book-recommendations

[rotund flint]

Shut up

Shut the fuck up!!!!

[fierce hedge]

F A K E

[rotund flint]

https://tenor.com/view/the-voices-meme-cat-gif-23917781

What channel was this supposed to be anyways lol

[fierce hedge]

[fierce hedge]

book recommendations lmaooo

[rotund flint]

LOL

[noble prawn]

I forgor!! I thought this was a channel to raise awareness about piracy

[versed magnet]

What ship should I buy as beginner pirate?

[fierce hedge]

friendship

[foggy igloo]

The pings are multiplying

[fierce hedge]

kidding, you can never buy friendship

try relationship maybe

[rotund flint]

And your banned

[worn oasis]

Im looking for a book on
stochastic wave eqn
And something on the Euler Lagrange Equations

[versed magnet]

:(

[pliant nimbus]

chain theory

[broken meadow]

Pong

[next abyss]

what happened to this server💀

[gray gazelle]

books on FFT, FT, fourier approximations, multidemnsional fourier and suchs

more on application, and insight rather than proof

[pearl kraken]

I thought someone pinged me

[hollow halo]

Check #changelog

[heavy moon]

Same I thought so too.

Is this April Fool?

[gray gazelle]

maybe

[gray gazelle]

same

[heavy moon]

[pearl kraken]

Yeah it's a troll

They'd have changed it back normally

[fervent magnet]

There’s piracy here?

I’m confused…bruh

[pearl kraken]

Book piracy

[coarse spear]

What happened to the server

I was off for a week

Everything is renamed

[heady ember]

Everything is explained in mniip's link https://tinyurl.com/3pk9aura.

[coarse spear]

I see the thumbnail

[heady ember]

Fuck

[coarse spear]

Good try

[heady ember]

"Failure"

[cedar ridge]

where the good book lists at

[silver herald]

Pinned Messages are a good start

More precisely - "Good" is relative to you

[gray gazelle]

Who pinged me?

[pulsar kiln]

same

[fierce hedge]

None was pinged that's just the server picture

[hollow shore]

https://tenor.com/view/annoying-who-pinged-me-angry-gif-14512411

[heavy moon]

We got pranked.

By the new mods.

[fierce hedge]

The new mods were a scam

A scam done by the actual mods

[fierce hedge]

They had the role Moderator compared to Moderators (the actual mod)

and now they're muted

[tawdry musk]

I spent actual 5 minutes figuring it out

[gentle arrow]

typical namington renaming this to umineko

[grizzled tulip]

This is obv Namington haha

[night tendon]

i forgot what this channel was originally called

[empty mortar]

[rich sun]

vn-recommendations

[night tendon]

wait u muted?

sed

[quick hornet]

Earth to earth. ...The obvious culprit wields a mutable blade.

[crimson leaf]

I recommend Golden Fantasia

[fierce hedge]

Is that a video game recommendation?

[crimson leaf]

It's an umineko recommendation

[fierce hedge]

what is that?

[rich sun]

a seacat

[fierce hedge]

,w define umineko

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by numbpy#2527

[fierce hedge]

umm....

[lapis heart]

Only those who have been recommended know.

[quick hornet]

vague umineko spoilers

[fierce hedge]

So, doki-doki literature club hood edition?

[quick hornet]

???

[fierce hedge]

nvm, just had a brain fart

Anyone has a video game recommendation? NO sports or racing games pls

[quick hornet]

umineko no naku koro ni

[rich sun]

The only recommendation in this channel

[quick hornet]

not true

you can also recommend

• umineko no naku ni chiru
• golden fantasia

i might accept ciconia recommendations too but they're on thin ice

[fierce hedge]

google says it's a light visual novel

[quick hornet]

light, no

visual, yes

[rich sun]

What does light even mean? (Why are light novels called light?)

[fierce hedge]

mb, it was written soft visual novel whatever that means

[quick hornet]

wasei-eigo (japanglish)

[crimson leaf]

Doujin soft

[quick hornet]

its basically their equivalent of "young adult" if that makes sense

[sudden kindle]

I like hard novels

[crimson leaf]

Basically made as a hobby

[rich sun]

I see

[sudden kindle]

Solid novels

[trail yarrow]

How did an honorable get muted

[hazy elk]

"Complex made simple", Ulrich is the best complex analysis book ever, teaches the perfect amount of theory for a first pass (and lots of cool topics in part 2), extremely clear writing, derives many theorems in a non-standard way which makes the proofs intuitive, there aren't too many excercises, but the ones there are not too hard/easy but really makes the content sink in. Gets to the interesting stuff much faster than something like Ahlfors.

I wish I knew about this book in the beginning of my semester : (

The writing is crisp

I am anti Ahlfors now, too wordy and unorganized

[sage python]

Yeah my impression of Ahlfors is that there's way too much chit chat

[crimson leaf]

Is there a book on harmonics that has good coverage of applications to number theory and combinatorics

[distant bobcat]

which one is better for linear algebra

hoffman and kunze or lang?

[sage python]

My impression is Hoffman-Kunze

[sage python]

Harmonics meaning harmonic analysis? Or are you saying something specific?

[timber copper]

Game/manga

[sleek flame]

The Visual Novel. I don't know why we have this in the server right now. But I finished all 8 episodes.

The manga is more explicit with the 'solutions'

[timber copper]

Manga is solid if ur not used to vn format

Yeah

Takes away from some of the fun

[sleek flame]

However, the music makes up for all of it

Fucking zts and dai

[timber copper]

Zts the goat

[sleek flame]

Wingless is my favorite track

I could endure trying to study a paper by Rieffel if I have it on

[timber copper]

I really like the ambience in novelette

Not my fave track tho, but good study music

[quiet dust]

Does anyone know any links to senior thesis presentations ?

I have mine next week and I really want some examples as I don’t know how much information to put

[empty mortar]

umineko is no more

[sleek flame]

https://tenor.com/view/battler-battler-ushiromiya-ushiromiya-battler-umineko-umineko-no-naku-koro-ni-gif-22885500

[crimson leaf]

Yeah Harmonic Analysis

[cedar rain]

Are there any solutions for Falconer's "The Geometry of The Fractal Sets "

[mellow wren]

I'm looking for some resources on like intro infcat theory

[cedar ridge]

someone bring this guy back

funniest man ever

[solemn rover]

Do you have any background in classical simplicial homotopy theory

[mellow wren]

yes I have read some material on simplical sets

[solemn rover]

Honestly, Jacob Lurie is a clear and cogent writer and I think you can just crack open "Higher Topos Theory" and start reading it, and if you have things you're confused about you can ask for background resources on that.

If you already know some stuff about simplicial sets and you know category theory in general well you are probably reasonably well prepared.

[mellow wren]

ah cool
Somebody already mentioned that but tbh I was sorta scared that it might be super terse ala Markus Land's book but good to hear I'll check it out

[solemn rover]

Yes, I see. No, it's not super terse. It's very clear and straightforward.

I don't know what your learning style is. There are youtube videos here. https://www.youtube.com/@homotopytheorymunster8393

[mellow wren]

ah cool
Tbh I like books more but I'll check it out

[solemn rover]

I think I would also recommend grabbing a copy of Joyal's "Notes on Quasicategories" and/or "Theory of quasi-categories and its applications".
There is also "Introduction to Quasicategories" by Charles Rezk and also "Stuff about quasicategories" which is less organized.
I haven't really read these so much as plundered them for theorem references.

Sorry. I am a pack rat and I download a lot of books.

[mellow wren]

lol same don't worry haha

my hard drive is actively suffering because of it tbh

[mellow wren]

But thanks a lot this is really an incredible amount of info

[finite crane]

harmonic ana + number + combinatorics is literally Tao

just read Tao's course notes on harmonic and analytic number theory and maybe ergodic theory

[vagrant mason]

what are the best books reccomended to not only learn calculus but have enough practice problems to really excel in it? i was reccomended single variable calculus: early transcendentals by james stewart but i wanted to hear what others might reccomend as well as experience with this book if they used it

[hollow dew]

what books do i read if im bad at math

im new

[dense roost]

A teacher recommended a book to me called "Fermat's last theorem". If follows the story of a man who solved an infamous old problem which is simple to understand and it also walks the reader through mathematical history. It's very accessible to all levels of reader and I enjoyed it so I'd recommend it if you're looking for an interesting maths book

I wouldn't say that it will significantly improve your maths, but it's more just an interesting read for all levels

[upbeat vine]

Complex Made Simple is definitely a beginner-must book. It is not only a CA book, but also a "proof-reading" book. It makes you ask why are some notations well-defined (like how is H(D) n C(D̅) sensible given both have different domains), why does one proof work, and why won't an obvious another doesn't (like for Schwarz lemma) and many other instances.
Ahlfors is for a Graduate student who have already taken CA recently in their undergrad years. The main selling point is that it will prove some weird lemma here and there and derive all theory from that. For example, in beginning Ahlfors proves a weird lemma regarding analyticity of integral on a circle C of f/(x-z) where f is continuous on C and from that, we have unique extension for removable singularities, Cauchy formula for derivatives, Cauchy estimates, Morera, Liouville etc. Also another point is that Ahlfors covers some complicated ideas regarding the first few chapters which are rarely even mentioned in other books. Like conformal mapping of parabolas/circles, or even just simpler things like constructing a function from its real part. This is to the extent that quite a lot of stack-answers on CA are just copy-paste of "Ahlfors says this".
That being said, Ahlfors is definitely not beginner material since it very rarely introduces definitions and assumes the student knows almost all the terminology beforehand.

