book-recommendations

[forest marsh]

do i need calc

[weary cape]

U can take a look at it if u want

Not sure myself but I see the word "algebras" in there I don't think its anything easy...

[forest marsh]

I passed Algebra in 10th grade

[primal summit]

not the same algebra

[weary cape]

Its not the same

Its not y = xsmth

[visual oasis]

thanks for the detailed responses, that looks like a good pdf as a starting point

[primal summit]

you need at least most of an undergraduate degree's worth of algebra, topology and functional analysis courses to start thinking about C* algebras

[weary cape]

Ah

[forest marsh]

how can i get that

[weary cape]

What math have u finished

[forest marsh]

precalc starting clac 1

[weary cape]

Ah

[primal summit]

please move the convo to one of the discussion channels

to not clutter this channel

[weary cape]

OH im so sorry

[primal summit]

it's all good

just don't want a full-on conversation to start here

[gusty smelt]

oh yeah I have heard some people say condensed sets are the future of operators (like sri lol)

[gray gazelle]

Interesting POV to be honest, not sure how much it holds in practice though

[gusty smelt]

yeah idk much about this stuff (condensed sets)

[gray gazelle]

Then there is Toric Varieties trying to challenge Probability

The rest of Math should just get rid of AG/AT tbh

[gusty smelt]

lol

[foggy relic]

did you get that from anisomoprhism lol

[gray gazelle]

From Almost_Sure twitter? Yeah

[foggy relic]

no like the discord user anisomorphism

#chill

[visual oasis]

yes I'm starting my 2nd year of masters next year

by next year I mean in sept

[primal summit]

I was talking to a different user, someone above was asking about what maths you would need to know for C* algebras

[visual oasis]

oh lol didn't scroll up I guess that wasn't adressed to me

my bad

[primal summit]

lmao it's all good 🙂

[sleek osprey]

any all encompassing trig book that explain trig well

[clever pier]

James Stewart - Algebra and Trigonometry or James Stewart - Precalculus.

[sleek osprey]

alright thanks

[sleek osprey]

does it include all the topics

[clever pier]

It could have a bigger section on Complex numbers, but it's fairly complete.

[sleek osprey]

what does the cover look like

theres a lot of versions

[clever pier]

I think it has that building from Westworld Season 4 on it. Blue cover, 4th edition.

[sleek osprey]

4th or 5th

[clever pier]

I have 4th.

[sleek osprey]

alright ill get the 4th one then thanks

is it a diificult book

[clever pier]

You will encounter a lot of new concepts.

[sleek osprey]

alright but like around year 11 level right

[clever pier]

Yes, it's a good introduction into subjects that will come up in Calc 2 and Calc 3.

[sleek osprey]

alright thanks ill download it

[coral prawn]

wait our usernames are kinda similar

[frosty basin]

https://www.amazon.com/Elementary-Topology-Ya-Viro/dp/0821845063 i think this book is very good for self study

tho it has a bit of unorthodox approach

[fierce hedge]

It's a good book, it was recommended to me by eigenyuwu I think

[frosty basin]

you mean the topology book that i mentioned above?

[fierce hedge]

yess

(although don't take my word for it, I have yet to study it properly)

[gusty verge]

Introductory book for Convex and non convex optimization with numerical problems?

[visual oasis]

I took a look at connes book, and the order of chapters is kind of perplexing me

[unkempt owl]

Does anyone recommend the uk mathematics trust books

I bought the geometry of a triangle from them today

Its 600 pages tho

International maths olympiad geometry of a triangle

Anyone got their books before?

[rigid barn]

What are some cool correspondence books of mathematicians? Was looking at this https://univerlag.uni-goettingen.de/bitstream/handle/3/isbn-3-938616-35-0/hasse_noether_web.pdf?sequence=4&isAllowed=y when I thought about how something like that might be interesting to read.

[lavish void]

What intro linear algebra / calculus 1 textbooks do you guys recommend

[full egret]

for intro linear algebra I've been using Edwards and Penney

not sure it's the best thing out there (probably not) but it's what my professor uses in class, so...

[remote sparrow]

#book-recommendations message

#book-recommendations message

[orchid mortar]

:O thanks for this

[quartz nymph]

helo

i am new

[marsh yew]

Can someone recommend me a book that can cover calculus needed for Ray Tracing ?

[civic surge]

Hi, I'm taking my firts course in Real/Functional Analysis the next semester and I'm looking for text books with lots of exercises. The course is divided as follows:

1 - Supreme and Sequences
2 - Cardinality
3 - Metric Spaces
4 - Continous Functions
5 - Compactnes
6 - Normed Spaces
7 - Sequences and Series of Functions
8 - Lesbegue Measure
9 - Measurable Functions and Lesbegue Integral

I've been reading the Abbot's "Understating Analysis" and I like it, I think it has a really modern approach and is very well written but it doesn't cover all the topics. Could you recommend me something that goes a little bit deeper on general Metric and Normed spaces?

[chrome yacht]

I'm sure you'll like Amann Escher volume 1 for the coverage upto chapter 7 in your course. Unfortunately volume one does not even cover the Riemann Integral let alone measures; you'd have to get to volume 3 for that. You might also want to take a look at Pugh or Rudin's POMA.

[civic surge]

Thank you both, I'll definitely take a look to the Amann Escher, it seems to be more modern. I've taken a look at the baby rudin and I find it incredibly harsh to read but if I don't find anything else that suits what I think I need I'll go with it. Pugh looks a lot to what I'm looking for in a book, but it doesn't seem to fit the course chronollogically. Maybe using both is a good idea, what do you think? Cause the baby rudin seems to cover the course better and the Pugh seems to make a bigger effort on explaining the intuition behind stuff and it also has a lot of exercises.

[sage python]

Hmmmm

[fierce hedge]

I am pretty sure volume 2 does riemann integration. Volume 3 is cal on manifolds if memeory serves me right

[remote sparrow]

carothers

[rigid barn]

The same talk was repeated with some variations in May at Ohio State University, and then in June of the same year in the “Aspects of Mathematics” Conference at my alma mater, the University of Hong Kong.
....
A somewhat longer version with more technical details will appear concurrently in thr proceedings of the “Aspects” conference, published by the University of Hong Kong. In particular, some of the proofs omitted from this article can be found in the Hong Kong proceedings.

From Lam's article "Representations of Finite Groups: A Hundred Years, Part I", does anyone know where I can find these "Aspects" proceedings? Googling didn't help and there was no reference in the article.

[frosty basin]

after finishing with abbott, i suggest you dive right into rudin's pma, since pma was written explicitly for people with purpose like you, not for first approach

[fierce hedge]

I personally think pma after abbott will be very redundant. Better to use something more advanced like carothers

[steep spade]

What books would y’all recommend for a second course in linear algebra? I’m looking for something around the same level as Axler’s Linear Algebra Done Right

[tender river]

steve roman linear algebra done wrong sergei treil

[steep spade]

No idea this existed lmao

[grand thistle]

hoffman kunze is good too

[finite gale]

#book-recommendations message

Relevant

[steep spade]

thank you

My friend actually has friedberg's book so I can get it for really cheap

Imma probably gonna go for that too

[jolly pumice]

can anyone recommend me a book on manifolds

[mellow wren]

do you already know point set topology?

[jolly pumice]

i just know the basics of the basics

i know that they resembel a euclidean space

[mellow wren]

Okay...
Do you know like analysis/linear algebra

[jolly pumice]

i mean it's kind of needed

[mellow wren]

yeah that's why I'm asking
You should probably read up on topology a bit more if you wanna read more in depth about manifolds
But Loring Tu's book introduction to manifolds is a good one

[jolly pumice]

oh my god thanks i was just curious about this topic

i only read some articles about it

[grand thistle]

i like tu's book

too

[jolly pumice]

oh my god it's really good still on the first pages i like how they clarified that a euclidean space is actually a prototype

[frosty basin]

would it be a bad idea to read tu's book without any knowledge of multivariable analysis like ones that are discussed in rudin chapter 9~11 or spivak's calculus on manioflds?

[jolly pumice]

I just read some pages

I think you should ask the ones who read the work

[frosty basin]

oh okay

[civic surge]

Thank you. That make sense!

[civic surge]

In what sense is the Carothers more advanced? And why do you think it would be less redundant than the pma?

[fierce hedge]

Rudin has almost the same content as abbott, he just does things in more generality. Compared to that carothers starts with Metric spaces then does Function spaces and then Measure Theory which btw Rudin also does but much much worse.

[jolly pumice]

Tu's book is designed for students with a solid foundation in linear algebra, calculus, and some basic topology. While it does not assume prior knowledge of multivariable analysis as extensively covered in Rudin's Chapter 9-11 or Spivak's 'Calculus on Manifolds,' some familiarity with the concepts of multivariable calculus would be beneficial.

