book-recommendations

[onyx wren]

and some are free

like hatcher

[crimson leaf]

Yes it's fine if the author post them online (though publishers can get them in trouble if they care to.) But it's against tos for us to post pdfs to copyrighted materials and can get the server shut down

[remote sparrow]

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

maybe look here?

[karmic thorn]

Thanks

[fierce hedge]

Most likely Kenshin meant copyrighted material

[karmic thorn]

That name though

[remote sparrow]

If this is a question, then in this case it happens to be that they can be shown to be equivalent, provided all your steps are reversible. However, all you need to prove a value solves a statement involving an algebraic equation, like "Show x = 2 is a solution to 2x = 4", is substitute x = 2 to show it is true.

[sage kelp]

Okay I’ll give it a shot. I think it looks interesting. Thanks

[novel obsidian]

iirc mit ocw has a course on integral equations, im sure there'll be reading there.

[karmic thorn]

Oh? I'll check, thanks!

[buoyant vessel]

@remote sparrow

[gray gazelle]

Whatever works best for self-study

Spivak is too hard for a self-study student who has never done calculus before I think?
My favorite Tarkovsky is Solaris

Book is written for a course not self-studying

[uncut zealot]

Any properly written book can be used for self-studying

Or can be used to accompany a course

[gray gazelle]

It's written to be used in a course, which means they assume you have a teacher or something, nothing about this book says self-study or well-written besides your words

Maybe it's well written if you are tutoring

anyone got a book recommendation for group theory

[mossy sedge]

anyone knows a good book about the history of mathematics? that doesn't go into proofs and theories, just general history that a middle schooler can understand

or the history of science

[crimson leaf]

Check pins for good abstract algebra books

[rich heron]

Do you know any good Complex Analysis books?

[remote sparrow]

undergraduate or graduate

pins are mainly graduate, gamelin excepted (some institutions use stein and shakarchi for honors undergraduates)

[sage python]

None of them are like, computational but

Freitag-Busam works for undergrad as well, and my impression of Conway's writing is that it'd be easy for middle schoolers lol

[foggy relic]

Serge lang algebra

[remote sparrow]

ruel, brown, and churchill is a common complex variables book. bak and newman is more sophisticated but still firmly undergraduate. ablowitz and fokas is a beginning graduate reference for those who are more interested in an applied perspective.

[glacial crypt]

from what I've been told this feels more like a second course in algebra rather than a first

[remote sparrow]

someone just saying group theory could either be an undergraduate on a quarter system where they will take abstract algebra for the first time, or they could be a graduate student that needs some advanced literature on group theory

[grand thistle]

does anyone have a course or problem list /supplement for lang’s algebra?

i’m talking either like a list specific problems that are good to solve (maybe like from a homework set for a class following the class)

[lean pagoda]

George Bergman wrote a lengthy companion to Lang's Algebra

I'm not familiar with it myself and I'm not sure how much additional content it contains, just remember seeing it on his homepage (but if it's anything like his other writings then it's probably worth a look)

[daring ravine]

recommended stats texts?

[remote sparrow]

undergraduate or graduate. what is your background

[daring ravine]

Undergrad

I took stats already but kind of goofed off and regret it a bit

[remote sparrow]

wackerly, mendenhall, and scheaffer is a standard rec

tho with how common it is, it might have been your course text

[grand thistle]

oh this is exactly what i was looking for thank you

wait isnt this the guy who also wrote the rudin supplement

bergman saves the day once again

[oblique girder]

Any recommendations on books for sheafs/sheaves? Taking a course on sheaves, and the lecturer says that the course syllabus isn't covered by any books, so just looking to see what's out there

[foggy relic]

rumors

it starts from scratch

exercises can be difficult though

[crimson leaf]

The book says in the preface that it expects you to be familiar with some algebra and that reading his other two books would make you very prepared

[foggy relic]

the prerequisites mentioned in prefaces are not always the actual prerequisites!

all you need is mathematical maturity to stat

[hazy elk]

In my experience prerequisites in the preface are usually not enough to have a "good time" reading

[indigo mesa]

lang can be used as a first course

i don't like it though

[dapper root]

U can also put ur hand in an open fire

[indigo mesa]

might do that

but if they're worried about prereqs maybe just choose artin instead

seems to be a better option (i haven't really read this one so this is going off of what i heard)

[hazy elk]

For some reason the problems in Artin never hit the spot for me

The exposition is really nice tho

[heady ember]

[glacial crypt]

if putting my hand in an open fire teaches me algebra i'll be glad to

why not D&F

[foggy relic]

slow and boring

it has some decent problems though

but takes a while to get tehre

[sage kelp]

DeGroot Probability and Statistics

[karmic thorn]

Lang's GTM Algebra could only possibly work for a first course if it goes along with a classroom/instructor

It's not a suitable text for a first course in algebra for self-study unless you have substantial mathematical maturity (presumably from other parts of math, or a nonstandard background)

[foggy relic]

You can read it concurrently with Aluffi

best combo imo

[karmic thorn]

That's such a bad take lol

I recommend Artin, or even Jacobson if you have seen or done linear algebra

[hazy elk]

I think giving Herstein a try for intro group theory is cool, it has so many interesting problems and after that you could supplement with something like Hungerford and continue learning more algebra from Hungerford (or even DF)

[blazing canopy]

I can give a negative recommendation. My professor used Dummit & Foote as my first abstract algebra course, after I had finished a rigorous linear algebra course, and I would call myself a very strong math student, but I had some difficulties, I think primarily with sections related to finite groups because I did not have a strong background in combinatorics or discrete mathematical thinking. Later I read Artin and would have appreciated his more linear algebraic approach to the subject.

[hazy elk]

Armstrong's book is also nice for a first course imo

For group theory

[swift dome]

linear algebra is literally a headache for me

[buoyant field]

there should be an entire channel for stats 😦

[undone finch]

hey, thoughts on friedberg for linear algebra (5ed))? what else should i study to complement its content?

[remote sparrow]

check pins

also, hoffman-kunze and axler are good to have in your library, even if some people think axler's treatment of determinants and eigenvalues is bad

[foggy relic]

It’s non existent

Axler is missing a ton of content

[remote sparrow]

although you should probably wait to buy axler if you want the latest edition, coming out august 2023

okay but you don't need to follow one book. doesn't matter if you think axler is lacking some content or not, just use another book to fill in perceived gaps

[foggy relic]

Good linear algebra books are hoffman kunze, Shilov, manin

Haven’t seen FIS

[undone finch]

im liking friedberg so far, but i only read the two first chapters and it was mostly content i was already familiar with

the exercises are more on the easy side

[foggy relic]

Try one of the three I recommended

[remote sparrow]

shilov is cheap

[undone finch]

im checking out its summary

yeah shilov sounds good but i doubt i'll have the patience to read it whole

nor do i need to, i think?

im also following dummit and foote for algebra concurrently and i want to finish this in my lifetime

[frosty yarrow]

what does rudin cover that isn't covered by introduction to real analysis by trench?

[sage python]

Trench's order of material is weird

But yeah it seems to cover less topology, less about uniform convergence, no differential forms (though frankly Rudin's treatment of it is utter dogshit), no Lebesgue integration

[atomic hemlock]

What do y'all think of Peter Olver Linear Algebra? I have it from the free springer textbook during COVID lockdown, with Axler's (too advanced for me). Is it ok as first book?

