention anything about calculus or have any examples that involve calculus

typically first linear algebra books are written with the fact in mind that students have likely seen calculus already

[vagrant sedge]

Hi. Has anyone here read Zeidler's functional analysis texts? Are they still good/relevant? I mean the two-volume (not the 5-volume) set.

[snow fiber]

hello guys. Does anyone have a pdf file of "THe calculus 7 (TC7) " by louis leithold? Thanks

[hearty sluice]

THE calculus

[zealous light]

The 7th sequel of Calculus

[gray gazelle]

Any books for grad level calculus? Like phd level limits and derivatives

[stray veldt]

no

[gray gazelle]

Based question

[gray jungle]

fortunately , math at the higher level isn't simply "harder calculus" , but if you are willing to peak into how its like you could consider a intro to proofs book followed by a subject called real analysis.

altho i dont know your background but i would assume by your question you finished basic calc?

[gray gazelle]

I was just joking jej

[gray jungle]

[heady ember]

Differential Geometry

[tough zealot]

there are multiple ways to generalize the derivative
diffgeo is just one route and even there, there is multiple "paths" (npi)

[grand thistle]

what are those ways?

ive only heard of stuff like exterior derivative and lie derivatives

think grad div and curl are encompassed in the notion of an exterior derivative? not sure

[tough zealot]

if you add the hodge star (and possible the covariant derivative of general tensors sure)
already there, youve got multiple, like you mentioned

there is also the frechét derivative in analysis
also, notions of weak derivatives and distributional derivatives there and possibly fractional ones

[grand thistle]

cool!

it's amazing how you can generalize things like the derivative and integral in so many ways

[sudden kindle]

Grad level calculus

Misnomer

[remote ginkgo]

landau

[heady ember]

You mean lambda?

[remote ginkgo]

tf

[gray gazelle]

@grave thorn any math finance recs?

[hasty turret]

Ask ryc

[gray gazelle]

Spivak's calculus on manifolds I think is quite nice. Not sure what you mean by 'phd level', since these topics are usually covered in undergrad/early grad though.

[vagrant sedge]

take a book on sobolev spaces

[sturdy shore]

my man said he was joking and still got like 3 serious recommendations for phd level limits and derivatives

[vagrant sedge]

And, yet, no one mentioned banach limits
https://en.wikipedia.org/wiki/Banach_limit
also, derivatives through densities using measure theory is a thing

iirc with banach limits, you can get to things like limit of (1, 0, 1, 0, 1, 0, ...) being 1/2

[remote sparrow]

besides the cauchy-schwarz master class and hardy, littlewood, and polya's book, what are some other inequality problem books/references? anything from elementary (i.e. using just basic algebra or geometry, little to no calculus) to advanced treatments would be appreciated.

[remote ginkgo]

go dig up ramanujans notes

[rain dove]

Hey, how are you?

I went to a french school

I skipped all my lessons of my last year

And I was a pain to my maths teacher in the last two years

I do not remember anything from the last four years, but I want to learn my maths again

I can do basic algebra with one unknown... I don't remember pythagoras theorem... What should I read?

[zealous coyote]

People seem to like 'em

[lapis sundial]

Nice cliffs too

[zealous light]

🎸

[zealous coyote]

Terrible truck traffic though

[sturdy shore]

evans appendix b

[lapis sundial]

YO

Banger

Love a bit of eric

[zealous light]

Had me take a break from my study playlist to listen to it

[grave thorn]

"a course in financial calculus" by Etheridge

[gray gazelle]

Calculus? Sounds suspicious

[grave thorn]

It assumes measure theory

Its actually very good

imo

[gray gazelle]

Mhm. I'll make sure to check it out sooner rather than later

Thank you

[remote sparrow]

what are some old books y'all would like to see published or reprinted by dover (or some other low-cost publisher of your choice)? i think it's high time a book like feller's book on probability deserves a dover edition. or maybe moise's calculus book.

[gray gazelle]

Can someone recommend me a good geometric topology book?

[pale scarab]

Not necessarily a book recommendation but I am looking for magazines similar to chalkdust that has interesting articles and fun problems approachable to someone with just a bachelor's degree so nothing too technical

[pale scarab]

Higher math for beginners by Zeldovich and Yaglom is really good book on calculus I would love to own a dover copy of

[rugged sapphire]

I've never read a book before but I want to gain some knowledge can someone recommend me a book?

