book-recommendations

[fresh skiff]

[dim pendant]

I believe that he claimed it was. I could be wrong, perhaps I'm thinking of one of his analysis books. But honestly keep the grad book around as a reference. Don't use it to learn algebra from scratch

It's so almost perfect except he shoves all the exercises to ends of the chapters so you don't know what exercises are supposed to be done with which sections in mind

[fresh skiff]

are you talking about his UG book?

or his ALGEBRA ?

GTM one

well my plan is to revise LA => AA by silverman and D&F
maybe after a bit of LA i touch IVA by cox (ideals varities and algorithms)

[dim pendant]

Algebra

[proud abyss]

what is a good math book for learning the beginning of math

like

basics

from 0

but like really good

i cant explain myself

[dim pendant]

What's your background? If you're thinking high school, you can to through Khan Academy and just redo arithmetic and start on algebra. If you're thinking rigorous mathematics, the stuff math students do, you'll want to start with mathematical logic, and from there you can do set theory.

[proud abyss]

so mathematical logic is the first thing I should go for to begin building on

[rough umbra]

I kinda disagree, I think if you mean like rigorous mathematics, you should start with intro algebra or analysis. Logic/set theory can wait

Foundations first is a weird choice

[proud abyss]

why?

what I wanna do is

I wanna grasp what math has to offer entirely at some level

not master all of it

but to understand what its tryna say

I feel like this should be like building a big skyscraper

[rough umbra]

When I say foundations I don’t mean like a solid foundation for your learning/the basics, I literally mean the field #foundations

[proud abyss]

ahh

well what I see happen a lot is that

I usually go ahead wth algebra or analysis

[rough umbra]

It’s just not generally done bc you’ll probably be unmotivated and not have many examples or much maturity yet. Mathematical logic or set theory are usually upper year courses

[proud abyss]

but whenever I come across more words and logic things and intuition etc.

I get stuck a lot

[rough umbra]

What have you tried reading so far?

[proud abyss]

nothing I wanna begin from something though

Im 12th grade rn

in highschool

[rough umbra]

Ahhh

[proud abyss]

I used to want to

major math

but I now wanna do medicine but

math stays as like

my peak hobby

I taught myself a lot of LaTeX in just 4 days cuz I thought I proved the collatz conjecture

but I found out the definitions of Odd and Even aren't enough for me to explain what I think

so I wanna learn more math

to be able to do that

one day

I used to just

take math problems I cant solve

and spend weeks

on paper

until I could solve it

[rough umbra]

Ok, if you’re interested in analysis, I’d recommend Understanding Analysis by Abbott. If you’re interested in algebra, I’d recommend Algebra by Artin

[proud abyss]

I see

ill write those in my notes

to look for them

[rough umbra]

There’s some good reviews for a bunch of fields by dami in the pins of this channel

[rough umbra]

But for now this is probably the right entry point

[rough umbra]

Shouldn’t be hard to find them 🫡

[proud abyss]

yeah i found them

but i got other things to do for 20 days

{final exams}
]

ill keep them there

to find them later

otherwise id forget

[proud abyss]

alr

also

i have a question

would you say wikipedia is a good source for learning some things?

like the last 4 months I've learned a ton from wikipedia

but idk if thats healthy

cuz it feels

like reading newspaper

idk

[rough umbra]

It’s helpful for definitions and overviews of fields yeah

And as a reference for theorems and stuff

But for like learning a topic, probably aim for books (video lectures can be good too if that’s more helpful to you)

[proud abyss]

video lectures are defined by the speed of the one teaching it and the quality of how well I learn is also defined by the person teaching

usually I learn things better when someone either properly explains them and doesn't skip over things every 5 minutes

or I just

learn it pen paper

[normal crystal]

if only they invented a speed multiplier for videos

[fresh skiff]

we have to prove local and semi local convergence of our method (in thesis). Idk how to do this, nor we have learnt this in our classes. Any resouce to learn that?

[novel solar]

I learned one variable calculus in 12th grade but wanted to approach it rigorously so, i stumbled upon the book "Calculus 1" by Tom M. Apostle. I covered the part "The idea of Integral" but as I started the "Applications of Integration" i thought, without going any further I should first build my proof reading/writing ability to take the most from the book. Hence, I started with another book "Mathematical Proofs A Transition to Advanced Mathematics" by Gary Chartrand.

Would you do these if you were in my position ?

[rough umbra]

Imo you can learn proofs through learning proof based math rather than a dedicated book on proof techniques. I’d probably just recommend artin algebra or Abbott analysis depending on which you’re more interested in first

Ofc it’s up to u

[novel solar]

Would you give me an overview of those two books

[rough umbra]

Understanding Analysis does intro single variable analysis (sequences and series, limits, convergence, etc etc), you can do real analysis after it. Assumes no background besides high school calc. Algebra covers intro algebra (groups, vector spaces, rings, fields and Galois theory). Assumes no background, I’d probably recommend skipping around rather than reading the whole thing tho (like I think u should probably do rings/fields before rep theory for maturity reasons)

See the pins of this channel for good reviews

[novel solar]

How do I see those pins ? I'm new to discord so

[fresh skiff]

i used and using Abbott for analysis and its nice. I tried to use Artin but failed :(
i stuck (i was watching Prof gross videos)

• using this book

[fresh skiff]

#real-complex-analysis for real analyssi
#groups-rings-fields for algebra (abstract algebra)
Remark: click on this blue name (hyper link actual) you will reach there

[novel solar]

Thanks

[rough umbra]

For clarification i meant the pins in this channel

[fresh skiff]

oh ok

[novel solar]

I just read on top of the first few pages of the "Abbortt Analysis". In just a few pages they covered proof techniques, set theory basics even the cantor's theory. The first page started with proof.

Is this really doable if i don't have any experience in proofs ? I started to have interest in the book.

[rich sun]

Abort Analysis!

[tender river]

Doing this is how you build experience doing proofs...

[verbal roost]

can someone recommend me a good statistics book

[novel solar]

I got it, first I will do the first 6 chapters of the Gary Chartrand's math proofs and then will jump on the Understanding Analysis.

Thanks for the advice.

[vital bane]

You don't really need that

Abbott teaches you how to write proofs

[rough umbra]

^

[dim pendant]

The hardest part of writing proofs is coming up with the proof

Actually understanding how they work isn't something that needs a 200 page book

Unless you're insane (sorry not sorry, logicians or Idk what you guys actually do)

[foggy quest]

most of these books only spend one chapter on math proof notation. The rest tends to be applications to discrete mathematics

It's good material, generally

[marble fern]

Hey

Anyone has a pdf explaining projective geometric algebra?

Can't find a pdf online

Please ping me if yes

[dim pendant]

What is it used for

Perhaps you can find a resource about what it helps accomplish and end up with your request

[remote vortex]

The hardest part is mustering the willpower to deal with the tedium of writing down the proof clearly and rigorously once you've actually come up with it

[grim ore]

Theres definitely a lot of perspectives to address projective geometry, either from topological -> diff geo or alg geo

So is there any specific niche that you want to look at it in context for?

I havent really heard of a book on just proj geo

If I had to think about it, beltrametti et al would be good but i also dont know what proficency level you are looking for

I found some interesting thesis papers on proj geo, one of which is by hs students in the MIT Math camp, just search up like "thesis on projective geometry" and im sure youll find loads or even on arxiv

Also thesis papers are pretty nice to read for getting summarized information on a topic (for masters level) or the current to date info of research on a topic (usually PhD level)

[dim pendant]

I had a "free PDF copy" of a decent book on it but it's been lost to tint

Time

[true sail]

Name of the book?

[dim pendant]

Would tell you if I knew

I imagine I found it by searching "books on projective geometry" and clicking Reddit/MSE links

[old elk]

excellent paper, the one who wrote this was very detailed, thanks to the one who passed this on.

What is the AI like for creating exams to sit for master's degrees?

[dim pendant]

The Ai? There's a website whose link is floating somewhere around one of these channels that just uses a simple algorithm to gather problems from a number of sample exams

[grim ore]

That name seems familiar

Might be bc of Vakil being his advisee lowk

Probs read his work on smth then

[royal lotus]

Wings of Fire

[old elk]

Where is this link?

[dim pendant]

Found it

https://jonathanlove.info/qual/

[old elk]

What a beast these exercises are, I don't understand anything at all.

[grim ore]

YES this is that site

I love this site

[toxic willow]

Hi, I finished my undergraduate majoring in CS. However, I think I didn't learn proof based math well. So, I'd like to re-learn undergraduate math in a math major way. My question is can Spivak Calculus and Hubbard & Hubbard Vector Calculus cover Calculus I II and III?

