book-recommendations

[patent trail]

Thanks

[inland elm]

okay, here is a full thread about texts for this content https://mathoverflow.net/questions/7834/undergraduate-differential-geometry-texts

that’s where i found those notes

the notes themselves look pretty self contained, but having a full book may be nice

[remote sparrow]

kristopher tapp is good for diff geo of curves and surfaces

[fossil arch]

yeah when people refer to diffgeo it’s either difftop (sometimes straight to riemannian/symplectic/kahler/so on geometry) diffgeo or curves & surfaces in R^n diffgeo

I thought I was getting myself into calculus on curves & surfaces in R^n but ended up in difftop and now I find that a lot more interesting

[patent trail]

yeah thanks again for clarifying that up otherwise i would have gotten stuck a long ago, studying end topics

if you have time still, do you have any suggestions for abstract algebra?

[fossil arch]

what are you looking to learn about?

[patent trail]

it will be my first time taking it

[fossil arch]

start with group theory and pick a classic like aluffi/artin/d&f/whatever other hip new books people recommend are

[patent trail]

i dont know at all, but some source i have seen does callbacks to relations and stuff

[inland elm]

do not start with aluffi lol

[fossil arch]

relations get covered even in analysis courses

[fossil arch]

a lot of people like it but I think category theory when you’re first learning is intimidating

[inland elm]

i think it's a good second read through, form the little i've seen

but starting someone off with CT is not something i would suggest

it takes a serious level of mathematical maturity. it's worth checking out to see if it makes sense, but i don't think blanket recommendations to start with aluffi are being considerate of the person learning

[patent trail]

which one is the most beginner friendly

[inland elm]

"dummit and foote" is pretty good, i also thought "friedberg" was good for a first course

[crimson leaf]

Friedberg has a book on group theory?

[patent trail]

i tried googling friedberg for abstract algebra but i keep getting recommendation for linear algebra book of it instead

[inland elm]

oh

fraleigh im sorry

[crimson leaf]

Rotman first course in abstract algebra is good

[inland elm]

i was reading friedberg and mixed them up my bad

[patent trail]

oh no worries, thanks for clarifying

[inland lichen]

i wouldn't recommend aluffi for your first go of Abstract Algebra, dummit and foote or contemporary abstract algebra by Gallian (this is what I had for an intro to abstract algebra class)

[mellow wren]

Judson or Artin

D&F isn't a good intro text

[topaz rune]

[inland elm]

brezis is self contained on that regard

assumes measure theory i'm pretty sure, or covers it very briefly

but goes all the way up to calculus of variations via sobolev spaces

[topaz rune]

What’s the title?

[inland elm]

Functional Analysis, Sobolev Spaces and Partial Differential Equations

i don't know if it's the treatment of calculus of variations you want but it's one option

[inland lichen]

the most formal calculus of variations book I have seen is by Gelfand and Fomin. It's a bit old, but the writers a very good mathematicians and it has good reviews

the book is called... Calculus of Variations

[topaz rune]

I would prefer something recent (like 2005+) for good typesetting etc

[inland lichen]

honestly the version I see, typesetting looks fine

but ill see if there is something more recent

[topaz rune]

Ideally I’m looking for one with connections to theoretical mechanics or optimal control theory. For both calculus of variations is quite fundamental, but most books I’ve seen that combines these topics either lack a bit of rigour or only treat the CoV on 10 pages of a subchapter

[inland lichen]

What I will mention though is that CoV as a standalone topic was hot in the 20th century but no longer. So most comprhensive books on it will be from that time, some of them with very good condition. I would suggest once more the gelfand and fomin book

An old but applied one I found is:
Calculus of Variations: with Applications to Physics and Engineering by Weinstock (1960s)

Finally, a good recent book you can check out is:

Calculus of Variations by Jost and Jost (I think the second jost is his wife, Xianqing Li-Jost)

it's written in the late 90s, good typesetting and i've used his book for geometric analysis

I think this last book might be what you are looking for. If too theory based, the applied one might focus more to what you want

[topaz rune]

Thanks for the suggestions, I’ll check it out

[inland lichen]

yea this last book is for you probably. The deeper you go into the book, the more functional analysis starts appearing (hilbert and banach space theory, measures, etc)

[topaz rune]

Hmm libgen doesn’t seem to have it

[foggy relic]

aluffi is good as a first book @patent trail

literally starts with naive set theory

[gray gazelle]

@topaz rune @inland lichen Nonlinear functional analysis: a first course by kesavan. Or other nonlinear functional analysis books have really good shit on this topic.

[inland lichen]

I wouldn't say it's a good first book for someone who might be new to the abstract notions within it. he takes a categorical approach which might start off to strongly for someone new to it

as they said "it will be my first time taking it", so i'm sure a straightforward text on groups, rings and fields will be much more suited than Aluffi

that's just me though haha. I didn't start with Aluffi, so maybe starting with it isn't too bad...

[inland lichen]

Looks interesting, guess @topaz rune will have to check it out and see if it fits their purposes

[gleaming nova]

do you guys have any recommendations for graduate level probability textbooks?

I need some probability theory stuff

[inland lichen]

have you taken measure theory?

[gleaming nova]

yup but the textbook doesn't have to be measure theory based

[inland lichen]

Alright

So the typical book is by Durett or by Billingsley but I didn't like them. The book "Foundations of Probability" by Kallenberg was nice for me

On the otherhand, you can just look at MIT's 2012 graduate level prob page and check the links (particularly the notes by Amir Dembo from Stanford):
https://math.mit.edu/~sheffield/fall2012math175.html

Of course you might have to jump between sources and just read the chapters you're interested in

[gleaming nova]

Oh yeah I should've mentioned before that I have Durrett's book

[inland lichen]

yea i didnt like it

[gleaming nova]

I'll check out all the others tho

thx for the reccomendations

[inland lichen]

https://adembo.su.domains/stat-310a/lnotes.pdf could try, but it's extremely rigorous. It all depends what your goals are

Here's the foundation book contents, you can see it covers about everything one would expect in a complete round of graduate level probability:
https://link.springer.com/book/10.1007/978-1-4757-4015-8

after that you kind of find books for specific topics i.e. martingales, stochastics, etc

[gleaming nova]

wow thanks for all the help

I didn't know there were that many things published online

Imma do some more digging for that too

[inland lichen]

in any case you can always check google and find pages like this:https://math.stackexchange.com/questions/3955639/rigorous-graduate-probability-textbook-for-self-study

that's usually what i do anyways, check stackexchange, reddit or other special links i found that have lists of math books and opinions on them

Good luck!!!

[gleaming nova]

yes sirrr thank you so much

[inland lichen]

as you go higher into mathematics, there are less books and mostly everything becomes online posted notes

[shrewd kraken]

what book is like in depth

i swear if you ctrl f “in depth” for me its be like 100 times

but the more in depth the better

but like anything that explores a concept to completion is all i want

[inland lichen]

im not sure what you mean

[sage python]

It's not gonna be easy because topics branch a lot

For almost any interesting thing out there, it's not super "open and shut"

There are questions you can ask and often eventually those questions go completely out of left field and become their own subjects. And eventually it builds to research level stuff

[shrewd kraken]

so i want a highly specific subject

[shrewd kraken]

i think sloth king did

[inland lichen]

In any area of math?

[shrewd kraken]

im a but desperate

so sure why not

[inland lichen]

Haha no, i can’t give you something you don’t have the prereqs for.

Sorry i jumped midway into the convo, so if you can tell me what you know i can tell you where to go from there

[shrewd kraken]

why not at least let me know so i can build up to it?

im like calculus area with general math-ish

[inland lichen]

I’m happy to but some things require like a decade of build up and some less haha

[shrewd kraken]

ive heard about other topics enough to like at least have some prior knowledge

[shrewd kraken]

i can try

[sage python]

It's kinda hard to think of such stuff

[shrewd kraken]

id just really like to have some closure with a topic

at least 1

[sage python]

There's local closure that's more attainable

In the sense that, okay you could always ask more questions

[inland lichen]

Here’s a highly specific topic within your reach

https://www2.math.upenn.edu/~wilf/gfology2.pdf

Not much beyond some basic calculus and combinatorics

But a very enlightening topic that will prove useful

But as Sloth is saying, local closure is more attainable. No topic in math is ever really completed

Some die out of popularity, like Euclidean geometry in the past but there are probably no researchers in it nowadays

[sage python]

But there's a point where it's like, alright you've answered a big question you had asked

Namely linear algebra

[shrewd kraken]

i want to be comfortable with it

curriculum just doesnt branch out enough for me

i understand why

but it bother me

[inland lichen]

Are you in school or uni?

