book-recommendations

[gray jungle]

you can definitely find something faster

[gray gazelle]

I see

[dire torrent]

hey about that, hoffman or friedberg? which has more content(in terms of the actual coverage, excluding exercises)?

I bought Friedberg. Is it too short on content?

thank god.

[gray jungle]

my analysis progression in the past 2 years was roughly Most of tao I --> rudin Ch5-6-7-8 --> rudin 2 for complex analysis + introduction to numerical analysis Atkinson+ Katznelson for basic functional stuff and hilbert spaces --> folland for measure theory & bit of functional + henry cartan Differential calc on banach spaces --> Rudin Fa for functional analysis

[gray jungle]

Hoffman is a bit more old school and a bit denser but they cover similar content

hoffman goes into a bit more stuff towards the end

[dire torrent]

@gray gazelle hmm..I've always thought about that. Moreover, you have a ton of online free resources like Youtube incase of any doubt or frustration. Even then aren't little struggles part of the process?

[gray jungle]

i do recommend hoffman and kunze over friedberg just cause i love there exposition but im also biased

hoffman and kunze is THE book that got me into mathematics

and influenced much of myself today

it has its problems but highly underrated

[dire torrent]

how the damn did you get to study linear algebra without even getting into mathematics?

is it covered in high school or smth?

[gray jungle]

i left finance and math was the only thing that seemed like id enjoy

[dire torrent]

ohh..

[gray jungle]

and it turns out it was the best decision i ever made

so there is that

[dire torrent]

You are the chosen.

About proofs, have you read Hammack's?

[gray jungle]

i didnt read any proof book , tao is where i learned them lol

[dire torrent]

okay..but I liked it so much

Oh you meant proof books in general?

You guys literally have mathematicians' names

Which is kinda nice.

[craggy elbow]

I am in my third year of high school in Mexico, which I believe is 9th grade in the US. I really like math and algebra and was wondering if anyone could recommend a good book on these subjects. I would love to get into the world of math

[stuck zephyr]

look up for openstax.com

[wary igloo]

I’ve read a few books in linear algebra. Hoffmann and kunze remains to be my favorite

[lusty ermine]

can someone point me on some good practice resources for direct sum of subspaces

[sudden vale]

How's Chern-Chen-Lam for studying differential geometry (not for the first time, but not very accustomed to diff geo either)?

[stone axle]

Did you follow a lecture series along with the book?

I’m currently reading it along with Paul halmos’

But my friends keep telling me that this combo is usually used by graduates and not suitable for my level

[wary igloo]

I didn't even realize there was a lecture series - no, I was reading it similar to how I was reading baby rudin in undergrad: read theorem statement -> try to generate some concrete examples to get intuition -> try to prove myself -> fail -> read author's proof -> work related exercises

Halmos' text is really good also - using multiple sources (if time allows, not sure how many math classes you're taking at once) gives a wider perspective on the subj

[hasty flower]

book recommendations?

interesting

if i had to recommend a book

i heard a tale of two cities is rather interesting

[remote sparrow]

carothers

[heady ember]

sorry was blind, didn't see "second course"

[woeful ravine]

Chern-Chen-Lam is definitely good for graduate level differential geometry. I personally used Geometry of Manifolds by Bishop & Crittenden, which appears to cover roughly the same topics as Chern with some slight differences

[remote sparrow]

you could also jump into measure theory if you want

#book-recommendations message

there are some intros tailored for undergrads who only have knowledge of real analysis on the real line

no metric spaces

or you could read a brief metric spaces book and then go into a more abstract book like folland

[remote sparrow]

axler and schilling work too

[vital bane]

damn really?

[swift dome]

Unit 4: Graphs: Basic terminology, multi-graphs and weighted graphs, connectivity, walk and path, circuits and cycles, shortest path in weighted graphs, Algorithm of shortest path. Hamiltonian and Eulerian paths and circuits, Eulerian graphs, Hamiltonian graphs, Konigsberg bridge problem, Chinese postman problem, Travelling salesperson problem,
Planar graph and Euler’s formula. (11 Hrs)
Unit 5: Trees and cutsets: Trees, rooted trees, path lengths in rooted trees, Spanning trees and cut sets. (3 Hrs)
These are some of the topics that I want to do on a deeper level, so is there any good resource I can use to practice this from any site YouTube or book recs?

basically its groups , fields , rings and graphs

[severe stream]

in what kind of class would i learn about kelly bets/kelly criterion and do you have any reqs?

[rustic grove]

Does anyone here know how to read Djvu files and do they look normal when opened?

[stray veldt]

djvu is just a collection of images

some pdf readers can open them, for example evince

[rustic grove]

ok thanks

[remote sparrow]

if you're on windows, windjview is good

sumatra pdf is also good

[lean pagoda]

personally, converting djvus to pdfs is my favourite past time

as for viewing djvus, zathura is a pretty good and lightweight document viewer

[remote sparrow]

https://djvu.sourceforge.net/

https://windjview.sourceforge.io/en/

there's apparently a macdjview

looks like it's in early development though

[rustic grove]

Thanks

[velvet glacier]

Which one should I start with for self study, I have no previous calculus experience (except all of 3blue1brown's videos)
Thomas calculus, Stewart or Spivak

I have no one to teach me calculus and I am not a bright student

[rustic grove]

The best thing you can probably do is to find a calculus course page on the internet for some specific maths course and follow the resources + syllabus given. Also I would suggest Stewart or Thomas.

[velvet glacier]

I want to study it in school where I dont have electronics

so physical books

And which book would be good for JEE?

calculus maths

[rustic grove]

Oh you're doing JEE, Idk then sorry

I mean you can use any calc book, but idk any specific to that

[vital bane]

j*e 🤢

[velvet glacier]

Huh?

[gray gazelle]

Also worth googling https://www.google.com/search?q=calculus+for+JEE&oq=calculus+for+JEE&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCTUzMTVqMGoxNqgCALACAA&sourceid=chrome-mobile&ie=UTF-8

There are even video recommendations

[ocean mulch]

I stumbled upon Galois theory by Stewart, and speed ran through it. I must say it's a great book.

[velvet glacier]

Hmm what about Aton's Calculus

[ocean mulch]

Not in depth enough if you have a class on Galois theory, but it's enjoyable for a Sunday's reading

[vital bane]

which stewart?

[ocean mulch]

Ian?

There are many?

[sudden vale]

As far as I know, Chern does not deal with flows (or maybe I haven't read till there yet), which seems to be present in every other text on diff geo I've seen around (Loring Tu, Lee)

[half siren]

Any book recommendations that explains the Poincare conjecture and Perelman’s proof in a comprehensible way that is balanced in terms of reading flow and mathematical technicalities?

[gray gazelle]

what do you guys think of aluffi's undergrad algebra book?

notes from the underground that is

[stray veldt]

looks interesting but i only really looked at the toc

its the one that does rings first, right?

[gray gazelle]

yeah

[rotund birch]

Can someone recommend a calculus book but not a boring book , I am already familiar with it but never used a book though.

[gray gazelle]

Spivak if you have some familiarity with proofs

[rotund birch]

I don't know actually I have bought that book and I kinda regret it , do you think it is enough

Like the problems doesn't include a lot of bashing

[gray gazelle]

bashing?

[rotund birch]

I mean it doesn't really have incredible Integrals , in most cases you have to prove something

Really appreciate your time bruh

[gray gazelle]

Yeah, Spivak is a good book if you’re interested in a theoretical approach. If you’re interested in something more computational, Lang’s A First Course in Calculus (i think that’s the title) could be good

[rotund birch]

Thanks bro

You mean serge lang

[gray gazelle]

yes

[rotund birch]

Do you have a harder book

[gray gazelle]

Harder how? More difficult problems or more advanced content?

[rotund birch]

Difficult problems

And I guess the more difficult problems included the more advanced content will be illustrated

[gray gazelle]

i’d recommend looking up lists of difficult integrals in that case

[rotund birch]

Oh okay

What do you think about analysis

Can't it be considered as calculus in some sense

Or they aren't the same thing

[tiny epoch]

Hey, goodnight. I was wondering if you guys have some advice do prevent a vicious cicle that I'm noticing in my maths studies, and if any of you can relate this too. When I pick a text book of my interest, I can keep with until a certain point with some fluidity, but the when I get stuck with some definition or proof of some Theorem that drives me crazy for some hours, days or even weeks and I get so unmotivated, with self destructive and limiting thoughts which makes me give up on the text book, but theeeen I regret, and then try again and the same thing happens, and the cycles continues... So what I'm probably doing wrong, and what tools could I use to overcome these "epistemological obstacles"(let's call it that)?

[rotund birch]

That's all of us do the same thing believe mev

But

You have to learn some important skill which is skipping

Believe me it will save your Time and you aren't required to understand the entire textbook from the first read , things might be clearer by the Time

And that doesn't mean you have to Skip whatever you stuck in

You may define a considerable amount of time to search it up and trying to see where you stuck exactly

And you might be misreading, That's a common thing

So take a rest and read again

You will probably find out that you have screwed something

[tiny epoch]

Thanks man, I was actually thinking that I was stupid and that it was an unusual experience

About skipping It is for me a huge chalenge, in my mind I'm running away from the boss

But I gonna try, I must to

[fleet solstice]

What's a good budget Precalculus textbook, to self teach yourself math?

[stuck zephyr]

What do you mean by "budget"?

