book-recommendations

[tulip blade]

Ive spoken two to grad students that came wanting to do algebraic complexity theory but switched bc its too hard🤣

[mossy flume]

lol

I'm taking a models of computation course that's working through Sipser rn

And I'm taking a graduate level algebra course rn

So

Looks to be a good thing to look further into both at the same time

[gray gazelle]

does anyone know any algebra book for math olympiads?

[tulip blade]

Its definitely a good thing to look into. Im js the field is notoriously difficult research wise. If you plan to do tcs then itll never hurt to know more algebra/ complexity.

Who knows maybe youll make a big break through. Someone has too.

[hasty turret]

What is complexity exactly?

Stuff like big O?

[mossy flume]

Sort of yea

[tulip blade]

Big O is just notation thats used in all areas of math

[mossy flume]

So study of time and space needed to run certain algorithms

Decidability of some problems

[tulip blade]

Complexity just classifies computable problems by their inherent difficulty

[hasty turret]

I don't know if I should try complexity theory. I have found complexity extremely boring in my classes

[mossy flume]

An interesting type of question is "can I reduce this problem to this other problem which we know is hard and so this first problem must also be hard"

[hasty turret]

Idk if my classes suck or if I am genuinely uninterested

[mossy flume]

What text are you using?

[tulip blade]

Then read ab it and see if you like it

[mossy flume]

What kind of material have you learned

Sipser is a great intro TCS text

[mossy flume]

Leaning more to the Algo / TCS side yea

[hasty turret]

Well,Nothing actually. I have no idea how complexity even works. My experience is CLRS and that turned me off from algorithms for a long long time

[tulip blade]

Also see the book called introduction to theoretical computer science by boaz barak.

[mossy flume]

CLRS is shit

It's a reference manual at best

[tulip blade]

^^

Jeff erikson is my goto algos book

[mossy flume]

Yessss

Erickson's text is great

I actually took algos under him last semester

And will be doing another course under him next sem

What an amazing professor

[tulip blade]

Ya i figured youd like it i remember you saying you go to uiuc

The book really seems to have pedagogy in mind.

[mossy flume]

http://jeffe.cs.illinois.edu/teaching/algorithms/

Amazing writing

[tulip blade]

Clrs is boring imo

[mossy flume]

Ye

I'd read through this

That's more an algos text

I'm working though Sipser for a models of computation course rn

And thats also great

[mossy flume]

Can't go wrong with either and I'm sure this text is good also

[hasty turret]

Ok this somehow just changed my whole perception of algorithms lmao

This actually seems useful

Like not just a bunch of algos you can look up at anytime but actual content

Why is CLRS even popular anyway

It's just a "lookup table" in the form of a book

[mossy flume]

I've got no idea

[stray veldt]

CLRS has pretty good exercises tbh

[devout sphinx]

Looking for a bunch of non-challenging exercises (short proof/computational) in multi variable analysis. From change of variables to differential forms.

It looks like Multivariable Mathematics might fit the bill

But I’d be open to other suggestions

[gray gazelle]

Does anyone know a good book (like Stewart for calculus) on Linear Algebra? A plane geometry book? Geometry in three dimensions?

[smoky zephyr]

maybe linear algebra done right

a lot of people use it for linear algebra

[gray gazelle]

Yes thats a good one covers the topics i need thanks

You know any good vector and fourier analysis book?

[smoky zephyr]

no

[silver jasper]

looking for recommendation to Tensor products
I am studying lattice-based cryptography in mathematical point of view

[stray veldt]

don't know what generality you need, but you can try the tensor product chapter in gathmann's comm alg notes

https://www.mathematik.uni-kl.de/~gathmann/class/commalg-2013/commalg-2013-c5.pdf

[slate quarry]

Regarding plane geometry, I've studied from Lang & Murrow: it's a pretty good book and I love it, but if you are looking for something more advanced, maybe is not the best option.

[gray gazelle]

That looks like a good foundation

But does it include geometry linear transformations of planes etc?

Or do I find that in a linear algebra book?

Geometry with matrices and 3d

Not sure what book fits that

[copper stratus]

any book recommendations for multivariable calculus, specifically for physics?

[gray gazelle]

Stewart's Multivariable Calculus?

[deep knot]

Hi, do you have philosophy of maths recommendations for me? I'm not as familiar with the literature as I'd like, though based on some half-baked memories, I know I'm sympathetic to an anti-Platonist stance

[stray veldt]

for a brief overview, you can read shapiro's thinking about mathematics

[gray gazelle]

Tan's Multivariable Calculus

[analog dock]

hi does anyone happen to know where i can get a cheap copy of spivak's calculus?

[gray gazelle]

Amazon

[lime sapphire]

tfw $100 is cheap

[gray gazelle]

Tfw?

[runic hatch]

Math books usually seem pricey

Maybe try searching for second-hand versions

[grand thistle]

second hand r much cheaper yeah

[undone ferry]

hi
i'm a self taught web dev
what is the best books or topics that i should read and understand to be better developer ?

Thanks in advance

[pulsar geode]

does anyone know of a good standard differential equations book with geometric/graphical intuition?

[slate quarry]

You can look at the table of contents here: https://www.amazon.com/-/es/Serge-Lang/dp/0387966544 I'm sure it will clear off your doubts.

[marble solar]

Don't use Stewart for MVC ~ Thomas' University calculus is pretty good

[gray gazelle]

Sadly it dont

[iron granite]

Is Lang's Linear Algebra sufficient or even good?

[gray gazelle]

Velleman philosophies of math ig

[tame plaza]

that feeling when

[placid pollen]

Opinions on these, which is better for an advanced Math undergrad? The first looks like it has better reviews, many said they know many books but this is their favorite introduction. The second has almost as many positive reviews and seems to me a little more advanced but maybe I'm wrong.
https://www.amazon.com/dp/0486613887 (Flanigan Complex Variables)
https://www.amazon.com/dp/0486646866 (Silverman Introductory Complex Analysis)
Would also welcome a recommendation that isn't expensive, so no Ahlfors, Gamelin or Lang. Those I'd rather read electronically until they have a reasonable price.

[fluid bay]

stein and shakarchi's complex analysis is free, and pretty commonly used

[timber mesa]

how is it (legally?) free

[fluid bay]

The pdf comes up on google search => legally free

[smoky zephyr]

this but kinda unironically

[gray gazelle]

http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf

Im about to finish this and I want to read serge langs basic mathmatics where should i start there

[gray gazelle]

Can i start Rudin “Principles of Mathematical Analysis” before calculus

[quick hornet]

yes, but it'll be harder.

you won't have intuition for much and the constructions will seem unmotivated

i'd rather recommend a more readable mid-ground like spivak's calculus

rudin is a great reference but not very pedagogically sound

but if you hate yourself, it's technically doable.

[weak violet]

what would be a real analysis book that is pedagogically sound

[quick hornet]

well basically anything is better than rudin lmao

everyone has their own hot take there

tao, abbott, whatever

[gray gazelle]

Zorich

[hasty turret]

rudin is better than rudin

[frosty girder]

apostol da best

[runic hatch]

They all have their own styles

[gusty smelt]

I like rudin the best lol

it was the book i learn analysis from

[runic hatch]

I’d recommend searching online for a preview of the usual recommended books and seeing what works best

[gusty smelt]

idk i think after u get through ch2 things are pretty alright

[gray jungle]

have seen browder analysis book being mentioned around

i mean people criticize tao a lot to spending too much time on set theory and reals contruction and not doing as much analysis but its honestly a great gateway to something at the levels of rudin if you are not familiar with abstract math , it helped me get some solid foundation and i enjoyed the exercises and the proofs he left and i just think its a great intro to analysis pedagogicaly as opposed to something much more unmotivated like rudin which i used more as a reference for alternative proofs and nice exercises in my 2nd analysis course and from my own experience i felt much more comfortable tackling metric space analysis after doing a good chunk of tao.

again in not an expert but thats my own experience

but take in mind i went into uni not knowing much calc
so if you are a bit stronger you can jump into something more throughout

[modern stone]

How comprehensive are Paul’s Online Notes?

[mystic orbit]

thanks for letting me know

[rapid lily]

I like those notes I used for Calc III and some linear algebra

covered everything that I covered in my actual class so I’d say comprehensive enough

[night prism]

Outside of scope of coverage, I think it’s mostly where texts lie in a spectrum of how much you want the author to “teach” you, and (on the other hand) being presented a minimum and discovering much of the subject matter yourself (through exercises or filling gaps)

[modern stone]

Nice

[runic hatch]

Yeah his notes cover quite a bit of material

Seems like the usual stuff for first/second year calc 1-3 + some ODEs

[modern stone]

So it’s enough to learn the theory for single variable and multivariable calc?