[sturdy shore]

you can try, but the little I've read of that book suggests me it is about as difficult as Axler's book is

[gray gazelle]

Which one is suitable for self-study?

For a first course

[blazing canopy]

I personally think Artin's book is the most suitable, though I personally only read through it later.

[junior isle]

Any thought on Jay Cummings proof book? Trying to decide between It or the book of proof by hammack

For self study

[remote sparrow]

both look good

cummings is a lot wordier and more conversational, which is a plus for self-study

[junior isle]

I got hammack's

But thanks for the feedback anyway

[remote sparrow]

cummings has a corny sense of humor, but it's not terrible

like, dad jokes and stuff

[remote sparrow]

pinter or judson

benedict gross has youtube lectures following artin though

if you do use pinter, make sure you do the exercises

some core material is found there

google some syllabi for suggested exercises to work

[proven copper]

does anybody know a book similar to Calculus (Michael Spivak) but for multivariable calculus?
I just finished calc 1, I'm reading the beginning of his book and I REALLY enjoy the way he explains things. He presents things with more rigor than I saw in my course but doesn't make it in a way that is impossible to understand. It's just a satisfying book to read the theory.

[sage kelp]

Check Velleman also

[sage kelp]

Check out Multivariable Calculus by Theodore Shinfrin

[remote sparrow]

shifrin is recommended at the back of spivak's book. hubbard and hubbard's book is also good.

[remote sparrow]

*multivariable mathematics

also hubbard and hubbard is substantially cheaper as a print copy

https://matrixeditions.com/

don't buy hubbard and hubbard's multivariable calculus book from amazon; they're sold at a substantial markup there. use the authors' website, linked above.

[sturdy shore]

shifrin also has a complete set of video lectures for the book, up on yt

[proven copper]

thanks guys

[proven copper]

are there books with Spivak's type of approach but for linear algebra?

[sturdy shore]

both hubbard and shifrin are integrated LA + multivar calc books

[lean magnet]

hey, just wanna find stuff more rigourous than stewart

I tried spivak but the questions is a bit too much of a challenge

a book geared towards self learning would be appreciated, thanks

[loud cradle]

+1 for shifrin's multivariable mathematics. I personally find Hubbard and Hubbard very longwinded and actually harder to understand than Shifrin if you already know linear algebra and want it presented that way

[narrow fiber]

hubbard^2 is a wonderful book imo

[remote sparrow]

#book-recommendations message

[remote sparrow]

try velleman's book

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

[lean magnet]

ty

[proven copper]

thanks

[proven copper]

I found that this Shifrin also has a linear algebra book, is it good?

[remote sparrow]

never looked at it or heard it recommended

only multivariable mathematics

[proven copper]

ok, thanks man

[remote sparrow]

some advice for buying math textbooks, especially brands like springer which have become notorious for selling shoddily bound books - don't buy new. buy used, and look for books in very good or like new condition. those are books that are more likely to be sewn-bound.

tangentially, i found a 1956 copy of E. L. Ince's Ordinary Differential Equations at a little pop-up shop on campus and paid $9.75 for it. it's a dover book. but man is the quality of its construction amazing by today's standards. the book went for $2.65 back in the day. it's a paperback, naturally, being a dover book, but the pages are sewn in fucking signatures. can you imagine that today in a dover book? though it's possible this is a one-off thing, given that inside the book they mentioned the book was a special collaboration.

[loud cradle]

my oldest Dover books boast about their binding on the back cover:

“We have made every effort to make this the best book possible. Our paper is opaque, with minimal show-through; it will not discolor or become brittle with age. Pages are sewn in signatures, in the method traditionally used for the best books, and will not drop out, as often happens with paperbacks held together with glue. Books open flat for easy reference. The binding will not crack or split. This is a permanent book.”

they don't say any such thing on the newer ones

[light umbra]

Can someone please recommend some good sources to learn discrete mathematics alone

[undone finch]

what part of discrete math?

like which topics

[light umbra]

so basics for now I guess.....i havent received a time table yet or a text book

[undone finch]

are you doing it for an university course? because discrete math courses vary a little on the content

they usually recommend rosen, but i'm not the biggest fan of the book

[light umbra]

yes for uni

I didnt learn it hs tho so im quite new to it

[formal bronze]

Is it normal where you're from for people to study discrete mathematics in high school?

[undone finch]

discrete math here for compsci students used to start out with content you'll find on How To Prove It, like mathematical induction, sets and relations

now it's changed completely, so it focuses more on counting, discrete probability and graphs

[light umbra]

some kids who study with me told they did study a bit in hs

[formal bronze]

I see.

You could look at 'Combinatorics: The Art of Counting' by Sagan, for enumerative combinatorics
'Graph Theory' by Reinhard Diestel, and 'Elementary Number Theory' by David Burton.

And see if they fit your needs.

[undone finch]

also if your goal is algorithm analysis you'll want to learn asymptotic functions too

[formal bronze]

Although these seem to be very basic books considering the fact that people there study all this in high school itself.

I didn't even know about these books except Burton until I joined college, I think I started off very late.

[undone finch]

i recommend diestel for graph theory, i used it. not exactly an easy read, but its pre-requisites are as minimal as it can be

try to at least do the exercises with a "-" next to them if you're using diestel

[light umbra]

so far its just prepositions,propositions, converse, contropositve and inverse, logic circuits stuff like that rn the stuff im learning

[undone finch]

ooh yeah how to prove it covers a lot of this, i think?

[formal bronze]

So set theory and logic? You should check out Kunen's book, although again, it would be elementary if all of this was done in high school.

[formal bronze]

'Introduction to Algorithms' by CLRS(search the acronym, you will find the book) would be a good book for the analysis of algorithms, but most people I've met say that it is a very basic book that only gives a surface-level treatment of the subject.

[undone finch]

i know thomas cormen's book, i think a fraction of it is relevant for one semester discrete math schedule

there's also concrete math by knuth.... but i never checked that one out

maybe someone else can say something about it

[formal bronze]

I only know of his book on algorithms, does he have another book on discrete math?

[undone finch]

no no i was talking about intro to algorithms

[formal bronze]

Oh ok

[formal bronze]

Do you mean that it is too basic for a one semester course on discrete math?

[manic cairn]

I read cormen

My best friend worked through cormen when they were 13

[undone finch]

no, i mean that most of its content wouldn't fit in a one semester course, and i'd say not for a 1 semester course on discrete math specifically

[manic cairn]

and they got National level CS awards

[formal bronze]

Yeah, for some reason I find it not that easy to go through, but everyone seems to have done it before even entering college.

Was it part of your school syllabus in CS?

[undone finch]

i didn't read it before entering college but i was assigned exercises on it regularly during first year compsci

it's got some advanced topics but i find it accessible personally

[light umbra]

so thomas cormens book,kunens book

and 'Introduction to Algorithms' by CLRS

[formal bronze]

the first and the third one are the same book

among the books you mentioned now

[light umbra]

ohh ok thank u 2 soo much🙏

[undone finch]

np! 😊

[proud gazelle]

FIS vs H&K ?

I watched mit's course on linear algebra, I also read an introductory book, but I want a proof-based abstract one

currently Friedberg, Insel, and Spence vs Hoffman and Kunze are the two candidates, I think I'm going with H&K but is there any reason to use one over the other?

also in terms of exercises, are they both good for self study?

[glacial crypt]

LADR is proof based (although people say they dislike how determinants were treated)

[warm creek]

If I wanted to read up on Even Permutation and Odd Permutation where would I look? I have looked into wikipedia and wolfram math world but their explanations left me confused.