The book covers a range of topics, including smooth manifolds, tangent spaces, vector fields, differential forms, integration on manifolds, Lie groups, and more. Tu presents the material in a clear and concise manner, providing detailed explanations, examples, and exercises to reinforce understanding.

Even though Tu's book is a comprehensive introduction to manifolds, it is still a challenging subject. Some readers may find it helpful to supplement their study with additional resources or textbooks that cover multivariable analysis to solidify their understanding of the underlying concepts.

In summary, while it may be possible to approach Tu's 'Introduction to Manifolds' without prior knowledge of multivariable analysis, having a basic understanding of the subject and its associated concepts will greatly enhance your learning experience and comprehension of the material.

after reading all 430 pages this is more or less what i thought but i think it's better to review all possibilities with the other readers

[fickle bough]

I think the exercices are much better even if the content covered in the sections is somewhat the same

[blissful pulsar]

"What Is Mathematics?" by Courant, Robbins and Stewart. Does it good book for relearning math?

[remote sparrow]

i don't think so

it might be good as a retrospective after you relearn the math covered in the book

[gray gazelle]

Basic Mathematics by Serge Lang is pretty good

[thorn canyon]

I checked pinned messages, after Gilbert Strang's Intro to linear algebra, which book among "linear algebra done right" and "hoffman and kunze" would be better for someone, who is not from pure math background?

[remote sparrow]

doesn't really matter

but friedberg, insel, spence discusses applications more

ladr seems popular in the physics discord

but if you're looking for something more applicable to fields like cs, FIS at least discusses finite fields

hoffman kunze is fine too

[thorn canyon]

I see, then i'll have to sort by number of pages.

[junior isle]

Is serge lang's linear algebra book good for self study?

[blissful pulsar]

So should I study it?

[remote sparrow]

no

you should study from a different book or resource

use courant's book if you want to reflect on what you've learned before

it's not a review book either

[blissful pulsar]

Tbh, I stayed apart from Math so basically I don't know Math I would say.

[blissful pulsar]

Courant book? Which one?

[remote sparrow]

the one you just mentioned

[blissful pulsar]

Why does it includes bad practices or what? I also heard on Serge's book that some math formulas are wrong in answers section of the book and also lack of some concepts that is not included.

[remote sparrow]

courant's book is not a book that tries to teach math

it's meant to tell you what studying mathematics is like

lang's book has some errata yes, but it's fine

you can probably just google if there's an errata sheet

[blissful pulsar]

Augh okay.. Then I would go for Serge book.

Aight thx

[frosty basin]

can i ask people here's opinion on serge lang's undergraduate analysis

[gray gazelle]

I'm liking the books General Topology by Stephen Willard and Topological Vector Spaces 2nd edition by Narici and Beckenstein

[frosty basin]

hows willard different from munkres?

[gray gazelle]

The book talks about nets and filters and star refinements and also talks about uniform spaces.

[frosty basin]

isn't that a bit too much for undergrad?

[remote sparrow]

general topology is also taught as a graduate course

[fierce hedge]

True but nets and filters are still a bit unusual for a topology course

Maybe not grad topology

[sage python]

It's not an undergrad vs grad thing, grad-level topology means stuff like algebraic/differential/geometric topology

[clever seal]

Need recommendation for Linear Algebra (early university)

[frosty basin]

what major are you in

[clever seal]

Math

[swift dome]

need some recommendations on statistics book that covers undergraduate stuffs.

[gray jungle]

@clever seal

[clever seal]

Read it! Thanks..

[fossil arch]

I'

Oops accidentally hit enter sorry

I'm a bit confused about the SS vs Gamelin thing. You say SS requires more background than Gamelin (namely epsilon-delta); that makes me think that Gamelin doesn't use much e-d stuff, but isn't that how analysis is done? Or do you mean that Gamelin teaches e-d whereas SS just assumes you already know it?

[sage python]

As I recall, Stein-Shakarchi kinda has a rough time making up its mind about what you should know going in

Like, probably calculus at the level of Spivak should do

[fossil arch]

What would you say is the most conversational of all those books, besides Ahlfors?

I really hate theorems in the middle of stuff

[sage python]

Gamelin I think introduces you to proofs basically

[fossil arch]

Especially when it's not bolded

But I love authors who exposit a lot and take care to be explicit and not very "clean" with their proofs (or when they are they explain how/why)

Gamelin sounds right for me since I also love looking at things geometrically LOL

[sage python]

My impression is that Ahlfors is definitely the worst offender in this regard. I think Gamelin's on the chit chatty end with less organizational nonsense

[fossil arch]

Coolio, thanks! Are there any other notable complex analysis books that have released since then, or do you have any updated opinions on book recommendations?

[broken meadow]

conway

[fierce hedge]

I have heard good things about complex made simple in this channel itself you can search it

[fossil arch]

I'm gonna skim Conway too just to see, I actually liked D&F :hehe:

[fossil arch]

Ok!

[broken meadow]

maybe i am Spupid or something

but i liked dummit and foote and did not find it to be super dry

[fossil arch]

Same!

[broken meadow]

thte examples were Gud

[upbeat vine]

Ahlfors doesn't exposit as much as he just rambles and concludes that he has proven something. On the other hand, his proofs are quite quite slick and flows naturally from one topic to another topic. The flow is so natural you would be surprised he has proven something and you would have to go back to actual pin where the proof started and where it ended.

[hazy elk]

Ahlfors excercises are quite different from excercises in other math texts too imo, they can be very annoying sometimes but many a question has a supremely elegant solution which just needed a change in perspective (which you will find satisfying if you solve it but the solution will be there on stack exchange too)

Its a good book for a first course only if you have a good instructor who will explain each paragraph of Ahlfors in detail imo

[upbeat vine]

Yeah his exercises are not only different but also arranged very bizarrely. An exercise about log of analytic function (which he hasn't even defined yet) could appear in the initial portion of the book (confusing the students) and sometimes an exercise to just prove zeroes or analyticity of a function could appear very late in the book. It is definitely more of an instructor manual than a book. But once you are familiar with the material, you will find yourself more going back to Ahlfors than anything else because his presentation is very easy to recall.

[fossil arch]

Oh I HATE that dude

Thanks for the wonderful comments

[radiant grove]

any reccomendations to get hands on practice for scientifc computing? i know michael T heath is a good book for gaining more knowledge on the subject

[sudden kindle]

Zakeri Complex Analysis

Its the best CA book

I am offering an anti-rec for Ahlfors

Its bad

[gentle arrow]

hmm today i think i am going to use narasimhan

[heady ember]

LMAO Yamin shilling their professor's book again

[steep spade]

Not really a book recommendation but do y'all have any video lectures or lecture notes for a second course on linear algebra (proof based) same levels as Axler, Friedberg and Kunze?

[sudden vale]

How different is Loring Tu's book on introduction to smooth manifolds from John M. Lee's book?

[sturdy shore]

https://www.youtube.com/playlist?list=PLflMyS1QOtxwiN5oOuyY4W_8fZlTTnRcF
this is my favorite, follows Axler but fixes some of its flaws throughout the lectures (at least introduces determinants a bit earlier), sadly it is missing all the lectures after real spectral thm, and some of the uploaded ones also cut off suddenly

[sturdy shore]

Tu is considerably shorter and delays the actual introduction to manifolds and covers some preliminary concepts first (Tu says to make sure students review/learn their topology in the meantime), friendlist book you can find that gets you into manifolds probably

Lee has a lot of extra stuff though

and expects a bit more mathematical maturity and more topological background out of the learner

[sudden vale]

I've been reading Lee recently and I found it comfortable till now (although I've only done the first chapter till now, which introduces manifolds, manifolds with boundaries, smooth structure on manifolds through smooth atlas, and a lot of examples for smooth structures on manifolds). I wish to know whether I should continue with it or switch to Loring Tu

My background - I'm an undergrad who just finished my second year. I've had a rigorous course in Topology and multivariable analysis. I also had two courses on linear algebra in my first year.

[sturdy shore]

if you are comfortable with Lee then you can just keep going lol, but also doesn't hurt to look at other books

[sudden vale]

I'll also look through Tu. Thanks

[remote sparrow]

axler has a playlist for his own book

he kinda repeats what's in the book already tho

in fairness it's his book

[steep spade]

Wow I had no idea about this, it’s actually very useful and well put together. Thank you so much!

