book-recommendations

[sage kelp]

Real Analysis by Pons
Basic Analysis I by Lebl
The Way of Analysis by Strichartz
Introduction to Real Analysis by Bartle and Sherbert

[remote sparrow]

vladimir arnold is not a "practical" approach

as in it will not teach you how to solve basic odes

[tender cedar]

hey

I'm looking for books to study multivariable calculus but focused around machine learning problems and that sorta thing

bonus if it's a proof based book

but I'd like it to have some applications towards machine learning as well

[pale badge]

I see, so George Simons is the way, I did read a little of each and I noticed that too, but wanted to ask before committing

[remote sparrow]

@sturdy shore hrbacek and jech is print-on-demand now

i'm done with buying new books

only gonna buy used now

[remote sparrow]

i mean if publishers are only gonna sell pods, at least have the decency to sell a softcover edition

at least those are easier to lay flat

[buoyant vessel]

|| imagine not pirating||

[remote sparrow]

ofc one of the fucking pages is loose

guess i'm returning another book

[remote sparrow]

note: do not buy used books from half-price books via amazon

let's just say their appraisal of a book's condition is a little...generous.

[tepid prairie]

All my books have been reused and they always look like they've never been used lol.

[remote sparrow]

i bought a cheap copy of abramowitz and stegun from HPB, and i won't be returning this one, since the book is bound in signatures, so i could get this sent to a bookbinder to rebind it if i want to, but right now it's good.

[remote sparrow]

yeah i just got a copy of browder in very good condition and it is sleek af

[tepid prairie]

They've always been perfect for me.

[remote sparrow]

good has been anywhere from "good" to "very good" for me

[tepid prairie]

All of mine (10+) have been excellent. Maybe no one uses Dover books in the Library's or wherever they get the used goods from.

[remote sparrow]

maybe

a lot of my collection is not dover, though

and i mostly buy dovers new anyway

[tepid prairie]

Maybe a marketing scheme. They say used for the cheap people and just send you a new one anyway, idk.

[tulip saffron]

Does there exist something like a roadmap to statistics or a book list?
I know the basics of mathematical statistics, but when it comes to statistical analysis, statistical computing and so on I know nothing about them

I really want to learn these. And I guess I want to reach the level of a master student in statistics. I do prefer books with R codes but I know it gets harder to find these when the knowledge gets deeper

[little summit]

better solution: free pdf /j

[remote sparrow]

i'm aware

i just prefer physical books

[crimson leaf]

I got mine on abebooks from them it was much better than expected but probably a crapshoot

The one near my house usually has a few "upper level" math books in stock

[remote sparrow]

both of my recent books were from hpb

one was the fucked up schroder copy ("""very good""" condition btw) and one is the acceptable abramowitz and stegun copy (also """very good""" condition)

although they definitely misrepresented the condition of the book; it's good condition at most

[remote sparrow]

there are no local hpb's near my house

[hollow shore]

@remote sparrow do you know where I could get a clean TeXed up digital copy of Hoffman and Kunze?

(if there exists any)

[lime sapphire]

I doubt there is any

I'm sorry but you'll have to get used to old scanned pdfs

[fierce hedge]

The scanned versions are okish enough and you might be able to save a lot by buying the international edition

[karmic thorn]

Looking for an introductory textbook on differential geometry that talks about tensor calculus and geometry of curves and surfaces at length, although doesn't necessarily address smooth manifolds or similar in as much depth.

I can find plenty of books that cover the geometry of curves and surfaces but my class is taking an odd/perhaps physics-brained route of going through tensor calculus first, which is not addressed by any of the books I've looked at

[vocal notch]

yo yo !

im looking for huge stats book!

[thick sigil]

Guys i am having a problem with PDF’s. When i try to download Young and Freedman’s University Physics form libgen on my İPad, throughout the book images and illustrations are missing and blank. But when i download it to my android phone there is no such problem. How can i solve this problem?

Like this, the illustration in the left is missing and just blank

[stable hawk]

hello can anyone recommend any books to understand the topology aspect taught in complex analysis/ to better understand complex analysis in general?

[magic raft]

https://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf

maybe youll find something appropriate there

[fierce hedge]

Piracy websites are a strict no here. It violates Discord's tos

[remote sparrow]

i have not seen anything

[remote sparrow]

i assume do carmo doesn't fit this bill? i haven't looked thoroughly at tapp's book, but it might interest you

[karmic thorn]

I'll have to look at do Carmo again maybe, but I don't think he talked much about tensors

I'll look at Tapp, thanks

[scarlet steeple]

hey looking for a book that covers relations, equivalence relations and particularly partitions extensively in any given chapter or section

[remote sparrow]

many intro to proofs books do so

[scarlet steeple]

perfect

have anyone in mind that is particularly good im not looking for baby explanations but just definitions theorem style with good excercises

@remote sparrow

[remote sparrow]

maybe chartrand, polimeni, and zhang's book

[scarlet steeple]

ok gotcha thanks

[elder moth]

I'm reading the Group Theory textbook review section of the pinned comments. I have some questions, if anyone would abide.

[elder moth]

1. Some of these books have "linear algebra knowledge recommended" qualifications, and I'm not sure how much linear algebra is recommended. Are there any more accurate qualifiers? Would vector calculus be sufficient, or are we talking about like a proofs-based Linear Algebra experience being required?

2. I'm trying to build a sort of pyramid to string theory, and my overwhelming urge is to start at group theory and then move through topology and algebraic geometry and then do GR/QFT on the physics side afterwards before touching String Theory. My rationale is that I'd be able to handle the material better when I figure out what some of the more esoteric concepts in QFT imply from a math perspective. Is this a sound procedure?

3. I'm trying to build this pyramid in a way that's robust enough to allow me to push out into some other hobbies, such as jumping into category theory or maybe doing topology-based neural network stuff. Are there any additional recommendations based on this?

Assume I've done your equivalent of the freshman level math proof course and know enough real/complex analysis to not be entirely lost

[narrow fiber]

I cant say much about your general plan because im not so deep in physics but sooner or later you will need linear algebra

and my advice is to learn it sooner

[elder moth]

How much linear algebra?

I'm asking if like, getting up to using it to solve PDEs is sufficient, or if I need an actual linear algebra proofs textbook

Do I just need to know what a matrix is or should I be able to prove things about vector spaces? If it's the latter, how deep do I need to go?

[remote sparrow]

linear algebra is just extremely useful in general

[elder moth]

I understand as a tool it's useful, but do I just need to know how to manipulate the objects to start one of these group theory textbook recommendations that says "linear algebra recommended" or do I need to be able to prove things about these spaces?

Cause if I do need to do proofs and such with linear algebras, I'm just gonna start with Artin, but if I don't need to be able to do that I'm gonna pick one of the ones that just goes in with the assumption I can like Jacobson or Dummit & Foote

[elder moth]

I'm just gonna do Artin and maybe graze over the obvious parts of chapter 1

@sharp yew You didn't need to delete your stuff, you can have the channel again

[spare ridge]

what is the 'morally correct' approach to representation theory, in particular that of lie groups

[sage python]

What do you mena by approach here?

[woeful ravine]

It depends, for basically all advanced math you need a basic foundation of linear algebra

[spare ridge]

i mean it in the usual sense, i'm not at all familiar with representation theory so i'm guessing there are different approaches e.g. studying representations of algebras before groups and so on

[heady ember]

Enderton's Elements of Set Theory jkjk don't

[buoyant vessel]

why not

im reading it

rn

[woeful ravine]

If you are looking for something that gives a good introduction on representation theory, https://math.mit.edu/~etingof/replect.pdf is good

[heady ember]

One doesn't necessarily need to learn axiomatic set theory. I am, but just for fun.

[buoyant vessel]

ok

clerk recommended em that book

and its fairly basic

@rustic ivyread it now

[heady ember]

Hm idt Clerk replied to jayz?

[buoyant vessel]

no clerk recommended the book to me

months ago

[heady ember]

Oh I thought you meant the guy I was referring to since you used "em"

[buoyant vessel]

" I would say look at the book by Enderton on set theory and just skim through it to see how comfortable you are with the ideas, first.
An intermediate book is "A Mathematical Introduction to Logic", also by Enderton, which covers more than just set theory.

If you are able to read the Ebbinghaus, Flum and Thomas book then go for it. Actually, I prefer the book The Foundations of Mathematics by Kenneth Kunen, but they are both good. The book by Kunen has a very heavy focus on set theory but it is still a good introduction to mathematical logic generally.