A book that's easy to understand please

[golden locust]

I haven't read it myself but I've heard great things about green eggs and ham

[delicate hemlock]

I'm more of a Goodnight Moon enjoyer

[rugged sapphire]

I'll try reading those 2 ty ty

[wise crater]

A Cohomological Viewpoint on Elementary School Arithmetic

credit to daminark for the fun paper

[rugged sapphire]

Tysm

[hallow oriole]

if you've srsly never read a book before you might find it easier to start with things like audiobooks

[wise crater]

they're reading a book with how long your reply is

big brain man!

[hallow oriole]

shush

[rugged sapphire]

Where can I listen to audio books?

i read manga but books that has no pictures feels like it has no feelings into it

[hallow oriole]

audible and scribd are the most popular places iirc

[rugged sapphire]

that's why i never got the motivation to read books

[hallow oriole]

hm

[rugged sapphire]

oh okay okay ill try those

[hallow oriole]

have funn

[rugged sapphire]

tyy

[eager jolt]

Hi guys! Does anyone happen to have the book "Awesome Polynomials for Mathematics Competitions" in pdf?

I would like to read it, but I can't buy it

[wise crater]

have you tried the usual places?

[eager jolt]

What places do you mean?

I'm just not very experienced in such matters.

[wise crater]

if its a proper book the usual spot would be libgen, if its an academic paper try scihub

[eager jolt]

Thanks very much

I'll check now

@wise crater Looks like this book is not there

[wise crater]

can't help ya much more than that bud, good luck searchin

[eager jolt]

Thanks

[haughty warren]

any book recommendation for a senior high student?

(anything that relates to math)

[grand thistle]

what's your background?

[lime sapphire]

Galois’ Dream: Group Theory and Differential Equations by Michio Kuga

[valid coral]

Stewart’s Calculus idk

[keen orbit]

Hi what are the best topology books for a person who wants to newly start learning topology (high school student)

[heady ember]

Point set or not

[manic seal]

I am looking for a book to teach me ordinary differential equations that is not lacking in rigor but does not lose too much on rigor either

[keen orbit]

I am starting from the start so probably point set

[gray gazelle]

Any blog recommendations

Blogs like Tao's, Astral Codex, etc.

[grand thistle]

if it’s just metric space theory you’re looking for rudin chapter 2 is pretty good, if you’re looking for general topology, i think munkres or lee topological manifolds are popular

[heady ember]

Lee

[gray gazelle]

it's not always good to begin from point set topology, you won't get intuition for why some concepts are being introduced

[keen orbit]

Where do I start from then?

[gray gazelle]

if you can bear with lack of intuition for some things, then you might start with point set topology

otherwise some books which introduce you to real analysis usually have a chapter about topology
I also read some books about topology which didn't even introduce topological spaces in my early stages of university, but they were in Polish and I don't know their titles

[keen orbit]

No I like to know where do the things come from

Also aren't there some prerequisites for real analysis and topology ?

What are they can you tell me

I want to know what to self study for now

[gray gazelle]

you only really need some elementary set theory (elementary meaning it's not advanced set theory)

i.e. manipulating sets etc.

[heady ember]

~~Enderton ~~
jk you prob shldn't

[keen orbit]

Wdym by manipulating sets ?

Like AU(BnC)=(AUB)N(AUC)?

[gray gazelle]

knowing what set difference/intersection/union is, knowing what functions are, their preimages, images, things like that

and knowing relations between them like, de Morgan laws, knowing what equivalence relations are

[keen orbit]

Oh these

Idk I think continuing calc is more interesting

I reached definite and indefinite integrals and I was going to start with techniques of integration but then went to topology

I think I'll continue in calc then move on to linear algebra

I don't know

[gray gazelle]

The book that I really read most of is Dugundji's Topology but it;s point set topology and some people even say it's more like a reference text

so it won't introduce you to metric spaces until really later on, and the exposition won't really be proper

so it's not a good book to read at this stage

many people say that Munkres is a good book when it comes to topology, it's sort of a standard choice

I don't know how it deals with metric spaces, but supposedly it's good

[keen orbit]

Ok do you advice me to continue calc then go linear algebra or dive into topology rn?

[gray gazelle]

you don't need much linear algebra to learn about topology, this appears mostly in real analysis

I don't know, I'd like someone more experienced with teaching process to speak here, I'm not qualified for this

[keen orbit]

Just give me your opinion if you dont mind

[jade monolith]

Hey guys! Could someone recommend me a book about advanced math?