[swift dome]

https://archive.org/details/DemidovichEtAlProblemsInMathematicalAnalysisMir1970

[noble prawn]

sir, what?

also, is this good start to understand proofs?

[warped kayak]

Im currently going through a Differential Geometry book that Im really enjoying (by Barrett ONeill.) Im interested in filling out my knowledge with studying Differential Topology as well. As someone who is just learning via self study, I was wondering if anyone had book recommendations for the subject. A few books Ive heard about include:

Introduction to Smooth Manifolds by John Lee
An Introduction to Manifolds by Loring W. Tu
Differential Topology by Alan Pollack and Victor Guillemin
Topology from the Differentiable Viewpoint by John Milnor

If anyone wants to add to this list, or point out a book they liked the best, Im all ears. Thanks!

[swift dome]

Good works by Hammack are also recommended by my university for my course

It's an excellent book for beginners.

[noble prawn]

Oh, thank

Sad that the library doesn't have a physical copy 😦

[swift dome]

[noble prawn]

how about this one?

I was trying to get Strang's but not available in the library

[subtle mango]

lee's books tend to be really good

i really like his writing style

[swift dome]

A classic text for linear algebra is Serge Lang's introduction to linear algebra.

But if it's not offered, perhaps you should just take the course with as many books as you can since they don't really important.

[noble prawn]

Being a law-abiding citizen is hard... especially when you are poor

[noble prawn]

I will be taking the classes next semester so... I am just trying to self study right now

[swift dome]

Thankfully, my uni library has some of the quality books I need for my course.

[coral prawn]

imagine not pirating

[swift dome]

and also good luck

[noble prawn]

My discord crashed as soon as you mentioned that word

[fierce hedge]

super reactions suck

[coral prawn]

fr

[sturdy shore]

if you are interested in proofs you should avoid strang like the plague anyway, his books have none of it

[fierce hedge]

yeah like why tf the police emoji has a vortex in which it was succed into

[swift dome]

simply rely on tao analysis books

[coral prawn]

based

[dense drift]

Made this for someone else, but might as well post here. A list of maths-relevant Very Short Introductions books

• Algebra https://academic.oup.com/book/973?searchresult=1
• Applied Mathematics https://academic.oup.com/book/800?searchresult=1
• Combinatorics https://academic.oup.com/book/971?searchresult=1
• Fluid Mechanics https://academic.oup.com/book/43189?searchresult=1
• Fractals https://academic.oup.com/book/734?searchresult=1
• Geometry https://academic.oup.com/book/40044?searchresult=1
• History of Maths https://academic.oup.com/book/601?searchresult=1
• Infinity https://academic.oup.com/book/972?searchresult=1
• Logic https://academic.oup.com/book/684?searchresult=1
• Mathematics https://academic.oup.com/book/473?searchresult=1
• Number Theory https://academic.oup.com/book/29773?searchresult=1
• Numbers https://academic.oup.com/book/382?searchresult=1
• Probability https://academic.oup.com/book/413?searchresult=1
• Statistics https://academic.oup.com/book/409?searchresult=1
• Symmetry (really about Group Theory) https://academic.oup.com/book/728?searchresult=1
• Topology https://academic.oup.com/book/28477?searchresult=1
• Trigonometry https://academic.oup.com/book/28465?searchresult=1
  (This list is almost complete, I've left out some because it isn't clear to me whether to count them as maths or compsci, some on individual scientists/mathematicians, and one that is on the dark side.)

Was asked by an undergrad for book recs, what did I miss?
Strong popular-level books:

• Literally anything by Ian Stewart. My faves are How to Cut a Cake (https://www.amazon.com/How-Cut-Cake-Mathematical-Conundrums/dp/0199205906) and Why Beauty is Truth (https://www.amazon.com/Why-Beauty-Truth-History-Symmetry-ebook/dp/B00CW0MQAI).
• The Man Who Knew Infinity: A Life of the Genius Ramanujan by R. Kanigel (https://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/1476763496)
• 50 Visions of Mathematics by S. Parc (https://www.amazon.com/50-Visions-Mathematics-Dara-OBriain-ebook/dp/B00JSRY88Q)
• The Code Book by S. Singh (https://www.amazon.com/Code-Book-Science-Secrecy-Cryptography/dp/0385495323)
• Goedel, Escher, Bach: An Eternal Golden Braid by D. Hofstadter (https://www.amazon.com/Gödel-Escher-Bach-Eternal-Golden/dp/0465026567)
  Ones a bit more advanced, aimed at undergrad level: (I read them all in first year)
• Gamma: Exploring Euler's Constant by J. Havil https://www.amazon.com/Gamma-Exploring-Constant-Princeton-Science/dp/0691141339
• An Imaginary Tale: The Story of √-1 by P. Nahin https://www.amazon.com/Imaginary-Tale-Story-√-1-ebook/dp/B005AUSOJE
• (Those first two are both Princeton Science Library, which I recommend checking out the whole catalogue of)
• Roads to Infinity by J. Stillwell https://www.amazon.com/Roads-Infinity-Mathematics-Truth-Proof-ebook/dp/B00UVAPWJI
• The Pleasures of Counting by T. W. Korner https://www.amazon.com/Pleasures-Counting-T-W-Körner-ebook/dp/B00JOK9HJM
  Misc
• Proofs and Refutations by I. Lakatos, though it is philosophy it is also arguably the only phil maths book worth reading.

[gray gazelle]

Any good recommendation for a 1-semester course that covers galois theory,then modules and basics of homological algebra and category theory and finally some intro to representation theory?

[dense drift]

Relevant books from the recommendations in the Cambridge syllabus:
Galois Theory

E. Artin Galois Theory. Dover Publications
I. Stewart Galois Theory. Taylor & Francis Ltd Chapman & Hall/CRC 3rd edition
B. L. van der Waerden Modern Algebra. Ungar Pub 1949
S. Lang Algebra (Graduate Texts in Mathematics). Springer-Verlag New York Inc
I. Kaplansky Fields and Rings. The University of Chicago Press
Rep Theory
J.L. Alperin and R.B. Bell Groups and representations. Springer 1995
I.M. Isaacs Character theory of finite groups. Dover Publications 1994
G.D. James and M.W. Liebeck Representations and characters of groups. Second Edition, CUP 2001
J-P. Serre Linear representations of finite groups. Springer-Verlag 1977
M. Artin Algebra. Prentice Hall 1991

[obsidian valley]

I mean there are a bunch of books that do this

[hasty turret]

Wdym by "one that is on the dark side"

[obsidian valley]

pretty much any algebra book if you pick the chapters properly

[dense drift]

It's on financial mathematics

[obsidian valley]

Rotman was discussed a bit earlier, that does all of these topics in the back half.

[gray gazelle]

How about artin or dummit & foote

[obsidian valley]

Both are fine

like I said any modern algebra book will cover all of this if you choose the chapters correctly

it's really just a matter of whose writing style you like the best I guess

[dense drift]

As I recall Dummit & Foote is a bit terse in the proofs

[gray gazelle]

The only chapter missing seems to be category theory

[obsidian valley]

Rotman does this

[gray gazelle]

Ok i'll take a look

It seems to cover everything yes

Is it readable?

[obsidian valley]

people do read it

@finite crane was posting about it earlier

D&F does category theory in the appendix also

idk if its a good treatment

update its not its like 4 pages

[worn oasis]

Anyone have a rec on Stochastic Diff Equations?

[vagrant mason]

When do you think Ahlfors should be read? Like how much should a person know before getting into the book?

[gray gazelle]

Thank you @obsidian valley for all recommendations, i will borrow rotmans book from the library tomorrow

[sudden kindle]

D&F is the best place to learn field theory and Galois theory imo

The rep theory of finite groups chapter in D&F is pretty good too

[fierce hedge]

what about rings and modules?