Or should I supplement it in this regard with something else

?

[gray jungle]

i like the mit lectures for mvc

[rapid lily]

Yeah you could learn from that sometimes though I wish Paul’s online math notes had more problems but it is easy to find more problems once you know what kind of problem it is

[hollow spoke]

Anybody would like to give their reviews on Zeev Nehari's complex analysis? I am going to read this book, but before that i would like to know about this

[modern stone]

These ones?

https://youtube.com/playlist?list=PL4C4C8A7D06566F38

[gray jungle]

yes

[modern stone]

For single variable calculus what would you recommend in terms of video series?

[gray jungle]

haven't used 1 so i wouldn't know

[foggy relic]

3b1b and David Jerison are good

[subtle mango]

khan is also good for calc 1 and 2

[modern stone]

Nice

[modern stone]

Would I need to supplement it with something else?

[subtle mango]

imo no

[modern stone]

Or do I simply need to do a lot of problems?

[subtle mango]

khan provides plenty

[modern stone]

good

[gray gazelle]

book for beginner number theory

[jade tendon]

Any good recommendations for books on Euclidean geometry built from the axioms?

[quick hornet]

from my personal experience, i have not seen any better sources than an annotated version of Euclid's Elements

which really seems like it should be the wrong answer

but to be honest, axiomatic euclidean geometry isn't really actively pursued (it's mostly a solved field) and is more of a thing studied for historical interest nowadays

[devout sphinx]

I really like the byrne edition

it's colorful

https://www.c82.net/euclid/

the website is super slow

I remember I read planimetry by kislev in high school and liked it

[jade tendon]

Interesting. Would you recommend anything on top of some linear algebra, p.s. topology, and group theory as prereqs for non-euclidean geometry?

[quick hornet]

"non-euclidean geometry" is honestly kind of a broad term by modern standards lmao

"most" geometry is non-euclidean, we generally sort mathematical geometry by what "parts" of the geometric structure you care about

that said, that should be sufficient though knowing some analysis would help

intro analysis is kind of the "euclidean analogue" of a lot of the things you'll see in other parts of geometry

in the sense that it's really the study of limits, continuity, and convergence in euclidean space

[jade tendon]

Okay perfect. I've covered limits, continuity, and convergence in R^n thus far, starting on differentiation soon. Many thanks

[sinful ibex]

Give me a good tutorial to algebra and theory of numbers to olimpiad math

Im scholer

I have workbook to it, but i cant solve eq from this

Like for this

"intro to an algebra and theory of numbers" for school olimpiads or smth like this

[manic cape]

Any recommended texts or lectures for commutative algebra?

[stray veldt]

i like gathmann's notes, freely available https://www.mathematik.uni-kl.de/~gathmann/de/commalg.php

very down to earth, but not as extensive as most books i guess

[flint bay]

what are people's favorite category theoretic treatment on algebra

for reference

[flint forge]

I think aluffi is basically the only one

[flint bay]

yeah i figured

my algebra courses for my first/second/third pass were all from dummit and foote lmfao

[modern stone]

Thoughts on the book Topology through Inquiry?

[timber quail]

still interested?

@swift dagger
You can start with this article : https://arxiv.org/pdf/1710.04019.pdf (its short but it will take time because it doesnt include all the details, so you might want to check references)
Then this book : http://yusu.belkin-wang.org/CTDAbook-DeyWang.pdf (the book is a bit advanced, but the first 60 pages will give you the basics)
I personally recommend watching some videos about the topic to have an intuitive understanding before tackling the books.
If you are willing to code too, working on real data , I have some links

[atomic hound]

So, good book on type theory,would ya?

...

....

...

[tardy walrus]

…

[frosty girder]

...

[grand thistle]

...

[jagged ginkgo]

Can a continuous polynomial function also be a piece wise function

[quick hornet]

[f(x) = \begin{cases}x^2 + x & x \geq 0 \ x^2 + x & x < 0\end{cases}]

[hasty eagle]

Namington

[smoky zephyr]

[novel obsidian]

how do we determine whether a field is "solved"?

[quick hornet]

producing an algorithm that solves it is sufficient

and tarski did exactly that

[novel obsidian]

I don't know what "solve" means in this context

[quick hornet]

i.e. given a statement expressible in euclidean geometry (using tarski's axioms), there exists an algorithm to determine in finite time whether that statement is true or false.

you just follow the algorithm

no cleverness necessary

[novel obsidian]

That makes sense

[quick hornet]

now tarski's axioms aren't quite full plane geometry (there are various unsolved tessellation problems, for example, as well as the famous moving sofa problem)

but they describe most of it, in that they axiomatize the kind of constructions the field of "euclidean geometry" talks about

[novel obsidian]

do you think this is possible in other areas of math?

[quick hornet]

by Goedel's incompleteness theorem, it's not possible in general

but it can be in specific cases

decidability is an important topic of study in logic/computability/model theory

famously, the theory of real closed fields is decidable

which is considered a very important fact by people who care about this stuff.

[novel obsidian]

mhm, thanks

[sterile remnant]

Hello everyone, I hope this is the appropriate channel to post (since the end purpose is to ask for textbooks)

I'm studying physics (in my 3rd out of 5 years for my integrated masters degree) and I'm looking to solidify my advanced math background, since I want to go for theoretical physics but we don't have any advanced mathematics classes.

My background is:

• Linear algebra (2 classes, 1 basic one and 1 on inner product spaces, Jordan forms, quadratic and bilinear forms)
• Analysis (To avoid confusion(?), more formalized calculus e.g sequences, limits, continuity, differentiability, integration and series. Nothing about metric spaces etc that I believe is part of a Real Analysis course)
• Multivariable Analysis (Again, differentiation and integration in 2-3 dimensions with all the relevant theorems)
• Ordinary Differential Equations
• Partial Differential Equations (We followed Strauss' textbook)
• Complex Analysis
• A 1-semester course in Algebra (Basic Finite Group Theory only)
• Possibly some elements of other fields that were included/mentioned in the above

I am interested in/want to learn:

• Differential Geometry
• Topology/Algebraic Topology
• Lie Groups/Lie Algebras & Representations
• Functional Analysis
• The prerequisites I'm missing for the above!

I'm looking for textbooks for the above subjects (prerequisites first!) that aren't too rigorous since I'm not especially good at following complicated/abstract and I'm definitely not at a level where I can attempt to do any of them on my own

It would be nice if the textbooks had come chapters/units dedicated to applications in physics. I've found that the various texts that are offered to physics students condense the mathematical background needed too much and only use the absolute essentials, which isn't something that I prefer.

Finally, an example of a book of the likes I'm looking for is Naive Lie Theory by John Stillwell, which I've found to be great in giving insights about Lie theory

[swift dagger]

I did my minor in CompSci so yeah coding with real data might be a big help. Thanks for the links I'll give them a read when I get the chance

[slow roost]

You can probably start reading Lee's Introduction to Topological Manifolds as your first taste of topology with an aim toward differential geometry

the next book Intro to Smooth Manifolds covers lie groups and lie algebras (among many other topics)

and the final book does riemannian geometry

all three are superb

if Lee's topological manifolds is too tough an intro to topology, try Munkres

[sterile remnant]

I'll look into those, thank you for the recs!

[patent mango]

What are some good books for Matrices and determinants? Like it should contain everything about it and more problems too.

[karmic thorn]

Any textbook designed for a first course in linear algebra that is not Axler's Linear Algebra Done Right would be fine. Strang's book might be good if you want to get a good grasp over the computational aspects and lots of problems.

[patent mango]

for high school

is it good?