[fresh skiff]

i guess its for graduate level

i only select linear algebra and was unable to do any single problem

[trail hemlock]

yes it can

[dim pendant]

Use Zorich

He basically teaches you analysis but also provides calculus exercises so you don't drown in the epsilons and deltas

It's meant for folks who want the best of both worlds

[fresh skiff]

I am able to complete linear algebra 1 from Oxford archive. Then i guess i would use algebra maybe by D&F and silverman before again going to linear algebra 2

Sounds good?

[toxic willow]

thanks, i ll take a look❤️

[paper star]

Heyyy

I want book recommendations for vectors and trigonometry to complete every concept, can anyone kindly suggest some books for this?

[dim pendant]

Khan Academy

They have all the trig you'd need for both geometry and precalc/algebra 2

So you're prepared for Calc

[grim ore]

<@&268886789983436800>

@slate tide

[dim pendant]

Umm, they better not be turning pandas into chess boards wtf

[dim pendant]

This has recently been brought up in discussion in the server and the general consensus was that this should generally be avoided for the time being

The return for setting it up is, right now, too minor compared to the effort required to do so

And the whole point of learning pure math is to get and verify answers yourself

[boreal barn]

any good source for co-ordinate geometry?

[heady ember]

How many times do you wanna do linear algebra 🗿

[grim ore]

silverman EC? What other book does he have (/srs)

Also for lin alg?

I kinda exclusively know him only for geo stuff and nt

at cryptography too

[pale mica]

I've got "an introduction to the theory of numbers" by hardy and wright, is it good?

[sudden kindle]

Its a standard text used in some undergrad number theory courses, up to you to decide if its good.

[timber mesa]

Bookshelves

[gray gazelle]

Would it be good to go through functional analysis (Rudin and Conway) at the same time as harmonic analysis (Grafakos), or should I do one before the other, and if so, which one?

[elder stratus]

the two subjects are mostly independent and can be read simultaneously

[grim ore]

@timber mesa We dont have perms in the thread :(

[dim pendant]

This has no exercises, uses outdated notation, and is too general without a plan.

[fresh skiff]

I make sure this is the last time (atleast for now I dont wanna go again and again)i am going tho.
The previous time i didn't pay attention on understanding and later forgot most of the stuff

[fresh skiff]

Oh yes his famous book on AG right?
He has a book on abstract algebra (abstract algebra an integrated approach).

[timber mesa]

oops how about now

[heady ember]

Just review the relevant content when you need to

[fresh skiff]

this also make sense

[grim ore]

Yeah he has a good amount of books but I never knew he made a core math text lol

More so topics

[fresh skiff]

did you take a look at his this book?

[grim ore]

No I had not

[fresh skiff]

lemme show you, exactly what things took my attention

[grim ore]

Ive read a decent amount of his other ones, namely AoEC, EC Topics, Intro to Math Cryptog

[fresh skiff]

cool

his table of contents

[stuck birch]

Best book to learn AP Calculus AB in simple english non complicated word (sorry english is not my strong language)

[grim ore]

Id recommnend Khan Academy for the most part, or you can even go through Openstax

Calculus AB is just the first calc text

But openstax might be a bit complicated to read for those who may not have strong english

Khan Academy accomodates appropriately for the most part since education is heavily diasporic in America

[stuck birch]

So Khan Academy is the best choice for me?

[grim ore]

I sadly cant really say because I dont know you or what english level you are at, but most people like khan academy for being simplistic and teaches you well

What is your native tongue?

[stuck birch]

Bisaya/Cebuano

[grim ore]

Thats from the philipines right?

[stuck birch]

Ye

Thats chavocano i believe

[grim ore]

gotcha gotcha

[stuck birch]

Did u take AP calc AB

Or calc

[grim ore]

I took it back in hs, im a undergrad student now

[stuck birch]

Wat book u use

[grim ore]

We didnt use a book, class lecture notes teacher made

But the uni students use OpenStax here

https://apcentral.collegeboard.org/courses/resources/ap-calculus-teacher-recommended-resources

This might also help

https://openstax.org/details/books/calculus-volume-1

Openstax is free and no account needed

[stuck birch]

Oh thank you so much @grim ore ill check it rn

[heady ember]

Just sail the seven seas

[dim pendant]

Arr-right matey!

[paper star]

Guysss, i really need a suggestion from any of you. So i just finished my 10th grade and need a book or any kind of lecture for vectors, which would mostly cover the college level vector and goes from dust to advanced and also comes with a lot of examples and exercises.

[vital bane]

Linear Algebra by Gilbert Strang

[paper star]

Doesn't this need matrices as well?

[vital bane]

it teaches you matrices (more generally they are called linear transformations)

[paper star]

so I'll get to learn vectors and linear algebra in a single book?

[sterile pelican]

If you learnt abstract algebra first you can learn Linear Algebra by Berberian

[paper star]

I just know some 10th grade algebras and recently I've self-learned calculus

Calc 1 actually

[sterile pelican]

Ah then sadly Berberian isn't for you, I just thought to share this fascinating book I found from the other maths group before I got here

[paper star]

Ah then i should just choose Gilbert book?

[sterile pelican]

If you know basic trig and algebra, and had learnt calculus, I know at least Lang's "Introduction to Linear Algebra" works

I am unfamiliar with Strang so I suggest you wait for what the others say here

[paper star]

I've just checked Lang's one but apparently that should not be good for learning vectors (especially I'm trying to learn vectors for physics)

[sterile pelican]

Where do you hear that from? The first chapter is vectors but if you want applications then sure there are other books but this sets your linear algebra foundations right in my view

Just wait for the others then since I don't do physics really

[cunning elk]

for basic mechanics comparable to intro level uni/AP physics you don’t really need much wrt vectors

besides knowing what they are and how to interpret them geometrically

maybe you’d need to compute the occasional dot or cross product

but doesn’t come up often unless you’re in a more challenging version of the course

[dim pendant]

Youtube and Khan Academy should have everything you may need

[cunning elk]

for topics of level this low it’s probably fine ye^

[dim pendant]

As Richardo said, you don't need much at all, just to get what they're doing for you in physics

[cunning elk]

usually they make you add them or whatever in the simple 2d/3d cases

it’s not that deep in general, just go component by component

[paper star]

Thank you so much, I'll then just watch some lectures on college vectors and dive into physics to solve probs with that

[vestal junco]

Anybody know a good book to start off learning 1. Tensor Calculus and 2. Complex Analysis?

[vital bane]

Are you a physics student learning these subjects to learn more physics?

[vestal junco]

Both

Pure math

+physics

But I prefer reading pure math textbooks prior to applied ones

[vital bane]

Usually "tensor calc" isn't a thing pure math people pursue since it is subsumed into differential topology and differential geometry

I could be wrong though, I myself haven't seen many tensor calculus pure math books or people studying it (other than physics/engineering students)

For complex analysis you could check out Conway or Gamelin or Stein and Shakarchi

see here for more details: #book-recommendations message

[fresh skiff]

Goats

[dim pendant]

For tensor calculus try Eigenchris on YouTube.

[fringe wadi]

guys, if i wanna learn olympiad maths, which book should i start with? (books with good explanations ofc

[real marsh]

https://www.imo-official.org/problems/IMO2023SL.pdf

[real marsh]

https://shop.amt.edu.au/products/pst is actually a good book

[young dew]

I've heard books by Titu Andrescu are great, the AOPS books and PSS Arthur Engel if you want depth

[wet sentinel]

Anybody has recommendations to study graph theory? Preferably both books and yt videos/playlists if possible

[molten gulch]

Diestel graph theory

He has videos and a book, check his website

Reinhard diestel

[narrow mesa]

i second this although the lectures kinda of boring but they are good for intuition

Also anyone have an abstract algebra book recommendation ?

[molten gulch]

At what level

[grim ore]

hungerford

both of them

[narrow mesa]

undergrad but honestly am fine with graduate texts i like a challenge

[grim ore]

Hold your horses

[molten gulch]

~~Lang ~~

[grim ore]

I actually do recommend ug baby hungerford, but artin and D&F (sometimes also used as a grad text) are good options

[narrow mesa]

they have been held

[grim ore]

i learned abs alg from baby hungerford

[narrow mesa]

ok bet

[grim ore]

It also starts with rings and fields first so its easier to understand with limited math knowledge

limited with huge quotes tho

[narrow mesa]

this felt offensive yet considerate at the same time

[grim ore]

wdym? I actually enjoyed reading hungerford and imo was a lot better at the time compared to the others

Also ppl hate when algebra texts start rings and fields first, so I usually clarify because its like a huge nono

I only know two books that does this

[narrow mesa]

i meant by the limited math knowledge

but yeah i get you

aight thx

[grim ore]

Oh yeah, I took abs alg without lin alg, and luckily i only needed lin alg for groups

Thats what i meant

groups and galois was a second sem topic for my uni and i took those two concurrently which worked out

[narrow mesa]

nicee

[mossy flume]

I would learn lin alg before abstract algebra

[molten gulch]

Which ones? Grad rotman, grad aluffi, and hungerford?