[sudden kindle]

I used Atiyah Macdonald

Idk whats the best source for that

[coral prawn]

Mcdonald-

[fierce hedge]

The commutative algebra book?

[sudden kindle]

Yea

[grand thistle]

any books that cover the following topics without assuming too much knowledge in physics (im thinking hs physics at most)?
Probabilistic interpretation of quantum mechanics, self-adjoint operators and physical observables, noncommutativity and the uncertainty principle. Spectral theory for (unbounded) self-adjoint operators. Stone's theorem and other topics.

this is the syllabus of potential topics if more info is needed

they recommend Keith Hannabuss' "An Introduction to Quantum Theory" but i can't find it anywhere

[sage kelp]

Can anyone tell me how Lang and Marsden and Weinstein Calculus book compare?

[upbeat vine]

I would say don't read Ahlfors as a main text. Read something like Complex made simple and after completing a topic, check into Ahlfors if he had a nice argument or a nice trick he mentions somewhere.

[gusty smelt]

I requested a copy from my library btw, ill scan this at some point

[grand thistle]

ah okay thank you sm

[finite crane]

Hall quantum physics theory for mathematicians

it assumes you're a mathematician without knowledge of physics

you should at least know real analysis and linear algebra before reading it

[grand thistle]

ohh cool i've heard of that one actually

i'm going in with some measure theory background and a bit of functional analysis hopefully

[finite crane]

it's about the only accessible book

[grand thistle]

right

[finite crane]

that wouldn't embarrass a mathematician

[grand thistle]

haha

[glad raft]

the preview for normal l biggs' discrete mathematics books is very nice to read

are there any other thorough books like it for discrete math?

[chrome yacht]

#book-recommendations message give this one a look

[glad raft]

thanks :)

[shadow owl]

Yo

What’s a good discrete structures/math text book

Looking for a good pdf

[swift dome]

Mathematics: A Discrete Introduction" by Scheinerman

if that what you looking for.

[shadow owl]

Yes thanks

I appreciate it

[jade anchor]

Anyone ever read Algebra: Chapter 0 by Aluffi before? Any opinions on it? Prepping my studies for graduate school and have been recommended it several times! 😄

[chrome yacht]

#book-recommendations message here's a review i could find

[jade anchor]

Ah thanks for the help! I didn't think to look back through time on the stream.

[worn oasis]

Asking Again----

Im looking for a book on
stochastic wave eqn/ Stochastic DEs in general

And something on the Euler Lagrange Equations

[raw vale]

Does anyone have recommendations on books to study Mathematical logic, like from the start and maybe also books with problems on the subject?

[topaz kayak]

I liked cheri by colette

I know romance is all mushy but it was kind of neat

[vocal junco]

Any reccomendations for precalc?

[narrow relic]

Modern Introductory Analysis by Mary Dolciani

[swift dome]

Introductory Logic
Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books) by Alfred Tarski, haven't tried it out but the reviews for this books are good.

[fleet bramble]

Whoa?

[foggy relic]

shit wrong channel, my bad

saw the logic message and thought it was the one i was thinking of

[fallow cypress]

Mileti Modern Mathematical Logic

Assuming you mean the field of mathematical logic (like the incompleteness theorems and stuff)

"A Friendly Introduction to Mathematical Logic" is also quite good

[sturdy shore]

I'd also add goldrei in addition to mileti and L&K

[gray gazelle]

guys i need book recomendation i have read diary of a wimpykid

and matilda by roald dalh

[upbeat vine]

Read itsy bitsy spider by Rosemary Wills

[crimson leaf]

Charlotte's Web

[warm sparrow]

best book for linear algebra?

[finite gale]

read dami's lin alg book review and see if you can pick one that suits you

[warm sparrow]

kk

thanks

anything for combinatorics?

[gray gazelle]

its a rhyme

[gray gazelle]

read it in primary

[grand thistle]

does anyone know of a (mathematically rigorous) crash course on odes that's concise and has computational exercises?

something like one of those standard ode books but not stretched out over hundreds of pages

more condensed into like 70-100 pages if possible

[swift dome]

A Walk Through Combinatorics by Miklos Bona

Tried it and it's really a great book , if you are beginner in it.

[gray gazelle]

does anyone here knows an encyclopedia for mathematics that could be used as a reference for definitions ?

[coral prawn]

Wikipedia.

Quite literally

[fierce hedge]

Just google search I guess

[finite gale]

does anyone have any leanings for (or against) lang's algebraic nt vs weil's basic nt?

[gray gazelle]

i need a book that covers Topology of Rn. please 😔

[gray jungle]

Probably first chapter of spivak or munkres calc/anal on manifolds .

[cinder quiver]

Any introductory real analysis books?

I want to study it after finishing calc 2

[swift dome]

maybe go with tao analysis books.

[gray jungle]

I second recommend tao , especially if you're new to proofs.

[cinder quiver]

Okay thank you

Much appreciated

[sage kelp]

I would recommend Bartle and Sherbet or Bloch

[cinder quiver]

I got Terence Tao's analysis 1 (3rd ed) so far

[graceful dawn]

Set is boring

[heady ember]

No

[prisma inlet]

Anyone have suggestions for elementary abstract algebra textbooks?

[heady ember]

Look in pinned

[graceful dawn]

In Tao

[sterile harness]

Anyone know a lecture series/book that is not too rigorous but is good for developing intuition?

[finite gale]

Uh on what topic?

[sterile harness]

Anything not combinatorics

[graceful dawn]

That's like rest of the math.

[sterile harness]

well yeah, I don’t mind anything besides combinatorics

I’m not asking for something that covers all of math, just any resource that is not combinatorics

[gray jungle]

There is simply too many topics that are not combinatorics , you need to be more specific if you want a productive answer.

What is your background and what are you interested in?

[sterile harness]

im in proof based linalg, anything from analysis, algebra, or topology interests me

or some sort of geometry

it could be any of those i dont mind

[gray jungle]

If you know multivar calc , then "differential geometry" by andrew pressley is a good book.

Artin "abstract algebra" is a fun one.

Hoffman & kunze "linear algebra" is one of my fav books.

[brittle breach]

topology and geometry , Tadashi Tokieda

[sterile harness]

LOL ironically I’m watching that right now

[fleet bramble]

Tao and Stein and Cohn about measure theory if u wanna read those things

[mossy flume]

D&F is dry af

[broken meadow]

i think DF is just fine

[remote sparrow]

#book-recommendations message

[noble prawn]

Thanks

[fierce hedge]

You can try Judson, I have read first few chapters and I liked the pacing

[fierce hedge]

not very suitable for self study, good in a classroom setting

You can always read the initial topics from one book and then switch to knapp for the above topics

[remote sparrow]

judson and pinter

[amber olive]

any book recommendations for ring theory? preferably one with a good amount of solved examples?

[hasty turret]

Dummit and Foote

There are more examples than you want

[midnight edge]

I second this.

Also a first course in noncommutative ring theory by lam might be worth checking out.

A lot of exercises.

[pseudo forge]

i third this

[uncut zealot]

I fourth the rec of d&f. If you want specifically commutative rings you want a commalg textbook like eisenbud or atiyah-macdonald.

[graceful dawn]

All the Math You Missed ---> how is this book?

[fierce hedge]

I just saw Math sorcerer recommending it, maybe try it yourself. There's a copy of it on a certain biblical library

[fierce hedge]

Are there any abstract algebra problem books?

[frosty yarrow]

does anyone know if dummit's abstract algebra has solutions to any exercises?

[ocean berry]

Can someone tell me what is the ring theory

[fierce hedge]

it doesn't

[thorn cloak]

anyone know any more "advanced" calc 3 books? My class is using Flanigan calc two, but the exam problems are so much harder than that, and thomas calc + stewarts as i use both for extra practice... Is hubbard and hubbard a good choice?

[amber olive]

thank you guys! I'll give dummit and foote a look. thanks so much 🙂

[atomic hemlock]

:q

[frosty yarrow]

ah man. any other "introductory" level abstract algebra books that have solutions to at least some exercises? I don't really like the one in the vook recs channel

[next wolf]

yo i got a good one if you want it

"A first course in abstract algebra" by john b. fraleigh

there is a solution list here: https://www.academia.edu/10524726/Instructors_Solutions_Manual_to_accompany_A_First_Course_in_Abstract_Algebra_Seventh_Edition

[fierce hedge]

Thanks!

[fierce hedge]

I think Gallian has a solutions manual, try that

And Herstein also but it's a bit old school

[flat jackal]

Do u have any recommendations for self studying multivariable

My budget is £40 so preferably a good book that’s readable for around that I guess

Like preferably I would go by a textbook and then YouTube videos beside to help learn the content

[graceful dawn]

For basics resources are free over internet. Unless you want to help an author.

