book-recommendations

[rancid hollow]

Almost as similar to work with as the Riemann integral but Iirc more "powerful" than Lebesgue in functions I->R

https://en.wikipedia.org/wiki/Henstock–Kurzweil_integral?wprov=sfla1

[remote sparrow]

https://www.amazon.com/Calculus-Variable-Dover-Books-Mathematics/dp/0486838064

https://math.stackexchange.com/questions/731087/joseph-kitchens-calculus-reference/766183#766183

found a calculus book that looks interesting. apparently people view it as comparable to spivak or apostol. i haven't found any pdfs for the book yet, though.

interestingly, i found a spanish language pdf of this book, but no english version is available.

it's a tad more expensive than the typical dover, but at least it's widely available.

[sturdy shore]

I personally thought Lee's book was more difficult, worse pedagogically and sequenced worse

but the only one who can say for sure is you

just give it a try

[fossil arch]

Why?

[sturdy shore]

why to which of those 3 lol

[fossil arch]

All three?

Especially worse pedagogically

Right away I like it more

Lee talks so much more

Bless his heart

[gray gazelle]

It's amazing that you know manifolds and you work with them. I always wanted that but I'm really lazy and stupid in understanding such concepts

[fossil arch]

I don't Hin, I'm learning :) you're not lazy or stupid at all

You can do this just the same as I can, even better if you have a stronger math background

[sturdy shore]

I mean, that's the one thing that I can't give a reason to other than vibes, because I'm also a learner. All I know is I learned better from Tu than from Lee, but it could just be because I tried Lee first, and that made it easier to read Tu giving me a bias

I can say why it is sequenced worse though. I really prefer how Tu places partitions of unity into the middle portion of the book and manifolds with boundary all the way down to the integration section, which is when they become necessary. On the other hand Lee does both of those right in the beginning and also just a boatload of topological properties of manifolds. That way of sequencing is better for a reference/second read type of book but the way Tu does it just felt way better in exposition

[gray gazelle]

thank you for this motivation.. I really appreciated it feather

[maiden halo]

still not bad for 800 pages!

[gleaming void]

Do you guys think that if I want to learn proofs "A Long-Form Mathematics Textbook" - By Jay Cummings is a good book for me to read?

[remote sparrow]

yeah

[gleaming void]

ok thanks :)

[fickle bough]

I've heard a lot of good things about his I'm going to check it out thanks

didn't know he had the treatment I was looking for, now I'm definitely getting it

[mellow wren]

Chapman Pugh

[remote sparrow]

*charles pugh. also pugh doesn't start from the peano axioms. properties of the naturals, integers, and rationals are assumed. at best he sketches how to construct the reals from the rationals.

CT wants to start from the naturals

[mellow wren]

I mean his name is Charles Chapman Pugh so

tho I mean sure I can see what you mean

Tho CT never really mentioned he wants to rigorously build up from the naturals so I assumed he'd be OK with covering it with less rigour (because Pugh does still talk abt constructing the rationals and then dedekind cuts to get the reals are covered in pretty OK detail imho)

[dusky berry]

is "calculus by larson and edwards 10ed" is good book for someone who doesn't know any calculus and good for people who want to teach calculus?

[remote sparrow]

it's fine

[gray gazelle]

my personal domain for zlib just got seized, now im worried

[marsh veldt]

F. West wanna monopolize knowledge after stealing from third worlds for decades

[desert oriole]

damn

[alpine rover]

anyone know a clear, well-written abstract algebra text that's good for self-study

maybe less advanced than dummit & foote

[heady ember]

Look in pinned

[alpine rover]

i'm using artin right now, looking for something with better exercises

[hazy elk]

The excercises in Herstein and Hungerford are quite good

[fierce hedge]

Judson is a good book but exercises are generally on the easier side compared to Artin. Pinter has a lot of exercises not sure about the level. Herstein is the gold standard for exercises although some can be very difficult.

Dnf also has very good exercises at various levels

[fierce hedge]

How does hungerford compare to Herstein?

[hazy elk]

The theory in Hungerford is definitely more advanced and requires you to put in more work. Has coverage of a lot more topics than Herstein.

But I think it's better as a 2nd look at algebra

[alpine rover]

thank you

will look at those

[gray gazelle]

good book for advanced calculus?

(or principles or real analysis)

[spiral sky]

Spivak and Rudin

[fierce hedge]

I see, so it's Lang level?

[hazy elk]

Haven't read Lang, but Hungerford is definitely not incredibly terse. An advanced undergraduate/graduate student should be able to read it like any other math text they are expected to read at that level. The proof details you'll have to fill out don't require so much ingenuity

[crimson leaf]

Hungerford also has a first book

[fierce hedge]

Is it Hungerford's Algebra (yellow book) or Abstract Algebra: An introduction?

[clear wasp]

Do you guys reccomend any books for math for someone goingto highschool next school year

im 13 btw

[cobalt arch]

Concepts in Abstract Algebra by Lanski is a relatively unknown book but seems to be very clearly written with complete proofs and is compared to Hernstein but with more focused content by a reviewer.

[remote sparrow]

https://www.reddit.com/r/math/comments/136sb5m/is_there_a_measure_theory_book_for_dummiesidiots/

new thread

might get some interesting comments throughout the day

[fierce hedge]

Couldn't find any pdf anywhere but MathSorcessor's reviews for this book looked interesting enough so I bought it. Hopefully it'll reach before my exam

[wanton spade]

Any good books on combinatorics?

[inner token]

For anything high-school algebra Precalculus trig or Calculus related use Khan Academy, but if you want a nice stepping stone to higher math work through this : https://www.people.vcu.edu/~rhammack/BookOfProof/

[ocean mulch]

Herstein's 2nd ed is great, I can say. He has 3 different proofs for a Sylow's theorem, and introducing things quite gently.

The only problem is he didn't go deep into modules, which is quite sad. But for a beginner, I would recommend it.

[remote sparrow]

A Walk Through Combinatorics by miklos bona

[ocean mulch]

Depends on the level

[brisk horizon]

Hi guys, I’ve always loved math, but I kind of didn’t have the best teachers when I was younger, so now I’m trying to regain my love for it. Do you guys have any resources that I can use? Like books, websites, and YouTubers, anything would be appreciated (if not, that’s okay). thanks guys

[coral prawn]

What's your current level?

Like, what maths do you know, and/or what do u wanna learn?

[brisk horizon]

I'm going to be honest: not very high. I stopped paying attention past fractions, and now I feel like I’ve fallen so far behind in my old hobby, and honestly, any math, really. I’m just trying to get back in the game.

[mellow wren]

I'd recommend probably using Khan academy to get up to calculus

[coral prawn]

Ic.... how about trying out Khan academy's website then? Perhaps u could try out their algebra 2 class, stuff like that, see how u perform

[brisk horizon]

Yes, I have been doing that. What a marvellous tool it is, but I was just spreading the word to see if I was missing out on any obscure resources.

[coral prawn]

I wouldn't really recommend any books unless you find yourself really needing it, since.... aside from those school textbooks, not really any mathematical text teaches basic algebra. But if you really want one, James Stewart's precalc book should do the trick. Never tried it, but I've seen it recommended here for those who'd like to learn precalc. He also has a calculus book. I read a few chapters, it was nice, but I switched over to spivak due to personal preferences

[brisk horizon]

Thank you I’ll have a look at them tomorrow morning

[coral prawn]

Oh, and you should know that pirating is illegal, so you totally should not not use libgen nor PDFdrive, if you get what I mean

Have fun

And all the best

[brisk horizon]

Me a pirate. Never… and thank you

[worn oasis]

Im looking for a book to complement dummit/ foote for a graduate course

[finite crane]

just read Rotman's Advanced Modern Algebra for algebra

[coral prawn]

I wanted to read a book that has to do with the complex plane, stuff like euler's identity etc... idk how to describe what I want, if I said this and left it at that, people would point me to a precalc book. If I said "I want smth advanced", then I'll probably get a complex analysis book in return I'm kinda looking for smth in between.... any suggestions?

[finite gale]

how's spivak going

but to answer your question, if you want stuff like euler's identity, that is quite literally in a precalc book

[coral prawn]

Yeah... Ik, but I don't really know what to describe what I want- more like smth that covers.... um.. Maybe stuff on using trig, inverse trig, logarithmic functions on complex numbers- ummm.... *OK dammit I'm not really sure myself 💀 * that still feels like smth u will see in a precalc book

[finite gale]

ok, so have you taken precalc?

[coral prawn]

Yeah

[finite gale]

then you should already feel comfortable with trig, inverse trig, euler identity

if you want to learn about complex logarithms, you're most likely going to find that in a complex analysis textbook

[coral prawn]

Yeah. I was looking to cover more stuff relating to these concepts so that I can read them at my own free time, I felt like it'll help bridge my jump to complex anal. But I wasn't sure if there was smth "in between" that

[finite gale]

i think it would be most suitable to continue doing spivak, and then do some real analysis, and then if you choose to do so at that point, to continue towards complex analysis

going ahead of yourself now is really not going to do much good or make much sense

[coral prawn]

True I probably should chill out

[finite gale]

spivak should be plenty alone for you to read in your free time

[coral prawn]

Tks tubular

[fierce hedge]

Maybe Dr. Euler's fabulous formula. It's not a textbook per se but I have heard it's good

[proper harness]

Hi, which books give the most detailed information about the Riemann sphere?
I know it's in the realm of complex analysis but looking more for detailed stuff for applications.

[hazy elk]

What point of few do you wish to see the Riemann sphere in? iirc in Artin's chapter on representation theory there's a small discussion of it and how it ties into group actions. In Ahlfors ch 1 there's a lot of explicit calculations and formulae on the Riemann sphere relating it to the complex plane. Pretty sure it's also looked at as an example of one point compactification in Munkres.

