book-recommendations

[vast jackal]

supplement both

[dusk wind]

Read about WEP or something you don't really need a book for that

[long sigil]

I like books because in the good books, the author takes time to explain problems at length, and one example builds into another.

[vast jackal]

yea

[long sigil]

It's OK, for now I'll just go with Introduction to Mathematical Cryptography

[vast jackal]

i mean if you really want to go deep with it then start quantum cryptography

[long sigil]

Exactly why I need a book to teach me the basics

I want to try making my own plaintext scrambler LOLOL

And maybe scramble images too.

... don't ask me what kind.

[vast jackal]

there is some prequisites for it like advanced math

[long sigil]

Which is why I said I needed a good book for beginners...

NVM

I'll just go with Introduction to Mathematical Cryptography

[vast jackal]

VIDEOS will do much better but depends on your preferences

[long sigil]

Thanks for the help...

[vast jackal]

https://cs50.harvard.edu/law/2019/weeks/4/

just putting it incase your interested

[molten mason]

Anyone gone through John Stillwell's Classical Topology and Combinatorial Group Theory or Elements of Number Theory

[crimson leaf]

What's your goal and what's your background

[umbral night]

Linear algebra Gilbert Strang is it enough for me to go for Machine and deep learning and quantum mechanics

[dusk wind]

certainly not

[rare estuary]

It's certainly a decent place to start though

[umbral night]

Then which should I refer

[dusk wind]

into the abyss of time

[maiden halo]

if you aren't going to be helpful, don't reply

[dusk wind]

you took that comment seriously?

[molten mason]

Those two subjects require multiple fields of study and many months to learn. Linear Algebra is just one of the many things you'll need to learn and that book is a good start, but you can't do it with just that book.

[dusk wind]

imagine

[umbral night]

I don't want to waste time on two books . I want rigorous books in linear algebra , I have gone through some glimpses of Schaum series.

[dusk wind]

oh my

[umbral night]

Which book sufficient

[dusk wind]

well you could read the book by tom mitchell, since it's only 1

[umbral night]

It should help me in QM also

[dusk wind]

you might want to do a typical degree program though

but certainly go for the tom mitchell book

[umbral night]

No time for some semwster

[dusk wind]

your conception of help is limited

[molten mason]

I mean those are two entirely different fields, with different types of math involved, that's why people get whole degrees in each field. There is an intersect but that's not going to be covered in a simple manner.

[dusk wind]

its alright let em cook

[molten mason]

#book-recommendations message

Check the pins, also Strang's Linear Algebra and It's Applications isnt in the list but would be good for machine leanring

[umbral night]

I mean not that advanced but advance enough to be proficient in QM and deep learning.

[umbral night]

I didn't understand what he said , he talked about R and C stuff.

[dusk wind]

the best way to go about it is probably to read some book about deep learning and whatever it says in the prerequisite section

[wild haven]

any good "intro to topology" and stuff similar textbooks/workbooks ?

[umbral night]

Anyways thanks I got axler which met all my requirements

[finite gale]

Standard is munkres, but I did not like it; I think darq knows an alternative but I don't remember what it was

[rare estuary]

Lee Intro to Topological Manifolds?

[finite gale]

Maybe

[agile jackal]

I am Malala is a very interesting book as well as ikagai

[jagged nymph]

Is there any online free book available for GCSE 0580 extended math, plz recommend

[long sigil]

My goal is to learn Cryptography

Background: Just assume I've forgotten most of what I've learned in college.

[broken meadow]

You might want to learn elementary number theory first then (?)

consider Niven and zuckerberg’s text for an intro that doesn’t require abstract algebra

[long sigil]

Hmm, ok thanks

[uncut zealot]

I agree with Metal's suggestion. Another possible route is to just dive into elliptic curves with something like Silverman-Tate (I think especially chapter 4? whichever one is the finite field chapter). I don't think the prereqs there were too steep when I read it - though, abstract algebra would certainly help.

[mortal lark]

What is a good trigonometry book that have simple explanations, good layout and great practices problems on Amazon for self taught?

I have someone interesting on learning trigonometry while they go on deployment, meaning they won't be able to have access to internet, so I hope there are book that would help teach them without the use of internet. Since it's not possible to do so.

[uncut zealot]

Basic Math by Lang?

[molten mason]

What's their reason to learn trig and what's their goal? That'll dictate what book.

[molten mason]

https://mecmath.net/trig/

This is a gold resource, 180 pages of pure trig, and they have a physical copy for $11

[dusk wind]

thats probably a lot better than anything you'll find on amazon, short of high school books or something on internet archive

[rare estuary]

I also like this book if you want something focused on trig

[high sedge]

Hi, I studied math education in undergrad and have taught for 7 years (the most advance classes I taught were AP Stat and AP Calc AB). I have been wanting to study math in grad school but it seems like I am lacking DEQ and Analysis. Are there any books you guys recommend so I can have enough knowledge to study for GRE Math subject test?

[earnest wolf]

Abbott's textbook is just extraordinary

[marble solar]

I'm a big fan of Thomas' University Calculus text, the theorems & proofs there are pretty good for getting a basic handle on baby Analysis. Boyce & DiPrima will be more than enough in the differential equations department. As far as Linear Algebra is concerned, I'm a fan of Schaum's outline to Linear Algebra

Although if you're going back to school after a while of not being in school, a MS/MA in math might be a good fit for you (many of which don't require a GRE)

[shrewd citrus]

I can second Boyce & DiPrima for diffeq, have some fond memories of that book

[dapper topaz]

Why analysis isn't taught in a general form like in the books Analysis I, II and III by Amann and Escher from the beginning? Is it necessary to study Real and then Complex analysis. I would like to study from the book I mentioned, but I'm afraid I can lose some important ideas

[marsh ingot]

Then you can try

[earnest wolf]

i mean, i found escher to be 'useful' only as a reference

idk abt u

[blazing osprey]

Is there a concise beginner's book that teaches mathematical fundamentals so that by the end the reader has enough of a footing to go into any area that interests them, as well as be able to work on olympiad style problems? I've heard of Polya's How to Solve It and Lang, but these books are both very long.

[tawny copper]

I would recommend just doing problems. Mathews "problem solving tactics" is good

Arthur Engel's book is also good, but its somewhat more difficult. Gowers has a playlist live solving problems from that book

[rustic grove]

Polya's book is quite an insightful read

[novel obsidian]

What are people's opinions on Munkres' Analysis on Manifolds?

[ocean mulch]

It's alright

But for UG, you might want to look for smth else to complement

[quick hornet]

my diff geo prof hated it but had us use it anyway because "theres nothing better"

take that as you may

[rigid barn]

It's where I finally learned how multivariate derivatives work, so I feel attached to that chapter, rest I feel is clunky/outdated (I don't think anyone learns about manifolds as submanifolds of R^n these days).

[novel obsidian]

I wanted to use it as a supplement to spivak CoM

because CoM is quite terse

[novel obsidian]

what other options are there

[rigid barn]

They cover pretty much the same ground, yeah.

Personally (although I know nothing about DG), my radical recommendation would be to learn multivariate differentiation (Munkres is good, so is Tao) and just jump to Lee's "Intro to Smooth Manifolds" (assuming you know the basics of topology), although it's an enormous book.

[novel obsidian]

I've got Lee's topological manifolds hm

how does that book fit into the bigger picture

[rigid barn]

It's the 1st part of an informal trilogy by Lee, with Smooth the 2nd, but I feel like most of it can be skipped depending on what you want to do. If you know the basics of topology and want to learn about manifold calculus you can just go straight to SM; if you don't know topology, you can read the first ~4 chapters of TM and then go to SM. Or you can avoid Lee altogether and read Tu's book, which requires only knowing partial derivatives (so however you cut it, you need to learn multivariate derivatives).

[novel obsidian]

My motivation behind wanting to read CoM was to read Bredon

[rigid barn]

Bredon is tough, but hypothetically self-contained (you'd be better off asking someone on #diff-geo-diff-top, I know pretty much nothing).

[novel obsidian]

Well I was looking through it and I already decided that there's no way it's self contained

It's hilariously terse in places

which is why I wanted to read CoM, first 4 chapters of Lee's TM before at least

[rigid barn]

IIRC strictly-speaking it is, because he introduces topology from scratch, but I wouldn't expect anyone to learn topology for the first time from this book.

[ocean mulch]

CoM?

[novel obsidian]

spivak calculus on manifolds

[ocean mulch]

Ah

[rigid barn]

I don't think CoM would help with Bredon, they do completely different things.

[ocean mulch]

Depends on what you want to master

[novel obsidian]

What about chapter 2 of bredon?

[rigid barn]

If your absolute goal is Bredon and you have no knowledge of topology, I'd suggest reading the first 4 chapters of Lee's TM or Munkres, and just going for it.

[ocean mulch]

If you want to master multivar calc, then I guess spivak

But if you like more geometrical stuff, like diff geo

[novel obsidian]

Can I really read chapter 2 of bredon without having ever seeing stuff like the implicit function theorem?

I'm trying to stay broad in my math education atm, which is why bredon looks so attractive because it covers some algtop and some diffgeo and some general topology

[rigid barn]

Well hypothetically you could, but if you want to warm up for that you could read Munkres I suppose.

[novel obsidian]

or spivak lols

[rigid barn]

Personally not a fan of Spivak, but whatever floats your boat. Spivak's short, at least.