[flat jackal]

Ye but I don’t like reading of an online pdf that’s like 200 pages long

[blazing canopy]

You can use a printer

[remote sparrow]

proof-based or not?

[flat jackal]

No

Just like

Triple integrals and stuff

And vector planes

[remote sparrow]

so you want to cover this material but without proofs, correct?

[flat jackal]

I didn’t know there was proofs in multivariable ngl

If there is then ye I’ll study it

[remote sparrow]

if this is to prepare for your third semester of calculus, usually that class does not focus on proofs

[flat jackal]

No I’m in year 12

I just wanted to self study a course over the summer for fun and for my PS to

Because after second year FM I’m not exactly sure on what course to do, will probably be multivariable or linear algebra tho

[heady ember]

You can probably start on anal if you want as well

Lin alg is probably a good pick though

[remote sparrow]

you can just pick up an old edition of stewart calculus used for cheap

[obsidian wharf]

I personally really enjoy Calculus III- Pauls Online Math Notes - Lamar University

got me through calc 3 with an A

[solemn rover]

"Examples of Commutative Rings" - Harry C. Hutchins

[brisk ice]

Getting it physical doesn't make it shorter but yeah having stuff physical can be nice

[flat jackal]

Ok

Thx

[plucky dragon]

wrong mention.

[plucky dragon]

please don't take this message out of context

[astral breach]

guys what is the de facto and de jure book of advanced geometry after completing "Elements by Euclid"

[hasty turret]

Harthstone's geometry

[astral breach]

is it analytical or purely euclidean

[astral breach]

i mean all the other books treat higher subjects analytically

suppose menelaus theorem

they will introduce some weird concepts like vectors and all

and then learn that

then learn menelaus theorem

[finite crane]

Euclidean geometry is only for high school. Nobody cares about it after high school. At most you use a few basic notions from it to develop higher stuff

[astral breach]

can't they just prove it using basic euclidean concepts?

[astral breach]

ooh

[hasty turret]

Did you unironically go through Euclid's elements

[astral breach]

yes

actually

ofc modern interpretation

bcz there wasnt even an equal"=" sign in the original

[hasty turret]

Upto interpretation what book I mean

[astral breach]

ISBN 978-0-6151-7984-1

[karmic thorn]

Many lines of geometries (plural) have sprang into existence in the last few hundred years, especially the last 200 years

[astral breach]

yes

[karmic thorn]

Depending on your interests or backgrounds, you may pursue any of these as a followup

[astral breach]

like non euclidean geometry

[karmic thorn]

Right

Hyperbolic geometry could be a place to start

[astral breach]

hmm

guys how did they prove that there are contructions which can't be solved by compass and straitedge

[karmic thorn]

Galois theory

[astral breach]

another like compass geometry

and straightedge geometry

using only one tool for a construction

[astral breach]

is it in Bachelors?

or Master's?

[karmic thorn]

I don't know the full details (many accounts online, both for the general audience and mathematicians), but the idea is to translate the geometric problem of compass and straightedge constructions to that of a corresponding algebraic structure (constructible numbers), and then study of symmetries of the algebraic structures helps you say something concrete about the constructions too

I may be conflating the problem of unsolvability of quintics through radicals with geometric constructibility

But "galois theory" is the keyword for sure

[astral breach]

yeah

[hasty turret]

Well the idea is to consider the field of "constructible elements"

And use some field theory/Galois theory properties to say stuff

[karmic thorn]

It depends. You can possibly graduate with a masters in math without ever seeing it in a class

[astral breach]

ill add that to my study list for summer after set theory advanced ig

[karmic thorn]

Or be exposed to it in the second year of your undergrad

[karmic thorn]

Not entirely related but still an interesting followup is metric geometry, which (at least in my vague impression from reading random arXiv preprints) is concerned with nontrivial problems in Euclidean geometry (or more generally, metric spaces), sometimes depending entirely on the metric setup (other times you may work with extra structure on the space, spilling into territory of differential geometry for instance)

[astral breach]

btw how much logic should one learn and recommend a good logic book for Maths Majors?

[karmic thorn]

Here's an interesting (open) problem that I recently learnt about: a Jordan curve in the plane is any injective, continuous function from [0,1] to R^2 (simply think of a continuous closed loop that does not cross itself anywhere). Say that a rectangle R can be inscribed on the curve if you can draw all vertices of R on the curve. Can you always inscribe a square on such a curve?

[karmic thorn]

Nothing more than understanding basic truth tables, implications, contrapositives, etc.

[finite crane]

Just read pinned doc in #proofs-and-logic and go straight to real math books like Tao's analysis

[karmic thorn]

You pick up the rest from writing and reading proofs

I started my journey with Tao's Analysis

I have mixed feelings about it being a good choice

On one hand I'm a big simp of his writing and insights

On the other hand is time/efficiency and organisation of material, especially if one is reading the book on their own as a gateway to math proper

[astral breach]

i will try that for sure

i know most of the ones in the pinned docs

[coral prawn]

[cedar ridge]

where can i get
a lot of good/fundamental qs in undergrad complex analysis
atm taking a ca course where we're lacking baby step qs

[coral prawn]

check pins, there's a list made for CA books

u may find 1 that catches yr interest

here

[cedar ridge]

ye problem is i'd have to do it side-by-side with my subject; coz the presentation + ordering differs

when im mainly just looking to fill in more qs

[crimson leaf]

Probably look for lecture notes online or video lectures

[gray gazelle]

Book recomenedation for someone trying to learn Linear Algebra

I can't post a pic

anyway I'm looking for something that covers:
Linear Algebra: Introduction
Linear Algebra: Matrices
Linear algebra: vector spaces and linear maps
Linear algebra: eigenvalues ​​and diagonalization

for entrance exam

[subtle mango]

see #books-old

[gray gazelle]

it talks about R and C

I have no clue what that is

I have no background knowledge of linear algebra

[subtle mango]

wut

if u scroll up there's a section on lin alg

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

[gray gazelle]

oh wait i pressed on pins

wrong thing

[subtle mango]

this is linked there, this should be sufficient

[gray gazelle]

My bad

[subtle mango]

ah np

[gray gazelle]

thank you dude, appreciate it 🙏

[gray gazelle]

should I do MIT's multivariable calc since it seems to be a pre-req

my highschool didn't teach multi variable calc

[subtle mango]

dunno why it's a prereq, i assume you won't need it

(if anything i would say lin alg should be a prereq for multi)

but yeah looking at the syllabus you probably won't need it

maybe for the "linear algebra in engineering" part at the end?

[gray gazelle]

gotcha

[gray gazelle]

yeeah won't be needing that

[subtle mango]

but that part is likely not relevant for an entrance exam

[gray gazelle]

would you have an estimation of how long it would take to finish Linear Algebra till the point where I'm ready for my entrance exam, trying to create a timeline

[subtle mango]

depends on how much you need to know

" Linear Algebra: Introduction
Linear Algebra: Matrices
Linear algebra: vector spaces and linear maps
Linear algebra: eigenvalues ​​and diagonalization"

if you're going by what you said above uhh

[gray gazelle]

^

[subtle mango]

lemme think

maybe 2 or 3 months?

"how long" is a difficult question to answer in general

[gray gazelle]

gotcha would you have hours

[subtle mango]

i don't have a precise timeline for you

that's probably something you'll have to think about

[sick fox]

hello!
anything (books) that would help for engineering? like the very beggining gonna start uni in a bit

[subtle mango]

"diagonalization" is a kinda broad focus lol

if they mean canonical forms as well then maybe 3-4 months

[gray gazelle]

no what I mean is like when you say "2-3 months", do ou mean like 1 hour everyday for 3 months, wdym

[subtle mango]

there's some engineering servers in #old-network, those might help

[sick fox]

thank you!

[subtle mango]

in all honesty i don't really know how many hours per day

i don't necessarily follow "x hours per day" kinda thing so i never really thought about it

i'm just thinking regarding like

consistent studying and whatnot

1 hour per day should suffice

[gray gazelle]

alright, thank you

I'll start off with that

[gray gazelle]

any important pre-reqs before I get started, just to see if there's something I should may brush up, have no clue what lin alg even is

[hazy elk]

@gray gazelle I think a better thing you can do is do the first four chapters of "linear algebra done wrong" (omitting all the topics that aren't relevant to your exam)

And also watch 3b1b's linear algebra Playlist at some point

[gray gazelle]

ah gotcha if it's target focused might be good then

[subtle mango]

this is good motivation for lin alg

[subtle mango]

stuff like solving polynomials and whatnot

[hazy elk]

If you're studying for a test, the most efficient use of your time is doing previous year papers btw

[gray gazelle]

yeah but my knowledge is very short, some topics I've never even heard off

[hazy elk]

Yes yes, after you cover the basics *

[gray gazelle]

gotcha

[gray jungle]

you can also consider schaum's outline of linear algebra , it has a lot of exercises.

