book-recommendations

[static crest]

ahlfors is good

[sudden granite]

we need an acronym

spivak is good

[karmic thorn]

I could start a flame-war by calling Gallian a good book.

[gray gazelle]

i found this in my sympgeo prof's notes

@obsidian valley explain

[static crest]

physicist moment

[obsidian valley]

I've been a secret grad student all along.

[sudden granite]

jesse has some explaining to do

[gray gazelle]

did you TA mat257 2018-2019?

i had a TA in that class named jesse

and

uh oh!

[obsidian valley]

No comment

[sudden granite]

yo can we talk about books

[gray gazelle]

jesse dox'd

[obsidian valley]

You had a nice solution to #3 on the 257 midterm though ;)

[sudden granite]

Why is Thomas' Calc better than Stewart's Calc

[gray gazelle]

but you didn't TA 257

[sudden granite]

[gray gazelle]

i know my 257 tas

well

knew

[obsidian valley]

[gray gazelle]

what even were the 257 midterm questions

i remember them being... difficult

taking complex analysis with bierstone has made me realize why that guy loves polynomial equations so much

one of our midterm questions was to find the specific values of a, b, c such that (system of like 4 polynomial equations) is a manifold

[static crest]

lmao

polynomials are pretty cool though

can't blame him

[tight crag]

@gray gazelle that question is a very important one

[gray gazelle]

hope you like linear algebra

it was $$x^2 + y^2 + z^2 = 1, ax^2 + by^2 + cz^2 = something$$

[hasty eagle]

(T*(Terra), -dτ)

[gray gazelle]

so not actually that bad

if i tried hard enough i could find the original midterm

im deciding between Halmos: Finite-dimensional vector spaces and Shilov: Linear Algebra

i would be glad if someone can tell me what are the pros and cons of each book

[hollow peak]

halmos is a classic

shilov is cheap

[gray gazelle]

but how about their contents?

which covers more material and which is easier to read?

A good book for sequence and series?

[narrow talon]

I’ve heard Shilov is good if you Really like functional analysis

If it has the work “Halmos “ on it, it’s something nobody reads but everyone references (maybe I’m wrong, but for the most part...)

Matejp why just those two books?

[gray gazelle]

Also need a good book which covers all topics in mathematics at superficial level? As an easy read.

[tranquil ocean]

What do you mean by all topics? That would be a billion page book

[obsidian valley]

One sentence about every subject

[gray gazelle]

I mean to make someone more curious, like a 15 year old very interested in mathematics and already knows calculus etc..

[obsidian valley]

Yeah

[tranquil ocean]

Yeah, the infinite napkin by Evan Chen might be a good place to start

[obsidian valley]

I would check the Napkin

[graceful bridge]

I think the Princeton Companion would be the best answer to this.

[obsidian valley]

Does it have exercises?

The nice thing about the napkin is that it has exercises

holy shit i didnt realize it had 200 pages of set theory

I've been referencing evan chens set theory course notes

I will use this instead

[graceful bridge]

Reading about all topics in mathematics is not meant for beginners

[gray gazelle]

The napkin is nice I think.

[tranquil ocean]

Yeah idk, even the Napkin can be pretty discouraging, since its not very easy. I almost gave up trying to study math because I wasn't good enough to solve the exercises in Napkin

[obsidian valley]

The complaint I heard about the napkin was that he lulls you into thinking you understand because he describes it so well

[graceful bridge]

I think doing exercises is pretty much going in depth though

[obsidian valley]

I should spend some time with it

idk looks like a pretty easy book to me

[gray gazelle]

🤔

[stray veldt]

is this even a joke

it just seems cute

[tight crag]

It is infinite

Lol that's so cheesy

[stray veldt]

no you

[tight crag]

Yeah it's weird that they would say subgroup

Instead of subset

This property exactly classifies infinite sets but not infinite groups

[gray gazelle]

Princeton companion is verbose.

I think I should gift arfken

[graceful bridge]

I think it has some value that the overviews of different subfields are written by specialists, because they will also have a great overview and know what the essence of the subject is. That's why I like Princeton companion, but on the other hand it's not intented to read like a textbook, it's more of a reference. I used it yesterday to get a nice overview of a subject I was curious about.

[quartz pawn]

@gray gazelle try architecutre of mathematics. It's not a super laypersons book it's a book that like a second semester math student could pick up and start learning out of.

[obsidian valley]

If you're just gifting something maybe just pick a specific subject and give them that

I'll always recommend The Calculus Gallery by Dunham as a fun book that walks thru a lot of history and also gives nice proofs of different results

I think it's good for someone who has learned calc at a hs level

[gray gazelle]

I was reading a lot of reviews and recommendations on the internet and those two seemed to be the best for what I need. What books do you recommend? I'm still open to other books!

@obsidian valley I already gifted The Calculus story, Infinite powers

[obsidian valley]

This will be different, I think.

It's very much a book of proofs

with some history sprinkled in

but if you don't want to gift another calc book idk

don't give them the princeton companion lmao

[gray gazelle]

@obsidian valley do you have any good recommendation for linear algebra? im currently thinking about halmos, shilov and cohn but im open to any suggestion

[obsidian valley]

huh

idk

Axler

I haven't read many LA boosk

so i wouldnt know

check #books-old

[gray gazelle]

i dont know ive seen a lot of negative opinions about axler because he doesnt talk about determinants

@jesse Dunham is good. This is actual math compare to those I mentioned

[graceful bridge]

Wait, are you asking for a gift to a 15 year old?

[gray gazelle]

Yes

[obsidian valley]

Yeah it's a great book

I read it when I was 15/16

[graceful bridge]

Lol, I missed that. Then I would avoid any academic textbook. Go with something more recreational, like Journey through genius, smt by Simon Singh etc

[obsidian valley]

though I think I'd get more out of it today

than I did then

[gray gazelle]

Journey through Genious was 1 year back

Simon singh had some code breaking book I think and fermat?

I am 30, and at 15 set theory was boring subject for me.

[graceful bridge]

Several good options on this list: https://www.goodreads.com/shelf/show/mathematics

[obsidian valley]

NOT GODEL ESCHER BACH

[gray gazelle]

Godel I didnt like. Wasted money

[obsidian valley]

[graceful bridge]

Yes, I didnt mean that specifically (even though it's a great book)

[obsidian valley]

Godel's Proof is fun and short and would be approachable for pretty much anyone

[gray gazelle]

How to solve it, this I have and hvnt read yet

And it was pretty expensive here

[narrow talon]

@gray gazelle what type of linear algebra are you looking for? I like strange for the most part for non-proof based La, Axler is something that was mentioned and while I reference often, the lack of determinants does make it a less complete than I’d like

[gray gazelle]

Sequence and series comes under Real analysis or function analysis?

real, but they absolutely see use in the latter.

[gray gazelle]

i think strang is too "applied", for example, were doing everything with general fields etc. while strang does everything in R^3 from what i've heard. On our website they recommend Cohn: Algebra 1 (i cant find any reviews for that one) and Serge Lang: Linear Algebra (which, from what I read is too advanced and is meant more for graduate students)

i dont know what type our algebra is, but basically we started with vector spaces, than quotient spaces, isomorphism theorems, then linear maps and then we went on to matrices and their operations, we just defined determinants last week

i probably missed some things too

Is there any nook for spherical/polar coordinates?

[gray gazelle]

i believe they come under real analysis

[stray veldt]

probably a calculus book

[hollow peak]

lang LA is just outdated imo

[gray gazelle]

So calculus is the only place we use it.