[grand thistle]

check out an abstract algebra book and look for stuff on the symmetric group

some linear algebra books discuss it as well when talking about the determinant i think

[warm creek]

Yeah I figured that out by reverse searching the odd permutation and even permutation in this server 😅

[cinder tundra]

are there any good books for analysis on manifolds (aside from Munkres), as i would prefer more options when it comes to reading.

[distant spear]

friedberg any day for me

[crimson leaf]

CH 3.5 of D&F on alternating groups is about these

[remote sparrow]

spivak's Calculus on Manifolds is a common choice, though be sure to check the errata. also zorich's Mathematical Analysis II covers this. volume I also treats functions and differentiation in several variables in less generality.

[cinder tundra]

thank you! much appreciated

[simple raven]

how much books you should read in calculus or abstract algebra to move on?

[scarlet steeple]

well ideally 1 but it all depends, abstract algebra is also a very large subject and not everything you learn in an introductory course is the end all be all of algebra

you should be able to do almost every exercise in the book and many others with ease if you really want to be 'done' with any specific introductory topic.

[cinder tundra]

unsure what you mean by "move on", it depends on that a lot, no?

[gray gazelle]

either one or zero for calculus (you can learn this stuff from lectures)
and for abstract algebra it depends on how deep you want to go

[patent anvil]

hello I am looking for a good reference book for vector analysis

[heady ember]

If you want something more than Spivak's Calculus on Manifolds, you can try Lee's Series of 3 books or Loring Tu's book, both on diff geo. These are common recs from what I have heard around here

[agile bone]

hello, I'm trying to relearn math from the beginning, what books do you recommend for Basics Mathematics?

Prealgebra

Beginning and Intermediate Algebra

Geometry

Precalculus

Trigonometry

Calculus

and lastly linera algebra

[sage python]

Idk about book but Khan Academy seems to be the recommendation nowadays for \le high school math

Also for calculus in particular Paul's notes seem to be good

I do know some calculus books but at that point there's some branching depending on whether you want theory or not

[remote sparrow]

Books are not necessary for pre-algebra and algebra, but if you like books, you can look at some of Gelfand's books. Someone recommended Hung-Hsi Wu's basic math books before. Mostly you can just use Khan Academy, Purplemath, and Paul's Online Math Notes. For geometry, try Kiselev's two volumes in geometry. Most precalculus classes are mainly review of algebra and trig, so precalculus books are often geared that way. So you could buy an all-in-one book like Stewart's precalculus book. A more theoretical precalculus book would be Lang's Basic Mathematics. It teaches you how to prove basic things. Calculus can go off into two tracks - a more theoretical track and a track that focuses more on how to solve computational problems. A firmly theoretical first course in calculus can be found in Spivak or Apostol's calculus books. Note Spivak has a book called Calculus on Manifolds; do not use that book. A book that tries to balance theory and calculation would be Velleman's calculus book. A book that is firmly in the problem-solving side of things would be Stewart's book, even though it does prove some things for completeness. For linear algebra, consider Meckes' linear algebra book. Some free alternatives would be Hefferon or Beezer's books (both are also available as cheap paperbacks). Another low-cost alternative would be Mike X Cohen's Linear Algebra: Theory, Intuition, and Code. It assumes no calculus at all. The other linear algebra books can be read without knowing calculus, of course.

[narrow relic]

For precalculus I recommend this: https://archive.org/details/modernintroducto00dolc

[agile bone]

ty for the responses

[sage kelp]

It would be amazing to write down references, you must have some excellent ones

[fallow cypress]

oh I like that book :)

[remote sparrow]

looking at bass' graduate real analysis book

it's only the second edition

he is no longer publishing a paperback copy

well, at least it was very convenient to print with lulu

literally the first book where the project creation process was basically a complete cakewalk

[rancid obsidian]

A book about permutations in analysis?

[gray gazelle]

Guys what would be some good books on topology?

I've heard about Munkres but not sure how it is

[heady ember]

I have heard people here recommend Lee's intro to topological manifolds

[remote sparrow]

hatcher has a list containing reviews of some topology textbooks

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

[fallow cypress]

"The standard textbook here seems to be the one by Munkres, but I’ve never been able to work up any enthusiasm for this rather pedestrian treatment" LOL

[sage python]

Lee Intro to Topological Manifolds if you want a book

Or chapter 1 of Bredon's Toplogy and Geometry

Hatcher has some notes which seem good too

[simple raven]

as deep as a computer scientist needs

[remote sparrow]

computer science is super broad

can you narrow down what field of CS you're interested in?

i've only heard of algebraic coding theory, which presumably uses a ton of algebra

but obviously that's just a narrow section of CS

[simple raven]

AI or cybersecurity

[remote sparrow]

AI is a lot of stats, so analysis is likely going to much more helpful than algebra

cybersecurity...if you're focused on cryptography, there may be some algebra knowledge required

[swift dome]

Want some classic book recommendation for real analysis

[simple raven]

by analysis you mean real analysis and complex analysis right?

[swift dome]

I'm an undergrad student

[remote sparrow]

just real analysis

but complex analysis is nice to know

[swift dome]

Real analysis

[remote sparrow]

stats is pretty much just on real numbers

[swift dome]

I think complex analysis is not in undergraduate

[remote sparrow]

rudin

https://tenor.com/view/soyjak-spinning-spinning-soyjak-soyjak-jazz-hands-excited-spinning-wojak-gif-25231392

[swift dome]

Ty

Rudin daddy

[remote sparrow]

petition to rename baby rudin and papa rudin to twink rudin and zaddy rudin

[remote sparrow]

just depends

gamelin, bak and newman, or ruel, brown, and churchill are all suitable books

sometimes undergrad complex analysis is called complex variables

[simple raven]

any recommendations for a book to start abstract algebra with?

[remote sparrow]

pinter or judson

they are both super cheap as paperbacks

judson is legally free online

and both have some computer science applications

judson has some coding exercises too if you care to do them

[simple raven]

thank you again

[true river]

book for definite integration any?

[hasty turret]

You want cryptography? Or security?

I think the crypto book is good

[heady ember]

New profile pic eh

[vocal dragon]

does anyone have any recommendations for books to read before taking an olympiad?? high school level

pls dm me thank Uu

[rapid ruin]

Number theory books to prepare for rmo

Wait its not rmo anymore

Ioqm

Grade 10

[celest mist]

Hello can someone suggest some books i can get for free to develop problem solving for a hser

[heady ember]

What do you want to learn?

I don't think "problem solving for a hser" is specific enough

We have users here varing widely in what they are learning, even at hs

[glacial crypt]

like for example, grass is giving themselves active mental mutilation with a set theory book

and also a real analysis book

see the pins for book reviews

[celest mist]

Basic hs stuff

[grand thistle]

there's the art of problem solving books if ur looking for stuff like algebra 2, precalc, calculus

also "How to Solve it"

[celest mist]

Oh ok thx

[grand thistle]

depends on what ur looking for tho

these are kinda olympiad/comp math based books

[celest mist]

I dont want to do competitions

[mystic orbit]

Whatt does pedastrian mean? Lol

This is twice now that I've heard the term

[hazy elk]

boring

Is the meaning

[heady ember]

Khan Academy and Pauls' Online Math Notes are common recs for hs math

[west topaz]

hie

any book recommendations for class 9th ?