But if you want I can share my textbook I use for precalc

[fleet solstice]

Ohhh

How so?

[fleet solstice]

Like one that's somewhat cheap

And not bad of a book

[stuck zephyr]

Wdym?

[fleet solstice]

Is it like a digital textbook?

[stuck zephyr]

Yes

[fleet solstice]

Oh

[fleet solstice]

Yeah that would be nice then 😭

Thank you 🙏

[stuck zephyr]

You're welcome

[rotund birch]

Ur welcome bro

[mental pier]

any good recs for bayesian statistics?

[rare estuary]

I have been reading Bayesian Data Analysis by Gelman/etc

It's available for free and has associated lecture videos and code demos

[dusk wind]

any good books on machine learning

[magic spade]

There are many. What aspect? How theoretical/applied? Beginner or advanced?

[dusk wind]

Beginner - written in the last 5 years and by someone that, if they were to have amnesia, would still be able to write the book and explain it's contents
Advanced - same, without up to the reader as it's base

the Tom Mitchell book looked good but 1997

[magic spade]

Did you take a look at Understanding Machine Learning by Shai?

[dusk wind]

I'll check

not a fan of the writing style and 2014

[magic spade]

What do you think of this https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www.di.ens.fr/~fbach/ltfp_book.pdf&ved=2ahUKEwiPmZ3l88GCAxVEF1kFHeCgDTIQFnoECBcQAQ&usg=AOvVaw0UAUxy8wDGamS40sm3bDZy

[dusk wind]

yes

[magic spade]

np

[gray gazelle]

calculus, as in the typical content covered in standard university calculus sequences, is a toolbox of ideas and results taken from analysis. the reason why i distinguished between the two earlier is that a calculus textbook will approach the ideas very differently than an analysis textbook (or a book like spivak)

[rotund birch]

Oh I get it now

so I can skip calculus and proceed to analysis

Since I wanna learn mathematics behind calculus not merely as a set of techniques and algorithms

[gray gazelle]

you can, though it’s somewhat atypical. if you do, you should either read and work through the proofs of spivak or read a proof based book on linear algebra and another on discrete mathematics(Concrete Mathematics maybe?) before attempting analysis

[rotund birch]

Oh I have heard about a book called concrete mathematics

Do you know what was the name of the author

[gray gazelle]

graham, knuth, and patashnik

[rotund birch]

Thanks bro really appreciate it

[gray gazelle]

of course. have you taken a calculus (both single and multi variable) course(s) before?

[rotund birch]

Single only

Didn't get through multivariate calculus

[gray gazelle]

ok, it might be valuable to study that as well before analysis, particularly as it serves as a nice motivating example for linear algebra

[rotund birch]

Okay sure I guess tom abostol book would be an appropriate Choice for multivariate calculus

[gray gazelle]

i’ve heard good things about apostol

[rotund birch]

Yeah, it has great reviews

[keen orbit]

isnt there one for spivak ?

one for multivariable i mean

[gray gazelle]

yeah, Calculus on Manifolds

[rotund birch]

Haven't heard about it

[rotund birch]

Didn't know about it

[gray gazelle]

its a pretty terse book though, and the prereq is Spivak Calculus and linear algebra. A more friendly (though still excellent and intense book) is Shurman's Calculus and Analysis in Euclidean Space, which has the same prereqs.

[rotund birch]

I am a junior in high school btw 🙂

[gray gazelle]

if you want, I can DM you my self-study list

[rotund birch]

Sure

I would be so thankful

[keen orbit]

me too

i am self studying abstract alg rn to go to linear algebra by werner greub

[gray gazelle]

what book are you using for algebra?

[keen orbit]

D&F

[keen orbit]

do you know this LA book ??

[gray gazelle]

I've heard of it. Its intended for a graduate course in linear, right?

[keen orbit]

idk maybe yes

[gray gazelle]

solid

[swift dome]

Unit 4: Graphs: Basic terminology, multi-graphs and weighted graphs, connectivity, walk and path, circuits and cycles, shortest path in weighted graphs, Algorithm of shortest path. Hamiltonian and Eulerian paths and circuits, Eulerian graphs, Hamiltonian graphs, Konigsberg bridge problem, Chinese postman problem, Travelling salesperson problem,
Planar graph and Euler’s formula. (11 Hrs)
Unit 5: Trees and cutsets: Trees, rooted trees, path lengths in rooted trees, Spanning trees and cut sets. (3 Hrs)
These are some of the topics that I want to do on a deeper level, so is there any good resource I can use to practice this from any site YouTube or book recs?

[undone ether]

I know that this is technically for books, but in terms of movies PLEASE watch A Beautiful Mind.

[woeful ravine]

From what it sounds like you want introductory graph theory. I would recommend looking at chapters 4-7 from Introductory Discrete Mathematics by V. K. Balakrishnan, as it's very accessible. There are many books that you choose from, but it's not really important exactly what book you decide to use.

[vital bane]

[heady ember]

Imagine publishing a paid copy

Real men publish open access

[daring lake]

Anyone have read it here? How does it fare against Rudin or Royden?

[remote sparrow]

#book-recommendations message

keep scrolling

[mystic orbit]

Check out artin!

It does algebra and linear algebra in tendem

and his treatment isn't so pedestrian

[novel obsidian]

Are you saying his treatment is pedestrian or isn't? I'm lost

[velvet glacier]

Can anyone review Howard Anton's Calculus for me?

I purchased it on amazon

[daring lake]

thank you

[sudden wing]

Can someone please recommend a good calculus book

[daring lake]

If you want easy prose, Stewart

If you already had a brush with calc, then probably Spivak or Apostol

[velvet glacier]

What about Howard Anton

His calculus book

It's.... Quite thick, thickest book I have yet seen

[daring lake]

I haven't really read it so I didn't recommend it

[tiny epoch]

Apostol, undoubtedly

[sudden wing]

Thanks

[gray gazelle]

I need an engineering type ode book which is very gentle and reads nicely

[undone rapids]

I wanna read much more about functions, especially about multi-valued functions and maybe a little bit on calculus. So what is the best book or books?

[gray gazelle]

https://ocw.mit.edu/courses/18-024-multivariable-calculus-with-theory-spring-2011/

you can see this

[coral prawn]

any recommended books for mathematical methods? Or is this too vauge of a topic to even have a book covering this?

[gray gazelle]

are you a physics major?

mary l boas has a book i think

[undone rapids]

is this free?

[gray gazelle]

of course man!

[undone rapids]

amazing

as i see theres no video or something like this. Is this just a lectures in text and problems fore them?

[gray gazelle]

https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/

this has videos

[undone rapids]

thanks

[coral prawn]

Ooo, ic, yes I intend to learn math methods for phys

[fierce hedge]

I am sure there are some physics books on this topic

[gray gazelle]

https://www.cambridge.org/highereducation/books/mathematical-methods-for-physics-and-engineering/FC466374D5B94E86D969100070CA6483#overview

this is another option too

[fierce hedge]

I was not sure if engineering maths would do the job but that should work

[radiant sentinel]

Could somebody provide me some source for reading about how we can define what we are doing when dealing with, say summation of a divergent series? Like the sum of infinite natural numbers can have many values depending on how we define it

[stray veldt]

there seems to be an overview on wikipedia

in general this question is too complex to answer

[upbeat vine]

https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

And the relevant hyperlink: https://www.tricki.org/article/Smoothing_sums

[radiant sentinel]

nvm

Thanks tho, appreciate your help

[patent trail]

I need a recommendation for a first course number theory exercise book (i already have source for an explanation)

Also i need a linear algebra book which explains dual space

(Ping me if replying please)

[gray gazelle]

Halmos’ linear algebra book includes a fairly detailed exploration of dual spaces

[jovial parrot]

It is very old

[jovial parrot]

LADR (prolly get new edition) has dual spaces, idk how much though

[gray gazelle]

still perfectly readable with only a couple outdated bits of notation

[naive trellis]

Complex Manifolds ans Calabi Yau manifolds book recommendation?

[heady ember]

FIS has a section on dual spaces, you can flip through it and see if it is sufficient for your needs

[patent trail]

Thanks

[heady ember]

Np

[sudden kindle]

This is the appropriate channel for #book-recommendations

[naive trellis]

lmao

average day of algebra taking over

[ashen pier]

Are any books able to be recommended here, or just things related to Mathematics?

[naive trellis]

maths

[heady ember]

No, any books are fine

See channel description

[finite gale]

this is like telling a high school student to ask their question in some advanced channel where their problem clearly does not belong, and saying it was once answered there, and encouraging another person to do it also

obviously to a lesser extent but book recs are definitely fine here

i would be not surprised if someone in adv lounge were to ping them back here lol

[ashen pier]

Alright, thanks, Habuki, Grass, and... :3???

I mostly read academic stuff anyways, even if it's not all math-related.

[finite gale]

you can ask for any other literature

(see channel description)

[ashen pier]

Hope you'll be interested in what I have to show later.

[finite gale]

though for the most part people ask here for math books/resources

[ashen pier]

Understood.

[naive trellis]

lol

[heady ember]

Hi tubu

[finite gale]

hi gwass (i realized after i sent that that you already said that)

[woeful ravine]

It really depends what you want exactly. Huybrechts's Complex Geometry is great but it doesn't cover Calabi-Yau manifolds in full depth (see chapter 6 section 1). Do you want a book that covers this subject extensively, or are you just looking for a general text in complex geometry?