[keen orbit]

I mean if you were in my place what would you choose

[gray gazelle]

I'm biased because I really like topology. Usually people learn calculus/linear algebra before things like topology

I think it's good to know some real analysis before topology though

[keen orbit]

Oh ok tysm for your opinion and help have a very nice day

Real analysis needs calc and linear algebra if I am right so I'll get into these for now prob

[gray gazelle]

I hope you have a nice day too

[keen orbit]

Tysm

[tawny copper]

Someone know where I can find "Continuous symmetry" by Barker?

[gray gazelle]

Geometry of cuts and metrics by Michel Marie Deza and Monique Laurent

[regal wasp]

Spectral sequences?

And branch cuts perhaps?

[solemn rover]

I learned spectral sequences out of Godement's wonderful book Topologie algebrique et theorie des faisceaux

A common first spectral sequence to study is the Cech-de Rham spectral sequence which is presented in Bott-Tu.

Chapter 5 of Weibel's book on homological algebra gives some examples and basic theory.

Switzer's book on algebraic topology has a chapter on spectral sequences with a few good examples.

[fierce hedge]

This looks beyond graduate

[tacit ice]

Hello people, I am Thomas.
I am trying to find a book that can help me improve my theory about maths.

I am a GCSE student in the 2/8 math set

I am trying to reach number one but I am struggling to improve, If there is anybody with good book recommendations I would be happy.

Thank you 🙂

[remote sparrow]

you can read an intro to proofs book if you want

a discrete math book would also serve the same purpose

usually these books have a chapter dedicated to proofs in calculus but if you haven't had any calculus yet you can skip those chapters

[gray gazelle]

I thought that was the point. To recommend something interesting, but not necessarily easy to read

[tacit ice]

THX

[lime sapphire]

You don't really need books at GCSE

I'd recommend doing sheets depending on your level from a website called mathsmadeeasy

And just practice

[lapis sundial]

Are there any nice/good/canonical/natural/functorial books for learning (topological) K-theory?

Not sure where to begin - kinda working backwards from papers atm

[tropic thorn]

I am currently reading mathematics for machine learning has anyone read it ? So i can get some insights on how to read it.

[gray gazelle]

Mopar: The Performance Years
by Martyn L Schorr

[topaz rune]

I’ve skimmed through it what you wanna know

It’s basically a compilation of undergrad math that is relevant for ML, might be a good read for people who forgot much math and about to start a ML course

[tropic thorn]

Im having rought time with vector calculus

I went through multivariate and vector calculus in uni

But we never did anything related to matrices nor tensors

Do i have to understand the details of the computations for ML or is the overall concept/intuition enough?

[zealous light]

Understanding linear algebra at a strong level is required for ML. I'm not sure the extent to which you understand the overall concept/intuition, but computational details are really nice to know, but a lot of algorithms and decompositions you'll never have to do by hand

[fallow cypress]

Yes you should understand the details because if you don't understand the computations, then you probably won't understand the overall concept very well

You should understand it to the point that you'd feel comfortable talking to someone about it if they asked you how an algorithm works

[tropic thorn]

Ok thanks everyone

[acoustic crypt]

book recommendations as in reading?

[remote sparrow]

?

like for fun?

[acoustic crypt]

no like what is the channel for

[remote sparrow]

not math?

book recommendations

doesn't have to be math

but being in a math server, you're probably less likely to get book recommendations for non-math topics

[acoustic crypt]

yea as in reading books

[remote sparrow]

yeah mainly books or papers i guess

[acoustic crypt]

k

[remote sparrow]

you just ask randoms what book should i read for x topic

pretty common question here

[acoustic crypt]

ok thx

[gray gazelle]

What are the good ones here

[gray gazelle]

Crime nad Punishmet
To Kill a Mocking Bird

[crimson leaf]

No country for old men and things fall apart are good

[gray gazelle]

@crimson leaf is it similar to the movie

[crimson leaf]

Yeah the book is by Cormac McCarthy who is a legend and he originally wrote it as a screenplay

[gray gazelle]

Ah bet hopefully they have it at my school/library if not I'll do Crime and Punishment which I wanted to do last month

[broken meadow]

King lear, the stranger, a lesson before dying, to kill a mockingbird are nice

[zealous light]

The Stranger and The Blind Assassin

[timber copper]

Things fall apart, native son, and Beloved

[zealous light]

Oh shoot, yeah things fall apart is good too

[timber copper]

okonkwo my beloved 🍠

[gray gazelle]

These are all classics tbh, great book list.

[austere osprey]

can someone suggest a easy book to understand these topics for compitition level..