[gray gazelle]

Pedestrian means a person walking on the sidewalk ig ?

[fierce hedge]

I guess it means dull

[crimson leaf]

Pretty much unimaginative is another word

[gray jungle]

The mathematicians in this pedestrian server

[rapid ruin]

.

[pure iris]

Any recommendation for numerical analysis books with theory and computational exercises?

[swift dome]

check out #competition-math they have quite good resource

[proven crown]

why would competition math have numerical analysis resources

XD

[gray gazelle]

i found this on github , what do you think , about the books and the order provided ?

[sudden kindle]

Terrible

[undone finch]

took a rough look at it, don't have much to say about the books but i don't understand many of the dependencies on this chart

[novel obsidian]

A good rule of thumb to follow is all of these charts are dogshit

[undone finch]

taking 4 steps in order to get to naive set theory and proofs doesn't sound necessary

this makes topics sound like they have a much higher entry barrier than they do

[fluid skiff]

Automorphic forms and representation theory volume 1 seems like a good book

[mystic orbit]

Uh... Philosophy?

Who's this roadmap for? Lmao

Artin is there but

Number theory and then abstract algebra?

And also, linear algebra and then artin?

I guess it's trying to be as general as possible

But that comes at the cost of being suboptimal to everyone except a very very very specific demographic

[sage python]

Yea this doesn't make much sense

Honestly just do Artin, Schroder, and Bredon

[mystic orbit]

Any read map that goes through more than 3 topics is useless imo

[sage python]

And then Narasimhan

[mystic orbit]

Just ask people here for guidance lel

[alpine rover]

curious about this topic, are there any popular road maps?

never seen this before

[mystic orbit]

~~sheafification ~~

[hazy elk]

I think roadmaps are stupid for a young person learning math because you should learn what interests you and it's impossible to find that out without reading a bit first, and your interests keep changing as you read more, so a long list of books is pretty pointless

[shadow forum]

disgusting name, dude

[lusty trail]

Lol

[gray jungle]

It could probably be a good idea to just make a roadmap to learn the fundamentals everyone should know (ex: logic and set theory - la- basic number theory - real analysis - intro discrete - abstract algebra - probability - topology - complex analysis etc etc)
And then focus on specialized paths later.

Hard to go wrong with the order unless you are too ambitious

[remote sparrow]

my school uses burden and faires. it looks like a pretty standard book.

[remote sparrow]

my school requires number theory or a second course in linear algebra as a prerequisite for abstract algebra

it doesn't seem super necessary but maybe they don't want students to jump off into the deep end

[mystic orbit]

Bruh

Wat

I know 15 year olds that didn't do any LA before abstract algebra

[remote sparrow]

well, most of my classmates only had number theory

i mean everyone had lower-division linear algebra

[dense mantle]

anybody know much about percolation theory? reading recommendations?

poking around online, it feels like the subject is either contained in a chapter of a more general book or its coin-flippy as to whether or not its written well or dense asf for no reason

[crimson leaf]

Percolation by Bollobas is the one a professor recommended to me if I was interested

[mystic orbit]

@halcyon mesa Why ? Lol

Ofc

lumin isn't the only one lol

[smoky schooner]

whats wrong with sheafication

[mystic orbit]

It's uh

A wee bit infamous

(the book list, that is)

[quick hornet]

probably just a general mathematical maturity requirement rather than a content one

since the only thing in linear algebra U intro number theory is "basic proofs"

and comfort with abstract definitions i suppose

which is an underappreciated skill when teaching at the entry level

[foggy relic]

Lang, Browder, May*

/halfjoke

but also half not 🙂

[sage python]

Well Bredon also does difftop 😛

I'm thinking since Artin covers linear algebra and algebra

Schroder starts from calculus and gets through most of what you need in undergrad analysis

Bredon does the extra point-set you need for metric spaces, then does differential and algebraic topology

[gray gazelle]

over 12 hours and no one talks in this channel?

I found this cool book about tests of convergence for double series

prerequisites seem to only be some functional analysis

[west topaz]

any book recommendations which contain practice questions?
for classes 9 and 10?

[formal bronze]

What is your objective here? 'Classes 9 and 10' could mean very different levels of mathematics, depending on the context.

[dense night]

im assuming classes 9 and 10 are from the indian school system, which is the same as gcse (year 10 and 11) in the uk or grades 9 and 10 in the us

[formal bronze]

I see.

Standard textbooks should do then.

[west topaz]

i completed them
so i wanted some more book recommendations

[formal bronze]

Which topics?

[west topaz]

algebra mainly

[molten linden]

good book for probability and stats?

something which preferably builds from the ground up

[molten linden]

also one for differential equations

[solid laurel]

William Feller - An Introduction to Probability Theory and its Applications

[gray gazelle]

not sure about that

it's definitely a good book but does it cover what's in the modern curriculum

[fickle granite]

How good is Tenenbaum for ODEs?

Looking through the contents it seems solid (I was specifically looking for a text that discusses series solutions), but now I'm thinking of sitting down with this book for a more rigorous self study of ODEs

[crimson leaf]

Calculus based probably Ross, measure based there's a lot

[remote sparrow]

it's good

https://www.maa.org/press/maa-reviews/ordinary-differential-equations-7

here's a review you might be interested in

[hearty sluice]

Resources for learning plumbed manifold theory?

[dapper root]

Lmfao

No way that’s a real term

😭

[sharp turtle]

hi guys, someone has an exercice book recommendation about analysis ?

[remote sparrow]

real analysis?

[ebon marsh]

Hi I want to learn measure theory
does anyone have book/class recommendations
I'm not in university

I've had real anaysis

I've been recommended sheldon axler's book. Any yay/nays for that

[sage kelp]

Is Chartrand Mathematical Proofs book solid for foundations?

[remote sparrow]

some suggested books are in pins

axler's book is legally free online if you want to take a look at it

[remote sparrow]

like, metamathematics and axiomatic set theory? no

as in preparation for future math classes? yes

[sage kelp]

Yes, as prep for upper math level classes

[remote sparrow]

yes it's fine

[sacred swan]

Any book recommendations for an introductory text on Delay Differential Equations?

[remote sparrow]

@fallow cypress ugh, of course mileti's book is a print-on-demand

oh well

still fine with my purchase

[acoustic imp]

Cohn’s book was good

[fallow cypress]

he had a free copy on his webpage at some point

[remote sparrow]

he still does

it's a draft copy technically though

[fallow cypress]

ah

[vernal compass]

Terence Tao’s

[ebon marsh]

Oo

[grave thorn]

Jacod/Protter

Rudin

(RCA)

I personally also like Malliavin "probability and integration"

[sturdy shore]

the parts I've read of axler were good, yay for that

he definitely pays attention to pedagogy more than most authors do

[dapper root]

[grave thorn]

Undergrad analysis should be enough

[narrow fiber]

Oh wait

Oh my god I misread

I thought he said he didn't take it lol

[grave thorn]

LMAO

Well yeah that changes things

[cursive orbit]

if u don't know any analysis, then pugh has a decent (but not terribly standard) treatment of measure theory once you get to the end

oh wait I misread too

💀

[west topaz]

@gray herald here book recommendations DAMN

[gray herald]

ikr

[grand thistle]

how does this book compare to jacod and protter's?

it's material (judging from the toc) looks like exactly what i want to learn, but ive already started and am on chapter 6 of jacod/protter so not sure if i should change or not

looks like this covers a lot more analysis too, which im a fan of

[orchid mortar]