Another book which you might find more interesting/fun is "Computability and Logic" by Boolos. It's good to mix it up, it goes in a different direction than set theory. "

clerk always responds so much text

cute

[heady ember]

In the context of how much set theory there is, yes. However, if one is not interesting in learning foundations, axiomatic set theory is basically unnecessary most of the times.

[buoyant vessel]

foundations is so cool

[heady ember]

And also, foundations first is generally regarded as a bad idea.

[buoyant vessel]

foundation dont seem to be useful

tho

[spare ridge]

can i skip rep theory of finite groups in these notes if i just want to do reps of lie groups

[woeful ravine]

well if you currently have very little knowledge on representation theory, i would say no

[spare ridge]

why

[woeful ravine]

well what is your goal?

[spare ridge]

rep theory of lie groups

[woeful ravine]

i would recommend a foundational knowledge on rep. theory

If you want to focus more on lie groups, i would recommend Fulton and Harris's book on representation theory

but it is not as good as an introductory text

a good percentage of the book is about lie groups

[narrow fiber]

fulton harris is great yeah

I think it's good to go through at least its first 3-4 full chapters to get a general sense of rep theory

[gusty smelt]

I was not a fan of etingof

it was a bit like, unfocused for me imo

lol dami remember etingof

[sage python]

What do you mean John? We had a smooth ride with that book 🙂

Absolutely no rage 🙂

[narrow fiber]

I have mixed feelings on etingof and by that I mean I'm also not a fan largely

I love the bit where he goes like

Derive the entire rep theory of sl(2) or something in like 7 exercises

[gusty smelt]

But yeah just like

read any Lie group/algebra book

they have p good stuff on rep theory of it

usually

I learnt a lot from bump "lie group"

[narrow fiber]

Bump is what my prof says he teaches his more advanced material from

[gusty smelt]

based

[narrow fiber]

He likes knapp a lot because like. knapp was his thesis advisor which is a very fair reason lol

[gusty smelt]

lol nice

[elder moth]

Yeah, gonna do Artin, then an algebraic geometry text, then a topology text, then Susskind's theoretical minimum to catch up on the bits of physics I'm missing out on

[remote sparrow]

algebraic geometry before topology

[sturdy shore]

zariski rolling in his grave

[foggy relic]

Susskind bad

[foggy relic]

In addition to FH, Serre is also good

Hall is OK depending on what you want

[gray gazelle]

Just got my Copy of Reinhard Diestel's Graph Theory Book

This is based

[swift dome]

any good problem books specially for matrices

[scarlet steeple]

anyone know any good books that has a chapter on Turing machines?

[remote sparrow]

i think sipser and kozen both should have one

most intro to theory of conputation books should

[remote sparrow]

i don't think there are problem books on matrices per se, but you may be interested in garcia and horn or horn and johnson

[scarlet steeple]

thanks again

[azure salmon]

any recommendations for good beginner calculus (calculus 1) that can help a bit and aren't too hard to understand?

[alpine rover]

Hopcroft, Motwani, Ullman - Introduction to Automata Theory, Languages, and Computation

[azure salmon]

integrals specially aren't my strong suit

[elder moth]

Well that's just more evidence that I need to read the books

[sage kelp]

Thomas’ Calculus

[cinder tundra]

idk about books, but there are a few resources for those, what do you mean by "matrices problems?" like problem solving, challenging linear algebra problems in matrix form? or just to learn the basics

[cobalt arch]

Any axiomatic books on combinatorics?

[ancient grove]

Any recommendation for a counting Principles books for beginners that is focusing on the Proofs

[azure salmon]

There are like 15 different editions are they essentially the same?

[solemn rover]

No. Calculus is completely reinvented every five years. The calculus taught in 2005 is so obsolete right now that even bringing it up is barbaric

From 2010-2020 we collectively switched from Leibniz differentials to Newton's fluxions

but then that was too confusing so we switched back.

[swift dome]

Challenging linear algebra problems

[sage kelp]

Yeah, just use any edition

[solemn rover]

Topology is fairly unimportant as a prerequisite for basic algebraic geometry of irreducible varieties over an algebraically closed field. It's much more important to know commutative algebra.

[fluid bay]

shafarevich is an example of an AG book that doesn't assume any topology

[narrow fiber]

true but it is very classical and not in line w the modern AG treatment from my understanding

I haven't studied from it at all though

[fluid bay]

that's true, but its not so classical it doesn't use topology, it just doesn't assume any. It takes an approach like "define a closed subset of affine space to be the vanishing set of some set of polynomials", and "we claim closed subsets are closed under finite union and arbitrary intersection" as opposed to something like "the zariski topology indeed defines a topology on affine space."

i.e. it just tries to be a little more self-contained than other AG texts

[cinder tundra]

you could always look at the berkely prelims, though going through all those papers for specifically matrix qs may be a pain. There's a book literally called "Linear Algebra: Challenging Problems For Students." I have access to some papers in my college that they use to select the best maths undergrads for 5 year scholarships, there are a good few fun matrices problems there.

[hasty turret]

Spivak calc

[molten linden]

is advanced engineering maths by erwin kreyszig a good book for ODEs?

our instructor is teaching us diff equations from that

[hasty turret]

I guess depends on your purpose? I suppose it is good for engineering

[molten linden]

it's a CS degree

[hasty turret]

Prob overkill

[molten linden]

aight

I'll use that

[gray gazelle]

why do u have my old about me 💀

[hasty turret]

What is that hex dump about

[gray gazelle]

i just put it in my about me randomly; idk why people copy my about mes so often

[hasty turret]

wdym by advanced exactly

[heady ember]

So, in other words, computations.

[vocal notch]

looking for book that will help me understand the methods and stats that are used within studies

[remote sparrow]

https://math.stackexchange.com/questions/1041720/great-books-on-all-different-types-of-integration-techniques

https://math.stackexchange.com/questions/1096701/nice-book-on-integrals

https://www.amazon.com/Almost-Impossible-Integrals-Problem-Mathematics/dp/303002461X

[mystic orbit]

we don't call those advanced problems

we call them jee brainrot

@coarse frost

[coarse frost]

What the hell

[mystic orbit]

both real and complex analysis?

see pins, prolly

@gray gazelle actually, mb

those aren't introductory books

those are for measure theory/functional analysis

for intro real analysis there's browder, abott, pugh and ofc rudin

I've only done rudin tbh

[gray gazelle]

real and complex analysis by Rudin

[mystic orbit]

but I've heard a lot of good stuff about all of them

abott is more gentle whereas rudin is super terse

pugh is weird but in a good way

[gray gazelle]

I mean, in what other book do you have both real and complex analysis

I think it's usually split into two books

[mystic orbit]

I think they wanted recs for both topics

not necessarily a single book for both

I see

I meant principles of mathematical analysis by rudin btw

real and complex analysis isn't an introductory text

[gray gazelle]

why not

I think its fine

[mystic orbit]

measure theory isn't typically an intro material

measure theory is like

grad stuff (somehow)

[gray gazelle]

if its a 3rd course then it'll probably be there anyway

[mystic orbit]

lmao

yeah

well

I'm getting confused by bonsai's needs tbh

but I think they figured it out

[gray gazelle]

I had measure theory in undergrad

it's fine, just a little more abstract course

[mystic orbit]

that is indeed a common occurance

but then again

some people do their whole undergrad without seeing general topology so

[gray gazelle]

I think that's normal

[mystic orbit]

[gray gazelle]

general topology was an additional course in undergrad for me

they've done metric spaces

as the standard course

[distant spear]

what does general topology include?

[gray gazelle]

general and topology

are you asking what it is or what does a standard course consist of

[distant spear]

latter

is it just a point set topology course

or does it include alg top as well

[gray gazelle]

yeah general topology and point-set topology are the same thing

it can include some fundamental groups at the end of the course, but not always

so no AT

[distant spear]

i see

[gray gazelle]

general topology sounds like a stupid name
because it's "general" but doesn't include point free topology

for example

there's homological algebra

you have a lot of different kinds of homologies (and cohomologies), some for topological spaces

[mystic orbit]

[mystic orbit]

the power of habit, 100%

it's my favourite self improvement book ever

[mystic orbit]

uh

I...

dunno

it's a book

books have PG rating?

wat

who tf is hamza? lmfao

I do no know hamza

I see

I do not want to know hamza

I (unfortunately) have heard about him

no changing that

(unfortunately)

yea

hmm

<@&268886789983436800>

this kid is defenitely younger than 12

[glad prairie]

damn darq talking to himself...