[mossy flume]

linear algebra gets applied to many things and gives a good motivation for certain constructions and stuff in abstract algebra

[grim ore]

I personally had Shifrin and Hungerford on the top of my mind when i said that, but youre right

Also grad hungerford does groups first

[rough umbra]

vectors are part of linear algebra

any linear algebra book will also teach you vectors

[remote sparrow]

grad aluffi is groups first

@grim ore

[molten gulch]

Ah I swear one of the aluffis did rings first

[remote sparrow]

yes

[grim ore]

yeah the ug one

[grim ore]

yep

Ive never seen it talked about tho over chap 0

[wet sentinel]

this is suitable for undergraduate students right ?

[grim ore]

i believe the graph theory class in my uni for ug uses it

so maybe yes

[wet sentinel]

alright ty

[wet sentinel]

tysm for your recommendation

[grim ore]

oh wait

i was dead wrong

dont listen to me

[grim ore]

its grad text

[wet sentinel]

ah so it isnt suitable ?

but doesnt it not assume much background

[grim ore]

I found it to be the opposite, also explictely mentioned in the preface that it jumps straight in without wanting to hold a persons hand

https://diestel-graph-theory.com/

Sample chapter looks crazy imo

[rough umbra]

my intro graph theory class uses it fwiw

[grim ore]

I swore my uni's graph theory did too but i feel like i might be wrong

[grim ore]

Invitation to Discrete Mathematics by Matousek and Nesetril and also Introductory Combinatorics by Brualdi

A pretty good prof in our dept uses these texts

A more advanced harder prof uses this: Agnarsson and Greenlaw, Graph Theory: Modeling, Applications, and Algorithms

[grim ore]

I havent take the course yet, but I know Valery who teaches this text teaches well but expects that you know the content by heart

So it must be good

[wet sentinel]

alright tysm

[dim pendant]

Np

[grim ore]

Ive actually been wanting to have an introductory category theory text recommended if anyone knows one

Ive tried avoiding it for as long as possible, but its starting seep through the gaps in my knowledge

It can be at any lvl, grad or ug

ug cat theory would be crazy to take tho lol

[vivid mango]

I found Basic Category Theory by Tom Leinster nicefor UG. Maybe you can try the OG MacLane Categories for the Working Mathematician

[grim ore]

Thank you!

Woah, Basic Cat Theory is public on arxiv

[vivid mango]

🙂

[dim pendant]

This is the correct answer

I believe there is also decent writing of a tiny bit of basic category in Jacobson's Basic Algebra II

And similarly in Aluffi

[grim ore]

Someone in my uni is reading mac lane rn and its overdue

[dim pendant]

Lmao nahhh

That's one of those books that ought to be rewritten for audiences who want the historical treatment

[vivid mango]

Hey, would anybody like to read Brouwer and Haemers "Spectra of Graphs" with me over the next month or so (perhaps too optimistic)? I am starting to read the book from scratch. (Maybe DM if interested? Idk how discord works ...) (also lmk if this is the wrong channel to ask in)

[dim pendant]

Same content just modern language

[grim ore]

maybe ask in #advanced-lounge

Or the graph theory channel

This would be better ^

[vivid mango]

where is this ? I don't see it

[grim ore]

Its not dedicated, but #combinatorial-structures

[molten gulch]

Aagnarsson taught us discrete maths last term, he's also that prof we say has very mixed feelings about us after we proved the binomial theorem that one day

[grim ore]

danggg

[graceful moon]

I think all of Toms notes are public

His Galois theory and ETCS are, I’m pretty sure his notes from when he taught general topology are too

[grim ore]

Gotcha

[graceful moon]

I don’t love his notes tbh, I think they’re too wordy, I took Galois theory realised his notes were like 100+ pages long and dropped it lol

They are nice, they’re very well explained, but I just like a denser presentation generally, I don’t like feeling like I’m reading a novel

[grim ore]

Do you like mac lane more?

I like dense tbh

I too hate novelesque texts

[dim pendant]

To densify any text, skip the text bodies

[vivid mango]

you probably loved Lang's presentation of Galois

[graceful moon]

I haven’t read it, I still need to teach myself Galois theory because I took categorical quantum information instead lol

But I’m tempted to, I think a short and punchy text is what I would like, it’s generally my preference and I hope that I’ve done enough algebra at this point to cope with it (another reason I chose not to do Galois theory)

[dim pendant]

Milne notes should be good

You can just do the stuff before the infinity Galois theory

Just under 100 pages

[graceful moon]

Milne was what I was planning on using

I’m not opposed to the infinite Galois theory stuff either, I haven’t come across it enough to know

[dim pendant]

My philosophy of algebra is to skip the advanced sounding stuff until I know I need it

Which you might deduce given my very clearly vocalized tension with books like D&F

[graceful moon]

I’m not sure I’m of the same position, I think category theory and homological algebra I’d agree with that take but in general I’m very happy to just piss about with nice algebraic objects

[dim pendant]

I imagine this is due to a difference in our backgrounds

I discovered category theory and modern algebra in 10th grade and studied them after spending time with calculus, diff Eqs, and topology

But then I slacked off and learned no math for years

So now I rush through everything since I'm so behind

I take the shortest path to my interest and pick up what I need when I come across the need

[gray gazelle]

are you an engg guy ?

[dim pendant]

The heck is that

Oh, engineering. No, I'm just impatient

[rough umbra]

Category theory in context by riehl maybe?

[dim pendant]

nooooo definitely not this

I mean it's fine but it's a bit much for anyone other than a world class graduate student

[rough umbra]

afaik its aimed at advanced ug/beginner grad and is gentler than maclane?

[dim pendant]

It doesn't read like it

The first object she mentions in order to motivate category theory is group extensions

I get that it's in context but man 🙏

[rough umbra]

id say advanced ug/beginner grad students will have seen short exact sequences before, no?

[gray gazelle]

what would be an actual answer to this question ?

some great proof backed books for linear algebra ?

[rough umbra]

#book-recommendations message

[dim pendant]

If you're American, there's a decent chance you will not have

if you're European, almost certainly

[restive falcon]

this is not true lol

you don't need to understand every example

that's part of the reason why there are so many

[dim pendant]

It's the opening section 😔

[restive falcon]

oh that bit's literally just the historical background

[dim pendant]

ain't no way dude

I just opened the pdf to verify this and you're right

section 1.1 starts after the discussion

I thought she genuinely decided to open her book with a proper categorical discussion of group extensions

[restive falcon]

I will second the suggestion of category theory in context by emily riehl

[grim ore]

Ill look at that too then!

Thanks @restive falcon @rough umbra

[wind oak]

anyone know if tao's analysis 2 is a good selfstudy reference :> (i havent read his analysis 1 but i skimmed the topics and my class included most of it)

mostly looking for a book that covers some more advanced topics relative to my school's standard analysis 2 book, which only covers analysis in Rn

[remote sparrow]

post syllabus/course description

[wind oak]

im nto in the clas tyet (im takign it next semester) but it fololws fitzpatrick advanced calculus

these chapers

wait i cant post pictures

o

if u can find a table of contents, it's most of the topics in chapters 10-20 but skipping chapter 12 which is on metric spaces

https://bookstore.ams.org/amstext-5 theres a table of contents on here, uits everything from euclidean space to the end of the book

[remote sparrow]

can you copy and paste a description from your university's online course catalog at least?

i'll look at your book

[wind oak]

https://www-math.umd.edu/offered-courses/388-math-411-advanced-calculus-ii.html

[remote sparrow]

https://web.archive.org/web/20240607120914/https://sites.math.washington.edu//~folland/Homepage/AdvCalc24.pdf

https://matrixeditions.com/5thUnifiedApproach.html

https://www.amazon.com/Multivariable-Mathematics-Algebra-Calculus-Manifolds/dp/047152638X

these books are more or less equivalent to the suggested textbook

i'm sure fitzpatrick is probably fine though

[wind oak]

o well im not looking for an equivalent, im looking for something more advanced

i was unsatisfied with the depth of the book in analysis 1 and i feel like ill probably feel the same in 2

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-662-48993-2

https://www.amazon.com/Calculus-Manifolds-Approach-Classical-Theorems/dp/0805390219

please look at these then

they cover similar content, but they assume more maturity on your part

[wind oak]

okii thank u ill give them a look

[stark turret]

Theoretical cs book recommendations?

[weak plover]

what subfield ?

[fresh skiff]

any resource for learning convergence of numerical methods using local and semi local approach

[stark turret]

idk 💀 any of them?

[weak plover]

if u wanna learn complexity, arora-barak would be really good. if u want to learn algorithms, u should look at either kleinberg-tardos, clrs, or dpv. if u wanna learn about programming language theory then software foundations would be really good

[tender river]

sipser intro to theory of computation

[analog lava]

can someone recommend something that covers basic homotopy theory and spectral sequences (with a focus in topology) other than hatcher 😄

[rough umbra]

Maybe
tom Dieck - Algebraic Topology
or
May - Concise Course in Algebraic Topology

[analog lava]

right. May seems like a good thing to check

tysm

[rough umbra]

Ofc

[novel shoal]

Hi, which book after reading Gilbert Strang's Introduction to linear algebra?

and which book after calculus (single & multi) from mit ?