[novel obsidian]

that's part of the motivation. The other part is (was) tterra constantly talking about how amazing it is

[rigid barn]

Idk, I'd just go for it. There's a disease many of the people here have (including myself) where they pick out books, compare and contrast and read reviews, construct elaborate plans, and then end up not doing anything.

Just pick a book and read it, if it's bad, drop it, read another.

[novel obsidian]

gotcha

thanks for the advice

[unborn jackal]

book/blog recs for (computational) geometry (for computer science olympiads?)

or anything regarding (np) problem solutions involving computational geometry

[narrow prairie]

https://cp-algorithms.com/geometry/basic-geometry.html

[molten mason]

That link is amazing.

[unborn jackal]

oh ty

also found this https://victorlecomte.com/cp-geo.pdf

[tawny copper]

https://link.springer.com/book/10.1007/978-0-387-27226-9

For this book, they show this cover first. But in the checkout they show this other one

Which one will I get lol? I hope the second one

[mellow wren]

I've got heavy beef with diamond and Shurman
I consider their book to be pretty shite

[tawny copper]

ok, but my question was not about that

asked because maybe someone had the same ambiguity with some book

[tawny copper]

Anyway, I am curious now. Why do you say that?

[mellow wren]

You'll get the new one dw

[tawny copper]

.

[mellow wren]

Half the book is spent doing annoying calculations that at the end of the day aren't that useful
Here calculation mean rows upon rows of mind numbing algebraic manipulations that you'll end up blackboxing
Chapters 3 and 4 are so horrendous that they managed to ruin the entire book for me
The rest of the stuff is pretty good but towards the end if you already know elliptic curves it isn't that useful since a good deal of the content talks about that
The chapters I enjoyed were 1, 2, 5, 6 and 9
Tho realistically 6,7 and 8 don't go into as much detail as I'd have liked because they forgo the alg geo knowhow needed to really get into this stuff

[tawny copper]

I skimmed chapters 1-3 some time back, and it seemed fine to me idk

[ruby orbit]

hey can someone recommend me a book on basic geometry? i gonna do 2nd year in CS and i realized i`m lacking a lot in this matter

[polar kraken]

Are you referring to just Euclidean, or non-euclidean as well? Are you looking for a more theoretical/proof oriented approach, or more applied?

[molten mason]

Anyone gone through Fast Fourier Transform: Algorithms and Applications by Rao, Kim, and Hwang?

[harsh stirrup]

who reads Tom Gates series?

[harsh stirrup]

İ dont know

[harsh stirrup]

just study on internet

its free

[ruby orbit]

Euclidian, but it can be proof oriented or applied, i'm looking for something just to fill the gaps

[ruby orbit]

got a bad experience studying in the internet, i prefer studying with books and using the internet to search for exercises

[mystic orbit]

you could just ping me, you know?

[mystic orbit]

and yes, it was indeed lee's intro to topological manifolds

[finite gale]

I do not like pinging people

[smoky zephyr]

i hope you pinged him for that reply

[finite gale]

I didn't :3

[coral prawn]

Nice one

[mystic orbit]

but I like to be pinged D:<

do you not like to be pinged?

[finite gale]

I do not like to ping nor to be pinged

[rain wren]

oh, aight

[smoky zephyr]

[stuck pike]

Best books on the 4th dimension?

[marsh ingot]

4th dimension? You just need a multivariable calculus book

[stuck pike]

ok lol

[remote sparrow]

@small cobalt do you have any detailed thoughts on Advanced Calculus: A Geometric View by callahan compared to Mathematical Analysis II by zorich?

[mystic orbit]

no.

[remote sparrow]

i am thinking of whether i should buy callahan's book or A Guide to Marxian Political Economy by teinosuke otani during the springer sale

i already have zorich

[mystic orbit]

there is a lot of interesting math to explore in the 4th dimension that doesn't fall under calculus

[marsh ingot]

Then what do they mean by 4th dimension?

[mystic orbit]

R^4 I would imagine

[stuck pike]

just about the idea of it and yea also that

[mystic orbit]

I can't recc anything tho tbh

[crimson leaf]

Can you be more specific and maybe state your background a bit?

[marsh ingot]

But R^4 from what branch?

[mystic orbit]

maybe look into low dimensional topology?

[marsh ingot]

Because you can see it from Analysis, Algebra, Topology, Geo Diff

Etc

[mystic orbit]

yea, you need to be more specific than just the ✨✨✨4th dimension✨✨✨

[rich sun]

The Wild World of 4-Manifolds

[mystic orbit]

is that an actual book?

[rich sun]

Yes

[marsh ingot]

Yeah, because the question is so ambiguous

[mystic orbit]

oooo

[stuck pike]

@crimson leaf Euh its not related to uni just in my free time if it exists in the real world and if so what it is

[crimson leaf]

What's your math background

4th dimension is almost meaningless if I'm being real with you

[mystic orbit]

I wouldn't worry about it existing in the reala world

[stuck pike]

I’m in engineering first year uni

😹

[mystic orbit]

altho, I am not a ph*sicist

[stuck pike]

Some people say it’s time

Don’t really know if that’s correct

[mystic orbit]

to mathematicians, the 4th dimension is just $\bR^4$ lmfaooooo

[hasty eagle]

DarQ

[mystic orbit]

any physical manifestation of the 4th dimension is irrelevant to mathematics

[stuck pike]

Not really

[marsh ingot]

Lol

[crimson leaf]

It could be any vector space who's basis is formed by 4 vectors as well

[marsh ingot]

C^2

[stuck pike]

I guess it’s more physics indeed

[crimson leaf]

You might be interested in looking into Minkowski space but that's as far as I could lead you

[marsh ingot]

But that is Riemann manifold, they need so much background to arrive there

[rich sun]

(pseudo)

[stuck pike]

Thx

[crimson leaf]

I'd only heard about it as a 4 dimensional vector space with some extra stuff equiped

[marsh ingot]

Well yeah since the Levi-Civita connexion for R^4 is just the directional derivative

[stuck pike]

With the 4th dimension I mean this: we are 3 dimensional creatures when we draw a square which is 2 dimensional we can see everything that the square has to offer . No depth everything exposed. If you expand this logic to a dimension higher would a 4 dimensional creature be able immediately see everything we have to offer since we are 3 dimensional creatures? Just like we see a square

[marsh ingot]

Thats what Kenshin said, Minkowski space that is R^3 x R^+ the 4th coordinate the time thats why is positive

[stuck pike]

Oh ok

[pliant falcon]

Lorentzian manifolds are of interest to Mathematicians

[grave thorn]

math people dont care if Lorentzian manifolds actually exist in the physical world

[pliant falcon]

Ah okay, that's a fair statement

I guess I misunderstood my b

[mystic orbit]

"my n" was WILD

[pliant falcon]

STOP 😭
My keyboard praying on my downfall

[sturdy herald]

Yo

Have any good book recomandations?

[remote sparrow]

https://matheducators.stackexchange.com/questions/364/resources-for-teaching-riemann-integration-in-higher-dimensions-and-on-submanifo/

[marsh ingot]

https://vxtwitter.com/miniapeur/status/1740860740721066239?t=ZSDqs8hVkZqrhKfN4UmdaQ&s=19

[rare estuary]

Tbh I would rather face Voldemort

[stuck zephyr]

[undone pine]

Not sure if this is the right place to ask about this, but I’m currently going to machine learning refined and I was wondering what books should one read after completing this one? Any recommendations? Ideally want to learn more about neural networks. This book only seems to cover fully connected neural networks

Machine learning refined by Jeremy watt

[dense loom]

Jaynes' book "probability theory: the logic of science"
Currently reading it, it's great 👍

[dusk wind]

3D isn't high enough, aliens always see us

[trail hemlock]

alr fine ill go read flatland again

[fading hatch]

hello i prepaped a book list for self study, i need someone to check the list

[finite gale]

Where's the list and what's the topic

[fading hatch]

Book of proof - Hammack
Elementary linear algebra- Howard anton
Steward calculus Early Trascendentals
A first course in differential equations - Dennis G Zill
Partial Differential Equations - Walter A Strauss
Visual Complex Analysis - Tristan Needham
Principle of Mathematical Analysis - Walter Rudin
Abstract Algebra - Richard M Foote
Number Theory - George Andrews
Topology - Munkres

[mystic orbit]

[finite gale]

I think that it's not really realistic to make these sorts of lists

[hazy cloud]

is that baby rudin?

[mystic orbit]

you don't need to plan that far ahead

[mystic orbit]

yea

[hazy cloud]

Agreed

[finite gale]

So just pick something you want to learn right now and just start reading

[fading hatch]

its just for reading, i dont have exams or stuff like that

just personal reading

[mystic orbit]

this is easily a year or two's worth of study

[fading hatch]

i plan a year

[finite gale]

But also there's not really any point in "just reading" as you won't really learn effectively if you don't at least try some of the exercises

To check your understanding

[fading hatch]

yes i will also try the exercises

[finite gale]

But I also do really think that it's just better to choose something off the list and don't worry so much about what to do after that

After all, your interests may shift after reading your first text

[fading hatch]

ok

[finite gale]

Especially since you seem to have computational calc on there

[gray gazelle]

I would like some recommendations on books on

1. differential equations ordinary and partial
2. Discrete math
3. linear algebra

[gray fractal]

Birkhoff for ODEs. Strauss for PDEs (not very theoretical). Knuth has Concrete Math.