[foggy relic]

Lang algebra

[subtle mango]

resources (eg textbooks, lec notes, etc) for complex geometry/topology?

likely will read it after a course in complex analysis and a diff one in diff top

[subtle mango]

https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf
thoughts on this one?

[split sorrel]

any reccomendations for differential forms?

an introductory type of book would be nice

[sturdy shore]

what is your math level?

[split sorrel]

around introductory course to ode level

and have dabbled around in various fields of math

[sturdy shore]

there are a bunch of multivariable calc books that include a treatment of differential forms, popular ones are shifrin and hubbard hubbard
there is bachman - geometric approach to differential forms that might be suitable for you

[junior isle]

Book for self learning linear algebra? Im in calc 2 but also learning proofs with book of proof, and id like to start linear algebra afterwards

[sturdy shore]

finally there is walschap - multivariable calculus which is like the first 2 I mentioned but at a considerably higher level, if you want a challenge this one is for you

[inner token]

I'm a linear algebra done right by axler stan

Well motivated and the exercises are fun

[junior isle]

But is it appropriate for a beginner? It says its supposed to be a second exposure on the subject

[inner token]

Students in college generally get a computational linear algebra course while they take Calculus, where you learn to row reduce, find eigenvalues, diagonalize matrices, but you don't prove anything. Having a computational background doesn't hurt but i don'tthink strictly necessary; maybe you could work through that and a computational book in tandem. Just an idea@junior isle

[junior isle]

Ok, which computational book would you recommend, given that It has at least some answers to he exercises?

[inner token]

Permission to dm @junior isle ?

[junior isle]

Sure

[remote sparrow]

#book-recommendations message

[finite gale]

i don't think it's necessary to take a computational linalg course before a proof-based one

like it's very much unnecessary

[remote sparrow]

yeah the matrix algebra stuff is also very tedious

just try a couple small examples by hand then program it on a computer

[finite gale]

like even if you take a proof based course/textbook, you're going to do some small computational examples to make sure you understand the material

you don't need a full on computational class to teach you that

[remote sparrow]

all the books i recommended are proof based

[finite gale]

in fact, i'd say that an intro computational class on linalg is probably a waste of time, if you're going to take linalg again afterwards

[remote sparrow]

hefferon's book is not computational, but it is definitely not an abstract linear algebra textbook like fis or hk

it will prepare you for those books pretty well tho

nice thing about hefferon is that he has a full solutions manual

plus youtube lectures

[finite gale]

i mean you can always just ask for help in this server or find some solutions online or something

if that's really the concern

[remote sparrow]

hefferon wrote the solutions himself, and it's easier than waiting for help

you can then use this server if you need further clarification, but at least you'll have a solution already available from a reputable source

it's pretty much a full package for self study

[junior isle]

Once i finish the book of proof ill use It, thanks!

[sturdy shore]

it's not, but you definitely need to learn about stuff like gaussian elimination, which axler won't teach you

though the answer to that is, don't use axler if you are in this situation

[finite gale]

doesn't axler also define determinant in a pretty scuffed way?

(i have not used axler that much, but this is what i've heard)

[sturdy shore]

the issue is not how he defines it, how you define the determinant doesn't matter once you prove the other ways to define it are equivalent

the issue is that the determinant is banished to the last chapter of the book

[proper harness]

mainly as projective space
I'll check out Ahlfors, thanks!

[tawny jetty]

Anyone know a good book, online course, or other resource on Evolutionary Game Theory?

I saw this class: https://math.dartmouth.edu/~m30s21/. Looks like they recommend Nowak, M. A. (2006). Evolutionary dynamics. Unfortunately, they don't have homework sets I can follow :C

[unborn estuary]

Anyone here read zorich? How long did that took and did you work on the exercise?

[hazy elk]

Sorry but I don't think Ahlfors has any reference to it being a projective space. I think Artin might tho, on his chapters on matrix groups (The later ones related to representation theory). I don't remember explicitly what it is that he does because its been a while since I opened Artin. Maybe other ppl can give you a better reference.

[obtuse forum]

Any good manga, or military novels anyone would suggest

[proper harness]

hm yeah

I looked at it and it only had 3 pages on the Riemann sphere specifically plus some stuff about Moebius transforms

[rigid barn]

What's a good advanced (i.e. not just the utmost basics, like the Frobenius endomorphism and the classification) resource on finite fields, particularly their applications to other areas?

[marsh veldt]

Holyland?

[dark elm]

hmmm for the manga, it depends on what type of manga you'd like. are u into more of a slice of life, or fantasy, sci-fi, etc.?

[obtuse forum]

Anything really

[dark elm]

if so, then i recommend One Punch Man for starters xD
the art is great and it has a bizarre plot for a story about a hero
Aside from that, I also recommend The Promised Neverland, it's a great thriller for a manga
and lastly Bananafish - this might be centered for women i think since it's kind of gay, but the plot is very good and is kind of related to a military setting, since you also want to read military novels

i have many more that i would want to recommend, but i think these might suit u for now because some mangas might overwhelm you/maybe not get u interested since idk if you already read mangas before

[obtuse forum]

I’ve read some of the mangas

[dark elm]

and right, One Punch Man is still an unfinished manga, so if you want a manga that is finished then i think you should stick to the popular ones that are finished like Naruto or Dragon Ball

[dark elm]

ahhh, then can you recall which mangas you have read?

[obtuse forum]

I think volumes 1-4 so far I can’t remember

[dark elm]

well that's okay, these are just my recommendations

[obtuse forum]

Fair

[dark elm]

there are many more good mangas that you can surf in the internet too, so it's your choice

[obtuse forum]

Yep like Tokyo ghoul

[fierce hedge]

The promised Neverland's S2 sucked ass, I hope that's not the case with the manga. I really liked the season 1 and the whole premise

[dark elm]

i also liked s1 too! and i think it was better in the manga because a lot of people said that the manga was better
even my friends recommended me to read the manga instead of watching the anime

[fierce hedge]

Ah, cool. Btw I also have a manga recommendation if you're into Android types stuff like future where Androids are just like human. It's called - Pluto

It's like what if Androids were almost like humans and had emotions and stuff

[cedar ridge]

very good

climaxes too early tho lol

[safe lintel]

Can anyone recommend me a good calculus book at an early-mid university level (Meaning I know the basics, but I'd like to go for more)?

Is "Calculus: Early Transcendentals" recommended?

[worthy venture]

yes

stewart's book is a pretty accurate representation of calc 1-3 classes. you can also use pauls notes which has is definitions essentially copied from the same book

[safe lintel]

Thanks

[worthy venture]

if your major is eng or physics u should also take a look at mathematical methods or engineering and physics by K. F Riley et al.

[safe lintel]

Do you mean this https://www.amazon.com/Mathematical-Methods-Physics-Engineering-Comprehensive/dp/0521679710/ref=sr_1_1?crid=20PYDE0KTK4Z9&keywords=mathematical+methods+or+engineering+and+physics+by+K.+F+Riley+et+al&qid=1683307740&sprefix=mathematical+methods+or+engineering+and+physics+by+k.+f+riley+et+al%2Caps%2C227&sr=8-1 ?

[worthy venture]

yeah

u can find a pdf of it. im not sure where

[safe lintel]

Thanks for the recommendation, I'll get it

[worthy venture]

np. both are available free. i forget where the pdf file download is

[safe lintel]

Ty, I'll manage to find it

[analog lava]

yo is the rising sea friendly

with like noobies

AG vakil

or do i have to know all of AM

(atiyah mcdonalD)

[worthy venture]

there a free pdf of that book

[fierce hedge]

Does this mean; is the rising, sea friendly or is the rising sea, friendly?

[analog lava]

second

[fierce hedge]

Is that a book on ag? Or some notes

[analog lava]

book on ag

[merry echo]

Where can I get that green book

I can’t find pdf nor amazon

Does anyone know

[remote sparrow]

there are many green books

what book are you talking about

[dark elm]

can someone recommend me a book from the theory of interest aside from Finan's book, "A Basic Course in the Theory of Interest and Derivatives Markets"?

[sudden granite]

do you guys have any literature recommendations

[remote sparrow]

https://www.amazon.com/You-Give-Mouse-Cookie-Book/dp/0060245867

[loud cradle]

if we're doing children's books then it would be a shame to omit https://www.amazon.com/Everyone-Poops-Taro-Gomi/dp/1797202642

[spiral forge]

Hey is there any have read the book 'Calculus on Manifolds' written by Spivak? I wonder is the book out of date today and is it appropriate if I want to read the textbook 'Differential geometry of curves and surface' written by do carmo.

[sudden granite]

thank you

next on my list after the hungry caterpillar

and chrystheanium

[fierce hedge]

https://waittp.wordpress.com/2018/02/28/the-rising-sea-foundations-of-algebraic-geometry-a-review/
According to this review, nope

[sudden granite]

reading is actually cracked though

shout out to all the russian authors out there writing the most gut wrenching heart throbbing darkest books ever

[inner token]

I don't know what to study analysis-wise. I want to practice up to take a PhD prelim.I have Pugh and baby Rudin and plenty of problems i haven'tdone out of them, but I'm thinking about getting Royden or something else that's a level above those two. What's your advice? Should I spend time on the books I have to strength my foundation or is it worthwhile to move onto the next level?

[analog lava]

if ur taking a quali in real analsysi

there is a text specified just for this

real analysis for qualis

not a text but ig just notes but it is very well-contained

[inner token]

@analog lava cool I'll check it out

[wide dune]

Mindboure Mathamtics Text book

[night geyser]

do you guys think 'All the mathematics you missed but need for grad school' is suitable for someone not yet undergrad?