I would also recommend looking at https://www.scholarpedia.org/article/Calabi-Yau_manifold

[naive trellis]

im mor intetested in cy3 than complex geom in genral

[heady ember]

Its alright lol

[naive trellis]

cuz i main ricci flow n stuff but bc yau shing tong recently got shaw i wanna have a brief look at cy3

[wraith sandal]

Hello, does Chartrand cover what is necessary for logic and set theory in order to study advanced math like analysis and algebra?

Cuz im new to these topics

[woeful ravine]

If you actually want to learn about Calabi-Yau manifolds formally, you'll need a decent background in complex geometry.

It's not really something you can just take a brief look at

I suppose you could just look at an introductory article / yt video

But there aren't really any books that would be suited for you from what I gather

[naive trellis]

I know, but I don't really need like a fuck ton of info

Lol

[woeful ravine]

This article gives a decent intro to the subject: https://www.mat.univie.ac.at/~westra/calabiyau3.pdf

[naive trellis]

Thanks

Also I'm reading sheridan's Hamilton RCF, is there any recommended follow up materials?

[woeful ravine]

I've never seen this specific book and can't find it online so i'm not sure. Can you send a link or the TOC?

[naive trellis]

https://scholar.google.com.hk/scholar_url?url=https://www.maths.ed.ac.uk/~nsherida/ricciflow.pdf&hl=zh-TW&sa=X&ei=HGVUZZXRF_Ol6rQPyJ25sAU&scisig=AFWwaeY2BPs_IuBAqniLBZ43hxil&oi=scholarr

Introductory RG

[woeful ravine]

Just looking online there's a book of the same name & over 600 pages long https://books.google.com/books/about/Hamilton_s_Ricci_Flow.html?id=dQYPCgAAQBAJ

[naive trellis]

Hmm

[woeful ravine]

I'm not that familiar with this subject so can't really help further

[naive trellis]

Sad

[woeful ravine]

I don't really know what further reading you need though. Maybe look for some papers

[naive trellis]

Yeahhhh

I'm thinking about studying parelman's paper

[vital bane]

you dont need much logic or set theory to study analysis and algebra

just naive set theory is enough

you'll pick up more logic and set theory and proof techniques along the way

[daring lake]

^ most analysis and algebra books will also have a section/chapter on set theory and proofs

[vital bane]

yea and even topology books do! (like munkres screw u darQ)

[distant smelt]

yo

i suck at geometry

i need books

or resources for practice

[daring lake]

geometry at school?

[distant smelt]

i mean, entry level olympiads in my country(india)

any recommendations?

chat died lol

[daring lake]

I mean, idk what level you are asking for

[distant smelt]

what levels do you know?

[distant smelt]

https://www.mtai.org.in/wp-content/uploads/2023/09/IOQM_Sep_2023_Question-paper-with-answer-key.pdf
like this

[dusk wind]

"He's the kinda guy to load up minecraft on a private server"

[naive trellis]

munkres is w book

[daring lake]

I don't know any other geometry book than Euclid's elements

[daring lake]

i am currently reading general top from it

[dusk wind]

couldn't find any good books on geometry besides like 100 different Euclid rewrites

[marsh ingot]

Lars Hörmander books? I was trying to search one but cant find it 🥲

[naive trellis]

What geometry?

In general or any specific field?

[dusk wind]

general

[daring lake]

hs

[naive trellis]

Munkres is W for topology

[dusk wind]

but by then you can just read about trig lmao

[naive trellis]

Differential Geometry not so aure

[naive trellis]

fr 😭

[dusk wind]

I dont even remember anything from geometry but it all shows up again in trig so it doesnt really matter

[daring lake]

i just start making angles up till it feels right

[dusk wind]

theres this though

https://ia600701.us.archive.org/28/items/euclid-elements-redux_201809/euclid-usletter.pdf

which is easier to read than whatever gibberish made of other rewrites

[naive trellis]

trigonometry is lwk bs

[manic drum]

Can someone recommend me a book with problems and solutions. I'm mainly interested in probability basics, discrete and continuous random variables

[wheat trout]

andrei moroianu has a not very long (around 200 pages) book called lectures on Kahler geometry. In last chapter, he discuss a bit about CY manifold. Not a dedicated book but can be a good start.

And if you already have some background in smooth manifolds, you can skip the first few chapters.

You can start directly from part 2 in complex geometry.

[naive trellis]

Kewl

I'm actually studying riemannian geom lol

[wheat trout]

Werner Ballmann also has a 180 pages notes called lectures on Kahler manifolds, where he gives a rundown on the yau's proof of calabi conjecture. It has some discussion about ricci curvature though CY manifold is not the focus of these notes.

The last chapter of Huybrechts's complex geometry talks about deformation of complex structures, which can be used for CY manifolds. If you are particularly interested in deformation, you could read that.

Personally I feel like Huybrechts's book feels very much algebraic. It is nice if you have some familiarities about algebraic geometry.

[thick monolith]

Hello, I am looking for a book that will properly educate me on the subject of geometry. I don’t really know what a sphere is and how to interpret it as an object mathematically (like as a set of points for example). I have no issue with parameterising 3d objects. But when I see the parameterisation of a hypershere I’m not really sure what I should be thinking about or interpreting. Like what does the 4th dimensions mean in this context, it’s not temperoal so what the hell is it? You can’t just pretend the 4th spatial dimension exists (or can you)? Anyway, and books that educate me on higher dimensional geometry would be appreciated and teach me how to understand geometric spaces (only know of vector spaces and euclids space for n=3)

[graceful moon]

I’d actually recommend a linear algebra book if you’re struggling with the concept of higher dimensional spaces

[gray gazelle]

Guys, what book would you recommend for highschool student learning basic undergraduate mathematics

?

And also physics

1st year content is fine

And I am self-studying

[gilded ferry]

You didn't specify your level of understanding so it's hard to recommend you something.

• Mathematical Analysis by Zorich (both volumes)
• Topics in Algebra by Herstein
• Undergraduate Physics by Young
• Topology by B. Mendelson

[gray gazelle]

I can solve almost everything till grade 12, I don't like statistics and probability. I can fully ols e the calculus parta nd the algebra and 3d geometry and vector + coordinates geometry (need revision)

In physics, mech 1(netwon) and 2(fluids and thermodynamics stuff like that also waves), electromagnetism and modern physics (haven't practiced much)

@gilded ferry

Shall I go ahead with books you mentioned

?

[gilded ferry]

NOPE!!!

[gray gazelle]

Then

[gilded ferry]

Try

• Book of Proofs (really important)
• Calculus by Apostol (both volumes)
• University Physics by Young
• Abstract Algebra by Gallian

I think those are good introductory books

Don't neglect YouTube playlists on those topics

[gray gazelle]

Ok thanks can I understand fenymen lecture? And the book of real anylsis by jay cummings

?

[gray gazelle]

Thanks, I will purchase them

[gray gazelle]

Are they useful, I can't find useful stuff most of the time

?

I know about mit and openvourse

[gilded ferry]

What matters is if they are useful to you. If MIT's coursework works for you stick with it

[gilded ferry]

Is your goal to understand Real Analysis?

And the Book of Proofs is free btw

What I'm getting at is that if you have access to a library avoid buying them because they can get pretty expensive

[vapid pagoda]

Not sure where to ask this, but as a pure mathematician (geometer) idly interested in complex systems theory, does anyone know a good book to read? I have no idea how well the maths in that area is developed so maybe there's nothing suitable

[graceful moon]

I’d also recommend a differential equations textbook if you’re interested in physics, Boyce might be good if you’re starting from 0, maybe Riely mathematical methods if you’re looking for a more physics based outlook

[gray gazelle]

No, I thought it would help me understand other things easily

Is it necessary?

[gray gazelle]

From where can I get it ?

[gray gazelle]

I don't have access to that much good library, mostly all of the books there are of literature and humanities

[gray gazelle]

For me ?

[graceful moon]

Yes

[gilded ferry]

The internet

[gilded ferry]

I don't know your goals so I can't say. I'm more focused on maths, computer science and neuroscience

[gilded ferry]

Understandable

[gray gazelle]

Actually can you also recommend books of computer science, I am going to take that in uni

Like I know the basic of programming, just that and I can create basic things like library management system

Using ktinket and puthin

Python

Tkinter

[gilded ferry]

Visit MIT's computer science area. It's a really good source/guide

[gray gazelle]

You mean website ?

[gilded ferry]

Yes.

[gray gazelle]

Ok thanks@gilded ferry alot for recommendations. You too@graceful moon

[gilded ferry]

You're welcome

[gray gazelle]

@gilded ferry using latest edition is not required for the books you mentioned right ?

If so, I can use internet archive and other stuff like that

[gilded ferry]

Yeah

[gray gazelle]

Ok thanks

[ornate saddle]

Not directly related to mathematics, but maybe in the field of applied mathematics, I need some book recommendations on "solid mechanics" and "theory of plates" that are mathematically rigorous in terms of derivations of formulas at graduate level for mechanical engineers, if there are, by any chance.

[wraith sandal]

Hey thanks, but for naive set theory should I read a book like halmos or the book I mentioned covers that?