[shrewd kraken]

school

i study outside so im a bit ahead tho

[inland lichen]

Yea i was like u

[shrewd kraken]

then again the topics are usually niche

[inland lichen]

And i felt like u

But let me tell you the path ahead so you don’t worry like i did. There will be a lottttt of time to study and explore all areas of math, so much you will wish you could live forever and explore it all

But alas, you only have so much time in life and should enjoy more than that

Pick up any topic that may seem feasible and give it a shot

Don’t worry about getting to the end, because you won’t get there

[shrewd kraken]

yes

[inland lichen]

For examplec, if you want to transition from your school math calculus to uni math major calculus, try this book: https://theswissbay.ch/pdf/Gentoomen Library/Maths/Calculus/Michael Spivak - Calculus.pdf

It’s a famous book and don’t be fooled by the title of the book. It’s called Calculus by Spivak, but in reality it is an introduction to analysis. Give it a try!

[shrewd kraken]

yes

[shrewd kraken]

no

[shrewd kraken]

another intro to analysis?

i have like 4 why not

and i havent read a page of either

[inland lichen]

This will be more digestable as ur still in the calculus phase, other analysis books could be tough. Another nice one is Understanding Analysis by Abbott

But if you don’t want analysis tell me haha

It’s just the most reachable thing from your position

For exmaple, you can go a long way with combinatorics

It only requires algebra and sometimes calc, but it’s an extremely deep and complicated field

[shrewd kraken]

i also have that book

[shrewd kraken]

see thats the problem

i want a small field

[inland lichen]

Aint no small fields at the point you are at

[shrewd kraken]

that doesnt have to be “explored”

[inland lichen]

However, try the generating function book

It doesnt have to be explored

[shrewd kraken]

combinatronics looks cool

[inland lichen]

The generating function book will teach you things you might not learn in any regular math course

[shrewd kraken]

i may not have as much time for math as im getting into python

[shrewd kraken]

what book?

[inland lichen]

The link i sent

[shrewd kraken]

oh gfology got it

[inland lichen]

That’s good! CS goes hand in hand with mathematics

[fierce hedge]

point set topology, there isn't much to do after you've read the basic stuff

Unless you want to do algebraic topology

[inland lichen]

Im not sure id recommend topology to someone who hasnt done any proofs yet

But then again, people are more capable at different stages in their life

[fierce hedge]

True but my point of topology being a limited field still stands

I mean point set topology

[shrewd kraken]

[shrewd kraken]

wait i did geometry proofs?

[inland lichen]

I don’t think it’s limited, but I get what you mean. What a math major learns from it is much smaller than all other topics.

certainly there is still research in set-theoretic topology. I think there aren’t any big overarching questions

[shrewd kraken]

are those like something…?

and topology does look kind of understandable

[inland lichen]

I dont think they will compare in rigor to topology. If you want you can give it a try! Topology by Munkres is the standard

And it will help you with everything in your math future too

[fierce hedge]

Topology in general is vast asf and has a lot of use especially AT but I don't think there's any research in point set topology

[inland lichen]

You’re young, try things. It’s not wasted time and you will learn a lot along the way

[shrewd kraken]

i guess

[fierce hedge]

honestly yeah, just pick things that look interesting

[shrewd kraken]

my interests aren’t very mainstream

like the concept of physical and temporal dimsensions

noneuclidean geometry

and non base 10 numbering systems/floating point stuff but thats computer science related

[fierce hedge]

wdym non eulclidean geometry is pretty mainstream I think

[shrewd kraken]

it is but there isnt much on it as it can vary a lot

[inland lichen]

I can’t say there is active research as other fields, but certainly a lot still in question: https://staff.fnwi.uva.nl/j.vanmill/papers/papers1990/opit.pdf

[fierce hedge]

oh yeah, I meant in the sense of active research. I don't know of any proff doing active research in point set topology, mostly it's low dimensional topology.
Then again, I might be very biased on this.

[inland lichen]

You could look at some elementary number theory

That is also reachable from your level

[shrewd kraken]

that stuff is cool

[inland lichen]

A Friendly Introduction to Number Theory by Joseph H. Silverman.

That’s what you should look for

It’s the most accessible to you

https://www.math.brown.edu/johsilve/frint.html

Click chapters 1-6 they are freely available

https://www.math.brown.edu/johsilve/frintch1ch6.pdf

It may feel like it starts slow, but read each page diligently and you will there is a lot to think about, even for things which are obvious to you

[inland lichen]

Nah haha, I agree with you. Don’t think set topology compares to homotopy theory/k-theory in popularity

[tawny crater]

recommend "concrete mathematics" it's a combinatorics textbook and discusses some niche topics. Every chapter has research problems at the end if you want to cut your teeth

[vital ocean]

hello guys, does anyone know a good book to learn solid angles?

[shrewd kraken]

ok ill take these into account

[gray gazelle]

I just finished a pre-algebra book can someone recommend me next?

[alpine rover]

Blitzer College Algebra

[heady idol]

does any one know a boo for long devison

[wicked thunder]

I don't think anyones written a book on long division

[sand flame]

Hello. I have just completed some introductory Calculus and am looking for any good recommendations for a linear algebra book. Does anyone have any recommendations?

[loud shell]

Введение в алгебру - Kostrikin

[inland lichen]

Hey, would you like an introductory linear algebra book that is less heavy on theory and more on matrix computation or would you like a theoretical and abstract that is typically taught in an Honors Linear Algebra course?

[remote sparrow]

#book-recommendations message

[signal geode]

Can anyone tell me if the Pre Calculus of Sheldon Axler is good for the subject it intends to teach?

[inland lichen]

I haven't read his pre-cal book but I've used his linear algebra and measure theory books and I didn't have much complaint. His books are well written

[sand flame]

I don’t even know. I ended buying on old used book from a thrift store because the new ones are quite expensive. It’s called Linear Algebra and it’s Applications.

[inland lichen]

that's Strangs book, it's good

it's less heavy on theory, but it's a comprehensive and gentle introduction

[sand flame]

It’s from someone else I think. It’s by David Lay

[inland lichen]

ah

[inland lichen]

i looked at it, looks like similar contents to strangs. give it a shot! the reviews seem good

[crimson leaf]

Lay is okay

We used it for my course

[sand flame]

Yeah. I’m gonna see if I can get through a lot of it before summer is over. Thank you for the assistance!

[strong monolith]

Can anyone recommend me a good book or textbook on linear algebra and differential equations?

[sand flame]

We were just talking about linear algebra books if you wanna scroll up a little ways.

[ebon warren]

solid angles?

[soft wasp]

Hello oxide

:( saw you left the other server

[jade field]

hi autumn :)

[remote sparrow]

separate or combined

[strong monolith]

combined @remote sparrow

[remote sparrow]

goode and annin

[wary compass]

Hello, I enrolled in this project and I’m supposed to learn the definitions related to it. Could anyone suggest an introductory text that deals with : (Littlewood conjecture, lattices, harr measures on lattices, orbits stabilizers, invariant measures) Just to get myself familiar with the definitions. Right now I’m struggling to even find the definition of Harr measure on lattices. Group of lattices being SLn(R)\SLn(Z)

[heady ember]

Probably be more specific. Proof based or computation based lin alg? What types of DEs and at what level?

[mellow wren]

This feels a little bit all over the place lol
Idk for lattices but it sounds to me like you need both some group theory and some measure theory to learn ABT this stuff (and probably some topology)

(Also I assume you mean Haar measure)

[sweet scaffold]

Harr measures

[strong monolith]

@heady ember Proof based linear algebra, For DE it’s introductory course and says “First and second order ordinary differential equations, linear differential equations, numerical methods and series solutions, Laplace transforms, modeling and stability theory”

[sweet scaffold]

Blanchard diff eq

[strong monolith]

Thank you!!

[alpine rover]

Zill Diff Eqs

[sweet scaffold]

Incel spence friedburg lin alg

[alpine rover]

Anton Lin Alg

[sweet scaffold]

Nooo

Not anton!

(Lol)

[mellow wren]

Like lattices are a somewhat niche subfield of Lie group stuff so I don't know really what you can read on that
Maybe the Wikipedia page?
https://en.m.wikipedia.org/wiki/Lattice_(discrete_subgroup)
For measure theory Folland Real Analysis covers what you're looking for tho its quite long
And idk for like group theory you can read either Artin Algebra or Judson Algebra

[alpine rover]

insel* lol

unfortunate name

[sweet scaffold]

Its a special type of linear algebra called incel lin alg

No relation to that book or person (we love them)

[rancid hollow]

tfw 0 vector orthogonal to all and therefore an incel 😞

[knotty sentinel]

did someone mention me

[alpine rover]

orthogonal or incel?

[knotty sentinel]

what do you think...

[alpine rover]

/s

[wary compass]

Thank you, I think I'll be focusing on lattices, since its a new concept for me. Also it's a 5-week project, I don't think there will be any results coming from it...so I'll just learn as much as I can

The problem is I haven't been able to find much about lattices online, other than the wikipedia page

[rigid barn]

Is anyone aware if this books is available in English, German, or Russian?