I'm looking for a book that gives a kind of overview of a lot of different areas

[inner token]

It's a good book

I'd say it's worth a look if you want a survey@night geyser

[gusty gorge]

if you're familiar with a lot of notation, I'd recommend mathematics and its history by John Stillwell

[hazy elk]

Princeton companion to mathematics

[gusty gorge]

For most pre-undergrad students, how to solve it by George Polya is also good, but its overview is basic, with notations for proofs and such

[prime oak]

opinions on the bourbaki textbooks? ive not really actually read anything about the texts themselves

[ocean mulch]

It's rigorous

Horribly rigorous

It's to set standard in Math, hence the rigour.

[inner token]

Great book but it's a lot to work through

[gusty gorge]

Very true, it took me 3 months to finish

[prime oak]

is it worth going thorugh?

[ocean mulch]

Depends on your goal

Do you wanna do math very rigorously? Or just wanna learn Math?

Bourbaki is like a Bible, it's hard to access, and probably too much anyway. It's better to use some translation, i.e. other introductory books.

Bourbaki was never meant to be introductory anyway. It was to be a guideline for math.

[woven spoke]

Which textbook prefer for learning calculus 2 from profeccor Leonard video?

[trail yarrow]

Hello guys, currently I am in undergrad real analysis reading Rudin. I hope to take graduate analysis next year, but WITHOUT having taken measure theory already. So, I was wondering if anyone knew of good measure theory books to self study (i.e., can't be that hard to read, like, say Rudin...)

[finite crane]

Not worth. Just ask here for any subjects

[limber narwhal]

hi, i'm in highschool and want to learn about abstract algebra. does anyone know any books that give a nice introduction to the topic?

[gusty gorge]

I recommend A First Course in Abstract Algebra by John Fraleigh

[desert oriole]

has anyone read "algebraic inequalities" by sedrakyan?

[limber narwhal]

alright ty!

[remote sparrow]

i heard axler, schilling, tao, and bass are good.

[remote sparrow]

pinter or judson

[limber narwhal]

👍

[fierce hedge]

If you haven't seen matrices in your hs, Judson might feel a bit much. Try Pinter then

[limber narwhal]

i think i'm alright with matrices since i've read a few books on linear algebra. would that be enough?

[gusty gorge]

if you think you're comfortable with them, there's no harm in trying

[remote sparrow]

schilling's website for his book also has a full solutions manual

which is free

axler and bass are free online

oh yeah, you said you did baby rudin already, but if you still feel uncomfortable with metric spaces, you can give a look at carothers, which covers metric spaces in a more leisurely way. after metric spaces, it covers function spaces and some measure theory.

[crimson leaf]

Bass' book is cheap too

[remote sparrow]

^

it should be noted that bass isn't officially offering a hard copy of the most up-to-date version of his book through the self-publishing arm of amazon anymore, though. the book on amazon is the 2nd ed., while the pdf he offers is the 4th ed. however, an easy workaround is to get it printed through lulu.

[desert oriole]

.

[gray gazelle]

What’s the best textbook for calculus 3?

[thorn cloak]

Stewart’s and Thomas calc are fairly standard

Shifrin is a bit more advanced from what I heard

[remote sparrow]

depends on what you want to get out of calc 3. you can use a book that doesn't emphasize proofs as much, such as stewart or larson, or you can use a book that involves proofs, such as hubbard and hubbard or shifrin.

[gray gazelle]

Yeah one that doesn’t emphasize proofs is good

[brazen heron]

Can someone recommend a book that I can use to learn the mathematics of Einsteinien relativity? My background is vector calculus, linear algebra, discrete math; I have a master's in computer science but haven't done any work with tensors before.

[ocean mulch]

Special relativity or general relativity?

Because you don't really need fancy math for the former, but do for the latter

[brazen heron]

The latter

I was defeated by the Wikipedia page on Einstein's field equations

[ocean mulch]

I heard good things about Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll and General Relativity by Robert M. Wald

But don't take my words for it, I'm no physics major...

[brazen heron]

I'll look into them, thanks. My main hurdle is that I've never worked with tensors and have only an elementary understanding of field equations from when my CS education touched on Maxwell's.

[ocean mulch]

Mine didn't even touch Maxwell's, you'll be fine

[brazen heron]

Mine touched them very briefly, in a CE course we were all required to take that also touched on topics like silicon doping.

[ocean mulch]

I'm sure you can quickly review tensors. Any course notes on the topic will do, it's not that complicated to understand, provided you have a background in linear algebra already.

[gusty gorge]

I was gonna say, if you're into doing some special relativity, I read Special relativity and classical field theory by Susskind and Friedman, that does cover some tensors too

[brazen heron]

I'll probably end up doing some of both. My starting point is a strong lay interest in astrophysics combined with some minimal coursework in uni. I know about things like space-time curvature, singularities, and geodesics, but I haven't gotten into any of the math behind them.

Special is a strict subset of general, isn't it?

Dealing with straight lines?

[gusty gorge]

Special is a subset, but it also takes place in minkowski space, so not strictly euclidean

[brazen heron]

This sounds worth a read, at least. I don't have a lot of experience with "field theory" other than electromagnetism, and it sounds like it may be rather foundational.

[gusty gorge]

informationally it's pretty good, but be warned that it doesn't have any problems inside it, just theory

[remote sparrow]

https://www.reddit.com/r/math/comments/139tpf4/learning_complex_analysis_as_a_physicist/

new thread

might have some interesting stuff

[spiral sky]

What is a good algebra book with a view towards alg num theory (Alg geometry) and alg topology, also looking for a book on complex analysis with a similar porpuse

[heady ember]

Look in pinned

[fickle whale]

I understand this is vague, where could I find more material discussing/applying the groups listed on the right of pic related

[grand thistle]

i used folland

i liked it

it was a fun book

the first two chapters especially

are nice

[gray gazelle]

thanks for this!!! i was looking for a book with practice exercises haha most of the books i saw only explains the concept and examples good thing i checked the pins

[smoky nebula]

yo so I have an exam on graph theory on tuesday and I was wondering if someone knows where I can find ressources to study cause our textbook is useless

[fierce hedge]

@gilded lagoon what text did you use for abstract algebra?

[gilded lagoon]

We used Dummit and Foote in undergrad but it's kind of trash

There are no wrong answers, you learn algebra by getting practice using it to prove things, where you learn the basics is not important as long as they make you do lots of exercises.

I think Artin, Lang, Dummit and Foote are all basically equal, but Lang has a reputation for being very hard to read.

[smoky nebula]

is your pfp sophie scholl?

[gilded lagoon]

yah

[smoky nebula]

cool I read a book about her last year in german class

[gilded lagoon]

She was a pretty amazing person.

[smoky nebula]

do you have good ressources to study graph theory?

[smoky nebula]

fr

[gilded lagoon]

No I don't really know anything about graph theory.

[gusty gorge]

Have you read gibbons?

[smoky nebula]

no

[gusty gorge]

Algorithmic graph theory by gibbons is what I used in my graph theory class

[smoky nebula]

OK I'll check it out ty

[fierce hedge]

Ah, cool

[pliant falcon]

Gravitation - Misner, Thorne, Wheeler

[gray gazelle]

I think they use tensors for machine learning math

I messed around with models using tensorflow and scikit. I'd get all kinds of errors based on the shape of tensors not matching up

[ocean mulch]

Yes, but to ML-ers, tensors = vectors with extra dimensions

In particular, there won't be subtleties of covariance and contravariance, and the related algebras, and all these Einstein notations

[kind elm]

Yea ML tensors are different than actual tensors

to them an array is a 2d tensor

[fickle whale]

that doesn't sound right to me

shouldn't an array be a 1d "tensor"

a 2d array, i.e. a matrix, is a 2d "tensor"

[ocean mulch]

Yes, an array is 1d tensor, i.e. a vector

2d array is 2d tensor

[kind elm]

had a brainfart, meant a matrix

[pliant falcon]

tensors are much more abstract than that. You can represent some tensors by a matrix are a multidimensional array of numbers but they are their own algebraic objects in their own right

[kind elm]

we were discussing tensors in ML

[kind elm]

baby rudin has a section about measure theory no? It's a good intro

[sturdy shore]

I've personally not read it, but this is the first time I'm seeing someone say Baby Rudin's measure theory section is good

[sage python]

It's kinda deficient as far as I can tell

Just oh yeah let's toss in epsilon measure theory at the end

Instead of actually including it

[nimble otter]

Can somebody recommend me some books about probability and statistics

[remote sparrow]

introductory or higher?

calculus-based or not?

[nimble otter]

Higher and calculus-based

[nimble otter]

[remote sparrow]

so you've already taken a class in probability or statistics then?

[inner token]

Casella and Berger is good

Unless it is your first pass, in which case I think degroot is good. I know it and solutions are available online

[nimble otter]

I just wanna teach myself. I don't like listening course by my teacher.

[grave thorn]

baby rudin measure theory is just horrible

[kind elm]

I haven't done much with measure theory, so I just assumed it was good, like the rest of the book

I went through it OK

[grave thorn]

the last and second last chapters of rudin are bad

everything else is good

[wicked sinew]

Elements of mathematics by John Stillwell

Godel Escher, Bach An Eternal golden braid by douglas r hofstadter

I am a strange loop by douglas r hofstadter

sophie's world by jostein gaarder

[heady elbow]

i can't find a copy of calculus by michael spivak

so does anyone have any other good calculus books that are similar?

[remote sparrow]

what do you mean?

it's sold on amazon and there are many pdfs on the web

[heady elbow]

yea i ain't in the us

and all the pdfs are someone that scanned them

i want a pdf that i can print

[remote sparrow]

https://math.stackexchange.com/questions/731087/joseph-kitchens-calculus-reference

https://www.amazon.com/Calculus-Variable-Dover-Books-Mathematics/dp/0486838064

it's a dover book, so it's reasonably priced, at least for someone living in the U.S.

maybe not for you

but it's supposed to be comparable to apostol and spivak

as for a printable PDF, maybe look into local print shops that will print files as-is, no fiddling required

[final sluice]

Any recommedations for studying Galois Theory?