Linear algebra by some Germans (forgot the names).

[marsh ingot]

Evans for the first one

[gray fractal]

well, there are two books by Halmos on linear algebra.

[gray gazelle]

thanks, a lot

[remote sparrow]

#book-recommendations message

#book-recommendations message

[fading hatch]

?

[remote sparrow]

#book-recommendations message

[fading hatch]

what?

ah oj

thanks

[remote sparrow]

#book-recommendations message

https://www.math.ualberta.ca/~thillen/pde-book-page.html

#book-recommendations message

#book-recommendations message

#book-recommendations message

[gray fractal]

hmm, Folland's book "Fourier analysis and its application" has good amount of PDE stuff

[molten mason]

Linear Algebra by some Germans, a.k.a. Friedberg, Insel, and Spence

[molten mason]

Those are fine. What everyone has said is correct however it's always good to have more than one reference/textbook. You might end up with multiple topology or abstract books as you progress.

[crude sage]

Anyone know of books, webpages, etc. that give brief descriptions on the core undergrad subjects (maybe also the subjects following those)? I'm not looking for something comprehensive like eg the Princeton Companion, but something to get a better idea what could be in my near future

[molten mason]

What do you mean? Most university websites will list the classes/subjects.

For example my university requires Calc 3, linear algebra, and proofs for all undergrad math majors. Then there's 5 "emphasis" you pick from that'll tell you what other classes you need such as I believe the applied emphasis requires differential equations, the pure emphasis requires analysis and abstract algebra, etc.

[crude sage]

This is true, but the impression I get reading the academic schedule is that math is the study of stats and PDEs. The program requirements are quite hands-off (you need single- and multivariable calculus, intro LA and stats, and so many credits from courses of this level and above). It can be kind of misleading and unstandardised as well. Some of our courses have titles like "rings and fields", but don't cover one of rings or fields (they are moved to another course, which doesn't have rings or fields in the title)

Maybe my question could be better phrased as "where can I find out what stuff is accessible after studying intro real/complex analysis, basic rings/fields/groups, and a bit of topology"

[foggy fiber]

You could start with MAA's CUPM Curriculum Guide to Majors in Mathematical Sciences: https://maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/cupm/2015-cupm-curriculum-guide. It contains course reports, program reports, etc. From there, you can find textbooks in the references section for each topic discussed.

[crude sage]

Woah, this is awesome, thank you!

[crude sage]

After a bit of thought I have realised that looking at other universities' requirements could be a good idea lmao. It is a good suggestion

[foggy fiber]

There are a few mathematics roadmaps out there that can help guide you through these type of questions.

For example: https://raw.githubusercontent.com/TalalAlrawajfeh/mathematics-roadmap/master/mathematics-roadmap.jpg

I don't necessarily agree with some of the textbook choices, but how the subjects flow is reasonable for most.

If you're looking for things specific to abstract algebra (rings, etc.), give this a read: https://maa.org/sites/default/files/Abstract Algebra - Course Area Report (Sep 25 2023)_0.pdf. Lots of textbook options towards the end.

[molten mason]

Ah that's interesting, yeah many undergrads at my university don't ever take a course on stats or PDE. Abstract Algebra is two semesters and so is Real Analysis but that's mostly for those wishing to go to graduate school. Topology isn't required for any emphasis, it's just an elective, but it's required if you want to apply for grad school.

There's so many courses and specialities and textbooks. I would say browse all the major forum websites and Google around what math classes/courses/textbooks/prerequisites for XYZ and then work backwards from there.

That's what I've basically been doing, for example I know everything I'm interested in requires Complex Analysis so I already bought a textbook in it and will take a course on it later.

[molten mason]

That first link is amazing, nice to see it in a neat flowchart

[molten mason]

Also if you know you'll be taking some class in the future, lookup past syllabi for that class and see what textbooks they use too. For example Ordinary Differential Equations at my school is an in-house text and i was able to find the PDF and study in advance

[crude sage]

@foggy fiber the graph-like informatic was pretty interesting as well

[crude sage]

I think you're going in the opposite direction: you know what you're interested in, so you know what prerequisites you need and books that might be helpful. I'm not sure what there is to study towards, but I know a bunch of introductory books

[molten mason]

Ah that makes sense too, I have that moment often. "What's next" "What does this even lead to"

[daring lake]

Anyone have read the complex analysis section of Rudin's RCA?

How does it fare against something like Lars V Ahlfors ?

[gray jungle]

its pretty good imo , the approach uses some measure theory and emphasizes a connection between graduate real analysis and complex analysis here and there and he also gives some results in more generality than what you might need or see in ahlfors but its pretty solid , even chapter 10-11-12 should be enough for Basic CA.

[daring lake]

Ah okay, good to know

Another question, if you don't mind. Is Rudin's RCA well contained? As in it does it miss out any key results which might have been done in Ahlfors or Gamelin, I haven't studied any content related to complex analysis yet.

[gray jungle]

Id say rudin requires more background , the main things i found rudin doesnt cover that ahlfors does are stuff like basics of complex numbers , power series , uniform convergence , basic topology ( which is in his PMA tbf) also doesnt go too much into reimann-zeta or elliptic functions

[daring lake]

Good to know, thanks

I think I will start first work with Ahlfors, then move to ch10 Rudin

[lime moat]

can anyone suggest a book for operator theory? I am an undergraduate student trying to understand differential operators

[novel hound]

Just realized RCA fails Borcherds test for a good complex analysis book 😄 https://www.youtube.com/watch?v=qXWRL6NHlWc&t=1025s

[molten temple]

yeah rudin treats the subject a bit unconventionally lol

[foggy fiber]

Try Simon's A Comprehensive Course in Analysis series. I think Part 3 and Part 4 cover differential operators in different forms.

https://www.ams.org/publications/authors/books/postpub/simon

[marble solar]

I'd say that Rudin's Complex Analysis section is best supplemented with another complex book. Working with Ahlfors and Rudin is a great idea

[marsh ingot]

Rudin thought that you already know about the subject lol

[daring lake]

Good to know, that's what I intend to do

[gray gazelle]

clyde

[gray gazelle]

"Calculus: Concepts and Contexts" by James Stewart is a very nice one

[rare estuary]

Free though?

[gray gazelle]

It is available online for free

just type --> <book name> + pdf

and click on the first link

https://www.zuj.edu.jo/download/calculus-concepts-and-contexts-2nd-ed-james-stewart-pdf/

here

this link works

atleast for me

haha no worries 😉

Nope

India

[rare estuary]

https://tutorial.math.lamar.edu/

[gray gazelle]

alrighty imma leave now

bye

[rare estuary]

Lol, ok

[gray gazelle]

https://media.discordapp.net/stickers/869226275762479154.png?size=160&name=ducky_joe_salute

[autumn spire]

does anybody have a book pdf for olympiad?

[autumn spire]

anyone?

[molten mason]

Use the search in top-right, there's dozens of different ones mentioned here depending on exactly what you want.

[narrow prairie]

https://www.math.ucdavis.edu/~kouba/ProblemsList.html

[weary violet]

hey i am currently studying in 10th class so can you guys suggest me a good book which can be helpful for me?

[gray gazelle]

For?? What?

[weary violet]

for practice

and concept a little

[autumn spire]

just for boards or olympiads and stuff

i am also in 10th

rd is enough for boards

if you want to do olympiads imo you should use pearson

[gray gazelle]

Does reading and understanding Advanced Calculus revised edition by Lynn H. Loomis and Shlomo Sternberg requires a math knowledge higher or equal to an university level?

[solemn sigil]

Hey can someone recomend some books on Topology

[daring lake]

Munkres

[solemn sigil]

ahh thanks

[vast jackal]

internet archive

[vast jackal]

go to MIR PUBLISHERS in Internet Archive and then search for <Olympiad> you can see lots of similar problems that are used

[vast jackal]

know your topic and then study your ass of it

[strange vector]

Does anynone know discrete math book that is rigorous and concise? like rudin equivalent of discrete math

[autumn spire]

thanks, bro it really helped

[vast jackal]

you alr know sets? notations?

[strange vector]

yes i studied linear algebra and real analysis

[vast jackal]

they have lots of good old books thats pretty hardcore, sometimes they make some wrong value of that and you need to check out

[autumn spire]

ok

[vast jackal]

idk if this is a good one but MathStackExchange gives a good recommendation sometimes https://math.stackexchange.com/questions/1533/what-is-the-best-book-for-studying-discrete-mathematics

[strange vector]

I read this but none of the books written like rudin, they are more towards to computer scientists

[vast jackal]

Even your profile is the 'father of computer science' Alan Turing

[strange vector]

yes but he was also a mathematician

[slender cargo]

Just looking at the Wikipedia page, the term "Discrete Math" came about as a Computer Science support course.

in the 1980s

[vast jackal]

discrete math has lots of applications in CS so yeah that's why

[strange vector]

right but even some algorithm books are math heavy like sedgewick's analysis of algorithms

but almost all discrete math books written for computer scientists

[molten mason]

Yeah at my university the "Discrete Math" is a Computer Science Major-only course that just sums up various mathematical topics

[molten mason]

What's your end goal though? What are you trying to accomplish?

[vast jackal]

even google said this "Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development."

[strange vector]

i want to learn discrete math

yes i know discrete math is for computer scientists in general but it's still math

[vast jackal]

well then study some books about discrete and just ignore about the CS stuffs

[slender cargo]

I think Discrete Math is just a hodge podge of topics? It's not very specific. Maybe learn Abstract Algebra?