[gray gazelle]

will check that out

[hazy elk]

Also is the exam for a pure math program? Or is it like a general entrance test?

[gray gazelle]

general entrance test

[hazy elk]

Ah then you prolly don't want to read linear algebra done wrong (cus it is sorta intended at ppl who want to go into pure math)

Sorry for the confusion

[gray gazelle]

I want to do maths in uni

[hazy elk]

Hard to give a recommendation without knowing the kind of qs on the exam tbh

[gray gazelle]

I just have to pass general entrance test to get in

[hazy elk]

Are there proof based questions?

Or is it like mcqs and stuff

[gray gazelle]

which topic should I check for

Linear Algebra: Introduction
Set language
Logic
Combinatory analysis
Apps

Linear Algebra: Matrices
Matrix calculation
Determinants

Linear algebra: vector spaces and linear maps
Vector spaces
Linear applications

Linear algebra: eigenvalues ​​and diagonalization
Base changes
Own values
Rank

[hazy elk]

I didnt understand what you're asking. I was asking if you're expected to write proofs as answers in the exam or is it a standardized test with multiple choice questions

[hazy elk]

This seems to me like an entrance test for prospective math majors... is that right?

[gray gazelle]

I think you have do your working out, but I don't think you have to do proofs

[gray gazelle]

no

general uni test

After i cover math section, i move onto physics

[hazy elk]

Interesting, mind saying which country this uni is in?

[gray gazelle]

switzerland

EPFL

[hazy elk]

I see

[subtle mango]

oh wait this is much better

no canonical forms!

ok yeah a free iso’s recs suffice

[gray gazelle]

Excellent, I'll just get started on Lin Algebra gone wrong then

[hazy elk]

Good luck

[gray gazelle]

thank you

[hazy elk]

You can use the server when you're stuck too

[gray gazelle]

I have to pass the exam no matter what

[gray gazelle]

That'd be nice

[hazy elk]

Give yourself time, it'll be a bit challenging to understand if it's your first math book, but it's definitely doable, good luck!

[cinder quiver]

Noted

Any introductory linear algebra books?

That also cover everything

[remote sparrow]

#book-recommendations message

[gray gazelle]

https://4chan-science.fandom.com/wiki/Mathematics#Calculus

are the recommendation here any good?

[turbid mural]

book recommendations for mathematical logic ?

[gray gazelle]

for calculus

or anything

it's from 4chan so i wonder

[turbid mural]

what ?

[gray gazelle]

oh sorry. thought you were replying to me

[turbid mural]

np

[cinder quiver]

For calculus

You can use Adams and Essex 'Calculus - a Complete Course'

7th edition

[cinder quiver]

Thank you

[remote sparrow]

mileti, enderton, or goldrei

[remote sparrow]

yes

[heady ember]

Look at Clerk's recs in pinned

[gray gazelle]

Yo you guys got any book recommendations for me? It's could be like interesting topic like some physics or maths but not too complex that I don't understand.

Actually it's fine if it's complex maybe I'll learn some new words and things

[orchid mortar]

Since anything goes: https://transp-or.epfl.ch/books/optimization/html/index.html

[gray gazelle]

Oh..😮

That's definitely something.

[orchid mortar]

It even comes with lectures!

[gray gazelle]

Mmm

I gotta read this in break time

[fierce hedge]

> GNU octave

[orchid mortar]

na ignore that, he has py code

[coral prawn]

Ooooooooh.... what kinda optimisation and algorithms does it talk abt here?

[orchid mortar]

It starts with standard theory. Some sections on linear+quadratic for focus. In terms of algos it is quite comprehensive, going I'd say more than a standard course

[coral prawn]

icic

definitely will give it a look ty

[hasty turret]

<@&268886789983436800>

[gray jungle]

Optimization is not that bad....

[distant nacelle]

Is there something like the handbook of ring theory

Where from I could get most established results and current areas of research in it

[wraith rampart]

Hey guys, I want to learn mathematical proof methods, or some books which can give a mathematical perspective. Do you have any recommendations?

[gentle arrow]

#proofs-and-logic message

[wraith rampart]

thx

[remote sparrow]

#book-recommendations message

[sterile harness]

No piracy here!

[jagged cargo]

https://www.maa.org/sites/default/files/pdf/ebooks/pdf/EGMO_Contents.pdf
https://www.maa.org/sites/default/files/pdf/ebooks/pdf/EGMO_chapter2.pdf
i found only the contents and chapter 2

[thin hollow]

combinatoircs books

[remote sparrow]

what have you previously learned up to this point?

[heady ember]

Alternatively you could jump straight into smt like Schroder. Dami thinks its quite beginner friendly and in my lil bit of experience so far it is, at least comparatively

[thin hollow]

Calc 1-3 linear algebra probability proof math

[remote sparrow]

a walk through combinatorics by miklos bona

[thin hollow]

is it good for problem solving

im also getting for interviews too]

[remote sparrow]

what do you mean by "good for problem solving?" are you asking if it has good exercises?

[swift dome]

Book recommendation for statistics and probability for undergrad students.

[slate barn]

based

[gray jungle]

[fierce hedge]

What did the message say?

[slate barn]

called us all small pp

[fierce hedge]

but pp is already in small letters

[coral prawn]

[remote sparrow]

Probability:
Introduction to Probability by Blitzstein and Hwang
Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer

Statistics:
Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer
Statistical Inference by Casella and Berger

for non-measure theoretic treatments

[swift dome]

is there are any book that covers most of the statistics and probability in one book at undergrad level ?

[remote sparrow]

wackerly, mendenhall, and scheaffer

[swift dome]

alright, thanks !

[remote sparrow]

Melvin Fitting and Richard L. Mendelsohn, First-Order Modal Logic
(Kluwer 1998). This gives both tableaux and axiomatic systems for various modal logics, in an approachable style and with lucid discussions of options at various choice points. Despite its more mathematical flavour, the book still includes some interesting discussions of the conceptual motivations for different modal logics. Read the first half of this book to get a compact but sufficient introduction to propositional modal logics, and also the initial headlines about quantified modal logics. Philosophers will then want to read on.

copied and pasted from peter smith's teach yourself logic guide

[hollow tusk]

On Dynamical Systems (DS). Can anyone recommend me a text to read after finishing Delvaney's book? My school doesn't offer courses in DS but am motivated and am a graduating undergrad whose taken many upper level courses in analysis (including measure theory at the graduate lvl) and algebra

[steep badger]

I was in the same sort of situation last year. If you’re interested in geometry, try recordings of McMullen’s course on ergodic theory on YouTube. There’s course notes, homework and solutions online too on his website,

[steep badger]

Otherwise, depends on your interests. If you like ergodic theory, try reading some chapters of Viana. Another option is Brin-Stuck? The book isn’t written particularly well and detailed though based on what I heard.

[steep badger]

If you are going to grad school, try contacting faculties and see if you can do a reading project.

[tender mason]

anyone know any good books for understanding calculus and questions on it

[hollow tusk]

@steep badger Truth be told I'm not sure if I want to do grad school anymore, but know DS is something I will for sure explore. Thank you for the resources! I'll be sure to look into them

[thorn cloak]

would you recommend this after reading blitzstien or does it not matter? I was going to read blitzstien but if the other one covers same + more i might just choose that

[hollow tusk]

single-variable?

[tender mason]

sorry i have no idea what that is i just started calculus so

[thorn cloak]

then yeah prolly single variable. Thomas calculus and stewarts seem to be pretty standard for calc 1/2

[tender mason]

wdym by calc 1/2

[thorn cloak]

like limits, derivatives, integrals, and series, all in one variable

[tender mason]

ah ok linear

alr thanks

[thorn cloak]

id also supplement this with wathcing 3b1b series on calc. I enjoyed it a lot and i think it could help build some intuition if you just just started learning it

np

[hollow tusk]

3b1b is goated

[thorn cloak]

ye he carried me through lin alg lmao

[hollow tusk]

Have you read anything by Katok? I've spoken with faculty in other uni's and regard him as the best, but the texts are monstrously big

It's insane to me that mitocw has no courses on ergodic theory

[steep badger]

Katok-Hasselbladt?

[hollow tusk]

yes

[steep badger]

Yes the book is monstrous and I would only think of it like a dictionary.

But I do have something I found recently that would be interesting.

Fisher, Hasselblatt book called hyperbolic flows

It looks fun.