To simply things

[stray veldt]

nah, you would use polar coordinates a lot

[hollow peak]

spherical coordinates pop up everywhere

[stray veldt]

but if you are unfamiliar with it, a calculus course is probably the first place you encounter them

[gray gazelle]

what do you mean by outdated

[hollow peak]

if you have a pde that is known to have radial symmetry, then switching to polar coordinates bears interesting solutions

in fact, that's one way to get explicit solutions from the laplace equation

[hollow peak]

his approach to it is very dry and kind of boring

it's unnecessarily terse when there are easier to read and just as in depth books out there

[gray gazelle]

Since you mentioned Laplace, which book is good for Fourier, laplace and z transform?

[hollow peak]

fourier transforms are far more theoretical than the other two, and it would be covered eventually if you just study analysis for long enough

laplace transforms come up mostly in ODE's I believe

z-transforms are an electrical engineering thing

[gray gazelle]

which book in particular do you think would be the best fit for me and why?

Those are special cases of Fourier?

[hollow peak]

my preferred book is Linear Algebra Done Wrong by Treil

very easy to read, good and light exercises

it's a good book

[hollow peak]

I'm not the most knowledgeable but the z transform is a form of a laplace transformation, and I think there is a relationship between laplace transformations and fourier

[gray gazelle]

Are pearson books good?

[hollow peak]

depends on the subject, I don't have a general answer

fourier transforms are of theoretical interest for many reasons, and it has neat unique traits

one big one is that it preserves the inner product in L^2

[gray gazelle]

Ok

[gray gazelle]

do you have any opinion on halmos, shilov or cohn ?

Just my personal opinion, not answer. Shilov is nice. Halmos is difficult to read. Cohn no idea.

This I checked 30 min back

[gray gazelle]

thank you, opinion is what i want to hear, noone can give a definite answer here

[lone sand]

:petTheCat:

i cant

):

[gray gazelle]

get nitro

post in #foundations and @ jesse will gift it to you

[lone sand]

i cant talk in #foundation ..

[gray gazelle]

#get-advanced-access

[lone sand]

got it

who's jesse tho..

I mean, I got the adv math.

But I still don't have nitro

[gray gazelle]

[lone sand]

awww u trolling me

):

[gray gazelle]

yeah but now you have a cool advanced role 😎

[lone sand]

AWWWWWW U TROLLING BRO I WAS SOOO EXCITED....

😩

[sudden granite]

yo @obsidian valley brooooo nitro please bro i'll self teach baby rudin if you gib nitro

🙂

[gray gazelle]

i am in an unbelievable amount of pain

[sudden granite]

get better soon

[narrow talon]

@gray gazelle Lang books in general are good presentations of their respective topics for robots or people who already know the topic. I know few people who use his books for much more than algebra, because to use a book as a reference you have to know the organization at least a bit, but Lang books are written so dry that you probably wouldn't ever read one enough to get a great feel for it (again with the exception of algebra). They're never quite as unpleasant as people make them out to be though.

I would say get a copy of Peter Lax's book if you can. It's an expensive book, but it's the book I most regret not bringing with me when I left the US. You can find a scan of it on l i b g e n if you can't afford it. Lax has become the text I reference far more than anything else and has basically everything you'd ever need to know about linear algebra in it, albiet with slightly worse presentation of the concrete stuff than Straang and is slightly harder to reference than Axler where they overlap (Axler is structured in such a way that makes it super nice to reference, Lax has more of that "both a textbook and reference" feel).

That said, Lax is the only book where you can find uniformly good presentation of spectral theory for symmetric and self-adjoint operators, matrix calculus, duality (in the functional analysis and optimization sense), matrix inequalities, stochastic matrices, Hahn-Banach, and unlike Lang, Lax shows you where to look next in a set of appendices that cover a ton of interesting ground. It follows a similar order to your course, and will grow with you whether you go pure, applied, data science, economics, sociology, ...

This sounds like an ad for Peter Lax's book haha!

[hollow peak]

you've actually convinced me to take a look at lax, and I wasn't even looking for a LA book

[narrow talon]

Seriously though, Lax and Rudin are my bibles. Brezis is my baby and Conway is the favorite child.

I have a weird relationship with math textbooks

[hollow peak]

conway for functional analysis?

[narrow talon]

Complex

[hollow peak]

i've heard that is the far better conway text

I have the functional analysis book and I dread it

[marble solar]

The complex book is weird

[narrow talon]

I haven't touched functional, I've heard it's really drab, but I really like complex. It's just a straight up fun book. I've read about half of it and am now actually working through it along with an undergrad class using Brown/Churchill (and using Rudin on the side for that good good potential theory).

Brezis is my fav functional analysis book. FA is the hardest topic to choose for me because there's a lot of good books with very different main ideas

[gray gazelle]

I took a look at Lax's book and it seems great i'll download it and read some parts tomorrow to see it's really what i need before i order it, but after your ad i think that's almost a certainty. I don't understand why i didn't find anything about this book before.

[hollow peak]

yeah I didn't know this book existed and now I really want to read it haha

[narrow talon]

Peter Lax is a great expositor and it's a shame this book isn't more popular. His functional analysis book is finally being recognizes for how outstanding it is, hopefully the same happens with linear algebra!

[gray gazelle]

just to verify are there two linear algebra books by peter lax or just one?

because amazon shows two titles

one is Linear Algebra. Pure and Applied Mathematics

and the other one Linear Algebra and Its Applications

is this the same thing?

Check the book image. I ended up buying two same book bcz of image diffrence

[narrow talon]

Yes but also no. Peter Lax "Pure and Applied Mathematics" is the first edition, "Linear Algebra and it's Applications" is second edition

[obsidian valley]

What?

[narrow talon]

I've read a bit of both and the first edition feels a lot more like a set of set of lecture notes, so I'd definitely say to stick to "Linear Algebra and it's Applications"

[sudden granite]

WDYM WHAT

oh god

all caps

[narrow talon]

I actually read from one of the first prints of the book, the 2nd edition was the main text for my first linear algebra class but while I was waiting for it to arrive I had to use the super old preprint

[gray gazelle]

i told someone to post in #foundations to get you to gift nitro but they messed up the ping

[prisma snow]

Who gifting nitro? I volunteer (as recipient)

[gray gazelle]

you volunteer to give me nitro? how generous

[obsidian valley]

die

lmfao

should i go to a piano masterclass on zoom or should i read more CoM

[gray gazelle]

CoM.

[obsidian valley]

[gray gazelle]

im going to do the snake lemma exercise

,iam studying

[hasty eagle]

Gave you the studying! selfrole.

[obsidian valley]

🐍

[sudden granite]

jesse

[obsidian valley]

NO

none of you contribute positively to #foundations

[gray gazelle]

ok thank you so much for your advice, although i think peter lax should be the one to thank you for making his book sell better!

[narrow talon]

Of course! If you ever have questions about analysis books or probability books hmu, I've used a lot of them and enjoy talking about them.

Tbh I'm very sad I've never met Lax, he's basically the pride and joy of Courant

They've preserved his office. Lax, Varadhan, and Gromov: The Big Three!

[sudden granite]

I POSITIVELY CONTRIBUTE TO #foundations!

[obsidian valley]

No.

[gray gazelle]

No.

[sudden granite]

**SAY SORRY. ** 😡

[wind canyon]

Anybody here have any recommendations for game theory books?

I'm interested in learning some game theory, I saw no books listed in the book section

[quartz pawn]

@tardy venture Michael Maschler's Game Theory is suppose to be the most comprehensive

[gray gazelle]

What about code theory?

[calm crane]

PIANO MASTERCLASS

gogogo

unless you aren't getting taught

then meh

[gray gazelle]

Can anyone recommend me a book just for Algebra for beginners? I'm out of school and I'm becoming overwhelmed with Google recs and a lack of resources...

[obsidian valley]

I am attending

I am not getting taught I refuse to play piano for others

its still sorta fun

[gray gazelle]

Do your Calculus on Manifolds exercises.