[gray gazelle]

the best book i have ever read is the Quran and im not a muslim

[safe wyvern]

What is this book on

[cobalt arch]

I think non commutative fields?

[gray gazelle]

Yeah

No one ever really studies those

I could not find a book

[gray gazelle]

literally when

[gray gazelle]

since 2 years ago when i read it not saying that other books are bad but it really held accountable for my own desires that i have never felt before and a shrug of emotion i know it sounds stupid but its really intresting to read and i encourage people to read it

[pseudo violet]

I thought you said the Quran was about non commutative fields and I was like "damn I've been missing out on this"

[fierce hedge]

So, basically like a self help book?

[gray gazelle]

lol

[gray gazelle]

i suppose but its hard to understand with the direct english translation so i got one with context

[mellow wren]

They do

Tho it's called the study of division rings

[mellow wren]

There's a book by Cohn called Skew fields that might be what you're looking for

[gray gazelle]

ill check that out as well:-)

[eager meteor]

this book is so hard dude

[strong monolith]

Hi! Can anyone recommend me a good discrete math book or textbook?

[buoyant vessel]

@green kelp knows...

hes studying it extensively...

[jovial parrot]

It’s you

[shadow owl]

Hello! I am an incoming freshman studying CS. I am very interested in math and was wondering how I can get ahead. I’ve completed calc 2, and I will be taking discrete structures in the fall

I am looking for a textbook that I can go through in my free time (not a discrete book but instead of a class that you guys think would suit me best). I assume you’ll either choose linear algebra or calc 3. Anyways, all hell is greatly appreciated

[tawny crater]

Any linear textbook works. You can do concrete mathematics by Knuth and that will make you very prepared for most CS subjects

That's not linear that's for useful math for cs

[shadow owl]

Ok i see. Thank you. Do you have any recommendations as to how I can successfully work through said textbook?

[tawny crater]

With a smile 😁

[shadow owl]

Good idea 😆

[tawny crater]

You sound like a diligent student. Just don't push yourself too hard, studying is a long term affair

I woke up today unmotivated and I need to make my study today a bit happier so this is something you'll keep coming back to haha

[shadow owl]

Thank you. I keep getting stuck in the mindset that I need to rush things. I found math (the beauty of it) in 2020 through YouTube videos and since then I’ve been so interested. All very surface level learning since then.

[shadow owl]

You’ll get through it

[gray gazelle]

good elementary real analysis book? (series and sequences and such, not measure theory)

[gray jungle]

do you want to work over R or metric spaces ? For the former i recommend "analysis 1" by terrance tao and for the latter i recommend "principle of mathematical analysis" by walter rudin

[gray gazelle]

I've heard good things about the rudin book, is analysis over R a prerequisite for the latter, or is analysis over metric spaces something you can learn independently of the other?

[gray jungle]

Its a matter of taste and background , if you have encountered proof based math before then you can afford to do metric spaces right off the bat

if this is your first time doing proof based math then tao is perfect

[gray gazelle]

I've done some proof based stuff, mainly some abstract algebra, I think I'm gonna check out a pdf for rudin and, if I like it, I'll get the paper version.

[gray jungle]

do note that metric spaces will lack some motivation that working over R can give , so you might need to check certain results you find "unintuitve" in the real case to get some grasp over them , otherwise you are good and good luck!

[gray gazelle]

Alright, I'll check it out, thanks!

[inland lichen]

I dont know, I worked through this book after taking calculus in the regular sense. The book is not hard in complexity, but transitioning from calculus computations to proof of the concepts underlying calculus is a step up in mathematical maturity. It takes time to digest the ideas, but i wouldn’t say it’s hard in terms of actual difficulty.

And also the book is called Calculus, but in reality it’s an introduction to Real Analysis

[gray gazelle]

where can I find books for free

[loud cradle]

library

[gray gazelle]

There is no good library near my house or in my city that offers good mathematics books its mostly for competitive exams

[ionic portal]

im planning on reading abstract algebra by pinter but any recommendations on the book i should read after that?

specifically in abstract maths

[hidden lily]

any recommendations for a multivariable calculus book (that i can possibly find online)

[alpine rover]

Stewart?

[alpine rover]

More abstract algebra?

could look at Dummit & Foote and Atiyah & MacDonald

[rigid barn]

What is the quickest and dirtiest introduction to cardinal and ordinal numbers? I don't need any serious set theory beyond that, just want to make sense of cardinality arguments and how ordinals are used in topology and other areas.

[hidden lily]

could i use this for self studying?

[sturdy shore]

the first two sections of dugundji - topology probably

specifically the second

[alpine rover]

yes

[rigid barn]

Looks like what I need, thanks. If you've got other similar recs, I'd be glad to hear it.

[sturdy shore]

don't think there are any other that I am aware of, "teach ordinals/cardinals while avoiding set theory as much as possible" is a pretty niche area that you'd find only in topology books (that I know of)

there's also munkres first section but I just ctrl+f'd ordinal and found 0 results so

[remote sparrow]

abbott, cummings, ross

[rigid barn]

OK, what about good intro set theory books from which I could pick and choose said topics?

[sturdy shore]

hmm, tbh naive set theory by halmos covers pretty much the same stuff in dugundji's first two sections so you could give that a look also

[gray jungle]

What does dirtiest intro mean?

[sturdy shore]

if you want it in the context of actual set theory, jech hrbacek introduction to set theory

the first half should be enough

[sage python]

Dirt, blood, feces, that sorta thing

Jk nah

The phrase "quick and dirty" means like, yeah we're playing fast and loose just to get it done

[gray jungle]

lmao , gotcha

probably the wikipedia article honestly

if thats there goal

as mentioned dugunji is only book i know as well that covers them

[lethal matrix]

apologies for the ping— would you recommend Tao?

[remote sparrow]

it is good

[ocean mulch]

Tao Analysis I is standard ref here actually

[gray gazelle]

@olive talon CUH WHY U LEAVIN CHICAGO COME BACK

[ocean mulch]

Eh... Munkres? But it's only the first half about differentiability in R^n. Then the rest goes quite deep

[gray gazelle]

guys I recommend the legend series by Marie Lu

[hidden lily]

could i use mitopencourseware as an alternative

or not as effective

[ocean mulch]

I've tried MIT courses only once, and that was for Oncology

From what I know, MIT coures are amazing, but idk about multivar calc specifically

[sage python]

Munkres' multi book feels kinda eh

My impression is that people who use it dislike it

Not good proofs of a lot of the theorems (def inverse/implicit function theorem I've heard complaints about, but I think it's not limited to that)

Problems aren't great

Does this stopgap fake Riemann integral measure theory

And the treatment of manifolds is a bit screwy

[lethal matrix]

introductory or would you recommend something more verbose for such purposes— perhaps Cummings/Abbott

[sage python]

Quite introductory

[gray jungle]

tao proves 4 is not equal to 0

[rigid barn]

It's what made differentiation in R^n click for me, so I have a soft spot for that chapter. Rest of it isn't as good tho.

[heady ember]

mod moment

[gray gazelle]

Chose rudin in the end for the generality

[crimson leaf]

What are the standard Linear Programming books? Upper udergrad and graduate preferably

[gray gazelle]

recommendations for diff geo or integral equations?

[gray gazelle]

Smooth manifolds by Lee and Riemannian Manifolds by Lee

[ocean mulch]

ehh.... good questions 😄

it's a huge topic, depends on what you know already

if you need an intro, or if you have a rough idea already and wanna refresh everything properly for once

[orchid mortar]

https://www.dynamic-ideas.com/books/q3ggobj67w504tsa95ae456yvndd2d

But linear opti isn't really enough, because a lot of things are simplified in linear opti

[grizzled tulip]

DAMINARK!

hiiiii

[gray gazelle]

Guys I finished pre-algebra book and I now want to learn algebra and I also need to learn trig for my high school is there a great book which covers both the topics? (btw I found this book from miachel sullivan should I continue from it, its named algebra and trig but I don't know if its my level, I know all elementary algebra except quadratic equations.)

[crimson leaf]

Yeah I just need to look at some lp because the opti course I took spent most of our time on unconstrained problems

[old elk]

Guys, could someone recommend me a book on complex variables to study functions and transformations?

[fossil arch]

Introductory functional analysis book with a conversational author, lots of motivation & examples, doesn’t spend the first 4 chapters talking about topology, and preferably biases Fourier/Harmonic analysis?

Rudin is exactly the reason I’m asking nopey nope nopers I’m just gonna run anytime I see that name from now on

Oh my god

I meant functional analysis

Oops

LOL

[buoyant saddle]

yo so I'm in Y12 rn going up to Y13, read Lang LinAlg, Artin, Baby Rudin

anything else youse'd recommend for a spin?