[wise python]

need help with these topics if some can then please

1)Linear Differential Equations of first order and Higher degree

2)Series Solution of Differential Equations
or
Special Functions

3)Laplace Transforms

4. Fourier Series
   Or
   Partial Differential Equations

[tender river]

if you're looking for a diffyq book nagle saff snider

[frosty basin]

which book did you use for multivariable analysis/

[sudden vale]

Calculus volume 2 by Tom Apostol and later Calculus on Manifolds by Spivak

[frosty basin]

isn't spivak very terse?

or do you see it as doable

[sudden vale]

Not really. I mostly did Spivak just to revise after I finished my course

[frosty basin]

oh thank god. because it would've been a nightmare if spivak was just like multivariable's rudin

or even worse, like chapter 9~11 of rudin

[sudden vale]

Wait, were you asking for book recommendation? I thought you were asking how strong my background is.

If it was for book recommendation, I'd say start with Apostol instead.

[frosty basin]

i was actually asking for a bit of both

but yeah, spivak came across as to terse to me

[silent knoll]

hi guys , can anyone suggest how to get started with combinatorix

[frosty basin]

https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9814460001 this book

[silent knoll]

i don't have much experience ,

just basic permutation n combination
so will it be fine ?

[frosty basin]

i'd suggest you to print out some pages via libgen and try the problems out

of course they'd be hard and you will get a bunch of problems wrong at first

however, if you find yourself not being able to understand what's going on even after reading solutions, then i'd suggest you do Discrete Mathematics first

[silent knoll]

oh ok thx @frosty basin

[winged matrix]

could somebody suggest something for ODE's

[glacial crypt]

https://sites.math.washington.edu/~lee/Courses/544-2019/hw.html

have you seen this?

apologies for the ping

it's the list of problems he assigns for his course

[sudden vale]

It is for ITM (Introduction to Topological Manifolds). I'm reading Introduction to Smooth Manifolds

[glacial crypt]

my bad

[sudden vale]

But yeah, there should be such a list for ISM as well, I'll try to search it. Thanks for letting me know

[tender river]

<@&268886789983436800> spamming

[marble wedge]

Best course for learning advanced maths for students who passed class 10?

[finite gale]

Unclear what class 10 refers to

[coral prawn]

grade 10 ig

[frank cape]

Henlo, I'm looking for an exercise "heavy" calc book to complement the Tarasov one. I'm somewhat familiar with limits and derivatives, both in theory and the algebra needed (I think lol), however I'm not well versed in integrals. I'm looking to go through this calc tour de force in roughly 45 days give or take

[finite gale]

If you want computation, stewart; if you want theory, spivak, though I'm not familiar with what tarasov does

[frank cape]

Seems like a primer on theory, honestly just grabbed it because it was in the recs and the typesetting is nice.

Oh well I guess stewie will do, thanks

[jade fossil]

how would you rate this book out of ten
Understanding Pure Mathematics by A.J. SSadler and D/W/S Thorning

[civic surge]

Is there a solution's manual for the Carothers??

[marble wedge]

CBSE Class 10th

[marble wedge]

yes

[blissful pulsar]

Is here good source for learning Math? https://math.libretexts.org/Bookshelves

I had considered to begin Serge lang basic Mathematics but I'm not sure which one is more eligible.

[wanton yew]

Any text for an intro to number theory book?

I’ve never done proofs also so idk if I also need a book for that

[sudden vale]

Try David Burton. That's an amazing introduction to number theory which goes easy on beginners. Incase you find it too easy or are done with it, you can go to Niven Zuckerman Montgomery and then Ireland Rosen

[remote sparrow]

you should know some basic algebra prior to reading ireland and rosen

[gray gazelle]

Has anyone looked at Abelian Varieties by Mumford?

[alpine rover]

any pleasurable reads on history of mathematics?

[remote sparrow]

https://www.reddit.com/r/math/comments/14612ea/any_math_books_that_present_a_subject_historically/

[alpine rover]

not the history of a specific subject

but mathematics overall

[viscid sky]

hey guys, any hard calculus book (have already finished calc 1 and calc 2 but wanna revise) (am studying calc for physics so any book with physical applications would also be great

[tender river]

spivak or apostol

[coral prawn]

ehh

I don't think spivak or apostol has "physical applications"?

[tender river]

any hard calculus book
book with physical applications would be great

if you want applications of math to physics, can always use a physics book

[coral prawn]

but they're studying calc for physics. would intro analysis be helpful in this case?

also @viscid sky vector calc or just calc 1-2?

[viscid sky]

i will begin with vector calc. thats why i wanna revise like integral techniques and those stuff

[coral prawn]

ah, evaluating tricky integrals and integration techniques?

[viscid sky]

and thank you so much @tender river i have also heard that these books are hard i will definitely check them out (i would love to take analysis in the future)

[viscid sky]

yeah

[coral prawn]

ic then go with what pika said then

[viscid sky]

btw, for PDEs do i need topology and measure theory or in fact in general for an engineering +physics student , do i need to take topolgy and measure theory?

[tender river]

a pde course in engineering only requires calculus (1,2,3, diffyeqs). if you wanna learn the theory of pdes (the stuff a math major learns) then yes you need functional analysis (which itself requires topology and measure theory)

[viscid sky]

oh i see, thank youu so much !!!!!! really appreciate it ❤️

[glacial crypt]

https://sites.math.washington.edu/~lee/Courses/545-2020/hw.html
https://sites.math.washington.edu/~lee/Courses/546-2020/hw.html

[ocean mulch]

Marakov

I think the title is Selected problems in real analysis, or smth similar

Or Putnam and beyond, if you feel extra spicy

[tender river]

makarov, podkorytov

[plain barn]

any good books to like, get really good at algebra?

like, algebraic manipulation and stuff

I know all the basics and I'd really enjoy just knowing a lot more

really like manipulating letters

in an equation

[rancid hollow]

just do calculus

lotso algebraic manip there

[upbeat vine]

I have recently discovered a wonderful and very very thorough presentation of the connection between functional analysis and PDE.
It is called Nonlinear Functional Analysis and its Applications by Eberhard Zeidler.
It is a five-volume exposition: 1. Fixed Point theorems. 2. Linear/Nonlinear Monotone operators. 3. Variational Methods and optimisation. 4. Applications to physics (including Schrodinger, Navier-Stokes and General Relativity)
Why is it great:

• The books are very very thorough and treatment of material is very general as well (compared to Evans).
• Appendix is very well-developed and stuff used is actually first developed instead of hand-waved: For example, in Evans, he doesn't really develop the theory of Lp(0,T;X) spaces (Banachness, reflexivity, weak convergence, weak derivatives, or even justify the action of the dual), but all of this is very well-treated in his appendices (just to pick one example).
• Ideas are properly compared as well: Relations between variational problems and boundary value problems; why use Freidrich extension as opposed to energetic extension etc..
• Nice structuring: Introductory chapters start with a properly outlined goal, and then when important there is a full exposition on the history ("History of Hilbert spaces", "... of Dirichlet principle and Monotone operators"; and the ending of the volume culminates with a list of theorems/symbols/schematic overviews/important principles.
• Problems! The author provides solutions? As comprehensive the exposition seems, the author provide solutions to a lot of problems and references for further development of results in the problems.

All of the above is mostly about the second volume which is one I have been using for the past few days.
If anybody is interested, the latter three titles are on Springer. If you need a pdf with a clickable table of contents, dm me: I have prepared them for the first three books.

[shadow hedge]

Can anyone tell me what book should I start next after finishing the book of proofs which I am currently working on. For context I start my math bachelors in an European university in 2 months and the first classes are analysis and linear algebra. In high school I did precalculus and some calculus like derivatives critical points, inflection points and some techniques of integration.

[marsh yew]

Does CS stuff like data structures and algorithms count in maths ?

If so, I have a question, otherwise ill wait

[coral prawn]

if you're asking for a CS book recc feel free to ask here.

[tender river]

try analysis and linear algebra textbooks

nice to get a head start, tao or abbott for analysis and axler or idk hoffman-kunze for linear algebra

[gray jungle]

tao analysis

[shadow hedge]

Would my level of calculus be enough to directly start analysis? Or should I do more calculus?

[tender river]

your uni has analysis in the first semester, doesn't it?

[shadow hedge]

Yes

[tender river]

you'll be fine then, you get better at analysis by doing analysis not doing calculus

[finite gale]

Different unis approach analysis differently, but generally calculus is enough for intro analysis

[shadow hedge]

So just knowing basic high calculus is enough for intro to analysis?