[remote sparrow]

i'm not aware of any math competitions that would involve ODE's, PDE's, or numerical analysis

do you mean exams?

in any case, a good first stop for ODE's that includes all the material you're looking for is boyce/diprima

for PDE's strauss is usually the first recommendation

[gray gazelle]

PDE's for competition math

[heady ember]

~~Just do taylor's PDE books ~~ (jk)

[languid cypress]

Does anyone have recommendations of books/resources that focus on algebra that is used in physics. Not basic algebra like rearranging equations and quadratic formula, but for solving systems of equations (not linear), as well as a nice amount of factoring for powers in general. I want this book because i am studying for IPHO

[austere osprey]

in my country there is exam for Ph.D.

[remote sparrow]

ah

it's the same everywhere else i'm sure

[pseudo orbit]

i m in class 11th

and my ncert is completed

now which book u preferred

[remote sparrow]

some common terms for those doctoral or master's exams would be qualifying exams or comprehensive exams

this looks like undergraduate material though...is this an entry exam?

the books i recommended should be sufficient i think

we don't have entry exams in the u.s.

[lone smelt]

Just started reading this book!

[hallow oriole]

nice!

[lone smelt]

So far love it!

[hallow oriole]

i'm glad!

[gray gazelle]

You can do the applied math track for this competition, lols

https://damo.alibaba.com/alibaba-global-mathematics-competition

[tawny copper]

What are good sources for getting good at Putnam type problems? I'm weak in most areas, though I especially need to train calculus.

[celest rover]

Any non textbook reading book recommendations?

[gray gazelle]

what does that mean?

[quick hornet]

war and peace

[median creek]

twilight

[zealous coyote]

The remains of the day!

[solemn rover]

Antigone

Crime nad punishment is really good

[royal gale]

Someone can recommend me a good book of physics to math students?

[solemn rover]

Rosencrantz and Guildenstern are dead was a really good movie, I assume the book is equally good lol

Native Son is gut wrenching

[solemn rover]

A lot of math students appreciate V I Arnol'd "Mathematical Methods of Classical Mechanics"

[royal gale]

Oh thank u man

And to learn Multivariable calculus, do you have other recommendation ?

[solemn rover]

The standard textbook by Stewart is probably suitable.

If you prefer rigorous derivations and want to learn to read and write mathematical proofs, the book by Apostol is good

Multivariable calculus is treated in the second volume

[royal gale]

Alright, I saw this comment in quora, what do u think about this?

[solemn rover]

By the way, a good book is only good if you have the background to read it, you might miss out about it

[solemn rover]

Hm, I think I agree with Kevin. It is a great idea to learn electricity and magnetism side by side with multivariable calculus.

By the way

I want to change my previous recommendation lol

I think the book by Arnold is advanced

I think an easier book on physics would be a good starting point

When I was in undergrad, I learned basic physics from the book "Physics for Scientists and Engineers" by Randall Knight.

See if you can find a free pdf.

[royal gale]

Alright, so I'll read it later

Thank u very much ❤️

[solemn rover]

no problem!

[royal gale]

Is better to learn linear algebra with the volume 2 of apostol or with a specific linear algebra book, like the linear algebra done right ?@solemn rover

[solemn rover]

I would recommend Apostol over Linear Algebra Done Right.
However, both of these give a more theoretical, conceptual treatment of linear algebra, with rigorous proofs.
If you want intuition for the meaning of these constructs, it is helpful to study a computational textbook which has more exercises that involve working things out by hand. I learned "computational" linear algebra out of the book by Lay.

But do not give yourself so many prerequisites that you never learn what you want to learn. Try reading Apostol and look at the book by Lay if you have trouble and want to do some numerical exercises that gain more intuition.

The video lectures by 3blue1brown on linear algebra also help with intuition

[royal gale]

Alright, thank you ❤️

You really helped me a lot

I'm learning this concepts because I will work with A.I in my lab of bioinformatics, and biophysics. But I love math too, so I like to understand where things come from

[hybrid sequoia]

Which one is better for polynomials? https://www.amazon.com/Awesome-Polynomials-Mathematics-Competitions-Xyz/dp/1735831514

Or

https://www.amazon.in/Polynomials-Problem-Mathematics-Edward-Barbeau/dp/0387406271

[rugged seal]

Is there a book which covers
-Linear programming(Simplex),
-unrestricted nonlinear programming(Gradient decent methods, Newton methods, quasi newton etc...)
-restricted nonlinear programming (Constraint qualifications, Karush-Kuhn-tucker, sequential quadratic programming)

i just threw in some terminology hope that helps

[topaz rune]

https://www.csie.ntu.edu.tw/~r97002/temp/num_optimization.pdf

[rugged seal]

thank you very much

[topaz rune]

Np, it’s a well known and popular reference so definitely a good choice

[brittle breach]

Takhtajan Quantum mechanics for mathematicians

[grave thorn]

Hall "quantum theory for mathematicians"

[forest sleet]

While we're at it, teschl "mathematical methods in quantum mechanics"

Or Spivak has a classical mechanics math book if you don't want quantum

Also friedli velenik if you want statistical physics

[gray gazelle]

Are these better than math methods that covers both subjects normally?