[karmic thorn]

Wouldn't hurt but be selective about the aspects you want to emphasise in case you have time constraints

It is accessible conceptually

[gray gazelle]

what are some good books to read during pursuing a computer science & math bachelors degree?

to get a better understanding of calculus/linear algebra/discrete maths, doesnt necessarily need to be only on 1 subject

im currently reading Cracking the Coding Interview which is brilliant but i need something more mathematics-oriented

[timber quail]

I worked on a project of TDA with deep learning
It depends on which language you prefer, there are packages in Python, R, and C++
I personally recommend python
For the packages,I think two are very useful gudhi, and ripser
Then if you want more advanced applications we used persistence diagrams (from gudhi and ripser) with deep learning (with keras)
If you are familiar with deep learning there is a layer called Perslay that helps you use the persistence diagrams (from tda ) directly.
In this github repository https://github.com/RandomAnass/TDA-DL
You can see first the notebook TDA_DL_report_part1 (its like how we learned), each time an object is defined (mathematically ) then used in a python code (you can also open the link in Colab -the first link- and execute the code yourself or edit it ...)
For the application (if you understood the meaning of TDA tools) you can see the notebook Results_TDA and replicate the same process on a set of data of your choice.
Some tutorials we were inspired by are in this link http://bertrand.michel.perso.math.cnrs.fr/Enseignements/TDA-Gudhi-Python.html
And for the package ripser you can check this : https://ripser.scikit-tda.org/en/latest/notebooks/Basic Usage.html
If you have a question about what's in the repository you can dm me

[atomic hound]

Type theory

[atomic hound]

Type theory

[atomic hound]

Type theory

I need a book on type theory

Really good book

[vernal dagger]

any good book on commutative algebra?

i'm looking for one that doesn't assume so much on ring theory

[pseudo forge]

Why is that book so hated on lol

[stray veldt]

https://www.mathematik.uni-kl.de/~gathmann/en/commalg.php this is pretty low tech

[pseudo forge]

We use it in our proof based linalg course

[stray veldt]

because axlers opinion on determinants is wrong

and well, the question specifically asked about determinants, so ...

[pseudo forge]

lolol

I was gonna take that course

The prof loves Axler's book

[flint forge]

I mean the question was literally about a good way to learn determinants

axler's book is probably one of the worst ways to learn about determinants

regardless of whether you like his approach or not

[stray veldt]

the book is good and in an actual class the professor can provide different sources for determinants making up for that quirk

[pseudo forge]

true

[brittle breach]

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

this is good for linear algebra, it is designed for first years so is accessible.
it has a nice chapter/appendix on coding theory

it seconds as a way to get better at proof written as well

[brittle breach]

and since you're a math major
I like Loring Tu's "Differential geometry"

[sly gale]

Anyone know of good reading over the geometric proofs behind quadratics and cubics?

[atomic hound]

Anybook on type theory?

[robust mortar]

https://www.goodreads.com/en/book/show/112252.Types_and_Programming_Languages

[wicked sluice]

I like Atiyah and Macdonald if you’re looking for something introductory. It’s kinda pricey, but there’s a pdf online. Chapters 2,5,9 are really nice imo

[void dragon]

this as well?

i'm pretty sure thats completely wrong

also why does the "s" sometimes look like "f" without the "-"

and sometimes it looks normal

[sudden kindle]

Yeah

[void dragon]

bru its basic plane geometry

why the integral

rather unfortunate

i would've preferred if they labeled points and referred to lines as AB or somehting

rather than the colours

[grand thistle]

😶

[edgy cradle]

are there some good books on numerical analysis

that focuses more on proofs than applications?

[split basin]

https://link.springer.com/book/10.1007/b98885 maybe this one?

[karmic thorn]

Numerical Analysis by Burden includes proofs of almost all results to the extent I can recall, and is pretty good as a textbook.

[hearty steppe]

Is that like a necessary book to read you think? Lots of people seem to not care about numerical methods

[atomic hound]

finally, someone give a book recommendation, thanks strexicious, pal. i would give you one dolor if know you

[north heron]

Hello, starting first college year in some months ( math, cs ) any book focused on natural number ( with a lot of combinatorics, arithmetics, etc... ) ? is douglas graph theory book very close to my search ?

[tulip blade]

I dont understand your question. What do you mean focused on natural number?

[gray jungle]

not sure if you want a discrete math book or a set theory book

[north heron]

hmm, discrete math book

i guess

[gray jungle]

probably concrete mathematics

[tulip blade]

I agree with @gray jungle that concrete mathematics is a good book. That will provide a solid background.

[north heron]

by Ronald L. Graham ?

[gray jungle]

yes

[north heron]

thanks

[glad prairie]

i have the physical copy of this

it's great

[tardy walrus]

RYC

[modern stone]

Is Linear Algebra Done Wrong a good choice for a textbook in linear algebra?

[wispy garden]

Does somebody have an good number theory book for beginners ? More oriented towards competition math

[modern stone]

yeah, it’s a reference to Axler’s Linear Algebra Done Right

How comprehensive is the book?

[livid ermine]

Computability and Logic George Boolos, John P. Burgess, and Richard Jeffrey

Have anyone read this?

Is it fine to read if you don't know that much logic from beforehand?

[gray gazelle]

What’s the differences between Rudin’s Blue Book, Green Book, and Red Book?

[forest sleet]

not sure about the colors, but Rudin Principles of Mathematical Analysis is undergrad analysis, Rudin Real and Complex Analysis is grad analysis, probably the 3rd is Functional Analysis?

i think real and complex is green maybe

i thought the other 2 are both blue though

[gray gazelle]

One is for babies, second is for papas, and third is for grandpas

[scenic sand]

The whole point of this site is that it's "A reproduction of Oliver Byrne's celebrated work from 1847" (i.e. his edition of Euclid's Elements) so as far as I'm aware none of it is original; also, the whole point of Oliver Byrne's book was that it makes Euclid's treatise, which was taught for millennia by then, more intuitive by swapping out words (e.g. "line AB", "angle a", or "triangle ABC") for their graphical representation (which you would've translated the words into anyway, either physically or mentally).

[scenic sand]

it's called a 'long s'. It used to be used anywhere before the end of a word

[void dragon]

thats interesting but what is it's purpose

ohhh ty

[scenic sand]

example

[void dragon]

so the last letter is normal

that's rather strange but ig it makes sense

[scenic sand]

Yeah, in most cases.

[void dragon]

mk ty

[scenic sand]

it's not an integral symbol but the integral symbol does come from it. The integral symbol is based on the word "sum" (written "ſum" back then or "ſumma" in Latin with the long s convention).

Σ (sigma) is just the Greek version of S btw and it's also based on sum. The integral symbol comes from the word sum because they thought of it as a special kind of sum (which it is pretty much).

[slow roost]

the real question is why they distinguished between an s at the end of a word and anywhere before the end

[scenic sand]

I have no idea but if I had to guess it probably parallels the greek σ & ς (the two lower-case forms of s or sigma in Greek), in that it was just, perhaps, easier and faster to write the one at the end and the other kind in the middle as in Ὀδυσσεύς (Odysseus). Originally all letters were capital (majuscule) but penwriting made it desirable to have simpler, smaller, rounder forms which are easier to write (IIRC) and this is were or lower-case (miniscule) forms derive from. I'm pretty sure the long s came from the Latin cursive form for s that the Romans used to use so again, it might be just a thing about saving time.

[quick hornet]

this is actually an interesting linguistic question

they come from two distinct phonemes that were written with different letters but merged into one pronunciation

one of these phonemes almost always occured at the end of words

[scenic sand]

oh really? nvm then, lol.

[quick hornet]

we don't actually know exactly how these phonemes were realized though

we think probably /s/ and /ɕ~ç/ i believe

[scenic sand]

how do we know they existed?

[quick hornet]

glyph tracking

originally we just find ⟨Σ⟩ and ⟨ς⟩

⟨σ⟩ emerged specifically in certain phonotactical contexts at first (before rhotics and glides i think?)

in a way consistent with it being a different pronunciation

but this happened like, really early in the development of the greek alphabet and there wasnt just one "greek tongue"

different regions of greece had very different dialects

so it's difficult to determine exactly what was going on there

[scenic sand]

I see, very interesting. Latin/English was just mimicking the Greek though, right?

[quick hornet]

the Latin alphabet comes from the Etruscan alphabet, which itself was borrowed from Greek yes

[scenic sand]

Right, there's the connexion.

Sorry

I didn't mean to turn this into a linguistics discussion

[quick hornet]

in any case, yes, the "long S" that used to be used in latin alphabets traces itself back to the word-final sigma

and the integral symbol is a stylized version of that

[slow roost]

interesting stuff

is there IPA for that really nice pop sound you can make with your lips

like a cork popping

and more importantly, does any language actually use it

[quick hornet]

bilabial click?

/ʘ/

there are multiple different realizations

[slow roost]

I think I can do two distinct kinds

but it's hard to describe what I'm doing

[quick hornet]

https://enunciate.arts.ubc.ca/ʘ/

[slow roost]

hmm, that sounds much more clicky than what I mean

it's more like a bubble popping sound

[quick hornet]

ejective maybe?

https://www.youtube.com/watch?v=mfrAlv-5P1c (plays at 9 seconds in)

[slow roost]

oh yeah, that's pretty much it. Cool!