[mystic orbit]

damn it, I should've screenshotted the convo first

that was mildly funny

[mystic orbit]

hmmm

do you smell that?

[glad prairie]

[mystic orbit]

(sniff) (sniff)

I smell copium

(get here faster next time)

[glad prairie]

my finger was literally on the ban button

[gray gazelle]

books and chill

[neat spindle]

May I know which discussion in books-prototype should I look into if I am studying a course that includes First and second order differential equations, initial value problems, series solutions, Laplace transform, numerical methods, boundary value problems, eigenvalues and eigenfunctions, Sturm-Liouville theory. Or do anyone have any book recommendations? Thx🙇🏻‍♂️

[remote sparrow]

boyce and diprima or most other commercial ode books with bvp

[neat spindle]

Wait actually I have 3 math course

1. Differential Equations
   Topics: First and second order differential equations, initial value problems, series solutions, Laplace transform, numerical methods, boundary value problems, eigenvalues and eigenfunctions, Sturm-Liouville theory.
2. Mathematical Analysis
   Topic: Sets and functions, real numbers, limits of sequences and series, limits of functions, continuous functions, differentiation, Riemann integration
3. Applied statistic
   Topic: A systematic introduction to statistical inference, including the necessary probabilistic background, point and interval estimation, hypothesis testing.

I am pretty much f*ked cus my professor notes are bullshit and they don’t even provide textbook recommendation or references

[remote sparrow]

real analysis look in pins and also here: #book-recommendations message

applied statistics, probably wackerly, mendenhall, and scheaffer

[fallow cypress]

If you're okay with websites, then try paul's online notes

(if you're not doing a proof-based course on odes)

[neat spindle]

I am okay with anything except notes from my professors

[neat spindle]

Thank you

[sage kelp]

I had never heard of Schroeder. Is it good?

It looks like a lot of content for like 500 pages

[remote sparrow]

ask daminark

it seems fine

https://www.maa.org/publications/maa-reviews/mathematical-analysis-a-concise-introduction

also see here

[narrow relic]

I think it's too concise to be really useful but I never actually read it.

[sage python]

Schroder imo is quite gentle by the looks of it

Like it even has "proof hints" that are rather prevalent in the first few chapters

[remote sparrow]

it's possible that while it may be handholdy, it may still feel more like lecture notes than a gentle book proper

[sage python]

Maybe? I wasn't quite responding to anything with that lol, just mentioning to aleps041 that the standout feature to me is that it seems to cover more than almost any other intro analysis book

And arguably starts as easy or easier

[sage kelp]

I have a love hate relationship with the MAA textbook reviews

In a sense it looks kind of similar to the way of analysis, but if I remember correctly that book has something around 700 pages, so kind of similar length

But this book is very attractive indeed because of the number of topics it covers

Are there any other similar intro analysis books?

[sage python]

Most books that cover this much material I feel like are a good bit harder

[sage kelp]

Who is daminark?

[remote sparrow]

look above you

[sage kelp]

Oh lol

Nvm

[tulip saffron]

please recommend me a best textbook for linear algebra
and hopefully I dont need to read a second book after that

[orchid mortar]

Friedberg Insel Spence

[tulip saffron]

is this THE book?

[odd stump]

yes

but its long and useless if you don't do the practice problems

[tulip saffron]

it doesnt seem to be a very long book?

[wheat remnant]

Is there a huge difference from the 3rd Ed to the 4th?

[narrow relic]

It's hard to find one that you wouldn't have to use a second book later, in my opinion

[tulip saffron]

do you have any recommendations for a book list? it is OK more than one book

[narrow relic]

I got a lot out of this one: https://archive.org/details/linearalgebramod0000pool_s5q6 (Linear Algebra: A Modern Introduction, 3rd edition by David Poole)

It teaches only the R^n case but that's fine if you are just starting out.

[tulip saffron]

thank you!

[narrow relic]

You're welcome, let me know how it goes, I'd love to hear your experience with it

[tulip saffron]

I will go with friedberg's book tbh

but it seems not longer than linear algebra with applications

so I wonder if it is THE book

[narrow relic]

Sure, it's more advanced than the one I mentioned I think

You should probably try to avoid finding just one book. One book will never have everything you need that is also presented in the best way for each. It's normal to have to combine multiple sources

[sage python]

FIS covers a fair bit

[narrow relic]

Browsing through that book brings back bad memories for me; I first saw it when I didn't have the "mathematical maturity" or whatever to read it

Just saw the typesetting and cringed

So I guess I'm biased against it because of that

I also hate "baby Rudin" for similar reasons

[tulip saffron]

yeah thats true

[narrow relic]

Also your view of what books are good at different levels will evolve (at least it has for me)

[tulip saffron]

Im finding the best book to begin with, actually I have learnt linear algebra before, but I hate my textbook (written in chinese)

[narrow relic]

Okay I see. I recommend rather than try to plan what you'll use perfectly in advance, you should actually start reading one of these books and see how it goes. Then if it isn't working for you, try another one.

If you are finding a book doesn't work for you, remember that it might not be your fault at all, it has to do with the fit for your way of thinking and also your background, etc.

[tulip saffron]

I gave up around jordan normal form of that book I think

[narrow relic]

Oh, you got pretty far then

The Friedberg book might work well for you then since you already know a lot about what is going on in linear algebra

[tulip saffron]

thank you!

[narrow relic]

So just get started on it 😀

[tulip saffron]

is this book so classic?

I saw all of u discussed about it

[narrow relic]

I have no idea, it was used in some classes at the university I went to

[tulip saffron]

thank you! I will give it a try

[sage python]

@tulip saffron how's your background in proofs actually?

And how much do you already know in linear algebra?

[tulip saffron]

what do you mean by proof? cause my background was taught in chinese

[narrow relic]

https://zh.wikipedia.org/wiki/數學證明

[tulip saffron]

I think I know the matrix, I gave up around jordan normal form, and I think Im pretty weak at linear transformations, linear space etc

or what space it is called

[sage python]

Like are you used to proving theorems in mathematics

[tulip saffron]

I welcome proofs very much

[tulip saffron]

I like it, and have done a lot in analysis

I think I can handle like the first 5 chapters

but get pretty weak at chapter 6 and 7

[narrow relic]

This book actually looks better than I remember, heh

Maybe I'll take a look at it again myself sometime this year

Thanks for posting that ToC.

[remote sparrow]

just found out judson has written a draft of an ODE book

looks like it has a lot emphasis on programming and modeling, which i approve of

there's no damn point in remembering all those silly little tricks

[narrow relic]

I tried his Abstract Algebra book, I thought it was okay

I hated the way ODE was taught in undergrad

[remote sparrow]

http://faculty.sfasu.edu/judsontw/ode/

check it out and see if it's interesting

we only need to hear about the trick once and maybe see a worked example, but only enough to know how someone implemented it on a computer

graphs and other qualitative analyses should be emphasized much more

[narrow relic]

Thanks for the link. I'm a bit too tired to process it right now

[remote sparrow]

also existence and uniqueness of solutions becomes a much more important result because you aren't going to work with nice toy functions

blanchard, devaney, and hall is another ODE book that emphasizes phase portraits, direction fields, graphs, and other qualitative analyses

i really hope the ODE curriculum gets updated

[orchid mortar]

Open source

[fluid harness]

I need to prepare for a maths olympiad

[gray gazelle]

eva is based '

[gray gazelle]

Does anyone know a calculus book that is rigorous enough but not too difficult? I tried Spivak and Apostol but I can't do the exercises in those books at all, exercises in books like Stewart are easier but its lack of rigor creates gaps in my understanding. So is there any books that is between Stewart and Spivak?

[heady ember]

Schroder might be worth a look

Its an anal book but might be more accessible than Spivak

[gray gazelle]

thanks

is there any problems with jumping to real analysis without taking calculus?