[hollow tusk]

You rock, thank you so much @steep badger

[remote sparrow]

wackerly covers the same ground as blitzstein and hwang but also has statistics

blitzstein and hwang is very readable though

[thorn cloak]

hmm i see. is stats super necessary if i plan to go deeper into stochastics?

[ocean mulch]

depends on what sort, but I haven't seen anyone who needs super advanced stats

and the basics comes as a byproduct of proba course here somehow

[thorn cloak]

i c

ty

[neat crown]

Does anyone have any recommendations for a good real analysis book that goes through the multivariable calc stuff? Just R^n is fine, I don't need general banach spaces

[remote sparrow]

schroder, browder, zorich

[neat crown]

Thanks

[sturdy shore]

do you already have one variable real analysis knowledge?

[neat crown]

Yes, although it's a bit shaky

[sturdy shore]

might wanna look at duistermaat kolk

knapp - basic real analysis is also possible

[neat crown]

Thanks

[ocean mulch]

Depends on the topic. I say Titu is the name to go to usually.

[raw jolt]

any useful book on cosmic string theory and time travel

[midnight edge]

Recommendations would depend on your level of education

The Art of Problem Solving by Lehoczky and Rusczyk.

[raw jolt]

i can learn as i go along

[midnight edge]

Yeah, but what is you education level?

[raw jolt]

Im 16

so like

high school level

but

i think you guys call it AP or whatever

basically A level maths and further maths

[midnight edge]

You'd probably have to start with the Stephen Hawking books.

A brief history of time and space, brief answers to the big questions, and so on.

[raw jolt]

hmm alright

What do you specialise in btw?

[hearty mason]

Yo, I need a good book for Trigonometry, any suggestions? (Im in 10th grade)

[fluid bay]

Khan academy

@lofty larkadit#6101

Oop they left

[gray gazelle]

in which hemisphere do you live

[signal charm]

why would it matter? khan academy is available everywhere discord is available (I mean, in North Korea you probably wouldn't be able to access it but neither would you be able to ask other people on discord)

[calm elbow]

google said 0 is neither positive and negative integer

so its both?

[coral prawn]

Wrong channel. Also, its just neither, not both.

[calm elbow]

sorry my bad

[lilac bronze]

Can anyone recommend any good books on cybernetics

I know it's not "purely" mathematics, a bit more interdisciplinary and engineering oriented

but still seems interesting

[humble talon]

Is "Proofs: A Long-Form Mathematics Textbook " good for self learning? I have a math minor, but haven't done any math in about 5 years

[remote sparrow]

yeah

[humble talon]

Okay, ill buy it

I don't wanna waste money on books i can't understand. but this seems cheap

I tried reading a different book. But understanding the logic behind the proofs made it a bit difficult to read

[past flame]

I have this book! sadly I haven't read too much so I can't give great feedback, but from a few chapters I can tell you that it is certainly comprehensible and not too deep or complex

The author seems to explain things in a reasonable way

[swift dome]

Hard copy of books might be costly, copy it with less cost.

[light solar]

Im sorry i know this is specifically for math but does any1 know any serverthat could help with doing research

Specifically for chapter 1?

[finite gale]

chapter 1 of what

[light solar]

Chapter 1 of practical research

Haven't put a single word in

[hasty turret]

Wdym by practical research

[light solar]

Subject in our stem

[heady ember]

[light solar]

We basically pick something to study upon on, something that will benefit the community

[dusky berry]

i don't know anything about calculus can someone tell me what is best calculus book for me?

[finite gale]

stewart calculus is a nice easy place to start

[dusky berry]

does it include calc 1 and calc 2 and calc 3?

[finite gale]

yes

[ocean mulch]

I heard Terence Tao's Analysis series is good, tho I didn't use it

[fierce hedge]

fair warning with Tao: It can feel like getting a bit dragged on

[dusky berry]

ok but i saw a book called "Calculus made easy" and "Hitchhiker's Guide to calculus" which is better i just want an introduction for calclus not mastering it

[fierce hedge]

and exercises clearly aren't Tao's strong suite

[ocean mulch]

Tao usually goes quite fast. I read his Measure Theory book, what a blunder. Couldn't follow beyond construction of measure

[dusky berry]

@ocean mulch @finite gale

[ocean mulch]

I heard about the latter. Ppl seem to like it, tho Idk.

[maiden halo]

what do you mean? not concise?

[gray jungle]

tao's measure theory book has a unique treatment , definitely worth reading after you've done some MT

[fierce hedge]

His intro analysis book takes 5 chapters to build R from scratch

[coral prawn]

Would suggest Spivak if yr interested in some exposure to mathematical analysis

[ocean mulch]

he just goes on and on, assuming everyone knows what he knows

though fair, I won't do better if I have to write a book. I don't know what you know and don't know.

[fierce hedge]

specify the book you're talking about for better context

[coral prawn]

He likes to chat with the reader, which can be painful when you're not understanding him/the context

[ocean mulch]

The last one I tried was his Measure Theory book

[gray jungle]

tao's analysis didnt feel that way to me , i can see his measure theory book being that way

[maiden halo]

isn't he one of the most prolific mathematicians alive...

[gray jungle]

Analysis I was actually quite motivated and easy going

[fierce hedge]

kmm, you haven't done any of his books you know

[coral prawn]

Oh wait u guys are talking abt measure theory

Nvm

[ocean mulch]

wdym from scratch? with Dedekind's cut and Cauchy's equivalence of sequences?

[coral prawn]

I did and am doing his book on intro to analysis

[ocean mulch]

exactly my point 😄 Idk about him, but I can see how he has that trouble. I know some ppl who think lightningly fast, and either you keep up with them, or you don't.

cus they can't understand why you don't understand

[fierce hedge]

yeah he takes one chapter for construction of N, then does ZFC, then construction of Q, finally completes Q to form R

[ocean mulch]

ZFC, lmfaooooo

[fierce hedge]

not just ZFC but set theory in general I mean but it's unusual for book to actually do ZFC

ZF I mean, he doesn't introduce C in that chapter

[ocean mulch]

Peano's axioms should be enough. ZFC is overkilling

[fierce hedge]

lemme post the contents

[ocean mulch]

It's like learning Latin when you're still struggling with French

[fierce hedge]

Chapter 1 is just motivation

[ocean mulch]

Idk, but math books are generally quite horribly written. I swore that I would remember what the pain felt like, so that I'd write better books if I had to

[gray jungle]

It depends , its still a pretty objective thing for the most part , its hard to tell what makes a math book "good" because that can be different for each person.

I love certain books that i know some people will absolutely hate and vise versa

[fierce hedge]

One book like that will probably be Artin, I don't hate Artin in fact it has definitely made me better in Algebra but feel like there must be better books out there

The geometric approach it makes is some times a bit puzzling not to mention the few unusual topics

[ocean mulch]

Don't read Serge Lang. I repeat, not Serge Lang.

he summarised everything about category theory in one section. This guy proved three isomorphism theorems in two pages.

Idk how anyone can learn from that book

[fierce hedge]

I think you mean his Algebra book?

[ocean mulch]

Yes

Oh, I thought you talked about Algebra book

[fierce hedge]

Yes but the original question didn't mention anything so it's better to specify which book we're talking about especially with lang

I think all Lang has done in his entire life is writing books

And AIDS denial lol

[coral prawn]

It's... that bad?

[fierce hedge]

Yeah, I'd say it's only worth it as a reference book although dnf would still be better

Then again I haven't actually read the book enough to comment

[coral prawn]

So.... found this book in a bookstore. I thought the author sounded familiar until I realised why: Sheldon axler from LADR and ross- that analysis text (I think? I can't rlly remember, but in any case) anyone seen this book? Any recommendations for probability?

[ocean mulch]

Depends on what topic of proba

[coral prawn]

[maiden halo]

This book was recommended to me as a good one. Or it might have been one of Sheldon Ross's other intro probability texts, but I think it was this one.
I've only skimmed it in a bookstore but it seems comprehensive enough, probably not good enough for a grad course though

[coral prawn]

gotcha

[desert oriole]

||google: bookname pdf||

and if the book is good then buy it

[desert oriole]

Trigonometry by I.M. Gelfand and Mark Saul

You can do the whole book in less than a week

its easy to understand

and then id try

103 Trigonometry Problems by Titu Andreescu and Zuming Feng

just buy it

[fluid skiff]

Any books or a series of books which teaches calculus and geometry in combined fashion with a very general setup involving manifolds and measures on locally compact abelian topological groups ....all this but starting from scratch.