[finite gale]

Yeah

[tender river]

having done book of proofs is more than enough early preparation

[gray jungle]

Intro analysis broadly speaking is (to a certain extent) calculus made formal (with proofs)

[finite gale]

Analysis is often taught as an intro to proofs class as well

[shadow hedge]

Alright thanks everyone

[marsh yew]

so Basically, is CLRS (Introduction to algorithms) the complete book for a CSE student ?

for Data Structures and Algorithms

[glacial crypt]

it's a pretty good reference book

at least when I used it the exercises seem not terrible

[marsh yew]

hmm

@glacial crypt someone told me to use this book

Data Structures using C

By Tenenbaum, Langsam and Augustein

They said it's a prerequisite to CLRS

[glacial crypt]

funny, I thought clrs is self contained. also, they don't specify any specific programming language for clrs

[marsh yew]

yeh

I mean in CLRS 4th edition, they state prerequisite is some data structures knowledge

[orchid mortar]

You probably can get by starting with CLRS even without other books

[marsh yew]

wait really ?

what if I have not much idea about data structures ?

I only know arrays and structs in C

[ocean mulch]

yes

although the treatment in CLRS is theory-heavy

[marsh yew]

I like mafs

[marsh yew]

What about dis

[ocean mulch]

I'd recommend wandering through online resources first, with titles in CLRS as a guide

Then come back to CLRS when you have the intuition for it

[ocean mulch]

it's great if you're a veteran in CS and want to understand the proofs

but otherwise, nah

[ocean mulch]

depends on what you do, CSE is a huuuuugggeeee field

If you do theoretical CS, it's a good start, but def not enough

[marsh yew]

I want to understand proofs

[marsh yew]

I want to get into that only

Theoretical CS is my aim

IMSc Chennai in India offers that course

[ocean mulch]

Well, have you played around with them before? Solving some coding problems, implementing them

[hasty turret]

What does CSE mean really

EECS?

[ocean mulch]

If not, stay away from CLRS, you'll get bored. When it comes to algorithms, you need a good intuition first

[fierce hedge]

I think it means Computer Science Engineering

[marsh yew]

I have done programming

I'm in CSE course in Uni

[hasty turret]

Well yeah but how is it different from "computer science"

[marsh yew]

I made a number theory calculator last sem

[ocean mulch]

Lol. Let's put it another way. Have you implemented binary tree?

[marsh yew]

I did calculate time complexity of shell sort and Euclidean algorithm

[hasty turret]

Do you like red black trees

[marsh yew]

Not yet, folks told me CLRS has data structures

I have other data structures in C book

[ocean mulch]

Ok, now we're talking

[hasty turret]

Ok you need Skiena

Not CLRS

[marsh yew]

Skiena ?

[ocean mulch]

I think Laaksonen would fit better

[fierce hedge]

At least in context of India there's two different ways you can study CS, one is BS/MS and then there's BTech/Mtech.
Usually CSE means Btech in CS like it's more applied idk

[hasty turret]

https://books.google.co.in/books/about/The_Algorithm_Design_Manual.html?id=S0QBEAAAQBAJ&source=kp_book_description&redir_esc=y
Basically a survey of what algorithms exist

[ocean mulch]

Grind this, https://cses.fi/book/book.pdf solve a couple of Div 2 B/C on Codeforces, then come back

[hasty turret]

Without going too deep into theory

[marsh yew]

Why are you guys advising me against CLRS ?

[ocean mulch]

Because it's too theoretical for you

[marsh yew]

For now

I see

[hasty turret]

Yeah

[ocean mulch]

This is equivalent of studying Algebra from Lang

[hasty turret]

I didn't know there was a cses book lmao

[marsh yew]

It requires that I know how to implement binary trees ?

[hasty turret]

I thought it was just a website

[ocean mulch]

My man, you have no idea how much I put into studying CS. Probably triple what I put into Maths

[hasty turret]

Also absolutely do the exercises in the cses site

[marsh yew]

Wait really ?

[hasty turret]

They are like the bread and butter of cp

[ocean mulch]

Not trying to flex, but yes

[hasty turret]

Well atleast the basic ones

[marsh yew]

Ohk

[hasty turret]

I did cses for interview prep

[ocean mulch]

It requires that you can make intuitive arguments why a data structure works, and what its complexity is. CLRS only fills in the details.

[marsh yew]

I see

[ocean mulch]

It's a Bible, you refer to it whenever you need something. No one really learns from it

[hasty turret]

Why do no books talk about loop invariants

Well like they are super important and handy

But I don't think there's a book that defines them

[ocean mulch]

Because you don't find it in algorithms book

You mean Hoare's logic?

[hasty turret]

I remember seeing "loop invariants" in CLRS

[ocean mulch]

It's a part of standard CS curriculum, but I never see any books mentioning it explicitly

[hasty turret]

He never elaborated on what it meant really

[stray veldt]

they arent

also CLRS does

[ocean mulch]

It's handy, but not important you just need to know what you're doing

[hasty turret]

Well I don't see CLRS proving correctness of quick sort using loop invariants

*Lemuto quick sort

[stray veldt]

what is lemuto

[ocean mulch]

I think every CS major should be taught Hoare's logic. The number of times I see ppl incorrectly implementing binary search is outrageous

[stray veldt]

there is a proof of quicksort using loop invariant in CLRS

[stray veldt]

when is it handy

[ocean mulch]

this

[hasty turret]

I think I have some intuitive understanding of Hoare logic

[ocean mulch]

you can rigorously prove what you'll have after the binary search

[hasty turret]

But it's 100% due to experience

[stray veldt]

who implements binary search in their daily life

[hasty turret]

Ask the Leetcode people

[stray veldt]

the algorithms you write in real life are way to complex to formally reason about correctnes, at least with standard tools

the intuition gained is kinda nice though

[hasty turret]

Yeah Hoare feels super useful for thinking about procedural code

Honestly can't you just learn algorithms with experience alone

[ocean mulch]

To be an engineer? Yes

To be a researcher? No

[hasty turret]

ngl, I can't even comprehend why someone would want to research algorithms

Well algorithms like what CLRS covers

Or TAOCP

[ocean mulch]

Lmfao, CLRS is for babies. It's like you have to cover analysis to do anything math-related

algorithm research at the highest level is madness

[hasty turret]

Well ok consider TAOCP

[ocean mulch]

same for TAOCP actually

If you ask any ICPC WF medalist, they will probably know the majority of the content in TAOCP

it's standard curriculum in olympiad training camps

[hasty turret]

Interesting

So what does algorithm research look like

[ocean mulch]

It depends on the topic

[hasty turret]

Fair enough

[ocean mulch]

you can look at improving the constant term hiding in big-O notation wrt some model of computations

Or improving the approximation constant, e.g. from epsilon^2 to epsilon

[hasty turret]

For me personally, TAOCP and CLRS seem like negative inspirations

[ocean mulch]

Who tf would even study from TAOCP and CLRS?

I only open those books when there's something I know to be true, but don't recall the details

[hasty turret]

So how do you learn algorithms exactly

[ocean mulch]

solving problems, mostly. Implement them, and argue rigorously about them yourself in context of problems

[hasty turret]

I mean enough to do research

[ocean mulch]

The same way you learn to do math research

You keep learning, the more you learn, the fewer ppl on the world know and understand what you do. Until one day you learn something only you know.

[ocean mulch]

as above, solving problems

I'm blessed to have gone through olympiad training tho. I'm not sure about others

[hasty turret]

I suppose my view of research being "reading stuff and not a lot of problem solving" is wrong

[ocean mulch]

Apparently you haven't done research yet 😄

yes, you read a hell lot, but at the end of the day, you do whatever it takes to solve the problem you care about

[hasty turret]

Well yes, my experience with "research" is background reading

[ocean mulch]

It's normal at UG level, dw

I got lucky and did something new, but that's not common

[hasty turret]

Competitive programming?

[ocean mulch]

No, I found some new algorithms

[hasty turret]

Damn

[ocean mulch]

Mind you, I went through olympiad training. Which means by the end of HS, I already knew a lot

[hasty turret]

Fair enough

[marsh yew]

What is TAOCP

[tender river]

The art of computer programming by donald knuth

(^ is not a recommendation btw)

[ocean mulch]

The Holy Bible, King James version

[marsh yew]

Looks like I don't want to do Theoretical Computer Science anymore

I'll happily stick with programming

[ocean mulch]

Everybody gangsta till they see a red-black tree

[marsh yew]

I'm interested in improving the shitty software written today

[marsh yew]

If I study it, I'll probably understand it

[ocean mulch]

Sadly you will still need to grind algorithms, because that's what HR puts, and because that's HR

[marsh yew]

HR ?

[ocean mulch]

Human Resource

[marsh yew]

I like DSA anyway

I'll do it because software optimisation is a thing

[ocean mulch]

The ultimate enemy of CS students

[marsh yew]

It's just that, I haven't found any book that does Data Structures that's not boring

[ocean mulch]

Also, you probably need to know a tiny bit of algorithms. I've seen ppl using bubble sort in software. Those ppl need a good 6-month bootcamp

[marsh yew]

I have one right now

It's called

"Data Structures in C"

By Tenenbaum, Langsam and Augustein

[ocean mulch]

Eww, C

[marsh yew]

I love C

[ocean mulch]

Yeah, you think you love C

[marsh yew]

What else would you implement data structures in ?