[obsidian valley]

die

later

[sudden kindle]

🃏

[gray gazelle]

cope

[obsidian valley]

[gray gazelle]

mayer vietoris is literal magic

how the fuck did anyone come up with this shit

[obsidian valley]

Luciana Simoes

it's just about to end

[tardy prawn]

hello friend

:(

mean

[steel viper]

i audited like half a linear class at nyu last spring before covid happened and used lax's book

it seemed pretty good

[calm crane]

bad

[obsidian valley]

It was pretty enjoyable to watch her teach the other people, I didn't really learn much but it was just nice to be in an environment like that again lol

[narrow talon]

@steel viper yeah, that’s where the book is used most

[waxen umbra]

mathamatics

[obsidian valley]

Absolutely.

[gray gazelle]

mathematics

[sudden granite]

maths

[knotty cedar]

Anyone familiar with From Counting to Calculus? I want to solidify my maths knowledge (find and fill in gaps... I moved a lot and from 3rd grade on struggled with math) so that I can dive into physics with a solid foundation. It came up as recommended on Quora. Curious if anyone has any recommendations...

I have at least one Ian Stewart book.

[hollow peak]

khan academy is really good for pre-college math

and it has exercises

[knotty cedar]

I've tinkered there. Would love a book of all kinds of problems/examples (word and just math), too.

I found the homework/word problems are what helped me learn chemistry well enough for an A.

Lots of trial and error...

[sudden granite]

Lang's Basic Mthematics is great for filling algebra and precal gaps

[pulsar geode]

any book clubs here/anywhere else online

[sudden granite]

wdym book club

[hearty steppe]

This channel doesn’t count as a book club?

[narrow talon]

There’s a subreddit for finding math book clubs

[pulsar geode]

oh what is it

and i meant book club as in reading a chapter a week then going over exercises or smth in a group

[narrow talon]

https://www.reddit.com/r/MathBuddies/

[narrow talon]

Exactly what it is

[pulsar geode]

oh thanks

and yeah that was in response to the other person asking lol

[obsidian valley]

Oh it's actually sorta advanced math too

cool sub

[marble solar]

Derivatives are pretty advanced

[ripe granite]

derivators

[obsidian valley]

sorta

I mean I expected it to be like highschool level so I was surprised

[sudden granite]

:petTheCat:

[pulsar geode]

any algebraic geo book recs? background in projective geometry and enough abstract algebra for cryptography

[calm crane]

uhhhhhhhh

you see

if you want to learn crypto

and barely enuf math for crypto

math books arent for you

use some book for crypto

like say

nigel smart's book

cuz crypto your focus is very different

you care about like

cpa cca ind etc.

[pulsar geode]

no i meant that my abstract algebra background comes from knowing crypto

what im trying to learn is algebraic geo

[calm crane]

ahhhh

mbmb misread haha

i also came from crypto

i read silverman arith of ec for ec stuff

jacobson basic algebra for abstract alg

AM+Hartshrone+Liu+Eisenbud&Harris rn for ag

[gray gazelle]

i will never learn algebra 😔

[marble solar]

yuh

[calm crane]

aa isnt even that hard to learn lol

legit

getting a medical degree is harder

in terms of effort

[obsidian valley]

What an odd comparison.

[marble solar]

This is Medical degree rejects coping

[calm crane]

everyone gets medical degrees these days

ok yall

next year

im applying to med schol

lets see how that goes

[marble solar]

It's ok bud, I'm a PhD reject

No shame

Only cope

[obsidian valley]

don't waste yourself like that ari

[calm crane]

interview:
can you do surgery
me:
yes i do liszt

wait no

interview:
can you do surgery
me:
dehn drilling and filling time

[sudden kindle]

[pulsar geode]

best hartshorne companion?

ive seen vakil and qing liu, not sure if there are better alternatives

[tranquil ocean]

There are so many algebraic geometry books depending on what you're looking for

[pulsar geode]

not really learning for a specific appplication in mind, just whatever has a nice combination of being well written/has good exercises/nice proofs would be great

[tranquil ocean]

What you're looking for also includes your background and stuff

Gathmann, Fulton's algebraic curves etc

[pulsar geode]

yeah posted the other day, but relevant background in projective geo/some abstract algebra

and a bit of ring theory (learned along with abstract algebra solely for cryptography)

[tranquil ocean]

There's also Reid's algebraic geometry book

[gray gazelle]

I'm looking for a multivariable calculus problem book. I'm taking differential geometry course this semester, and we haven't done multivar calculus in our analysis course yet, so I need something to prepare me for that

I'm currently watching KA videos on multivar, and it's lacking problems so that's why I need a problembook

[hollow peak]

have you done any multivariable calculus at all? or just no multivariable analysis

[gray gazelle]

No multivariable calc at all (at university), but I know stuff like partial derivative from hs

for good MVC problems see spivak's calculus on manifolds. it's not a problem book but it might as well be

Will it quickly get me up to speed?

depends on you

That's all I need, to understand diff geometry theorems

[hollow peak]

well it's only like 100 pages, only maybe 60 of which you need for what you're doing

[gray gazelle]

That's great

[hollow peak]

it'll probably take you longer though if you're not familiar with the topics, but it is self-contained

my only gripe is that neighborhoods are open boxes for some reason???

[gray gazelle]

i'd argue that every single part of the book is necessary for differential geometry but i also don't want to argue

[hollow peak]

well if you're taking a class on diff geo you're going to learn the end of CoM regardless

[karmic thorn]

What's different about the multivar calc in, say, Thomas' Calculus, and the way it is presented in Spivak's CoM?

[gray gazelle]

Do I need to continue watching KA, or I get the pictures in that book?

[karmic thorn]

The two differ in rigour?

[hollow peak]

yes ted

[gray gazelle]

spivak's CoM is a literal any% speedrun to stokes' theorem and i don't think any other books are

[karmic thorn]

I see.

[hollow peak]

KA?

[karmic thorn]

Khan Academy

[gray gazelle]

Khan academy, that's what I'm watching rn

[hollow peak]

oh, well if you want the more "calc 3" kind of thing then sure why not

[gray gazelle]

doesn't matter what you're watching or reading so long as you're absorbing the material and can do problems

[hollow peak]

CoM is more "here is rigorous multi for mathematicians who need these results"

"and very fast"

[gray gazelle]

oh that'll work for me I guess

can't call myself mathematician tho

yet

thanks!

[hollow peak]

it's meant to be accessible for undergrads, good luck

[gray gazelle]

it's my favorite book 😌

will shill it whenever possible

[polar tulip]

@gray gazelle a lot of people like CoM, if it works for you great. I personally couldn't make sense of it. Chapter 5 of pugh's book is where is clicked for me

Just to give you another option

[novel iris]

hubbard best multivar calc book

[cobalt arch]

https://lamport.azurewebsites.net/pubs/lamport-how-to-write.pdf
Is there a book along the lines of this paper?

Meaning a book that has machine checked proofs

[obsidian valley]

you’ve gone past “rigorous highschool geometry” into full theorem provers huh

have you opened a single textbook yet

or have you spent all your time attempting to find a book that proves every theorem assuming nothing but the axioms of zfc

just go learn Lean and write your own version of mathlib

[cobalt arch]

I am reading amann and escher's text on real analysis rn

[obsidian valley]

and no there probably isnt since writing machine checked proofs still isn’t something alot of people care about especially in elementary textbooks and stuff

you can find tons of results that have been proven in stuff like Leans mathlib if you really care

[cobalt arch]

that is unfortunate to say the least

oh nice!

[obsidian valley]

i think you need to learn type theory to learn Lean tho but dont take my word for it

[cobalt arch]

actually I am reading set theory atm because I need countable sets since I encountered them in ebbinghaus' text on mathematical logic.