[fossil arch]

Thanks for catching that 🤣

[buoyant saddle]

Like anything wild, just those are the books I've read so don't throw me like a bajillion prereqs honors grad textbook on cumfuck pre-algebras or whatever

[gray jungle]

We barely even started ch1 how will we cover the fundmanetal chapters without covering topoloy

[fossil arch]

As far as content goes idk it just seems so…specific

Very much Rudin style

All these wild definitions introduced at once relying on various XYZ properties, just feels so all over the place and it’s not at all what I expected LOL

Though tbf it’s my fault too since topology gives me the snoozies

[gray jungle]

well thats sorta the point we have the group too , we can suppliment basic results with some applications we find along the way

now addmitetly all of us are operator pilled so it might not be the fourier angle

btw feather , i have a great fourier book for you

one of my favs

[fossil arch]

SS?

:hehe:

[gray jungle]

An Introduction to Harmonic Analysis by Yitzhak-Katznelson

no i dislike SS

[fossil arch]

LOL

[gray jungle]

godly book

[gray jungle]

it gets fun from ch2 onwards i promise

[fossil arch]

How do you do harmonic analysis without functional analysis? Or does it just prerequisite the functional background required? If you can’t then how is this book different from what I asked for? I haven’t got the chance to look at it just yet but by title it sounds interesting

[gray jungle]

ive taken functional analysis before

this is my 2nd course

[fossil arch]

What a smarty

Sounds like it’ll be my read after this ;3

[gray jungle]

but it was still like basic stuff , and more focus on hilby spaces , didnt cover TVS

[fossil arch]

Yeah that’s what I was expecting this to be :hehe:

[gray jungle]

also if you want like Fourier with very brief FA and some measure theory knowledge at hand ,check out follands chapter on it

obviously wont cover any deep results but its pretty good

and there is a brief section on Haar measures at last chapter which is lovely

actually despite my dislike of SS 3 , the 4th one seems to cover Fa with fourier in 2nd chapter , so it might be what you need

Rudin rca too

[static prism]

probably taking topology sequence when i start my phd program in fall. my analysis is weak, and i only took a baby real analysis course over a year ago, and i don't remember much.
does anyone have recommendations for an intro to pointset topology i can look through which doesn't assume too much mastery over analysis?
alternatively, would it be more fruitful to review real analysis? not sure how crucial it is for topology.

[ocean mulch]

Lmao, I just saw An Introduction to Non-harmonic Fourier series by Robert Young

the title cracked me

[ocean mulch]

Munkres?

It's a standard ref, altho a lot ppl prefer the dirty intro by Hatcher

and yes, it's fruitful to review analysis. It serves a great intuition

[static prism]

hatcher looks more like a focus on algebraic topology unless i'm looking at the wrong book

[prisma loom]

Verily, it is naught a book, but a notes document.

Together, the one from Munkres and the one from Hatcher, doth constitute a splendid and admirable early introduction.

Ye: https://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf

[static prism]

ill check out this one. thanks 🙂

[inland elm]

if you did well in analysis at the time, you probably don’t need to review it before starting topology
the parallels will become clear as you go along and seeing the names again (like compact, continuous, open, etc) will probably refresh your memory

[gray gazelle]

has anyone read "lin alg for everybody" by lorenzo robbiano? if so, is it good?

[ionic portal]

any topology books whos introduction to set theory isnt as long as munkres?

[mellow wren]

Why don't you skip that part?

[gray jungle]

you can just skip the set theory lol ^ , its more of a reference when you need it

[clear storm]

I am learning algebra 1 using khan academy. Can i get a book that contains problem for that?
Its fine if it is little hard

I dont have any practice outside khanacademy's quizzes

[mortal birch]

this could help you http://www.wallace.ccfaculty.org/book/book.html

[ionic portal]

prerequisites to serge lang's graduate algebra without the examples?

can you read it with only mathematical maturity?

[finite gale]

It's a bit fast for a first pass

So I'd recommend having at least done some aa prior

But hard prerequisites are probably just linalg

[shrewd kraken]

wait

i thought serge lane’s algebra was the prerequisite

is there prior knowledge required?

[dapper root]

d/d2(2) = 1

[shrewd kraken]

uhh

wait i thought it was like alg and alg 2 basic concepts

i have things to do now

[dapper root]

Ummm

2-3 years??

Algebra 2 is like

9th grade high school

Abstract algebra is like, 3rd year of undergrad

In America

2nd or 3rd

[gray jungle]

i thought he meant algebra 2 as in 2nd aa course and got confused

[dapper root]

That’s like 4-5 years

Yeah because America is America

[ocean mulch]

Depends on the school

If you're at Bonn, sure 😄

[mellow wren]

Not really lol

Usually 2nd year from what I've seen
First year is more like analysis/linear algebra

Tho the linear algebra is pretty formally treated

[ocean mulch]

that's why I said it depended

some top schools do include algebra in their first year. And they make sure it's properly treated.

[finite gale]

I mean it doesn't really matter that much what order you do intro analysis / aa in as long as linalg was properly done at some point before then

[mystic orbit]

munkres?

really?

[gray jungle]

yes darq its a good book and you should read it

[mystic orbit]

never!

[sage python]

Munkres feels like it's kinda long and has dumb examples

"Dictionary order on [0,1]x[0,1] gives a topology" like take a dictionary order on some goddamn grass instead

[gray jungle]

That example is kinda meh but its a bit unfair to judge just based on this , there is plenty good explanation i found in munkres , such as quotient topology , homeomorphisms and seperation sections.

but its usually more so a nice reference i go to , i can see this being a nightmare in a systemtic study course where you have to pick specific topics to cover

the way i treat munkres is "Damn this simple point set topology fact is kinda annoying me rn , i wish there was a book out there that tries to explain it in a nice detailed way"

But ofcourse there is other great books out there

[sage python]

Yeah imo there's a bit of general point-set that you need to know but that's about it until you need something specialized

Ngl I've barely, if ever, seen Urysohn lemma used for instance lol

[loud cradle]

the C^infty version of Urysohn is handy in analysis where you can use it to approximate characteristic functions with smooth functions

[sage python]

Oh yeah bump functions are great. But say in metric spaces, it's very easy

You just do something like

d(x,B)/(d(x,A) + d(x,B))

[gray jungle]

Urysohn also lets you partition functions by unity , work locally and then go globally which is used for example in proving Reisz-markov-kakutani

[sage python]

The content of turning this into a smooth function is important

The content of doing this for regular spaces or normal spaces or whatever?

Doesn't feel as important

Is that the Riesz about measures?

Like oh linear functionals are measures?

[gray jungle]

Positive linear functionals 🤓

[sage python]

Signed measures 😠

But yeah okay that might be an actual thing. Tbh I didn't see the proof of that theorem in a ton of detail lol, and even my glance at it was mainly for metric spaces lol

[gray jungle]

good tool to have just in case you want to work on LCH spaces, which seems to happen often or not at all

depending on who you ask

[mystic orbit]

we practically spammed that during the latter parts of our reading group

[fallow cypress]

Tbh Urysohn's lemma is one of those things that's pretty enough for me to appreciate it without any usecases

[mellow wren]

Really?
Interesting
I've seen it quite a bit

[sage python]

Thing is vast majority of spaces I've seen are metric. Maybe weak topology on a Banach space is an exception, maybe also spaces involved in distribution stuff but I don't really interact with them much so idk a ton about their topology

[sturdy shore]

yeah, the space of test functions (whose dual is the space of distributions) is one space which is not metrizable

[pale eagle]

Hi everyone, I'm seeking some assistance on Math topics. Would anyone be open to DM'ing me?

[jovial parrot]

Good sniff test https://youtube.com/shorts/2c44_MxVnQs?feature=share

10/10 sniff there really strong

[inland elm]

goat

[prisma loom]

https://preview.redd.it/blqp4ie0trb91.jpg?auto=webp&s=446a3f08c9803946af43ffee7cfaac9e2bfe18da

[sage python]

Lol

[fossil arch]

What a banger drawing

Anyone have opinions on Einsiedler-Ward vs Brezis for self-studying functional analysis?

[upbeat vine]

Brezis is pretty good for self-studying FA. I would personally, however, recommend books by Eberhard Zeidler, particularly the volume 108 and 109 of Applied Functional Analysis

[alpine rover]

what's the easiest/most intuitive/easy to read/modern functional analysis book?

[gray jungle]

Introductory functional analysis with applications by Erwin Kreyszig is as easy/intuitive as FA books can get, author doesnt even assume measure theory.
idk about modern part tho.

[alpine rover]

thank you!

[urban prairie]

Hi

[wary vortex]

Good book for understanding co-ordinate geometry in depth

[rigid shale]

I have a somewhat related question

In all of the math textbooks, which one feels like it contains all the secrets of the universe?

[rigid shale]

In that case, does textbooks that are revolutionary exist?

[gray jungle]

revolutionary in what sense?

[gray gazelle]

Revolutionary as in we put guillotine on authors ?

The French one ?