Don't change a book if a book fits you

You can also read more than one book

Jacod Protter will give you more than enough for most probability

[grand thistle]

it kinda doesn't fit me tho i feel like

[orchid mortar]

RIP

Uhh yeah there are at least 20+ probability books, at least 5 of which I consider 'good' for foundations

find any you like

I mean I don't think anyone reads Kallenberg on first go

[grand thistle]

i felt like it kinda develops the measure theory "along the way" which i kinda don't like tbh

i feel like having a solid foundation then learning the probability might be better? so books that have measure theory in the first section i prefer i think

[orchid mortar]

in that case it does sound like the Malliavin one fits better (though I never saw that book before)

Malliavin, from Wiki, comes from harmonic analysis. Definitely a reputable author

I'd personally prefer Jacod since I'm more into applications

[grand thistle]

do u know if this is the malliavin from "malliavin calculus"?

that field looked really cool even though it's over my head

[orchid mortar]

Apparently it is

[grand thistle]

calculus of variations in probability or something

[grand thistle]

oh cool

malliavin's book looks very interesting

i like how he has fourier analysis integrated into the book

has all of the subjects i had been planning to learn since a few months ago

[orchid mortar]

go for it then

[grand thistle]

yep will do

[grave thorn]

Definitely more abstract

[grave thorn]

He started in harmonic analysis, then worked mainly on probability

[grand thistle]

any prerequisites that it has that jacod and protter's book does not have?

i.e. does it assume topology or something

[grave thorn]

It assumes topology

I would say you could get by with just the topology you learn in real analysis

[grand thistle]

so would basic knowledge of compactness (heine borel), properties and definitions of open/closed sets, definition of a topology and a hausdorff space be enough?

im pretty iffy on connectedness

also ofc things like characterization of continuity via open sets im familiar with

basically the topology from rudin pma

[grave thorn]

That should be good

[rugged seal]

Hello I am looking for a book about FDM and FME for (ellitptical) PDEs if possible the book should include:

-Introduction to PDE with examples
-classical solutions
-FDM
-weak solution (Sobolev-Spaces, embedding theorems etc)
-FEM

[proud gazelle]

what book to read to start with differential equations? I studied multivaraible calculus, linear algebra, and real analysis.

preferably something that has some rigour

[remote sparrow]

if you've had real analysis, i heard arnold's ODE book could be good

you won't learn how to solve some basic differential equations, but that's what computers are for

i've heard another rigorous book in ODE would be hirsch and smale's (without devaney - only first edition is like this) book. if you are interested in "cookbook" ODE, the best might be morris, tenenbaum, and pollard's or boyce and diprima's book with boundary value problems. morris' book has no bvp, but it does prove existence and uniqueness of solutions. most books nowadays treat ODE similarly to boyce, but boyce and diprima's book is the most comprehensive. a book that emphasizes qualitative and graphical analyses would be blanchard, devaney, and hall's book.

e. l. ince and earl a. coddington also have two elementary ODE books that are more theoretical, but remain elementary in scope. they are often cited as references for certain proofs in modern ODE books. they're cheap dover books, which is a plus.

[pale kite]

anyone have a book for learning algebraic number theory that assumes a good comprehension on algebra (i.e. modules)

[narrow fiber]

I'd say milne's notes are best but I also love marcus' "number fields"

[sage python]

Neukirch

Also probably Milne

[narrow fiber]

Neukirch is great as well but markedly harder, dignity ^

[sage python]

Idk Milne as well so I can't compare the two for you

(And tbh I only know the very first part of Neukirch)

[narrow fiber]

Idk many people who've gone through more than the first part myself included lol

Milne takes his time across what Neukirch blazes through in like, 40 pages / a typical first course syllabus LOL

[dapper root]

Maybe I should read Neukirch cuz I’m the goat

Actually I’m the Chmonkey

[narrow fiber]

The chmoat

[remote sparrow]

@stray veldt Since you mention using Amann Escher for undergraduate analysis, what had you taken prior to working through this book? Were proofs or some notion of proof sprinkled throughout your math education? Did you go to a relatively strong university? I know Amann Escher is a standard text for undergraduate analysis in Germany, but are there other standard texts? Or do German undergrads all go through Amann Escher?

[indigo mesa]

No it's not all german undergrads

I used it as a secondary source but my course was not based on it

prior to it i had taken nothing, that was my uni semester

[remote sparrow]

what was your pre-university background like?

[indigo mesa]

other standard texts are the Forster Analysis series for example

[indigo mesa]

nothing

[remote sparrow]

no calculus or algebra?

[indigo mesa]

dunno what that'd include

[remote sparrow]

did you go to some sort of high school before university?

[indigo mesa]

yes

lol

but i don't know what "algebra" is supposed to mean here

[remote sparrow]

well then why would you say your pre-university background is nothing?

[remote sparrow]

solving polynomials and simple stuff

like stuff on khan academy

[indigo mesa]

well ok HS education but nothing somehow related to uni stuff

[remote sparrow]

or paul's online math notes

[indigo mesa]

okay yeah we do that

we also do simple integrals and some differential calculus

but no limits or integration by parts or anything

[remote sparrow]

would you say you worked through some simple proofs there or was the course mainly about computing derivatives and integrals

i see

[indigo mesa]

it was nothing that somehow compared to uni maths

that's why i said nothing when you asked about pre uni background

sorry if that was misleading

[remote sparrow]

my opinion before today was that amann escher might be inappropriate to recommend to american students altogether

[indigo mesa]

not sure, i don't really get the american math major system

real analysis doesn't seem to be something you take in your first semester there

[remote sparrow]

american universities emphasize breadth a lot more

so you need to take some general ed. courses

[indigo mesa]

like gen eds?

ah yeah

[remote sparrow]

which i actually approve of

[indigo mesa]

yeah makes sense

we don't have those here

we just have to take a secondary subject

[remote sparrow]

people write off the humanities and social sciences and such a lot, but then they turn around and say misogynistic and racist stuff without any semblance of critical thinking

[indigo mesa]

indeed

maybe we should move this to another channel if we aren't actively discussing amann escher?

[remote sparrow]

nah it's okay

[indigo mesa]

but yeah i think amann escher is a great, a bit tricky sometimes, not an easy read but good

[narrow fiber]

How does amann escher compare to rudin pma

[narrow fiber]

Which forster is this btw

[pale kite]

tysm!!! 😄

[indigo mesa]

Otto

I haven't read rudin pma so i can't comment on that :/

[gray gazelle]

best book for a first course in Point set topology?

[narrow fiber]

Oh yeah i know of otto forster from his riemann surfaces book

[gusty smelt]

thats a p good book, the riemann surfaces one

[gray gazelle]

anyone?

[tulip blade]

Munkres is fine

[smoky schooner]

😩 fr

[remote sparrow]

got a used copy of schroder's analysis -- it's a gluebound in signatures

the glue is cracked

[heady ember]

Gluebound in signatures?