[quick hornet]

its present in georgian apparently

not in many other languages though

https://phoible.org/parameters/646674CE0AF099A6E69FB25363B53313#2/5.0/165.0 actually more than i expected

6% of languages

and its only an allophone of [p] in one of them (orma)

[crude sage]

How many exercises should one do when self-studying a textbook? Is it worth doing all of them, every other one, or maybe just the ones that look difficult? For reference, the book is Spivak's Analysis.

[grand thistle]

wait what spivak has an analysis book?

[slow roost]

I mean it depends what your goal is, how much time you have, etc

[crude sage]

Oh wait sorry it's Calculus lol

[grand thistle]

oh

[quick hornet]

this depends on you

no one will answer that question better than you can

but in general i like to skim exercises and attempt the ones that arent obvious

[slow roost]

yeah. I would definitely not recommend just doing every other one

actually read the exercises

[crude sage]

Fair enough, I guess I'm wondering if there's any obvious sort of minimum you'd need to understand the rest of the book

[slow roost]

some books put significant amounts of exposition in the exercises

[crude sage]

I haven't gotten far in the book (probably bc I'm trying to do too many), but it does seem to leave a lot of things as exercises

[frosty girder]

in general, it would be good to do the first few problems of each exercise, and skim the rest of them and see which ones u have no idea about how to even start it and do those

if u get some idea that some method will work, u can probably skip that problem

[frosty girder]

then it wont be bad to cover a lot of them

spivaks book is a semi analysis book, and hence the problems arent too easy

(i havent done much of it, i just have heard people say this)

[runic hatch]

Yeah his problems can be tough on a first go

[modern stone]

Is Stephen Abbott’s Understanding Analysis a good choice to learn analysis from?

lol

[livid ermine]

Have anyone read the book computability and logic by boolos and know how much logic you need to read it?

It says it's an intermediate course, but also that it's accessible to people outside mathematics

I only know the basics of logic, so I wonder if I should read some traditional logic text first

[wheat prism]

probability theory books?

[proper lotus]

introductory or graduate?

Also you can start with searching this channel

[wheat prism]

intro though i do have analysis

[proper lotus]

probabilitycourse.com

[edgy cradle]

btw is there 'graduate' version of multivariable analysis?

just like rudin is for undergrasduate single variable analysis

and stein is for graduate real analysis

[grand thistle]

isn't that what differential geometry and like manifold stuff is basically

[robust mortar]

probability jim pitman

[gray gazelle]

Depends on in which direction you are willing to go

Because what about functional analysis for example

Measure theory is also a good chunk of analysis

Maybe that's too much of a tangent

[edgy cradle]

https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-v/dp/0387905189

my school uses this textbook for first course in abstract algebra for undergraduates

along with dummit& foote?

is it possible? I mean the book is in gtm

[slow roost]

it's a pretty challenging book

but it's possible

they'll probably only cover the more elementary sections

D&F and hungerford though... that's kinda weird

D&F is already more than a first course can possibly cover

[edgy cradle]

tbh my school is like way too demanding

let me search up the syllabus

these are the topics for first semester

[slow roost]

nice

some of those topics I only got to in my grad algebra series

[edgy cradle]

actually syllabus for analysis is more ridiculous

[slow roost]

also, banach-tarski in an algebra course? wha?

[edgy cradle]

they cover chapter 1~8 of rudin in first semester

and 9~11 in second semester

[placid pollen]

God I wish that was me

[edgy cradle]

dunno what that is but sounds scary

[slow roost]

it's about measure theory

[tame plaza]

https://youtu.be/s86-Z-CbaHA

yeah, quite scary

[placid pollen]

boys, should I get Sheldon Axler's Measury theory book or Papa Rudin?

[edgy cradle]

i'm not in position to recommend cuz im freshman

but all my seniors absolutely hated papa rudin

[placid pollen]

sorry didn't mean to answer that; if I must answer I'd say those are the weakest chapters of baby rudin

I mean Sheldon Axler's looks easy, but because of that he covers less topics and I kind of like getting stuck and writing the intermediate steps with rudin

[edgy cradle]

https://www.amazon.com/Real-Analysis-Measure-Integration-2014-08-12/dp/B01JXWV1KS

i've heard good thigns about this book

https://www.amazon.com/Real-Analysis-Integration-Princeton-Lectures/dp/0691113866

and this one too

[placid pollen]

2expensive
Axler's comes in hardcover for 35USD

[edgy cradle]

i'd advise you to use lib/gen

[placid pollen]

oh stein's books look pretty good

[edgy cradle]

isn't axler free btw?

[placid pollen]

I have them downloaded

[placid pollen]

not a fan of reading at the computer

[edgy cradle]

do local print shopts reject printing them out for you?

[placid pollen]

Hm, I think I could get them printed and turned into a notebook

[edgy cradle]

yep thats my advice

just print out sections that you need

like don't print indeces and answer keys

[placid pollen]

Well regardless of that, I still have to choose between books that I have no more than superficial knowledge of their contents. So if someone has an opinion on Axler's Measure Theory vs Papa Rudin I'll listen. I think I'll get Axler's just because it's a cheap hardcover which is also colored

[manic cairn]

Lang’s measure theory book

[edgy cradle]

wait does lang have book on that too?

[manic cairn]

yeah

Real and Functional Analysis

[edgy cradle]

is it good btw?

ive heard that langs book on analysis was pretty good

[placid pollen]

I think Lang pretty much has a book for every subject in undergrad and first year graduate math

[manic cairn]

I love Lang’s style, and he reviews a bunch of point-set in the beginning

There are lots of exercises

[gray gazelle]

What’s a good site to buy springer math books for a cheap price

[tame plaza]

libgen

[cursive orbit]

springer mycopy

[fallen stream]

Curious George Builds An Igloo

[minor needle]

z-lib.org

[gray gazelle]

My nephew watches this show

[fallen stream]

Me george

[daring reef]

What's a good book for learning graduate-level real analysis a second time? I am taking a real analysis course this year that has mostly followed the material in folland (measure theory, radon measures, banach spaces, hilbert spaces, lp spaces, fourier analysis, etc.), but it was a lot of material that i dont think i will retain very well. what would be a good book for if I wanted to revisit the subject? (not folland pls)

[blazing canopy]

I do personally feel that Folland is one of the best, but otherwise you could try Knapp's book on analysis

[brittle breach]

Rudin

[daring reef]

im just scarred from folland unfortunately, will check out knapp and rudin ty

[blazing canopy]

one advantage of Knapp's analysis is that it's free online on his website. There are two volumes.

[daring reef]

oh sweet, there need to be more free books

wow this is a fat book but the table of contents looks great

[frosty dagger]

Lord of flies

Good book

[slim peak]

Springer via the MyCopy Softcover program

You need to log through your Institution's website

almost everybook will be available for 25$/€ and some for 40$/€.

[nova monolith]

hello!

ima copypaste my message

I have a question
lately ive been trying to learn math independently
and I know theres a lot of course on the web and yt
but i just dont know where to start
so
I was looking for some book recomendations 😄

[slow roost]

it depends what your level is

are you familiar with any proofs?

[nova monolith]

ok letme elaborate

[nova monolith]

p r o o f¿

[slow roost]

heh, guess that's a no

[nova monolith]

😦

hmm

[slow roost]

it's ok, just means there's a long road ahead

[nova monolith]

im not very advanced

currently

im studying trigonometric identities

:/

xd

[nova monolith]

i hope so

[gray gazelle]

The Bible

[nova monolith]

hmm

[slow roost]

for someone that hasn't gotten into proofs yet, a very readable book that gives a taste of what "real math" is all about is Timothy Gowers' Mathematics: A Very Short Introduction

[nova monolith]

oh that makes sense

just one more question

[slow roost]

but it's not like a textbook

[nova monolith]

well 2

i dont mind 🙂

[nova monolith]

why are "proofs" so important

[slow roost]

that's a good question

[nova monolith]

i mean

[slow roost]

we can get into all kinds of philosophy unpacking that

[nova monolith]

why is it the first thing that comes to your mind when asked

[slow roost]

but as a brief first answer, we want to be sure of the statements we claim to be true

[quick hornet]

the vast majority of higher mathematics is proving things

it's central

[slow roost]

yup

[nova monolith]

:0

[quick hornet]

the remainder is applied stuff that builds on what has been previously proven

[nova monolith]

okok so let me get this straight

we need to know how things are proven to understand them...?

or something like that¿

[slow roost]

no, not really

[nova monolith]

ok

im confus

[slow roost]

you can understand a statement and start using it without knowing the proof

the way people come up with actually new math is by doing proofs

all of the things you're learning in trig have been proved long ago

[nova monolith]

ohh

now im not confus

thankiu

but wait

just in case

what should i read after the very short intro to math

[slow roost]

umm

there's no objectively correct answer to that

most people that get serious about math learn calculus

so maybe you should work toward that

[nova monolith]

thanks!