[tawny copper]

no

calculus courses are usually more computational, while analysis courses are usually more theoretical. But there is no problem in doing more theoretical stuff before doing many computations

you will still do computations in analysis anyway

[heady ember]

It should be fine for Schroder

Iirc Dami even said that he wouldn't be suprised if a calc I student can read Schroder

However, of course as with any math book, some amount of patience and determination is necessary

[gray gazelle]

Any small books that are good for some uni level easy math for someone in highschool ? Like group theory and stuff
I have 20 days of school remaining and I am going insane with exams, I need a small math book that isn't from my highschool syllabus but atleast easy to understand

[indigo mesa]

maybe take a look at Lochs intro to proofs

#proofs-and-logic message

[karmic thorn]

@stray veldt v2 when

[formal bronze]

Algebra by Artin is good

It is a nice book to study group theory from

[gray gazelle]

OMG!! YES ❤️ thank you
I need to learn how to write proofs before delving into any math theory of sort at higher level like uni
Thank you ❤️

[narrow relic]

Thanks, I liked the original series (didn't like any of the movies).

[narrow relic]

There's one by Salas and Hille you could take a look at.

[old elk]

I think there should be some abstract algebra book that is dedicated to the good solution of exercises because sometimes I feel that there are missing topics to explain examples etc. for example in the case of group I feel that always explains the same as always and I have looked at several books.

[old elk]

Oooh I don't know if it's just me that I still have a lot to learn.
although basically I think the latter
Sometimes I think that I shouldn't be in mathematics.

[torn valley]

any book recommendations on combinatorics ? (any difficulty welcome)

[karmic thorn]

Bona, A Walk Through Combinatorics

[fierce hedge]

Herstein has good exercises (if you excuse some weird notations) and solutions to them are easily available on the internet

[clear peak]

I'm looking for a book that is basically full of word problems where I build and solve the equations myself. Most mathematical books I read don't approach math in a real world observable way. At least not when you get into higher level stuff. I don't need to figure out how many apples Susie ate after John took 2 out of 5 apples. Or how many pizza slices there are after 20 kids took a slice from a pizza that feeds 180. Or how much volume there is in a sphere. Do you guys know what I mean?

I will settle for python related math exercises so I can observe and manipulate problems

I'm in college working on calculus, but I also have a cousin who is in high-school who is also interested in math so any book that is not elementary is fine

[remote sparrow]

https://www.amazon.com/Calculus-Rigorous-Course-Aurora-Originals/dp/0486809366

[remote sparrow]

math puzzle books and recreational math books generally have a fair share of word problems

[clear peak]

Thank you! I'll check em out

[remote sparrow]

https://www.maa.org/press/maa-reviews/partial-differential-equations-an-introduction
https://www.maa.org/press/maa-reviews/a-first-course-in-partial-differential-equations-with-complex-variables-and-transform-methods
https://www.maa.org/press/maa-reviews/introduction-to-partial-differential-equations-with-applications

some interesting undergrad pde book reviews

[gray gazelle]

i also love depression and the feeling of loneliness

[tulip saffron]

may I ask why you all recommend Friedberg Insel Spence's linear algebra over Gilbert Strang's linear algebra and its applications?

[sturdy shore]

one of them actually proves stuff

for an engineer it might be alright (idk), for a mathematician it hides too much abstraction that it could introduce earlier, and books with no proofs are just not okay for obvious reasons

oh mb, the book I'm going off of is his other la book, didn't know he had 2

so what I said might be totally wrong and the book may be alright

[merry sphinx]

wait he has 2?

[sturdy shore]

yeah, the one I'm going off of is introduction to linear algebra

[merry sphinx]

yeah that's the one i'm familiar with

what's the other one?

[sturdy shore]

the one they just listed

Gilbert Strang's linear algebra and its applications

[merry sphinx]

oh i thought you meant friedberg had two

i see lol

[sturdy shore]

update: this book also has 0 proofs

[remote sparrow]

anyone have thoughts on tao's measure theory book?

[tulip saffron]

thank you!

so I think I'd better go with Friedberg Insel Spence's book

[merry sphinx]

there's also anton if you want a less rigorous version which still has proofs but also some applications

[tulip saffron]

thank you!
that book seems to be a very famous one as well

[merry sphinx]

yeah it's a nice intro one, i'm using it rn lol

found fis kinda dry

[wheat remnant]

Is there a major difference between the 3rd and 4th edition?

[remote sparrow]

of friedberg insel spence? i wouldn't know. you can read some of the introductory remarks in FIS where they mention any changes from previous editions and look at the table of contents, and judge for yourself.

[wheat remnant]

Yeah only because the 4th edition is floating around 100 and the 3rd is 10$ 😅

[narrow relic]

The Strang book is not rigorous

[tulip saffron]

do you think the same for his another book An introduction to linear algebra?

I see, it is the difference between an engineer oriented and a mathematician oriented

[narrow relic]

Both of them are not rigorous. If you want something at that level, you should read the book by Poole that I recommended. If you want something more "advanced" go with the Friedberg one or something else

[narrow relic]

No, it's just poor writing in my opinion (Strang).

[tulip saffron]

thank you! since I have taken linear algebra courses before I would go for the more advanced ones

[narrow relic]

It did the whole "R^n first" thing so I wasn't interested in it

[wheat remnant]

I’m assuming comp sci is going to want the mathematician route yes?

[narrow relic]

I'm not sure what you mean

[gray gazelle]

Absolute beginner in calculus.
High-school level in Algebra.

Can you recommend calculus and algebra books from beginner to advanced.

Like from calculus its like: Pre-calculus ---> Advanced
and Algebra also from just after solving linear equations --> Advanced.

[gray gazelle]

So like i want a list of books. I dont mind if they are 10 or 15 or 20.

might as well recommend books for trig (because of pre calculus)

also pls ping me

[wheat remnant]

Engineer oriented vs mathematician oriented

[narrow relic]

I don't think that is a real distinction. There's writing that makes sense and there's writing that doesn't make sense, that has holes and gaps of logic

Just read quality stuff at whatever level 😀

[wheat remnant]

Yeah, but the person you responded to had that inclination, I just wanted to know if there was a real preference based on the intended orientation or direction of application

[narrow relic]

I think the key is what level you are looking for. For example I recommended that Poole linear algebra book. It's an intro and doesn't have anything on e.g. dual spaces

It also mentions some "practical applications" of the subject to give you some real world ideas (although I skipped all those parts I could see how they might be motivating for some people)

[wheat remnant]

Okay gotcha, and is there gonna be a potentially “deeper breadth but harder” path depending on which book yeah?

Or is there just a more celebrated standard of learning the initial material regardless I.e. FIS

[narrow relic]

I'm not sure what you mean exactly but I think the answer is yes? 😀

[raven violet]

Hi guys, I’m new here. I have covered portions till Calc 2 and wanted a book rec for what I could be learning further. It for my own interest. Could you guys please suggest some books (not bounded just to calc)

[alpine rover]

how about Stewart's Multivariable Calculus (overlaps with Calc 3)?

[raven violet]

Thanks, I’ll check it out, are there any particular topics that you like?

[alpine rover]

Lagrange Multipliers, Multiple Integrals (Double, Triple Integrals), Vector Calculus (Line Integrals, Green's Theorem, Curl, Divergence, Stokes' Theorem)

[remote sparrow]

@sage python does browder have material on sequences and series of functions? i looked through the index and found no mention of pointwise convergence or uniform convergence. i saw some material on fourier series but nothing on power series, and i saw the term "converges uniformly" but i haven't stumbled on the phrase "converges pointwise."

[sage python]

Hmm

3.4 it seems

[sturdy shore]

it has a section on analytic functions

[remote sparrow]

that makes sense

most books tend to be a bit more modular and put all this material into one chapter

though it's weird that browder's index doesn't have uniform and pointwise convergence in there

[remote sparrow]

thanks again

[frosty sonnet]

my bad

[narrow relic]

Are you a chronicler of math books?

[frosty sonnet]

iuho

ub

j;kl;"

[remote sparrow]

you could say that

[narrow relic]

That's kind of cool. Are you familiar with Professor Roman's newer 4-volume series?

[remote sparrow]

http://www.romanpress.com/

[narrow relic]

Yup

[remote sparrow]

him?

[narrow relic]

Yes. I purchased the first of the new series

It is the only linear algebra manuscript that I have been able to find that I think answers my questions about similar linear transformations in a proper way.

[remote sparrow]

advanced linear algebra by roman doesn't do that?