[remote sparrow]

signatures just means multiple pages are grouped together like so: there's one page, then stack another page, and so on, then fold them

[heady ember]

I see

Mine seems to be in mostly good shape

A couple of dents but nothing too bad

[dense mantle]

random ask -- will be in the Comap MCM in a couple of weeks, and was wondering if anybody, well, knows where one might acquire the Mathematical Modeling for the MCM/ICM Contests Voume 1

https://www.comap.com/bookstore/1-bookstore/15-mathematical-modeling-for-the-mcm-icm-contests-volume-1-print

[remote sparrow]

send picture

esp of the binding

[remote sparrow]

yeah your book is gluebound just like mine

not quite print on demand but also seems like some corners were cut in production

the pages aren't truly sewn together

oh well, at least i know i couldn't have gotten a much better copy

amazon vendor said "very good" 🙄 but i don't feel like returning it

[heady ember]

The print and paper quality is quite good though

The text isn't blurry or anything

[remote sparrow]

when you open your book is the glue cracked anywhere?

[heady ember]

Haven't noticed that

[remote sparrow]

grounds for return? le "very good" condition according to vendor

the pages are fine

no writing

content is good

[crimson leaf]

Probably could return that lol

[glacial crypt]

rolles not an exercise? :O

I better not read it then

[heady ember]

Mine's in a much better shape

Glue wise it isn't torn out and stuff

[frail wind]

hi

i'd like to start studying math in books

i have some foundation, so i'm searching for something like highschool degree

[heady ember]

Highschool degree?

Wdym

For highschool stuff people normally rec Khan Academy and Paul's Online Math Notes

[frosty yarrow]

Any good books for learning series specifically?

[heady ember]

If you're learning it for the purpose of calc, Paul's Online Math Notes or Khan would probably suffice

[frosty yarrow]

I meant like, a book focusing on series (more than calc)

[heady ember]

Hmm

[alpine rover]

any proof based calculus books (that prove and don't just state the results we see in calculus like chain rule, FTC, ratio test)?

[heady ember]

Isn't that real analysis?

The closest thing I can think of that fits your description that's not analysis is Spivak

[tepid prairie]

Advanced Calculus by David V. Widder proves all of these types of things and takes nothing as assumed true.

[gray gazelle]

Spivak does a bit of both

[alpine rover]

thanks!

[gray jungle]

gradshteyn and ryzhik (don't)

[heady ember]

Just do real analysis

[tawny copper]

Maybe Stromberg intro to classical analysis. The entire book is not entirely focused on series, but it has a chapter or two that covers more than the standard texts. You can look into that maybe. I also like Krantz, a primer on analytic functions. Duren is also nice.

If you are doing series for the first time, its probably better to pick standard books on analysis btw.

I'm pretty sure there must be books that focus entirely on series. Hardy wrote one on divergent series, but I'm not sure how readable it is

@frosty yarrow

[glacial locust]

what grade is tat

[tawny copper]

there's a readable pdf of Titchmarsh and it starts with a chater on series, that book is interesting probably. I will look into that

[cinder void]

Book recommendations for SAT

Basic to advance

[frosty yarrow]

Ah okay thanks for all the responses, I'll check them out

[dense mantle]

certainly you don't mean the Scholastic Aptitude Test, as commonly administered in the United States for the purposes of a college entrance exam?

[sterile harness]

lol, just use khan academy dont buy anything

also that is not what this channel is, this is for actual math books

[keen orbit]

Hi everyone how are y'all
Is linear algebra by Stephen H. Friedberg better than elementary linear algebra,applications version by Howard anton or vice versa

[crimson leaf]

Two very different books with very different purposes. Friedberg Insel and Spence is a proof based text and anton linear algebra is a much more computational approach

[keen orbit]

Ohh okk

I think friedberg is better because it's proof based

Better than computational approach

[remote sparrow]

usually a university class

[foggy relic]

Loomis Sternberg

[sturdy shore]

stop giving troll recommendations

[rugged seal]

I am looking for a book about FDM and FME for (ellitptical) PDEs if possible the book should include:

-Introduction to PDE with examples
-classical solutions
-FDM
-weak solution (Sobolev-Spaces, embedding theorems etc)
-FEM

[cinder void]

Yess

[dense mantle]

just go buy a princeton review book

work through the practice tests (time yourself)

and you're chilling

easy Ws

[cinder void]

Okay thanks

[glacial locust]

holy shit i cannot read any of that crap

[remote sparrow]

it's one of the easier books

schroder goes step by step in the early chapters

[glacial locust]

and im going to learn this?

holy crap

[sturdy shore]

are you gonna major in math? then obviously

[dense mantle]

that's an early analysis book (usually, you do single variable with rigorous limits, integrals, sums/ series, sequences; then, multivariable, a bit of manifolds, a bit of measure theory)

the more math you see, the easier it becomes

this should be 1st or 2nd year of undergrad mathematics

[dense mantle]

I am not familiar with this text, but I did like Understanding Analysis by Stephen Abbott when I read it

[remote sparrow]

abbott is great

[remote sparrow]

it's daminark's recommendation

[glacial locust]

im in 9th grade and doing algebra with 2 variables now

[dense mantle]

lmao you've got some time...

[glacial locust]

yeah i think

[dense mantle]

most of this discord is high schoolers begging for HW help

[glacial locust]

im just interested in math

[dense mantle]

and then a mix of undergrads and grad students in the advanced section

[glacial locust]

thats why i came here

wanted to ask about some problem that i didn't understand the solution of it

but i unrestood it randomly

and didn't ask finaly

[dense mantle]

the most accessible and interesting way for you to immediately realize that interest is competition math

[glacial locust]

i can feel that already

[dense mantle]

otherwise you've got several "layers" of reading to get through before you're anywhere interesting

[glacial locust]

im laughing at my class that they don't know actuall topic we are doing

[dense mantle]

that's always going to be the case

[glacial locust]

🤷‍♂️

[remote sparrow]

you don't need to do competition math by the way. it's not representative of what undergrad or graduate math looks like, especially since problems in competition math are meant to be solved by design, just in some tricky way.

[dense mantle]

^^^^

[glacial locust]

i just like it

[dense mantle]

I think it's just a nice way for them to introduce ideas

[glacial locust]

i like the problems it creates

and the things it teaches me

[dense mantle]

besides... recreational math is a decent recreation

moving towards research, it is, indeed, not at all similar lol

[remote sparrow]

if you really want to try learning about proofs in a very gentle manner, jay cummings has a good book on proofs

[glacial locust]

bro im 9th grade

didn't finish middle school even

[dense mantle]

your age doesn't matter bruh

[glacial locust]

i know

[remote sparrow]

you've probably had geometry, though? although the way proofs in geometry is taught is quite stale...

[dense mantle]

if you want to learn, just go read

[dense mantle]

yeah 🤣 you learn how to write "proofs" in that class

[glacial locust]

i didn't have since like 2 classes

[remote sparrow]

you don't need to know much beyond a little algebra

[dense mantle]

they are just presented as "formally" writing out very obvious steps

[remote sparrow]

le two-column proofs

[dense mantle]

[glacial locust]

and its actually imposible to have my personal interests because every week we got at least 3 test or quizes

i want to get a+ in all of them

[remote sparrow]

just read in the summer

[dense mantle]

hop off discord and get to work then

[glacial locust]

thats what da dog gonna do

[remote sparrow]

or talk to an interested teacher if they could mentor you

[dense mantle]

I promise you, you never start having more free time

[glacial locust]

i already studied 7 hours today

and its 21:45 my brain exploading

[dense mantle]

the amount of free time you have monotonically decreases year to year

you just get better at using it

[glacial locust]

i need to learn at home because my teachers at my school they are not very well understandable

everyone somehow understands them

but i not

[dense mantle]

what country are you from?

[old elk]

Previous topics to study varieties?