[molten mason]

Yes but that's like saying you want to learn machine learning. The topic itself is made out of multiple other topics. For discrete math you could pick up some pure math books on graph theory and number theory.

[slender cargo]

Number Theory goes under Discrete Math also

[strange vector]

that's the problem, books written for computer scientists is not like classic abstract algebra or topology books

[slender cargo]

There's dedicated books on Graph Theory

[molten mason]

Related, can't wait for Springer to ship out my number theory text I ordered 🥵

[vast jackal]

Discrete Mathematics covers some important concepts such as set theory, graph theory, logic, permutation and combination as well.

[vast jackal]

envious of you lol i only use PDF's

[strange vector]

i know, my problem is they are not similar to math books, like there is 1 definition 20 examples and 1 theorem without proof

i ordered like 5 discrete math books, all are the same

[molten mason]

Their winter sale was $70-$110 hardcover textbooks for only $20, I couldn't resist buying a few

[vast jackal]

you're like me when i started Basic Mathematics small definitions lots of problems

[molten mason]

Serge Lang?

[strange vector]

i'm saying i don't like that type of books

[vast jackal]

cool well 20 bucks in my country is $$

[vast jackal]

yeap

[slender cargo]

Just start reading pure math books then. I don't think you're getting a book titled "Discrete Math" that is Rudin-like

There's no market for it

[vast jackal]

i agree then read the books you have bought so you can understand them better

[slender cargo]

I assume if you want to read the higher level stuff of topics covered in Discrete Math then you probably need to learn the foundational basics. Analysis, Algebra, Topology, etc..

(I say this as someone going back to school for higher math education, so I'm no expert on this.)

[strange vector]

i have some knowledge of algebra and analysis, my plan was learning discrete math and then reading algorithm books like dasgupta's algorithms or clrs

[molten mason]

I love that text lmao

[strange vector]

reading kenneth hoffman's linear algebra and baby rudin was so much fun but then i get these boring discrete math books

[molten mason]

Yeah you have the background for it

[slender cargo]

Just looking at the table of contents of Dasgupta's Algorithms, seems like you have the background. If you wanted to be exhaustive, you could pick up a book on Graph Theory and Elementary Number Theory

[strange vector]

thanks

[slender cargo]

But I get the feeling you don't need that much

[molten mason]

+1 to Graph and Number theory

[remote sparrow]

well, it was originally written for math 55 students at harvard.

https://www.math.harvard.edu/demystifying-math-55/

[tawny copper]

Not true

[tawny copper]

I am not aware of anything like this, but why would you restrict yourself to a single book? Also keep in mind that you will gain the most from doing problems

Bóna's book "A walkthrough through combinatorics" gives a good introduction for beginners. Maybe you could start there if you don't know much

[rare estuary]

I haven't actually read this one, but Concrete Mathematics by Knuth is apparently pretty hardcore.

I'm not sure if it's really like Rudin though

[agile spoke]

Wich is the best linear algebra book to study from 0?

[remote sparrow]

#book-recommendations message

[latent elm]

could you say a little more about these books if you've used them? I'm looking for a linear algebra book like Young/Freedman's "University Physics" targeted towards high schoolers for a programmer friend. ideally it should be very handholdy, have many pictures/worked examples, and focus on computation. the Hefferon book seems okay but might still be a little too dry

[remote sparrow]

does your friend know calculus

[latent elm]

yes. she's a college grad but basically forgot everything from her linalg course (even gaussian elimination)

[molten mason]

Linear Algebra and its Applications by Lay, Lay, and McDonald would be great. It's written like most modern day high school and calculus textbooks. Tons of exercises. tons of pictures.

If you google it, University of Colorado Boulder has the PDF online for free of the 5th edition.

[latent elm]

ah ths looks great, thanks!

[fervent marten]

https://artofproblemsolving.com/store/book/precalculus does anyone have this book?

I'm wondering if i should buy it or not

[remote sparrow]

https://maa.org/press/maa-reviews/linear-algebra-9

i like the book personally

i use it to review the basics

[molten mason]

Not personally, but it's been recommended multiple times in this channel before

[foggy fiber]

AoPS books are geared towards competition mathematics, so whether or not you find worth in it is likely more contingent on your goals.

[remote sparrow]

hefferon is free online, has lectures, and a full solutions manual

there's even a lab manual with some programming problems

https://www.amazon.com/Linear-Algebra-Theory-Intuition-Code/dp/9083136604

there's this too

doesn't assume any calculus

[foggy fiber]

I'm not sure you're going to find an equivalent from a single text (as someone else mentioned). The closest you will get is Knuth's Concrete Mathematics (also mentioned previously), but even that is just going to scratch the surface of rigorous discrete math. Once you have an overview of the topic, you're best bet will be to find a rigorous text that hits on the specific part of discrete math you want to learn more about (theoretical CS, logic, combinatorics, etc.). The rigorous books available for those topics are much easier to come by.

[heady peak]

Good books for abstract algebra that are at an undergraduate level?

[modern ruin]

okay i have no recommendations for a first pass because I think they're all just fine but once you have read an introductory book you should check out Algebra: Chapter 0 by Aluffi if you end up liking it

i know that's not what you asked for

[heady peak]

hmm okay

[heady peak]

what do you think about judson's abstract algebra? (if you've read it)

i found it for free online

[dapper root]

This was my first pass

I turned out okay

[modern ruin]

woah holy shit i’m getting deja vu lmao

i found this book in high school and read it as a first pass yeah

i think it’s just fine

i lost the pdf and never found it again until now - when you said “found it for free online” i was like “what are the chances it’s the same one that i used” and then i was like “wtf”

[heady ember]

Look in pinned too btw

[modern ruin]

u sure?

[dapper root]

I mean mathematically. My being down bad is unrelated to Aluffi

It’s more related to my chmizz seeming to be highly ineffectual

[left cloud]

i wonder what i was pinged for

[remote sparrow]

good

pinter is also good

pinter reads better, but isn't organized as well as a reference

it pairs pretty well with judson though!

and they seem to segway nicely into Galois Theory by david cox

[gray gazelle]

I wish this channel was threads format instead, would be so much easier to sort out the books from conversation. (Posted so mods can see this, sorry a bit off topic).

[gray gazelle]

silverman is the book I am familiar with and I think it's decent for a first pass

aluffi also has a ug algebra book which talks about categories implicitly

it's called algebra : notes from the underground

[weary violet]

thanks

[dusk wind]

threads would be an extra step, just use keywords and filters

[grim pivot]

Does anyone know of any good books for high school calculus?

[dusk wind]

you can use Stewart, Anton, or Leithold books

[grim pivot]

Thanks!

[dusk wind]

theres also https://mecmath.net and https://whitman.edu/mathematics/multivariable/ for free

[grim pivot]

Thank you

[dusk wind]

personally Leithold single variable would probably be high return

what math are you interested in

beyond academia the stuff you learn in high school is probably the most 'practical' beyond that anything else is abstract and will bore you

Do you like Algebra? You could look into number theory and maybe abstract maths

You could look into statistics etc

[patent temple]

May i ask. What math are you interested most?

[dusk wind]

Dunno

But if you find math in school boring you should find a different approach or blend it with the sciences

https://www.jstor.org/stable/2691501

[heady ember]

Le Homeless Catalogue (not including lin alg)

1. Axiomatic set theory --- Enderton's Elements of Set Theory is a relatively gentle intro text,

2. Linear algebra --- see pinned,

3. Real analysis --- Schroder/Abbott, again a gentle text.

4. has been my favorite so far, but axiomatic set theory isn't very applicable to other fields in general, even in math.

2 and 3 are quite common starting grounds for proof-based mathematics. But lin alg can be done computationally too if you prefer that; and is one of the most important math things to know.

[gray gazelle]

try playing hyperrogue maybe XD

[dusk wind]

still hunting down math games

Make a cube in graphics programming maybe

or a donut in that one guys case

[gray gazelle]

i also just started reading spivakmyself and I think it's pretty interesting actually

tho probably i would not feel the same if gpt4 didn't help me over some humps

[dusk wind]

AI makes errors so we don't have to

[novel obsidian]

wdym its not applicable, everything is implied by the axiom of choice

[heady ember]

There's a reason I wrote in general

And intro books don't seem to explicitly mention the use of AC much in my experience

There are most probably some instances where some understanding of AC (amongst other tools like transfinite recursion) is required... but I doubt you need a copious amount of it (esp. for intro material)

[molten mason]

Linear Algebra would be the most applicable to programming.

[dusk wind]

http://www.trillia.com/zakon1.html

https://trotter.math.gatech.edu/book.pdf

[gray gazelle]

Does anyone know a good introductory book to relativity?

[autumn spire]

https://www.dropbox.com/sh/fg0o8twv3og7bb0/AAAl1oE_kisaccmoZ9ZKZ781a?dl=0

It has something related to relativity if it helps

[dapper topaz]

Hi! Why probability isn't taught from a measure theory perspective from beginning? Am I missing something if I take measure theory probability as a first course?