[mellow wren]

so like a diff geo text?

the only problem is that last one

since haar measures I haven't really seen in diff geo texts

A good reference for that might either be Folland's real analysis book or a book called fourier analysis on number firelds

[chrome yacht]

I have no clue about "locally compact abelian topological groups" but i think you should check out the amann escher 3 volume analysis series, the final volume does have diff geo plus measures

[sleek canopy]

Tao's analysis does not do ZFC

unless I just badly misread the conversation

[fierce hedge]

It doesn't do it as a big thing on it's own but it does introduce them properly for resolving the Russell's paradox

[sleek canopy]

revising this: yeah it does "do" them by briefly introducing them and etc, guess that must have slipped my mind

[oblique beacon]

I'm going to be doing an applied real analysis course next semester. I wanted to know which books I can use to self study and prepare for it. I'm familiar with proofs and have done the typical calc sequence, LA, discrete. Was thinking about tao, abbott, and rudin. But I'm not sure which one would be best for a clear intro, the course textbook is awful...

I saw someone mentioning here that tao's analysis 1 is well motivated, I'd prefer something with good motivation and one which doesn't skip much.

[trail yarrow]

rudin would be an AWFUL choice. The book has amazing exercises, but is a better reference than something to actually learn from. I've heard tao's analysis is really good, and also "understanding analysis" I've heard is really good

Rudin gives NO motivation at all (yes, I am using that book right now for a class....)

[mellow wren]

A less common rec for analysis

Chapman Pugh

mathematical analysis

very good imo

very hard as well but very good

[remote sparrow]

http://math.ucdenver.edu/~jmandel/classes/5070s08/analysisSyllabus-08.htm

interesting syllabus for real analysis prelims prep

includes schroder's book

[oblique beacon]

okay thank you!! @mellow wren @trail yarrow I'll skim those 3

that syllabus actually looks useful too, bookmarked

[crimson leaf]

This seems cool I really like the writing of Schroeder but never had any resources

[mossy flume]

I liked Rosenlicht's analysis text

big fan

[narrow relic]

Also you might want to check out Introduction to Real Analysis 4th Edition by Donald R. Sherbert and Robert G. Bartle.

[granite girder]

Has anyone read zorich's mathematical analysis duology? How long did it take you to get through it with what average number of hours invested in it weekly?

[narrow relic]

I've not read it but looked at it, the notation is extremely clear, he writes math like I write it, using logical quantifiers in the right order as opposed to English sentences

It does have a lot of physics-y kind of examples which isn't my thing

My impression is that it's probably a great book but that you might not have to read every single line

One thing you should know about these analysis books is there's rarely "the perfect book" that you should read every single line of. For example the Bartle and Sherbert book has some material that I never read because it didn't seem relevant, so I had to go to other books for that stuff, but I still love the book for what I used it for.

[granite girder]

Thanks for the pro tip.

[narrow relic]

You're welcome, some people might disagree with me, but I haven't yet read one of these books cover to cover, I usually end up moving to another resource after going in-depth for a while on the first one

So I would just pick something solid that works for you and go with it as long as you're getting things out of it, and if it's not working, start checking out some other books

[granite girder]

Yes, I have already abandoned rudin for that matter.

[daring reef]

which intro abstract algebra book has the best exercises if I'm just trying to review the subject?

/ which book has the most difficult exercises

[desert oriole]

you have to know all the theorems and concepts

[remote sparrow]

I think @gray gazelle worked through at least part of it

[remote sparrow]

Well, i'm not sure if you'd want an intro book if you're just looking for review

[daring reef]

i mean intro as in like

[remote sparrow]

I guess artin or dummit and foote

[daring reef]

up to galois theory

[sleek canopy]

I've hears good things about Advanced Modern Algebra by rotman

[daring reef]

thanks ill check those out

[remote sparrow]

Lang has an undergrad algebra book

[sleek canopy]

👎🏻on anything written by Lang.

[remote sparrow]

I imagine it might be suited for review

[daring reef]

i guess for reference im trying to review so i can take a qualifying exam in grad school lol

[remote sparrow]

Lang is suitable for review, if not for a first pass whether undergrad or graduate

[fluid skiff]

Yeah i know this second one. Great book.

[fluid skiff]

Sure this sounds like a good series. I'll check it out.

[desert oriole]

i myself am not that good

im currently doing egmo(geo) and otis excerpts(algebra)

and also aops vol 2(finished aops vol1 a momth ago)

and handouts

yufei zhao and evan chen both have nicr handojts

i also did some problrms from arthur engels book

idk

im using like 20 different

[ocean mulch]

I picked the Red Book up in my freshman. What a mistake

[remote sparrow]

red book?

[remote sparrow]

@ocean mulch

[cedar ridge]

its putnam qs

[mellow wren]

Lang has a WHAT

Are you referring to lang algebra?

The famously not good algebra book that is not meant for undergrads

[remote sparrow]

https://www.amazon.com/Undergraduate-Algebra-Texts-Mathematics/dp/1441919597

[mellow wren]

Wow TIL

I was not aware of this

Is it any good?

I know his books are a mixed bag

[ocean mulch]

https://www.abebooks.com/9780201054873/Algebra-Lang-Serge-0201054876/plp

[ocean mulch]

aka this one

I learned quite a lot from it,but not a great book nonethless

Turned out I was not the only one
https://mathbabe.org/2012/01/03/ken-ribets-love-note-from-serge-lang/

[remote sparrow]

i have the third edition which is yellow

[night veldt]

is anyone vietnamese here?

[nimble otter]

Can someone recommend books about discrete math

I wanna learn it

[coral prawn]

Rosen was what's recommended to me. I got a physical copy of it yesterday and went through a few pages, was pretty great so far.

[nimble otter]

You are so kind, you already reply two questions of me. And I think you are a people good at learning!

[grizzled tulip]

#book-recommendations

[fierce hedge]

ah yes, self reference

[grizzled tulip]

lol sorry

When youre doing JEE questions and you dont realise the channels have switched from discussy to book-rec

[nimble otter]

I need it

or

[heady ember]

Piracy is not allowed here.

Not so explicitly, anyways.

[nimble otter]

oh i know it

[ocean mulch]

if you know, you know

[heady ember]

[nimble otter]

I delete it

Then, Can someone recommend books about college algebra

else

[ocean mulch]

Serge Lang

[nimble otter]

I need a good book hah

[ocean mulch]

No, just kidding, not Serge Lang. Maybe his Undegraduate Algebra, but I haven't tried that

otherwise, I would say Herstein's Topics in Algebra

[nimble otter]

Have you read it, or you hear else people say this book is good

[ocean mulch]

Unless you're Peter Scholze

[ocean mulch]

I read the first few chapters. It's quite ok, but I can be biased

[nimble otter]

ok, thanks

[sage python]

Careful, sometimes "college algebra" is used to mean... similar to precalc/high school algebra 2, but taken at a college

[desert oriole]

it is (but prolly because its my first book pn geo)

i skipped the geo section in aops vol 1

[spark shale]

Could anyone suggest me a good proofs book please, I'm looking to read and understand ideas
Education level - A level math

[heady ember]

Look in pinned, loch has a short intro to proofs

Also, you could probably jump straight into smt like Friedberg or Schroder provided some perseverance, as is standard in any math book.

[spark shale]

Tysm

[compact glacier]

awsm

[maiden halo]

I actually liked Lang's "Basic Mathematics". I used it to refresh some basic stuff I hadn't seen in almost 30 yrs. But I'm far from a mathematician

[quick hornet]

Lang was a terrible person and his textbook output was very much quantity-over-quality

But I'm not aware of anything else that does what Basic Mathematics does

In general I'd recommend picking any other book over Lang (not because of moral considerations, the dude is dead, just because he's not a great pedagogist)

[heady ember]

Np, happy to help! :D

[maiden halo]

oh wow, I just looked at his Wikipedia page... 💀

[coral prawn]

Tough truths

[dim forge]

Lang's Undergraduate Algebra is good. He gives a proof of induction in chapter 1 which I've never seen anywhere else. It only uses well ordering of the naturals, so it also works for transfinite induction. His exercises are also top notch. Herstein's topics in algebra or Artin's algebra are worth looking at as well. Dummit and Foote wasn't very good back when I was learning.

I'll just sketch the proof of induction since it's nice. Well ordering means that every nonempty subset has a least element. The naturals are well ordered. Now suppose we have the assumptions of induction, a statement p(n), p(0) is true, and p(n) being true implies p(n+1) is true. Let F be the set of naturals that p is false on. Suppose F is nonempty, so then there is a least element f and p(f) is false. Since p(0) is true, we must have f>0, and specifically f-1 is also a natural. Since f is the least element, p(f-1) must be true. But by the assumption of induction, p(f-1) being true implies p(f) is true. Thus a contradiction, F is empty and p(n) is true for all naturals n.