[glacial locust]

poland

[dense mantle]

ah interesting

[glacial locust]

but american school

i don't understand just his accent

indian one

its not like im racist

but sometimes i don't understand a single word from his sentences

[remote sparrow]

jay cummings' Proofs: A Long-Form Mathematics Textbook is a super readable book on how to read and write proofs

[glacial locust]

only the end of the sentence usually ended with yeah?

or yes?

[dense mantle]

mmm... probably a semester or two worth of algebra and topology would be helpful?

forgive me... alg geo not my forte

only skimmed bits and pieces

[glacial locust]

but its not like i need to study 8 hours per day to understand what we covered on today's lesson

[dense mantle]

you could probably get better answers in the alg geo channel than here

[glacial locust]

im getting that after 15 minutes

[dense mantle]

then what are you spending so much time studying

[glacial locust]

how can i say this

i don't want to sound like an idiot

yhh

stupid human

its gonna be so cringey i don't wanna to say this

i don't want to say why

can we just skip it?

[dense mantle]

no

[old elk]

Would you recommend anything else besides that ?

[dense mantle]

again... not my thing by any means. I just skimmed parts of harthshorne as it interested me

you should probably just talk to the people in the alg geo channel...

but yeah a full year of algebra definitely (naturally, it's algebraic geometry, right)

topology certainly helpful

at least, you'll see a lot of familiar words

not like point set top words, but all the projective plane shit

[glacial locust]

well after 5th grade i think i stoped studying school things at all, my grades were like d or f or e or what ever is that we don't have the letter rating but the number like 5 or 3. and i didn't study at all until last week when i realised that its the last time i will get comfortable and start actually studying for real because if i don't start now there will be no coming back and now i just needed to give it like 2 or 3 days to study the whole topic and know it perfectly

[dense mantle]

fair

I was the same way

I'm from SE USA

[glacial locust]

and i didn't even know im that smart

that i covered whole topic in 2 days

[dense mantle]

3rd year college in northeast now

[glacial locust]

and know everything perfectlyt

[dense mantle]

yeah uh nothing you cover up to first university is difficult by any means

[glacial locust]

huh?

[dense mantle]

I think the real goal is to keep you busy and developing the academic skills

some sort of baseline

[glacial locust]

i don't even know where im gonna go to college

like what section

[dense mantle]

you have 4 years to figure that out

[glacial locust]

like economy

or math and chemistry

or technology

[dense mantle]

just read more bruh

[glacial locust]

gime some book

for my age

[dense mantle]

on what topics

[glacial locust]

not for your age

[glacial locust]

algebra

[dense mantle]

LMAO

[glacial locust]

🤷‍♂️

[dense mantle]

naw bro I'm not gonna slap you with the stat mech shit I am reading

[buoyant vessel]

polynomials by E.J.Barbeau

[glacial locust]

yeah don't even show it to me

wait stat mech?

o shit

ok i pulled up?

[dense mantle]

yeah I haven't seen this one before but these problem books are great reads/ things to work through

[buoyant vessel]

yeh it's for highschool algebra but alot of hard questions, not abstract algebra

[glacial locust]

but how im gonna have time to read this book

i mean i will have

with no problem

[dense mantle]

yeah lmao you see algebra in this server and have to discern their age before you know how to answer the question

[buoyant vessel]

or just read AOPS books

[dense mantle]

^^^^^^^^^^^^^^^

I was just about to go link AoPS

https://artofproblemsolving.com/community

[dense mantle]

bumping this again

[buoyant vessel]

this one is good

[dense mantle]

and, once again, it remains a great way to just see a lot of math

[glacial locust]

?

[dense mantle]

yeah

that's one of several

I think the algebra specific book may be not as interesting

[glacial locust]

bro i think its even created by polish man

[dense mantle]

no he's american

[glacial locust]

ruszczyk is polish name

[dense mantle]

polish descent sure

[glacial locust]

then do you pronounce it

how

[sterile harness]

Richard Rusczyk has the most entertaining videos

I could watch that guy solve math problems all day

I think it's just "Russick"

[glacial locust]

thats what im doin

[dense mantle]

mm I've always read it in my mind with a "richer" sort of "Ruschick"

but I have no idea

[sterile harness]

They cover it at a higher level

It's much harder in AoPS books

[glacial locust]

3 variables?

[dense mantle]

yeah ahhh "linear equations" go well, well, well beyond y = mx + b

[sterile harness]

Not necessarily (3 variables, that is)

[dense mantle]

n variables

[glacial locust]

https://tenor.com/view/capybara-ok-i-pull-up-hop-out-at-theafter-party-gif-22734030

[dense mantle]

just go read it

[glacial locust]

holding hands up

[dense mantle]

and you'll begin to realize that, indeed, you know nothing

[sterile harness]

yeah that happened to me lol

[dense mantle]

honestly

[glacial locust]

what do you expect from 9th grade

im piece of shit compared to you

[dense mantle]

your ego with these topics

[sterile harness]

No he means you don't even really know algebra

[dense mantle]

is evident in your tone

[buoyant vessel]

[sterile harness]

Because school doesn't really teach it

[dense mantle]

because you have not been ass-blasted yet

[glacial locust]

what do you mean

[dense mantle]

two very different things come to mind for the two of us

when you mention algebra

[glacial locust]

of course

[dense mantle]

I don't really even study algebra apart from using it as a tool for the combo and probability things I really care about

for you its, roughly, "equations and quadratics"

for me its, roughly, "groups, rings/ fields, and polynomials"

[sterile harness]

no it's "variables"

[glacial locust]

yes

[dense mantle]

[glacial locust]

🤷‍♂️

what can i do

[sterile harness]

Go read that book

[buoyant vessel]

read Basic Algebra by Jacobson

now

[dense mantle]

yeah that's what you can do

[buoyant vessel]

[glacial locust]

ok

[dense mantle]

go read those books

we just dropped months and months of good reading on you

go do it

[glacial locust]

WHAT

[dense mantle]

"I spent 7 hours studying" my ass

do it faster

work harder

[glacial locust]

how

[dense mantle]

that's too vague/ broad of a question for me to answer

[glacial locust]

i just need to whatch some crappy youtube video to understand what is happening while solving things that will be on my test

you need to read books made by albert einsteins

[remote sparrow]

(do not)

[dense mantle]

unironically

[glacial locust]

but that doesn't mean i won't understand what is happening in that book

or maybe

[dense mantle]

Algebra: Chapter 0 by Aluffi is also a great algebra book

[glacial locust]

but that book doesn't even match what im doing now

you know what i mean

[dense mantle]

no it is a strict superset of what you're doing right now

[dapper root]

No it says chapter 0 he’s on chapter 1 already

[glacial locust]

[dense mantle]

shieeeeeeitttt ur right

[dapper root]

Maybe go back to kindergarten and learn what 0 is

💅

[buoyant vessel]

someday read this too

[glacial locust]

[buoyant vessel]

it has 6k questions in it

[dense mantle]

Jewish Problems

[glacial locust]

what the fuck?

[dense mantle]

[buoyant vessel]

become diligent clerk's apprentice-frepog

[glacial locust]

wha hapen

[dense mantle]

@glacial locust just think bro everything you're doing now can be found on chegg/ has youtube videos explaining exactly the method you need for your solution

[glacial locust]

i can't compliment you?