[gray jungle]

If we are talking about "important" math releases then there is many https://en.wikipedia.org/wiki/List_of_important_publications_in_mathematics

but most are not very interesting to read except historic value at this point

Disquisitiones Arithmeticae is one example of a "revolutionary" book that greatly changed number theory for example

once again , not interesting to read except historic value

[sage python]

Brezis is more "functional analysis as a prelude to PDE" while EW has a lot more

[fossil arch]

Idk I just like the content layout of EW a lot more

I’m not sure how to describe the difference but I’d put Rudin & Brezis in the same class and EW & Conway in another

or shall I say equivalence class

[sturdy shore]

EW I'd say is a much better treatment of functional analysis as a whole

as dami said Brezis is laser focused on FA that will be used for PDE, although the content is still applicable to a lot of places

as a result though, Brezis is considerably easier imo

not to say that Brezis is easy, FA is a difficult subject to begin with

[fossil arch]

considerably easier?

from what little I’ve gone through EW it seems a lot easier, at least to understand the concepts and follow the author’s proofs (with what knowledge I have currently)

[sturdy shore]

I'd say EW starts out easier, once you get to fourier series on compact abelian groups it becomes apparent that the level of abstraction in that book is not the same as it is in Brezis, which in contrast works almost exclusively over real vector spaces to simplify the work

still might be a controversial take obv, this is just my opinion

[fossil arch]

fourier series on compact abelian groups

[ocean mulch]

it's not as horrible as you think

[fossil arch]

It doesn’t sound horrible at all

[gusty smelt]

ew real spaces

[fossil arch]

Sounds cool as fuck

LOL

[gusty smelt]

I work exclusively on complex banach spaces

so that sounds v bad to me!

[ocean mulch]

Ha! you did that to yourself

[gusty smelt]

complex spaces are like

literally nicer

smh

[sturdy shore]

the theory is generally not so different, but ngl I skipped the spectral theory section on Brezis because why tf are you doing that over the reals man

it just feels wrong

[gusty smelt]

yeah lol wtf

anyhow read pederson

[fossil arch]

I SAW YOUR RECOMMENDATION

IN THIS CHANNEL

[gusty smelt]

best FA book if you care not about PDEs and the like

[fossil arch]

LOL

I was considering taking a look but after skimming EW I really liked it so I stopped, I’ll go access Pederson after lunch though and see >.>

[sturdy shore]

I don't like pedersen as a first book

at least it screwed me up

I think it is an amazing book but better appreciated if you know some FA already

[gusty smelt]

eh i disagree, it was my first and like, it taught me many unique perspectives and his exposition is really good

granted for most people his approach to like, borel func cal is a bit wierd

but i appreciate it!

[fossil arch]

Borel functional calculus? 😭 wat

[gusty smelt]

its one of the spectral theorems

[fossil arch]

ay caramba there’s multiple?!

[sage python]

Feather here's something

Convince yourself why if T is a matrix whose spectrum (eigenvalues) are lambda_1,...,lambda_n with multiplicity, and p is a polynomial, then p(T) has eigenvalues p(lambda_i)

Now imagine if we start taking analytic functions, or even continuous functions (uniform limits of polynomials)

Now imagine if T is a compact operator. Or a bounded one. Or an unbounded one

[ocean mulch]

holy shit, this fact is both trivial and mind-blowing at the same time

How didn't I notice this before?

[rigid barn]

IDK how new you are to FA (perhaps the books you've mentioned are significantly more advanced), but I think Alt's "Linear FA" is REALLY good as an intro, you could try that too.

[rigid barn]

Certainly. I'm no authority, but I believe the following texts are considered revolutionary by the wider mathematical community: Euclid's Elements, Diophantus' Arithmetic, Newton's Principia (not strictly speaking math perhaps, but close enough), Gauss' Disquisitiones, Cauchy's Cours d'Analyse, Dirichlet's lectures on number theory (as edited by Dedekind), Frege's Foundations of Arithmetic (sort of like Whitehead/Russell, but came first), Hilbert's Zahlbericht, van der Waerden's Algebra, Bourbaki's Elements of Mathematics. Everyone feel free to correct me, but my understanding is there haven't been any textbooks since Bourbaki that are acknowledged as truly revolutionary.

[sage python]

Baby Rudin

[rigid barn]

Baby Rudin is famous and popular, but he's essentially the US attempt to do a "European-style" analysis textbook (I believe he admits this himself in the preface). There were already texts like that in Europe, I believe.

[wicked thunder]

Is there a rudin in the womb

like before the baby is born

[rigid barn]

Aborted Rudin, the cursed lost treatise on non-standard analysis.

[fossil arch]

LMAO

[ocean mulch]

you mean liberal math?

( #math-discussion for the ref)

[topaz rune]

Yeah the treatment is similar to how first semester mathematics students in germany study analysis

[rigid barn]

https://tenor.com/view/i-know-star-wars-han-solo-gif-14764428

(i study in Germany)

[clever orchid]

Is there any good lecture series on LA (apart from strang's mitocw lecture series and axler's very brief video series) ?

[rigid barn]

You mean EGA?

I wanted to add EGA, but ended up searching SGA by accident instead (to check if it's a textbook) and that's seminar proceedings, so I ended up not adding it.

[rigid barn]

We used our professor's script, which was based on Broecker and Forster (and a little bit Dieudonne). Broecker is pretty close to AE.

I don't think any class uses the books themselves, 99% of the time it's the professor's script, which condenses the material down to manageable size.

• it's not all 3 books in 1 semester, lol, it's Analysis 1+2+3 for a reason

I assume you must come from RU/UK/BR, it's the same system as there.

[topaz rune]

Oh didn’t even know

Do the US math majors first have a few years of calculus and then start with math?

Or how is it done

[rigid barn]

As I understand it, outside of a couple top-notch institutions (e.g. Harvard/Princeton/etc.), they do a Calculus sequence (aka watered-down analysis) and only then in the 3rd year or so Rudin-level real analysis. It feels to me like a really stupid system, but afaik the justification is that math literacy is really low in the US, so first-year students can't be expected to do analysis immediately (although if the person is majoring in math, it stands to reason they ought to be more math-literate than their peers).

[flint forge]

normally 1 year

[topaz rune]

That indeed sounds very bad.

[flint forge]

I don't think this is the case in general

[rigid barn]

I may be wrong, but that's my impression.

[flint forge]

I think maybe its common if you start out at calc 1 that it can take >1year to finish the calc sequence but most universities allow you to test out of this

[rigid barn]

From anecdotes on reddit and here i've gathered there are people in their 3rd-year of mathematical studies who haven't "done proofs" and feel trepidation taking "proof-based" courses (proof-based as opposed to what, exactly?).

[flint forge]

and typically math majors often do skip this

[topaz rune]

I think it’s a bit dumb that the math majors even do calc, just go right into real analysis and proof based LA, it starts from 0 anyway

[flint forge]

you can

at lots of schools

insofar as math majors are required to take calc, usually the relevant calc course goes faster and includes more than a highschool equivalent

[topaz rune]

I see

[sage python]

Often if there's an honors and regular version of a class, the honors one can be more proofsy

[topaz rune]

The honours course concept is kinda cool, we don’t have it at all

[sage python]

Eg at UW Madison, for students who did a certain standardized calculus class in high school and got a certain grade, you can start in "Honors Calculus" which mixes multivariable calculus, linear algebra, and differential equations, all with some proofs

Uses volume 2 of a book by "Apostol"

It's over a year

[topaz rune]

Ah ok, the calculus seems to be very standardised in general

Like if you say calc 2 everybody knows what it is

[sage python]

Well, there's a system called AP in the US, that's what's standardized

It's not exactly like A-Levels or IB but it's a similar type of thing, if you're familiar with either of those

[topaz rune]

But I don’t think it should be possible to let the High school class be recognised for uni education, independent of the major

[sage python]

In particular, students can take "AP Calculus", and if they do well enough on that exam, they can get credit for college classes

[topaz rune]

But are these classes taught by professor or by school teachers? I have often heard bad things about US math teachers (ie no education in math etc)

[sage python]

They can be, but that's why your receiving credit doesn't depend on the grade your teacher gives you, but on the exam that's administered centrally

[topaz rune]

Ah ok👍

[sage python]

It's still not perfect ofc, a lot of students in calc 1-2 that I've TAd did AP Calculus and still took that, even though in principle it's redundant, because they weren't super comfortable

[topaz rune]

In germany you just do the Abitur (everywhere a bit different), which covers calculus, linear algebra and probability and then head off to university where the level is much higher (even for eg business majors) but starts from scratch

I think business majors also start their first day of math with proof by induction

[ocean mulch]

In France it's.... uh... complicated

[broken junco]

Any online resources for linear algebra? Like interactive textbooks or things of that sort?

[glass otter]

Hey y'all! Does anyone know a good textbook on Functions? I'm looking for a didactic book that teaches Functions from the very basics (injective, surjective, graphs, exponential, logarithmic, etc). I got "Precalculus by Stewart", but it seemed way to fast on the functions chapters...