[halcyon swallow]

oooh yall are so smmmarrrt ooooh gilbert? BRO u sound like a mad genius love dat energy hahahahahha

[hidden fractal]

Probably learn proofs

Then go on to introductory analysis and abstract algebra

For proofs, Polimeni, Chartrand, and Zhang is good; for analysis, Protter and Morrey; for abstract algebra, Michael Artin is good, but I also like van der Waerden

[novel shoal]

okay bro

[novel shoal]

thank you 🙂

[willow merlin]

does any1 have any review on a mathematical apology by Hardy?

[halcyon swallow]

um I just realized that I might have sounded extremely cringe.... but seriously how in the world do you begin to comprehend these books :0

like they sound super interesting and but like HOW like huh what the heck do you mean you want to learn this like what???

well good luck bro

uh? what? mathematical apology, do you guys speak in cryptic? like hello

how did you begin this journey of learning cuz I don't know how to commit like seriously like how how how how how

PLEASE this is urgent how are yall actually doing this cuz hm. I need to begin a life of less cringe, more socially accpetable nonstupid communication tactics.

wait, did I just say a bunch of stuff that is unnecessary :0 is that wrong or something but honestly :C I might have ruined this for me :C next time I will sound better like someone with confidence and sincerity.

is that better? :0 do i sound like a sigma, i mean a person of high social standing 😮 or do I sound too dry in the wrong ways!! anyways I know this is about mathematics but man i didn't know mathematians were this social! but this makes sense in this digital world :0

well to end this off in a good note, you are confident and badass (so cool, chill person statement) and keep up that dang good book comprehension and developing your cognitive abilities.

okay good bye. this was somehow still an essay full of cringe. you will see this change. I will talk more fluently in math. good day.

good luck to you.

[tender river]

[full cairn]

[drowsy nacelle]

𓇋𓈖𓂧𓅂𓂧 𓅃𓅂 𓂧𓅱 𓃭𓇋𓃭 𓃀𓂋𓅱 𓎼𓅂𓏏 𓅃𓇋𓏏𓉔 𓏏𓉔𓅂 𓏏𓇋𓅓𓅂𓋴 🥀 💔

[rich pond]

Does it need to be linked? (https://en.wikipedia.org/wiki/A_Mathematician's_Apology)

[drowsy nacelle]

prolly not 🪫

[remote vortex]

That said, a lot of mathematicians should apologize

[drowsy nacelle]

Thank you my friend

[willow merlin]

do you have any opinion on the subject

[rich pond]

It's a long time since I read it. However my personal journey being one of trying (without success) to understand algebraic geometry, I do see Hardy's point as one of who (as in students) to place your bets on.

[hasty linden]

any indian?

[lavish radish]

I have a protter and morrey calculus book from 1963

[hidden fractal]

I mean A First Course in Real Analysis

[lavish radish]

Was sitting in an old relatives basement along with other math books and he gave it to me

[dim pendant]

It's the same thing as realizing you like chemistry, or art, or learning languages. Something about it hits home and sparks your interest.

In A Mathematicians Lament, early on the point is made that math is actually hidden from high school students. In your algebra class you learn to guess solutions to polynomials, solve equations, work with properties of logarithms, and so on. But this isn't what math is about.

More specifically, such topics have been understood for at least a couple hundred years, sometimes many hundreds of years. Modern mathematics functions more like a combination of philosophy and art.

We ask questions about patterns and use reason to uncover their truths. We don't care about memorizing formulas like the quadratic formula or multiplying 4×4 matrices.

We ask questions like, what are all of the ways in which something can be symmetric? Are there infinitely many prime numbers that have a difference of 2? How do notions like area and volume generalize beyond rigid geometry? What is infinity like? Which smooth surfaces are really the same up to smooth transformations?

But this isn't shown to high schoolers because some of these questions take lifetimes to even get close to answering or even understanding.

So, how do we understand these books? We spend years working up from the bottom.

[ancient creek]

Thanks for these words ❤️‍🔥 . I don't think you need lifetime to teach yourself math, the way HS is structured just kills any curiousity and interest in something as math, everyone calls it "you need to be smart to understand it, it's not for me". Which is NOT true. If school and uni were structured in a way that inspired philosophical questions and creativity within students, nobody would think negatively about studying. What I have noticed is that young kids aged 7 to 10 have more interest and passion in studying math, art and then at some point it completely reverts. School becomes more of a responsibility and something one has to do for the sake of memorizing the exams. By the end of high school, kids already have no motivation to do anything cool with their lives and just go with the flow.

The REASON why everything treats mathematics as something completely foreign is because human brain is not meant to function as a simple machine algorithm, where you take this formula, it gives this output, ok good, now repeat thousand of times. It's not a discreet system, heck even AI llms now don't work like simple discreet algorithms.

I am 19 now and I went to uni to do engineering and I quickly noticed how math is even treated worse than high school. So I decided to teach myself mathematics the way it should be taught and I realized that it's incredibly intuitive and fun. The things that were taught to me previously in high school are just maybe less than 1% of what math really is.

I still don't know a lot of differential geometry and numerical analysis but it's crazy that whatever engineering schools teach and HS is mathematics from 300-400 years ago. So we are stuck in the past then according to this pattern.

[ancient creek]

The first thing I taught myself is measure theory and real analysis, I think they're pretty easy and fun, very logical too. Also it's not only the digital world where everyone is social, a lot of mathematicians are very creative and awesome people!

[dim pendant]

You definitely don't need a lifetime, but some really interesting results take lifetimes to resolve. That's all I mean <3

[ancient creek]

As long as you're happy yourself and want to pursue it why not!

[tiny gulch]

Reminds me of the ars longa, vita brevis story

[rough umbra]

Love that story sm

[tidal summit]

should me and a friend write a small book about an introduction to vectors and applications

(+ applications from different areas of math)

[normal crystal]

if you want

[ancient creek]

Please do! 🙏

[sterile pelican]

You remind me of a cute tiny book, of 144 pages, called About Vectors by Hoffman it has some applications I recall

[dim pendant]

It's actually a legal obligation to do so as soon as you come up with the idea

You have 90 days or we'll send authorities your direction

[dim pendant]

Agreed. There is much to learn in pursuit, and many ideas to try in the meantime. The journey can be more important than the conclusion.

I cannot imagine how much fun it is to be discovering new ideas and resolving small pieces of problems in your field of interest

Gottem

[broken bramble]

there are already so many

[dim pendant]

There is something to be said concerning the redundancy of the modern mathematical literature

but as a learning experience, any such project is fine and generally enjoyed

[trim kayak]

I took statistics for behavioral sciences and calculus in college several years ago. I want to study both of these topics some more. I have two textbooks that I plan to use. Should I focus on one first and then move to the other one?

Should I read chapters, take notes, and practice the problems?

Any tips or suggestions are appreciated. Thanks!

[strange sentinel]

Calculus before statistics is probably best. Reading and then doing the exercises is the usual order, and works well as long as you are careful with the latter.

[trim kayak]

Thanks!!

[trim kayak]

I've taken a statistics class for behavioral sciences and want to study/learn even more. Any recommendations for a good stats book?

[remote sparrow]

if you want just one book for probability and statistics, you can look at wackerly

i quite like https://stat110.net for probability tho

[trim kayak]

Is that the title and author?

[deep moat]

vouch!!

[deep moat]

If you want something beginner friendly, I suggest reading: W. Mendenhall, Beaver Introduction to Stats and Probability

bruh

there we go

after like 8 tires

[trim kayak]

Oh thanks. That looks like a good book. Maybe I'll look for a physical copy but this one is free. Hmmm. I like physical books.

[deep moat]

You can go with a GCSE stats book cuz thats more like rigorous for my take ahah

[fresh skiff]

Sour drop have you looked at Silverman's algebra book? (An integrated approach)

[remote sparrow]

no

[fresh skiff]

Okk

[sterile pelican]

So I want to ask I tried to self read some Blitzstein's Probability but I didn't quite like the exercises for some reason, you think I would like Feller more? I like books like Berberian's LA, Bloch's Real Analysis, and Anderson's Abstract Algebra for example

[remote sparrow]

https://a.co/d/bka7CG6

[trim kayak]

Are you studying or learning stats too?

[remote sparrow]

https://a.co/d/3d8AH6i

[remote sparrow]

sure. grimmett and stirzaker has a lot of problems too

[deep moat]

self-studying stats for fun

[deep moat]

I love this book

It's super intuitive

[trim kayak]

Oh nice. Me too. I need a good textbook

[sterile pelican]

Oh? How does it compare to say Blitz and Feller?