[ocean mulch]

Virtually any languages you use 🤷 I do CP mainly in C++

But tbh, you never have to implement a DS in real life

[marsh yew]

You do Competitive Programming ?

You also do Theoretical Computer Science ?

[ocean mulch]

And I do Math and Biology

🤷 I had a lot of free time

[marsh yew]

Great

I didn't have a lot of free time

[ocean mulch]

as I said, I think this will suit you better

[marsh yew]

Why is that ?

I am not into Competitive Programming

I did hear about ICPC though

Some folks from my Uni went, never made it past zonal level though

[hasty turret]

Maybe I should do codeforces

[marsh yew]

I started programming like 10 months ago, I don't think I have a chance against guys who have been programming since they were 8

[ocean mulch]

It's not for CP actually, it's a primer on basic algorithms. Even for folks preping for interviews, it will help a lot

[hasty turret]

Will give me something to do rather than just depress over lack of purpose in life

[marsh yew]

Ohk

Well I'll get to it soon

[marsh yew]

I did read some lines, competitive programming is a lot about doing stuff the fastest ?

[hasty turret]

Well that's unfortunately a part of it, yes

[marsh yew]

Like even using pre-built libraries and all

I dislike that

[hasty turret]

But ideally it's about finding the best "good enough" algorithms within a short period of time

[marsh yew]

I'd rather do things on my own

I dislike the OOP part of C++, Procedural C is good enough for me

[marsh yew]

Do you also have to combine existing algorithms ?

[ocean mulch]

Yes

[hasty turret]

How else do you think algorithms work

[ocean mulch]

No

[marsh yew]

Ohk

[ocean mulch]

Live longer, you'll feel grateful to know C++

[marsh yew]

Lol

[ocean mulch]

C is just, life on hard mode

[marsh yew]

Nah, I like C

C++ is ew

[hasty turret]

I like C

[marsh yew]

From what I've used both so far

C is da wae imo

[hasty turret]

As a stick to compare languages against

[ocean mulch]

Actually nowadays Rust is da wae

[marsh yew]

Hmm

[hasty turret]

"C++ is supposed to be C with classes but they added in templates and a lot of complexity"

"Java is supposed to be C with classes but everything is on the heap and memory management is free"

[ocean mulch]

C++ is good in the sense that it's still low-level so you have to understand hardware, but still have OOP and shit so you can transfer to higher level stuff like Javascript or Python

Knowing C++ is essentially speaking French and German, you have an edge to learn (almost) any European languages

[marsh yew]

Hmm

[ocean mulch]

If you're fluent in C++, you can learn (almost) any new language within a week

[marsh yew]

Haskell Disagree

[ocean mulch]

C is just too low level for that. They didn't even have for loops until C99

[ocean mulch]

Who tf codes in Haskell? Beside quant firms?

[tender river]

book-recommendations

[ocean mulch]

And also, it's a separate language style already

[hasty turret]

For loops existed in 1973

I just looked at K&R 2nd edition

[ocean mulch]

I remember some long time ago, there were options to use C and C99. In one of them I had to use while instead of for because the compiler just didn't want to compile

[hasty turret]

*1988

[ocean mulch]

Those were the dark days

[hasty turret]

Ok it's also a thing in the first edition

[mental parcel]

anyone have ron larson calculus 12e in pdf form

[remote sparrow]

that was not related to your comment, but i previously made some suggestions here #book-recommendations message and here #book-recommendations message

[remote sparrow]

spivak has a chapter dedicated to planetary motion. apostol considers a few applications for first order ODEs and the chain rule, namely related rates and implicit differentiation.

[dapper zenith]

Please recommend me something for group theory, my way of study is to hide proofs and then to try my best to proove it, currently I am studying from herstien, topics in algebra but finding it somewhat difficult from the automorphism section.

[sage python]

So, Schroder's shtick is more or less, start with analysis on R, use Riemann integration (in particular, characterizing Riemann integrable functions) as a segue into Lebesgue measure

Then do measure theory and calculus on R^n

The main thing he misses that I recall in measure theory is the differentation content

So e.g. you'd want to read chapter 3 of Folland

[gray gazelle]

Is there any good book for symbolic logic

[heady ember]

If you have some level of mathematical maturity, something like Jech's ug set theory book might be more suitable

to Enderton's Elements of Set Theory

[digital jacinth]

Can anyone recommend a website to take a complete course in python?

[loud cradle]

"dive into python" is pretty good

[orchid mortar]

I recommend asking Pydiscord, they are beginner friendly, have resources and are helpful in general

[coral prawn]

Any thoughts on Serge Lang's Linalg?

[fierce hedge]

Try it and let us know

[coral prawn]

I am, I'm at ch 1 and boy it's interesting but at the same time I wanna make sure it's more towards the abstract and not the computational side

[finite gale]

Check pinned messages

[coral prawn]

ic

[tender river]

none

[heady ember]

I again recommend you to stick to one book.

[coral prawn]

[lapis heart]

I will say that linear alg can have fairly computational heavy exercises and that's not necessarily a bad thing imo. I found it easier to understand concrete linear algebra first before moving on.
Even now, all examples I come up with to understand anything new are usually 'concrete' R2 or R3.

I dont think you should let that put you off reading a book.

[gray jungle]

highly disagree , using multiple books always gives more insight on any topic (with a main book to follow ofcourse)

[heady ember]

The context is that they have been jumping from book to book without making much progress in any.

[lapis heart]

The other thing I'll say (my opinion from my experience), there's no point learning in a more 'abstract' approach if at the end you're unable to do computations. To me, the abstract approach is supposed to give you a deeper understanding of the workings behind the various methods as well as some more general results.

If you take the abstract approach and are unable to do computations after, then I think it has failed you. It's not that there are 'no computations' in a more abstract approach, it's more that they have been omitted as exercises you're "expected" to be able to handle once you have understood the material.

So I don't feel like anyone learning linear algebra can "get away" from computations - they should be done as exercises at one point or another.

[coral prawn]

true that

[finite gale]

Honestly the only main reason to repeatedly switch books is to find one with good exercises when you're reviewing

Else there shouldn't be a need to keep switching books

[fierce hedge]

A decent algorithmic procedure is to have a more usual (popular) textbook and an easier one. I prefer anything that I have a physical copy of.
Start with the textbook and see how good it is. If you find you hate something in the textbook then switch it for something else.
While hate is a strong word you should only switch books if you just can't stand the book or say it's too dense for you.

[slim bramble]

true. found myself doing that too, and stopped when I realized that if I am serious about math then this won't be the first book i read about x topic, and will eventually gain that knowledge one way or another, so just get over one good reputed book and then move on.

[normal reef]

I'm looking for an introduction to infinite dimensional vector spaces, Hilber and banach spaces. any suggestions?

Possibly provide something advanced and something for begginers

[upbeat vine]

I can give you an intro for Hilbert and Banach and the resulting theory about them.
For the beginner: Eberhard Zeidler Applied Functional Analysis. Volume 108. Guided and solved exercises along with tons of motivating examples to show application.
For the advanced: Haim Brezis' book. Very well-written and clear, guided and solved exercises.

[crimson leaf]

I've been liking Linear Algebra As an Introduction to Abstract Mathematics by Schilling, Lankham, and Nactergaele it's been good for review

[turbid mural]

jech has an ug set theory book ?

[chrome yacht]

sure does

[heady ember]

Yes by Jech and Herbreck (cant rmb how to spell his name)

[turbid mural]

damn never knew that

[turbid mural]

i used analysis now by pedersen

[mental parcel]

https://gyazo.com/fa30bb9841834bd93a592049db9014e0 man how does this even happen

i never even knew that existed lol

[gentle arrow]

i havent reached part 2 yet so no opinion

[fierce hedge]

If Schroder also had decent sections motivating why we care for stuff, it would have been the greatest intro analysis book

[valid monolith]

Have a recommendation for that? Why we care?

[fierce hedge]

Both Tao and Abbott provide decent motivation. You can try both and see which one works better for you. For comparison Tao is a bit more chatty and leaves some logic as an exercise to the reader (these are very quick checks). Abbott has better exercises than Tao.