[vital bane]

naive set theory is literally just "a set is a collection of things" "union is the set of things that are in either of the sets" "intersection is the things that are common to both the sets" lol u dont really need a book for that

[wraith sandal]

Oh alright

[remote sparrow]

https://stat110.net

[wraith sandal]

Thank you

[vital bane]

https://youtube.com/playlist?list=PLZzHxk_TPOStgPtqRZ6KzmkUQBQ8TSWVX&si=Ali1xI6-tmh7tyl-

this is all you need to get started with analysis or algebra

[vital bane]

this guy is actually in this server i think

[storm fossil]

Anyone know of any very physically small math textbooks? They could be mini versions of famous textbooks or just ones that were designed to be that small. Companions are equally fine. Philosophy of Mathematics books could count if they're serious. Nothing in the pop-sci realm.

By physically small, I mean smaller than your standard 9x6 fiction book.

Subject matter doesn't matter too much, just as long as it's explicitly mathematical and not pop-science or a biography.

[wraith sandal]

I was on class lol, but thank you very much for your recommendation

[graceful moon]

I have a really cool old group theory book that’s pretty small, I don’t remember the author I’ll check when I’m home

It’s not like pocket sized or anything but it’s smaller than a normal book

[storm fossil]

Keep me posted, that could be fun 🙂

[graceful moon]

I don’t think you’d be able to buy it, it’s from the 60s or 70s I believe. I found it in a charity shop but it was pretty cool so I had to grab it, I’ll share a picture when I’m home

[gilded ferry]

Tell us the title, please

[graceful moon]

It’s Lederman introduction to the theory of finite groups of if I remember correctly, heading home now and I’ll double check

[hybrid meadow]

Not sure that this counts, but The Joy of Mathematics copy I have is pretty small and so was my A Course in Financial Calculus by Etheridge.

[mossy shell]

Any super resourceful books on algebra 2? Wanting to import a book to gpt to allow it to help teach what i want to understand

[stuck zephyr]

on openstax.com

don't use chatgpt for math it's not worth it

[mossy shell]

Ive been feeding it books on math and its been improving a ton

[stuck zephyr]

fr?

since when

[mossy shell]

Just yesterday i mean i gave it calculus and trig and algebraic equations and its been spot on

Ive only given it a big book on calculus so far though so i want to add some more

And just try it out

I’ll obviously be checking constantly but if i can get it working well i dont see why not

[stuck zephyr]

!nogpt

[hybrid sparrow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[stuck zephyr]

i never trust ai for any math content

but i guess good for you

[mossy shell]

I dont either i havent for legitimate purpose yet but im just trying to see if i can get it to work well

Also thanks for the site 🙏

[stuck zephyr]

don't mention it

[storm fossil]

Thanks for the recommendation. And for everyone else's as well. 🙂

Has anyone ever read the Godel, Escher, Bach book? I've heard good things about it, but no idea how properly mathematical it is. And a lot of philosophy books just end up being in woowoo territory. I don't expect it to be rigorous (obviously lol), but is it woowoo, a chill read, or what?

Any if it's not necessarily a good "math" book, anything somewhat similar that's more mathematical?

[fleet solstice]

Is it okay to read 1 textbook from one subject? Or should I read multiple books from the same textbook?

I kinda jus started the whole self teaching method so I'm curious on how to self study mathematics

[rare estuary]

I'm sorta in the same situation. Personally I've found that you should try multiple books and settle on 2-3 at most

[gray gazelle]

does anyone have any book recs for someone just getting into like mathematics and stuff.

[fierce hedge]

Yeaah, it's DMAshura

The only honourable who is cool

[woeful ravine]

How to solve it by Polya

And youtube

[fleet solstice]

Ohh okayy thank youu

[woeful ravine]

I personally think the best way to do it is to have 1-2 primary books that should be both rigorous and extensive and then some supplementary material, which could be books, articles, lectures, etc.

[fleet solstice]

Any tips on how you should read a textbook? Or jus read it regularly?

[rare estuary]

Main idea is to understand the material and practice using the exercises

For self-study, I think having the answers available is pretty useful

I don't think you should read a huge amount in one sitting if the material is dense/new to you

[woeful ravine]

Yeah I would say you go section by section, looking at theorems, exercises, and making sure you understand the concepts and definitions. Basically you use the book as a detailed reference rather than something you read like a novel

[fleet solstice]

Yeah thats true, I feel like w a lot of textbooks though, they give you the answers, but they should also give solutions aswell 😭

[subtle mango]

there's a very nice book i like called The Princeton Companion to Mathematics

it's really cool, it's like an encyclopedia + history of math

https://sites.math.rutgers.edu/~zeilberg/akherim/PCM.pdf

here's a pdf (i think it's okay to post this since it's hosted by rutgers.edu)

i think there's also one for Applied Mathematics

[rare estuary]

this is awesome, thx

[subtle mango]

yep :)

i have a physical copy because i like it so much

[woeful ravine]

It weighs like 5lbs though 😂

[subtle mango]

only?

i thought it weighed more

but yeah it's a very nice book

i don't carry it around with me lol i keep it at my desk

[woeful ravine]

Same

[subtle mango]

usually when i start studying a new topic and/or want more motivation for one, i'll just go and read its corresponding section

it's like my bible

[fleet solstice]

What makes a textbook good/reliable?

[remote sparrow]

hrbacek and jech's Introduction to Set Theory is small if you find a used copy

the third edition of mendelson's Introduction to Mathematical Logic is small

[subtle mango]

atiyah-mcdonald is very famous and pretty small

[remote sparrow]

some of lang's undergrad texts are very slim

saracino's abstract algebra book is small

older copies of older books can be quite slim

[woeful ravine]

As long as it covers the material that you want and has worked exercises it should be fine.

I would say skim through a couple of books & the table of contents to see if they seem good enough. definitely don't pirate through library of genesis btw ;)

[fleet solstice]

Wym by "don't pirate through library of genesis"?

Ohh wait

Is it like an illegal website for free books?

[gentle arrow]

piracy

[woeful ravine]

Considering the fact that textbooks are 50-200$ 99% of the time, it's basically your only option unless you can find it in the library

[rare estuary]

Yes, try to avoid breaking the law

[woeful ravine]

Piracy is a victimless crime & you will never run into trouble unless someone like an employer reports you directly, so it's not really an issue

But if you want to pay 5k for a couple dozen textbooks that's on you

[fleet solstice]

Nah

I got the library 😭

Except they give me like 20 days until I have to return the book 💀💀

But the most unfortunate thing abt renting out books in the library, is that they don't always have the books that you would want

Also how good are Baron's E-Z book series?

[buoyant flare]

🔥🔥🔥

[manic cairn]

General theory of relativity by Dirac is like 84 pages long

[dusk wind]

meanwhile pirate publishers exist

[vital bane]

[vital bane]

so is his QM book

[manic cairn]

I haven’t actually read it though

[vital bane]

short but sweet

[manic cairn]

either

because I’m not a physicist

[vital bane]

skill issue

[heady ember]

I'm currently reading Schroder's analysis book, a lot (most) of the times so far the exercises have been simple enough that I can almost immediately see the solution (other than sometimes when I'm just blind or the exercise is genuinely more thought provoking). So, should I do some exercises from like Rudin or something lol

A concern I have would be if Rudin (or any other resource) introduces a nontrivial theorem which is necessary to prove its exercise, but which is not introduced in my book.

[vital bane]

Yes

you should always do exercises from other books/problem sets as well

dont limit yourself to just one book

[heady ember]

Any resource you particularly recommend?

[vital bane]

Maybe try looking at open problems as well, you might immediately see the solution

[heady ember]

[vital bane]

well for metric topology I found these.. it's in my thread just scroll up a bit

a bunch of exercises

[heady ember]

how about for intro anal

[vital bane]

That is intro anal...

[heady ember]

top is like page 300 of Schroder

so i won't need that for now

[vital bane]

well what I'm planning to do is go through abbott then go through another book and do all the exercises

i.e apostol

so you can do that ig?

[heady ember]

All the exercises..

[vital bane]

you'd love tao's book, he starts off with set theory

[heady ember]

not enough

[vital bane]

and constructs R starting from N

[vital bane]

of course you need a book that starts off from ZFC axioms and cat theory

[vital bane]

well as much as I can in a few months lol

[heady ember]

I have never learnt cat theory

[vital bane]

so yea after you finish schroeder just do exercises from another book

Like a 2nd pass over the subject yk?

[heady ember]

Hm I see

Limited time though

[vital bane]

Why? you're in hs you have so much time, like 3 or 4 more years

[pliant wadi]

Irving Kaplansky's Set theory and metric spaces, pretty small and 100% thorough math

There's Baum's elements of point set topology by Dover publications. Pretty small book.

Dover publications books are generally on the small side imho.

[fierce hedge]

Rudin is comparatively difficult than Schroeder maybe try Browder. I think even Abbott has decent exercises

[heady ember]

No, next year is my last year in hs. Then... 2 years of compulsory military service

[vital bane]

doing difficult exercises is how you get better you have to keep challenging yourself

"If you only do what you can do, you will never become more than you are now"

-master shifu

[heady ember]

Yeah I know, that's why I'm planning to use jacobson for alg and why I'm asking in the first place lol

[vital bane]

ah forgot about that cant you take math books with you?