[sterile pelican]

In the same boat here lol

Also I was a stats and data science graduate 7 years ago but I know for a fact I didn't understand the material back then lol

[trim kayak]

@deep moat Would you recommend the Wackerly text or the pdf you sent me instead?

[deep moat]

If thats the case, go a head and read Naked Statistics. I haven't read much about it but based on what I have researched so far when it comes to stats book was that people recommended the naked to stats and for a more general, integrated material I suggest STAT 100 from PSU and a GCSE A Level Stats and Probability 1 Textbook.
There are many other books and courses regarding to stats and prob, but assuming that you're a reader, I think the books that SourDrop and I have recommended are good for self-studying stats.

That was so embarrasing haha

[remote sparrow]

some measure-theoretic definitions are incorporated, but the book isn't a treatment of measure-theoretic probability

[trim kayak]

I JUST downloaded the Naked Statistics pdf right before you mentioned it. Crazy.

I'll check those out, thanks

[deep moat]

All books that were recommended have the same content -- just explained differently

[sterile pelican]

Ahh that's nice helps prepare for that one day too, is it called Probability and Random Processes?

Any prerequisites I should be aware of?

[deep moat]

Heres an extensive list that someone I know gave me as a preperatory stats contest I joined 2 months ago. @trim kayak

[trim kayak]

Oohh thanks. I'm curious about this stats contest. Sounds fun. So many great resources, thanks!

Is there an easy way to save that list somehow?

[deep moat]

Uhh, you can send it to your own personal discord server...?

[trim kayak]

I don't have one

[sterile pelican]

Tiny side note though I am reading a bit of Regression and Other Stories by Gelman, it is quite fun not sure if I can call it "data analytics"

I mean it's applied regression stuff through R just thought to share it

[trim kayak]

Which stats texts do you have?

[remote sparrow]

some real analysis but nothing else really

[deep moat]

w. mendhall

[trim kayak]

That one looks good. I'm looking for a cheap physical copy now

[deep moat]

||You can get a reprint||

[remote sparrow]

there are a lot of good used copies of wackerly

thank goodness they've never come out with a new edition since 2008

[trim kayak]

Abe Books has the Mendenhall text for $7.00!!

[deep moat]

Woah thats super cheap

[trim kayak]

Right? And it's hardcover. Even better.

[sterile pelican]

Alright let me have a look thanks Sour!

[deep moat]

I don't relate sorry haha
I'm more of a pdf guy

[trim kayak]

Haha. How can you even learn and study from a pdf? Lol

There is a 15th edition of the Mendenhall text. Think the 13th edition is just as good?

[deep moat]

I just read them like a normal book?
Because for every topic that I learn I do the psets and if I finished doing the entire pset on the book I go online and find other problems to solve

[trim kayak]

Makes sense. I was just teasing. I like hard copy books.

[deep moat]

Yeah, I know lol
I hate hard copy books

[trim kayak]

Lol

There is a 15th edition of the Mendenhall text. Think the 13th edition is just as good?

Are/were you a math major?

[deep moat]

I'm an incoming Grade 12 highschool student lol

[sterile pelican]

I know for me at least I am able to retain stuff from a book

[trim kayak]

Oh haha. So many peeps here are college kiddos. Oops!

[sterile pelican]

I even print my pdfs if needed

[trim kayak]

Are you in the US?

[deep moat]

How much does it cost you?

[deep moat]

Nope. I'm from the PH :)

[trim kayak]

Ohh

[sterile pelican]

Depends I only print the first 50-100 pages just see if I will buy it eventually

Even that I print 2-4 pages per paper

Just to save cost

[deep moat]

Oh nice

[trim kayak]

What time is it there? Lol

[orchid monolith]

I am given a summer reading assignment for Advanced Placement Language and Composition in which I am asked to read 1 of the books from the list below:
● Educated by Tara Westover
● Hillbilly Elegy by J.D. Vance
● Quiet: The Power of Introverts in a World That Can't Stop Talking by Susan Cain
● The Glass Castle by Jeanette Walls
● *The Men We Reaped *by Jesmyn Ward
● There's Always This Year: On Basketball and Ascension by Hanif Abdurraqib
● Unbroken by Laura Hilldenbrand
● We Were Dreamers: An Immigrant Superhero Origin Story by Simu Liu
● When Breath Becomes Air by Paul Kalanithi
● Wild by Cheryl Strayed

If anyone has any recommendations, that would be gratefully appreciated. However, I do ask that you do not provide anything in your recommendation that may spoil the content of the book in any means, as I would like to gain some enjoyment out of reading.

[sterile pelican]

I read Educated by Tara Westover and enjoyed it

It was many years back though

[ripe pagoda]

i also read that for lang it was okay

[outer swift]

hi everyone, I'm self studying maths (I was always bad at it) and I'm finishing the pre-calculus book from Stewart from cover to cover. So far having a blast. I'm interested in calculus, what book do you recommend? The one from Stewart, too? thankz for your time and have a lovely day!

[graceful moon]

Stewart’s calculus is a very nice book, its standard in many universities. If you like Stewart’s style I say that’s a very good choice

Though you likely don’t need to read it cover to cover, it’s a pretty massive book

[outer swift]

His style is fine, although I prefer Gelfand's! but couldn't find anything like that on calculus 😦

[outer swift]

yep, you're right! Thank you

[fresh skiff]

Wow cover to cover. I wish i could learn the missing stuff from these subjects

[deep moat]

First of all, congrats on taking math as a learning challenge and being able to finish a very thick calculus book. Now, time for you to study Multi-variable calculus.... or just go with Calculus 2 (idk anything abt calculus cuz im no STEM major/strand)

[minor falcon]

Any good books to restart math from 0?

I feel like this whole time ive just been remembering formulas and understanding nothing

[deep moat]

Congrats! You're one step closer to being a decent mathematician.
Anyway, there are many books that cover all the basic fundamentals of mathematics. Usually, the books that I recommend to train the brain for problem-solving abilities is to read AoPs books-- Introduction to Algebra is a good place to start or just follow the AoPs website. In addition to AoPs, it's best to do some more problems to get a hang of a topic this is where Alcumus comes into play with bunch of topics in a single subject-- Algebra, Geometry, Combinatorics, and Pre Cal.
||You don't have to buy the books-- instead pirate them off the internet.||

For a more native, beginner friendly approach I suggest reading Blitzer College Algebra or an OpenStax Algebra Book (Go to the Developmental Math Section).

These stated above are all integrated approaches which is far more reliable than watching a youtube vide

Goodluck with developing your math skills!
Math isn't all about memorizing formulas, its all about understanding the why and the whats!

[dusk hemlock]

is this ai

[deep moat]

No?
Did you assume it because of the emdashes that I used?

Now that you're pointing that out... I do sound like one 💀

[dusk hemlock]

and the bolds

also the first sentence lmao

[deep moat]

Ahh I see
I just like to point some things out to give them a better emphasis

[dusk hemlock]

yeah ik

just most discord users don't do that and ai's do LOL

[deep moat]

HAHAHA mbmb

Just been active here on the book channel

[dusk hemlock]

i fear for when your essays get put into an ai checker

[deep moat]

Those things are unreliable

[dusk hemlock]

yeah

exactly why

[deep moat]

,nogpt

nogpt!

[dusk hemlock]

!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).

[deep moat]

okay thank you

[dusk hemlock]

i speak like ai irl sometimes

[stuck zephyr]

I don't think you need books if you wanna restart math from 0 unless you have a textbook but maybe try looking websites like khan academy should help you recover the stuff

[deep moat]

I have such a big rebuttal with Khan Academy and stuff, but this is a good advice ^^

https://www.youtube.com/watch?v=oEQaENxv70M

but overall though khan academy and other sources are just there to fill in some gaps in your knowledge

[minor falcon]

I really found out all of this just weeks after I graduted school smh 🤦

Ok so Introduction to Algebra is a good start

Pre algebras are just the simple addition subtraction things right

I think im pretty much well with pre algebra already

Or what counts to pre algebra (incase i miss something important)

[outer swift]

Gelfand's Algebra book clicked for me. But it's challenging

[willow merlin]

what is a rigurous book for finite dimensional linear algebra that is not axler?

if possible bourbaki style

[floral lantern]

Halmos/FIS/Treil/Hoffman and Kunze

[willow merlin]

which of them follow bourbaki style

[dim pendant]

Bourbaki

[sterile pelican]

Berberian’s LA if you know abstract algebra first

Well in particular if you finished the chapter on rings and ideals then Berberian’s LA is accessible

[molten gulch]

At that point genuinely just go read Bourbaki's Algebra treatises

[tiny gulch]

as someone who's never really used textbooks (at least not during my undergrad) i found this wholly unconvincing

also the guy is weirdly conspiratorial about khan academy and online math videos in general??