[marsh ingot]

Because Measure Theory is deep

[gray jungle]

Measure theory is usually a tough wall to pass for someone who just wants to know the basics of probability for practical purpose or just interest

Like oh i have to study most of lebesgue theory and understand theorems like caratheodry and radon nikodym just to define expectation and distributions

Ik many people will disagree but i think its perfectly fine to do a course on non-measure theoretic probability to get a feel for it and do the niche practical exercises of probability (which should be relatively chill for most people)

and then study measure theory on its own for a semester and then do actual probability theory

its not efficient but i think its the best path if you want to have a solid foundation

idk the type of person you are tho , maybe you are a beast and can breeze through measure theory then go into probability from measure theory angle, but im assuming the average math student here.

[strange vector]

you won't miss anything, and i think it's better that way. And the reason is it requires measure theory

[thorn cloak]

anyone have experience with Ross elementary intro to mathematical finance? any good suplmenetaries for intro to math finance ?

[vapid charm]

Hello, so when I studied calculus in a Swedish classroom, I had a few various textbooks which worked very well for me. They went from basic calculus to topics like integrating functions as well as solving differential equations. It also expanded pretty well of the usages of the concepts and I wonder if there are any textbooks which can sorta let me re-read some stuff I've done before but maybe learn the terms in english. Also I really don't like a lot of resources I find on youtube like 3Blue2Brown. It looks like he's just showcasing graphics with a vague explanation on them, and it never goes deeper than that, and I never find myself continuing what I did after watching one of his videos.

So please be more considerate with resources on youtube you recommend, I only wanna use them as a supplement.

[rare estuary]

If you're looking for a deeper look at Calculus in English, you could try Spivak's Calculus

If you want a more computational book, then Stewart is often recommended. I personally used Calculus w/Concepts in Calculus by Gulick and can recommend it

[autumn spire]

bro i was literally watching 3blue1brown and his calculus series

i think his explanations are pretty clear you should just solve a little more questions related to that topic

[dusk wind]

its difficult to have the same context as a book in a video, the videos should be supplementary as you read your respective chapters

regardless, compared to a lot of other calculus content on youtube 3blue1brown is still probably the best, as the others are either too slow or uninteresting/ not as clear

[molten mason]

Howard Anton has a good Calculus book as well

[dusk wind]

maybe a workbook like Schaum's and something like this https://activecalculus.org/ are good options

it could also be that the english terms might detract from the experience, which causes a disconnect

[molten mason]

Blackpenredpen, Professor Leonard, Ms Shaw math class, and there was one other guy, bald, can't remember his name.

Those were my personal YouTube recommendations for Calculus.

Couldn't do too much of the other channels

[dusk wind]

I tried to find alternatives to blue brown, but they all suck in comparison - Shaw I think but forgot the other ones

Well, there's probably organicchemistrytutor too but eh

[molten mason]

Yeah I couldn't do his videos or blue brown for too long. Just here and there.

I loved NancyPi, she really got trig substitution and binomial theorem to click on for me, but she only did like 20 videos then dropped off the face of the Earth

[vapid charm]

Thank you for these suggestions. Appreciated.

[vapid charm]

Thank you.

[vapid charm]

He does jump around a lot from concept to concept and when I am not following I struggle with finding the information to substitute with on the fly. He introduces a lot of concepts that in my case needs a proper explanation prior to watching it. So for that reason his videos are actually just exhausting and fills me with existential dread. I actually don't have time watching stuff that just isn't good for recapping anything.

[vapid charm]

That is probably a very small part of the problem. I think that the main issue with 3Blue2Brown is that he is basically talking about things that would make the most sense if you already remember everything from your classes on the spot.

[vapid charm]

Blackpenredpen is more to-the-point, but I always find myself needing to go back to even more raw explanations. His examples are SO good though, I don't mind that you bring him up at all.

[fervent marten]

so i would only need it in comps? or can i just use it for my math classes

[vapid charm]

I'm diverging a bit from the topic of books when I say this, but I want to add that I for some reason find swedish mathmatics lectures on youtube better than on english-speaking youtube and I have no idea why.

You don't have a swedish 3Blue2Brown, it's just not a thing.

They JUST cover the courses, tell you what books they are referring to etc.

[dusk wind]

ha ha

well, I don't know much about the differences, it could be biased but there is a chance that they would be of higher quality.
You could possibly have an easier time with their accent or presentation shrug but I don't know if youtube would be a good enough sample size for this. In general the content produced on youtube is free so... I expect it to be lackluster in some way, unless some professor is offloading their content there for ease of use. I always advise to try to get as much as you can in your native language or from a favorite teacher/organization as possible

Maybe try to seize content from some university in your preferred language

[vapid charm]

I don't want to translate material or try find a swedish aquaintance who knows about the topic every time I have a question about whatever I'm seeing.

Altho, it's not as relevant in THIS case.

So I am indeed overthingking things a bit.

Now and then.

[dusk wind]

no way to be sure, as everyone's interpretation is different, but you might have to take some of those extra steps on occasion.
If there was the perfect luck to somehow run into the swedish blue brown (maybe they are out there?) that would be good for comparison. There are still the videos by Strang & MIT though

[narrow prairie]

you can definitely use AoPS for math classes

they are great books

however they are sort-of hard compared to normal math books

and some of the stuff they cover isn't on any curriculum (like functional equations)

but if you like math it's a great choice

[fervent marten]

ok tysm for clarifying

[trail hemlock]

aops 😍

[rare estuary]

Does anyone know of a good series of lecture videos that cover the real analysis content roughly through PMA or Browder?

[remote sparrow]

http://analysisyawp.blogspot.com/

https://www.youtube.com/@wcwou/playlists

i am not aware of any lecture videos for browder

[rare estuary]

Thx!

[dusk wind]

https://lqbrin.github.io/tea-time-linear
https://web.stanford.edu/~boyd/vmls/vmls.pdf
https://jheffero.w3.uvm.edu/linearalgebra/book.pdf
https://amazon.com/Introduction-Linear-Algebra-Nathaniel-Johnston/dp/3030528103
https://amazon.com/Linear-Algebra-5th-Stephen-Friedberg/dp/B0B9HBT4XH
https://www.math.brown.edu/streil/papers/LADW/LADW_2021_01-11.pdf
https://textbooks.math.gatech.edu/ila/ila.pdf
https://realnotcomplex.com/algebra/linear-algebra/linear-algebra-and-matrices-by-martin-fluch

[ornate saddle]

Are there any "Multi-objective Optimization" books/notes/resources in general? It would be nice if it even included Python code of algorithms for self-study purposes.

[molten mason]

A whole playlist on Fourier Analysis, say less 🥵

[fallow cypress]

Anyone have any special relativity or general relativity textbook recommendations?

[remote sparrow]

are you interested in a physics textbook or a mathematical physics textbook

[rare estuary]

You have to handle the free part yourself (sometimes)

[crimson leaf]

You have to motivate yourself to self study really

[trail hemlock]

hes back 🙏 🙏

[fallow cypress]

Physics

Although mathematical physics would also be nice

[elder jasper]

Hey guys

Can you recommend me a book for functions

[molten mason]

What kind of functions...?

[manic cairn]

i just gave away my special relativity book (along with others) by A.P. French to a high school senior on new year’s eve. i think she’ll get a lot of use out of it, because it requires calculus and that’s about it.

it’s good, and puts a big emphasis on physical intuition beyond something like
“here are some lorentz transformations, here’s a few pages of computation deriving corollaries, now compute shit”.

[gray gazelle]

search the books name and pdf, or you could torrent them

textbook authors often make basically nothing of their books, the driver is usually to be recognized as an expert in a field, not make money off the publication

[manic cairn]

i’ve seen wald (GR) and penrose (techniques of differential topology in relativity) cited by mathematical physicists as places to learn about lorentzian manifolds in general

but i haven’t read them

and probably can’t anyway without more diff geo under my belt

[marble karma]

Libgen

[patent temple]

Thanks ill read them soon...

[heady ember]

See which one interests you the most, then stick with it if you would like to.

Or if you have interest in some other field, you could also consider learning that, even if it might be niche.

Like (axiomatic) set theory lol

[quasi haven]

Hi chat
I have a decent background in maths especially engineering maths. Is there any book to read about math in general which is like a story to the readers. Interesting facts and history like that

A professor suggested me I think Spivak book I can't remember the author

[gray gazelle]

Fermat's Last Theorem by Simon Singh

[worthy oasis]

I’ve done non-measure theoretic probability and measure theory.

What’s a good measure theoretic probability book for this situation?

Likewise, I’ve done a computational PDE course and will be taking functional analysis.

A text that covers PDEs in this context would be useful.

[marsh ingot]

Evans for PDEs

Want a book for functional analysis?

[worthy oasis]

Is there a book that covers PDEs and the required functional analysis topics?

Or are most PDEs books at that level going to assume functional analysis as a prereq?

[dense loom]

"elementary number theory" from Burton provides interesting facts and history (its lines about Pythagoras are quite wrong though, since we have scarce information about him)

[vast jackal]

they are easy

[steel cloud]

Modern algebra by Gilbert any review?