[heady ember]

But I have certain goals / time constraints

[heady ember]

I hope to get into the most background character of background character roles, so I have maximal free time to self-study more math

I hope to finish LA and intro anal by next year. Then basic algebra and a bit of Lee's top manifolds the year after, hopefully. Then hopefully I can get to complete Kunen's foundations of mathematics. So that I can read his set theory book by the start of ug

[heady ember]

How does Browder compare to Rudin, exercises wise

The way you said that makes me curious if you're implying something about that

[chrome tide]

Can any of ya'll tell me what's that most enjoyable readable math book out there I have got some physics books like "A brief history of time" by Stephen Hawking. So I want something similar. Thanks 😊

[vital bane]

"Humble Pi: A Comedy of Maths Errors" by Matt Parker might be fun

[chrome tide]

Thanks buddy

[undone jewel]

Anyone know if there's anywhere to get Algebra and Trigonometry with Analytic Geometry 13th addition free?

[dire stone]

is Linear Algebra Done Right a good book to take your first stab into that topic?

[magic moth]

the new edition is good

[dire stone]

i have the third, is that the new one?

[magic moth]

4th

its free

https://linear.axler.net/

[dire stone]

oh awesome

thanks

[magic moth]

like

not even ilegal to share

thats the author doing it

[silk forge]

Oliver Twist

[fossil arch]

Analysis book that's efficient and fast and not turbowordy with good exercises that's not named Rudin

Go

[magic moth]

Mir books

any of their analysis books

[vital bane]

abbott

[fossil arch]

Abbott talks a lot 😭

[vital bane]

no he doesnt

he teaches you everything from the ground up

there is a lot of intuitive discussion about the topic being covered

oh if you mean you're looking for a book to review analysis then rudin would be good

he doesnt talk at all 💀

[magic moth]

she said with good exercises

but tbh the exercises are fine in abbot

I just like to be spanked by my math books

[fossil arch]

Yes but I don’t like Rudin he talks too little

I like AM amount of talking and cute proofs and exercises

That sounds so dense 😭

I like analysis :3 just not Ruwudin

Just basic undergraduate real analysis lolsies

[dapper root]

NO MEASURE THEORY

[fossil arch]

In due time Chm

[dapper root]

Idk

I’m an algebraist

No

actually I’m a geometer

Of an algebraic kind

[stuck zephyr]

[dapper root]

[indigo mesa]

Amann escher

[fossil arch]

Ok German

Good taste though

[marsh ingot]

Dont like Rudin too

Sadly I pick their Riesz representation theorem, I regret

[marsh ingot]

Algebraic geometry?

[dapper root]

Indeed

[remote sparrow]

Mathematical Analysis: A Concise Introduction by bernd s. w. schroeder

[magic moth]

where u the one who recommended me Schroeder Sour?

[fossil arch]

Atiyah Macdonald

[mellow wren]

what are some good places to get going into arithmetic geo
Idrk what the field looks like so idk where to sort of go into it

[fossil arch]

Yo Neo you got a banger name

electrodynamics. ok edgelord slay slay

[remote sparrow]

don't remember

don't think so

[magic moth]

schroeder has both cauchy sequences and dedekind cuts right?

[remote sparrow]

pretty sure it's an axiomatic treatment, so no

[magic moth]

ur right

i was thinking of Ethan D. Bloch

[upbeat siren]

You guys happen to know any books that are able to cover most of the topics shown here? Maybe something that I can use as a reference (you can ignore the economic topics)?

Introduction to linear algebra: vector spaces, vector subspaces, dimension, linearly independent vectors, linear independence characterization theorem. Euclidean vector spaces. Generator systems, bases. Linear functions, image subspace (column space), kernel subspace, dimension theorem. Applications in portfolio theory and complete markets. Scalar product of vectors. Euclidean norm and Euclidean distance. Spherical neighborhood in Rn.

Real functions of n variables, level curve, limits and continuity. Differential calculus in several variables: differentiable functions, gradient, differentiable functions, tangent plane, theorem on the properties of differentiable functions. Quadratic forms, sign of a quadratic form, principal minors and principal minors of Northwest, theorem on the sign of a quadratic form. Hessian matrix and associated quadratic form.

Free optimization in multiple variables: first order condition, second order condition, optimization in the economic-financial field.

Constrained optimization with hard or relaxed constraints: Lagrange theorem, shadow prices, second order sufficient condition (edged Hessian); optimizing constrained with relaxed constraints, Kuhn-Tucker theorem. Optimization in the economic-financial field.

[fallow onyx]

Anyone got any good recommendations for highschool mathematics? N5 level in Scotland if that helps.

Probably a very basic level for the folks in here but I just need a decent grade

[marsh ingot]

I barely know a book for the first paragraph. To the 2nd one there is a good know I followed but its in spanish dunno if exist a english version

[upbeat siren]

https://youtu.be/S116mTfk2t8?si=-YnZbZdSs2Q55CDd

[fallow onyx]

Cheers

[upbeat siren]

😩

[marsh ingot]

Forgot what I say. I cant find the first book they gave for linear algebra

[upbeat siren]

I don't know if something is wrong with me, but I don't seem to find good linear algebra books

[marsh ingot]

Linear algebra by Jim Hefferon seems good, at least for what ppl say

Try this one

[gray jungle]

whats your goal with learning linear algebra ? are you a math student?

there is good la books depending on what you want from la

[upbeat siren]

.

that is my goal

[upbeat siren]

ty

[gray jungle]

books can cover these topics in different fashion is what im trying to say , a math student would want a theoretic la book like hoffman kunze / axler / friedberg
while a computer science or engineering student might prefare a book like gilbert strangs book

depending on your goal

#book-recommendations message there is also a list of la books reviewed here

[upbeat siren]

oh my teacher covers these topics in a very mathematical way. she even introduced us to algebraic structures: semigroups, groups, etc.

course has the word "applications" in its name but she doesn't even care about it 😆

[gray jungle]

id recommend hoffman kunze personally , its a bit old school and not the easiest book but imo the best reference out there

[upbeat siren]

ty

[graceful moon]

DLB maths on YouTube helped me when I was doing nat5

[graceful moon]

Linear algebra and applications by Nicholson is a good choice imo, a solid enough mathematical basis but there’s plenty of real world examples if that’s more your thing. I don’t know if it had much econ type stuff in it though

[fallow onyx]

Oh cheers, didn’t realise there was other Scots here

[dusk wind]

hows this book by strang? https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/1733146679

saw some of his MIT videos online, fell asleep even at 10x speed

[heady ember]

What do you think of Schroder's exercises, just curious

[vital bane]

kinky

[magic moth]

sure

[remote sparrow]

reasonable

[remote sparrow]

https://www.amazon.com/Mathematics-Economists-Carl-P-Simon/dp/0393957330

#book-recommendations message

colley is good for multivariable calc

you will also want a reference for matrix theoretic results

garcia and horn is good

horn and johnson is a reference text for more advanced results than in g&h

numerical linear algebra books are good too

a standard textbook is trefethen and bau

golub and van loan is a reference

@rich sun would you agree these are appropriate recs for someone studying econ?

[upbeat siren]

wow this book

has a lot of stuff

[heady ember]

I see

[upbeat siren]

a very interesting book, thanks a lot

[upbeat siren]

this one is solid too.

[upbeat siren]

Meckes' Linear Algebra is exactly what I'm looking for

[novel hound]

Hey again 😉 You may wanna see this: #book-recommendations message

[dusk wind]

wow big kudos for this lol

guess I'll use friedberg or shilov

[fierce hedge]

Interesting choice, did you like it? It has some unusual set of topics like continued fractions not usually covered elsewhere.

[fierce hedge]

Oh lol, so you didn't personally use that book? I'm assuming the teacher assigned some reading or something from the book

[dusk wind]

wow knapps book seems interesting

[dusk wind]

geometric overview of abstract algebra https://amazon.com/Abstract-Algebra-Applied-Undergraduate-Texts/dp/0821847953 by solomon

[dusk wind]

pretty straightforward book on beginner Algebra with super organized sections http://wallace.ccfaculty.org/book/book.html

[fleet solstice]

How good are Baron's E-Z book series?

[dusk wind]

check amazon reviews but probably about the same or worse than dummies
might as well just use Schaum's books at that point or course notes online

[fleet solstice]

I see I see, thank you.

What're some good Precalc textbooks then?

[dusk wind]

plenty of post on that here already, you can start from algebra again or look at https://mecmath.net/trig hell even the link I gave earlier by wallace has every subject on the main site. Otherwise https://stitz-zeager.com/Precalculus4.pdf and https://stitz-zeager.com/szct07042013.pdf or, https://edunettech.blogspot.com/p/open-textbooks.html (https://openalgebra.com) who wrote https://saylordotorg.github.io/text_intermediate-algebra/ or https://math.oit.edu/~watermang/math_100/100book.pdf or https://math.libretexts.org/Courses/Kansas_State_University/Your_Guide_to_Intermediate_Algebra (no trig, functions only)

just get better at practical algebra and some trig

[harsh dawn]

Which maths textbook is the best for IGCSE?

My math is really bad, looking for textbook to buy

Any recommendations?

[rustic grove]

The one for your exam board. I think IGCSE is edexcel...

[harsh dawn]

Alright thanks, will check it out

[sturdy nebula]

Hello!
What's your opinion about "AI:A modern approach" book?
And is it's language and the way it explains hard or it's because I'm bad in English?

[storm fossil]

Does anyone know if there exists something like 3B1B for Algebra? (Not Linear Algebra, but more of Elementary Algebra/College Algebra.)