Also Tao constructs N then Z then Q and finally R in the first 5 chapters. It is interesting if you've got time to read

[frosty basin]

serge lang's undergraduate analysis is a good book too

kinda surprised it is not as popular as many other books

[inland elm]

anyone know of any good books on module theory

[dapper root]

There really isn’t a book for module theory

If you need an intro, books on algebra suffice, D&F, Aluffi, etc

If you want to learn more it basically splits into two or three camps

Books on homological algebra will do stuff

Books on commutative algebra will do stuff (over commutative rings)

And books on rep theory will do stuff

[inland elm]

i’m looking to do homological algebra, i got weibel but it skips the theory and assumes you know modules already

[dapper root]

It sounds like you just need an intro

Pickup whatever book you learned algebra from and it should have a section on modules

D&F has some sections dedicated to it as does Aluffi I think

[inland elm]

i get the big ideas too, basically a vector space over a comm ring with identity

but i want a stronger foundation

[dapper root]

I mean

I don’t know what more there is to say honestly

[inland elm]

i used fraleigh and i think they skipped modules altogether

[dapper root]

Okay then

Pickup a different book

[inland elm]

nono youre god

good*

[dapper root]

And it’ll probably be there

[inland elm]

yeah thanks for the info

[dapper root]

The first statement is also true

But I see

[finite gale]

D&f has a section or two on modules

Lang chapter 3 is on modules

I don't remember specifically what they cover

[inland elm]

i also saw rotman has a chapter on modules too

was mainly curious to see what people found as a nice self-contained text wrt module theory

thanks all

[tawny copper]

are there texts on continuous inequalities, focused on problem solving if possible?

[frosty basin]

does gallian have modules too?

[tawny copper]

so like, where sigma symbols are replaced by integral symbols and n tuples of positive numbers by continuous functions defined on compact intervals lol

[fierce hedge]

nope it doesn't

[rocky turret]

Which book to do for logarithms (jee)

[ocean mulch]

Hardy-Littlewood-Polya

[clever orchid]

specific book for logarithms ? I don't know if anything like that even exists

[indigo mesa]

Which rotman?

Because the Hom alg one does Hom alg specific stuff for modules and assumed the basic theory

[finite gale]

I'm assuming the basic algebra one

[indigo mesa]

Right that exists

[fierce hedge]

A first course in Abstract Algebra???

I don't think that has modules

[finite gale]

No the other one

[fierce hedge]

He has another book on abstract algebra

[mystic orbit]

do aluffi

it actually has a pretty nice small section on homological algebruh too

you can start from chapter 3 section 5

[fierce hedge]

DarQ shilling Aluffi to everyone

[mystic orbit]

it's fun

¯_(ツ)_/¯

[mystic orbit]

I've never tried lang

[finite gale]

Lang is nice

I think

[frosty basin]

any prerequisites for pde?

[sturdy shore]

what kind of pde

for classical pde, vector calc/analysis on R^n

modern pde, solid functional analysis background needed

[gray gazelle]

Any suggestions for multivar textbooks?

I want to brush up on things like green and stokes before I start college.

[plush talon]

math books of the pearson publishing pretty good

[sudden vale]

Spivak?

[gray gazelle]

Alrighty, I’ll see if I can find a pdf!

Ik the course that I’ll be taking in the fall is highly proofs based, so I want to be decently familiar with what I’m going to encounter.

[plush talon]

I can send you any math books in the pdf format if you can't obtain them

[gray gazelle]

Found it.

Good grief, this seems rigorous.

I have a hard copy of Rudin on my bookshelf lol.

I found it at a local bookstore for really cheap.

Used ofc.

I’d send a pic but I don’t have image perms.

[gray gazelle]

how much was it?

[gray gazelle]

I bought it a few years back, but I think it was about thirty bucks.

I only read like half of it.

Got to the bit on set topology and my brain blanked.

Duly noted!

[sudden vale]

If you want something lighter, maybe Apostol?

[gray gazelle]

In any case, I won’t have to take an analysis course for a few years, so I’d say it’s a bit more important for me to focus on getting really good at multi.

[gray gazelle]

What does it include?

[gray gazelle]

Physics major?

[gray gazelle]

Prospective physics major. I’m a prefosh.

In that case, you could probably get away with not doing any analysis at all

Ah I see

ehh you do need analysis and multivariable analysis for diff topo

I’m going into theoretical physics, so it’s very important for me to get good at math.

I was reading a particle physics textbook earlier this summer, and I had to self-study a shitload of group theory to understand the way baryon supermultiplets work,

And spontaneous symmetry breaking type shit.

you definitely do for differential topology

I haven't taken differential geometry so I can't comment, but as for diff topo, I must disagree

[sudden vale]

You'd need considerable Topology also for diff geo

[gray gazelle]

I only have a rudimentary understanding of topology.

I definitely don’t have the prerequisite knowledge to thoroughly understand diff-top.

[sudden vale]

Go through Munky. It's like staple for topo

[gray gazelle]

It’s not too relevant to what I’m reading atm,

These days I’ve been reading Griffith’s for particle physics.

[gray gazelle]

If you ever do want to study it, I have a couple recommendations book-wise - those are the literatures my lectures were based upon

[gray gazelle]

What’re some applications it may have to physics?

[sudden vale]

You're a Physics major, right? Have you read Zangwill Electrodynamics?

[gray gazelle]

I wish I knew, but I have a very rudimentary understanding of physics, only about high school level since I'm still taking the IB diploma

[gray gazelle]

No, for most classical stuff, I just learned from my teacher’s lecture.

I only self studied undergrad material.

He was talking about diff-top.

[sudden vale]

I hated that book to the core. Too dense for an undergrad course in Electrodynamics in a damn Math degree

[gray gazelle]

Differential geometry and tensor calc are def on my list of things to brush up on. I watched a lecture a few months ago on deriving the field equations from scratch, and it took me nearly all day to even get used to the tensor notation I was looking at.

I have a superficial understanding of most topics I’ll encounter in undergrad, but I want to develop more depth of knowledge.

Last summer, for shits and giggles, I checked out the textbook Einstein himself wrote on special and general relativity.

I read Axler for Lin alg.

The special relativity section just involved standard Lorentz transformation type stuff, but tbh I couldn’t follow the notation in the GR section.

A lot of it was archaic.

Lovely! What do you plan on specializing in?

Ah. Lately I’ve been studying a lot of particle phys because I’m aiming for a research position at my school’s synchrotron next year.

[plush talon]

what nice to see people who dedicate their lives to mathematics and physics human civilization is devoloping by contributes of such peoples

[crimson leaf]

Hmmm new maybe but used like 60-70

[chrome yacht]

if you find spivak too terse then folland has an advanced calculus book too

[frosty basin]

i meant the one discussed from books like evans

[frosty basin]

i only need to do part 1. do i also need multidimensional analysis? or would single variable analysis(chapter 1~8of rudin i.e.) be enough?

[dense mantle]

I think if you have a solid vector calculus class

and can familiarize yourself with a bit of the geometry that you would learn (namely, what a manifold is)

you can get through a lot and fill in the small gaps along the way for most well-written books at the "first year of graduate" level

[sturdy shore]

first third of evans is classical, then it becomes modern, so adjust accordingly

[sturdy shore]

look at one of its appendices for "calculus" I think

you need to be able to understand that sort of stuff for the classical parts

[remote sparrow]

hubbard or shifrin

[frosty basin]

whats your opinion on appendix section of hubbard?

[jagged oracle]

are u from a2c

[gray gazelle]

I left that server a while back, but yeah.

[coral prawn]

a2c?

[foggy relic]

undergrad apps community

[foggy relic]

Pauls notes

for "proofs based" shifrin

[gray gazelle]

Thanks!

I do like how concise Paul’s notes is.

I used that to self study calc ii.

[foggy relic]

you can learn all of calc 3 in a couple hours with it

[heady ember]

Couple hours is probably a bit of an exaggeration

[weak nest]

couple dozens of hours you mean

[jade fossil]

.

[unique folio]

This is probs a little out of context for maths, but anyone have some good book recommendations for economics?

[rotund flint]

You can probably google

Are you looking into economics in general or econometrics

[clear plank]

Hello all! -- Not really looking for book recommendations but rather study resources for the ALEKS MATH placement test. Does anyone have any resources or general knowledge about the exams>

[weak nest]

ALEKS placement content is up to precalculus and it scales based on how you answer previous questions. I second the Kahn academy approach because their website has activities that are similar to the exam where you have to use some interactive software to draw a graph

[frosty basin]

would hubbard's appendix section and the whole textbook itself good alternative to rudin 9~10 or spivak?

i don't know if i didn't put enough effor or not but i can't stand those 2

[remote sparrow]

it should be

[frosty basin]

oh okay thanks

[gilded urchin]

does anyone have a good reference to learn differential geometry

[heady ember]

I have heard people rec loring tu and Lee's books here quite a bit

[frosty basin]

which type?

undergrad or grad one?

i know pressley is extremely good for undergrads

[glossy mango]

Hello everyone, is the art of problem solving book worth it ? to improve at problem solving or simply while taking undergrad classes eventually I'll get better and no need to bother with it

[dense mantle]

no

not for that purpose

you would be better off looking at problem books for the subject you're trying to study

AoPS is targeted at math below your level and for a completely different purpose/ endgame

obviously, the more time you spend with math in general (no matter what it is), the better you're going to get

but it would be much more time-efficient to go get a Springer problem book in analysis or whatever you need

[glossy mango]

yes! I am reading proofs by James cumming, and has his real analysis book, after proofs will be reading his real book, currently taking next semester calc 3

[ocean mulch]

Milnor 😄

But it's modern stuff. If you refer to classical stuff like curvatures and fundamental forms, then Idk

[gray gazelle]

I want to learn mathematics any books for beginners? (I am in highschool btw)

[frosty basin]

what is your current level of mathematics

[gray gazelle]

if you mean if I am good at it or not? the answer is I suck at mathematics.