[neat sonnet]

has anyone read gelfands algebra book? Thoughts for a beginner?

[neat sonnet]

Am I supposed to be able to read it and understand the problems without prior algebra knowledge?

[gray gazelle]

good books on probability ?

and statistics ?

[gray gazelle]

http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf Take this

[neat sonnet]

Can u explain why btw

Pls and thanks

[gray gazelle]

You do not know algebra so read some algebra

[gray gazelle]

Very simple and when your done read this https://www.docdroid.net/K1VENuF/basic-mathematics-serge-lang-pdf for proofs and more

You should most likely use khan more though in case you do not understand the books

[tender cedar]

guys what do you think I should review before I take ODEs without having too much trouble

[rich sun]

There's not much prerequisites aside from real analysis and linear algebra

[slow roost]

integration

[tender cedar]

no way

[rich sun]

Eigendecomposition and Jordan canonical form maybe

[runic hatch]

Is this your first course in ODEs?

[fallen stream]

You should take a look at "Curious George Goes to the Hospital"

[runic hatch]

If it’s your first course then HS calculus should suffice

[tender cedar]

yeah

I've taken calculus already so I just wanted to review some few concepts and was wondering what would be better to focus on

[grand thistle]

that one may be too advanced

[sage python]

Even if it's not required I'd get linear algebra

Depending on how much time you've got

[hearty steppe]

Linear algebra is pretty important to have formality in. I’m making up for the linear algebra I didn’t learn at the moment

So don’t skimp out on it

[night prism]

Hey me too, sounds like we’re in the same boat

[grave thorn]

What prerequisites are required for karatzas and shreve (link: https://link.springer.com/book/10.1007/978-1-4684-0302-2 )?

[amber otter]

this is a bit specific but I need some help. I wanted to recommend How to Prove It: A Structured Approach (2nd edition) to a study group just starting in properly studying mathematics, but most people there are Brazilian and don't know English very well. does anyone know of a book, similar in content and quality but in Portuguese, that I could recommend these people?

[halcyon hornet]

Any Recommendations(Videos or Articles) for understanding and learning the Real Definition of limits?

[frosty girder]

Dr peyams videos, and BpRp's videos on the topic are very nice

[halcyon hornet]

Thank You.

Why Does Blackpenredpen Hold that pokemon thing on his hand?

[frosty girder]

its his mic

lol

[frigid flare]

If you have the Stewart Calculus book the section on ODE is a good place to start. Also any exercises with exponential functions or fundamental theorem of calculus.

[frigid flare]

What level?

[edgy cradle]

https://www.amazon.com/Ordinary-Differential-Equations-Universitext-Vladimir/dp/3540345639

i've heard that this is a very good book on ode

but pretty rigorous

[halcyon hornet]

OH WOw.

[tender cedar]

thank you so much

[gray gazelle]

Intermediate

[runic hatch]

Arnold's ODE book is excellent, but I would recommend reading it after learning some more math

[gray gazelle]

University level

[amber otter]

.

[frigid flare]

Ok maybe Degroot and Schervish…not pretty but it seems intermediate to me …not for the freshmen business student but a bit of a bore for a math grad

[edgy cradle]

would you consider real analysis to be necessary prerequisite?

[gray gazelle]

That's what im looking for , thanks !

[runic hatch]

I’d say having some analysis knowledge would be quite helpful at least

[livid ermine]

Have anyone read the book computability and logic by boolos and know how much logic you need to read it?
It says it's an intermediate course, but also that it's accessible to people outside mathematics
I only know the basics of logic, so I wonder if I should read some traditional logic text first

[feral light]

Hi guys, maybe who having books about works of Ramanujan?

[brisk sluice]

Knowing about Markov and martingale properties in a discrete time setting.

[grave thorn]

What about functional analysis?

or measure theory

[brisk sluice]

It doesnt look like you need to have a deep knowledge in any of those fields but its probably a good idea to know basic ideas of measure theory before doing anything further in probability

[worldly canopy]

any good books for starters?

[brazen estuary]

Does anyone know a good book about vandalism

Oh this is for math books mb

[worldly canopy]

wtf is wrong with you

[brazen estuary]

Wym

💀

[worldly canopy]

searching for vandalism??

[brazen estuary]

Yeah?

[grave thorn]

https://www.google.com/search?q=books+about+vandalism&rlz=1C1CHBF_enCA905CA905&sxsrf=APq-WBteXQdG6BMW8M9IsW8MFXxtaPf69A%3A1650946768589&ei=0HJnYqTLI6OqptQPjOGeWA&ved=0ahUKEwik87z977D3AhUjlYkEHYywBwsQ4dUDCA4&uact=5&oq=books+about+vandalism&gs_lcp=Cgdnd3Mtd2l6EAMyBAgjECc6BAgAEEc6BQghEKABSgQIQRgASgQIRhgAULkBWOAFYOkHaABwAngAgAF-iAHsAZIBAzAuMpgBAKABAcgBCMABAQ&sclient=gws-wiz

[worldly canopy]

nvm

[brazen estuary]

Hmm

Kaos vandals in motion seems good

Thanks

[gray gazelle]

Is there a online version of that how to win friends and influence people book

Preferrably free idk if thats a thing in book culture where there is just pdfs of books tho

[brisk sluice]

yes

[gray gazelle]

where

[cosmic rivet]

any suggestions for books that have problems testing aptitude

I mean logic and reasoning

[gray gazelle]

The bell curve

[cosmic rivet]

have you read it?

[gray gazelle]

No but i heard its good

[cosmic rivet]

can you approximate the number of problems

[runic hatch]

Pretty sure that’s not a book about problem solving

Seems to focus on discussing IQ (hence the title)

[cosmic rivet]

oh!

this is not what I am looking for

I mean to say a book having problems similar to those asked in general aptitude competitions

[runic hatch]

Maybe try the Art of Problem Solving book?

You could also search online for past papers

[cosmic rivet]

that's a good idea!

[runic hatch]

Yeah I’d say your best bet is to search for past papers for your specific test

[cosmic rivet]

do you have this book or you've only heard about it

[runic hatch]

For the book, I’ve only heard about it too

I’d recommend seeing if you can find a preview or online copy first before buying it

[cosmic rivet]

sure

thanks

[bronze nacelle]

I found it on libgen

[gray gazelle]

Is there any book/pdf that has questions on and explains:

Trigonometry (trig equations, identities) and algebra (inequalities, rational expressions, exponential eq)

Mainly similiar to gcse further maths?

[high agate]

http://mis.kp.ac.rw/admin/admin_panel/kp_lms/files/digital/SelectiveBooks/Mathematics/How to Study as a Mathematics Major - LARA ALCOCK.pdf

How to study as a maths major, useful should you be going from undergrad to grad studies

[frosty girder]

lara alcock has some more intro books i think

has anyone read them? how are they?

[flint forge]

not a book rec but does anyone know of a good source for like

not very hard calculus problems

i dont want to write them

[edgy cradle]

openstax? maybe

it has solutions

and most of the problems weren't as hard as stewart

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

btw i find this book wonderful

more rigorous and has more contents then abbott and ross

[runic hatch]

Paul’s online notes?

[edgy cradle]

but not as condensed as rudin

[flint forge]

I've been using pauls yeah

they have very thorough solutions which is nice

[edgy cradle]

https://openstax.org/details/books/calculus-volume-1

have you looked at this book

[smoky zephyr]

there’s a book called 3000 solved problems in calculus that you can find online

i would assume that they aren’t too hard

[edgy cradle]

do you mean schaum's outline?

[frosty girder]

pauls notes have some good problems i think

i can send many levels of calc problems if u want

(i basically have like lists of questions, that range from basic to hard to being annoying)

[gray gazelle]

can you kindly DM me hard to being annoyingrange of problems 😄 ?