[remote sparrow]

https://www.maa.org/press/maa-reviews/math-through-the-ages-a-gentle-history-for-teachers-and-others-1

maybe this

[hollow cedar]

Hey guys
Is it worth buying HTML and CSS book by Jon duckett to learn from scratch?

[hexed obsidian]

if you want to study maths extensively and practice challenging questions get black book for jee mains and advanced

[rapid lily]

What is a good path for studying the aspects of functional analysis which generalise results from Banach and Hilbert spaces, or the parts which investigate spaces outside of Banach and Hilbert spaces for their own sake? Is the book "Topological Vector Spaces, Distributions and Kernels" by Trèves a good option for this?

[hexed obsidian]

if you're just starting out, then yes

[rapid lily]

Ok thanks

[fierce hedge]

To those why have done Herstein - Does Herstein never do group actions? I also couldn't find anything on the orbit stabilizer theorem weirdly like is it not that important or something?

[hazy elk]

Yeah he does all the group action stuff implicitly, idk why he made that choice tho

[past tiger]

if i will get an exercises for the math videos let's say from a precalc book like stewart so at this point math videos is better than reading books?
like if i watch a precalculus playlist for professor leonard lectures on youtube and after every lecture i solve a lot of problems from the stewart precalc book
at this point i will more understand the topics and it will be better than books?

because i hate reading

i am getting bored at it

[hazy elk]

Humans tend to remember and understand things better when their brains put in more effort during the learning process. Video lectures can lead to passive learning (and the content will evaporate from your head) if you're not careful about working things out yourself.

You should see whatever works for you though

[coral prawn]

yeah personally I tend to scribble/type down some pointers- the amount ranging from 10% to 90% depending on the content. Idk why, it feels "useless" and I ask myself if it slows down my learning at times, but eh, doing it makes me feel comfortable for the most part, so why not though whether I revisit what I written is another thing altogether

[clear surge]

ayo why set theory so boring

[heady ember]

Set theory is interesting

[clear surge]

A – (B ∩ C) = (A – B) ∪ (A – C)

[heady ember]

Naive set theory is not all of set theory

There's a lot of depth to set theory which I'm just scratching the surface of

[tender river]

lmao i just proved a theorem using Zorn's lemma

[heady ember]

Basic facts about ordinals and cardinals, AC, etc. There's even more at grad level, like forcing and independence proofs

[clear surge]

damn what shit am i studying

i need to study higher concepts fr

[coral prawn]

if you think a field of maths is boring/too easy, that's definitely because you just haven't seen enough of it some quote I saw on the Internet

[past tiger]

can someone tell me a best precalculus book for beginners?

[remote sparrow]

https://www.mathpop.com/hindustan-publishing-corporation-asia-

do you live in any of these countries?

hindustan took over spivak's company after his death apparently

they might be able to ship the book to you

[quick hornet]

caution: site doesnt have https

[tiny compass]

Could I know the best Best linear algebra books for self study that’s semi-rigorous

[worthy venture]

Introduction to Linear algebra by gilbert strang is a popular book

[tiny compass]

Hmm. I actually started using the linear algebra chapters in Griffiths Introduction to electrodynamics, so could I just learn using that is what I’m wondering

[worthy venture]

depends on your objective. Griffiths is great i havnt looked at mine very much yet but electrodynamics is more concerned with using vector calculus. Linear algebra as a course usually goes over some different things.

[tiny compass]

So it has enough for vector calculus and electrodynamics

Thx

[worthy venture]

eh

it focuses on vector calculus in terms of electrodynamics. but im not sure how much matrix analysis is done in the book

there is prolly a free pdf of strang.

[final sluice]

Any recommendations for studying Galois Theory?

[wicked sinew]

Logicomix - an illustrated
Novel by Apostolos Doxiadis and Christos Papadimitriou

very cool about Bertrand Russel's life

[remote sparrow]

#book-recommendations message

[quaint light]

There are some free online resource, you can learn basics from there first~

[shut shale]

yeah. Mozilla has really good foundational documentation on both HTML and CSS.

[lilac bronze]

I worked through Hoffmann-Kunze to start

Not sure if it was the best choice, but I understoodd the first couple of chapters okay

Been a while though so I'm not sure how my memory is on that front

[bitter raptor]

Planning on taking a class on quantum mechanics and a class in harmonic analysis next semester and I won’t really be able to take functional analysis the same semester or honestly at any official opportunity before my masters so I was wondering what people’s recommendations on books to self study functional analysis over the summer are

[thorn cloak]

am looking for a beginner book on ML. Heard both introduction to machine learning by Shai Ben David and Foundations of ML by Mohiri are good. Will these suffice or are there any other good books?

[crimson leaf]

My optimization professor said he likes Conway

[upbeat vine]

Brezis or Lax as main text and Yosida, Reeds-Simons, Barry Simons book for further motivations.

[inner token]

Can someone recommend a book for actuarial science/preparing for the actuarial exams?

[coral prawn]

Was wondering if anyone had any recommendations on CS books which focus on algorithms, time and space complexities etc with a lotta math in it; that is to say that it's mathematically rigorous/focuses on mathematics I'm a beginner to CS who just learnt how to code, I'd like to dip deeper into the mathematical side of CS but idk if that's recommended for newbies

[finite gale]

kleinberg and tardos was okay i guess

but honestly i don't think i ever really read any of it, just did some problems out of it

and tbh i don't really think you necessarily need to read any of it to do the problems

[fierce hedge]

The standard is CLRS but it's so huge I won't suggest it to a beginner. There are some online course (youtube) which are pretty rigorous.
I don't remember the name but the guy uses his own to teach algorithms. Personally, there isn't much very interesting maths in just analysis of basic algorithms.

[coral prawn]

Icic

[remote sparrow]

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

i heard this is good

it's free online

[hasty turret]

Udi Manber seems somewhat promising in that it treats algorithm analysis like a proper math topic

[weak nest]

Hey that's my school

[coral prawn]

[ocean mulch]

How about the Bible?

Donald Knuth's The Art of Computer Programming

Other than that, you have to ask someone who did Competitive Programming, that's where ppl find ways to make use of absurd maths. I did Competitive Programming myself, but afaik there's no single book that covers anything in depth, everything's almost folklore.

You can start with https://codeforces.com/blog/entry/91363 and https://codeforces.com/blog/entry/78520, and go from there, but each of these topics deserves a course on its own 😄

[coral prawn]

damn

thanks all of ya

[hasty turret]

TAOCP is like unusable for a beginner

Because MMIX is a PITA

It's like "hey you can learn slightly cool things but you need to write multiplication tables upto 20, 10 times before that"

But cf is very very good

Try the contest problems too at some point. Tho caring about the rating would get annoying after a certain level because a large part of a score is based on how fast you solve the problem and that means you get shitty boilerplate code

[coral prawn]

LMAOOOOO

[vestal cosmos]

What book/website /s is recommended for abstract algebra??

[fierce hedge]

For an intro to abstract algebra probably Judson or Pinter

There is a website for has a list of videos for going through dummit and foote

https://tdupuy.w3.uvm.edu/algebra-one/20/f/videos.html

[finite gale]

check pinned messages

[swift dome]

Judson is literally a classic one for abstract algebra.

[fierce hedge]

The only con for Judson I can think of is the lack of harder problems

[vestal cosmos]

Thankss

[cobalt arch]

Any books in number theory that prove elementary statements about properties of numbers? I want to learn how to prove elementary statements in all branches of math so if you have any recommendations, I would like to know them.

[flat moat]

Whos is "Calculus Concepts & Contexts" by James Stewart written for? I have the opportunity to pick up the third edition cheaply and was wondering if it is good for self study, how rigourous is it? What prerequisites are there?

[remote sparrow]

can you define elementary?

[gray gazelle]

Hi guy! My name is SHADOW! I am about to take my final exams! I am a 8th grader living in NC and I need to pass math or else I wll get retained. Can you guys suggest me some books?

[finite gale]

use khan academy

[remote sparrow]

From the preface to the fourth edition:

The principal way in which this book differs from my more traditional calculus textbooks is that it is more streamlined. For instance, there is no complete chapter on techniques of integration; I don’t prove as many theorems (see the discussion on rigor on page xv); and the material on transcendental functions and on parametric equations is interwoven throughout the book instead of being treated in separate chapters. Instructors who prefer fuller coverage of traditional calculus topics should look at my books Calculus, Sixth Edition, and Calculus: Early Transcendentals, Sixth Edition.

it should be fine if you're getting it for cheap though

if you want something more comprehensive just go with a regular edition of early transcendentals. old editions are also available for very little cost on amazon.

[flat moat]

Are you familiar with the book? I'm mostly curious on whether or not it would be managable to follow along or if the contents of the book are too difficult. I know enough calc so that my knowledge is comparable to calc 1

[remote sparrow]

yeah, i used that book in high school

i did some prestudying with the book before taking the class in high school

it's a fine book.

[alpine orchid]

Hi, just wondering is there anyone can find the solution manual for the solution manual for Advanced Engineering Mathematics 10th Edition by Erwin Kreyszig? I have been using this textbook but it doesn’t provide answer for even question

[keen rover]

do the thug shake

[ocean mulch]

As if it were ever a problem for that you can ask Lang

[cobalt arch]

I don't know if I can but one book that proves elementary mathematics is the book by landau foundations of analysis, that is the closest to what I want

I want a book that exhausts all possible theory of a concept when presenting it

This might not exist but if anyone has something close to that I would like to know

[ocean mulch]

Maybe Diendonné's Foundation of Modern Analysis

Everything is treated, but don't assume you need no prerequisite. He said himself that you better have some prior experience.

[cobalt arch]

Do you know of similar books in other branches of math?

[ocean mulch]

Tao has the classics in representation theory and random matrix theory I think

Or was it someone else for representation theory?

[cobalt arch]

Idk, I would just like a more elementary treatment which goes over basic proofs of many identities, inequalities, theorems about numbers etc.