It's easy to imagine how to tell people the beauty of calculus, geometry, and--to an extent--linear algebra (since you can focus on the very visual idea of vectors).

But it feels like Algebra and Number Theory rarely get the treatment of showing intuition and beauty. I think they're both beautiful, but I'm wondering if it's even possible to do a more strictly "here's the intuition and coolness of these ideas" like you can with calculus. Has anyone tried and succeeded? Doesn't necessarily have to be a video format, books work as well.

It just feels like there should be some fun and exciting way of describing the coolness of, for example, prime numbers and factorization, etc.

[dusk wind]

probably dora the explorer

[finite gale]

tbh i can't really tell what they mean by elementary algebra / college algebra

there's plenty "cool intuition" videos on various topics in group theory for example, though possibly not consolidated on a particular channel

but if they mean "elementary algebra" in the sense of high school algebra, there isn't really much to say

[storm fossil]

How did you get unmuted? I had your comments blocked. Weird.

[storm fossil]

I definitely agree that there's not much, but there's not nothing.

For example, Euler uses a string/rope analogy often in his Elements of Algebra book.

I assume you could at least show what factorization means, division, etc. You have a string, want to divide it into many parts, etc. Or if you want to multiply a few bits of the string to equal another, and realize that that string can be represented as a multiple of the bits, you get cancellation, etc.

I doubt it'd be a long series, but could certainly be more.

[dusk wind]

bro even a dog knows how to factor

[storm fossil]

In America at least, children are given 0 intuition behind algebra. And it's really unfair to say that there isn't any. Sure, some of it is arbitrary in the sense that it's just definitions. But there's some stuff we can offer.

[dusk wind]

also thanks for annoucing your personal preferences

[storm fossil]

How have you not been banned? I had you blocked before for being obnoxious.

[dusk wind]

this is not entirely true at all and is borderline obnoxious

also just so you know public opinion isn't a bannable offense so you can highroad elsewhere

[storm fossil]

<@&268886789983436800> I'm going to block them so if it's not against the rules, I won't be bothered by it. But they've been warned multiple times by moderators to knock it off. In what way is "bro even a dog knows..." on-topic, useful, contributive, or generally acceptable?

[storm fossil]

You have been blocked again. Take care.

[dusk wind]

bro is lost, some people just don't know how to have a dialogue, only drama with themselves

there are authors like this, where instead of writing for the reader they write for the publication or vanity

[stuck zephyr]

sigh

[lusty swift]

Hello can anyone suggest a book so i can learn tensor and topology? (I got a bsc in maths but haven't learnt deeply into tensors ,never known what topology is)

[finite bobcat]

Introduction to Topology by Bert Mendelson

Also, as a more textbook book: "Topology" by James R. Munkres is a classic and widely used text in many topology courses

[lusty swift]

Is this like a more depth book once you get into it perhaps?

[mossy flume]

Learning about tensors will vary wildly on context (algebra, geometry / topology, computational complexity, 💀 machine learning)

[finite bobcat]

ye i think it's pretty rigorous

[mossy flume]

Munkres good

[lusty swift]

I'm learning these for relativity studies tbh

[finite bobcat]

The book covers both point-set topology and elementary algebraic topology which I think gives u quite a good

overview

[mossy flume]

Oh yea physics is a thing

And tensors exist there also

Somehow it's all connected

[finite bobcat]

I heard General Relativity by Robert Wald is quite good

bridges the math and physics

talks about tensors and differential geometry and usage in general relativity

[lusty swift]

I'd like to study em like separately before I check on relativity classes though

[carmine dirge]

Can anyone suggest a book for classical and linear algebra for bsc maths?

[rustic grove]

LA: #book-recommendations message

[rustic grove]

AA: #book-recommendations message

[remote sparrow]

what's classical algebra

[finite gale]

as opposed to baroque algebra?

[rigid barn]

and romantic and modernist algebra

[vital bane]

post modern algebra

[dusk wind]

'modern algebra' hundreds of years ago

[dusk wind]

probably the math orchestrated by beethoven

[remote sparrow]

leary and kristiansen's A Friendly Introduction to Mathematical Logic, enderton's A Mathematical Introduction to Logic, cutland's Computability: An introduction to recursive function theory, and bridges' Computability: A Mathematical Sketchbook are some other small books

gamelin and greene is a very slim volume in topology

[woeful ravine]

I assume he means "standard" lol

Like a standard algebra textbook

[echo elm]

Does anyone have recommendations for any entry level/ basic pre-calc, calc, and or high school physics, books?

[opaque hill]

Yeah, there are some sources that show the intuition of Algebra and Number Theory in a similar way to 3Blue1Brown's approach to other math topics, although they're not as visually intuitive. For Algebra, you can check out books like 'The Art of Problem Solving' by Richard Rusczyk, it's an emphasis on understanding and intuition. As for Number Theory, 'Prime Obsession' by John Derbyshire looks at prime numbers and their significance. There are online platforms like Khan Academy and Brilliant.org which make it all feel more approachable, but that's your call.

[dusk wind]

scroll up

[storm fossil]

This is very neat, thank you for the recommendation.

[storm fossil]

Thanks a bunch! I'll check out both of these. 🙂

[silk remnant]

What would you guys buy between Hopeless series by Collen Hoover, Radio Silence by Alice Oseman or a more "deluxe" manga of junji ito?

By more deluxe I mean like, hard cover, great quality and other stuff

They're all about the same price

And I havent read any of them yet

[hearty steppe]

Hey any material out there for learning more about orthomodular lattices?

[novel hound]

You could check out something by Martin Gardner perhaps (for example: The Colossal Book of Mathematics or one of his many "puzzles" books). Or, something by Ross Honsberger (his Mathematical Gems 3 volume series is pretty good). There might be other authors like them too but these two come to mind atm.

[woeful ravine]

Elementary algebra is very straightforward, so I don't know how in the world anyone would ever need an intuitive intro. If you did though, I would say just look at some lower level competitive/recreational math problems because they're almost always designed to be interesting rather than theoretically significant

[storm fossil]

You think, for example, that the quadratic equation is intuitive for a 15 year old?

Not solving it, but the intuition behind it.

[woeful ravine]

I would say look up "visual proof of quadratic formula"

Youtube is a great resource

But yes, for teachers, understanding the intuition behind elementary algebra is very important

[storm fossil]

YouTube is undeniably a great resource. But the idea that elementary algebra is intuitive is just not reasonable. There are parts that are intuitive. "I have three boxes. That's long, let's just say b for boxes." That's intuitive.

But I think it'd be at best unfair to the Arabs who spent a few hundred years coming up with elementary algebra to say that it was just, by default, intuitive stuff.

[novel hound]

I'm not sure what your location is, but kids start doing olympiads at age 14 (AMC 8 in the US for example). And, I believe a lot of the motivation for algebra and number theory comes from puzzles and competition math. Lot of literature for this purpose. Can check out AoPS.

[woeful ravine]

Yeah I suppose it's just about what you know to begin with. For example, if a student understands the geometry of triangles, they can probably easily learn about trig functions and identities with the right motivation

[storm fossil]

I was checking out the Colossal Book thing. Looks really fun. I'll also take a look at the Olympiad stuff.

[novel hound]

check out the AoPS: "artofproblemsolving" website - lot of resources (books, lectures, camps, etc) listed there for different age groups.

[storm fossil]

I agree. Aside from any serious barrier, I think everyone can learn elementary algebra, geometry, and trigonometry pretty easily. But there's a really big difference between understanding what you're doing and using algorithms that you memorize. The former is missing in a lot of curriculum.

[woeful ravine]

I also would recommend looking at "USSR Olympiad Problem Book" by Shklarsky & Yaglom because it has >300 problems with a large variety in difficulty and its cheap

[storm fossil]

I remember seeing that USSR book years ago. Heard it was cool stuff.

[fleet solstice]

Ouuu thank youu, any recommendations for Alg and Trig?

Or are they mixed into the links that you've sent?

[finite gale]

Just use khan academy for stuff before calc tbh

Or maybe up to

[dusk wind]

everything I sent has everything so pick your favorites

khan academy is too slow imo way easier to just go through a workbook then use organic chemistry tutor vids at 10x speed

[finite gale]

There are also articles to read on khan academy I'm pretty sure

Regardless, you can skip around and just do the exercises if you want

[lusty swift]

Hello any books for tensors?(I asked yesterday but you guys gave the suggests for topology which I also asked)

[balmy isle]

where do u guys recommend to learn and solve discrete math problems? im afraid my teacher is gonna fail me for low scores

[graceful moon]

That kinda depends on what you want, a differential geometry or an EMR book could be better for you depending

[lusty swift]

It's for special and general relativity

I've already got some lecture videos in mind to learn the same but on the second video I got stuck cuz of the tensor aspects

[graceful moon]

There’s kinda lots of ways to approach it, you can take a more physics forward approach or a mathematical approach, it basically depends on how much differential geometry you want to learn

If you want to take the maths forward approach I’d go for Lee “introduction to smooth manifolds” then, I’ve not read this book myself but it’s the one recommend for my schools mathematical GR couse, “Introduction to GR” Hughston and Tod. If you want a very physics forward approach any upper level mathematical methods textbook should cover tensors, maybe like Arfken and Weber

[lusty swift]

Alright

Thank youu

[deep summit]

whats the best problem book for undergrad linear algebra

[maiden hemlock]

How to Win at Chess by Levy Rozman

[stuck zephyr]

Read dami's message

On pinned messages

[vital bane]

There is also "semi-riemannian geometry with applications to relativity" by barret o neil

[gray jungle]

Artin

[fierce hedge]

And Knapp (Knapp is slightly more advanced than Artin)

[gray jungle]

this is what he covers

enough for what ? a first course in Linear algebra? Yes

[heady ember]

Depends on your needs ig

Of course a full fledged lin alg book would cover more... well lin alg

[gray jungle]

I would recommend H&K over artin for LA but artin is a good book too

[heady ember]

I personally have enjoyed FIS so far

3 chapters in

[gray jungle]

• you can always suppliment gaps in artin using other books

[heady ember]

Friedberg insel spence

Alternatively, see the pinned review by dami.