[frosty girder]

i can send u the entire ones, the easy and the hard ones

which topics do you need

like, differential calc, integral calc, or diff equations

[gray gazelle]

no such choice ATM, i'd like to dabble with anything

[frosty girder]

(its still hs stuff so not too much variety)

[gray gazelle]

integral and diff equations perhaps then

[frosty girder]

okie dokie

sending in a sec

[gray gazelle]

thank you!

What books would you all recommend that would be considered the equivalent to Michael Spivak's Calculus but for Linear Algebra and Differential Equations?

[slow roost]

under what equivalence relation?

[gray gazelle]

In terms of how it proves everything and is very rigorous. Spivak has a certain style in Calculus, and I was wondering if there were books with a similar approach to linear algebra and diff eq.

[slow roost]

I like Friedberg, but it's not very big on the ODE side of things

but the treatment of finite dim vector spaces and matrices is rigorous and comprehensive

[gray gazelle]

What's the full title of the book/ full author name?

[slow roost]

Linear Algebra by Friedberg, Insel, and Spence

[gray gazelle]

Thank you!

[analog elbow]

hello

can someone recommend me a good topic about applications of numerical analysis methods?

[blazing canopy]

Can you elaborate further about your interests?

[analog elbow]

uhh idk maybe sth about the application of different methods like newtons method in different practical fields

[blazing canopy]

I ask because the applications of numerical analysis is basically "all of engineering and physics"

[limber tiger]

I'm doing my first number theory course next semester. Is there any books to recommend? The book we are using in the course is
Elementary Number Theory and Its Applications. Kenneth Rosen. 6th Edition; 2011 Pearson.

[timber mesa]

I like Burton's Elementary Number Theory

which seems to cover the same topics at a glance

[limber tiger]

Ohh i see

I'll make a note of it

[timber mesa]

another classic book is Niven-Zuckerman-Montgomery's An Introduction to the Theory of Numbers

which is a bit wider in scope and aimed at a slightly more advanced audience probably

[limber tiger]

Oh I see

I might take a read at that after the course if I'm still interested in number theory

I assume that it's pretty difficult for someone who don't know about number theory before right?

[timber mesa]

it covers the same basic stuff at first really

divisibility, congruences etc

there are more advanced books of course but by then you'll want to grab a book in either algebraic NT, analytic NT or any other specialized topic

[slow roost]

have you read Hardy's Introduction to the Theory of Numbers?

it's really old, wonder if it's still worth using as an introduction today

[limber tiger]

Ohh I heard of the author

I'll also put that on the list

[timid pier]

hello guys

i am in need of assistance

I'm trying to find a calculus textbook that can supplement my other two books that i bought

https://cdn.discordapp.com/attachments/961070650724851722/968381409716764672/PXL_20220426_052051891.jpg

so i consider this as supplemental
and im lookin at these two as possible main books

https://cdn.discordapp.com/attachments/961064331380928543/968741627508191232/unknown.png

not sure tho
ive read that stewart and spivak are long winded in explanations...

pls help

[slim nacelle]

Stewart is standard, also don't waste money buying books unless you have a very good reason for needing a physical copy

[timid pier]

oh

[timid pier]

ill stick w these two then

@slim nacelle

someone else told me that i dont need a textbook for examples and explanations

and i can i just go on the internet

[slim nacelle]

I mean sure all the material is so standard that it will be on the internet in various places

also appears in texts like Stewart and so on

Openstax has an open source calculus textbook that is reasonably good if you don't feel like pirating textbooks

[timid pier]

whoa

wots this

ya i dont feel like pirating

oh wow

i love this

thank u so much @slim nacelle

imma use openstax along with my two minibooks

[runic hatch]

If you’ve got access to a university library I’d check there first if you do end up wanting a physical copy

[timid pier]

good plan

[leaden cloak]

Anyone got any recommendations for an introduction to differential geometry?

[slow roost]

how much background toward it do you have?

Elementary Differential Geometry by Pressley is a nice concrete intro

if you want to get right into calculations about curves and surfaces

if you want to learn manifolds, Lee's books are great

[merry moss]

calcuuu starter kit

[timid pier]

yessir

[leaden cloak]

LinAlg and Analysis I'd expect to be the relevant ones. I don't really like books that have exercises that are basically calculation problems; I much prefer to prove some more general stuff.
Sounds like Lee's book would be a pretty nice fit.

[slow roost]

yeah you should be fine to jump into Lee. There will be some topology needed, but you can learn it as you go

[rapid token]

What should I read after finishing Understanding Analysis by Abott?

[foggy relic]

I would also recommend Pauls Online Notes

[gray gazelle]

Has anyone read Tom Apostol's Introduction to Analytic Number Theory or Daniel A. Marcus' Number Fields? Are they any good?

[fluid skiff]

They are great

[gray gazelle]

Pros and cons? Which ones are better? Are there better books than them on their respective subjects?

[fluid skiff]

Pros of apostol is very friendly

Cons is it doesn't cover much

So you may find tenenbaum book better in some ways

Same pros and cons with marcus

Alternative is Janusz Algebraic number fields

[gray gazelle]

Thank you!

[sly mist]

Any book recommendations for a first introduction to linear algebra? I have tried 'Linear algebra done right' by Sheldon Axler, but it has been too difficult for my current level of understanding.

[subtle mango]

linear algebra done wrong is a popular choice for a first course on linear algebra

[sly mist]

thanks

[icy ginkgo]

there is a way to print a book,comes very handy and comfortable

[alpine gate]

Hey!

So I just impulsively bought two books, those of divulgation from National Geographic

Does anyone know if they are any good?

Obviously Im not expecting a deep level, just want to know if they are interesting and well-structured for a panoramic view of certain topics

I bought the ones bout Hilbert and Cantor in case anyone knows them

nvm seems like theyre just a thing among spanish speakers

[tame plaza]

did you download them?

[brittle breach]

Loring Tu

I prefer his books over Lee's

[timid pier]

Yes

[copper stratus]

what do you mean?

[tame plaza]

if you have constant internet connection I don't really see a point of doing that since the PDFs aren't as up to date compared to just reading them on the website

[timid pier]

I read them on the website

But I just have it downloaded just in case

Lol

[runic hatch]

I mean it’s still good in case you want offline access anyways

[timid pier]

Ya

[runic hatch]

E.g. if you’re on the train and can’t get internet there

[timid pier]

yeah

[frosty girder]

friedberg insel and spencer is nice

[icy ginkgo]

Shitty for eyes, especially when u are a programmer

And it's harder to being focused reading from the screen

[manic seal]

do you have a "correct" book for linalg

[runic hatch]

I think your best bet is to find some online copy/preview for each of the standard texts and see what you like the best

Check the most recently pinned message for the usual suggestions for linalg

[leaden cloak]

His introduction to manifolds or Differential Geometry: Connections, Curvature, and Characteristic Classes?
And any reason why or does it just feel nicer?

[edgy cradle]

has anybody done multidimensional analysis by duistermaat?

how is its contents and how does it compare to spivak or fleming?

or is mokowitz better?

[karmic thorn]

@coral kettle was reading it, I'm not sure if he read the rest as well.

[brittle breach]

Differential geometry since that's what you're interested in.
you can use intro to manifolds for background.

[leaden cloak]

I see. Thanks.

[coral kettle]

imo similar vibe to spivak, just a lot lot longer

i didnt see the point of it and cut my losses before finishing manifolds

[golden creek]

Guys I have been gifted 'The Higher Arithmetic' ~Davenport. Is it any good?

I can not tell from early reading.

[gusty smelt]

I don’t know of that book but Davenport is a good writer in general

[gray gazelle]

The Bible is a good book

[gilded escarp]

anybody know anygood algebra 1 books

from stuff like graphing y=mx+b to stuff like radical equations

[karmic thorn]

Algebra by OpenStax

[edgy cradle]

is there a quick review book on elementary to high school math

i mean a book with bare minimum essentials of concepts thought during that period

which encompasses basic counting to precalculus

[brisk ice]

I know this is a math server but is there a recommended physics book that gets up to modern physics and calculus based. Just a nice book (something you can self study) that I guess would for your first 2 or 3 semesters of physics and has nice selection of problems with solutions either available somewhere or in the book.

[timber mesa]

maybe Berkeley Physics Course? I'm not sure if it has exercises or if it's calculus-based (particularly the mechanics vol.)

but it's a tad bit more advanced than say Serway or Sears-Zemansky

(both of which are great books)

[brisk ice]

speaking of courses I think mit has the OCW of most of the first few semesters of physics?

I assume those are of quality

[brisk ice]

That is a book?