[tender river]

some set of notes that fit the bill
https://pi.math.cornell.edu/~kassabov/math4330.fall19/math4330notes.html

https://stanford.edu/~dkim04/writings/LinAlg.pdf

[willow merlin]

i appreciate the resource ellpika

will read it

[lavish radish]

from one of his videos he says "pirating is a felony" LOL

in regards to johnathan david

[molten gulch]

Personally,we have MASSIVE issues with mathematics videos online that aren't outright lectures, but that's a rant for another day. We found his argument to not be too great but in the end we will ALWAYS prefer books to almost anything

[molten gulch]

It is, at-least in the US https://www.copyright.gov/title17/ https://www.law.cornell.edu/uscode/text/17/501 https://www.law.cornell.edu/uscode/text/28/1498

[lavish radish]

it was the way he said it

[molten gulch]

wait that's marine piracy law oops

[sterile pelican]

It might as well be isomorphic :^)

[molten gulch]

I mean, IMO as it is against the law, if you do it, don't fucking talk about it, and if you get caught, boo hoo, too bad for you

[tiny gulch]

Interesting

[molten gulch]

It's mostly that we feel like mathematics videos for popular audiences will cut or oversimplify important details for the sake of being accessible and many times that leads to conclusions and assumptions by readers/viewers which are factually incorrect or fail in more generalized situations

[tiny gulch]

Do you have an example?

[molten gulch]

Not off the top of my head sadly but we'd seen some over the years

[tiny gulch]

mhm, right

I remember 3b1b talking about this

where with pedagogy, sometimes the best approach involves being a little wrong at the start

and gradually correcting yourself over the course of teaching

[molten gulch]

I believe the basic idea is to start with a more restrictive or simplified assumption and as you develop more machinery, correct and expand the ideas

[tiny gulch]

Sure but you can also just be wrong on purpose

[lavish radish]

i watched one of citytutoringmath's videos the other day and found out i should be using basic algebra books from authors like serge lang's basic math instead of stewart's precalculus because it teaches basic algebra in a more rigorous way

[molten gulch]

True

[sterile pelican]

Truth be told even 3b1b did say videos like his are not a substitute for learning but for inspiration

[molten gulch]

This is true, yet many people do not understand or listen to this

[sterile pelican]

I am of firm belief that the true way to learn maths is through a book, and interacting with said book by mechanically writing down the proofs and steps

Khan Academy robs that by preprocessing that knowledge like it's fast food

My two cents obviously

I'd rather be slow and struggle with writing an e-d proofs to get a feel from it than to watch a video, or doing those interactive web apps

But the latter does help it's just that cannot they substitute the book way of learning

Again my two cents

[outer swift]

I don't know who that guy is, and am not a fan of Stewart's style either (it's fine), but you don't want to miss the "skill plus" and "discover + prove + discuss" sections in each chapter of the book. These are usually good to solidify your understanding

[sterile pelican]

Honestly, I dislike Stewart but it does the job

I like Lang far more

[outer swift]

I feel the same, didn't read Lang though

[sterile pelican]

Lang's Short Calculus book is a mere 300+ page

For single variable, and it was the book I self learnt after doing so badly in high school lol

[outer swift]

wow, that sounds very attractive

[sterile pelican]

But if your uni demands Stewart please use Stewart

[molten gulch]

No not really, a good book can supplant videos IMHO

[outer swift]

not really, self learning atm 🙂

[sterile pelican]

If that's the case Lang is a rigorous calculus book, it's not analysis per se so no e-d, and he does briskly goes through pre-calc

[molten gulch]

then why not just do an analysis book

[sterile pelican]

Does he know proofs?

[outer swift]

basic stuff

like, really basic

[sterile pelican]

So you know direct, contrapositive, induction, and contradicition?

[outer swift]

some of them, lol 🙂

[sterile pelican]

Hmm you can do Velleman first

[molten gulch]

if not, good excuse to learn them

[sterile pelican]

But Lang you can read it at the same time

[outer swift]

ty vm!

[sterile pelican]

I didn't know proofs when reading Lang

But Lang does introduce you proofs in a sense but you need Velleman to do the stuff after

[sterile pelican]

I am in full agreement

Doing those two first then we can talk about the other maths

[outer swift]

yap, seems very reasonable, thanks you 2!

[sterile pelican]

No worries!

[foggy gorge]

Do you guys know a good source on algebra?

I dunno how my basis in algebra is but I definitely have some knowledge. I want to learn more. Maybe in a proof and demonstration approach would be great

[sterile pelican]

I sadly don't I attempted algebra by reading, and finishing, Gelfand but I cannot recommend that lol

[molten gulch]

#book-recommendations message

[outer swift]

you didn't like Gelfand? 🙂

[sterile pelican]

I love Gelfand but I don't think people would like his algebra book lol

[rich pond]

Of those I enjoyed Aluffi’s Chapter 0

[sterile pelican]

If we are talking about modern algebra then I got nothing

I am currently doing Anderson's A First Course in Abstract Algebra and I do enjoy that book

[molten gulch]

When someone asks about algebra is it not assumed as Modern Algebra

[sterile pelican]

From his context I thought he is talking pre-calc stuff

[foggy gorge]

I'll try Lang's and Artin's

[sterile pelican]

Okay it is modern algebra lol

[foggy gorge]

Well, I want to learn how to solve equations other than quadratic ones besides learning some more theory

[rich pond]

Dare I put forward Cox Little and O’Shea?

Then I love computer algebra

[foggy gorge]

Once before I heard about Girard relations in a video about solving a rather complex equation without calculus (complex in terms of difficulty, not the set). I want to know this stuff because I've never seen it before

Maybe I've skipped it in the Stewart's precalculus book but idk

Im confused at the best

[sterile pelican]

I have that darn AG book lying at the corner to one day read it 🥲

I just want to finish RA, LA, and AA first

Well LA first in particular

[rich pond]

An AG entry point in LA is classifying general conic sections

(If I interpreted acronyms correctly)

[molten gulch]

If it's not complex in the sense of complex numbers or complexity theory, then dare I say it should not be called complex

[foggy gorge]

Well, a good foundation on complex theory would be great too

[molten gulch]

learn some real analysis and then learn some complex

[foggy gorge]

I'm self studying math because I actually want to learn math

[foggy gorge]

I have terence Tao's book on real analysis

[rich pond]

Complex analysis has a completely different flavor

[ancient creek]

I don't why but I think complex analysis is easier to understand than real analysis

[foggy gorge]

I didn't try reading it because I haven't learned anything about calculus yet besides limits

[ancient creek]

Has to depend on the book though

[broken bramble]

haven't read it but i've heard it's not great

[foggy gorge]

A friend of mine said it is very good tho

[ancient creek]

If you need very rigourous stuff, a lot of derivations. Mathematical analysis 1,2 by Zorich is good but complement it with something more visual , really good combo overall

[rich pond]

Tao tries to do a classical course structure while keeping distributions in mind

[foggy gorge]

What would be a good approach to get a good intuition on algebra stuff?

[rich pond]

The answer does depend on what algebra stuff you do know. What concept did you learn most recently?

[ancient creek]

Linear algebra done right very good introductory stuff

[willow merlin]

is it that good?

[sterile pelican]

(Psst or learn abstract algebra first then read Berberian's LA)

[foggy gorge]

Great question. I don't really remember because recently I've been focusing on trigonometry and geometry.

For what I can recall is that I've learned how to demonstrate the quadratic's formula. I've already gone through quadratic and cubic polynomial functions.

If it is related to algebra, then the last thing I've learned is the concept of limits

I have to skim through its axioms again but I found it very easy to learn

[willow merlin]

linear algebra wise you are in zero?

[foggy gorge]

I know some vectors properties and how to solve a determinant, but I still struggle a lot with their concepts and what to use them for

[foggy gorge]

I learned them in a high school context though

So far I know that if a determinant equals 0, then the linear equation has no solutions.

Why? I dunno

[willow merlin]

even recommending Axler or FIS in this context might be too much, try checking out anton maybe, but is not best, but is more approachable

[rich pond]

Anton was my school book.

[foggy gorge]

Should I try getting deeper in calculus first?

[willow merlin]

nah, if you want algebra do algebra

[foggy gorge]

Surs thing

Sure

[willow merlin]

where are u from?

[rich pond]

90s Norway Uni

[foggy gorge]

Elementary or contemporary linear algebra?

[willow merlin]

elementary

[rich pond]

Basic stuff like matching number of variables to number of equations and determinants detecting repeated equations

And missing variables

[foggy gorge]

Thx

[willow merlin]

it is a boring book tho

be aware

[ancient creek]

If you build base with axler linear algebra I think it's better than jumping into solving determinants and equations. If you haven't read more analytical math texts before, it might be difficult but worth it.

Depends what you like more tho

[willow merlin]

doesnt cover determinants, why?

[willow merlin]

also is it appropriate to be introduced to infinite dimensional vector spaces for someone who is in highschool?