[remote sparrow]

#book-recommendations message

specifically hefferon

[broken junco]

tyvm!

[fickle thicket]

I started learning MACHINE LEARNING, seems it has a lot of algorithms and math behind to deal with

Here is my LinkedIn profile https://www.linkedin.com/in/deepaksakthi-v-k

Can someone suggest a book for advanced Statistics ( ANOVA, P VALUES... CDF , PDF ) and algebra ( EIGEN ...)

[sudden vale]

Does anyone have idea how Kumaresan's "A Course in Differential Geometry and Lie Groups" compare to Lee's "Introduction to Smooth Manifolds" for a Differential Geometry course?

[left cloud]

are you serious? he said precalculus by stewart is way too fast lmao

[rigid shale]

Would Tao's Analysis I work here too?

It seems to feel magical as the formal foundations of math are laid out for me as well as his solid writing

[empty junco]

no

[rigid shale]

Alright then

That's my first book on Analysis tbf

[crimson leaf]

I would say last semester of second year, at schools in my state it's like you'd do calc 1, calc 2, then calc 3 & linear algebra & proofs, and then you'd take whatever is offered the next semester maybe analysis maybe algebra (some schools do both at once but most alternate to cover the second course in the semester the first course isn't running)

[proud gazelle]

what's unconventional about LADR?

[crimson leaf]

The entire treatment of determinants

[proud gazelle]

so If I read determinants from another book, are the other subjects alright?

[empty junco]

now you're thinking like a mathematician

[sudden vale]

🔼

[rapid spire]

I've just finished high school and I would like to self study higher level mathematics (preferably analysis). I'm not sure which books I should read to be fully prepared to pick up a real analysis book and understand whats going on so any recommandations would be appreciated. I already tried to read spivak's calculus but felt like it was a little too overwhelming because I'm not sure how to prove stuff.

[heady ember]

Schroder's analysis and abbott are common recs for a gentle intro to anal. Regardless of your choice though. you need to have some level of persistence to stare at exercises for hours with zero progress and find satisfaction/joy in completing challenging even if it takes a while. Its part of the process

[rapid spire]

appreciate it

[mystic orbit]

Why would anyone trying to learn about functions first time want to learn about monomorphism?

I'm not even sure why anyone would want to learn about monomorphisms at all!

[mystic orbit]

@lapis heart why sully?

[lapis heart]

Stop projecting your categorical insecurities on the rest of us...

[lapis heart]

Wherever they may be useful in, his point obvsly stands

Book recommendations need to suit their target

[mystic orbit]

I'm not projecting, my point is if even I don't know why they're useful how would you expect someone learning precalc to find them interesting

That's pretty far fetched from precalc lmfao

[grand thistle]

no

[lapis heart]

hells the point of defending your shtty joke

[mystic orbit]

It's not a joke

[lapis heart]

Well mind your phrasing then

[mystic orbit]

I literally don't know why I should care about them

[grand thistle]

wtf r monomorphisms again

arent they just injective

[mystic orbit]

[mystic orbit]

Lololol

In the category of Set, yes

In most categories that matter, really

But the definition doesn't even assume the category has a suitable sense for elements

[smoky zephyr]

[gray jungle]

exactly! that what im saying , next time someone asks for a book on trigonometry ile link them a book on Fourier analysis on LCG and tell them math is math

I resign , you win

[light cedar]

i need a book to study multivariable calculus

preferrably something very rigorous

[mystic orbit]

you can start with spivak calculus on manifolds

[light cedar]

"start"?

im gonna need multiple books?

how well does that book cover it

[mystic orbit]

it depends on how thorough you wanna be lol

spivak might be all you would need

[mystic orbit]

I liked everything up until the inverse value theorem

but the proof of that one is infamously hideous

there's also hubbard but that's waaaaaay too thorough

I liked that one even more

but you'll want to know what you're looking for or you'll be spending a month on quadratic forms for no reason lel

do you have a list of the topics you want to cover?

[light cedar]

is it weird that its only 150 pages

no i just wanna read books

multicalc was the first obvious option cuz ill be needing that for deep learning

[mystic orbit]

oh, do you know any linear algebra?

[light cedar]

i do

[mystic orbit]

it's pretty terse

[light cedar]

im doing a cs degree last year

but really wanna study all the math i could get my hands on

[light cedar]

will start with spivak then

[mystic orbit]

@light cedar for the record you don't need a lot of multivar analysis for deep learning

you just need enough for optimization theory

which is around the first 3 chapters of spivak

[light cedar]

hmmm yeah still gonna read the whole thing though 😄

question

which topics do tensor and metric calculus fall under?

multivar calc?

matrix calculus*

cuz i frlt like i need that for deep learning

gradients of tensors etc

@mystic orbit

[mystic orbit]

I don't know

I've heard of those terms thrown around but I don't know them beyond a guess lel

[sudden vale]

Any help?

[sage python]

It might be tricky because Kumaresan doesn't seem to be a well-known book

At a glance they seem like they serve subtly different purposes

Lee Smooth Manifolds is predominantly about the general machinery of manifolds

What's a manifold, what's a smooth map/function, equivalent definitions of tangent vectors, derivatives, tangent bundle, vector fields and Lie brackets, ODEs on manifolds, tensors, differential forms and integration, etc

Once you have that general machinery there are various things you can do

You can use this smooth structure to study the topology of the manifold. Appropriately called, differential topology

Stuff in this subject includes transversality/intersection theory, Morse theory, de Rham cohomology

There's not a strong line between the raw smooth manifold theory and the topology. Everything here is up to diffeomorphism

But yeah subtly it's that a book or class on "smooth manifolds" will mostly focus on the machinery, calculus, shit like that, while a "differential topology" book or class will have actual content

Differential geometry is another story, you need some structure beyond the smoothness. Diffeomorphism from R^n -> R^n will not preserve angles, distances, any of the stuff that you'd consider geometric

And on a smooth manifold there are no natural such notions. But if you put, say, a Riemannian metric (chapter 5 of the book you mention), now we can speak of stuff like that, and talk about these guys up to isometry

This is diffgeo land

Diffgeo books which aim to be self-contained usually contain some of the raw smooth manifold theory needed, though in much less detail than something like Lee. And that's what's up with Kumaresan by the looks of it. It has a chapter of reviewing calc on R^n, then 3 chapters that overlap with Lee. Seems to cover good ground without using too too many pages.

Then the last chapter is actual diffgeo

[sudden vale]

And what advantage/disadvantage would going through details of the "machinery" through Lee would serve over going through brief books like Kumaresan? Our professor would mostly be using Kumaresan for a course on Diff Geo and Lie Groups which would consist of Manifolds and Lie groups, Frobenius theorem, Tensors and Differential forms, Stokes theorem, Riemannian metrics, Levi-Civita connection, Curvature tensor and fundamental forms.

I have been reading Lee recently and I feel comfortable with it, and I wish to follow it throughout the course and further, but the concise nature of Kumaresan means that the professor might be done with stuff beforehand and I would have to catch up. For example, there are dedicated chapters for submanifolds and Sard's Theorem in Lee, whereas same topic is covered in Kumaresan very briefly (in about 6 pages)

[flint forge]

well, it is worth noting that the bottleneck for speed is almost certainly not literally reading the pages, but more understanding the math

and often times a book that explains more details actually takes less time to follow

than something that is very concise

[sudden vale]

Yeah, that is one thing. I do feel comfortable with Lee, but I take some while to read up stuff, since I prefer to take it slow in general.

Off the topic, but when do you think one should "leave" the stuff for while? Sometimes when I read a topic, I can follow and understand whatever is happening, but it doesn't "click", as in, it doesn't seem to come naturally. How often should I leave that as it is and hope that it'll come naturally as I proceed with the subject, and how often should I work with the topic again until it comes naturally?

[flint forge]

I think this is a huge personal preference thing

and its very goal dependent

for example, the amount of blackboxing one does when learning material in a class should be way less than the amount they do in real research, and both are different from topic to topic too

[chrome yacht]

matrix calculus is mostly multivar which requires at least a strang level course on linear algebra. here's a nice short course for matrix calculus if you are into deep learning https://github.com/mitmath/matrixcalc. this should cover almost all you need if you're only into applications

[sudden vale]

Hmm. I kinda feel stuck if I can't feel things coming naturally, which I guess might be a bad habit in math.

[chrome yacht]

if you have no experience doing analysis before and spivak overwhelms you with how terse it is then Advanced Calculus by Sternberg might be a good alternative too (funnily enough i believe it is even more abstract than spivak but the exposition is far better and you probably only really need differential calculus?)