[obsidian valley]

that is overkill lmao

countable sets are defined in ch0 iirc

of enderton

[cobalt arch]

😦

[obsidian valley]

probably ebbinghaus too

[cobalt arch]

Countable sets are encountered in chapter 6 or 7 of jech and hrbacek's introduction to set theory

[obsidian valley]

also there is literally nothing to be gained by learning Lean/theorem if you just want to learn the content

That’s not really true

its sort of true

[cobalt arch]

well at least I found the books that I will be reading from. Amann and escher's text is general and will be the backbone upon which all the theory that I will learn will rest.

it is a great book and it introduces a lot of stuff early on

chapter 4 it is

[gray gazelle]

Ugh I'll definitely finish it if I get through that rectangle

Why not just take a ball mate 😣

[valid moth]

Co(o)M

[novel iris]

what's a nice intro to simplicial homology? I've heard some bad things about Hatcher, so preferably something friendlier

[ripe granite]

hatcher is fine

just make sure you get all the signs right

[novel iris]

lol gotcha

[gray gazelle]

I’m a CS major trying to learn algorithms and data structures but I have a poor background in discrete maths. I was wondering if anybody could recommend me a good discrete math book suitable for a beginner with some experience in theorems and proofs.

Preferably a book with a solutions manual.

[tight crag]

I think the standard one is Rosen's "discrete mathematics and its applications"

I think it's a pretty good book

[graceful bridge]

Agreed, an alternative is Knuth et al - Concrete mathematics, which is intented for CS students, but it covers a bit more than discrete

[gray gazelle]

I’ve heard mixed things about Rosens book so I’m a bit wary of it but it does seem to be the standard textbook

Would going through rosens book give me a solid foundation for reading algo/ds textbooks?

[graceful bridge]

If you can be more specific about what you want to learn, I could give other recommendations, otherwise I agree that Rosen is the best choice

[gray gazelle]

Knuth is way above my level unfortunately

Hm well I want to study algorithms and data structures for preparation of swe interviews in mind

So I can’t say specifically what area of cs I’m interested in

[graceful bridge]

Well, some books in alg + ds will cover the necesseary math concepts. In CLRS it is stated that the mathematical prerequisite is familiarity with proofs (especially induction), but other concepts will be introduced

[tight crag]

I think Rosen is definitely not a waste of time as a book, it was very helpful to me

[graceful bridge]

For sure, better to overdo the math foundation a bit than lacking it

[gray gazelle]

Ok will go with rosens book then

Do you guys have any recommendations for a ds algo book?

I don’t have access to a computer on a regular basis so a lot of my studying will be handwritten coding

[graceful bridge]

CLRS Algorithms and data structures is very comprehensive and often the main choice

Sry the title is Introduction to algorithms actually

It uses pseudo-code, you can use it without implementing anything

[gray gazelle]

Thanks for the recommendation

If you don’t mind me asking, are you a cs major? If so are you still a student at uni and what are you working on as your job?

[graceful bridge]

If you're asking me: I minored in CS, Im doing masters in maths now

[gray gazelle]

@gray gazelle

[warm glen]

can anyone recommend a proof based multivariable/vector calc book that doesn't have a full year of real analysis as a prereq?

and that isn't marsden/tromba cos i hate this book so much

[quick hornet]

what level of "proof based" are you talking

something around the level of marsden tromba?

since my impression was that it didnt have many proofs

[warm glen]

it has some proofs, not many

[pulsar geode]

we're using gossett in my discrete class rn

[warm glen]

i just find it very dry

[novel iris]

Hubbard!

its not spivak but it's still rigorous

lots of exposition, written like youre a human lol

works its way up to differential forms and generalized stokes

con is some slightly nonstandard terminology, but otherwise great book imo

oh and the proof of implicit func theorem sucked

[warm glen]

as long as im prepared for diff geo after reading and understanding it the cons dont seem bad

thank u

[novel iris]

np!

[rancid sierra]

https://people.math.sc.edu/girardi/m142/integration/100problems.pdf

Hey does anyone know the name of this book

[sudden granite]

100 problems

[gray gazelle]

yeah we don't want problems

nobody wants 100 problems to deal with

[muted terrace]

how do you guys decided what books to put in the #books-old chat

like I have a pdf of my DE textbook and could submit it incase someone else out there happens to have the same one

is that not the purpose of the #books-old chat

[warped cedar]

I think it is more to seek recommendations and suggestions rather than to just come and look for books people have already posted

You can totally post your book

tho

[muted terrace]

Second one is my professor and this one is Full DE text book

[gray gazelle]

the mods are actually shills for the books listed in the #books-old chat

[grizzled prairie]

any book reccomendations to learn VHDL??

[sage python]

It was crowdsourced at first but nobody has had time to maintain it

[narrow talon]

Haha! I have the top review of Marsden and Tromba on Amazon from back when I took calc 3

I hated it

Now I wish I had spent more time with it

[errant sage]

Can anyone suggest me some good and hard analysis problem sets ? (Undergrad single variable introductory analysis)

[narrow talon]

Rudin problems?

[errant sage]

Harder than that ?

[gray gazelle]

Have you tried https://www.springer.com/gp/book/9780387773780

[radiant crown]

I have this one https://bookstore.ams.org/mmono-107/

the english edition is hella expensive though wth

[pulsar geode]

fpga programming by vhdl examples, pong chu

i used his verilog one a while back, i assume the writing wont be any worse

[muted terrace]

I used the exact same book in my digital logics class

[gray gazelle]

I got these. I think it's enough for basics

[dapper root]

that's not the higher algebra I want

sadge

[gray gazelle]

What should I read next? Real analysis and function analysis, topology. These I am reading just for my knowledge and I am a software professional.

[karmic thorn]

Riley is not a good buy.

Not for an introduction, at the very least.

[hasty turret]

Why is that book called "higher algebra"?

[karmic thorn]

Algebra is high.

[hasty turret]

It's literally highschool algebra

Unironically

[gray gazelle]

@karmic thorn : I have a basic understanding of most of the things as I had 2 + 1(repeat) course on this 15 year back. Then would it be fine?

[hollow peak]

pdes for scientists and engineers isn't really an intro text I think

it's a reference book

maybe I'm wrong nvm

[gray gazelle]

@hollow peak Ok, I am interested in physics as well. I saw some thermodynamics problem and I bought it

[hasty turret]

I mean, What's your objective?

[karmic thorn]

Probably skim through Khan Academy first(if you're comfortable with videos/on-screen exercises). Then proceed to something more concrete, like Spivak's Calculus, or maybe Tao's Analysis.

[gray gazelle]

@hasty turret : Me?

[hasty turret]

Yes

You can't study every subject out there

[karmic thorn]

Yeah, what is your objective? Would you just like to learn maths, or do you want to learn it for something specific?

[gray gazelle]

@hasty turret @karmic thorn Just for fun. Nothing specific. May not have any use in my professional life.

[hasty turret]

Then,Why do calc

and not analysis

[karmic thorn]

Then yeah, just pick up stuff which you like. Khan Academy should suffice for brushing up, maybe take a look at resources on Theory of Computation.

You can just study whatever you like as long as you have the pre-reqs.

[gray gazelle]

During my Engineering competition entrance exam in 2005 I couldn't solve (1/1+x^4) so I am sad and what to know most of the identities.

[hasty turret]

You want to write it again or smt?

[gray gazelle]

2005

[karmic thorn]

AIEEE

Smh

[hasty turret]

Ah yes,mains

[gray gazelle]

smh moment

[hasty turret]

I mean, That's history now

[gray gazelle]

15 years

Damn

[hasty turret]

Also, Don't buy books

[gray gazelle]

I am interested in many things. Can't explain why. No answer to it :(. I read always that's it.

[hasty turret]

Libgen

[karmic thorn]

Try not to get into that kind of maths imo.

That's boring maths.

[gray gazelle]

@long scarab: Then what?

[karmic thorn]

Get into real, fun maths, which is more challenging but also more rewarding.

[gray gazelle]

Did you read the ysharifi blog I pinned there

Ted

[karmic thorn]

I could not understand anything so I gave up.