[ocean mulch]

Oh, then maybe you should go with Hardy and Littlewood

[cobalt arch]

I would like to have a book that proves the most basic machinery from different branches of math and that is exhaustive

[ocean mulch]

I think Hardy, Littlewood and Polya have a thick book on identities and inequalities

[cobalt arch]

They do, I know about it

[ocean mulch]

Idk if that's possible. Maths is almost never linear, and there's no book can write about everything, even basic stuff

There's no one who knows all the uses of determinants, for example

[cobalt arch]

Yes that is to be expected

I guess I just want to be able to prove stuff because I struggle even with basic statements

[ocean mulch]

Can you elaborate a bit more? I'm not sure what you need here

[cobalt arch]

I thought having such an exhaustive book of proofs of basic statements would help to consolidate these statements in my mind

[cobalt arch]

I guess a book like the one you suggested about inequalities but for other branches too

[maiden halo]

I've seen "The Book of Proof" by Hammack recommended here before

[cobalt arch]

I know it but haven't read it. A more exhaustive treatment is that by polimeni and zhang (I think)

[ocean mulch]

Well, you have to pick a topic

[cobalt arch]

Maybe number theory to begin with

[maiden halo]

Chartrand is the first author

[ocean mulch]

Manin and Panchishkin's Introduction to Modern Number Theory

[cobalt arch]

Prereqs?

[ocean mulch]

It scratches a bit of everything and goes reasonably deep. I wish it went deeper about cyclotomic polynomials and proofs of Catalan's conjecture, or Pell's equation, Mordell's equation, Alex-Thue, and so on, but I guess that's to be expected. It's quite thick as it is already

[ocean mulch]

None

[cobalt arch]

Seems like a good book

[ocean mulch]

Maybe get yourself comfortable with Chinese Remainder, Euler's theorem and Fermat's little theorem, but that's about it

[cobalt arch]

Do you have any for algebra?

[ocean mulch]

Lang

You mean elementary algebra, or modern algebra?

[cobalt arch]

Both xD

[ocean mulch]

I'm a fan of Herstein myself, but he omitted a lot of stuff, especially group actions and modules

[cobalt arch]

For elementary algebra I know but it is an old book

[ocean mulch]

It's not like Math at this level gets outdated 😄

For modern algebra, I don't know much actually. I gathered my understanding whilst working in other fields, so...

[cobalt arch]

Seems like the number theory book follows an axiomatic approach but I am not too sure, would you say it is axiomatic?

[ocean mulch]

One thing about modern algebra is the ideas come from multiple fields and it blossomed quite early, unlike number theory.

[ocean mulch]

I don't think so, I read it quite comfortably

[cobalt arch]

So the book covers analytic and algebraic nt?

[ocean mulch]

Yes

[crimson leaf]

Rotman's first course in Abstract Algebra starts with number theory then goes into some stuff about groups then rings, linear algebra, fields, and back to groups and rings

[fierce hedge]

How does he do sylow without group actions or does sylow doesn't require group actions?

[loud cradle]

he gives three proofs, one of which is Wielandt's, which of course is naturally stated in the language of group actions, but he gives basically the same argument without using the terminology

then he gives a proof by induction on |G|, which iirc is similar to the one given in hungerford

the third one uses cayley's theorem to find an isomorphic copy of G in S_n (where n = |G|) and uses properties of the symmetric group

[fierce hedge]

ahh, interesting. But it's weird that he does group actions but just not calls them group actions. I think he also doesn't do orbit-stabiliser theorem

The only reference of orbit I found was in context of symmetric groups

[loud cradle]

he kind of does orbit-stabilizer, but his treatment is weird. For example, in the proof of Cauchy's theorem:

but this appears to be the very first reference to "class equation"

[fierce hedge]

alright, better than nothing I guess

[loud cradle]

i guess herstein is interesting if you seek an exposition (and exercises) that squeeze out results using the absolute bare minimum background

i think there are now far, far better treatments at this level

[hazy elk]

What do you consider far far better?

[fierce hedge]

I have heard Artin is good but I felt it was dense while dnf is too dry what would be something in between. I know Judson and gallian, any other book?

[crimson leaf]

Rotman A First Course Abstract Algebra

Also Fraleigh A First Course Abstract Algebra

I've really liked Rotman so far been reading through the section on rings and used to it supplement my course I was taking last semester in groups. Advanced is also good (the old version not the new) but he skips on out on some stuff and goes deeper into topics probably great for a review

[blazing canopy]

Was reading your discussions above about group theory. Sadly I don't think I ever understood the purpose of Sylow's theorems 🥲

[crimson leaf]

The only thing I got out of last semester is easy classification of finite groups like you can "easily" prove which order groups are not simple by Sylow's theorem 3

[blazing canopy]

Yeah the classical application of sylow is classification, but I never really "understood" Sylow intuitively. In part it's because I never went very deep into group theory. Ultimately it is essentially like a combinatorial result and I just haven't yet gone through the effort of figuring it out

[crimson leaf]

We crammed in Sylow's theorems so I barely even remember the proofs

[blazing canopy]

I used to joke that if I got the teaching assignment to teach Algebra then I'd be forced to figure it out

But it never happened

[crimson leaf]

My advisor ended up with something like that for a class he hasn't taken since undergrad for next semester

[blazing canopy]

that's great. Every course I teach has strengthened my knowledge in that topic. Even teaching basic courses like linear algebra were very valuable, especially earlier on

[crimson leaf]

I've had a similar experience with algebra last semester, I ended up going to the library near the end of the semester to help some of my friends a few people from class I didn't know since they studied in a group. It helped me figure out what things I didn't have a precise understanding of and so I'd look those up and I'd cover a lot of my gaps that way it was cool

[fierce hedge]

By advanced you mean the advanced section? Cause the book itself is named Advanced modern algebra (hence the confusion)

[crimson leaf]

There are two A First Course Abstract Algebra (I mentioned this one above) and Advanced Modern Algebra

They cover almost exactly the same content (early on) but the Advanced one left more to the reader and had some deeper (and more difficult to grasp) results

[fierce hedge]

Correct me here but does that mean the advanced one is less advanced?

[crimson leaf]

Whoops I meant Advanced not Abstract my bad 😅

[fierce hedge]

Ah, cool

[crimson leaf]

I was reading D&F before Rotman since it's the one my class uses but I don't like how they order the material as much as Rotman does and his exposition is better imo he has very good motivation (comparatively.)

[fierce hedge]

Also, there is no rotman book by the first name. Are you talking about, a first course in abstract algebra?

[crimson leaf]

Yes

[fierce hedge]

Or maybe 'An introduction to the theory of groups' but this only does group theory to some very advanced level

[crimson leaf]

I guess I've been giving out the wrong name for months

[fierce hedge]

[crimson leaf]

That tracks though since it's the same name as Fraleigh's book

[fierce hedge]

Yeah I mean math books have the most generic names possible

[crimson leaf]

I think the worst is Jacobson "Basic Algebra"

[fierce hedge]

Dami will be pissed at that lmfaoo

But you need to remember that it's supposed to be grad level

I got fed-up after around 30 pages

and switched to Judson

[fierce hedge]

@heady ember

[crimson leaf]

No not book

Name

It's just a horrible name

[heady ember]

Oh lol

[hazy elk]

I think Isaac's book might also be worth looking at for intro algebra

[heady ember]

Basic algebra that's how you know the author's about to beat the living shit outta you

[hazy elk]

Just read a few sections and they were golden

Rotman is also very based

[fierce hedge]

Had me in the first half, I forgot the context

[fierce hedge]

He's actually calling you basic

[heady ember]

[gray gazelle]

Hey guys this summer im going over ODE's for my PDE course, But I am also curious in geometry. Im a high school drop out and never took a high school geomerty course. Does anyone have a good recomendation of a book I can download to read on the side when im bored of calculus to fill this gap of mine?

ping me if you have a recomendation please

[loud cradle]

newer and not as well known but very good based on the parts I've seen is Algebra in Action by Shahriari: https://www.amazon.com/Algebra-Action-Course-Applied-Undergraduate/dp/1470428490

[fierce hedge]

Hints, complete short answers and odd problems solved!! Holy shit this is noice

[loud cradle]

with regard to group actions as we were talking about earlier, he takes pretty much the opposite approach to herstein:

various group actions and their consequences (including the sylow theorems) are the focus of chapters 4-10 and only in chapter 11 does he introduce homomorphisms!

[grand gorge]

Hi, do you have any recommendations for books about machine learning and turbulent flow or general fluid mechanics. Especially in rocket science. Any this and similar recommendations will be appreciated.
Because I'm not in this subject, I'm just looking for the best gift for someone

[merry echo]

I was talking about that green book for interviews

Anyone know where to get

[gray gazelle]

I need easy introductory books for combinatorics and graph theory (does not need to be a single book), any recommendations? For combinatorics, recommendend me anything aside from Bona's as the exercises in the book are overkill for me.

[mellow wren]

I'm looking for resources on harmonic analysis so I'm curious if anyone has any good recs

[ocean mulch]

Like, Fourier analysis but on a sphere?

[cloud moth]

anyone pls recommend me some books for 10th grade

[ocean mulch]

I used Spherical radial basis functions, theory and applications by Hubbert et al,

But I'm not sure if you mean this topic, or something else more theoretical

[mellow wren]

More like generalized Fourier analysis

[desert oriole]

reminds me of basic nt

i really thought it would be about basic nt

[formal bronze]

You can check out 'Graph Theory' by Reinhard Diestel. And for combinatorics you could check out 'Combinatorics: The Art of Counting' by Sagan, although it mainly deals with enumerative combinatorics.

[plucky sage]

I am about to buy books what book is good at explaining precalculus and calculus?

[remote sparrow]

usually precalculus and calculus are treated in separate books.

stewart has both precalculus and calculus books.