[narrow relic]

Oh, not sure! I haven't looked at that one

[narrow relic]

Hard to tell, that book looks more advanced and it might not have time for the things I'm mentioning

[remote sparrow]

i found another book a while back also called "Advanced Linear Algebra," except the author is nicholas loehr

https://www.routledge.com/Advanced-Linear-Algebra/Loehr/p/book/9781466559011

table of contents available here

seems to also have more material on matrix theory than roman

https://www.amazon.com/Advanced-Linear-Algebra-Nathaniel-Johnston/dp/3030528146

found this recommended to me

this nathaniel johnston also has lecture videos on youtube if anyone is interested

https://www.amazon.com/Introduction-Linear-Algebra-Nathaniel-Johnston/dp/3030528103

there's also this intro level book

might be worth looking into

[remote sparrow]

one of the amazon reviewers said this isn't a sewn book

loehr seems quite comprehensive

abstract algebra and elementary linear algebra seem to be prerequisites

https://www.amazon.com/Combinatorics-Discrete-Mathematics-its-Applications/dp/1032476710/

author works in algebraic combinatorics

possibly an interesting alternative to bona's book?

[remote sparrow]

going through the table of contents, seems to give more topics of an algebraic flavor, which is not surprising

[mossy flume]

combo in a more algebraic flavor? 👀

I wanna take algebraic combo (offered at my uni) but the prereq course is hell supposedly

[remote sparrow]

From the preface to the text:

Part I of the text covers fundamental counting tools including the Sum and Product Rules, binomial coefficients, recursions, bijective proofs of combinatorial identities, enumeration problems in graph theory, inclusion-exclusion formulas, generating functions, ranking algorithms, and successor algorithms. This part  requires minimal mathematical prerequisites and could be used for a one-semester combinatorics course at the advanced undergraduate or beginning graduate level. This material will be interesting and useful for computer scientists, statisticians, engineers, and physicists, as well as mathematicians. 

Part II of the text contains an introduction to algebraic combinatorics, discussing groups, group actions, permutation statistics, tableaux, symmetric polynomials, and formal power series. My presentation of symmetric polynomials is more combinatorial (and, I hope, more accessible) than the standard reference work [84]. In particular, a novel approach based on antisymmetric polynomials and abaci yields elementary combinatorial proofs of some advanced results such as the Pieri Rules and the Littlewood–Richardson Rule for multiplying Schur symmetric polynomials. Part II assumes a bit more mathematical sophistication on the reader’s  part (mainly some knowledge of linear algebra) and could be used for a one-semester course for graduate students in mathematics and related areas. Some relevant background material from abstract algebra and linear algebra is reviewed in an appendix. The final chapter consists of independent sections on optional topics that complement material in the main text. In many chapters, some of the harder material in later sections can be omitted without loss of continuity.

[mossy flume]

ooooo

[weary wigeon]

Any good books on topology

[sterile harness]

anyone know where I can get a new hardcover copy of munkres

[gray gazelle]

is there a good channel for pre-calculus and calculus courses
or should I just follow james stewart books

?

[narrow relic]

Thanks, I'm going to stick with the Roman thing that I bought from his web site.

But it's nice that you've sort of catalogued all this stuff at least mentally.

[glacial crypt]

pedestrian treatment

[weary wigeon]

Speaking of which what about munkres book on topology. It's cheaper

[silk arch]

Book replacement for University Physics with Modern Physics, Hugh D Young; Roger A. Freedman?

[remote sparrow]

halliday resnick or serway jewett are common alternatives

they're all quite similar though

pretty sure openstax has calc based physics books

and there are several other free online textbooks

[karmic thorn]

@orchid ruinI'll have to remove your message, we discourage sharing pirated material and links to access the same here because of Discord regulations

(I'm sure people who have to access those books know about the sources to access them, too 😛 )

[remote sparrow]

https://karagila.org/wp-content/uploads/2016/01/ests-wh.pdf

found a page containing some suggested readings for set theory

https://www.maa.org/press/maa-reviews/linear-algebra-and-matrices-topics-for-a-second-course

seems neat

this review also links to some other maa reviews

[gray jungle]

why not ? lol

[flat lantern]

now I'm gonna have to wait another 3 months

[karmic thorn]

[woven sparrow]

I'm looking for a PDF that gives a formal reasoning for these properties below:

Intuitively, I understand that these are true, but I do not know the rigorous, formal, axiomatic approach to prove/assert these.

[humble tusk]

currently reading this to prepare for discrete math; lots of exercises and beginner friendly explanations

[dapper root]

O C ND E

[foggy relic]

GIC N SE

[novel obsidian]

L GI AN ETS

Fuck you i fixed it

[solemn rover]

L GI ND SET

more like... L G RINDSET

[novel obsidian]

W grindset more like

[solemn rover]

Real.

[woeful ravine]

If anyone is looking for a more advanced book on logic and set theory, this one by Yu. Manin is great

[humble tusk]

would you recommend this book as a companion for a discrete math course?

[solemn rover]

I don't think this is appropriate for a companion to a discrete math course. It is best for a bit after

[woeful ravine]

No, that book covers topics at a very high level, for an introductory book on discrete math I would recommend V. K. Balakrishnan's "Introductory Discrete Mathematics"

[humble tusk]

awesome, thanks for the insight :>

[woeful ravine]

It has tons of applied examples and exercises and is very will written. Plus since it's a Dover book you can get a copy for <10$

[humble tusk]

my professor gave me a copy of “Discrete Mathematics” by Ross/Wright 2nd Ed, it has a ton of problems but am definitely on the hunt for other texts (discrete math is totally new to me), thanks for the recommendation 🙏🏻

[crimson leaf]

Concrete mathematics is good for discrete math

[woeful ravine]

Balakrishnan's book (as well as a few other books), imo, cover everything that you need to know for an introductory course. It has set theory & logic, combinatorics, generating functions, recurrence relations, graph theory, and a little bit on computational complexity theory. For something more advanced, there are a lot of good books covering combinatorics and graph theory in more detail that I could recommend

[gray jungle]

Any good books on banach algebras?

[dapper root]

<@&268886789983436800>

[foggy relic]

Banach algebras arent all that bad...

@gray jungle what specifically are you looking for

also what do you know already

[gusty smelt]

for the basics, i recommend pederson chapter 4

(as I always do lol)

[gray jungle]

Im currently learning functional analysis , measure theory , general topology and theory of bounded operators , i have taken complex analysis and abstract algebra if its relevant here.
Just looking for a introduction to the subject really.

[gusty smelt]

.

pederson's "analysis now"

its a functional analysis book

[gray jungle]

Dope , ile check it out

[gusty smelt]

pederson himself was an operator algebraist so its really good introduction to things like banach algebras and C* algebras

[gray jungle]

Sounds great , ty for the suggestion

[neat spindle]

may i ask for suggestion for textbook for a course that includes A systematic introduction to statistical inference, including the necessary probabilistic background, point and interval estimation, hypothesis testing.

here's an pastpaper of midterm and final for reference about what the course is about

no worry the pastpapers is free to download on the internet and it's completely legal and safe

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwju7qeO3__8AhWs-TgGHVkuDnUQFnoECBAQAQ&url=https%3A%2F%2Fwww.researchgate.net%2Fprofile%2FDavid-Booth-7%2Fpost%2FWhen-mentioning-the-null-alternative-hypothesis-is-not-required-in-research-Any-good-reference%2Fattachment%2F5c7137463843b0544e67b8aa%2FAS%253A729440560611329%25401550923590628%2Fdownload%2FMathematical%2BStatistics%2B%2528%2BPDFDrive.com%2B%2529.pdf&usg=AOvVaw2FpmGiWOyJL2XW1_ZgW78I

[neat spindle]

currently i only have this online book but i am not too sure if it's enough for this course

[gray gazelle]

Quick introduction to proofs I can read with my friend?

[crimson leaf]

If you want something very quick check pins in #proofs-and-logic

[narrow relic]

You can prove those yourself using basic logical facts

[woven sparrow]

elaborate

[narrow relic]

I'm not sure how to elaborate; have you ever taken for example a discrete math class?

[woven sparrow]

I can prove the exist ones using forall

[woven sparrow]

nope

Guess I need that

[weary wigeon]

There's a discrete maths channel btw

[narrow relic]

Yes. Chapter 2 of this book has some of the material you will use: Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition, by Ralph Grimaldi

You should also look into something called Fitch Natural Deduction which will show you how to do subproofs

[woven sparrow]

Thumbing through this book right now, but not really a fan of how its presenting its statements

[narrow relic]

You might know better; it helped me a lot when I was at the beginner level

[woven sparrow]

Its rigor feels lacking. Using truth tables to prove statements is pretty beginner level.

Also, my main complaint is here:

It just says this as fact.