[visual bear]

what are some good books to get started in CS

[strange vector]

for math: kenneth rossen discrete mathematics and its applications
for programming: Structure and Interpretation of Computer Programs

[visual bear]

Is this one any good “Algorithms and Data Structures: The Science of Computing”

[strange vector]

don't know about that book but if you want algorithms book, sedgewick is really good

[dusk wind]

https://discretemath.org/
https://discrete.openmathbooks.org/dmoi3.html
Discrete Mathematics for Computing

[marsh ingot]

Topology and linear algebra

[graceful moon]

Analysis and linear algebra are the usual pre reqs

[marsh ingot]

Books like Conway or Megginson

Or

Rudin

[graceful moon]

A solid basis, like at least what’s needed for a metric spaces/ topology course

[marsh ingot]

Cmon is a good one after you suffer a bit. Idk Rudin books is like love and hate relationship

[graceful moon]

That’s the topic list for the analysis class that’s a prereq at my school, plus a course in metric spaces (open closed sets, topologies, completeness, compactness, separable spaces, connected spaces)

That’s a truly terrible picture but I’m not retaking it so

[autumn spire]

thanks again these are really nice books
helped a lot

[tawny copper]

What are books on topological groups and/or abstract harmonic analysis?

[broken meadow]

Deitmar

[native cradle]

are there any good introductory books for linear algebra

preferably in the public domain

I want to understand the basic concepts and proofs, but that;s not in my syllabus, hence the question

[dusk wind]

#book-recommendations message

[fervent marten]

what are the best AoPS books? mainly used for competition

[narrow prairie]

depends on your level

I think most people advice against the two competition volumes and just tell you to get the subject-specific books

[grand minnow]

Any good books that have some nice beginner exercises for calculus? and any books about calculus that would be good to go through? I'm currently reading "Calculus for the Ambitious"

[spring marlin]

Can someone recommend but really good books for geometry? Starting from the very basic and going till graduate level, can be multiple books obviously

[fallow cypress]

I like this book, thanks!

[languid bloom]

I'm currently enjoying Calculus Made Easy by Silvanus P. Thompson and Martin Gardner which I believe is regarded by most to be an amazing resource

[grand minnow]

Perfect, thank you for the recommendation!

[queen rampart]

if you want to be truly ambitious but still firmly within reason: calculus by spivak

like this is definitely still a calculus text rather than a real analysis text (even compared to something like abbott) but if you want to challenge yourself it's excellent

[grand minnow]

I’ll add it to the list!

Also if you don’t mind me asking, is there any good order of books I should follow to start learning more pure math like number theory, category theory, etc.?

I’m currently going through a book called “Mathematical Proofs” by Gary Chartrand, Albert D.Polimeni and Ping Zhang

[drowsy basin]

Any picks for the abstract algebra exercises book?

[spring cave]

I' ve covered stewart Vol.1 at this point, would it be a waste of time to cover Apostol's Calculus or is it worth it anyways?

[fervent marten]

what would be the best one for AIME and USAMO? I am already pretty confident about AMC 10 and 12. I'm taking pre-calc as an 8th grader so I guess my level is above average.

ok thanks!

[queen rampart]

most of it is "whatever is interesting"

I do really like evan chen's *infinite napkin" for a kind of "here is an overview of everything"

https://venhance.github.io/napkin/Napkin.pdf

[grand minnow]

Holyyyy, 920 pages 😭

[hasty flower]

i like evan chen's EGMO

[queen rampart]

it's like here is an outline of 50 or so pages on almost all of maths

[hasty flower]

euclidean geometry in mathematical olympiads

[queen rampart]

it also has a great diagram at the start of what depends on what

[hasty flower]

i also recommend titu andreescu (105 number theory problems, 104 trigonometry problems, e.t.c)

[queen rampart]

apostol's calculus is more analysis than calculus; i.e. it's quite rigorous. idk how much stewart does analysis rather than just here is how to do limits and derivatives

[queen rampart]

so in short: whatever interests you. set theory is obviously hugely important but after that it sort of goes either abstract algebra, topology, or analysis and then everything is one of those 3

category theory is weird because on its own it doesn't depend on anything but it's completely (almost) useless without something else

I guess I'm ignoring discrete maths here (graph theory, logic, proof systems, all that jazz)

[queen rampart]

is there any further context or is this just any abstract algebra book

I'm guessing we're talking first look, nothing super complex

[drowsy basin]

I need material to practice on

[queen rampart]

gallian, hungerford, fraleigh are the more beginner ones

[drowsy basin]

to get proficient

[queen rampart]

fraleigh then

[drowsy basin]

thank you

[queen rampart]

dummit and foote is a huge-ass tome of a book

people call it boring but it has everything you will ever need and is aimed at the first time algebra audience

[grand minnow]

Perfect, thanks for all your suggestions! I'm already going through set theory so I guess I'll just strengthen that first

[queen rampart]

how to prove it by velleman

[fallow cypress]

dummit foote has an insane number of exercises

[queen rampart]

the most recommended book for practicing proofs and by extension set theory

because most of learning proofs is either sets, or functions (and treating them as sets)

[fallow cypress]

Tbh your interests will probably drift over time so I would probably just finish the book you're reading right now because proofs are gonna be vital to anything you learn next and then see from there. One book I like is Linear Algebra Done Wrong by Serge Treil, which is free on his webpage

[queen rampart]

LADW is like, determinants and applied linear algebra right

actually doing stuff with it

[fallow cypress]

No, it's a pretty typical intro to proofs linear algebra book

I mean it covers determinants, but every intro linear algebra book should

[queen rampart]

I thought it was the one that...well, is the opposite approach to axler's linear algebra done right

infamous for not touching determinants until the last chapter and being suuuper abstract

[fallow cypress]

The name of the book is a parody of Axler

[grand minnow]

Ye, the book I'm on right now covers both proofs and set theory so it's a good starting book

[fallow cypress]

But the book itself seems typeset a lot like Axler, so I think it probably draws inspiration from it

[queen rampart]

yeah I've tried to work through axler a few times and gotten halfway each time and I don't think I saw a single number lol

[fallow cypress]

LADW is similar

[queen rampart]

ah

[fallow cypress]

It's supposed to be a first course introducing a student to rigorous proof-based mathematics and abstract linear algebra

[spring cave]

Stewart is exactely as you described, with a few friendly proofs here and there. I'll keep going with Apostol then. Thank you.

[viscid atlas]

What's the difference between Spivak and Apostol?

[jovial parrot]

Axler?

[fallow cypress]

Axler's a good book, probably wouldn't be my choice for a first introduction

[jovial parrot]

Isn’t LADW Axler tho

What’s linear algebra done wrong

[narrow prairie]

For AIME the AoPS books are maybe sufficient, but you could also take a look at the Everaise handouts which are more up-to-date and more competition-oriented.
Everaise 1: https://drive.google.com/file/d/1B-gJJQUtcOKAaHeNGzRL1assWxEwtu0j/view (easier)
Everaise 2: https://drive.google.com/file/d/1MSfgZqRZghfVRn8csvcLMZYGIRaYHV1o/view (harder)
For USAMO you will need something more since it is proof-based and very different from AMC/AIME. EGMO by Evan Chen is the gold standard for geo while MONT is the gold standard for number theory. For alg and combi you can find many handouts online like the OTIS Excerpts.

The best advice there is to give for competition math, though, is to just solve lots of problems. There is no book that can replace experience.

[fallow cypress]

No

Axler's book is Linear Algebra Done Right

[jovial parrot]

Yeh

Ppl call it ladw tho since they don’t like his determinants

Wait a second

[rich sun]

LADW is something else

[jovial parrot]

Ru telling me LADW

What the fk

That’s a different book this entire time..?!!?

Wth

[remote sparrow]

https://www.amazon.com/Special-Relativity-Springer-Undergraduate-Mathematics/dp/1852334266

https://www.amazon.com/General-Relativity-Springer-Undergraduate-Mathematics/dp/1846284864

https://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390

[molten mason]

I'm crying. Yes lol

[plain barn]

gratest plot twist of my life when I searched "linear algebra done wrong" on google just to check

I thought it was a joke

[molten mason]

+1 to How to Prove It by Velleman. Then afterwards Linear Algebra by Friedberg personally

[jovial parrot]

Lol

I never would have thought

I wonder if Axler knows about this

Someone should ask

[fallow cypress]

Yes it's a different book

[fallow cypress]

Definitely

[jovial parrot]

I imagine Axler is a humorous person

[fallow cypress]

Thank you so much! :))

[queen rampart]

I think spivak is slightly less rigorous

[late light]

Try demon slayer

[crimson leaf]

I don't have anything for relativity but I have read parts of one of the Springer Undergrad Mathematics Series books and skimmed 2 other and I think they are pretty good. They're rigourous but not too demanding and I find the writing in all 3 was at a good level for a nice lighter book

[dusk wind]

this is pretty interesting

[fervent marten]

thank you so much. this helped a lot

[crimson leaf]

I think the napkin is pretty pointless for actually learning anything though and that you should just read some books instead

[tawny copper]

disagree

[crimson leaf]

Would you care to expand on that

[dusk wind]

reading generalized books is largely pointless, and with 900+ pages this is way off the mark

kinda why books on 'discrete math' is kinda eh because it's a bunch of different topics into one but too general

[crimson leaf]

I will clarify my point a bit in that I think it could be a good way to see some things or even refresh a few important details. But as for learning the topics I think most books are much better suited

[plain barn]

I mean napkin isn't really for learning I think it's about getting someone curious about a field

like you see "hm wonder what's this differential geometry is about" and then you go there and there's a lot of intuition and very simple exercises

and you go all :00000 that's so cool

[tawny copper]

Yeah, sure. For actually learning a topic one shouldn't (just) use Napkin (that is not why it was written either), but as a starting point it can be pretty useful

[plain barn]

and it actually gives stuff that's in the subject it's not just pretty pictures saying "imagine summing up a function..." it gives you some of the vibes of actually studying the subject

at least that was my experience, I only got interested in diff geo cus of its section in napkin

[dusk wind]

you could keep the outline and toss out all else and it'd be just as good

trying to be general about these subjects (literally explained the problem in the preface of 40 mins vs 40 hours) is not a good idea

it's interesting, but it's definitely not optimal

[viscid comet]

Any suggestions for texts to learn about hilbert spaces and their applications (while also not costing 9000 dollars)

[near jewel]

Any recommendations on discrete mathematics? I've heard Conrete Mathematics, by Knuth; and, Discrete Mathematics and Its Application, by Rosen, are some of the choices.

