book-recommendations

[keen orbit]

That's why I was asking about a more abstract one to get the general ideas

[sage python]

Alright. I should say some ideas like inner products necessarily restrict attention

But yeah now I see what you're looking for

[remote sparrow]

even when books restrict the scope of the fields they're working with, they still prove theorems that hold for general fields

[keen orbit]

Then what's the difference

[sage python]

Sure but it can be a subtle point of what works in general and what doesn't. Sometimes it's general field, sometimes characteristic not equal to 2, sometimes it's characteristic 0, sometimes it's an algebraically closed field, sometimes it's R/C, sometimes just R or just C, etc

[keen orbit]

Sorry I may be annoying but I am asking these questions to know the difference and after that know which book to read

[sage python]

I wasn't responding to you with that but to Sour Drop

But yeah basically, some of the theorems that stick to R and C will generalize (either to general fields or some specific class of them), other's don't. For someone who only cares about R and C that's fine, others might not like it

[keen orbit]

I am talking in general because I am probably wasting your time

[sage python]

Ah no worries

[keen orbit]

Ok so can you recommend me one or more book(s) which stick to R and C and generalize some to all or specific class of fields and one or more book(s) that goes for general

I want to see a sample of each then I can choose

That's my last request and I am sorry again if i am wasting your time

Also if you have something rn then go and dw abt me

[sage python]

You worry too much you're not wasting time

[remote sparrow]

all of the books i recommended mainly concern themselves with R and C or just R

meckes does start with arbitrary fields but encourages you to think of F (the arbitrary field) as just R or C

[keen orbit]

Oh just like Sheldon and friedberg

[sage python]

Axler is bad

Avoid it

[keen orbit]

Ok I will

[remote sparrow]

friedberg is arbitrary fields i'm sure

[sage python]

Linear Algebra Done Wrong is a book that focuses on R/C

[crimson leaf]

Friedberg doesn't do characteristic other than 0 though does it?

[flat jackal]

yeah sure

[keen orbit]

I tried friedberg but then avoided it

[sage python]

What did you dislike about it?

[flat jackal]

i think I know all the vector stuff know, if would be good to extend my knowledge tho

[empty junco]

halmos focuses heavily on C

but also notes when characteristic is important

[sage python]

Doesn't he start off fully general?

[keen orbit]

It used to give many definitions in exercises which I found some in axler's stated in the section such as direct sum if I remember correctly

[empty junco]

because he's the goat

[sage python]

Just that once you're on inner product spaces and shit everything zooms in on R/C

Thing is Halmos is less comprehensive I feel than something like Shilov or Hoffman-Kunze

Maybe try Shilov tbh

For the abstract take, people seem to like it

[empty junco]

halmos misses like

jnf maybe

[keen orbit]

I'll try it and compare it to what I saw in axler's and friedberg's tysm for leading me

[empty junco]

also cramer ig

[empty junco]

well mot miss just doesn't do it in a based way

hmmm

what does it miss would you say

[keen orbit]

Is shilov's book the one from 1971 which has a pic containing cones and planes inteesecting them

[remote sparrow]

yes

[keen orbit]

Ok tysm for your time and have a nice day/night depedning on your time rn

[foggy relic]

Shilov is very good

Highly recommend

I read linear algebra done wrong before

pales in comparison

[foggy relic]

bc i didnt know of shilov at that time, not because i read it as a prerequisite

[keen orbit]

Ohh ok then shilov's is better because you tried both and are recommending shilov's

[keen orbit]

Is shilov's book the one from 1971 which has a pic containing cones and planes intersecting them

[sage python]

Yup

[remote sparrow]

btw i thought you didn't like shilov

[sage python]

The whole shtick about doing determinants right away feels like a bit of a meme

But I'm not gonna say outright that it's bad, it could work

And people seem to like it

[fickle bough]

how does he justify delaying determinants for that long I know he wrote some article somewhere about it but never got to finding and reading it

[remote sparrow]

the article's title is "Down with Determinants!"