[narrow relic]

Well if you're beyond that, you can look at Fitch natural deduction

[woven sparrow]

I mean, obviously it makes sense. But I'm a mathematician. Things that are obvious are unacceptable

[narrow relic]

Erm, well... I'm not sure how you could decompose that statement into something more basic, perhaps you can

[woven sparrow]

Thanks I'll look a bit deeper into this first book then switch to that one if not satisfied.

[narrow relic]

Fitch natural deduction isn't actually a book, it' s a technique of writing proofs

I don't know an official book that covers it

[woven sparrow]

It's that it follows from nothing but loose intuition. There's no axiomatic foundation for the reasoning of their statement. Just that it's true.

That's what I meant by lacking in rigor.

[narrow relic]

I have tried to find better books but I'm not a logic expert.

[woven sparrow]

I must admit though that this book is better than most, sadly

[narrow relic]

I learned a lot of this from some notes for some computer science class in Europe

[woven sparrow]

My search attempts have yielded nothing but cs101 courses which give even weaker detail than this

[narrow relic]

Here, let me find that link for you if I can

Since you seem to be at the same point I was and I remember how annoying this situation is

[woven sparrow]

Hah. Found the very thing I was looking for at the start

[narrow relic]

Does it prove those?

[woven sparrow]

checking

nah

Just gives an example of how they're true

But no rigor in derivation

[narrow relic]

Okay, the course I learned this from has been deleted from the web

[woven sparrow]

boo

[narrow relic]

It wasn't perfectly rigorous either though

My best recommendation is to try to find a book that teaches logic and that at least mentions Fitch natural deduction as part of the course

[woven sparrow]

for sure

The hunt continues then

[narrow relic]

Fitch himself wrote a book but I have not read it: https://archive.org/details/symboliclogicint0000fitc

[woven sparrow]

Okay looked into a bit

Looks like it's just a proof system that contrasts to the "hilbert system" which uses axioms and deductive reasoning

As I look further, it doesn't appear to be what I am searching for

Looks like I'm your average Hilbert system enjoyer

[narrow relic]

Heh okay!

[woven sparrow]

At least I know discrete math is one part of this, though

So that's a step forward

[narrow relic]

I think you are beyond the discrete math part of this though

[woven sparrow]

ah

[narrow relic]

You need to pick one of these logic systems and understand it

So in my case I learned one of these "natural deduction" systems

[woven sparrow]

duh I'll just go into #proofs-and-logic. What's wrong with me

[narrow relic]

Yeah I am not an expert on any of this! I've seen sequent- based systems as well

Good luck 🙂

[safe nova]

Hi could anyone recommend books to self study maths so that I can understand mathematics from Knuth's The Art of Computer Programming? You can assume that I have only basic highschool maths knowledge.

[stray veldt]

basic highschool knowledge could actually be enough

alternatively a modern discrete math (for computer scientists) book

[safe nova]

like?

[stray veldt]

maybe rosens discrete mathematics and its applications

[split bluff]

@woven sparrow you can prove some if not all of with a proof by contradiction

[woven sparrow]

[split bluff]

For the third one, suppose for all x, p(x) and q(x), then (for all x, p(x) and, for all x, q(x)) or ~(for all x, p(x) and, for all x, q(x))
suppose ~(for all x, p(x) and, for all x, q(x)), (get a contraficcion) then it must be the case that (for all x, p(x) and, for all x, q(x))

I'm on the phone and can't write it better but the proof is basically using the principle of bi-valence

Either p(x) or not p(x)

Prove not p(x) is invalid, therefore p(x)

[woven sparrow]

I can prove third and fourth using first and second, so I'm not worried there

So, say, how would I prove first and second?

Or I guess I could prove first and second using third and fourth

lemme look at your proof

[split bluff]

I think one can use the method i mentioned,for the first one, let m(x) be the consequent of the implication m(x) = (for some x, p(x), or, for some x, q(x))

_Assume the left side,
--then either m(x) or ~m(x)
--- suppose ~m(x)
---(proof that ~m(x) leads to a contradiction)
-- since ~m(x) is invalid, therefore m(x)
-then left side implies right side (m(x))

~m(x) will be equivalent to two universal quantifiers

So, you will get for x, ~p(x) or, for all x, ~q(x)

[lunar saddle]

does anyone have good book recommendations related to learning C as a complete beginner? I realise this might be a bit of a stupid question as there are tons of them out there it's just I have no idea which one is actually worth my money

[split bluff]

Both are contradictions to the assumption (left side) that for some x, p(x) or q(x) since for every x, ~p(x) or ~q(x)

[woven sparrow]

"Assume the left side"

What is the left side?

[split bluff]

@woven sparrow anyways, i know about thia technique from "how to prove it" by velleman, 3rd edition, page 105

Left side is for some x, p(x) or q(x)

Assuming ~m(x) is a contradiction to this claim

Remember that what you are trying to prove has the form p -> q so you can assume p and try to prove q, since proving q is kind of awkward, we assume ~q to try to get a contradiction with our original assumptions (p) and since ~q leads to a contradiction, then it must be the case that q and the proof is completw

[woven sparrow]

I'm not seeing the (proof that leads to the) contradiction tbh

[keen kestrel]

From which field of math is this?

[split bluff]

You get a contradiction to the claim that for some x, p(x) and q(x) if you can prove that for every x, ~p(x) or ~q(x) which is precisely what you get when you negate ~m(x) (right side)

@keen kestrel logic

[safe nova]

this -> https://www.amazon.com/Programming-Language-2nd-Brian-Kernighan/dp/0131103628

[lunar saddle]

have you personally read/used this book?

[safe nova]

hm not really, but it's better than the ones our uni gave us supposedly

[keen kestrel]

I just don't get what this ~ sign mean so I spent zero time thinking through this proof

[split bluff]

Negation

Im on the phone and can't use the correct symbol

Once i get some time i'll write the proof of the first exercise

On latex or on paper

[woven sparrow]

This sounds like a proof using existential quantifier though. I feel like this just leads to circular logic.

[woven sparrow]

ping me when you do

[split bluff]

Will do

[cobalt arch]

Any axiomatic books on combinatorics?

[ancient grove]

I would be delighted if someone suggested me a good book to learn on set theory and counting principles

[lunar moon]

Anyone got recommandations for books on foundations? General overview works but i would prefer it to specialise in the algebraic geometry aspect of foundations. Thanks!

[weary cape]

What is a good book for learning linear algebra?

I don't know calc 3 yet nor did I start real analysis and I only have a very basic understanding of proofs but is that necessary?

[remote sparrow]

#book-recommendations message

[remote sparrow]

by foundations do you mean axiomatic set theory and mathematical logic?

[remote sparrow]

maybe nicholas loehr's Combinatorics? it doesn't start with a proof of the sum and product rule of counting, but a proof sketch is given in the book using induction and the definition of cardinality

[remote sparrow]

by set theory do you mean naive or axiomatic set theory? and by counting principles, do you mean combinatorics?

[ancient grove]

Naive set theory and combinatorics

[crimson leaf]

Book of proof starts with both of those things

[weary cape]

Thx! :D
What makes this a good book may I ask?

[remote sparrow]

besides meckes, they're all cheap or free online

[weary cape]

Ohh lol okay. Have you read it?

[remote sparrow]

yes, i have copies of both meckes and hefferon

they should be both fine

[weary cape]

Cool

[remote sparrow]

they both start by showing you how to prove basic stuff

@tame tree likes meckes

i recommended it to them actually

hefferon has a complete solutions manual available plus lectures however

either way both are good

[weary cape]

hmm okay

I have this really old book on linear algebra and it's digestible...but still find it hard reading it so I wanted a different book to maybe gain a different perspective.

[remote sparrow]

what's the name of that really old book?

[weary cape]

It's called "Matrices and Linear Transformations" from Charles G. Cullen at U of Pittsburgh. Addison-Wesley publishing company printed in 1967.

It's supposed to be for sophomores taking linear algebra and matrix theory (says in the preface)

[remote sparrow]

oh, that's available as a dover edition now

is it a library copy or your parents/guardians'?

[weary cape]

Bought it at an antique store lol

[remote sparrow]

ah

it's $18.95 on amazon albeit as a paperback

but yours is probably hardcover and nicely bound

[weary cape]

Yeah it's a hardcover lol. (Had some inspiration from the Math Sorcerer)

I picked it up for 4$ actually

[remote sparrow]

nice!

[weary cape]

Mhm yeah old math books are cool to have around and I enjoy reading them but I also feel more inclined to read more recently printed stuff simply because they are easier to read at least in my case.