[timber mesa]

five books

[brisk ice]

oh ... appears so

[timber mesa]

since you're looking for something that gets "up to modern physics" I thought of that

[brisk ice]

do you think it is worthwhile to look into the mit lectures or do you think a book should suffice. idk how important "labs" or even demonstrations will be if I am trying to self study.

[timber mesa]

eh you won't lose a ton without labs

experimental physics is its own thing ofc

and has some importance in a physics degree

but it's basically applied statistics

[timber mesa]

I don't know how the MIT lectures are and I'm not a physicist

just a math guy with physicist friends lmao

[timber mesa]

and in my undergrad uni I read some of vol. 1 for physics 1

vol. 2 is allegedly pretty good

and a typical physics degree roughly follows the outline of these 5 books

[brisk ice]

Yeah here I would mainly I guess just want to get through 1,2,3 of this. Eventually have to take statics, dynamics, and thermodynamics and also doing degree that falls somewhat in the realm of electrical engineering.

[timber mesa]

ah okay

sure you won't need 4 and 5 then

[brisk ice]

I already have credit for mechanics (first semester physics) through college credit transfer from highschool but it has been a long while and felt the course was a bit lacking and I don't recall much of it

[timber mesa]

the thing is, most physics textbooks at that level don't assume a lot of calculus but I'm sure there's at least some that do

can't say I know of one

[brisk ice]

oh I thought all "university" physics books were calculus based

I know "college" physics is consider more algebra based or at least has simple formulas that can be applied

Anyways, thanks, I'll look into it.

[blazing canopy]

It's hard for me to imagine a single book that starts from the basics and gets up to modern physics, especially within an equivalent of 2-3 semesters.

There's just a lot of material, including background mathematics, to cover.

[sterile remnant]

Young's University Physics. God knows how they managed to fit all that stuff in a single book, if you can call that monster a book even. More like a brick.

Perhaps it would be better to find a number of smaller textbooks, each dedicated to a single subject. I will second the Purcell recommendation for electromagnetism, although it does not have any solved exercises inside (but since it's so popular, I'm guessing you'll be able to find them online easily). I will also add Hecht for Optics. For Quantum Mechanics, Griffith's book is the standard introductory book, and uses more calculus than other, more advanced books (such as Shankar) that tend to follow a more algebraic approach I guess.

Not sure what to recommend for other topics. Maybe Pain's book for oscillations/waves. Following MIT OCW might also be good in some cases. Why don't you ask in the physics discord server? I'm sure they'd be able to help you much there

[hasty turret]

How relevant is Principia mathematica to modern Logic

[stray veldt]

not unless you are a historian

[gray gazelle]

Calculus by Tom m apostol if like to suffer

[lost maple]

Hi! Looking for some (plural!) recommendations for some good workbooks and problems books with exercises encompassing all of algebra, trigonometry, and high school geometry. I got some from Schaum's but I'm not qualified to vet for their quality.

(btw pls @ me if you've got an idea!)

[near zinc]

are there any good books that talk about applied maths

like fourier being applied to certain things, or cracking numeric passwords that kind of thing

[split peak]

do you guys have any book recommendation for the maths needed in data science? ( or coding in general)

like the bare minimum maths needed

[brittle breach]

Their is a book "The art of computer programming by Knuth"
he touches on some of the math you would need for programming

[gray gazelle]

You can look up "data science from scratch". And jump to the maths chapters.

[forest sleet]

Thoughts on Cinlar, Kallenberg, Shiryaev, or LeGall for a probability textbook/reference?

[hearty steppe]

I hate to break it to you but if you want to be the best possible data scientist you can be, you probably should spend as much time studying math as you can and I wouldn’t suggest stopping.

If you want state of the art understanding you start with Casella and Berger because that’s where the rigor you’ll need will be

What your doing as a data scientist is a combination focus of statistical inference theory and computer science theory

So you SHOULD not be math averse and expect a bare minimum here. I’m giving you a bare starting point because math is hard and more people should take learning it more seriously

And I speak as someone who considers themselves barely decent at mathematics in terms of how much more I need to learn.

You’ll spend a lifetime being as good as you can with it, trust me, if data science or similar areas are where you want to end up

[stray zinc]

Hi. So I'm wanting to start my math education over from the basics, but I'm not really sure how to approach it. Does anyone know of a semi-complete list of topics that are essential for pre-algebra that I can use as a starting point?

Would beginning with a pre-algebra book and keeping an eye out for any gaps be sufficient?

I graduated high school in the US and made it to algebra 2 for what it's worth.

I considered going through khan academy up to pre-algebra, but I don't really want to waste time learning to count
Any advice would be great

[quick hornet]

Would beginning with a pre-algebra book and keeping an eye out for any gaps be sufficient?
probably, most of these sources tend to assume students know basically nothing beyond "how division works" because many schools are very bad at teaching that to students (and pass them along anyway)

even this honestly seems overly conservative given you passed algebra 2, it typically comes back faster than you'd think — but it doesn't hurt to skim through old material, I guess.

[stray zinc]

Thank you!

[marble solar]

Read

how to be good bussinessman

u will learn people psycology

[livid ermine]

Have anyone read the book computability and logic by boolos and know how much logic you need to read it?
It says it's an intermediate course, but also that it's accessible to people outside mathematics
I only know the basics of logic, so I wonder if I should read some traditional logic text first

[regal wasp]

What’s the general consensus on Terence Tao books/notes? Are his basic analysis books any good? I went through his lebesgue/measure theory one and that was very good, especially the exercises, but are his analysis 1 and 2 books a similar caliber?

[frosty girder]

i wont say the first 2 books are good

they lack problems, are too wordy, and are just not good for a first time reading of analysis

however, they are better as supplements

[runic hatch]

If you’ve gone through his measure theory book without any major issues I feel like you’re already pretty set for basic analysis

You could probably go through Rudin pretty quickly to shore up anything else you’re missing

[brittle breach]

nah

[hearty steppe]

What is sad in the land of physics majors is most of them go into a program without knowing about relativity or quantum mechanics. Its just as bad as people going into computer science programs and data science programs asking about what the minimum amount of math they need to learn is lol

Man people really are that unmotivated to get into things these days huh

And physics majors that think math is just syntax for their understanding of physics. Like bro no it’s more than that

Math in part is how we derive how those systems work and their components. So that’s a lot more than syntax lol

[lost maple]

Hey now, I'm very motivated, I just so happen to also be an idiot

[hearty steppe]

Motivation is important, but passion is even better

What separates people who are good at something vs decent is passion

[normal sentinel]

looking for recommendations for algebraic number theory. rn im using milne's notes which are good but im just looking for resources to reference

ah just checked chat history. neukirch and lang

[cursive orbit]

I doubt the average math major goes into math knowing anything about many core topics in math either

[heady ember]

Moth be like: Are you sure about that

[sage python]

Alphyte said average so

Kinda covered that case

[heady ember]

Yeah ik he meant normal hs student

Moth is abnormal

Though in a good way I suppose

[gray gazelle]

If i just finished serge lang's basic mathematics

Should i take calculus or linear algebra first next

And is serge lang a good author if anyone else has experience with him

[obsidian sand]

is chrystal's elementary algebra a good book for a noob who likes maths?

[heady ember]

You can check out the pinned msgs for algevra books

[obsidian sand]

it doesn't seem to be on there, but disquisitiones arithmeticae is

and they're both really ancient and i've heard of both so i'm going to take that as chrystal's book being good

[hearty steppe]

What’s average to you? Average American? RIP

Fake math education is how the American school system teaches math.

[cursive orbit]

in which other country does the average intended math major know stuff that should be taught in undergrad?

[hearty steppe]

If you are going into a math program, I hope you spent a good amount of time learning math extracurricularly

Cuz it’s going to break your grades otherwise

[heady ember]

Moth: Learns algrbraic geometry

[hearty steppe]

I’m speaking from personal experience mate from going through an undergrad CS program which is not exactly math but it’s enough math to make you flunk out

[cursive orbit]

?

you're expecting high school students to self-study upper-division material before applying for a math program?

[hollow vector]

is algebra for dummies a good source?

[night prism]

I wonder about this a lot

Undergrad math seems like the biggest sudden “jump” between levels of difficulty

That is, high school into undergrad (not considering independently done studying)

[obsidian sand]

bigger than undergrad to graduate?