[gray gazelle]

Only subject I disliked during my maths course is Set theory.

[hasty turret]

Engineering competitive exams are annoying af

[gray gazelle]

Since I don't have any objective you could suggest me anything

[karmic thorn]

@gray gazelle I highly recommend starting with Tao's Analysis 1, or a book on Linear Algebra.

This will give you a taste of what pure maths is. If you don't like all that, maybe start with something like Spivak's Calculus.

[gray gazelle]

@karmic thorn : As I posted above Higher Algebra of Hall any good?

[karmic thorn]

Not worth it imo.

[hasty turret]

It's hs math

[gray gazelle]

No

I mean not worth

[karmic thorn]

It's literally stuff you can cover up in a short span of time from a free resource like Khan Academy.

Infact, just use Lang's Basic Mathematics.

That+any standard calculus book will cover more than HS maths.

[gray gazelle]

I am now going through Tao Analysis I pdf. What additional info I get from these compared to those I posted above?

To make maths interesting right, there wouldn't be any more info than that?

[karmic thorn]

Tao's book is almost self-contained, but brushing up on calculus before would be good.

[gray gazelle]

I think now set theory is also important. Any specific resource?

[karmic thorn]

It's hard to predict what you'd find interesting, but if you feel there's a certain portion which you're finding very challenging, come back to it later and fill-up the gaps if necessary.

[karmic thorn]

Tao has a chapter on set theory in his book, although it takes the axiomatic approach so not good for a first read. Velleman's How To Prove It or Hammack's Book of Proof should be a good resource for basic set theory.

[gray gazelle]

I see Hammack is an easy read.

[karmic thorn]

Yes, it might be a good idea to go through it first.

[gray gazelle]

How to Prove it I already have physical copy. Never read 😄

[karmic thorn]

Lmao

Might be worth reading it.

[gray gazelle]

Elements of the Theory of Functions and Functional Analysis --> Any good?

Functional analysis

[hasty turret]

[karmic thorn]

No

Functional Analysis is a relatively advanced topic.

[gray gazelle]

Advanced that PDE?
Also How to Solve it – A New Aspect of Mathematical Method: 34 (Princeton Science Library) by G. Polya?

[obsidian valley]

depends on how deep you go I'm sure

[karmic thorn]

PDEs are advanced as well, although they're covered in a greater depth in maths than they are in engineering, I guess.

[obsidian valley]

you usually don't touch FA until after real analysis, no?

[gray gazelle]

I don't know about FA and RA. I got recommendation in Amazon and books were rated high. Just asked. I have a habit of buying books whether I read or not.

[karmic thorn]

Yeah, FA is probably something you look into after covering substantial amount of real analysis and linear algebra.

[obsidian valley]

buy an analysis book

[gray gazelle]

Tao

[obsidian valley]

How To Solve It is like a book for highschoolers/people in intro to proof

[karmic thorn]

Relatable. Btw I have a copy of Riley purchased from Amazon as well, which is why I recommend against it. I haven't read any more than 30 pages in that 1000+ page encyclopaedia lmao.

[obsidian valley]

so if you're reading an FA book you definitely won't get joy out of how to solve it

[hasty turret]

Don't buy Rudin

[gray gazelle]

When you said Reily, Is Arfken also the same?

[karmic thorn]

Yes.

[hasty turret]

Get Pugh

[karmic thorn]

They're more like a handy reference for physicists and engineers.

Not a book you read to learn and get introduced to the subject.

[gray gazelle]

I have a Kindle version of Arfken. Format is bad and I never read it.

[karmic thorn]

Kindle versions are meh.

[gray gazelle]

I started with Griffith's ElectroMagnetism and I saw the math used there and now I reached here.

[karmic thorn]

Here's the progression I suggest to get you started:
1)Review stuff from Khan Academy. Concurrently study from Lang's Basic Mathematics and Velleman's book.
2)Do some calculus from Khan Academy. Maybe complement it with a book like Spivak's calculus.
3)Start with linear algebra from any book, Strang/Schaum, whatever.
4)Start with an analysis text like Tao/Pugh/Abbott.

[gray gazelle]

You all suggesting Khan? Around 2010 I tried Khan and their explanations were bad. Never tried again. Must have improved a lot.

[karmic thorn]

It's way, way different now I guess lmao.

2010 must have been its infancy phase.

[obsidian valley]

How much math have you done? lol

You might be too advanced for KA

[gray gazelle]

Did lot of math, but not continuously. Gaps of years between them.

[karmic thorn]

Maybe you could do away with KA, then.

Just pick up Lang's book

And Velleman

[obsidian valley]

oh nevermind I scrolled up

lol

[gray gazelle]

You don't need much pure math for Griffith's though. Multivariable/vector calculus is all.

I was around 5k rank if you understand AIEEE>

[karmic thorn]

Then dive into Spivak or an analysis book, or a linear algebra book if you like.

[karmic thorn]

Nice.

[obsidian valley]

i mean if your algebra/calculus has deteriorated that much you should poke around on KA but I doubt it has

[gray gazelle]

Linear algebra I liked.

[karmic thorn]

Yeah, might be a good idea to brush up on the basics, then get started with a book on linear algebra.

Linear algebra is very important both within maths, and in applications outside.

[gray gazelle]

Are Olympiad questions good in touching all areas?

[hollow peak]

it seems you don't really know what you should be looking for but you already bought books

olympiad will be too hard and pointless

[karmic thorn]

I mean

Just pick up any book

And try to work through it

[gray gazelle]

@hollow peak I was trying to understand. I never tried Olympiad in my childhood.

[karmic thorn]

Keep doing hit and trials, go with whatever you find interesting.

If you want to learn it on a very serious scale, maybe pick up any undergrad math course outline and try to follow it loosely.

[long scarab]

Hi

[worldly basalt]

Comp math doesn't appeal after certain time

Questions for some reason start feeling like "what tf am I doing here"

[jade anchor]

Anyone here ever read The Book of Why by Judea Pearl? Would love to chat with someone about it. 🙂

[gray gazelle]

I would be curious to hear about this book as well

@gray gazelle Is it mathematics?

Its supposed to be a casualish book on causal stats

Rating is around 4 by 3000+ppl. Should be good.

[jade anchor]

I am actually nearly done with the book - it's been fantastic and eye-opening so far! Really great read. I am reading it with another buddy but was curious if anyone here has had a chance to look at it yet.

It is a gentle introduction to what is called "do-calculus" and how it has made making causal inference both easy and possible. Lot's of great nuggets in the book thus far!

[gray gazelle]

There are a lot of calculus books. I have 3.

[jade anchor]

I only skipped one chapter - Chapter 6 - as I wasn't too interested in its discussion on brain teasers.

[gray gazelle]

A book named in russian. Contains toughest problems. One of the question was volume of spehere in tetrahedron. Anyone knows the book?

[karmic thorn]

Literally every Russian maths book ever.

But to narrow down your search, try some books written for contest maths in the Soviet era.

Fomin's Mathematical Circles is one I can remember.

[gray gazelle]

Checked. Not that. That was extremely difficult. I gave to my teacher. She returned it next day saying couldnt understand anything.

[karmic thorn]

Check their olympiad prep books. ¯\_(ツ)_/¯

[gray gazelle]

Hi everyone

Can I get some recommendations on books for trigonometry

With more focus on the inverse functions

That's a bit more rigorous in it's explanations

For instance in solving sin(x) - cos(x) = 0, we can divide both sides by cos(x) since cos(x) = 0 is never a solution

Or another instance, we can sine both sides of an equation but in doing so we introduce a plethora of extraneous solutions

stuff like that

Or am I mistaken about what a book should do

are these more rigorous things intentionally left out for the reader to think about manually

I'm not sure about a book that does this, I would say the reader should think carefully as to whether a "solution" is actually correct

Maybe some introduction to proof type books might discuss common pitfalls/little details like that or something

ah I see

I do suspect my difficulty with trig has less to do with trig and more with functions in general

With respect to how the number of solutions can be changed and stuff

Thank you for the tip on the proof books

I'll look online for a bit

[gray gazelle]

@karmic thorn : I decided to go ahead with Tao's Analysis 1. Just wanted to get your suggestion on 'Principles of Mathematical Analysis '.