[dense mantle]

just wait

[glacial locust]

yes

of co

what do you mean wait

[dense mantle]

soon enough you'll be working on things that don't even have textbooks written for them

just the papers bro

[glacial locust]

i think i can imagine it

[dense mantle]

some half finished codebase for some idea some bro had for some numerical scheme

[glacial locust]

how do i will know that the answer i will get is the right thing

[dense mantle]

well

you've seen us talk about proof writing

soon enough you will no longer be working out equations to come to a number

[glacial locust]

what do you mean

[dense mantle]

you will be writing, for lack of a better word, "short math essays"

[glacial locust]

o shit

i know what you mean

i think

i mean i can visualise it

[dense mantle]

for which either your work is obviously correct, has some small errors, or is a completely incorrect direction

[glacial locust]

how will i know that its going to the right direction

im adding you to friends

you will be my mentor

or book recomender

[buoyant vessel]

idolize clerk too

[glacial locust]

you just crushed my brain in 300 centilions of pieces

i mean

[dense mantle]

lmao aight

[glacial locust]

i knew it that it will happen some day

[dense mantle]

I think most of the undergrads

in this server

could drop enough on you to do that

don't limit yourself to pinging me

[glacial locust]

you are the 1 one that know more than me and helped me

[dense mantle]

I am far from the local max in this server for any particular topic

[buoyant vessel]

clerk=local max for foundations

[glacial locust]

but should i read the book right now?

like i think i don't need it now

my test will be from the book things

[dense mantle]

yeah why not

[glacial locust]

and i know the book things

[dense mantle]

bro if you want to learn something you can just go read about it

you don't need to wait to have a test on it

hell, depending on how large of a university you go to, it could very well be that there is no course pertaining to whatever you're interested in learning

[glacial locust]

i like this things

[dense mantle]

the moral of the story is to go read more and work on more problems

that is strictly how one gets better at mathematics

[glacial locust]

i can't even imagine how much power you all guys got

[dense mantle]

not much

[glacial locust]

[dense mantle]

I'm still far asf from writing a paper

[glacial locust]

do me some problem

rn

maybe not here

because its book recomendation

channel

[fiery radish]

ok

[upper wedge]

I need a book to help me learn the basics of math again. Like arithmetic and all that stuff. Any recommendations?

[frail wind]

wow, could you be less stupid?

[mystic orbit]

Who's local max

[buoyant vessel]

clerk

[mystic orbit]

Clerk=clerk for foundations?

[buoyant vessel]

clerk=global max of server

[mystic orbit]

Ohh

I thought there was a user literally called local max

[buoyant vessel]

[sterile harness]

I’m talking about the SAT

It is not necessary to buy anything to prepare for SAT math

[small lantern]

hey guys odd question but is there a resource i can cite to show that 1 can be represented as a fraction?

like is that a polynomial/real number operation?

like in grde 5 u learn that 1/1 = 1

and that 2/2 = 1

then in secondary school u learn that a polynomial over an equal polynomial is 1

but how would u actually cite that?

[pallid frigate]

Hey guys 🙂
I'm looking for a Linear Algebra book to use as a reference alongside my books from the university (they're in my native language).
Can you guys recommend me of a book?

I've found "Linear Algebra and its Appliances" and "Linear Algebra Done Right", but as I was looking through their table of contents it didn't cover all of the topics in my Linear Algebra courses.

I have two Linear Algebra courses...
Linear Algebra 1 - Preparatory review; Linear equations and Rn; Matrices and determinants; Fields and the field of complex numbers; Vector spaces; Basis and dimension; Linear transformations; Eigenvalues and eigenvectors; The Euclidean n-space.
Linear Algebra 2 - Inner product spaces; Bilinear and quadratic forms; Canonic forms.

[sturdy shore]

hoffman kunze, also check pins

[pallid frigate]

Thank you, I'll look at that. And sorry, I'll check the pins.

[remote sparrow]

The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics

[stone orbit]

Sequence of books to get me from where I am now to Galois Theory?
I’ve taken Calc 3, ODEs, done some competition math, but i’m completely new to abstract algebra.

[fallow cypress]

Dummit-Foote maybe? I imagine you're not just literally just looking to get to Galois Theory as fast as possible but want to learn a decent amount of abstract algebra along the way

In which case Dummit–Foote is an excellent resource

[remote sparrow]

pinter or judson are good

[stone orbit]

^thanks to both

[dense mantle]

https://www.amazon.com/Abstract-Algebra-Applied-Undergraduate-Texts/dp/1470468603

this is a young book

and I will admit personal interest in plugging it, but I do like it as an undergrad algebra book

I think it's laid out a little more "naturally?" than D&F and some of the others... idk. if you want to have that as an extra resource, it is on libgen etc already

[mystic orbit]

wow, could you be less toxic?

And instead bring something valuable to the conversation?

[mystic orbit]

Read channel description.

[vital bane]

he did, he's showing everyone how not to talk to people on the internet

[undone finch]

halloooo i've been trying to find good references for exterior algebra, anyone has recommendations? :)

[little summit]

im trying to find some analysis books, here are some that were recommended to me, could you add to this list?

Tao's Analysis I & II
Spivak Calc
Pugh
Ethan D.Bloch “the real numbers and real analysis”
Zorich
Parzynski and Zipse
Jay Cummings’ real analysis
Schroder and Browder
Real Analysis by Pons
Basic Analysis I by Lebl
The Way of Analysis by Strichartz
Introduction to Real Analysis by Bartle and Sherbert

[glacial crypt]

abbott

[grand thistle]

amann and escher

[grizzled rock]

good books to get started on imo prep ?

[distant spear]

Pugh

[gray gazelle]

Ethan D. Bloch "the real numbers and real analysis"

if u need a rigorous detailed intro but its a bit dry

[little summit]

nice thx!

[glacial crypt]

and of course

[fierce hedge]

Zorich

[sterile harness]

right, mb

[remote sparrow]

my school uses parzynski and zipse. jay cummings' real analysis book is another good choice. daminark recommends schroder and browder. another author is pugh.

[desert thorn]

I am looking for an undergraduate Linear Algebra book that is good for learning how to prove "basic" linear algebra stuff. I've passed the courses so i don't really need to do much computation anymore, but my grip on the theory needs to be firmer. I'm awful at proving, i really should've appreciated its importance much earlier - so i want to work on this as well. Trying to kill 2 birds with 1 stone basically. Any recommendations?

[crimson leaf]

FIS is my recommendation but in the pins there's good LA books

[desert thorn]

Friedberg, Insel and Spence? I'll give that a look. Thanks.

[cinder trellis]

Does anyone know if Michael Spivak's "Publish or Perish" publishing company has its own website? I've tried to find it online but came up with nothing...

[undone finch]

i def had good experiences with it. i think more people use hoffman-kunze though so it's def one to look for. i have the impression that friedberg-insel-spence exercises are easier on average, it's up to you if this is an advantage or not

there's also shilov

haven't read a lot of it because i use it mostly as a companion to FIS. i find it good but it's uhh unorthodox to say the least

[remote sparrow]

https://www.mathpop.com

[desert thorn]

easier is good until it isn't. A challenge is important, but it has to be right for the level you're at - not all study time is good study time.

[undone finch]

i guess you gotta try. easy is relative too

you can work through chap 1 in a few or one day, and see how you feel about it

[desert thorn]

Yeah, no other way to find out than just try it. And i feel like a lot of self-study material ends up being a matter of preference. So "best" is always relative.

[pale badge]

Vladimir Arnold ODEs or George Simons ODEs? looking for a practical approach