[night prism]

I wouldn’t know because that’s not my field, but I’d argue still yes; at the end of undergrad math you have an idea as to how it goes, it just gets more convoluted

[hearty steppe]

Yea

Absolutely

Because I know how hard it is because I converted from CS to math

[night prism]

From high school to undergrad you go from take and bake problems to serious deductive (and inductive) reasoning

[obsidian sand]

what sort of cs and what level

and what level of math did you jump into

[cursive orbit]

then you've got unrealistic expectations of the average high schooler

[obsidian sand]

i've been thinking of doing that if i get the chance

[runic hatch]

Do you really need to study up to like the end of a first course in abstract algebra/analysis or whatever before starting uni math?

[obsidian sand]

considering how confused i was when i studied abstract algebra in my first year of uni, yes

[runic hatch]

Like unless you’re in some highly competitive stream they’re still going to try to gently curve you towards higher-level math

Admittedly if you do have the time/motivation may as well go for it

[brittle spindle]

hi any linear algebra book recommendations? for early undergrad uni

[heady ember]

Check pinned

[hearty steppe]

No the average high schooler has unrealistic expectations regarding what it takes to get through a good math program undergrad or post undergrad

[hearty steppe]

If what you do involves being decent at math, you will spend more than your college years to show for it

That’s the problem most graduating high schoolers don’t understand

[hearty steppe]

You probably should have familiarity with some of material by the time you get to uni if what you want to do is math

The best way to prepare for college is to not actually attend college until you know what your getting yourself into.

Even if that means taking a few years to prepare for a program you want to get better than subpar passing grades by chance

Cuz you will spend more time making up for bad grades if you end up wanting to go to grad school. Which most people won’t have a choice since the job market will demand it, like it kinda is now for decent paying work

[cursive orbit]

?

[hearty steppe]

Studying math at the college level is where real math introduces itself

Not the bullshit you learned in high school

If you went to the type of school I’m thinking of anyway. I doubt charter schools are much better, rather than streamlining more “special needs” people who have a leaning toward a subject to be put in the right classes

[cursive orbit]

the average high schooler, who takes AP math courses and spends several hours a day studying/doing homework trying to get into a good program with little extra time to study university-level math should spend an additional several hours a day to study that

[brisk ice]

What percentage of people would you say do a degree for money over interest and passion for the subject?

[cursive orbit]

very realistic expectations

[hearty steppe]

I’m special needs so that’s why i quote it

[hearty steppe]

The same percentage of people that are probably fucked in the long run, probably

[hasty turret]

80%?

[cursive orbit]

and I don't see why "ready for college" is equivalent to already knowing the material you're going to be taught

[brisk ice]

Because I mean I wonder how many people actively seek more about their study then just from the required classes

And only doing classes because it is required for the degree I would assume.

[hearty steppe]

Depends on the type of person you are and how good you pick things up on the fly. I don’t consider math to be a subject you can rush through like a semester college course per topic. If you want to do well you gotta have some pre-exposure before the program I think.

[brisk ice]

Yeah that is crazy but I assume it happens

I guess If you had interest you might already be looking at the stuff

[hearty steppe]

I mean math is just not an area I’d tell people to go complete a degree for on a whim especially at a prestigious school.

Like I’d say spend 2-3 years learning on your own and find a program that interests you. You will know when you are ready.

Math in my opinion needs that much preparation if you don’t have much background but you decide you want to major in math

It’s like studying physics but a different flavor of difficult

[cursive orbit]

imo that's a pretty elitist take

[brisk ice]

so what do you do in those 2-3 years though?

Like you either would be working and not going to school or doing this stuff during highschool

[hearty steppe]

You look at Ivy League programs and try to learn what you can regarding core reqs

[cursive orbit]

the only people who should study math are those who have successfully studied it on your own

[hearty steppe]

Working and studying

At the very least

[sage python]

Cat man I'd quasi-disagree because a lot depends on the individual and the program

[forest sleet]

you don't need to start in abstract algebra and real analysis as a freshman in college, even at prestigious schools

[hearty steppe]

It’s tough. I’m hoping to get into a grad program for math at some point, and I don’t have the option to get a masters

[brisk ice]

btw maybe this should move? #book-recommendations

[hearty steppe]

Yea I would say prime time to go for a program is when you are sure you can handle the course loads your dealing with

For me, I know I’m not ready for a grad program yet

[sage python]

Yeah prob let's get back to books, move this to either discussion channel

[brisk ice]

But don't you think you would do better in school then on your own?

I mean you do need skills to be able to learn on your own but i think having an instructor and someone to speak with I think would help

[hearty steppe]

Yea sorry to like get all involved about the discussion about it here. I had a bad experience in the past preparing for anything after high school and my K-12 years were not great to me regarding schooling

[hearty steppe]

This is what people who aren’t neurodivergent would say. It’s not fun when college classes or K-12 didn’t work for me. I’ve been learning at an ok pace. It’s not super quick but it’s been getting better

I’m not struggling as much asking tons of questions in a bunch of channels as much so that’s something

[brisk ice]

I suppose creating your own environment is nice but what is going to happen when you eventually have to go to the school which follows some standard structure you are opposed to?

Being that you get to set your own goals and pace

[hearty steppe]

This is why I’m spending four days a week at my desk for as long as I can until I know I’m ready for the right program.

I know how difficult the courses could be, and I know it’s gona take some time to get there.

I’m banking on hopefully 2.5 more years of self study

And maybe get PhD before I’m 45 years old lol

Realistically speaking

Yes I’m in my 30s

[brisk ice]

are you suggesting this for people going past a 4 year degree and already have the 4 year degree?

[hearty steppe]

Uh if they’re neurodivergent I guess. I suppose I have bias toward my own experience

[brisk ice]

I guess the ultimate goal in this case would be research for you?

[sage python]

I guess that hits one of the key things

[brisk ice]

But that means you might be stuck in a bad job for x amount of years

[sage python]

Namely be careful about how specialized the advice that works for you is

[hearty steppe]

Yup

[brisk ice]

and that could be rough :/

[hearty steppe]

I don’t really have good enough people skills to navigate my way through a bunch of project management-esque jobs. I’m tired of writing software and people give me a hard time about getting data jobs without a grad degree

Yea I mean part of the problem is being humble about where I am in my studies and knowing I just gotta keep focused

I have a potential machine learning internship opportunity to look forward to this summer so that’s some additional potential leverage

Part of it is luck in networking with the right people while struggling with people skills altogether

[brisk ice]

so would you redo how you approached starting school?

we should probably move to #discussion

[hearty steppe]

I wouldn’t be able to, given the circumstances that occurred. Id literally have to take a time machine back before I went to 2nd grade and tell myself to get homeschooled lol

Oh my bad yea I’ll resume there

[brisk sluice]

Hi friends! Does anyone have any cool resources regarding an introduction to type theory and how its used in computer programming?

[gray gazelle]

does anyone know a highschool textbook that talks about surface tension and adhesion and cohesion and stuff

mainly surface tension though

@ me if u do

[hollow spoke]

Please suggest me a book for Complex Analysis which covers some advance topics.

[forest sleet]

Ahlfors or Simon A Comprehensive course in analysis 2A/2B

[atomic stag]

I'm having difficulty in solving
long integration questions that requires 4 to 5 different techniques of integration in same question

(I'm currently in grade 12 India) Asking for a book recommendation

[heady peak]

any good recommendations for books on introductory level undergrad probability theory and statistics?

(ik i asked this in another channel, but that was because i didnt know this one existed)

[slow roost]

Feller, Introduction to Probability Theory and its Applications is nice

[mystic orbit]

you want a book specifically about integration technics?

I don't think there is such a book

you should probably just do a lot of exercises to get better at integration

[sage python]

Simon's series is nuts

[warm karma]

Does anyone have good Online & Free textbooks that I can use to study AP Calculus BC?

[mystic orbit]

khan academy

khan academy is just the holy grail of HS resources

[warm karma]

Alright, I already have used it a ton for Algebra 2 especially lol so no harm in doing more I guess

Khan academy basically carried me through exponent stuff

[grand thistle]

i have a pdf of some but idk if it’s any

good

and if they're in 12th grade idk how useful it would be for high school calc

[prime prawn]

READ BRAVE NEW WORLD

[heady peak]

so you'd say it's good for people that have very rudimentary knowledge in probability?

[slow roost]

it doesn't assume any prior knowledge of the subject

but it's also a fairly challenging book

so, it really depends

if you're not used to challenging books that go theorem / proof / example / theorem / proof / etc, it could be too much

[loud cradle]

another caveat depending on your needs, feller volume 1 only covers discrete probability

for a more "well rounded" intro (but nowhere near as deep as Feller), the various probability books by sheldon ross are pretty decent

[scarlet jewel]

ok