[manic cairn]

lang, real and functional analysis

[heady ember]

piracy

[molten mason]

Me patiently waiting every day for Springer to ship that book to me lol

[viscid comet]

9,,, years,,, later,,,

[mossy flume]

from the book sale?

how long ago did you order

mine didn't take that long

[manic cairn]

how long have you been waiting? it’s an extremely popular book that sells out often and they need to print more

yours might be in the next batch

[mossy flume]

damn I guess I ordered loser unpopular books

😔

mine came quickly

[manic cairn]

yeah, in 9.5 seconds

[molten mason]

I ordered 4 or 5 books on Christmas. I figured they have just been super busy with the holidays lol I've heard of people waiting weeks

I'm just so pampered by Amazon's same day and next day shipping

[manic cairn]

something that i’ve found over time is that i don’t actually need to buy any more books or even get more books generally; i haven’t finished half of the books i already have

same with lectures, or sheet music, with practicing

[molten mason]

Literally same lmao. And I won't finish these any time soon.

But they'll look great in my office

[mossy flume]

i haven’t finished half of the books i already have
and you're letting that stop you why?

[mossy flume]

same but my bedroom lol I don't have an office

[manic cairn]

because i am wasting time on something that isn’t actually useful by itself

math is not a spectator sport

[molten mason]

I think Stillwell's Elements of Number Theory is probably the only one of the batch I'll start soon-ish.

I'm still going through Friedberg

[mossy flume]

Stillwell is a good writer

I have his book Naive Lie Theory

cute little ready, very much enjoyed that

[manic cairn]

also, note this quote from Marilynne Robinson’s Gilead:

“I get much more respect than I deserve. This seems harmless enough in most cases. People want to respect the pastor and I’m not going to interfere with that. But I’ve developed a great reputation for wisdom by ordering more books than I ever had time to read, and reading more books, by far, than I learned anything useful from, except, of course, that some very tedious gentlemen have written books. This is not a new insight, but the truth of it is something you have to experience to fully grasp.”

[kindred bane]

Can anyone recommend problem based book for topology?

[sudden kindle]

Elementary Topology : A Problem Textbook by Oleg Viro et. Al

[spring marlin]

Can someone recommend some really good books for geometry? Starting from the very basic and going till graduate level, can be only theory with examples

[vast jackal]

AOPS

[strange vector]

Edwin Moise - Elementary Geometry from an Advanced Standpoint is really good

[spring marlin]

AOPS intro to geometry ?

[spring marlin]

Does it go up from the basics ?

[strange vector]

yes

[spring marlin]

I dont mind multiple books as long as they begin at the very basic and then go up till like graduate

[spring marlin]

oh thats nice, have u read it yourself ?

[strange vector]

i read its first 200-250 pages and was really good

[spring marlin]

i see

nice, thank you very much

[spring marlin]

did u supliment it with any problem solving book?

[strange vector]

no

it's self contained i think you don't need supplement books

[spring marlin]

i see

[spring marlin]

is it by felix klein

the one i see on amazon says "elementary mathematics from an advanced standpoint" and then geometry

[spring marlin]

or edwin moise?

[strange vector]

no, that one is another book.

yes Edwin Moise

[spring marlin]

ah got it

apparently its not available

sucks

[heady ember]

🏴‍☠️

sail the seas

[spring marlin]

man

i really wanted a paperback

[kindred bane]

Thanks

[junior isle]

What's a good follow up to jay Cumming's analysis book?

[trail hemlock]

omg i loveee that book

[junior isle]

Its really cool

But it's an introductory text

I have the physical book

[trail hemlock]

yeah me too

and the proof one

after it is tried to do the tao books, and i’m working through them p slowly

so if u are confident then probably those, and ofc if u are really confident there’s the rudin

[junior isle]

Ok thx

[daring lake]

walter rudin's PMA

[strange vector]

Rudin or Apostol's analysis, both are very good

also, not so popular but Amann & Escher real analysis is really good if you like abstractness

[magic moth]

try complementing Rudin with apostol's calculus

[solar ridge]

Does anyone have "free" books recommendations on Geometric Analysis? I don't have money and inflation are going nuts and the nearest library from here is 3000+ kilometers

[strange vector]

you can download free pdf's from libgen or z-lib

[solar ridge]

I tried but I don't find any

[strange vector]

https://libgen.is/search.php?req=Geometric+Analysis&lg_topic=libgen&open=0&view=simple&res=25&phrase=1&column=def

it listed 11 pages of books

[solar ridge]

That's not really the one I meant but thanks ig at least all this stress will probably be worth

[solar ridge]

How did you even download from libgen

[strange vector]

click one of the book and pick one of Libgen & IPFS & Tor or Libgen.li

[solar ridge]

I picked libgen.li now what

Whenever I clicked a button the web just bombard me with ads

[strange vector]

dont you use adblock? I use ublock origin and no ads

i can send you screenshots if you want

[solar ridge]

Thanks but it's downloading currently

[strange vector]

nice

[strange vector]

if you have trouble finding books, you can send me a pm. I can't afford books too so i download them from libgen or z-lib

[solar ridge]

What's a pm

[marsh ingot]

Cant say that here

[strange vector]

message

[solar ridge]

dm?

[strange vector]

yes

[solar ridge]

Oh ok thanks

[solar ridge]

You thought it's easy being a student who could barely afford living and needed 500.000 to buy just one book?

[marsh ingot]

Didnt say anything about buy a book. Only that here on the server dont support piracy

[solar ridge]

It was piracy?

[gray gazelle]

what should i read after serge lang first course in calculus?

[daring lake]

Maybe you can try Real Analysis

[gray gazelle]

oh

which book would u recommend

for it

[daring lake]

Actually I do not know what serge lang covers

[gray gazelle]

i think serge lang do have

real analysis

[marsh ingot]

On #math-discussion ppl told you not to discuss about that

[gray gazelle]

oh u mean in the calculus

book

[marsh ingot]

Here we just recommend books, they way you obtain them is by your own

[solar ridge]

Well I didn't know it was because of piracy

[daring lake]

I recommend Rudin's Principles of Mathematical Analysis

[marsh ingot]

Its on the server rules

[gray gazelle]

its against discord TOS too

[solar ridge]

How did I know libgen was piracy

[daring lake]

are you just studying for leisure, or are you in any degree program?

[gray gazelle]

oh sure! 👍

own my own

yh

no degree program

[daring lake]

I see, then yeah, real analysis is a good place to step into slightly more advanced, proof-based subject.

[gray gazelle]

am i gonna need to read some book on proof writing before jumpin in analysis

[daring lake]

or you might also do Linear Algebra

[daring lake]

I would say pick up on proof writing by reading proofs
I didn't read any proofs book. Just picked up from reading existing proofs from real analysis books

[gray gazelle]

oh

thanks for the advice! i appreciate it

[molten mason]

Yeah I've heard good things, and of course I have the pdf of it already, I'm excited for it

[molten mason]

That's a good quote.

[heady ember]

Rudin may be am unsuitable choice if you're new to proofs.

It's notoriously terse and unpedantic.

[manic cairn]

unpedantic?

i think i can see what you mean, nvm

[queen rampart]

oh dear god no

please for the love of god no

[queen rampart]

apostol's calculus, abbott's understanding analysis, zorich's mathematical analysis, tao's analysis

if you want to challenge yourself, pugh's modern analysis

for the love of god do not do rudin

[heady ember]

Schroder is great too

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

[gray gazelle]

oh lol 💀

[gray gazelle]

nice

[queen rampart]

rudin is infamous for being incredibly thorough but also a) really hard and more importantly b) really bloody boring

[gray gazelle]

I see

[glossy zealot]

People recommend Jay Cummings for beginners in analysis as well

[heady ember]

"boring" is probably in reference to a lack of exposition, I would suppose.

rather than boring content

[daring lake]

skill issues

[queen rampart]

yes

[daring lake]

Good one

I like bartle too

[glossy zealot]

Something to note about these books is that they do not usually have the same structure

I looked up few books, while they have similar core content, they may approach things differently

[queen rampart]

some of them will do analysis only on R^n and some will dive straight into any metric space

[glossy zealot]

So it is best to read the outline to see if it fits the course you are taking

[daring lake]

I recommend reading several books if you have the world's time

I found Bartle + Rudin to be an amazing combo

[glossy zealot]

Yea I would like to have several books too, and at least one verbose book cuz I like the details

[daring lake]

I have like 7 elementary analysis books now

I have only solved 2 though

[glossy zealot]

There’s free analysis books too I think

One by Trench iirc

I have never checked it though

[queen rampart]

tao's

[glossy zealot]

Analysis 1 is free?

I did not know that

[queen rampart]

both 1 and 2 are

[daring lake]

Tao,.. idk.... it felt too verbose

[glossy zealot]

Very nice

Tao’s book will probably take a lot of chapter before the actual analysis part

[queen rampart]

it goes from literally nothing to analysis

if you don't want that, you can start at chapter 5 (or 6?)