[crimson leaf]

My only problem with D& F is the ordering is sometimes a bit weird like group actions and homomorphism being thrown in early then parts of the subjects scattered throughout the book before reaching the meat of the topic

[narrow relic]

I think the Mary P. Dolciani books do what that book does but I'm not sure since I've never seen the Lang book, only heard people talk about it

[remote sparrow]

hungerford's Algebra (not his Abstract Algebra) seems like it would work too

[crimson leaf]

The pins would be a good place to check

#book-recommendations message

[fierce hedge]

Usually induction is used to prove the well ordering of natural numbers so this is interesting to say the least

[dim forge]

Really? Wouldn't well ordering come from how the naturals are constructed?

[fierce hedge]

The 2 proofs of well ordering I've seen rely on induction argument. It seems natural cause integers also follow the same axioms as natural numbers minus the induction. So, it's not unreasonable to guess that without induction well ordering won't work

[sturdy shore]

it's also common to assume well-ordering as an axiom and prove induction

well-ordering and induction are equivalent, as in you can prove one from the other

[gray gazelle]

any good book for logic that isn't super syntactic in nature like Mendelson or Kleene?

[granite girder]

Yooo, zorich's mathematical analysis 1

It should be fine because that book is also meant for a first rigorous course in analysis

[remote sparrow]

Maybe enderton, goldrei, or mileti

[sleek canopy]

Van Dalen is a decent book

[clever orchid]

What are the pre-requisites for studying Terry Tao's Analysis-1 ? Can a freshman (1st semester) student understand this book ?

[sleek canopy]

The primary thing I would think is just math maturity; if you don't have a ton of it it may take you a while to get through but I don't necessarily see why you shouldn't be able to?

[clever orchid]

So , I can start with appendix-1 Mathematical logic and then continue with chapter 2 ? , becuase I don't have that "mathematical maturity " as of now , you know high schoolers only do computation(calculus) and don't have to worry about the underlying maths that is making it possible in the first place, while analysis-1 requires a lot of proof writing.

[gray gazelle]

uhm... thx I'll check them out

[gray gazelle]

thx

[gray gazelle]

try to read it, you will understand everything eventually, but if you find it hard to understand what's going on I recommend looking into "the real numbers and real analysis" by Ethan D. Bloch, it might clear things up

when I was a freshman I tried like 10+ books and the only one that worked for me (clicked) was Bloch's book

didn't try Tao tho, its a good book indeed

[clever orchid]

Alright, thanks, I still have some time with me to do the pre-preparations for uni , so I thought analysis-1 would be the best place to start, so even if I don't understand anything (which would probably be the case) I'll have time to learn it using some other books and materials. I just wanna use this time productively and get rid of my math fear.

[gray gazelle]

just understand how stuff is constructed from Peano Postulates and how proofs are written and ure ready to learn the rest in uni

[clever orchid]

Yeah , I'll try to learn those things from Terry's book, starting with proof writing.

[gray gazelle]

uhm

well

u know what to do if u get stuck

[clever orchid]

Try Bloch's book ?! or some other reference

[gray gazelle]

nice u got the book name correctly

[merry sphinx]

any algebra books that aren't super thick like d&f?

i've heard of gallian but i've also heard he's got a bunch of typos

[finite crane]

Peano axioms include induction
and induction is equivalent to well-ordering

so you can choose either as axiom

it's more of a matter of taste

[sleek canopy]

Herstein's topics in algebra is pretty concise, rotman's advanced modern algebra is pretty good

[maiden halo]

I've seen mention of Dolciani several times here. I might get a cheap used copy

[narrow relic]

There are a bunch of them, at different levels.

[desert oriole]

what did he do (i only know of his aids denial)

he was anti vietnam war

i think that isnt that bad

was mr serge really that bad?

Do you guys avoid reading books written by terrible people?

[coral prawn]

Some comments I've heard about his texts complain about the dryness of his texts, as well as the quality of the content covered

[coral prawn]

Namington specifically mentioned that even putting him as a person aside his pedagogy didn't sit well with him

[desert oriole]

ah oh ok
if his book arent that good, why are they so popular then?

curious

[coral prawn]

(I quote from this server, didnt read his book other than on linear algebra)

he summarised everything about category theory in one section. This guy proved three isomorphism theorems in two pages.

[desert oriole]

oh

Ive heard that langs book shouldnt be used for learning the topic.

Just for reviewing the topics

prolly because the explanations arent that good

[coral prawn]

Well... probably cuz of his controversy not really sure, after all, there's a lot of reasons why one could get famous, even for the wrong ones

[desert oriole]

Oh ok thank you.

[crimson leaf]

He also quit his job over Columbia's treatment of protesters and was very against Huntington because afaik Huntington was trying to say the people of South Africa were happy under the apartheid

[desert oriole]

idk if I understood that right, but why would that be a bad thing

[coral prawn]

Perhaps this would be more of a discussy thing

[crimson leaf]

The algebra professors I have asked about his book keep it around as a reference book, like you said not really for a first pass

[desert oriole]

#874142022997516318 message

[desert oriole]

oh ok

i like rotmans book

[coral prawn]

the one on abstract algebra?

[desert oriole]

yes

[coral prawn]

How u finding it so far?

[desert oriole]

i like it

idk which page im at

[coral prawn]

[desert oriole]

its way harder than i thought

[vital iris]

Lol no way Lang being against the Vietnam War is what's stopping you from reading him

[desert oriole]

THE THING THAT IS STOPPING IS MY KNOWLEDGE OF ALGEBRA

i thought him being against the vietnam war is something good

@vital iris

Its just the two things i know abt him

and was wondering why he is a terrible person (someone said that he is a terriblr person)

id read langs book if it was easier to understand

[rapid lily]

That was just someone providing their opinion that he is a terrible person. There is not too much to say about it.

I really like his Real and Functional Analysis book

[desert oriole]

i wanted to understand why the person thought abt him like that

[sturdy shore]

based on what others have said here before, it's not just that he was an aids denialist, but he was using his academic credentials to push his denialism

[rapid lily]

You should probably ask them specifically then

[desert oriole]

thats why i pinged em in my question

[rapid lily]

Oh ok

[sturdy shore]

fwiw the books I've taken a look at he never came across as a bad writer at all

but the algebra one specifically is definitely a reference type of book for someone who already knows a good deal of algebra imho

[desert oriole]

this the message

[coral prawn]

Thoughts on pop math books?

[orchid mortar]

sin

I read too much pop math in my youth

[coral prawn]

LOL what kinda pop maths books were they? What topics did they cover?

[orchid mortar]

https://www.maa.org/book/export/html/116744

I also read Villani's pop math, and Feynman stuff

Useful to get wowed but not really useful after

[coral prawn]

Feynman LOL

[coral prawn]

Mhm

Could he handy for motivation but aside from that definitely not for educational purposes

[minor bolt]

HEllo I need help here. I am in high school and very good at math but is there any math books I can buy to keep me studying.

[mossy flume]

what sort of math have you done so far 👀

and what have you liked

[minor bolt]

geometry, algebra 1

[narrow relic]

#book-recommendations message

[remote sparrow]

basic mathematics by lang

[civic nebula]

hey can anyone reccomend a good book for under grad math?

[remote sparrow]

what subject

[celest sandal]

Can anyone suggest me books with hard and tricky word problems? ranging from Grade 9-12

[remote sparrow]

i think martin gardner has written some math puzzle books

[celest sandal]

Thanks for suggesting that amazing guy!
Gonna try out his books.

[remote sparrow]

raymond smullyan has written some logic puzzle books but i'm not sure how good they are

[celest sandal]

thanks. It's hard to find with specific people with their collection of specific puzzzles and problems. Generally all I find is textbook problems from various schools before this. Thanks

[coral prawn]

I read that as sullyman 💀

[remote sparrow]

👨

[fallow cypress]

Anyone have dynamical systems recommendations?

[remote sparrow]

presumably besides the ones in #books?

[fallow cypress]

Oh lemme check that first

[remote sparrow]

also hirsch, smale, devaney seems good

[fallow cypress]

ty!!

are those three separate books or one book

[remote sparrow]

one book

[fallow cypress]

kk

[sage python]

That's more ODEish dynamics

I like Brin and Stuck

Also lots of lecture notes online, I think including by Milnor?

[fallow cypress]

I hear Robert Ghrist is writing one too so I wanna find a draft or smth

[remote sparrow]

hubbard of vector calculus fame has an ode book from a dynamical systems perspective

https://link.springer.com/book/10.1007/978-1-4612-0937-9

[fallow cypress]

Cool noted down all of them, ty so much!

[fierce hedge]

Can anyone confirm if this textbook is in black and white only or does it have a colour version