I think its author is what you all suggested to avoid?

[hasty turret]

Don't

[quick hornet]

rudin's PMA is a famously hard textbook.

personally i dont think its as bad as its reputation suggests

but its still fairly jarring

for a first course in analysis

[crystal kraken]

Avoid rudin as your first read

[gray gazelle]

One of the first thing Tao asks is the one doubt I had about summation of series. I will check later whether it also gives answer. 😄

[hasty turret]

I don't think he will

[gray gazelle]

Also I need recommendation of a good online graph plotter.

[hasty turret]

Desmos

Ok,What was your doubt? If it's too simple,he might expect the reader to be able to answer it without any aid

[crystal kraken]

He will tell you to go to some exercise on some page where he would ask you to answer the same question

[hasty turret]

Yea,That

[gray gazelle]

This one --- >Example 1.2.2 (Divergent series). You have probably seen geometric
series such as the infinite sum

So the same reasoning that shows that 1 + 1 /2 + 1 /4 + . . . = 2 also gives
that 1 + 2 + 4 + 8 + . . . = −1. Why is it that we trust the first equation
but not the second? A similar example arises with the series

[gray gazelle]

Is it good or bad

[crystal kraken]

In a way, good coz by the time you reach to that exercise, you'd have studied enough stuff to answer the question yourself

[gray gazelle]

@hasty turret : Is there any graph plotter for complex plane?

[hasty turret]

I think wolfram works

[stray veldt]

the problem with plotting complex functions is that there is a lot of different ways to do it

wolframalpha does it ok

if you want more sophisticated methods you probably need more powerful software

i.e. mathematica offers https://reference.wolfram.com/language/guide/ComplexVisualization.html

[grave egret]

What % of the exercises should I be able to do if I've understood like the chapter?

(Schilling).

[gray gazelle]

All?

[stray veldt]

be able to do or actually do?

i think you should be able to do most of them

but its not necessarily required to actually do them

[molten wave]

I think you want to be confident in your ability to do all

and then actually do one of each type or something like that

depending on how similar the exercises are

[hearty steppe]

What mniip said 👍

[gray gazelle]

How fast one should complete a maths book if the basics of the books are known 😄

[quick hornet]

depends on the level of the text

i'd say i know the basics of algebraic geometry but if you asked me to do all the exercises in, say, vakil, it'd probably still take me quite some time

months at the minimum

(hartshorne would be faster but thats because i already did all of it lmao)

(even then it took me like 1.5 years, skipping chapter 1)

(though i didnt really know "the basics")

[karmic thorn]

Recommendations for an introduction to automata theory?

[gray gazelle]

@karmic thorn Automata Theory Language & Computation By Pearson. This I have read. But not sure whether it's the best. But it's simple.

[hasty turret]

I guess that's good

[karmic thorn]

[prisma snow]

Why?

Okay, just delete it then lol

[gray gazelle]

Yeah that's good

[ornate grove]

who learns French

I need help

I need to spell “vu buvez” (drink) but I’m getting it wrong

[stray veldt]

this is #book-recommendations on a math server

[gray gazelle]

@ornate grove If you can help me integrating xtan(x)e^x I will help you.

[ornate grove]

x

[quick hornet]

"vous"

[gray gazelle]

Once I complete Tao what's next?

[hasty turret]

Finish it

[gray gazelle]

Complex Analysis - Lars Ahlfors How is this book?

[marble solar]

Very good

The only thing is it doesn't focus on computation as much as other books

And it might assume familiarity with real analysis

[gray gazelle]

ahlfors is very good

the guy who directed ahlfors' doctoral thesis was born like a block from my house

rolf nevanlinna if you've heard

And Ross for Probability?

[marble solar]

🤷

I've heard Durrett is the go to

[narrow talon]

Not Durrett for sure! Don’t get me wrong it’s a great book, but read it either after you have taken a course in basic probability or graduate level real analysis (ie. somewhat familiar with measures)

[marble solar]

🤷

[narrow talon]

I’ve never liked Ahlfors, tbh it seemed pretty computational and dull, maybe so didn’t get far enough into it

[marble solar]

Computatonal? Ahlfors?

Did we read the same book?

He has so few exercises that require computing

[narrow talon]

Haha! I quite like Conway so if you’ve used that at all maybe that would point towards what exactly didn’t appeal to me about Ahlfors

[marble solar]

I've heard mixed things about conway

with weird notation

getting into algebra too early

[narrow talon]

Yeah I know it’s somewhat divisive, but I quite enjoy it regardless

I’d like to work with Rudin more this semester for complex. That’s also not so popular

[marble solar]

It's not popular because Rudin doesn't teach you

Rudin just does what Rudin wants

[narrow talon]

Bs

[marble solar]

and whether you get it or not is up to you

Ok

I've read PMA and Real & Complex, worked through most of the two

[narrow talon]

Rudin isn’t playful but he does give some intuition. The only thing I dislike is that he gives you very little idea of what results are actually important

[narrow talon]

Me too

[marble solar]

The convex function stuff in real & complex is pretty lackluster

[narrow talon]

I see we have pretty different mathematical/pedagogical tastes

[narrow talon]

Yeah I’ll give you that one

[marble solar]

Basically anything that's done in Rudin is done better with more detail and better exercises in a different book

Rudin is popular because it's small, and makes professors think to motivate. It's like lecture notes

[narrow talon]

That’s true of pretty much every book I think

[marble solar]

Spivak's Calculus and Calculus on Manifolds is pretty hard to beat

[narrow talon]

I like the topics Rudin covers, how easy it is to reference, and many of the exercises

[narrow talon]

Very different level, especially for RaC

[marble solar]

It's clear that Pugh's Real Mathematical Analysis beats out Principles

[narrow talon]

Also CoM suffers far more than Rudin on the issues you’ve mentioned

[marble solar]

There's more insight, more exercises, and more material

I think Calculus on Manifolds has the right amount of details and doesn't pull tricks out of a hat

On every other page

[narrow talon]

Can't speak much for Pugh, I like Johnsonbaugh and Pfaffenberger for the level of PMA

[narrow talon]

It's pretty much a problem book. CoM is to vector analysis as Varadhan is to probability

[timber mesa]

it teaches multivar while leaving half the important stuff to the reader lmao

and that includes filling in the details on some proofs

[gray gazelle]

Why is computation bad? Thats how we test our understanding.

[quick hornet]

no, we test our understanding by doing exercises

sometimes those exercises are computational, but they dont have to be (if your goal isnt to learn how to compute)

[marble solar]

||If you're goal is complex analysis qualifying exam, you best do residue out your ears||

I still can't do basic complex analysis integrals

Go Bruins!

lol

[gray gazelle]

$$\int_{-1}^1 \frac{dx}{(x-a)\sqrt{1-x^2}}$$ for $a \in \bC\setminus[-1,1]$

[hasty eagle]

(T*(Terra), -dτ)

[gray gazelle]

pain

[marble solar]

See if you had just gone to UCLA

You wouldn't have to learn that

It's only like one question on the final out of 9 or 10

[gray gazelle]

Journey Through Genius - (eg)How newton came up with a solution, even after reading it I dont understand. 😩 I hv no intuitional skills.

[marble solar]

So you can get an A without doing that like everyone did

[worldly basalt]

Moonbears just flexing his Uni

[gray gazelle]

my complex analysis final last semester had three residue integrals on it

good thing we had like

48 hours to submit it

im looking at some of the past complex analysis quals and the ones from waaay back look so easy

[narrow talon]

K&K vs Goldstein for a first introduction to physics/classical dynamics?