[forest sleet]

What do you mean?

Like functional analysis books?

(I'm not sure what"both subjects" refers to)

[misty wyvern]

The subjects of Physics 1 and Physics 2, evidently

[lime sapphire]

Tfw u need to learn dg for classical mech 😭

This is spivak's btw^

[forest sleet]

classical mechanics is on symplectic manifolds

they use it in physics classical mechanics class too

just maybe not with all the definitions

However iirc for that book you don't need the diff geo until Part 3

[grave thorn]

Classic mechanics can get very abstract very quickly

[blazing canopy]

There is value in learning the general mathematical concepts in order to understand physics better, but sometimes the general theory obscures the physics making it impossible to really understand what is physical and what is mathematical

[misty wyvern]

There is no value in learning math, only pain.

[gusty bane]

Anyone know any good books for learning trigonometry

[remote sparrow]

https://4chan-science.fandom.com/wiki/Mathematics

https://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144

try looking through the precalculus section on the wiki

but start first with khan academy

generally you don't need a book-length treatment of this subject to move on

[gusty bane]

thanks bro ham

[hollow shore]

http://mecmath.net/trig/

[remote sparrow]

https://aimath.org/textbooks/approved-textbooks/

you can check here for free open source books too

[shut radish]

Looking for introductory books to fractals. Always been interested in patterns and chaos theory but didn't learn about the existence (or theory?) of fractals and its relation to chaos and it looks really cool.

A couple I've seen recommended are
https://www.amazon.com/Chaos-Fractals-New-Frontiers-Science-dp-0387202293/dp/0387202293/r
and
https://www.amazon.com/Fractal-Geometry-Mathematical-Foundations-Applications/dp/0470848626/

[hearty steppe]

You want to learn dynamical systems theory, which is my area.

Brin and Stuck and Strogatz are your starting points for that, Brin and stuck gona take you time to progress through but you probably will think fractals are less impressive as your working through it

[misty wyvern]

What's your favorite book on ergodic theory, at a research-level say for PDEs and stochastics people

[hearty steppe]

I still haven’t started my Ergodic theory reads and probably won’t get to them until next year at the rate of how busy I am 😦

I would recommend what I found for myself but I’m sorry

You can check my thread to see what books I’m interested in checking out in #1019651305947549806

[shut radish]

Why less impressive? I like the somewhat philosophical side along with the presence of patterns along with it.

[hearty steppe]

By the way while your working through those Ergodic theory texts, you should be aware of the quantum gravity research resource I posted because that stuff is going to play well with Ergodic behavior when you have to work with more nondeterministic behavior

A lot of the fractal stuff becomes popular attention on a surface level mainly cuz of some of the content that Wolfram put out through his book “A New Kind of Science”

It’s more of an extended look into complex dynamics and dealing with stuff like strange attractors which are key to chaotic behavior

I mean it’s still interesting but your gona find a bunch of other stuff that motivates towards fractals and more or less, past fractals

[shut radish]

Cool

[hearty steppe]

So don’t rely on Wolframs book. It’s a good book I think, but it’s loaded and not necessarily what I would call a beginner friendly book to the subject of dynamical systems with more focus toward complex dynamics and strange attractor based behavior

[misty wyvern]

I am in fact working on some mathy QFT stuff and am struggling with some avenues of argument being totally cut off due to me not knowing enough ergodic theory.

Sads

But that's what specialization means 🎺 can't be good at everything

[shut radish]

Seems contradictory being a believer in creationism, but the idea behind complex systems which may seem random but are designed through a pattern which was previously designed by an outer pattern which follows another pattern just makes me incredibly excited.

[hearty steppe]

Complex dynamics is another way of saying we have compounding events that happen at scale when we have a system with rules involved and we let it play out.

You have a lot of stuff dealing with the state space mapping associations to possibility spaces (probabilistic like distribution weighted outcomes). As the behavior scales out in terms of time steps for our system, complexity unfolds

With the Mandelbrot set we have some complex function with a constant that is held at a fixed point. The fractal behavior that gets plotted in our graph is all the possibilities in which our complex function with our fixed constant, is essentially giving us a range of outputs and we get a really trippy looking pattern?