[fickle bough]

the determinant cartel is about to send people after him

[remote sparrow]

https://golem.ph.utexas.edu/category/2007/05/linear_algebra_done_right.html

axler made a comment in this long discussion

[crimson leaf]

Maybe I'm just dumb (a very real possibility) but I get that axler thinks determinants and the characteristic polynomial give little insight and is overly complicated. But his approach I find to be much more complicated

[sage python]

So the thing is

Some linear algebra classes don't really give proper motivation for determinants

They say oh a determinant is, take a matrix, beep boop beep here's a number

Oh guess what invertibility = 0 determinant, so let's think of eigenstuff in terms of char poly

[restive hawk]

yeah

[sage python]

Problem is, eigenstuff is geometric by nature. An eigenvector spans an invariant line under a linear operator

So now your conceptual understanding of invariant lines has now factored entirely through number crunching

[crimson leaf]

We did some geometric motivation and then he basically just went afterwards "you got the intuition I assume every knows how to compute them"

[gusty smelt]

I mean the intuition for dets is really easy

[sage python]

The real strat is... don't think about determinants just as number crunching. You should think about determinants via exterior algebra, signed area

[gusty smelt]

say its area of paralliloped

exactly

and then the properties we want just follow from being multilinear and alternating

(i'd hesitate to use words like exterior algebras when explaining it to some 2nd year for instance)

[empty junco]

they gon learn

[gusty smelt]

Like you look at 3d and draw the paralleliped when one vector is a combination of the other 2

[crimson leaf]

This was a remedial/introductory course for 1st year master students

[sage python]

I mean I'm paraphrasing here somewhat. I'd need to think more about whether we should actually just go for it with the exterior products or not

[gusty smelt]

and oh hey look, a degenerate cube

volume = 0

oh wow this area captures ideas of linear independence perfectly!

[crimson leaf]

Usually people from other disciplines like physics or cs or coming from very weak schools

[gusty smelt]

I am more fine introducing exterior algebras then i think?

[sage python]

Yes but idk I've always felt on some level that ability to handle abstraction in math isn't a raw brainpower thing

Like, if you're smarter you can pick these concepts up more quickly/"fill in the rest of the sentence"

So some stuff can remain unsaid and all

But you can make the abstract stuff make sense, it might just take more time

[gusty smelt]

I think exterior products are more motivated once you did this thing with the determninant tbh

but also in a first year LA course this is the end of their usefulness

which is why I actually am not a fan of introducing them in first year

[sage python]

Possibly. I think multilinearity kinda comes up twice, in bilinear forms and in determinants

[gusty smelt]

multilinearity is useful enough ig

[sage python]

Hence why I'm entertaining the possibility of just giving full treatment of it anyway and making "the payout" of it be determinants + bilinear forms

[gusty smelt]

hmm imo both of these are kind of like, trivial cases so they should be motivation

rather than payout

[sage python]

Phsyics people like tensors in general anyway

Diffgeo at large

[gusty smelt]

sure but I dont like the thing of just saying "in a year or so these will be useful in diff geo!"

Like my school treated tensor not in LA but in diff geo, and I am fine with that

although maybe in LA some of it should be treated

[sage python]

I'm sorta fine with it, at undergrad level I think students should be willing to just say alright I'll trust that this is important to learn so I'll learn it. And it's easier here when it's just linear rather than in differential forms where you now have to juggle around smooth functions

Also minors now make a bit more sense

Since they're terms that come up when you take smaller exterior powers

[gusty smelt]

eh i mean this is kind of bad because diff geo is something that will be much later after LA

so by the time they get there, they will not have used it and forgotten it for example

I think "it is useful later" should be a last resort

[sage python]

Full blown diffgeo yes, but differential forms... it was less than a year for me 😛

[gusty smelt]

ok u went to uchicago that is an exception

[sage python]

I mean it's not just UChicago it's because they came up for me in Guillemin-Pollack

[gusty smelt]

In most places, LA is a 2nd year course, and you dont see tensors being useful until in 4th year UG courses or grad school

although in kenshin's context I am fine with teaching tensors in the LA class because its a remedial grad course

[gusty smelt]

also really I am only ok with this when said "later" is in the same course

[finite gale]

i think i saw tensors for the first time quite a bit earlier than when i actually learned what they were

[sage python]

Or even Spivak Calc on Manifolds lol, just my analysis class skimped a bit on differential forms

[finite gale]

because i really did not understand them when they were thrown on a pset for the first time

[gusty smelt]

I'd say a first year LA class should cover atleast inner products, so a natural time to talk about bilinear forms does arise there

and maybe one can mention A \otimes B there

but a first year LA class is already overtaxed with having to teach a lot while at the same time dealing with people who are for the first time seeing "real math", so idk if I'd want a full treatment of tensors

[empty junco]

the treatment of tensors/the exterior algebra in spivak calc on manifolds is a crime against nature

[sage python]

So I've heard

[restive hawk]

What is a good introductory book to combinatorics?

[remote sparrow]

do you know calculus

[restive hawk]

not really

no

[remote sparrow]

Mathematics of Choice: Or, How to Count Without Counting by niven and Introduction to Graph Theory by trudeau

[restive hawk]

ty

[fierce hedge]

So far I've only seen Vinberg motivates determinant as signed area. He shows all properties using the signed area geometrically.