[silk quartz]

Goldstein was an upper division text for physics majors.

[narrow talon]

Yeah I know, but I still hear it recommended often for a first course for math people

[silk quartz]

Goldstein really glosses over most of Newtonian mechanics.

Which I suppose is fine, if you already have some background in physics.

[narrow talon]

Nah I don’t, so maybe K&K

[silk quartz]

I wouldn't recommend it as a first course for math folks, though.

[narrow talon]

No? What would you recommend?

[silk quartz]

idk. I haven't used all that many intro physics texts to have a strong opinion.

The text I used for undergrad was The Mechanical Universe

https://www.cambridge.org/core/books/mechanical-universe/6560B1D01F709A198345C53E6AC8C981

[narrow talon]

I’d like to avoid slogging through a massive intro to physics book

[gray gazelle]

What about theoretical minimum? Leonard Susskind.

[novel iris]

That's more of a physics book for laypeople who know some math

Also goldstein is grad level, k&k is like first year mechanics (a very good book for what it does)

[marble solar]

I wasn't good enough to stay

So I'm flexing my inability

[tight crag]

[karmic thorn]

Taylor's Classical Mechanics is good for an intro.

[hearty steppe]

I still prefer University Physics by Young and Freedman. I’ve been good with that book for the past 7 chapters I read so far

[marble solar]

Halliday and Resnick it's the best

[gray gazelle]

You're talking about walker or krane?

krane is better imo

[hearty steppe]

Halliday and Resnick?

Anyway I feel like unless you are trying to major in physics, Young and Freedman should be a good start

[narrow talon]

It’s pretty impossible for me to major in physics at this point, looking to at least be able to work through something like this: https://www.cambridge.org/core/books/statistical-mechanics-of-disordered-systems/EBD1B478730D420FA380F510D8C3EC65

[hearty steppe]

Depends on what you are trying to do

[narrow talon]

Young and Freedman is exactly the massive intro to physics book I wanted to avoid. I’ll probably end up going with Taylor/K&K

[hearty steppe]

Start from the basics and then focus where you think you’ll gravitate

Young and Freedman has been great so far

I’ve been getting through it without much issue

[narrow talon]

Statistical physics & condensed matter physics

[hearty steppe]

I’m like 8/40 chapters in

Yea go thru young and freedman

[narrow talon]

Why?

[hearty steppe]

My focus will be soft condensed matter

Trust me

It’s been a great intro read for me so far and developing that formal background in physics will take time and patience

[narrow talon]

Wym formal background?

[hearty steppe]

Seems big but I am about a quarter the way thru it after a couple months

Well learn the fundamentals

Then worry about where your heading

[narrow talon]

I would like to finish dealing with classical mechanics at the very least before fall

[hearty steppe]

You realize classical mechanics is one whole area of physics right? There is classical mechanics and then there is quantum/relativity

[marble solar]

Halliday and Resnick it's a classic physics book

Not in the classical mechanics sense

[hearty steppe]

Your not gona learn all of one giant area of physics in a few months mate

You’ll learn the fundamentals

Of classical

[marble solar]

I think you can get a reasonable introduction to move on in a few months

[narrow talon]

I’m aware, and I’m avoiding it’s depth rn, I’m not interested in symplectic manifolds at the moment but I’m absolutely interested in Hamiltonians

[hearty steppe]

Yea that’s exactly my point moon

[marble solar]

The entirety of the field would be nigh impossible to know well in a few months

[hearty steppe]

Ok so start with Young and freedman

[marble solar]

I prefer Halliday and Resnick over Sears and Zemansky

but they're both solid cat man

[hearty steppe]

Then worry about the more advanced book recs like Taylor or K&K later

[narrow talon]

Why are they more advanced?

[hearty steppe]

At least get thru the classical mechanics section of Young and Freedman first

[marble solar]

https://www.thriftbooks.com/w/physics-volume-1_david-halliday_robert-resnick/3136775/item/4360586/?mkwid=|dc&pcrid=474981229867&pkw=&pmt=&slid=&plc=&pgrid=117539251328&ptaid=pla-988288505448&gclid=EAIaIQobChMIqKHn1b7m7gIVYQJ9Ch1xjAZXEAQYAyABEgKEY_D_BwE#idiq=4360586&edition=3262834

[narrow talon]

Like, what makes them more advanced?

[marble solar]

This is what I used Jason

[hearty steppe]

Before doing Taylor or K&K

[marble solar]

This book is at a step up of Young and Freedman

[hearty steppe]

Yea start with Young and Freedman

[marble solar]

I had a friend that used this before going to Physics PhD program thoroughly. I prefer this as a first glance

[hearty steppe]

It’s like the best introductory book

[marble solar]

Young and Freedman went too slow for me and too methodical with numerical examples, etc.

[narrow talon]

👍👍

[marble solar]

Halliday and Resnick is faster, more intense, better problems IMO

[hearty steppe]

That’s the thing about young and freedman. If you have no formal background, that’s what you need

Dont give him a hard time learning physics for the first time lol

[marble solar]

It's how I learned physics

I think it was good

[hearty steppe]

Well I prefer how I learned physics so far!

.>

[marble solar]

😄

[hearty steppe]

And I’m 8/40 chapters in young and freedman

That’s like 1/4 of the book in a span of 4+ months

And that’s a book that covers at least maybe 7+ semesters of physics

[narrow talon]

What do you mean formal background? I’m literally starting a PhD in a field of math intimately connected to stat mech

[hearty steppe]

Oh so you have some physics background

[marble solar]

Heck and reck is the way to go then

[hearty steppe]

Well then go for the intense introduction by all means lol

[gray gazelle]

Isn't young and freedman like a pretty basic book

[marble solar]

Just work the problems lol

Have a blast

[narrow talon]

Sort of but only from the point of view that “Hamiltonian is energy don’t worry about it”

[hearty steppe]

No the young and freedman version I have covers Modern physics too

So it covers relativity/quantum mechanics

[marble solar]

Are you doing ergodic theory/statistics/brownian motion

[gray gazelle]

It just scratches the surface though

[hearty steppe]

Young and Freedman is a very big book. It does go in depth. It’s covered nice depth for me so far

It’s over 1500 pages AFAIK

It’s a very big book

If you have the modern physics version

[gray gazelle]

It's typically used in late hs to early undergrad

But it is only a very basic intro

[hearty steppe]

So your referring to the one that doesn’t include modern physics

Modern physics one is another thousand pages

I think

Or 800 pages

[gray gazelle]

No I've seen the modern phys edition

[hearty steppe]

It’s really big book

[narrow talon]

Right now, continuous stochastic processes and data science stuff yeah

[hearty steppe]

But yes of course it is surface level stuff. It is meant to introduce you up to modern physics

But it’s a lot of content

[gray gazelle]

I feel it's kinda bloated

[marble solar]

Young and Freedman is too slow for someone with his background

Taylor or even Landau would be good

[narrow talon]

But I’m looking too work in mean field/agent based models and disordered systems during PhD

[gray gazelle]

Landau - yes

That's a more proper book

[hearty steppe]

It depends on how much he knows. He seems to be confident in what he knows so let him think that’s enough until he feels overwhelmed that’s all I gotta say.

Maybe he will be fine with your recs. All I know is just cuz you know a lot of math, doesn’t mean you will intuitively know a lot of physics

[karmic thorn]

Landau isn't really a place where one would learn a lot from. Does it even have exercises?

Taylor's Classical Mechanics is great, I reiterate.

[hearty steppe]

Young and Freedman has been amazing for me so far but then again, I have no formal background in physics

[gray gazelle]

Taylor's is good too

[narrow talon]

I have looked at Landau and Arnold (both have been recommended) but do feel like at that point physical intuition is gone for me

[hearty steppe]

Honestly mate if your getting into soft condensed matter and stat mech, you should learn the surface of quantum mechanics

[gray gazelle]

And it also covers Hamiltonian dynamics

[karmic thorn]

Yeah, and it starts with the very basics of Newtonian mechanics.