[sonic basin]

There’s a textbook that I use for school that explains a wide variety of topics, including calculus but it’s what’s used for English exam board curriculum

[flat sand]

Calculus Made Easy by Thompson & Gardner is a great supplemental book. It is great for actually building intuition about what you are going to study. It's an oldy, but great book.

[sage python]

Do you need much PDEs for Folland? Seems it needs mostly functional

[mellow wren]

functional pretty OK
PDEs pretty shit lol

[sage python]

Irony what directions are you looking at within harmonic?

[mellow wren]

whatever leads me towards langlands

[sage python]

Because even "generalized" can mean a lot of things

Oh okay Langlands headed

And Spectt there's a veeery low probability that Elixir, a 10th grader, knows linear algebra already

[mellow wren]

I think a larger problem is the mathematical maturity needed to learn algebra lol

[sage python]

Well the background determines mathematical maturity, I just mean that

First off assuming he had linear algebra, especially proof-based linear algebra, algebra is a next step but I wouldn't suggest Lang yet because that's a huge commitment to algebra before doing any e.g. analysis

[finite gale]

i mean a high schooler can very reasonably learn abstract algebra

[sage python]

Yeah, Artin would be a reasonable recommendation for a bright high schooler

At least if they already did calculus

[finite gale]

tbh i kinda wish they taught some abstract alg in high schools

[sage python]

But 10th grader chances are didn't do calculus or linear algebra. We're very likely talking \le precalculus

[finite gale]

instead of spending so much time on running in circles on basic precalculus concepts

[sage python]

And for that I recommend Khan Academy

[finite gale]

i think stewart calculus is better for calc 1-2

[mellow wren]

eeehhhhh
I think you're maybe overestimating how well a HSer can prove stuff lol
I mean I had a first order logic class in school so I at least had some basis for proofs
But idk if people have this in every country

[sage python]

Also if you're interested in Langlands, Folland abstract harmonic isn't bad. Also consider Deitmar-Echterhoff, as it gets into shit like the Heisenberg group, SL_2(R), trace formula

[finite gale]

i don't really think there is much to "learn" for writing proofs

[mellow wren]

personally knowing first order logic helped a lot to gain intuition for proofs

[sage python]

Irony: I guess my point is, I think Artin was literally to in principle be an introduction to proofs

[finite gale]

like it's kind of just a natural thing to do

[mellow wren]

ah OK I didn't know that lol

[gusty smelt]

The correct way to study representations of discrete groups is von nuemann algebras 🙂

[sage python]

Spectt it's... complicated

[mellow wren]

thanks!

[sage python]

My current research direction is Ramanujan complexes/high dimensional expanders, but I also like dynamical systems

I mean I don't know arithmetic geometry but as far as I'm concerned it's good stuff

[mellow wren]

why the NT hate 😭

[sage python]

Like I think overall, my favorite zone to operate in is representation theory and connections to dynamics, number theory, harmonic analysis, combo etc

[gusty smelt]

We actually had a talk on number theory in the conference.

[sage python]

But my second choice could very well have been arithmetic geo, one of my top advisor picks going into grad school was one

Oooo looks like good shit John

Also now that we're off reference talk and just doing math let's migrate

[gusty smelt]

Tru

[sage python]

To wrap up, Khan Academy seems to be the way to go for most high school math re @cloud moth

And re @plucky sage Khan is an option for precalc, and for calc (though also look at Paul's Notes). If you want something to buy... Stewart is standard but imo too expensive. Thing is I don't have alternatives I'm familiar with unless you're gunning for proof-based math

Given robyn said "analysis textbooks", the level of analysis is prob not measure theory yet

Which is what the pinned message refers to (Tao's got a single measure theory book but 2 volume for pre-MT analysis)

I haven't looked at it much myself, it seems like it spends a fair bit of time on foundations. Set theory, building up number systems, etc

[mellow wren]

A rec I like for analysis is Chapman Pugh

[sage python]

Takes a good bit of time, idk if I'd have the patience for it, but people who use it swear by it

Pugh I feel like is Rudin with better exposition but extremely awkward take on topology lol

[mellow wren]

Lol yhea it's tough

[mellow wren]

I like his topology chapter but I already knew point set at that point so it wasn't that much of a struggle lol
But his other sections are great imho

[sage python]

I think Schroder and Browder are the two best approximations I know to "a correct" introduction to analysis book, perhaps possibly Tao idk

[mellow wren]

and an astounding amount of problems

[gusty smelt]

Can’t go wrong with the classic

[sage python]

But nothing really hits the mark of how I'd do things

[gusty smelt]

Use rudin.

[sage python]

John I kinda see Browder as Rudin done right lol

I mean Rudin 1-8 is still pretty good, 9 is okay, but 10 is stupid and 11 is... eh

I think the measure theory should be done sooner

[gusty smelt]

Right I mean you aren’t using rudin beyond ch 8

[sage python]

And Rudin's treatment of it is very half-assed

Browder is basically, replace Rudin's dumbass treatment of multi with Spivak Calc on Manifolds

One slight difference that... idk may or may not be a good idea, is that he sections things off so the first part is explicitly single variable and second part is explicitly multi, namely that he doesn't do the topology at the start like RUdin

Rather he discusses limits of sequences/series/functions right after his intro shtick on the real numbers, uses that for calculus, then does topology, uses the topology to do function spaces, then does multivariable calculus

[gusty smelt]

I see

[sage python]

Okay so here's my hot take

No point in doing multivariable Riemann integration

[gusty smelt]

I mean honestly people could,probably do any book here and be fine

[sage python]

Which as I recall Zorich does lol

[gusty smelt]

That’s a cold af take smh

[sage python]

I mostly recommend Browder in place of Rudin nowadays, and then Schroder as a slower intro, basically replacing Spivak as an entry point

Since Schroder is more gentle than Spivak but by the end gets farther than Baby Rudin

And neither wastes time on Riemann integration on R^n

[finite gale]

if browder is rudin done right, then what is rudin done wrong?

[gusty smelt]

Damis ramblings.

[sage python]

John my ramblings are why you chose math smh

You would've been a premed otherwise

[gusty smelt]

[crimson leaf]

Yeah book paralysis is a real a problem lol

[gusty smelt]

Imo if you have a bunch of choices you should just read their pref@ e and maybe a few pages

And decide

Preface

[crimson leaf]

I've been reading Tao recently it's actually pretty good if you skip ch 1-4

Though if he recalls a previous result I'll flip back to it

[gusty smelt]

I’d recommend having some LA going in still

Artin has a way about his LA, very matrix centric

And la is foundational to p much all of math, so you don’t wanna be stuck with a matrix centric perspective imo

Uh like begining abstract algebra? Artin lol

I liked it’s selection of topics, like it really got me@interested in higher math when I read it as a kid

[crimson leaf]

MIT uses Axler for proof based LA and Artin for more advanced Algebra

For their easier algebra course they use Judson

[sage python]

Does Artin not eventually get to the more abstract stuff in linear algebra?

Maybe Knapp is an alternative? Idk it's good to see both perspectives

[gusty smelt]

They do but it’s still a matrix centric perspective

Like all their proofs heavily abuse matrices etc

I think it’s good to see

But like, it shouldn’t be your first exposure imo

[tulip blade]

Harvard uses LADR

[loud cradle]

maybe there's some value, if only to show that the two notions agree for functions that are integrable in both senses. Also, there's a subtlety that a function can be multivariable Riemann integrable without being Borel measurable, which provides some motivation for why completion is desirable

[thin kernel]

Any book recommendations for self learning functional analysis?

[sage python]

That's why I said multivariable

Maybe you do Riemann integration on R, take a geodesic path building up to measure theory

Then do product measures and boom that's integration on R^n

[sage python]

Are you interested in functional aimed at PDE?

Or more general stuff? Etc

[thin kernel]

More general stuff since I haven’t taken a pde course

[loud cradle]

agree in general, but it's only for n >= 2 that you get the "riemann integrable but not borel measurable" situation (e.g. take a function on R^2 that is zero everywhere except for x=0, where as a function of y, it's the characteristic function of some nonmeasurable subset of R)

which imo gives some motivation for why it's desirable to complete the product measure on R^2

[fierce hedge]

nah, for self learning it's horrendous. The pacing is incredibly fast, it'd work better with an instructor not sure by how much.

[sage python]

Gotcha. My undergrad class did Kolmogorov-Fomin which is well-written but out of date terminology and covers little. Grad had 3 references: Lax I didn't look at much, mainly Brezis which is very targeted, in particular toward PDE though one could argue that it should have shit like distributions and spectral theory not just for compact operators even if you're aiming at PDE, and Buhler-Salamon which seemed decent

Einsiedler-Ward is pretty broad, e.g. does Banach algebras in direction of the prime number theorem

[fierce hedge]

The amount of group theory done in chapter 2 was half of my entire group theory semester lol

[sage python]

Okay chapter 2 being half a semester is a bit crazy to me

FarhanA I think Delerik likes Grandpa Rudin for functional? I'll ping him if he wants to give some commentary @finite crane

[thin kernel]

I did not hear good things about that book

[sage python]

I haven't looked at it at all myself lol, hence why I'll defer to Delerik's commentary

[crimson leaf]

I don't think it's that crazy my course only got through Ch 1-4 of D&F in the semester which looks to be about Ch. 2 of Artin and parts of Chapter 7

[dapper root]

??????????

4 chapters in a semester?

[crimson leaf]

Yeah we pretty much covered group theory

[thin kernel]

Any opinions about brezis?

[fierce hedge]

almost same, we had entire classes on parts of abstract algebra that are usually done in 2 semesters. So, different classes on group theory, ring theory, field and modules, galois theory and finally a commutative algebra class. Also, none of them are optional.