[shut radish]

I was introduced to the Mandelbrolt set and the Koch snowflake as an example of what fractals are.

[hearty steppe]

I think Hofstadter’s butterfly may be a more recent one I was introduced to, sort of.

[shut radish]

Oooooh I like this. The symmetry and congruity.

The outer nodes will also contain the same design on the inside as well repeating consistently with the opposite side.

[hearty steppe]

I think Ergodic theory makes fractals more appreciable because you can consider the iterative continuous association of the points being plotted for the fractal patterns

But I don’t suggest jumping straight into Ergodic theory book without going into a more intro level dynamics text

There’s a lot of cool associations you can make… you can dive more into areas of dynamics like percolation theory, bifurcation theory (this is where we learn about attractors, and perturbations btw) to name a couple

[wooden frost]

whats a good college algebra book with difficult problems ?
i checked few like Stewart, swokowski and they all seemed to have easy problems

[heady ember]

Look at pinned

[noble lance]

any good books for GSCE revision

math teacher recommended them CGP books, what do yall think

[weak violet]

whats an abstract algebra book with good problems

[heady ember]

Dami has reviewed some algebra books

[weak violet]

i dont see anything about problems specifically though

[heady ember]

Books that are said to be good generally have some decent problems

You can flip through a pdf and see if the problems are challenging/good enough for you

[gray gazelle]

Dummit and Foote has lots of problems

[languid cypress]

Anyone know good books for geometry that can be used in physics?

[zealous light]

The book “Linear Programming and Network Flows” by Bazaraa and Jarvis seems to cover most of the topics in the course description if you want to look it over to see what to expect. I haven’t read it, so I can’t comment on how readable it is, but it seems sufficient

For a look at linear programming and convex optimization in general, Boyd and Vandenberghe seems very popular

[timber copper]

first half of linear and nonlinear programming by Luenberger and Ye should go over the course content

some sections go over network flow problems and there's also an appendix about networks

[viral oracle]

Hey, Im thinking about some book for my linear algebra course. I cant decide between Strangs Intro. to lin. alg. and Lin. alg. done right by idk who. The question is which one should I get? I heard that both are great but Ive heard that Strangs is written more to be read as a whole, which is something I dont want, I just want to find things that are interesting for me. Thanks for advice.

[zealous light]

Ooh this seems very nice

[timber copper]

Yup, definitely liked the book! Used it for my optimization course I took in ug

[viral oracle]

Also thinking about Finite-dimensional vector spaces by Halmos, which seems to be more rigorous

[sturdy shore]

what is your math background

[viral oracle]

1st year of uni, started lin alg course two weeks back

but geniuely enjoy that subject

[sturdy shore]

halmos will absolutely murder you

arguably axler's book (done right) is also meant to be a 2nd book on lin alg and not a first one, but it is still pretty accessible imo

both halmos and axler focus much more on vector spaces/linear maps instead of matrix computations

I've never read strang's book(s) but I have watched some of his lectures before, felt much more like a "standard" course

focus on echelon form, LU stuff etc

[viral oracle]

Ive heard that Strang wrote this book in such way, that you must read the whole book, because he uses different approach on teaching it

So what do you think that I should go with? I am studying signal analysis, so I want rigorous approach and truly understand lin alg

[hazy elk]

@sturdy shore your about me is very nice

[viral oracle]

also i only have one course on lin alg

[hazy elk]

Might steal it

[sturdy shore]

I stole it from a book myself so I cannot stop you

[sturdy shore]

halmos if you have the guts, otherwise axler

there is also linalg done wrong which I've never read but have heard good things about

tbh a lot of books in that pinned post have their own advantages

[viral oracle]

also heard of that one but i dont have it in my school library

[sturdy shore]

I don't think it ever got printed

it's free online and that's that

[viral oracle]

Alright, thanks alot👍🏼

[gray gazelle]

what are the most intensive fastpaced but also rigorous math books.

[wooden frost]

so i checked pinned comments but couldnt find any college algebra/precalculus book with hard problems
do you recommend any specific college algebra book with challenging problems ?

[granite viper]

Fast-paced and rigorous?

[brittle breach]

J.P. serre course on arithmetic

and his other books

[remote sparrow]

maybe basic mathematics by serge lang?