[frosty basin]

do you know how to solve quadratic equations?

[gray gazelle]

yeah

[frosty basin]

and system of linear equations?

also do you know what a function is?

[gray gazelle]

I know pair of linear equations

I don't know about functions

[frosty basin]

which country you live in? mind telling me?

if you are from usa then i can help you better

[gray gazelle]

I am from India my friend

[frosty basin]

i don't know your countries curriculum

so since which grade have you struggled?

or did you constantly struggle in math?

[gray gazelle]

mostly grade 9th

[frosty basin]

mind telling me the state?

so i can go take a look at curriculum

[gray gazelle]

uttar pradesh it is.

[flat jackal]

U know the Thomas calculus book

[gray gazelle]

I am in CBSE board not state board 🙂

[flat jackal]

Is there an edition with linear algebra to since it’s missing it

Like the 14th edition I’m on about

[frosty basin]

oh then i can't give you advice on curriculum

sorry my friend

[gray gazelle]

Its ok.

but is there a book I can solve to learn mathematics?

I am also poor in some basic concepts

what is that

oh

I am at library genesis is there a particular book I need to search for beginners ?

[frosty basin]

https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Science/dp/1119293634

the book only assumes that you know how to add and subtract

[gray gazelle]

yeah i mean I am in 10th grade that I ofc do. I am just shaky at some particular concepts

[frosty basin]

the book is only going to take you like 3 days, i advice you to just skim throught the book even if you know the concepts

just to find out if you have holes

[gray gazelle]

Ok thanks brother, I will tell you after I am done with this book I will not try to rush this book.

[frosty basin]

for the first book i advise you to go through it quickly

just find out if you have some holes

and for the second book i advise you to take time and solve 1/3-1/5 of the problems

solving every single problem is a waste of time

[gray gazelle]

I can't open the second book you gave me

can you tell me the name?

[finite gale]

uhh

[gray gazelle]

ok thanks

[finite gale]

im pretty sure there's some #rules breaking here

[frosty basin]

okay sorry

[gray gazelle]

can I dm you if I need help?

[frosty basin]

sure

[frosty basin]

has anybody seen bak&newman complex analysis book?

is the book more difficult than needham or brown/churchill?

[gray gazelle]

does anyone know good book for algebra?

[formal bronze]

Try 'Abstract Algebra' by Dummit and Foote

[gray gazelle]

i am not extremely advanced in algebra. is this an advanced book? meaning do I need a lot of information on algebra for the book or is it a full introduction to the topics?

[formal bronze]

Ok now I see that you have the Pre-university role

Forget what I said then. I don't have any recommendations for high school 'algebra'

Apologies

[gray gazelle]

ok

its fine

[frosty basin]

algebra by blitzer

[minor nebula]

someone knows a good book for stadistics, maybe something that has good exercises to prectica?

[sharp juniper]

Might not be directly mathematics but does anyone have a recommendations for a second course quantum computing textbook?

We had read from Rieffel and Polak in my undergrad course

[remote sparrow]

it is

but it's still a non-honors book

pretty sure almost all problems have answers in the back

[clear plank]

@gray gazelle @weak nest thanks a ton!

[flat jackal]

What’s the best book for advanced calculus

[flat jackal]

Like a book that covers all of calculus 1-3 with a lot of problems and isn’t hard to read (bad format?)

Also I can’t find linear algebra in any books from the US which is strange?

Wait nvm cause I’m looking at calculus books yeah💀

I’ve got the Thomas calculus one 14th edition to

doesn’t have integral transforms in tho

Looks like a good book apart from that though

[crimson leaf]

Does anyone have a course outline for Knapp Basic Algebra? I'm more so looking for problems related to each section since they're all kinda lumped together at the end

[junior isle]

Thomas calculus fits your description but its not "Advanced calculus"

Advanced calculus would be proof based imo

Although It is a good book

[crimson leaf]

Not that I know of I'm just picking up cause it has good multilinear coverage

Also modules and fields have good coverage it seems

[frosty basin]

so its not in level of stein&shakarchi or freitag&busam?

[fierce hedge]

Yes, although we switched books for abstract algebra part to Rotman. Knapp has pretty unusual and sometimes horrible notation. He also does few proofs in a bit convoluted ways. I'd say H&K and LADR have better exposure for Linear Algebra not sure about the abstract algebra part.

In general Knapp is just not a first time book, it feels more of a revision of things you already know.

[crimson leaf]

Yeah that's how I feel about the groups section so far. He's gone through some things very quickly, however, I wanted to switch from Rotman cause I wanted to address some stuff he doesn't cover. Also his thing about sign for permutations to me is a bit much.

[fierce hedge]

How's DnF coverage of these topics, I think rings and fields are strong part of DnF. (Not my opinion)

[crimson leaf]

Not sure really, it's my algebra professor's favorite book so we used it for groups last semester and we'll doing rings and fields this semester. I just don't like the way the introduced things in the groups so I stopped using it and started using Rotman near the end of the semester

[fierce hedge]

Lmfao looks like there's only way to find out, one that I am sacred of. To actually read it myself

[fierce hedge]

Just so we're on the same page we're talking about Advanced Modern Algebra 1st edition right? Then I am curious as to what topics does he leave.

[crimson leaf]

Knapp

As for Rotman I was reading first course in abstract algebra

[fierce hedge]

I wanted to switch from Rotman cause I wanted to address some stuff he doesn't cover.
I am talking about this

[fierce hedge]

Ohh, I see

Advanced Modern Algebra 1st edition

Opa why would you updoot your comment lmfaoo

[gray gazelle]

LMAO

[fierce hedge]

We will soon find out

[crimson leaf]

I did advanced modern algebra until I saw he had first course I think advanced modern is similar to Knapp but in Rotman's style of course

[fierce hedge]

It's not just me, few people are hs students so it is genuinely tough for them

Otherwise Knapp wasn't that bad

[crimson leaf]

The easiest books I would say are like Fraleigh and Gallian but if you like Rotman's style his undergrad book is good, same structure

[fierce hedge]

'DF is pretty boring/dry' that's the most common sentiment I've heard towards it. Plus you're free to use whatever book you like, the psets are not from a particular book.

[frosty basin]

DF is easy?

like its not the hardest book out there but gallian/fraleigh is more approachable

i'm currently studying gallian+D&F at the same time

D&F has better explanations imo

like ross analysis

i get that rudin is too terse and difficult to be used for first time but ross analysis is just too gentle and easy

[sage python]

A professor of mine, in reference to AG books, said this about Vakil

"People like this book because it's gentle. Like if the difficulty is 1000, when you divide that by the infinite number of pages the difficulty per page is zero. So it's a pleasant read. Of course, you can start reading it on the day you're born and you'll still be reading it on your death bed."

This is even more true for D&F

[heady ember]

[gusty smelt]

lol

[sage python]

It's even funnier to imagine this in his Australian accent

[tawdry copper]

Anyone have any ideas about an introductory information theory book?

[solemn rover]

thomas and cover is good

[flat jackal]

I don’t take physics but I imagine a lot of maths crosses over between physics, maths and engineering anyways. I’ve only looked at laplace transforms for solving differential equations and particular integrals but not Fourier series or anything else related if there is

[bitter token]

Hello! Do you guys know any olympiad books that actually teach the content? All the ones I cam accross (that I found on AoPS) mostly have problems

[ocean mulch]

Lol, but Fourier transform is a particular of Laplace transform. How did you learn the latter but not the former?

[ocean mulch]

Engel is pretty good at combinatorics, I learned a lot from it

There's also a very good book on induction, can't recall the name atm

[bitter token]

Alright, I will look up this one, thanks!

Do you know any algebra books?

[ocean mulch]

Ahh, Titu's Mathematical Induction

[ocean mulch]

What kind of algebra? The high school algebra?