I don't think that helped much with how much I suck at algebra but it is what it is

[crimson leaf]

I guess we did cover a bit of number theory and reviewed some stuff like first week

[fierce hedge]

we had a different class for number theory

advanced (algebraic) NT was optional and pretty much no one was interested so it never happened

[crimson leaf]

We have a number theory class too but we just went over what we needed congruences, modular arithmetic, Euclidean division, stuff that was covered in intro to proofs. We have an Analytic NT course like that

[sage python]

None of you guys had good taste smh

[crimson leaf]

Offered every year never gets enough students

This year it got 2 students 3 short of what's needed to run a course

[fierce hedge]

(we didn't have much say in any course smh)

[crimson leaf]

Yeah we don't get much say it's pretty much take what you can get at my school

[fierce hedge]

can't even afford that, my class had a total of 5 students, my senior had only 2 students

[crimson leaf]

Like last semester I took graduate optimization, research, seminar, algebra 1, ode, and probability

[fierce hedge]

ah, sounds like a typical uk degree (maybe not typical)

[crimson leaf]

My other options were number theory, geometry, math physics, and actuarial science

I got a low level university for math in the US

[fierce hedge]

ah, okay. Mine was a very decent college in india and still

[fierce hedge]

If Artin counts as good taste I don't want it. Like if I wanted a text that dense, I'd rather do Jacobson

[sage python]

I meant taste in the sense of, none of you wanna do algebraic number theory

You said it wasn't offered due to lack of interest

[sage python]

Clean writing, again it kinda only does the functional needed for certain things in PDE which... 🤷

[fierce hedge]

We had 3 NT proffs among which only one was algebraic NT and he wasn't that keen in taking a course 🤷

Hell we couldn't convince our department to float a mathematical logic course

[sage python]

Weak willed

[finite gale]

what about analytic nt

[sage python]

There are flavors of analytic NT. Mine is the best

[crimson leaf]

What is your Dami

[finite crane]

brezis does not even cover topological vector spaces
when functional analysis is mostly about the study of infinite-dimensional topological vector spaces

grandpa Rudin is a decent reference though you could also read Simons-Reed for more color

[stray veldt]

you self-assigned the study role

you can change that in #info or using /roles

[grave thorn]

I've noticed that a lot of books on functional analysis (especially those geared towards applications like PDEs) focus only on Banach/Hilbert spaces. This probably stems from an isomorphism between the Cauchy completion of an LCTVS and a projective limit of Banach spaces (meaning tons of problems can be reduced to the corresponding problem for Banach spaces).

[gray gazelle]

Is Shilov not a good book? Why would you say you didn’t get it..? is his exposition poor?

[orchid mortar]

Could also be a problem of fit

[slim peak]

To be fair, Brezis actually just provide the necessary amount of Functional Analysis to reach Banach spaces and related topics in the scopes of Sobolev spaces for Partial Differential equations. Having that in mind, the only thing we can complain about is the fact it doesnot treat distribution theory (and then complete metric vector spaces)

I personally would recommend to be somehow solid on normed vector spaces, before reaching more general structures.

But this is very personnal

[thorn orchid]

Hi there, I would like to study calculus, any book recomendations? Thank you

[ocean mulch]

What level?

[uncut zealot]

Spivak Calculus

[sage python]

Huh I just remembered I have grandpa Rudin, got it from some free books schtick. Maybe I should read it

[uncut zealot]

I just got the whole trilogy from some actuary I met at a bar

Like a week ago

[ocean mulch]

A: An actuary? and B: math books at a bar?

[uncut zealot]

Retirement party for an old professor. The actuary was an alum who also had an MS in math and hadn't touched the books since the '90s

[ocean mulch]

Ah, that makes sense

[remote sparrow]

https://www.amazon.com/Fundamentals-Mathematics-Introduction-Proofs-Numbers/dp/0470551380/

The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers.

Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study.

i saw the slides for this on schroder's website (yes, that schroder who wrote the oft-recommended analysis book)

seems interesting

i also saw a guy shilling this book 4 years ago in this discord

unfortunately no pdf online

probably not of interest to most students given its primary focus is on the number systems

[heady ember]

I actually found it online last time after quite some searching

[coral prawn]

Well, the first few pages jumped straight into determinants and all

[cobalt tiger]

Looking for stuff to read/podcasts to listen to before the Oppenheimer movie comes out 🙂

[gray gazelle]

What would you want the reading/podcasts to be about?

Nuclear Physics?

[finite crane]

I watched ramanujan's the man who knew infinity movie

it ended up showing nothing about his maths. the only thing I learned is that he writes on sand

so don't expect anything technical from movies

[shrewd kraken]

👍

you just spit straight fax

[maiden halo]

I thought this book was really interesting. I have the 1st edition. https://www.amazon.com/Manhattan-Project-Creators-Eyewitnesses-Historians/dp/0762471271

[rancid hollow]

good books for category theory? started reading through 'categories for working mathematician' but am wondering if the definitions may get a little dated? idk shit about category theory tho

[finite crane]

I read through that myself

I think awodey may be a more modern source

but cat theory only makes sense when you have more examples to think about

[coral prawn]

😭😭😭

[remote sparrow]

i sent you a DM btw

[fierce hedge]

And that he was pure veg which indirectly costed him his life

[fierce hedge]

For ug level category theory Awodey or Eugene Chen maybe and for grad level Riehl is good (note I haven't tried any of these)

[nimble gazelle]

who knows a good Linear Alg book

[remote sparrow]

is this your first time taking linear algebra

[nimble gazelle]

yess

currently studyin it rn am in determinants

[remote sparrow]

the books i like most treat determinants quite late

[nimble gazelle]

no worries i'll skip to the topic

and revise on the prev ones

[nimble gazelle]

do u know one that isnt too heavy on theory

[remote sparrow]

#book-recommendations message

you probably want the cohen and klein books

[nimble gazelle]

okies

[remote sparrow]

i think they treat determinants earlier

you want linear algebra for machine learning applications right

[nimble gazelle]

yes

[remote sparrow]

still, it's a good idea to eventually familiarize yourself with vector-space, basis-free based linear algebra, as opposed to limiting yourself matrix algebra

conceptually basis-free arguments are much easier to grasp, even if more abstract

[nimble gazelle]

hmmmm i'll just keep learning everything that i can

that i can apply to my projects that is

lemme show a bit of what i do

[remote sparrow]

learning the theoretical aspects can certainly help you, even if you don't go deep. in computer programming, ideally you should know what you want to do at a high level. coordinate-free arguments are much cleaner and help you plan out what you want your program to do, but of course the implementation will be with matrices, since computers can actually compute that

[nimble gazelle]

check #chill

[nimble gazelle]

indeed

and i have a whole year

[remote sparrow]

are you self-studying?

[nimble gazelle]

yes

[remote sparrow]

you should give meckes or hefferon a try at least

[nimble gazelle]

after Lin Alg i'll move to calc then prob and stats

[nimble gazelle]

i will

[remote sparrow]

they're both easy and meant for first timers

hefferon has a website to go with the book

has lectures, solutions manual, a programming lab manual

pretty cool

also covers theoretical aspects quite nicely

determinants are useful for many theoretical purposes, but calculating them for matrices bigger than 3x3 gets ugly real fast

[nimble gazelle]

ikr

usually in programming we use the Numpy library find the determinant of any square matrix

np.linalg.det(
[1,2,3,4],
[5,6,7,8],
[9,10,11,12]
)

somethin like this

[swift dome]

[nimble gazelle]

[finite crane]

For theoretical purposes, knowing how to calculate det is important. But not calculation itself. I taught an advanced linear algebra course without any need for calculation or using the computer

In particular, instead of remembering the det formula, the students should understand it's multilinear, alternating and 1 on Identity matrix

From those you get everything else

[nimble gazelle]

[dawn venture]

what is a good book for metric spaces that has alot of questions with solutions

[uncut zealot]

Basically any undergraduate real analysis textbook. I think Munkres does some stuff with metric spaces too, if you want to learn just a bunch of point-set topology.

[remote sparrow]

gamelin's topology covers metric spaces rather extensively

lots of answers and hints in the back

not aware of solutions for carothers, but it covers metric spaces pretty well

[gray gazelle]

Do you think the book you referenced is useful for someone who has never been exposed to topology prior?

[valid socket]

@gray gazelle I think Gamelin is pretty good for a beginner.

[grand thistle]

has anyone used Loring Tu's differential geometry book

i've read like half of chapter one

and it seems pretty good so far

i mainly need the euclidean theory for my purposes (thinking of learning GMT)

differential forms (on Rn) and things like that especially

[hollow peak]

Yes, he covers all the essentials for using differential forms

I think the jump from learning the basics of forms to straight up GMT might be very hard, but Tu does indeed do forms

I saw in the other channel you're interested in plateau's problem. Just know that modern treatments do this in a riemannian manifold, which will take a lot more than euclidean geometry

[grand thistle]

right right

im thinking of using

krantz/parks

it has all the basic diff geo including differential forms

and the measure theory i think i'm familiar with mostly except the weird suslin set stuff

[hollow peak]

I just looked at krantz for the first time and it looks good for your purpose then

You might struggle with things doing global analysis or federer but what you're doing is fine

[grand thistle]

yeah, everyone scared me off federer and said it was like the hartshorne of GMT lol

honestly it looks really dense so i understand

[hollow peak]

Federer is fucking nuts

There are books literally written with the express purpose of guidimg through federer lol

[sage python]

Have you seen Federer Theorem 4.5.9?

[hollow peak]

No, what is it

[sage python]

It's... legendary

[grand thistle]

wtf

i just looked at it

LMFAO

[sage python]

31 parts

[grand thistle]

i've never seen anything like this

[sage python]

4 pages to state the theorem

And then 20something to prove it

[grand thistle]

im scared to even ask what it's saying...