[glossy zealot]

I do appreciate how thorough it is

It is better to have good foundation

[queen rampart]

but if you've not done proving stuff around peano axioms then it's nice

[molten mason]

He also has a books on Introduction to Linear Algebra, Undergraduate Algebra, and Undergraduate Analysis

[manic cairn]

i learned to write proofs from serge lang’s Undergraduate Algebra and (after that) munkres’ topology

[manic cairn]

note that there’s both Linear Algebra and Introduction to Linear Algebra as separate books

same with Algebra and Undergraduate Algebra

[molten mason]

Yup

Big differences between them lol

[manic cairn]

and Undergraduate Analysis vs Real and Functional Analysis

the difference between linear algebra and intro to linear algebra isn’t that big

the difference between the undergraduate algebra and analysis books vs the graduate ones is huge

in theory the graduate versions of both are self contained

but in practice they would be extremely difficult if you don’t know any algebra/analysis beforehand

[gray gazelle]

oh

[dapper inlet]

Where can I find a good Calc 2 book ?(i can't find the channel on mobile)

[gray gazelle]

i should try goin through undergraduate algebra

[dapper inlet]

I swear there was one above

[hard egret]

hi

[lapis arch]

I want a book for olympiads

[manic cairn]

even chen’s egmo and anything by andreescu

[lapis arch]

can I get pdfs?

[civic valve]

Just watch 200 integrals, that's enough i guess

[gray gazelle]

its against discord TOS

[manic cairn]

not a book, internet data heavy

[lapis arch]

no like the list of books

[dapper inlet]

Is that a YouTube channel lol

[civic valve]

YouTube videos

17 hours kinda i guess

[dapper inlet]

Is that all calc 2 is?

[gray gazelle]

black pen red pen

[civic valve]

Only integrals

[lean pagoda]

A bit of a non-answer, but since you mentioned that you were self-studying and not in a university program, I think the best suggestion would be to simply read what interests you (assuming that it roughly matches your current level of mathematical maturity)

[civic valve]

what also in calc 2?

[civic valve]

Except integrals

[lapis arch]

I was about to say that

[dapper inlet]

I see

[lapis arch]

series

sequences

[civic valve]

Ah, doesn't matter, it's like Sigma?

[civic valve]

I just know when sequence is divergence or convergence

[lapis arch]

the notation, yes

[civic valve]

Nothing more

primitives i guess to but it's almost the same as integrals

[lapis arch]

I mean I am not American

so idk what's calc 1

[civic valve]

me too

[lapis arch]

2 or 3 for that matter

[civic valve]

Calc 1 is derivatives and limits

I guess

[dapper inlet]

Yeah it ends at an intro to intgerals

[molten mason]

I have Friedberg for my undergraduate LA, I have the PDF for Lang's LA books but haven't gone through them too seriously.

The Algebra and Analysis Lang books I have the PDFs for all 4 and have very very lightly skimmed all of them. Trying to actually go through his Undergraduate ones currently though. His Algebra I probably won't be going through for a couple years maybe except for the chapters on Linear Algebra. His Real and Functional Analysis I plan on doing after Undergraduate Algebra and Undergraduate Analysis These 3 books are my 2024 goals. If I have time then my plan after those 3 is his Complex Analysis

After I have all that down is when I want to start expanding to non-Lang books in those topics and more into Topology in general.

[civic valve]

I just watched 100 limits, 100 derivatives, 100 integrals, i guess it's enough for me, we'll start calc 1 and 2 in next-next month

[manic cairn]

the linear algebra chapters of algebra is just a lot of representation theory

don’t plan what you read after the book you haven’t read yet

it’s impossible to predict

[molten mason]

Not set in stone, but still like having a plan.

[remote sparrow]

carothers. you may also look into Metric Spaces by magnus or Metric Spaces by o'searcoid. alternatively, you could jump into axler's measure theory or a variety of measure theory books that only assume single variable analysis.

[remote sparrow]

do you have detailed thoughts on zorich?

[hasty eagle]

No selfroles matching notdying.
See ,selfroles --list for the list of valid selfroles.

Jan 4, 2024, 6:32 PM

Removed the studying! role from you.

[queen rampart]

my preface, and the size of pile of salt you want to take it with, is I have tried to properly self-study and get a few chapters into many books and then spend an equally long time looking for "best book to study X"

so I've certainly started a lot of analysis books

I keep going back to zorich because: it's big. it covers not just R^n and has more than just a brief mention of multivariate calc, but it starts nice and slowly unlike e.g. rudin

[remote sparrow]

what do you think of the exercises

[queen rampart]

fine? good?

[remote sparrow]

numbpy would disagree

[rare estuary]

Is the title Real Mathematical Analysis or is this a different book by the same author?

[remote sparrow]

that's correct

[manic cairn]

which one?

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-319-17771-7

[queen rampart]

yes that's the one I WAS THINKING OF

[manic cairn]

is this the same book you were referring to or a different book by the same author

[queen rampart]

idk where I got "modern analysis" from

[rare estuary]

Np

[remote sparrow]

i was talking about zorich

but xenophon wanted to ask about pugh

[quasi haven]

Hi chat, But recently I want to know about general maths, the story of maths.

Is there any book which gives mathematical pleasure reading about these? May not be technical but more like something to read during coffee break and in park.

[hasty eagle]

You already have the selfroles studying!, do you want to remove them? (y(es)/n(o))
(Tip: use ,iamnot to remove roles without this prompt.)

Removed the Talks role from you.

Session timed out waiting for user response.

Jan 4, 2024, 10:09 PM

Removed the studying! role from you.

[zealous coyote]

One good book is a graphic novel called Logicomix

[manic cairn]

mathematics from the birth of numbers by Jensen is good for this

the cover is a close-up of the rhind papyrus

[vapid zodiac]

does anyone have the download of the algebra and trigonometry book 2 solution key?

[trail hemlock]

this aint no piracy server

if its a textbook look on quizlet all answers are always there for hs math textbooks

[narrow relic]

I thought the way he writes proofs in the graduate analysis books is annoying, it's like he tries to use as little notation as possible.

His Linear Algebra book is one of the best I've seen although it leaves out some key stuff that I luckily knew from elsewhere.

[near jewel]

Posted this before, but looks like chat drained it -

Any recommendations on discrete mathematics? I've heard Conrete Mathematics, by Knuth; and, Discrete Mathematics and Its Application, by Rosen, are some of the choices.

[gray gazelle]

yeh knuth book is good

[cobalt badger]

As a first exposure to Abstract Algebra (specifically group theory), what book should I go for?
I was thinking Fraleigh and Brand over Dummit and Foote for a first exposure, but what would you guys recommend?

Also, lecture notes would be cool too

[dusk wind]

https://amazon.com/Discrete-Mathematics-Applications-Grami-Ph-D/dp/012820656X
https://discretemath.org

[queen rampart]

fraleigh is nice and easy

hungerford is nice
dummit and foote isn't too hard at all it's just very very dense and a little boring

artin is good if you really really like linear algebra

[cobalt badger]

Ok great, thank you!

[white laurel]

which of these books are best for learning topology as a complete beginner?

K. Jänich, Topology, Springer
pr
J.R. Munkres, Topology: a first course, Prentice-Hall

i am familiar with quite a bit of linear algebra an multivariate calculus so that bitt should be fine

[livid ermine]

Does anyone here have experience with DN-cohomology for tropical semirings?

[dusk wind]

Fundamentals of Abstract Algebra by Malik would be good if not for the font

[livid ermine]

I think munkres is a very readable good.

Only background you need is knowing basic proofs.

And knowing very basic set theory.

Like read the first chapter in munkres, it contains the necessary stuff you need to know. If its not extremely difficult for you, I think munkres will be very nice.

[white laurel]

ill check it out ty

[pliant falcon]

What's DN?

[white laurel]

domain network

you're welcome

[pliant falcon]

OK phew

Worried there for a second

[pliant falcon]

I'm unapologetically stealing this

[livid ermine]

deez nuts cohomology

😆

[pliant falcon]

[livid ermine]

feel free to amend if you have more believable jargon

[scarlet saffron]

Heya', can you recommend a book about numerical methods for systems of differential equations?

[gray gazelle]

How good is Kolmogorov Fomin (Intro to Real Analysis) as a first book on analysis for someone who is fairly comfortable with proof writing? How does it compare to, say, Baby Rudin in style and content?

[sage python]

It's quite good

"Kolmogorov is so much better than Rudin" me after I started reading

[sage python]

@gray gazelle to elaborate, since I had to head out

K&F I think has smoother/nicer writing. I think I remember its level being pitched somewhat awkwardly. It talks about compactness, but then is like "So you remember Heine-Borel right?"

Also the terminology is old

[rare estuary]

Since you're handing out RA wisdom, do you have an opinion on Pugh's Analysis book compared to Rudin or Browder?

[sage python]

Pugh feels kinda awkward to me somehow, but it has a religious fan base. Probably better for multi than Rudin's nonsense take on differential forms

I think Browder feels like the best of the trio. Basically Rudin but with multi replaced by a more Spivak Calc on Manifolds pov. It does wait to go into full blown topology until it does a full treatment of stuff on R (I could be swayed both ways on whether this is a good idea), and it does measure theory before multi so that its multidimensional integral is Lebesgue (very good choice)