[remote sparrow]

seems like you're taking a first course in linear algebra. try meckes' linear algebra book. for free alternatives, try linear algebra by jim hefferon or linear algebra by robert beezer.

you could also try linear algebra: theory, intuition, and code. i haven't read it myself but there are lots of good reviews for the book.

it's not free, but it's at a very low cost, on par with a print copy of hefferon.

[gray gazelle]

Any rigorous books on zfc

[jaunty acorn]

I am learning real analysis for my graduate level econ course,I do barle sherbet but so i want books which are very rigourous and intresting

[forest sleet]

any real analysis book should be rigorous

by interesting do you mean interesting topics, or interesting presentation (as in not super dry)?

A natural interesting topic after intro analysis is to continue in real analysis and do some measure theory

or probability theory

[remote sparrow]

as in set theory? maybe enderton's Elements of Set Theory could work. hrbacek and jech's Introduction to Set Theory is a common reference as well. these are undergraduate texts.

[gray gazelle]

Jech's Set theory
For graduates

[remote sparrow]

oh, and avoid Naive Set Theory by halmos. not that it's a bad book or anything, but it's literally not about axiomatic set theory (you know, like avoiding russell's paradox and stuff).

it's definitely good enough for most math students, but not if you wanna learn the nitty-gritty of set theory

[gray gazelle]

i want very axiomatic set theory like from scratch

also any very rigorous (famous) logic book

[remote sparrow]

enderton's introduction to mathematical logic is pretty good as an undergraduate text

you could check out peter smith's logic matters blog

[fallow cypress]

I've heard enderton is logic for people who already know logic xD

[remote sparrow]

maybe

there are lectures by antonio montalban for enderton's set theory and logic texts

so at least you won't be completely on your own

[heady ember]

Enderton Elements of Set Theory

[heady ember]

Enderton's A Introduction To Mathematical Logic

[grand thistle]

halmos is really good i like it

but yeah it’s hard

if you’re ready for a rudin like book on linalg then go for it it’s amazing

probably have another book that gives u the basics tho

doesn’t cover matrices until like 100 pages in and that might mess with the pace of your class

[fluid bay]

also worth pointing out that lang, axler (LADR), and Halmos should all be pretty much equally rigorous

in the sense that there aren't any facts that will be used that you have to take on faith in these books

[remote sparrow]

umm ackshually axler explicitly says that the real and complex numbers will be assumed and not constructed

🤓

[fluid bay]

true 🤓

[gray gazelle]

Hi, can someone recommend Analytic Geometry book please?

[narrow relic]

Does this book properly do the "square brackets" thing for adjoints or whatever?

I remember glancing over it and thinking it over-simplified things

[gray gazelle]

Set theory by jech

[proud lantern]

Any pdf book that covers the first year linear algebra in university? I can't find any book to buy in pdf as I have impaired vision. Especially ones in Swedish

[hard beacon]

hmm maybe this will help more: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/

https://ocw.mit.edu/courses/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/pages/differential-equations-and-linear-algebra/

[proud lantern]

I looked into it and it seems like my father has an old copy of the book used in the lectures by Professor Strang. I think I might be able to cover it by watching the books and zooming in on the questions with my phone. Thank you ❤️

[hard beacon]

complex analytic variety?

[sinful otter]

you guys have any book recommend for getting in myself into learning math?

my native langauge isnt english and I have no idea what or where to start studying math in english

[gray gazelle]

What grade are you in?

[sinful otter]

emm... I dont know xD

for me, it's 2nd year of high school here.

[gray gazelle]

alr so that's 10th grade/sophomore

you're studying geometry currently?

[sinful otter]

em...

i just finish my 1st term of school.. yea.

i did study vector in 3 dimiansion, complex number and trigonometry at school

[stable dagger]

what is good algebraic geometry book for complete beginner?

I'm not good at manifold theory yet

[marble solar]

Fulton's Algebraic Curves

[hybrid sparrow]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[wooden frost]

is there any publisher that have good problem books in different mathematic fields like geometry number theory algebra and what not (for high school students ofc)

[gray gazelle]

Just the thing they cover in normal Calculus book, but M curious whether there are books that cover that specific topic extensively.

[quick hornet]

analytic geometry as in geometry with coordinates?

any form of geometry that is

• not topological
• not euclidean geometry
  will count

"analytic geometry" is kind of a weird label for that reason

maybe you have linear algebra in mind though?

since really analytic geometry as presented by calculus courses is the geometry of ℝ^n

which is a topic in lin alg

[crimson leaf]

For high school you could check out Lang's Basic Mathematics, it covers all of these topics though it is a bit more rigorous than maybe you'd be used to, worth the read though

[gray gazelle]

Apologies, should have given more info. Currently, m taking Calc 1, and during my pre-calc, I was really weak in Parametric, Parabolas, Ellipses..... I was using Stewart's book at the time. So, I hope there are books that cover that topic extensively.