[trim kayak]

Is Introduction to Probability and Statistics by Mendenhall an Intro to Stats book or is it more advanced?

I have been looking through the pdf of the 13th edition. It looks pretty good but doesn't seem to have a lot of math with examples. Wondering if this is a good book to get.

[dim pendant]

Can anyone recommend to me books that are like the opposite of dry

Cuz I'm not really convinced of any non-subjective distinction

[normal crystal]

Fluid Mechanics
Hydrology
Oceanography

[hardy adder]

I'm currently rereading "probability with martingales" and it's not like a laugh a minute but it's one of the more well written and engaging maths textbooks I've read. Has the rare distinction of actually being a good cover to cover read.

[still panther]

I like gillman's rings of continuous function for a non-dry read

allufi's chapter 0 maybe

van der waerden's algebra?

[hardy adder]

I'm also reading bits of "automatic sequences" by allouche and shallat and this one may be more subjective because a lot of the material is very... Fiddly and technical. But the results are sortof wild and the authors seem to be having fun.

[trim kayak]

Any recommendations for a stats textbook to read through and learn on my own? I've taken Statistics for Behavioral Sciences before but want to learn more.

[ancient creek]

If you want to, why not. I don't think age matters here, but I would do basic linear algebra first similar to axler.

[hollow peak]

I read this book last week and it's quite literally life changing

Enumerative Geometry and String Theory by Katz

[trim kayak]

Any recommendations for a stats textbook to read through and learn on my own? I've taken Statistics for Behavioral Sciences before but want to learn more.

[hollow peak]

And it's written for a strong undergrad audience, so it's a pretty easy read

[ancient creek]

Determinants is just a simple example on what schools focus more on as "application". In my opinion, I don't think it's right, it doesn't expose students to the art of math in a good way.

[hollow peak]

I kind of feel the opposite

Determinants are basically the crown jewel of a first linear algebra class imo

[loud cradle]

based

[hollow peak]

being able to translate information about rank into subminors and Laplace expansion is very practical and beautiful

Even if the equations themselves are terrible, it becomes beautiful with a little multilinear algebra context

(hence why I don't think LADR is a particularly good resource)

[normal crystal]

they're not so into Stats here in general
asking repeatedly won't change that
maybe Statistical Rethinking🤔
he has video lectures on YouTube too

[ancient creek]

Hmm that's a good point. The way teachers teach differs as well from the books, I like LADR for its structural approach but it does lack good intuition of the context.

So if someone can first introduce more practical approaches to students and couple it with the structure of LADR, that would be very powerful.

[normal crystal]

tfw you're the only one who answers and they still 😡

[loud cradle]

the latest edition does determinants in the multilinear algebra context
still does char polys before the determinant though, so all is not roses

[broken bramble]

what are the prereqs for it

[hollow peak]

strong understanding of linear algebra and multivariable calculus

it helps to have some inutition about manifolds

but he technically throws in crash course chapters for stuff related to topology

[trim kayak]

There are alot of people here who know and are into learning stats. That's why I asked about a recommendation. Geeze.

[full cairn]

It's just that you asked the exact same question twice in a 7 min interval. And it seems like you asked the same question yesterday and even got some answers. Were you not satisfied with the answers you got?

[normal crystal]

tbh, the people here are more interested in the probability side if so
from what I've seen
anyway, I gave you a legit suggestion

[pulsar veldt]

Need recommendations for number theory ^^

[pulsar veldt]

I'm a begginer

[full cairn]

Elementary Number Theory by Burton is good

[pulsar veldt]

Pre reqs?

[full cairn]

Very few prereqs, I think it should be understandable for a high schooler

[pulsar veldt]

Ok, I gotta take a look

[remote sparrow]

https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

[trim kayak]

@remote sparrow I know you recommended this book already. I just wanted to see what others would recommend too. I have Mendenhall's book in pdf form. It looks good but a little dry. I may get a hard copy but not sure yet.

Any other recommendations?

[remote sparrow]

i don't feel there's a reason to look at anything else for an intro to calculus-based stats

blitzstein and hwang is really good for probability

[trim kayak]

Okay. Just curious. Thank you!

Do you think I should focus on an intro book if I've taken stats before?

[remote sparrow]

no need, the book i mentioned is self-contained

[rough umbra]

True !! I think introducing it this way first, before the formulas/computation, is cool

[jovial sky]

Any good physics textbooks that has clear explanations and that by the end of it I have a strong hold on it ?

[floral lantern]

What kind of physics

The bulk of any project physics book is in the problems

Many of the “elegant” explanations for things aren’t very comprehensible until you’ve already seen things concretely in physics

[jovial sky]

General physics

[floral lantern]

A good book with lots of hard problems is Morin’s “introduction to classical mechanics”

He has a second book on electricity and magnetism

That is also good

At the introductory level

[jovial sky]

Well I expect sometinhg to study to start well in the university

[floral lantern]

A more general book is Halliday resnick and krane

The latter covers lots

Morin’s books will set you up very well

[jovial sky]

Thaks imma check it out

[trim kayak]

@floral lantern Are you familiar with calc or stats at all?

[floral lantern]

Calc yes stats no

[trim kayak]

Ahh ok

[full cairn]

Damn, how many stats recommendations do you need?

[trim kayak]

Alot. Is that ok?

[full cairn]

Lol, it's okay with me, it's just funny. You've asked like 5 times, you've asked Sour Drop twice, and you're pinging random people asking if they know any stats. There's probably also dozens of recommendations online. At some point you're just gonna have to sit down and read, because nobody can tell you what book is best for you except you

I'll throw my own recommendation into the mix: An introduction to mathematical statistics and its applications by Larsen and Marx

[dim pendant]

Take that advice extremely seriously

I wasted years by worrying about which books I should actually study

The best one to study is literally whatever you can get access to

Oh but this book has X pace, oh but this book covers Y, but this book takes approach Z

Eventually you have to just start

You're here for the math, not the book theory

[grim ore]

literally this, sometimes esp in unis you also cant really choose and decide what book your prof will assign anyway

studying ahead is cool and all, but courses are planned ahead regardless of your personal affiliations or preference

like if i had to suffer through Lang Algebra bc of my prof, sucks to suck but thank god I didnt (jk obv, maybe)

[dim pendant]

So God help me that I never have to take stats

I will literally study for an extra sem to avoid having to deal with any stats class or book

[timber mesa]

yeah skimming books to decide, or even reading from many sources in parallel are good pieces of advice to follow in general

one single book hardly ever gives you a complete view on the subject

mainly since every single person has their own POV on it and which topics are important

or which topics are fit for e.g. an undergrad or a grad student or an expert looking for a reference monograph

[grim ore]

Also some books are more catered to some learning styles than others

[molten gulch]

obligatory "fuck we hated stats class"

worst class we'd ever fucking taken

[grim ore]

Ive seen books that are more like reading a story book vs some that are only like def, thm, prop, pf with no exposition

i will never take a stat class in my life hopefully

[dim pendant]

I just don't care about anything to do with stats like lmao

[grim ore]

i might have to sadly

[dim pendant]

Props to those who take a masters in it

[dim pendant]

Rip bro

[trim kayak]

Thanks for being so helpful guys. 🙄😬

[dim pendant]

I mean you have gotten book recommendations most of if not each time you asked for books

Help yourself by getting started

[full cairn]

Wow this girl is angry

[normal crystal]

guess it wasn't just me

[dim pendant]

Must just be rage bait or something

[vital bane]

https://tenor.com/view/axe-lotr-gif-5532799

All of Statistics by Larry A. Wasserman

[vital bane]

class \neq subject

[molten gulch]

true

[vital bane]

so you mean "we hated the stats class" rather than "we hated stats"

[molten gulch]

yes

[deep moat]

based

[plain belfry]

recommend introductory to upper undergrad level algebra books

i have hopped around fraleigh, herstein and now dummit and foote

i like dnf more than the other two but something feels missing

i just wanna know what other people used and like so i can try them out as well and pick one to complement my primary text

[dim pendant]

I quite like Jacobson's "Basic Algebra" series (the first book is for undergrads)

Even though there is dense writing, Jacobson provides lots of examples, has a slightly unique ordering of topics, is straightforward, and makes algebra feel easy, I think

Definitely best for someone who has seen some algebra before, but a good shout even in the modern day

[sterile pelican]

I am still reading Anderson’s “A First Course in Algebra” he starts with rings first and offers a lot of quick exercises after reading a section, warm-up exercises, then finally the proper exercises. I think book is great overall as a first course, and after doing a section on quotient rings I can immediately go and learn Berberian’s “Linear Algebra” due to that

[dim pendant]

Anderson's rings first philosophy is an interesting concept. I imagine that it's an easier entry point in terms of exercises. I'll definitely look into this.