So the formal pre-reqs are no more than a first course in differential equations and linear algebra(I don't think he considers either to be pre-reqs, but I think they'll certainly be helpful).

[hearty steppe]

PhD program involving stat mech and condensed matter tho? Wait is he also interested in mathematical/Computational biology as well?

[narrow talon]

Not at all

[hearty steppe]

Ahh ok a lot of people in biophysics server need to know stat mech and condensed

Was just a hunch

[narrow talon]

Ahh neat! And yeah maybe quantum later but it’s less important rn

[hearty steppe]

Yea if your messing with stat mech and condensed, you’ll need a little of it for some intuition I’ve heard

Like probably barely surface level

[narrow talon]

Absolutely, especially for some of the systems, I won’t argue there

[hearty steppe]

All depends on what your doing.

Me personally, I’m trying to be a mathematician that does biology

Not the same as being a statistician or data guy that analyzes biological data sets.

[narrow talon]

I’m gunning for spin glasses atm

[hearty steppe]

Ahh ok. Well I think a good strategy is read Young and Freedman and what Moon recommended at same time. That way if you get stuck, you can always go back to Young and Freedman cuz it’s so accessible to people new to physics

And you’ll probably breeze thru the first dozen chapters based on your level of confidence

[narrow talon]

Sure, how long are the chapters?

[hearty steppe]

Well they can get long-ish but long to me is how easily digestible. I find concepts in physics to be sneakily abstract in a different flavor than mathematics.

This is why I am hesitant to recommend intense introduction to physics. If you don’t already have a strong intuition for physics, it is a different flavor of hard than math

There are graduate level math people on this server that struggle with classical mechanics and stuff a person who actually studied physics would perceive as “basic”

I’m still new to physics myself and I can say that the flavor of hard is based on perception. I’m still too new to learning physics to have an opinion

They are hard in their own way but they are both the hardest subjects for different reasons

Physics is about abstraction of the universe in how it works while math is abstraction in quantification/computation. They are different flavors of the hardest things to conceptually understand for human beings (more or less)

[marble solar]

I disagree with the young and freedman recommendation

Taylor would be fine

[gray gazelle]

isnt young and freedman like algebra based physics

[hearty steppe]

I mean I thought Taylor was a bit too densely worded and confusing for a first read. But also, maybe he should just read both books at the same time? That’s what I would do.

Actually I make it a habit if I’m not sure what book works for me is read a chapter from one book, and if it’s not confusing the hell out of me so far, keep going. Otherwise read a chapter from one book then go thru a chapter or so of another

There’s calculus in young and freedman from where I’ve gotten to so far

[gray gazelle]

oh mb

[hearty steppe]

Yea the chapter I just finished referenced using partial derivatives for conservation of energy equations

So like it goes right into multivariable Calc stuff within the first couple chapters but yea it tries to be mostly approaching physics from the ideal models first for the first dozen or so chapters

I am anticipating it to start getting hard-ish with the math with using Diff Eq stuff in maybe chapter 15 or 16.

Like when you move away from the simulated simple “ideal” models. You get a bunch of nasty systems of equations and stuff

This is when you add more realistic parameters to account for non conservative opposing forces and etc

Air resistance, etc

[lone linden]

Anyone know of any good books for learning geometry using vectors? Aiming at a high school audience with nothing beyond calculus. Trying to also avoid algebra if possible (trying to gear towards students who just like geometry and don't have to study other branches of math yet) but is not required. Taking any and all suggestions....also any good advanced trig books?

[gray gazelle]

Please explain Axiom 2.5 (Principle of mathematical induction). in Tao's book for eliminating 0.5 , 1.5 etc.. numbers from Natural Numbers. I understood mathematical induction , but it't clear from the example how it's skipped.

[hasty turret]

Ask in #proofs-and-logic

This channel is for book recommendations

[gray gazelle]

Probability Theory: The Logic of Science by E.T Jaynes. How is this?

Introduction to Topology by Bert Mendelson

[karmic thorn]

I don't think you can have geometry in terms of vectors without appealing to algebra lmao.

But Lee's Axiomatic Geometry looks good.

[quick hornet]

geometry in terms of vectors

uses no algebra

you're welcome

[molten wave]

that's A-B

if you studied algebra you would've known the difference

[dapper root]

Yeah

Smh

[broken meadow]

Smh

oh "difference" nice one mniip

[late harness]

Does anyone know what happened to the "New math" initiative in France in 1961, headed by Georges and Frederique Papy? I just got hold of two of their textbooks and they're not bad.

The books are called "Modern Mathematics 1" and "2".

They lean heavily towards teaching mathematical intuition.

[hasty turret]

How do you teach Intuition out of a book

[late harness]

Perhaps it's not the right word, but I believe that's what they are trying to achieve, by creating examples and exercises that are very intuitive. If students are able to copy that, that's what I thought.

[gray gazelle]

Concepts of Modern Mathematics - Ian Stewart

[swift flame]

Is this the book??

[swift flame]

Do you have the pdf of this book?

[timid vector]

what would be the preqs for something like shafarevic algebraic geometry?

[ripe granite]

undergrad algebra

[strange mulch]

There was a New Math movement in america during the 60's that argued that the common man who was taught long division and long multiplication didnt really have any intuition for the arithmetics, they merely just applied an algorithm and that it was noted that children never got to grasp that arithmetics was commutative nor distributive and many things more in mathematics taught at elementary. New Math in the 60's is what common core is today basically but it is apparently not constrained to just arithmetics. As what the french did though i have no idea.

Here is Tom lehrer making fun of the new algorithm taught to kids in the 60's:
https://www.youtube.com/watch?v=UIKGV2cTgqA

I guess "teahing intuition" is just stepping back fromt he old traditional of forcing children to swallow facts and rather try to make them reach conclusions on their own. As in why is sin < x < tan x

[strange mulch]

Or why limit sin x / x = 1 when x approaches 0 which the rigor proof is an integral of some quotient with a squareroot which doesnt really bring much intuition to somebody who was just taught what a limit is

[late harness]

@swift flame No, I found them at an antiquarian.

I would like to get my hands on the rest of the series.

[faint charm]

how accessible are apostol's calculus books?

[static crest]

for self learning?

not the best

[faint charm]

ive realized lmao

do you have any suggestions?

[gray gazelle]

just read spivak

[faint charm]

no sarcasm?

[obsidian valley]

just read spivak

no sarcasm

we don't do that around here

[faint charm]

thank you, apostol was kinda flipping me over

[hearty steppe]

Try Professor Leonard Youtube channel

[swift flame]

Can some1 suggest a book for multivariable calc practice?

[hasty turret]

Try the multivariate chapter exercises in baby rudin

[marble solar]

Apostol volume 2 is always good

Another one is open stax calc 3

If you want hardcore that's spivak calc on manifolds

[fossil arch]

Do you guys have any recommendations for 'best' calculus (single & multi variable, can be separate) books for learning calc?

I've already got some practice with calc but I'd like to 'restart' with stronger fundamentals

[hasty turret]

Spivak?

[fossil arch]

Isn't that analysis?

Or like an intro

[hasty turret]

It's calc

[fossil arch]

I don't have much experience with proofwriting (or reading), do you think I can still make full use of it?

Actually no experience writing, I've read the "sqrt of 2 is irrational" proof and that's it 💀

Would Loch's intro to proofs be enough? 💀

[hasty turret]

Yes

[fossil arch]

Alrighty

I'll give it a shot 😁 I'm excited, heard a lot about this book

Hope I can handle it...

[marble solar]

Spivak or apostols volume 1 nd 2

[fossil arch]

Spivak is downloading right now, my wifi's kinda fucked so it might take a while...