[light cedar]

i studied calc 1 and 2 i do know some analysis

not real analysis level stuff though

i want to study real and complex analysis aswell after multivar calc

[mystic orbit]

Wait what

Bruh

Sry, I assumed you did when I shouldn't've coz real analysis is mostly a math majors thing

Anyhow, real analysis is a prereq for spivak

So you'll prolly have trouble reading that

[gray gazelle]

wait rly?

[mystic orbit]

It's not for Hubbard tho

[gray gazelle]

isnt spivak for learning real anal?

i thought the only prereq is some proof writing

[mystic orbit]

Spivak's calculus on manifolds

[gray gazelle]

ohhh

[gray gazelle]

is this for functional analysis?

[mystic orbit]

No it's for multivar analysis

Functional analysis is quite far from manifolds afaik

[gray gazelle]

idk im kinda clueless on things higher than basic real analysis

[light cedar]

hmmm im actually not sure what real analysis is, lemme check

i think i studied it in calc although im not sure

most of the stuff for real analysis on wikipedia im familiar with

question, real analysis = analysis?

[flint forge]

real analysis is a subject within the field of analysis

[light cedar]

i know how to analyze functions over R and plot them, find minima points, check for integral,series convergence, differentiate,integrate,plot,asymptotes etc

[flint forge]

that is not real analysis

[light cedar]

oh

shit then ill have to study real analysis first

[flint forge]

real analysis starts out by putting all of the manipulations and definitions of calculus on a rigorous footing

and then goes far beyond that

[light cedar]

hmmm so i need a book on rral anlysis

[light cedar]

does hubbard go into real analysis?

if hubbard covers both real analysis and multivar i might aswell choose it over spivak

how about advanced calculus from harvard university? that should be sufficient no?

[flint forge]

that would not be a real analysis course

[gray jungle]

You dont need real analysis to learn multivariable calculus if thats your concern , if you do want to learn real analysis then there is many books : tao analysis , abott etc .

[flint forge]

harvard has distinct real analysis courses

[light cedar]

lol i think i just need to visit a library

hubbard is fucking 300$ on amazon

wtf

210 + shipping for 300

[remote sparrow]

you don't buy it from amazon

you buy from the publisher's website

[subtle mango]

we sail at dawn 🏴‍☠️🏴‍☠️🏴‍☠️

[remote sparrow]

the publisher is matrix editions

[flint forge]

just p*rate the book

i know im not supposed to say that

[light cedar]

reading on phone sucks

[flint forge]

there we go

[subtle mango]

max thats what i said

:(

[flint forge]

u used emotes

i dont have time for that

[subtle mango]

aww

[flint forge]

seriously though never ever buy these massive $100+ books

its not worth it and the authors see pennies if anything from it

[subtle mango]

i paid like $120 for baby rudin 😭😭😭

[flint forge]

why

[subtle mango]

wanted physical copy

[flint forge]

first of all you can for sure get baby rudin for less than $120

[subtle mango]

yea lol it was from my school bookstore

[remote sparrow]

depends if it's paperback or hardback

[flint forge]

okay so ur a mark

[subtle mango]

major blunder

i have no idea what that means

[remote sparrow]

also international edition factors in

[flint forge]

its a joke, mark is a term for the target of a scam

or more generally someone who would make a good target for a scam

ive overpaid for bookstore books before tho

its so convenient

[pallid pollen]

Not about books, I attempted to discover any websites that provide full video courses for math majors, such as this one from Oxford, an open courseware, but they don't have much video and only a few problem sheets.
https://courses.maths.ox.ac.uk/course/index.php?categoryid=99

[gritty gale]

https://www.openculture.com/freeonlinecourses#Math Courses you might like this

lots of free video here

idk if it's right for whatever level you're doing tho

[pallid pollen]

Undergrad

[gritty gale]

oh yeah you should be at least reasonably well served by this

[pallid pollen]

I'm simply seeking an opportunity to acquire comprehensive education (math major) since my current university doesnt meet my expectations ; (

[gritty gale]

oof

[pallid pollen]

Thank u

[gritty gale]

sorry to hear it

ur welcome tho

tbh i'm probably not in the best position to advise you specifically given i'm not in a country that uses majors

and also i studied physics

so all the pure stuff here kinda goes over my head

[pallid pollen]

Anyway, thank you for your sharing

[flint forge]

You can also google "[subject] lecture series" and often you get lucky for some subjects

[light cedar]

thats horrible

[flint forge]

well, they get paid an advance to actually write it

but its a good reason not to feel bad about p*racy

[hazy elk]

Learn binding (or just spiral it tbh) and print out copies for yourself

[hazy elk]

Ig you can also add "NPTEL math", ICTP's and Richard Borcherds' , IHES' YT channels. There are many courses that cover stuff from intro ,pretty advanced courses and research level workshops on YT, just need to figure out the topics you want to learn and type in keywords

[pallid pollen]

thank you for your dedicated advice

[hazy elk]

Actually, thank you for the oxford link

The course notes look really nice

[wicked thunder]

Why would you even read physical copies of books? They don't even have a dark mode.

[sudden vale]

Nah, physical copies feel good to read from and mark on.

I just get my books printed lol. Does not cost me more than around Rs 1 (around 1 cent) per page.

[marble wedge]

Hey I am in class 11 Sci and I have exams tomorrow and have to prep for sets, relations, functions, inequalities and AP. Can anyone suggest me some good books for good questions?

[sudden vale]

NCERT😃

[marble wedge]

Already done

also solved R.S.Aggarwal

[sudden vale]

Hmm, shouldn't that be enough for a school exam?

Solve RD if you wish, or maybe DC Pandey. You can also try the black book

[marble wedge]

Dude i am in a institution where different management teaches for jee prep students and we have way more diff level

[marble wedge]

I want the black book's pdf

[sudden vale]

Ah, DC Pandey was physics, I forgot

[wicked thunder]

The black book 👀

[marble wedge]

Yeah isnt that for chem?

[valid monolith]

What is the black book

[wicked thunder]

It sounds ominious

[sudden vale]

No.

[sudden vale]

It is, to students prepping for a particular college entrance test here in India

[marble wedge]

Its a book on organic chem by shish mishra and r. ramu petkamsetty

[sudden vale]

No, it's Vikas Gupta dude

[marble wedge]

😂

Seriously i feel that too

Reminds me of deathnote

[valid monolith]

Og

The name is really the black book

Lmao thought was like a name people give it

[marble wedge]

there is also a edition for maths

I have chem one

need the maths pdf

oh found jeebooks

[valid monolith]

Do you know the authors?

[sudden vale]

It's not

[marble wedge]

yeah ig

[sudden vale]

People call it the black book because...well, it's black

[marble wedge]

Its actual name is advanced problems in maths for jee

[valid monolith]

I can't post aceeenshos

But i said that because the first thing it showed was a black book with black book written in

[marble wedge]

And its deadly cuz it crashes confidence as its for jee advanced aspirants

[valid monolith]

Now i am more interested

[sudden vale]

It's not that bad. If you wanna destroy your confidence, look at Sameer Bansal lol

[valid monolith]

Advanced level papers?

[marble wedge]

[sudden vale]

Yes, but not that hard

[valid monolith]

Was just confirming the name

[sudden vale]

Oh

[valid monolith]

Found the amazon page, thx

[sudden vale]

Integrated school?

[marble wedge]

jee has 2 exams mains and advanced and advanced is harder than mains

[marble wedge]

Yeah i have to go to school and they teach us instead of regular school teachers and also prep for jee together

[sudden vale]

Ah, PW or what?

[marble wedge]

Nah

PW is a dummy classes

I have to go to school

[sudden vale]

Ah, I was thinking something else.

Anyways, try the black book. Don't think you need anything more than that as of now

[marble wedge]

Ohok

Hey @sudden vale How's Cengage vs Sameer Bansal?

[sudden vale]

Haven't seen Cengage. Bansal was good if you've already brushed up calculus multiple times and have exhausted all the other resources and just need to master it.

[torn epoch]

Can you give a recomment for analysis books?

[sudden vale]

Depends on your level. Are you just starting out with Analysis for the first time?

[chrome yacht]

Amann-Escher

[torn epoch]

No

[torn epoch]

Thanks

[chrome yacht]

you're looking for an intro book right?

[torn epoch]

No actually i want to learn higher level analysis i know the basic things

[chrome yacht]

ah amann escher is a fine book for a second, more involved reading i hope you'll like it

[mystic orbit]

uhhhhh

I mean

multivar is a type of real analysis

and unlike spivak, you don't need analysis knowledge for hubbard

the only prereq is like

ap calc BC

[mystic orbit]

not hubbard

they get everything coz they own the publishing company iirc

[light cedar]

could i read hubbard and then spivak?

or would i still need more knowledge before reading spivak

[mystic orbit]

that would be superfluous

hubbard most likely covers everything in spivak

[light cedar]

ohh great then imma get hubbard lol

[mystic orbit]

I mean, hubbard is 5 times as big

[light cedar]

great

[mystic orbit]

literally

[light cedar]

i mean, im planning on just reading and i dont see myself stopping even after finishing the first book

[mystic orbit]

https://cdn.discordapp.com/emojis/1128036478669312022.webp?size=48&name=upthumbs&quality=lossless

[light cedar]

its that multivar calc seemed like the best option for now

thanks 😄

[mystic orbit]

that'll take you a while tho, I'll tell you that

hubbard is HUGE

it's like more than 3 courses

in one book

[light cedar]

hah still ok, i can sure find some resources that provide the necessary knowledge for deep learning if i run into something i didnt know while studying that

thats what ive been doing so far

[mystic orbit]

aight then have fun!