[remote sparrow]

i agree

love buying old math books

esp since new books have terrible binding

[weary cape]

TRUE

[remote sparrow]

😡

https://hefferon.net/

http://linear.ups.edu/

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

https://www.amazon.com/Linear-Algebra-Cambridge-Mathematical-Textbooks/dp/1107177901

anyway here's the links to the books i recommended

[weary cape]

I think I will just order the paperback for 22 it seems worth it (lin alg)

[remote sparrow]

hefferon? yeah it's not a bad price at all

[weary cape]

Yeah I first thought it might be in the 50$ before checking the price to my surprise this is a very affordable price for me

[grand thistle]

anyone know any good resources for and the prerequisites to algebraic geometry from an analytic perspective? I want a good mix of both analysis and algebra, and i've found Miranda's "Algebraic curves and Riemann Surfaces" but it seems way too advanced for me. is there any undergraduate level pathway to books like these?

id assume complex analysis and basic algebra like groups, rings, fields are necessary

and probably galois theory and commutative algebra too

it'd be great if anyone could direct me to any resources for the prerequisites too

i've decided to learn the algebra from Aluffi's book because i've picked it up before and enjoyed his exposition, and now that i know some group theory it should be smoother sailing than just going from scratch

[gray gazelle]

You mentioned no topology or manifolds, those are important especially for the analytic development

[grand thistle]

ah yeah forgot that was very important

[gray gazelle]

What I plan on doing is just doing the things I know I am missing then just diving in when I am done with those, then if I notice something wrong (a gap) when reading the material (in this case Geometrically defined Algebraic Geometry) I can just get a supplement on that content with some other book

[grand thistle]

right right that’s fair
do you have any suggestions on a commutative algebra textbook that is aimed at kind of what i’m looking for?

[gray gazelle]

I'm not sure, but everywhere I go recommends "Atiyah-Macdonald" for a concise, but complete course that is precisely enough you need to get into AG; whereas, "Eisenbud" is if you have more time for the details

[lunar moon]

yep, ZFC set theory would be of particular use

[mystic orbit]

Less gooo

Which chapter you at? :3

[mystic orbit]

You should ask @stray veldt

[grand thistle]

starting group theory chapter today

im alternating algebra and analysis like day by day so it might go kinda slow

[glossy nova]

hello

i need something to read

on unbdd operators

and not just proving the spectral thrm(something more advncd(

does anyone have anything?

[cobalt arch]

does it start with the most basic axioms of combinatorics and explicitly deduce everything else (theorems) from them?

like the general topology book by sierpinski

[oblique hatch]

Cheap ish first book on differential geometry (I know this may be too low, but soft limit £24, hard limit £30?)

[remote sparrow]

i guess? generally combinatorialists take the sum and product rule of counting as basic axioms even though they can be reduced even further to set cardinality and properties of the natural numbers. things don't need to progress from zfc to be ultimately justified axiomatically.

[cobalt arch]

I understand that but I would like an axiomatic approach to combinatorics, thank you for your response

[agile patrol]

hey guys 🙂 can you recommend a good intro nonlinear optimization textbook?

[crimson leaf]

Idk if you'll really find that

[cobalt arch]

why do you say that?

[crimson leaf]

Because I've never seen an axiomatic combinatorics book like you're describing

[cobalt arch]

That doesn't mean it doesn't exist XD. But I understand what you mean, I haven't seen one either

[soft badge]

Anyone got calculas book rec that goes ofer university basics?

[mystic orbit]

@gusty smelt do you know smth?

[gusty smelt]

Hmmm I mean I just use pederson ch4 but that’s bc I have like, limited uses for it ig. I just need spectral theory and stones theorem oof

[mystic orbit]

[gusty smelt]

I read a bit of schmudgen though, he prolly covers more advanced topics

And the exposition was fine but I’m an operator algebra person so not my favorite

[mystic orbit]

Oops, forgot to ping sausage

@glossy nova

[gray gazelle]

any books on computation theory?

good formality and follows definition-theorem-proof

something like that

[remote sparrow]

enderton or goldrei are good baseline choices for zfc. hrbacek and jech is a bit more challenging. for logic, consider enderton plus montalban's yt lectures or mileti's new book.

[mossy flume]

the defacto intro book is Sipser's text

I've also heard good things about Arora and Barak's text

[gray gazelle]

you say that like, every few days

it feels like

[remote sparrow]

i've heard dexter kozen's undergraduate cs theory book is good

it seems to be organized by "lectures" rather than chapters

doesn't seem to have any exercises

a few reviewers say it's a good supplement/complement to sipser

[remote sparrow]

people gotta know what they're paying for nowadays

[lunar moon]

ty

[robust robin]

guys]

recommend me some trigo books

ror

[glossy nova]

Just slept for 13+ hours

Lmao

[glossy nova]

Will check them out! Thanks

[mystic orbit]

I for 10

[glossy nova]

WHEN I WAS 13

I COULD SLEEP LIKE

5 HOURS

AND BE FINE

NOW

9 HOURS IS ESSENTIAL

MAYBE THATS WHY I STOPPED GROWING

[sweet wren]

My sister's 4 years younger than me and almost my height. When I was her age I was much shorter
I am confident she'll grow taller than me in the future (bc i lacked sleep too)

[glossy nova]

sad

my brother is taller than me

2 years younger

[sweet wren]

[sage kelp]

Intro analysis book that includes topology?

[glacial crypt]

topology on what

[mystic orbit]

What kind of topology are you looking for?

General topology?

afaik all rigorous analysis books have a chapter on metric topology

[sage kelp]

Idk 😦
I gather its point set?

[mystic orbit]

General topology = pointset

[sage kelp]

Yes! That I knew

[strange bluff]

Hi guys. Could someone recommend me book about geometry? I'm on the second year of my studies and just ended a basic cours od geometry and i would like to know more about it. Im intrested im book considering a lot of exercises and I'm more intrested in not-euclidian geometry than euclidian.

[mystic orbit]

Hmm

You should prolly just choose a good analysis book

As I said, all analysis books got the topology you need for analysis

[glacial crypt]

rudin

[mystic orbit]

And if you need any nore pointset for whatever reason you can just use another reference

[sage kelp]

I was thinking of an intro analysis book, and then jumping to Rudin but didn’t want to lose the chance of getting exposed to topology

[glacial crypt]

abbott has chapter 3 (he says everything after compact sets is optional but I'd do it)

ISBN: 1493927116

[sage kelp]

Thanks

[fickle coyote]

Any books for functions
I like functions

[random sonnet]

does anyone have good linear algebra book recs for highshoolers?

dont mind the username/pfp

[hasty turret]

Friedberg Insel Spencer

[random sonnet]

how is it?

[hasty turret]

Good

[glacial crypt]

uhhh

thats a very dry book

[gray gazelle]

you want an introduction to set theory book

[random sonnet]

any other suggestions?

I'm not in a rush

[fickle coyote]

yeah

[glacial crypt]

axler's LADR

theres also something called

linalg done wrong

I think

which is open access

[gray gazelle]

Jech made an introduction

https://www.amazon.com/Introduction-Revised-Expanded-Chapman-Mathematics/dp/0824779150

with Hrbacek

[fickle coyote]

thanks

[remote sparrow]

#book-recommendations message

[glacial crypt]

wheres the rant about bindings

[remote sparrow]

axler ladr will also be open access by around december 2023

[hasty bay]

im looking for a good book or any source for field extensions

we just started it and im kinda lost

[tulip blade]

Idk just google field extensions notes

Are you using a book for your class?

Id just look at that or a standard abstract algebra book like algebra by artin

[hasty bay]

no

my teacher gave us a pdf

but its just a summary

[dapper root]

I think D&F has a pretty good section on field theory

And Lang's is quite thorough, probably unnecessarily thorough for your class

[warm glen]

i heard morandi's field theory book is a gentle read but also very thorough

[hasty bay]

yes i dont think were gonna do a lot of details

we have polynomials,extension of fields and finite fields

its like an introduction then we will have another module the next semester only on extension of fields

[gray gazelle]

If you want to be a Math Major, maybe Artin?

If you don't want to be a Math major, refer to Sour Drop's Rec, I heard similar Recs from John Baez.