[fickle bough]

Is rudin's book on measure theory and complex analysis well written

is it more in line with 1-8 of PMA in terms of writing quality or some of the later parts which don't feel as well written

[restive falcon]

why the predisent of cnada wrinitg maths book???

[fierce hedge]

prob finiding a new job before he's sent out of office

[flat jackal]

is there a best book for differential equations?

[alpine rover]

idk, but Zill is the best I’ve found

[hollow shore]

this is uncanny

I was gonna post about ode book recs since I will be taking it this semester

if anyone has some book/lecture notes recs, let me know

[crimson leaf]

Depends on what kind you want

[frail gyro]

Can anyone recommend the best book for real analysis or theory of real functions (besides bartle)? HELPES ME, COLLEGE LEVEL MATH MIGHT BE DA DEATH OF ME

[hollow shore]

a good balance of theory and computations

I did some looking up

is viorel barbu's text a good one?

[fallow cypress]

abbott is very slow and gentle

terrence tao's is also very slow

you might be interested in them

they are both very good expositors

[spark basin]

@fallow cypress then rudin is fast?

[naive jackal]

hii can you guys please refer me books on probability?

like the beginner ones

because i dont know anything abt it

[fallow cypress]

I'd say it's pretty terse yeah

Makes you figure out a lot of it on your own

Which isn't really bad

[fresh moat]

aops' introductory book on counting and probability is good

[naive jackal]

thank you its so costly in my region TT

but ill try to find its pdf instead

[crimson leaf]

Imo this makes Rudin about the same speed as something like abbot since you're spending more time figuring things out. Not a bad thing though

[fallow cypress]

Yeah I liked Rudin

[flat jackal]

i would say a book with a lot of problems and a lot of techniques in solving them, as well as solutions and a book that’s not too swarmed in text

[crimson leaf]

I guess you want zill then since most higher level text probably won't have solutions

[flat jackal]

lemme search it up

[fresh moat]

its rlly worth it

[delicate hemlock]

Are there any standard references for Picard-Lefschetz theory? Maybe something analogous to Milnor's book on Morse theory

[pliant stream]

What is your level of math?

For me, the standard is grimmett and stirzaker

[naive jackal]

its high school

[pliant stream]

A bit vague

since this is a math server, the answer is if you don't know calculus yet, you should learn calculus first

Otherwise, there are statistics books, some certainly of questionable quality, but these can be read without calculus knowledge

[quiet moon]

HELLO?

[clever fox]

HELLO!

[crimson leaf]

Well the first two problems are 1 this is a math server and 2 I don't think Neil Degrasse Tyson has many papers in which he solves a problem in physics

[naive jackal]

oh sorry i meant like 12th grade high school

i do know calculus

like the basic stuff they taught in 11th and 12th

outside of that i dont know

[bleak pebble]

dear all I am searching a good book ok spectral graph theory. I am particularly interested in the link between eigenvalues of adjcency matrix and walks and paths on the corresponding graph. This is due because I am challenging by the recent paper Unsolved Problems in Spectral Graph Theory https://arxiv.org/abs/2305.10290. Any suggestion?

[fossil arch]

Any cute books on less-common integration techniques?

Like anything more than the standard stuff you learn in a basic calc2 class

For example, I’d consider the standard technique for the Gaussian as a “less-common” technique

Or any of those wacko substitutions people on MSE use for those wacko integrands

[remote sparrow]

#book-recommendations message

[fossil arch]

sour bop (☞⁰ヮ⁰)☞

thank you king

[remote sparrow]

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

[frail gyro]

thank you thank you

gonna look those up

[fossil arch]

4 chan science fandom 😭

[onyx cobalt]

[chrome yacht]

i recommend amann escher

[fossil arch]

I second Amann-Escher

I also like Abbott a lot, and Pugh for a visual resource/supplement after you’ve had some experience with the concepts

[pliant stream]

NO

Strichartz FTW!!!

[heady ember]

There's a book called almost impossible integrals, have you checked it out before?

[fossil arch]

Springer book springer book springer book yay!

I have not

[pliant stream]

SPRINGER BAD

[fossil arch]

I will skim through it :D

[pliant stream]

WORST print quality for MOST expensive book

everything these dyas is just made WORSE and WORSE

[mystic orbit]

[fierce hedge]

Gen alpha crying in a corner

[pliant stream]

i just learned that gen alpha follows gen Z

...

[desert pulsar]

I love this website because I stumbled on their guide to self-studying maths when I was in high school and they suggest you learn non standard analysis with infinitesimals as your first introduction to calculus.

[coral prawn]

how'd that go?