Or modern algebra?

[bitter token]

Olympiad Algebra

[ocean mulch]

I never got the difference between it and number theory tbh 😄

[grizzled tulip]

Do we have a Desmos role or something

[bitter token]

I think the only things that are covered in olympiads for algebra are inequalities, polynomials and functional equations

[ocean mulch]

nope, I got nothing in mind for that atm

[bitter token]

Alright thank you!

[ocean mulch]

well... functional equation is partly covered in Titu's Induction. I feel like it contains all the tricks, but I'm certainly wrong on this

inequalities... I don't have any English texts for that one

[bitter token]

Lol

That’s fine I will start with those

[hasty turret]

Does anyone care about functional equations outside Olympiads?

[grizzled tulip]

Im actually getting somewhere with Physics

in Desmos

[flat jackal]

I learnt it out of interest. But I’m not gonna re visit it for a few months now cause I have to do vector calculus first

[gray gazelle]

It's usually taught earlier in an ODE course, from my experience.

[gray gazelle]

Hi

Bye

[jade fossil]

how would you rate this book out of ten. I'm looking for a good book.
Understanding Pure Mathematics by A.J. SSadler and D/W/S Thorning

[gray jungle]

Curious what lead you to post this in this specific channel

[grizzled tulip]

?

[heady ember]

Book recommendations

[fierce hedge]

#discussion

[grizzled tulip]

Oh. Sorry

I didn't realise

Agh

Didn't see the channel name, I was like, okay this is discussion. Sorry

[gentle seal]

Any good books on octonions?

[hexed basin]

Hi , can someone suggest me good resources from where i can study directed angles with problems from the easiest to the hardest pls ?

[tawny copper]

differential equations are functional equations 🤓

zeta functions are defined via functional equations 🤓

[chrome yacht]

rosen

[gray gazelle]

Hello Mathematicians

[cloud vigil]

Hi

Is Cengage Worth buying

Any other book recommendations

[acoustic inlet]

Hi Everyone,
I am currently studying Engineering. I want a book for linear algebra which along with formulas, can help understand concepts through visualizing the topics and how it is useful.

For example, I am currently using a book where the introduction of the determinants chapter says that "it is used to solve system of equations using cramers' rule"

but It should describe what a determinant actually is like as we know "Determinants are the factor by which areas change when a linear transformation is applied"

So, Do anyone have a book suggestion for such a use case?

[hasty turret]

read Hoffman Kunze's determinants chapter

[acoustic inlet]

Hi, really appreciate your reply, is the whole book based on linear algebra? Actually I am pursuing Machine Learning and as its precursor I need to learn Linear Algebra, Probability and Statistics and Calculus.

[hasty turret]

I do not recommend the entirety of Hoffman Kunze if that's your goal

[blazing canopy]

For visualization I don't think any of the standard books are really that spectacular, definitely disagree about Hoffman Kunze. I would look at video lectures

[empty junco]

you could look at

linear algebra via exterior products

[acoustic inlet]

Hi, thanks for replying, I have gone through the 3Blue1Brown, Essence of Linear Algebra series, and that series is the reason why I want to dive deeper

[empty junco]

by winitzki

[blazing canopy]

Unfortunately I don't have any recommendations on hand, I just know that while some books do have some visualization, videos that are specifically designed for the visual presentation are far superior in this regard. 3Blue1Brown is certainly the most well known but yeah it's not as deep

[acoustic inlet]

I was looking into the hoffman kunze book and the linear transformation part does not seems to describeing it visually

[empty junco]

my recommendation is very visual

[acoustic inlet]

Hi thanks for replying, yeah I am searching your recommended book online

[acoustic inlet]

This is what I am looking for

[empty junco]

though there's probably a lot more content in there than you'll need

[blazing canopy]

I haven't read the book but if it's really about exterior algebras then that might be a little bit different from the desired topic

[acoustic inlet]

No worries man, your suggestions is all what I needed

[acoustic inlet]

Yeah Bro, your book is also good, infact its a compact handbook, I really thanks you for your suggestion

[blazing canopy]

Haha I don't think I made any recommendation

[empty junco]

I'd recommend looking at

the start of chapter 2

as well as 3.2 and 3.3

[acoustic inlet]

ohh sorry I mistook you for the guy who suggested the kunze book, my bad

[acoustic inlet]

Yeah I am reading a bit from ch 2 start, the topic is explained in really simple words

[acoustic inlet]

I have gone throught the essence of linear algebra and its amazing

[blazing canopy]

I know that there are some visual linear algebra courses that are intimately paired with programming, usually in Python or Matlab

It might be useful to look at the course materials at some university and see what they do

I've mentioned this before, but I'm a pretty strong opponent of the idea of finding the "right" book that does everything the "right way"

It's easier to draw from multiple sources, which is far easier now that so much is available on the Internet

[orchid mortar]

There is a way to do this. Write your own notes.

[blazing canopy]

Actually I am 😁 but such endeavors can go beyond what a student might be able to afford

[acoustic inlet]

That's too a good idea

[chrome yacht]

https://github.com/mitmath/1806 for a course on linear algebra that involves code and visualization if that's what you're looking for (change branches from master for past courses)

[acoustic inlet]

Awesome 😃 thanks a lot

[orchid mortar]

Yo there are psets, nice

[neon niche]

can anyone recommend e book for aptitude ques. (majorly maths)

[fading pine]

Do you guys know what are the differences between Tao’s analysis and Stein & shakarchi’s analysis books? In particular, what are each of their prerequisites in self-studying them?

[dense mantle]

Just poke through both at the same time. Off the top of my head, the ToC in both are very similar

Better to get two perspectives and jump around than try to “memorize” one book

[fading pine]

I mean I don’t have the resources to buy two books that serve similar purpose

[dense mantle]

Then don’t buy them

You dont even need to pirate Tao’s book anyways?

[fading pine]

Oh they’re online?

I mean like at least I can poke around?

Bc I really do want to keep one physically

[dense mantle]

Yes

Tao should be free online

S&S would probably need to be… found by alternative means

[fading pine]

Ahhhhuh lol

[crimson leaf]

Stein & Shakarchi assumes you have read analysis up to Riemann integration before starting so you would read something like tao first

This goes for the first three books the 4th assumes you know measure theory

Unless you're referring to a different analysis book by Tao

[dense mantle]

There should be several

One is a first course

Then there should also be one very close to S&S/ Folland

[crimson leaf]

Yeah he has the two book set which is a first course and titled analysis 1 and 2 then he has epsilon in the room and he also has an introduction to measure theory

But I want to say episilon in the room assumes measure iirc

[fading pine]

Just the analysis i and ii

[fading pine]

Wdym, like read Tao first than Stein & Shakarchi?

[chrome yacht]

tao is an intro analysis book with minimal prerequisites (not even calculus), can't say the same for any of stein shakarchi's books in the series

[fading pine]

Ok so would recommend reading both volume of Tao before going to stein shakarchi?

[chrome yacht]

no i would actually recommend amann escher sure

[fading pine]

…that’s not really re-asureing

[chrome yacht]

tao is a fine book

[sturdy shore]

it's "an epsilon of room"

the book has a "quick review" of measure theory

and it is quick so yes, better know measure theory beforehand

[crimson leaf]

You know that makes more sense

[sturdy shore]

lol

[crimson leaf]

I always thought it was a really dumb name and now I know why but yeah I was pretty sure he intends it to go like analysis 1 & 2 -> intro to measure -> an epsilon of room

[jovial parrot]

idk about visualizing

but if you liked the last episode

go check out ladr

or another book like that

[lofty knot]

Does anyone have any idea of any books similar to Ikigai? I like Ikigai, so i wanna consider reading some more of that topic

[halcyon trail]

Does anyone have a reccomendation for a "big book" of statistics

Going from the lowest level all the way to advanced level (i.e Undergrad/Post Grad)

[tawny copper]

the pdfs of epsilon of room and measure theory terence tao have like 20cm of margins, so annoying

not readable

[upbeat vine]

Billingsley probability and measure.

[civic fable]

#help-4 message

[stuck zephyr]

ayo it's good to see you graduated from hs

I'm still stuck on it

but you can find books on tpl library

[stuck zephyr]

you can find some good books in toronto public library (if you live there)

[civic fable]

I'm not stuck on actually getting books, just not sure which books to get

[stuck zephyr]

what kind of books are looking?

wait lemme read it again lol

[stuck zephyr]

Discrete Mathematics and Its Applications by Kenneth H. Rosen and Mastering linear algebra: an introduction with applications /cFrancis Su. I'd suggest those books you may need on tpl library

are you doing engineering program by any chance?

[civic fable]

Nope, I'm entirely self-taught in the realm of programming

[stuck zephyr]