[gray jungle]

you can try Strang's book Linear Algebra and Its Applications ,there is also lectures by strang online

its one of the best (first) courses out there

one might argue its more useful to do a theoretic book for a math student but i think strange course is really good to build some motivation

https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/

[gray gazelle]

https://youtube.com/playlist?list=PLOAf1ViVP13jmawPabxnAa00YFIetVqbd&si=t3v6V8uY-r_l55JK

[gray jungle]

also has assignments/exams etc here

[gray gazelle]

I have been following this playlist

seems pretty good so far

for linear algebra

this follows a book

https://www.njohnston.ca/publications/introduction-to-linear-and-matrix-algebra/

[solemn anchor]

guys! is there any textbook recommendations for students that just finished ib and alevel further math, please lmk im out of resources D:

[graceful moon]

If you’re going to uni for maths something like liebecks introduction to pure maths could be a decent book

I’m not sure how much you do proof wise in IB, but that book is a nice introduction to proofs and it does it by giving you a taste of loads of different areas of maths

[opaque hill]

Congrats on completing IB and A-level Further Math!

But, could you specify? XD

[fleet solstice]

IB like International Bacculerate?

[remote sparrow]

#1059828221887135774 message

@vital bane see Metric Spaces by micheal o'searcoid

it has an instructor's solutions manual

Metric Spaces by robert magnus seems good as well, though it doesn't have a solutions manual

[split ether]

There are a variety of books that could help you with math, but I recommend books that exist.

[dusk wind]

https://tinyurl.com/booksthatdontexist

[wraith sandal]

What is a good book for an introduction to linear algebra if I want to study proof-based linear algebra? (digital is also ok)

[rigid barn]

#book-recommendations message

[gray jungle]

I recommend Hoffman and kunze

[wraith sandal]

Yeah but I have 0 knowledge on linear algebra

[gray jungle]

The book is self contained , as long as you are familiar with basic proofs its readable

[crimson leaf]

I like Friedberg Insel and Spence I picked that up when only knew row reduction

[gray jungle]

if you havent had any proof exposition maybe just Friedberg

[crimson leaf]

I always felt like H&K would better after an analysis or number theory course where you get to see how proofs come about

[dusk wind]

Friedberg

[wraith sandal]

I'm currently studying from chartrand's book, and im thinking to study to axler's until I know how to do proofs

[gray jungle]

Make sure to use the 4th edition if you use axler

[wraith sandal]

thanks

[rigid barn]

It's freely available online btw https://link.springer.com/content/pdf/10.1007/978-3-031-41026-0.pdf

[remote sparrow]

#book-recommendations message

[vital bane]

thanks!

[dusk wind]

The book by Cohen is clickbait

[jovial parrot]

Bruh

The cover is so much cooler than my 3rd edition

:angey:

Multi linear algebra o_o

[shell geyser]

i think it depends on the direction you want to go. if you want to learn more of the same kind of math as you did in further maths, you can't go wrong with a book on linear algebra or multivariable calculus. alternatively, you can take a look at some intro proofs (or some places group it under discrete math). for the first kind, i used thomas' calculus and lay's linear algebra and its applications. i don't think people here like those books much, but they're straightforward and easy to understand. for proofs, i would recommend lakins' the tools of mathematical reasoning, which is short and covers a lot of foundational material

[dusk wind]

beezers looks ok but hasn't been updated in a while unless you use the browser edition, reviews for Klein say its too verbose etc.
Friedberg or Hefferon is the way. You want to have more when you use a book, such as it's source and solutions, that way you or others can improve it and it costs nothing.

[misty storm]

does anyone here have a pdf of the art of problem solving intermediate algebra solutions manual?

[stuck elk]

What are good books on abstract algebra? I don't like the writing I've seen from Dummit and Foote and Pinter's A Book of Abstract Algebra is too shallow. I want something like DnF but with better writing, at least something that covers group actions, automorphism groups, sylow theorems, modules, algebras over rings, some galois theory, and some homological algebra

[heady ember]

Have you looked at Dami's pinned review?

[willow adder]

#book-recommendations message link to it

[sage python]

Those reviews should count toward my mathscinet citations

[stuck elk]

Nice, I'll check out Jacobson and Artin

[dusk wind]

how do you feel about strangs book on linear algebra?

[swift cipher]

I used it when I was an undergraduate. I liked it well enough.

[dusk wind]

interesting

[remote sparrow]

which book

he has a super low level intro and another book called linear algebra and its applications

[woeful ravine]

Lang's Algebra is more of a graduate textbook but I would def recommend it

Just because it covers a wide variety of subjects in a decent amount of detail

[dusk wind]

this is his newest intro book https://amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/1733146679

I watched a few of his videos but wasn't a fan, even though he's been at it for a while

bluebrown was more to the point sadly

[remote sparrow]

rotman is popular

[finite gale]

rotman is good

[fierce hedge]

+1 for Rotman

[stuck elk]

Thanks 😃 I will also look at rotman

[spiral surge]

Any good book recommendations that have linear algebra and differential equations at a second to fourth year undergrad level

Matrix solutions of PDEs. Handling Odes with linear algebra and integrating factors and Fourier/ Laplace and series transforms. Multiple methods at once per equation. Non homogeneity. And probably upto third order non linear ones

[graceful moon]

Boyce di prima and Mede, not my favourite textbook but it does have all that

[gray gazelle]

any good references for algebraic number theory?

[rigid barn]

Samuel is very short and extremely informative.

[gray gazelle]

thanks so much

[rigid barn]

There's a plethora of options, but I feel like this is the best possible starting one.

[manic cairn]

I know a book that covers group actions, automorphism groups, sylow theorems, modules, algebras over rings, Galois theory, and homological algebra.

It had better writing than Dummit and Foote too!

Algebra
—Serge Lang

It has a ton of excercises

and all of them are varied and different

over 50 for chapter 1 alone

[rigid barn]

Lorenz's Algebra 1 if you want an exposition geared towards fields and Galois theory (for algebras and modules see the 2nd volume, there's a great exposition of semisimplicity, but no modules over PIDs); unfortunately he doesn't cover homological algebra. Jacobson and Isaacs are my close 2nd favourites (Jacobson's 2 volumes in particular cover everything you mention, while Isaacs' exposition of fields/Galois theory is possibly my favourite and the place where the subject clicked for me). Don't go for Artin, it's only good if you're very new to math and barely know your way around things.

[manic cairn]

Everything you just listed, and much more is contained in chapters I-VI of Lang

[vital bane]

I hear lots of people saying serge lang's algebra is bad

why do they say that

[fierce hedge]

It's bad for the first time reader cause it's more terse than Rudin, it's more of a second/grad algebra level

That said, no ug book would cover homological algebra so Lang is fine

[vital bane]

you see that's what confuses me

because at the grad level you would usually be more specialized like you'd focus specifically in either representation theory, or comm alg or homological alg

so wouldn't you rather just use a separate book for those subjects?

it would cover more material

[solemn anchor]

ohokTYSM!

[fierce hedge]

That is what usually happens lol, for example you can learn rep theory from dnf or Lang but usually a different book is used. I think we used Liebeck and James, same for homological algebra etc.
So books like dnf, Lang or Rotman serve more as a one-size-fits-all kinda reference book

[vital bane]

I mean D&F i understand it's more like a "undergrad intro to these grad subjects"

[celest steeple]

Any good books/articles to help me understand properties of exponets

Nothing too special, I'm only in algebra 1

[gray gazelle]

Hi, what's a good book that has a lot of exercises in proof writing besides the most logical parts of operators and sentences? I need something more aimed at mathematical proofs.

[civic python]

Maybe "How to prove it" by Velleman? He touches upon many fundamental math concepts

[remote sparrow]

goode and annin has linear algebra and odes combined into one book. don't think it covers matrix solutions of pdes, though.

[crystal trellis]

i'm finishing up a course in intro to real analysis (advanced calc it's sometimes called) and am looking to dive deeper into the subject of analysis. does anyone have any book recommendations? I like examples and am still at a level where i need a bit of detail in proofs

but i dont need to be spoon-fed

if that makes sense

[gritty gale]

i haven't personally read it, but I've had

• Robert Gardner Bartle and Donald R. Sherbert, Introduction to Real Analysis, John Wiley 2000
  recommended to me in the past

[remote sparrow]

OP said they already finished a class in real analysis

[remote sparrow]

carothers

[gritty gale]

yes, but this was in the 'further' section of the list i was looking at, which suggested to me that it would cover the deeper stuff

[remote sparrow]

you can read axler or schilling measure theory if you want

[gritty gale]

at least towards the back half

[remote sparrow]

if they did all the traditional topics, like sequences, series, limits of sequences, limits of functions, differentiation, and integration, they should do metric spaces

bartle and sherbert doesn't cover metric spaces that much

or they can just do measure theory on the real line

[glossy zealot]

May I ask something a bit related to this?
Are topics of metric spaces important for an advanced probability class?