[hollow peak]

holy fuckimg ahit

[sage python]

Krantz/Parks seems good for... "that" side of GMT

GMT as far as I see has two brands

One is more, harmonic analysis, metric geometry, fractals

So think people like Larry Guth, Marianna Csornyei

I think this branch also matters in dispersive PDE but don't ask me deets

The other branch is more diffgeo (esp minimal surfaces), calc of variations, regularity

e.g. if you hear people talk about currents or varifolds

[grand thistle]

krantz parks would be more the latter right

[gusty smelt]

The fractal gmt is better when the things are non commutative :))

[crimson leaf]

The application of additive combinatorics to gmt seems cool

[valid socket]

This is a pretty good decomposition

[thorn orchid]

thank you

[shrewd kraken]

can math books become obsolete? i wanted to read some earlier english books about math (think newton-ish, maybe a bit older even), but i wondered what if id be learning “incorrect” math.

[kind elm]

yea kind of

Pre algebra mathematics sucked

hard to parse

[visual citrus]

Is Bird's Basic Engineering Mathematics worth reading or are there better recommendation? I want to get a head start before I start college

[coral prawn]

If they're dated over a hundred years back.... you may be reading incorrect info, and the content most likely would be rather.... how do I put it? Lacking as compared to modern books

[kind elm]

Have you tried reading Newton's Principia?

its post algebra but still a slog

[cobalt arch]

How is older math incorrect, I don't understand

[prime oak]

i liked simmons during my course

[cobalt arch]

Books might become obsolete but that doesn't make them incorrect

[coral prawn]

Sometimes people realise they mess up, make mistakes etc

It has happened before-

For Taylor series for example

[kind elm]

they can be incorrect in the sense that definitions and conditions become more restrictive in the future, etc

[prime oak]

the 1920s and 30s analysis books i read were pretty good

[kind elm]

just look at euler's formula for polyhedra

[coral prawn]

Well maybe, never really had a look at such "outdated" books, but generally it's safer to pick a more up to date one

[kind elm]

it went through a million changes

[prime oak]

true but i definitely wouldnt say it isnt worthwile going through them

[kind elm]

first it was all polyhedron, then some with a bunch of arbitrary restrictions, then only convex then it turns out convex is too restrictive bla bla bla

[coral prawn]

I mean honestly, unless you've a specific reason to pick books dated back decades/centuries ago it isn't good practice to use one as learning material lest you end up learning "outdated" info

[prime oak]

decades
depends on the subject lol come on

[cobalt arch]

Well for trigonometry does that hold too? Eulcidean geometry? Branches of math that haven't been active in the last hundred years.

Or not as active as other branches I guess

[prime oak]

ill say the only real reason i do it is because i find the writing style of those books nice

[cobalt arch]

I still don't understand how something can be incorrect when the logic is sound. Unless for convention of course.

Is elementary algebra by chrystal out of date?

For example

[coral prawn]

Perhaps, but why pick an old book when u can pick some new, more reliable and up to date books which can provide more insights as to, for example, irl trivia, fun facts, and cover more content which would be more relevant to the current state of maths?

[coral prawn]

I mean, sure, then stick to that

[cobalt arch]

It is an old book but so is the branch it is dealing with, convention might change from period to period but that doesn't render something incorrect when it stood in its time in its own right.

[mellow wren]

Tbh for a while now stuff has been pretty standardized
Unless you're reading stuff from like the 19th century everything will probably be the same with maybe some minor differences

[cobalt arch]

Because new books might not be as comprehensive and rigorous

Do you know many books for elementatry algebra nowadays that are actually rigorous?

[coral prawn]

While the content may not necessarily be wrong, it may not be as "up to date"

[cobalt arch]

Comprehensive?

[prime oak]

fun irl trivia on real analysis

[kind elm]

Usually what happens is someone has a theorem, they prove it. Proof relies on some hidden assumption that doesn't really matter in the times it was written, later times counterexamples crop up, so then ppl realize that theorem is more restrictive than it was thought out to be

[mellow wren]

well a lot of the time new books aren't as good

take like commutative algebra
The most famous reference to this day was written in 1969

[kind elm]

Imre Lakatos' book really makes that idea clear. Would reccomend reading atleast the first half

[coral prawn]

Oh? Perhaps I've mistaken then, my bad. But still, taking books from Newton's age?

That seems....

Uh.... a bit too old

[mellow wren]

yeah
I don't mean reading books from several centuries ago

[kind elm]

Proofs and Refutations

[prime oak]

last century is an okay cut off point i think

[coral prawn]

Was saying that cuz that was what the asker was inquiring abt

[cobalt arch]

If someone could recommend a more up to date book on elementary algebra or trigonometry I would actually appreciate it. But it has to be rigorous and comprehensive.

Not a lot of math books at that level are written like that today

[coral prawn]

Tbh why not

1. Just use khanacademy?
2. Maybe leave the rigour for later? Wdym by "rigour" when it comes to elementary algebra and trig?

damn tho u guys changed my viewpoint on 20th century books tks

[kind elm]

I mean, were the treatise of elementary algebra and trigonometry of old that rigorous to begin with?

[mellow wren]

I mean elementary algebra is as rigorous as can be lol
Trig too idk most sources for trig derive everything

[coral prawn]

Yeah, like

Most of the "rigour" can only come after u have a firm understanding of other core fields of mathematics

[prime oak]

some of those old texts that are "hard and difficult to get through" helped me try[who knows if i actually succeeded] to build up a much better foundation than most modern texts, so i just find that style nicer

[cobalt arch]

That the books contain the complete reasoning without leaving out parts that seem to be too hard or difficult. It seems like today's books on that level do that. They are incomplete and hence not rigorous enough. Or they might be complete and rigorous but not comprehensive enough.

[coral prawn]

lmao mfw I see books with poor latex

[prime oak]

i had to go through several books for courses which were

they looked like

they were written in word

id love to collect old math texts or something
a lot of very old books are still popular here because theyre always in circulation in the 2nd hand market, and are orders of magnitude cheaper than modern textbooks

[cobalt arch]

If you can point me to a newer book that is as comprehensive as chrystal's algebra I would like to know

[crimson leaf]

Idk Rudin is from 1953 and people love it still

[coral prawn]

Yeah, now thar u bring that example out I realise how much a joker I must've sounded

but even then, yeah, don't rely on books dating back to Newton's time~

[crimson leaf]

Depends Euclid's elements is still used as a base for some courses, you can really take it case by case

[prime oak]

i thought they stopped doing that in the 1900s

[crimson leaf]

Even stuff like Abstract Algebra haven't changed much since the 70s on the undergrad level

[coral prawn]

ic

[maiden halo]

Calculus Made Easy by Thompson was published in 1910; I've seen that recommended before

[valid socket]

I'm fond of the art of problem solving books @cobalt arch

[remote sparrow]

forsaken has a very odd and misguided insistence on building from the most minimal axioms possible

like insisting that the multiplication principle in combinatorics be built from zfc

which is possible ofc

so i'm guessing they will find your suggestion "insufficiently rigorous"

[finite crane]

unironically learn Tao's Analysis. he built from peano axioms

[orchid mortar]

I know 0 math but pretty sure minimality of axioms is not exactly an 'already-solved' topic

And yes I agree with you that even if it were, it wouldn't make sense to introduce math from there

[cobalt arch]

Odd sure but I don't think it is misguided. I just want to learn from first principles, although it is difficult to find such books.

[maiden halo]

then read the Principia Mathematica?

[sage python]

Watson what you're thinking of is called reverse math I think

[shrewd kraken]

i guess the theme i hear from a lot of people is that modern is better

[orchid mortar]

That's wow... logicians

[cobalt arch]

there is the metamath page which is more up to date

[shrewd kraken]

ill look a that

[ocean mulch]

Mordell would like to disagree

He drowned himself in the old, classical texts, and found ways to make improvements. A lot of ideas were contained within those pages

That's how he came to make so much progress in Number Theory, iirc

[shrewd kraken]

i see, they had a lot of raw ideas

but there were mistakes, no?

at least less than modern texts?

[ocean mulch]

mistakes are not necessarily bad

[shrewd kraken]

it gives a different idea than whats supposed to be correct

[ocean mulch]

Well, it's bad if the goal is to be correct.

It's to be expressive first, then we deal with correctness later.

Because there can be many ways to correct something

[cerulean cypress]

hi can you recommend any physics textbook for self study? the uni one that people use on first year

I'm trying to decide between halliday, serway and young&freedman

[sterile harness]

I think Halliday Resnick is the classic

[orchid mortar]

(I'm not a phys major) There's a lot of choices.

Open source:
https://www.lightandmatter.com/

Free online:
Feynman Lectures

H+R, Y&F is standard. Supposedly, Shankar is another good one. Also has lectures

Not seen Serway.

[cerulean cypress]

thanks for recommendations

[cerulean cypress]

btw how would you compare shankar to other two, just asking because I've never heard of shankar before

[orchid mortar]

All very fairly comprehensive
You can check from video titles of
https://www.youtube.com/watch?v=KOKnWaLiL8w&list=PLFE3074A4CB751B2B
https://www.youtube.com/watch?v=NK-BxowMIfg&list=PLD07B2225BB40E582

Mechanics + Gross intro thermodynamics being Phy 1 is standard.

[cerulean cypress]

oh okay thanks again

[orchid mortar]

E&M being phy 2 is also standard

Also these are quite 'introductory,' 1st-2nd year physics

[orchid mortar]

What doesn't seem standard to me: Relativity, Taylor series, Fluid dynamics (not too sure which exact part he covers here)

But it being 1st year, doubt he'd overkill

What introductory also means is that these topics all have advanced levels

There's advanced mechanics (usually dynamics?), advanced electromagnetism, and full on general relativity, advanced quantum mechanics (again usually dynamics?), fluid dynamics (no statics anymore)

[remote sparrow]

https://open.umn.edu/opentextbooks/textbooks/59

here's a review of crowell's Light and Matter

i read the book a couple of years ago because i heard this guy was an awful teacher (he taught at a nearby community college)

[orchid mortar]

Yeah I don't think it's the best, but I am definitely supporting open source