Note: You have to be comfortable with proofs, complex numbers, induction, and, ideally, Calculus

For Complex Numbers: ||https://youtu.be/OQz1ydBcQSA| or a good pre-calculus text||
For Proofs: ||Artin has an appendix that goes over some proofs, but you can also use the notes pinned in #proofs-and-logic||
For Calculus: ||Only slightly necessary as a maturity filter from what I can tell (Jacobians mentioned once), but you can pick it up quickly from Khan and Lamar's Notes||

[random sonnet]

thanks a lot guys will check em out

[gray gazelle]

Some good Abstract Algebra books that cover multilinear Algebra that isn't Bourbaki?

[sturdy shore]

knapp - basic algebra, but I can't speak to the quality of that section specifically as I haven't reached that far yet

[gray gazelle]

Is it a terse book or fairly readable, just as a heads up, I'll read anyway

[sturdy shore]

well, depends on what you are comparing it to, probably reads like a novel if you are comparing it to Bourbaki

from what I've read of it, the book is decently chatty but the proofs themselves can be short and to the point, so you have to pay attention

[gray gazelle]

That seems good, what are the prereqs? Just Linear Algebra, Proofs, and Maturity?

[sturdy shore]

it covers linear algebra so not even that is needed, I'd pin it as a graduate level text w.r.t. the required maturity though

[narrow relic]

Holy moly, I have an Algebra book by this guy and it's amazing, I had completely forgotten about it

Oh, hey, it's this very book

He doesn't cover similarity of operators as far as I know, though

[minor knot]

What is a good source to learn about Affine spaces?

[orchid mortar]

Is there really such a source that isn't basically linear algebra?

[minor knot]

Affine spaces aren't covered in the LA textbook I'm using

[orchid mortar]

Checking my own books, I see a chapter of it in Shafarevich and Remizov

Roman also has a chapter on it

[steep spade]

Can anyone recommend a workbook or collection of very challenging problems for calculus 3 (multivariable calculus)?

For reference https://www.amazon.com/Calculus-Multiple-Variables-Essential-Workbook/dp/1941691374 is a level below in difficulty for what I'm looking for

[woeful ravine]

Although it covers more than just introductory multivariable calculus, volume 2 of "Introduction to Calculus and Analysis" by Courant is good. https://www.amazon.com/dp/3540665692

It's not a problem book but it has a decent amount of exercises

[mossy shell]

What are your guy's opinions on the book a mind for numbers?

[oblique hatch]

Does CUP have a good introductory book on differential geometry?

[heady ember]

What's cup? Just curious

[karmic thorn]

Cambridge University Press, I'm assuming

[oblique hatch]

Yes

[heady ember]

Ahh I see

[rigid thunder]

If I needed to remember all the numerical methods undergrad material that I forgot since my courses were long ago, what book would I be looking for?

For the record - CS undergrad, not Math

[gray gazelle]

Are there some notes about adjoints in category theory, so that I can learn the definition and equivalent forms of it

[remote slate]

can you suggest a book to learn inequalities?

[karmic thorn]

Cauchy-Schwarz Masterclass is one I've heard about

[remote slate]

is it a first course on inequalities?

[gray gazelle]

I'll use Mac Lane

¯_(ツ)_/¯

[woeful ravine]

https://people.math.ethz.ch/~hiptmair/tmp/NumCSE/NumCSE15.pdf has probably more than you are looking for but I would definitely recommend it.

[rigid thunder]

at a skim it does have more, but it also seems to have C++ so that will be a very pleasant experience

[narrow relic]

Is this an appropriate complex analysis book, or are there some issues with it? https://www.book2look.com/book/9781107134829

I know nothing about complex analysis so I'm not sure if "follow[ing] Weierstrass' approach" is good or not

[stray veldt]

it means that the theory is developed mostly via power series

the content looks fine, it covers a ton of stuff in very little page count

cant comment anything more though

[dapper root]

I used it, it was fine

[steep spade]

It's great! Thanks for the recommendation

[graceful dawn]

Suggest me some book

[signal fable]

any book?

[remote sparrow]

kingkiller chronicles by patrick rothfuss

[graceful dawn]

No, math

Fiction pollute minds

[remote sparrow]

why didn't you say that to begin with

[graceful dawn]

I thought this is a math channel

[remote sparrow]

read channel desc

[gray gazelle]

algebra by serge lang

[mystic orbit]

why would you do that to them?

[remote sparrow]

it's good

[mystic orbit]

it's unfinished.

[remote sparrow]

idc

[mystic orbit]

oh it's yohan lol

[remote sparrow]

no manga adaptations at all? can i rec light novels that have manga adaptations?

[mystic orbit]

lol

:sotrue:

[remote sparrow]

emote embed fail

[mystic orbit]

it was intentional

[graceful dawn]

No, islam doesnt believe it

It's forbidden

[remote sparrow]

i mean, youjo senki is kinda like that

no game mechanics

[graceful dawn]

Concepts of modern mathematics

[narrow relic]

Oh great, thank you!

[narrow relic]

It's fine, thank you for your comments!

[glass harness]

Any book recommendations foran introduction to elements of set theory?

[remote sparrow]

enderton or goldrei

hrbacek and jech for something a bit more challenging

[analog lava]

Hi everyone

im learning about differential manifolds and how to generalize stokes theorems and basically multivariable calculus to manifolds

problem is i do not remember much if any of the intuition of the low lvl calc 3 things

is there any source that i can read /watch to remember the important things so they help when generlizing to manifolds?

ty

just the useful bits that would make me connect the dots

like fundamental theorem of line integrals and so on

[fallow cypress]

I kinda wanna read Reading Lolita in Tehran

I've heard good things about it

[foggy relic]

What's a good book? Fiction preferably

[fallow cypress]

One Hundred Years of Solitude?

[foggy relic]

will check out

[fallow cypress]

Midnight's Children is great

Slaughterhouse Five if you like sci fi and also if you don't

[foggy relic]

thats Rushdie right?

[fallow cypress]

Yup Midnight's Children is

[graceful dawn]

Animal Farm

[fallow cypress]

Animal Farm is pretty fun

[heady ember]

Is that the one with like a spider and pig or smt

[iron bay]

That’s charlottes web lmaooo

[gray jungle]

Its a political satire about the Soviet union using a story about animals starting a revolution against there farmer.

[graceful dawn]

Spider is in hobbits

Hobbits farm should have both ig

[fallow cypress]

What people don't remember about Animal Farm is that Orwell was socialist lol

It's so funny when right-wingers invoke Orwell to say that socialism would never work

[grave thorn]

Also kind of funny that he's an anarchist, and conservatives still invoke him

To say stuff about social issues

[fallow cypress]

Was he an anarchist?

I know he sympathized with the anarchists (CNT/FAI), but I thought he was a democratic socialist (in the old sense of the phrase, not the bernie sanders sense)

[grave thorn]

Okay maybe he wasn't an anarchist, but at the very least he was a libertarian socialist

[heady ember]

I have never read hobbits so its probably not that

[remote sparrow]

orwell was also a snitch

[runic aspen]

guys any book suggestions for a 9th grade, i want to know about calculus and more about geometry proofs, geometry in whole

[remote slate]

is inequalities a part of classical algebra?

i have to learn it form scratch!

[novel obsidian]

It could be argued that he was closer to anarchism than being a dem soc. He did fight with the anarchists in Spain after all, unless of course his politics changed in later years

[remote slate]

which book should I refer?

for the first course in inequalities

i don't have any prior knowledge

[remote slate]

anyone suggest a book

[gray gazelle]

Well if you could specify online or offline books. I can suggest both. For the online one I can even upload the pdf.

[ember slate]

what are the math needed for this book : "Structure and Interpretation of Computer Programs" ?

[heady ember]

No you can't. It would be against tos and the mods would have to take action

[orchid mortar]

Uploading of GNU/Open books are probably fine.

[gray gazelle]

Oh srry if that is so

[orchid mortar]

A lot of open sources don't mind direct links

[gray gazelle]

I am new

[orchid mortar]

But if you don't know what is the legal requirement, don't post anything

[gray gazelle]

Well, it is available online

I just found it myself searching the same thing.

[orchid mortar]

Available online, but do you know how?

By how do you understand what is a license?

[gray gazelle]

Like getting uploaded on the official website, I guess!

[orchid mortar]

Not every book has that

[gray gazelle]

'O'

So how do we understand that?

[orchid mortar]

This isn't the place to learn about licences I think

[gray gazelle]

But if I want to help in this section I gotta have a little bit of idea right?

[orchid mortar]

If it looks like an author's website you probably can post a direct link