[remote sparrow]

if it involves measure theory, then yes

@orchid mortar

[crystal trellis]

@gritty gale @remote sparrow thank you!

[marsh maple]

The outsiders is one of the most books of all time

[orchid mortar]

Yes, up to a point. You especially want to know everything convergence.
There's also higher level abstraction things I'm not too familiar about, but I think only the more/most abstract probabilists do such things. (My reference point is Salez whose works I read from time to time) I think most people expect you to know what's a Polish space, but I don't think everyone is well-aware all the time of things like doing probability in non-separable spaces. (99% of the time if you're applying probability it won't matter)
If you really want to know more, ask in #advanced-probability / real analysis advanced

[glossy zealot]

Thank you so much for your response!

[orchid mortar]

I'm just a noob, there's a lot more knowledgeable people. But I think I can apply probability okay-enough

Learning measure theory IMO is about learning how theoretical tools fail and how/when they don't, and to ground in mathematical foundation (e.g. [reasoning with] solid basic axioms) rather than like, learning about axiom of choice and how it results in non-measurable sets

[gray gazelle]

Aluffi is very certainly undergraduate and covers homological algebra.

[granite breach]

has anyone read both topology without tears and munkres topology

which is better to start self studying topology with?

[marsh ingot]

I have one but is in spanish

You want basic stuff or advanced one?

[granite breach]

i have never done topology, but i have done real analysis

i want advanced, but i need to do the basic stuff also

[feral dagger]

Hello. I am bad at Geometry. So I need Geometry book. Do someone know 9th grade book?

[inland elm]

if you've done real analysis then munkres should be good enough to start with

[strange valley]

Can anyone recommend me a real analysis book for self studying

[gray gazelle]

Tao is probably the best overall. Rudin is a nice speedrun book.

[heady ember]

Schroder's Mathematical Analysis: A Concise Introduction

Its gentle but fast, sounds contradictory but maybe not. Only gripe I have with it so far is that I wish there were more challenging exercises more frequent, but if you're new to proofs it might be perfect for you: In the first couple chapters he intentionally writes out proofs in detail and reminds the reader of things/details often, then he gradually phases this out (he explicitly says when this occurs, e.g. at the start of ch 4 and ch 5). You can always supplement the exercises with some additional resource if you find them too simple for your liking.

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

A fellow Schroder user (who started earlier): https://discord.com/channels/268882317391429632/1037160979198378024

Dami also recs Schroder for people new to proofs/anal

[strange valley]

I think it suits me as a newbie in real analysis.
Thanks

[heady ember]

Enjoy!

[strange valley]

I will try Schroder's Mathematical Analysis then Tao as an advanced book.
Thanks

[granite breach]

rudins principles of mathematical analysis

i hear its supposed to be hard, but i honestly thought it was very readable

[granite breach]

is munkres hard? ive heard its quite hard and i have no experience with topology. ive done a bit of metric spaces but thats it

[strange valley]

I'm now confused about which book I should start with

Maybe i will read the introduction then decide which book to start with

[heady ember]

What I meant:

[granite breach]

oh wow thats really good

maybe download both

and reference rudins to see an alternative approach to a proof, or more practise questions

and use this other book as ur main study material

[graceful moon]

I personally think Tao is fine to start with, both his analysis books are quite good

[gray jungle]

its as easy as it gets , but very wordy that i recommend utorontos notes with munkres as a reference

https://www.math.toronto.edu/ivan/mat327/?resources

[granite breach]

okay il start with munkres

[vital bane]

contradictory but maybe not

it's only gentle for you because you've done like 2 whole axiomatic set theory books before it

[vital bane]

Abbott is also another good option (the best imo )

honestly there's just no shortage of good intro analysis boos

[fierce hedge]

Tao isn't an advanced Book. They cover the same things, for something more advanced try Carothers

[ionic portal]

what is an abstract linear algebra book that covers a vast amount of topics

[heady ember]

I only completed one math book so far, that is, Enderton's Elements of Set Theory. I think one going into just about any proof based math book will get their shit slapped outta them, like I was with Enderton lol. But Schroder should make the learning curve less steep, than say Rudin.

[heady ember]

just start grinding

[heady ember]

Look in pinned

[gray gazelle]

Someone recommend a good book about the Orlicz spaces?

[novel obsidian]

In artins algebra are the exercises for each section doable after each section or is the whole chapter a prereq for the exercises, because there have been some that I've felt fall into the first category and some that don't

[viral oasis]

Need book recommendation to learn probability deeply. i know basic high school level stuffs like conditional probability and such but i want to learn more deeper stuffs

[vital bane]

if you wanna go deeper into probability, then I'd suggest you learn real analysis and some measure theory

[dusk wind]

just learn statistics

[orchid mortar]

Just read a higher level textbook, like Grimmett and Stirzaker

[rustic grove]

I think the exercises are in sections, but you need to have done the stuff before it for each chapter. For example if you do the subgroups questions, it will assume knowledge of the groups before it.

[remote sparrow]

roman

https://www.amazon.com/Advanced-Linear-Algebra-Graduate-Mathematics/dp/0387728287

i'm pretty sure he used microsoft word for some of the diagrams though

[storm fossil]

Has anyone had experience with any of the Art of Problem Solving textbooks? I'm specifically curious about the Calculus one. Is it rigorous?

And secondly, does anyone know why high school algebra textbooks tend to be freakishly long compared to calculus + books? Their Algebra textbook, which I believe is like... grade 8/9 (in the states) algebra is 650+ pages. Then the second algebra textbook (which I assume is Algebra 2 here in the states) is another 700+ pages.

Their calc book, which seems to be both Calc 1 and 2 is 330-ish pages. This seems to be true very often, where high school-level algebra is triple or even quadruple the length of calculus books.

I've always found it bizarre how many pages can be fit into subjects that really seem like they could be halved or even thirded (is this even a way of using this word lol).

I'd say it's problem sets or something, but Spivak's calc is ~650 pages and has some very good problem sets. And covers Calc 1 and 2 (granted it's an analysis book, but I think it's very successful at teaching calculus)

[grave thorn]

has not learned measure theory yet

[past flame]

Has there been conversations in here before about F.I.S vs. Axler for linear algebra book recommendations?

[silver stirrup]

does anyone know if James Stewart is a good calc 3 book?

(James Stewart Multivariable Calculus 8th edition)

and is it also applicable to physics

[graceful moon]

I’m guessing since you’re asking about physics you’re not too fused about it being super proofs based and are more into calculations, in which case I’d say it’s a solid enough book

[silver stirrup]

ok thank you

yes I'm looking for something applicable to physics more so

[graceful moon]

Yeah nothing wrong with Stuart it’s well written, covers everything you’d need, plenty of excercises and it’s popular enough to be easy to get

[silver stirrup]

ok thank you!

also why is it from ch 10?

[remote sparrow]

it's split from the bigger book

i recommend just buying the bigger book

more book for same price

[silver stirrup]

well price isn't an issue - just using libgen

[graceful moon]

Stewart covers basically all of calculus (calculation wise anyway) and I believe the first 10 chapters is just basic series differentiation and integration

[silver stirrup]

if i've read aops calculus I should be fine for the first 10 right?

[graceful moon]

I don’t think the multi variable stuff starts until (presumably) chapter 10, but I don’t know the book well enough to know the chapter numbers

[silver stirrup]

ok

well ty anyway

[gray gazelle]

Anyone know of any cheap Mathematics textbooks that go through from basics to advanced? Like ones that are worth investing in to?

[finite gale]

it's a bit unclear how basic is basic and how advanced is advanced

but if you're just looking for stuff up to calc, khan academy is free..

[gray gazelle]

I am talking like baby stuff to college. I just want to keep it around so I can refer back to it.

[finite gale]

i think khan academy is a good enough resource for that, since any pre-calculus textbook is more or less the same

[gray gazelle]

I like keeping copies like physical copies.

I dont like online resources.

Like I want to find an actual textbook series for mathematics.

And keep it.

[dusk wind]

khan academy is better than most clickbait books

[gray gazelle]

Do they have books I can keep on a shelf?

[dusk wind]

you can print your own books from the internet buddy boyo

[gray gazelle]

I don't have a printer.

[dusk wind]

I have posts on good free precalc books that might be sold in stores though

[gray gazelle]

Name?

[dusk wind]

pick any precalc book and study trig and that will be your 'baby stuff' up to calculus

check my posts in this sub

trig for example you can use https://mecmath.net/trig

in general though https://stitz-zeager.com https://math.oit.edu/~watermang/math_100/100book.pdf or http://wallace.ccfaculty.org/book/book.html are free for precalculus, but there are many others usually authors have other books in order of difficulty

[gray gazelle]

Thank you.

I'll use the first three.

[dusk wind]

good luck, let me know which ones you like best

[vital bane]

just you wait

[gray gazelle]

I wanted to see if I could learn Data Analytics, but I got discouraged and wanted to try the other option was to be go into Mathematician. Figured I would start from baby and go up.

[dusk wind]

it'll take a while but the algebras are easy, everything else might be a pain though

are you interested in stats?