I honestly think hubbard is perfect for someone that has engineery/physicy/CSy background that wants to start delving into rigorous mathematics

[light cedar]

perfect lol

[mystic orbit]

@light cedar if you're serious about buying the book you can find it in https://matrixeditions.com/ for a 100 bux

in general, books are cheaper if you buy them from the publishing company official website

and bezos doesn't get a cut

[light cedar]

should i usually look for newer editions?

i mean, does it make a difference? newer editions are often better right?

[mystic orbit]

certainly

tho I can't comment if it's worth it or not lel

I have never paid for books so I just look for the newest edition lel

[ocean mulch]

that's more like it

[wicked fractal]

Any book recommendations for algebraic number theory (PDF) ?

[woeful ermine]

Well I'm not sure excatly what you are going for, but here are a few recommendations:

• 104 Number Theory Problems - Titu Andrescuu (overall good)
• An Introduction to Diophantine Equations - Titu Andrescuu, Dorin Andrica, Ion Cucurezeanu (an amazing book for diophantine equations)
• Olympiad Number Theory Through Challenging Problems - Justin Stevens (again overall amazing, but may be too hard if you are not interested in olympiad math)

[dapper root]

https://www.jmilne.org/math/CourseNotes/ANT.pdf

[woeful ermine]

I was wondering does anybody have a good book (or anything really) about graph theory. I want to get started on that topic but have no idea how. I can't seem to find a good book on that topic, most of the times I find stuff related to programming and purely that (I know graph theory is more common in programming but surely there are some good books on it in maths).

[wicked fractal]

that already makes me scared of the new terms I have to learn

[woeful ermine]

I am looking for competition math graph theory.

[wicked fractal]

jk that looks exciting

thx chmonkey

[wicked thunder]

Learning new terms is the worst part of math

[gray gazelle]

What about new symbols?🫃

[wicked fractal]

at least when I started analytic number theory I was like "hey that looks very familiar"

but algebraic just makes me scared now

[gray gazelle]

What background did you have when you started Anal NT?

[wicked fractal]

real anal, complex anal, elem NT, harm analysis, measure theory etc

[gray gazelle]

Do... you need that much anal background

😅

[wicked fractal]

hmm

not really

but complex analysis yeah

[finite gale]

you definitely need complex analysis

[wicked fractal]

cuz when u go learn about the PNT analytic proof

all what u see is complex analysis

[gray gazelle]

Thanks guys, I'm reading Rudin/Hoffman-Kunze right now, I'll look at Ahlfors and an ENT when I'm satisfied with progress there probably

[wicked fractal]

I have a question about algebraic

What topics from abs algebra do I need the MOST

[finite gale]

uhhh

strong foundations in undergrad aa?

you should definitely be comfortable with galois theory

[wicked fractal]

usually galois is like taught at last so idk

yeah so galois theory is a must

[finite gale]

yeah

and depending on the text you use, you might want more, but i only know a few

[wicked fractal]

commutative alg?

[finite gale]

perhaps, but not sure

i think my alg nt class last year had some mentions from AG, but it wasn't used that much so idk

maybe someone else will give a better answer regarding that

[wicked fractal]

I see thanks. I was going to ask in #advanced-number-theory but I was hesitant lol

[dapper root]

Yes

But most texts treat it in-book

Ring and module theory, and then field and Galois theory. But also, a lot of them do that stuff in book

[gray gazelle]

are the art of problem solving books good

[late shadow]

Any Paul Lockhart fans have recommendations relevant to mathematical comp-sci foundations? (Discrete math, logic, proofs, sets, that sort of thing?)

(I know Measurement is proof-oriented, but I already have Lockhart's books)

[late shadow]

(For context, I'm a working programmer who did not go to college, looking to self-study computer science for fun.)

[narrow relic]

I have some very interesting logic books I can potentially recommend to you

But I doubt people who know this stuff from a mathematics perspective would like or find much value in them

[late shadow]

I'm interested in any good logic book (doesn't have to be math-focused). 🙂

[gray gazelle]

It may seem silly but i'm looking forward to beeing a
mathematician and i'm lost bc there is a lot of things to learn
So how can i start ?
And what books do i need to read as fundamentals ?

Fyi i just finished high school

[gray gazelle]

Hi, my class uses The Power of Logic by Snyder. It might be too easy, but it sets up nicely for Mathematical Thought as it covers propositional logic, general logic, etc...

[gray gazelle]

Do you know Calculus? I think that is very fundamental to your development, good luck!

[gray gazelle]

I know high school calculus

And I looked at some university level calculus "Unfortunately on YouTube "

[gray gazelle]

Is this book good as a basis for mathematical thinking ?

[weary cape]

Same

[late shadow]

I'm no mathematician, but coming out of high school, I think reading Paul Lockhart's "Mathematician's Lament" and "Measurement" would be a great way to get started.

I haven't even finished Measurement, but those two books really helped me see the difference between math in general and the specific subset they hammer over your head in school.

[fallow cypress]

This is more advanced than you asked for, but Elaine Rich's Automata Theory And Applications might be cool for you to flip through

It's relatively accessible and gives cool applications of the theory of computation

[remote sparrow]

i think there's a nice bundle option if you buy the ebook and student solutions manual

the ebook occasionally gets automatic fixes to errata

[gray gazelle]

In fact, I hate school system and used to ignore the teacher's explanation and study mathematics myself through some books and YouTube videos

[gray gazelle]

Thanks
I'll check them

[late shadow]

lol you will probably really enjoy Lockhart then.

[narrow relic]

Here are the ones I looked at:

[narrow relic]

Michael Genesereth, Eric Kao: Introduction to Logic
Gordon J. Pace: Mathematics of Discrete Structures for Computer Science
Mauricio Ayala-Rincón, Flávio L.C. de Moura: Applied Logic for Computer Scientists
Paul Teller: A modern formal logic primer
Mordechai Ben-Ari: Mathematical Logic for Computer Science

[narrow relic]

I thought the Mordechai Ben-Ari was the most interesting out of these books, if I remember right.
The Teller book and Genesereth/Kao are more like traditional logic I think
Ayala-Rincón/de Moura was pretty interesting, kind of like Ben-Ari in that it was more a computer science perspective

[late shadow]

Thanks!

[narrow relic]

You're welcome, let me know if you read any of them, I'd be interested to hear your thoughts.

[gray gazelle]

Have you read Knuth? How do you feel about it?

Sorry, just based on your interests it seems like you'd have read it

[narrow relic]

Knuth, you mean the discrete math book or the art of programming books?

[gray gazelle]

Discrete

I would like to go through both eventually though

[narrow relic]

I have never read it, I read a more basic "discrete math" book

Of those above books I listed, I only read several chapters of the Geneserth and Kao book. The others are just ones I found browsing around

But I thought the Ben-Ari one was very interesting

And I would probably read more of it if I have the time

[narrow relic]

I'd be really curious to hear what you think of the Ben-Ari book if you have the time to look at it

[late shadow]

I'll let you know. 🙂 Springer publishes a lot of good stuff, so I'll definitely have a look.

[narrow relic]

It's like the book I wish I had started with for logic

And I think it's fascinating how he sees it from a computer science perspective, in my opinion that adds a lot

[late shadow]

They have one called "A Logical Approach to Discrete Math" which I'm curious to read. It's endorsed by Doug McIlroy of Bell Labs, so it must be good. (but also may be above me at the moment )

[narrow relic]

I haven't heard of that one. Interesting.

All the ones I mentioned above are just logic books, no other discrete math topics.

[late shadow]

As far as discrete math textbooks, I got the Susanna Epp book due to the wide praise and despite the reports of plentiful typos (used 4th edition for $30) and the Aho & Ullman "Foundations of Computer Science" book (surprisingly it goes for like $10 used; also free to read online, along with most of Ullman's other books).

[narrow relic]

An alternative to the Epp book is Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: 5th Edition. That's the one I read a lot of.

[late shadow]

I'm excited about the Aho/Ullman book in particular because it claims to be designed for my exact purpose (taking a person who knows how to program and filling them in on the math they didn't study).

[narrow relic]

Cool! I've heard that book mentioned favorably.

[late shadow]

There are some modern books/courses with the same goals, like Jeremy Kun's "A Programmer's Introduction to Mathematics", but I'm a Bell Labs fanboy so I had to get it.