[neon tiger]

book on integration for practice with a lot of questions

[pale scarab]

Paul J Nahins integration book is good and a bit easier. You could always search through math stack exchange also they have some really wild ones.

[neon tiger]

this is really advanced i need more elementary high school level stuff

[gray gazelle]

Anything for 3d geometry and combinatorics

[gray gazelle]

there are not much differences between edition 2 and 3 right?

[gray gazelle]

just read books in English and your (written) English will get better

[neon tiger]

can someone please suggest something for this

[terse heron]

JEE Advanced previous year questions on Integration

This one

Or this one (if you really need some tough questions)

[terse heron]

Oh

Then I'd prefer this:- Cengage, it has lots of problems, from very basic to the very advanced level, all were graded

[neon tiger]

g tewani

ok

[terse heron]

You'll buy or download the pdf?

[neon tiger]

pdf

[terse heron]

Ok

[blazing wharf]

You giving him jee advanced in the name of elementary

At least jee main

Blackbook

[terse heron]

Bruh

[blazing wharf]

U gave him like it's nothing

[terse heron]

Cengage has elaborative theory

It has basics covered

[blazing wharf]

That I agree

But elaborative is a wrong term

It's good for like if you already know the basics

[terse heron]

Caution:- Don't get into JEE advanced exercises for now, Illustrations and Solved examples are sufficient

[terse heron]

You too preparing for JEE?

[blazing wharf]

Yeah

[terse heron]

Year?

[blazing wharf]

Umm me in 2024.

What about you

[terse heron]

Okk

2023

[blazing wharf]

Oh this year

[terse heron]

Yeah

[blazing wharf]

In January.

[neon tiger]

Actually I do so it's fine

[blazing wharf]

Ok

[terse heron]

What?

Bruh

[blazing wharf]

?!

[terse heron]

January?

Official date?

[blazing wharf]

Yeah main in January

[terse heron]

No

[blazing wharf]

Date idk

But month i know

[terse heron]

Atleast in Feb

[neon tiger]

I'm not even in 11th yet so I have no idea what you're talking about

[blazing wharf]

There is also a probality for april

[terse heron]

We're talking about an entrance exam

[neon tiger]

Are you guys preparing for engineering

[terse heron]

Yes

[blazing wharf]

Yes

[terse heron]

Yeah, I saw it from unofficial site

[blazing wharf]

I got to know from senior

Mean just asked him about the dates

[terse heron]

And I asked my junior about the dates

[blazing wharf]

Lol

[terse heron]

He told me in april

[blazing wharf]

But there is like practicals for state board. So they might shift it to april

[neon tiger]

What you guys gonna do after doing engineering

[blazing wharf]

Going for job hunting

[terse heron]

Become engineer kekw

[blazing wharf]

Actually company will hunt us

If we cracked

[terse heron]

I'll go for research prolly

[terse heron]

Oh, which state?

[blazing wharf]

I mean mostly all states having

You asking which state i am from

[terse heron]

Yes

[blazing wharf]

UP

[terse heron]

One of the toughest state boards right?

[blazing wharf]

Yeah

It was

Actually during my parents era

Rn i don't know it's state of difficulty

[terse heron]

You'll qualify for jee even if you get 69% or above in 12th

[neon tiger]

How much was your 9th percentage

I want to compare

[blazing wharf]

Which board

[neon tiger]

Cbse

[blazing wharf]

I am not of state board

I am of ICSE

[terse heron]

Oh

[blazing wharf]

Me got 90 in 9th

[neon tiger]

Are you aiming for iit

[blazing wharf]

Yeah

[terse heron]

Scored 100/100 in 10th maths (;

[blazing wharf]

Hood

[terse heron]

Yes

[neon tiger]

Ooh

[blazing wharf]

Good

Don't ask my 10th marks

[terse heron]

But now my jee maths is screwed

[blazing wharf]

Lol there is a difference in jee math and board meth

[terse heron]

Doesn't matter for jee right?

Now tell

[blazing wharf]

Yeah doesn't matter

Just get above 75% in 12

And ur done

[blazing wharf]

Nah

It is of no use

[terse heron]

Ok

[blazing wharf]

Which state you from

@terse heron

[terse heron]

AP

In hyderabad

Telangana actually