[sterile pelican]

It started from Hungerford I hear but Anderson’s book was battle tested for his students back then, which means I can slowly learn and marinate the concepts in mind due to the exercises. I also had recently started his groups chapter and he started off with transformations of geometry first

[dim pendant]

I cope too much. As much as I think group theory is awesome I hate actions

And group theory is really all about actions lol

[vital bane]

??

actions are goated

[tiny gulch]

Yeah I love actions

Some of the most useful homomorphisms out of a group

[dim pendant]

Sorry bros

I'm just in it for the representations

[tiny gulch]

I’m a sis :)

[dim pendant]

Don't worry, everyone and everything is a bro at the end of the day

[tiny gulch]

Ok but reps are like actions on a vector space

[tiny gulch]

Not me!

[vital bane]

reps are literally actions yea

[dim pendant]

I'm aware yeah

But they're the only ones I want

😔

[vital bane]

^

[dim pendant]

The only actions I need

[vital bane]

Actions are so based

[tiny gulch]

I mean you can convert any action to a representation

[vital bane]

set representation moment

[dim pendant]

All right you guys got me

Talking about actions at 2 AM

[vital bane]

,ti @dim pendant

[dim pendant]

This is just a result of a false assumption

I should be sleeping

[hasty eagle]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[tiny gulch]

,ti pseudonium

[hasty eagle]

The current time for pseudonium is 07:50 AM (BST) on Sat, 07/06/2025.

[tiny gulch]

nice

[vital bane]

Aussie...

[vital bane]

Bro: I should be sleeping
Bro 2 hours from now: still online

[sterile pelican]

Homomorphisms and isomorphisms are for love and for life for algebra

Because I am totally not into categories and all at some point of my life

[limber bolt]

what

[peak bluff]

what

[sterile pelican]

what?

[sinful panther]

Hi, I am looking for good books to study probability specifically to understand moment generating function & functions of several variables ( if you can provide the link it would be fantastic)

[sterile pelican]

Just for curiosity sake what’s second exposure to algebra book like? Not sure if it’s fruitful after say Anderson

Or I should just go for something else like Cox?

[foggy quest]

Dummit and Foote is used at my uni

[sterile pelican]

I could look into that

Maybe after Anderson

[snow saffron]

Can anybody recommend me a book for Stochastic Processes

[rain hound]

curried version

them being the same relies on vector spaces being closed monoidal

[tiny gulch]

It depends how you define action

[acoustic cliff]

What's this channel's consensus on Dummit and Foote? I've seen it praised and criticized all over the internet. Are there newer and/or relatively obscure books on Abstract Algebra you would recommend?

Surely there is more to AA than Hungerford/Herstein/Pinter/Gallian/Rotman/DNF

[full cairn]

I don't think there can be a consensus here, people either like it or they don't. I don't have a strong opinion on it; I think it's decent, good coverage, maybe a bit dry? Other good alternatives are Fraleigh, Aluffi (in particular his undergrad book Notes from the underground) or Artin

[molten gulch]

My opinion would be to just go to the library or ask a friend or find a copy somehow and just...look through a chapter or 2

[full cairn]

There's also Bhattacharya's Basic Abstract Algebra which is decent, and there are also more specialized books like Actions of Groups by John McCleary. There's probably dozens of books on abstract algebra, it's literally impossible not to find one you like

[warm roost]

Sup can someone tell me their thoughts on James Stewart calculus eighth edition early transcendentals instructor's edition please?

[sterile pelican]

I for one don't like it but it's the standard for most university texts and you should use it if your course asks for it

[sage python]

It's just generic calculus book n

[warm roost]

oh okay thanks a lot

[molten gulch]

It's a calculus textbook, it reads like almost any other calculus textbook, you'll be fine reading it

[warm roost]

btw does someone have a good textbook for begginers?

[normal crystal]

beginner what

[broken bramble]

https://personal.math.ubc.ca/~CLP/

[molten gulch]

Beginning in what? Geometry? Algebra? Analysis? Topology?

One must be specific in requests

[warm roost]

geometry algebra and analysis, i know basically nothing from topology

[dim pendant]

Do you know some basic calculus @warm roost

[warm roost]

yeah i do im like early precalc

calc1

typo

[molten gulch]

Precalc is not the same as calc 1

[warm roost]

i know

i meant calc1

[molten gulch]

Well if you are in calc 1, something like stewart's calculus book should be fine

[dim pendant]

do you know what d/dx [x^3+1] is

[warm roost]

3x^2

[dim pendant]

great

go learn how to calculate partial derivatives

once you do that

the book I recommend for you is called Elliptic Tales

it will teach you a little bit of abstract algebra, some topology, and some projective geometry

then you study some elliptic curve theory at an undergrad level you'd be prepared for

have fun 🫡

[warm roost]

thanks 🙏

[grim ore]

Honestly most of the time i want book recommendations, i usually just search in this chat which prevents me asking for stuff people haven’t already asked about; unless i’m on my phone

[dim pendant]

I go straight for reddit and MSE

if I'm asking for a book, chances are there are 2 posts on each site already asking the question

[vital bane]

Literal PEAK

🔥

🗣️

[dim pendant]

people here generally acknowledge that it's a strong book, but each person has their own criticisms and praisals of the book

[hearty grail]

Can someone please recommend me a geometry book for beginners, geometry in India is really mixed up so i wanna read geometry systematically, not just a jumble.

[grim ore]

what level?

[hearty grail]

beginner level, high school level

[trim kayak]

No way. Really? 😋

[spring shadow]

Books, or book covering topics up to and with the Taylor series, starting from the basics of calculus?
Requirement for the first year chemistry degree.

Preferably an analysis book.

[shell merlin]

Cloud and Wallfish by Anne Nesbet
highly recommend currently

Ecclessiastes

Set for Life

[molten gulch]

Abbott's analysis, Zorich. Rudin, basically any analysis textbook

but if you do want plain calculus, there's stewart's calculus

[spring shadow]

Thank you for answering.

[rain hound]

For plain calculus, the books on openstax are pretty good https://openstax.org/subjects/math#Calculus

about the same as any of the usual calculus books (such as Stewart) that cost $100 or whatever

but free for everyone

[molten gulch]

yes

[rain hound]

If you do analysis (probably not necessary as a chemistry major) I’d suggest Abbot. It’s the most accessible of any, and you don’t need the full rigor that a mathematician does.

[spring shadow]

It's a mandatory subject.

[rain hound]

Maybe it’s Europe or some other Continent where Analysis and Calculus are the same thing? In the US there’s a distinction, usually calculus is a more service course for applied math people, scientists, engineers. And analysis is for more theoretical math people.

good luck

[hearty grail]

pls reply

[slow roost]

high school geometry is kind of a mishmash of random topics from Euclid's Elements. The books written for those courses are all pretty similar in my experience, with little reason to recommend one over another

but if anyone knows of a book that's somehow significantly better, I'd be very interested to hear about it too

Geometry by Pearson is one of the most commonly used ones, you could try that

[vestal hazel]

taking differential calculus next semester, any suggestions?

[trim kayak]

Any book recommendations for statistics and calculus?

[trim kayak]

Wanted to see how many more rude comments I would get. Hahaha. I don't need recommendations anymore. I know what I want.

[mossy flume]

why would you get rude comments?

[trim kayak]

No idea but I got a few rude comments from some yesterday. I just asked for recs and there were a few peeps who were rude.

[trim kayak]

I took stats for behavioral sciences in college and want to learn more. Not sure??

[normal crystal]

second verse, same as the first
a little bit louder, a little bit worse

[dim pendant]

Rude comment = comment that I don't like

Welcome to the 21st century

You're no longer allowed to give people the advice to take what they've been given and learn, without being rude

Also, if you've already taken a course in stats, then finding new content is quite easy to do, and should only take 30-45 minutes.

Google "good book to learn statistics" or "good book for a second course in statistics"
look into the popular recommendations
choose options that cover material you haven't yet seen
look into the books to make sure that they're at a reasonable level
since you've gathered books with new content for you, accomplishing your goal, you can pick literally any of the remaining books and start literally this second

[naive lava]

you should just read the book: "lectures on edge of the wedge theorem"

[deep moat]

You know, you can ask ChatGPT with the search function by asking it some stats books... very reliable

[trim kayak]

I just did that a few minutes ago

[trim kayak]

Relax.

[dim pendant]

Why does everyone on the internet think that using logic is equivalent to being upset

You're just wasting your time with all of this book searching

Sorry for trying to help you realize it

I'll just let you keep looking on and on

[full cairn]

I just realized I have been a bit insensitive in my replies to musicmeg. Judging from the rolling eyes emojis it's clear that she's suffering from a very serious condition, the same as the girl in this news report: https://m.youtube.com/watch?v=MGXSPf9b-xI

[dim pendant]

LMFAOOO

[old terrace]

I’m studying for the math GRE. I’ve forgotten a lot of differential equations and multivariable calc because it’s been a while since I’ve taken them. Anyone know any good books for reviewing those subjects?