[desert pulsar]

They insist that it's much more intuitive but I honestly found epsilon-delta stuff far easier than trying to resolve simple limits with infinitesimals. It just didn't fit in my head. Of course, you also have the big elephant in the room of all the mathematical machinery in the background to make infinitesimals make sense.

And at the end of all of it, you'll have learned a really weird approach that no-one ever actually uses. What's the point of learning theory if you can't use it as a shared language to communicate your results to someone else?

[coral prawn]

this gotta be the top reasons on my list on why not to trust fandoms. Well said tho

[wicked fractal]

LMAO

[desert pulsar]

It's still better than all those dream fiction wikis that exist just to ruin search results.

[wicked thunder]

Reminds me of this guy who made a website and introduces model theory and set theory as an introduction to mathematics for "clever undergraduates". It looks interesting but I'm not qualified to talk about whether it's correct or not http://settheory.net/

[gray gazelle]

can somebody suggest me a good book for analysis

[mystic orbit]

omgggg

[gray gazelle]

"12th grade hs" can differ a lot e.g where I live, there's very minimal calculus

[chrome yacht]

#book-recommendations message #book-recommendations message

[gray gazelle]

alr alr thanks

[mystic orbit]

introductory I assume?

don't do tao, he introduces so much set theory you'll grow a beard before finishing it

do abbott if you're not very used to proofs

use pugh for something quircky

[gray gazelle]

If i've never taken proofs, am I in a fine position to take sheldon axler or stephen abbot

[mystic orbit]

heard good things about schroder and (brouwer?)

[mystic orbit]

you need at least some familiarity with proofs

have you done discrete math or smth?

[gray gazelle]

ok so if I've done 0 proofs whatsoever, where should I start

[gray gazelle]

no

[mystic orbit]

you can look at loch's intro to proofs

you can find it pinned in #proofs-and-logic

[gusty smelt]

you learn proofs by doing it, read one and give yourself extra time during the reading to write up proofs etc

[gray gazelle]

ok so I take it: Loch's intro to proofs --> Stephen abbot analysis

real anal will be my first class in uni so I would like to get some headstart in that, how much time would you estimate I would need to spend on loch's intro

[mystic orbit]

I dunno I think reading a brief intro to different proof techniques is pretty efficient

[gusty smelt]

eh i think its entirely unnecessary

[mystic orbit]

especially stuff like propositional calculus stuff

[gray gazelle]

i take it spivak isn't very good

[mystic orbit]

like how to negate them and how "if" is a combination of "not" and "and" etc

[gray gazelle]

is proof writing consistent across languages, e.g if I go through english books with proofs and then my uni class is in french, I'll be fine right

[mystic orbit]

depends on your background

like, if you did contest math you can do it in a day lol

[gray gazelle]

wdym

[mystic orbit]

it'll likely take you at least a few days I don't really know lmfao

[mystic orbit]

sry, I meant competition math

[mystic orbit]

ofc

math is math

https://tenor.com/view/math-meme-math-is-math-meme-mr-incredible-the-incredibles-the-incredibles2-gif-20591317

[gusty smelt]

darq would know, he also likes math in french!

[mystic orbit]

I did learn intro to proofs in french

[naive jackal]

ohhh yea then let me specify, ive learnt limits continuity differention integration

[flat jackal]

what is the best book for learning complex analysis

with a lot of problems+solutions too

[chrome yacht]

#book-recommendations message you might wanna read that

[remote sparrow]

it's browder

[mystic orbit]

oh yea

[tardy oasis]

brouwer is for fixed point theorem

[green estuary]

Hello guys, I am looking for a book (or a list of books) to study the real numbers i.e from the construction of the real numbers, to its "cool" propreties. I want to know more about transcendental/algebraic numbers. Furthermore, it would be cool to see some book that studies R as Q vector space and give applications to it ( I tend to see it as an example in every linear algebra book but I haven't actually seen someone who give an "application" of it).

[velvet briar]

@green estuary
So a construction of the real numbers is a real analysis book. Imo, look at Tao's analysis 1, great book. Easy self-study.

[green estuary]

Thanks for the recommendation!

Any other suggestion for the other topics is very much appreciated.

[scarlet steeple]

his book is too pendantic

[scarlet steeple]

rudin is good if you are already mathematically mature

[dense pumice]

Understanding Analysis by Stephen Abbott is very good imo, though it doesn't start from a construction of the reals, it starts with the axiom of completeness (Every set has a least upper bound) and goes from there

And there's a construction of the reals from the rationals at the very end

[heady ember]

Counterexample: I competed Enderton and have not grown a beard

[steep spade]

Book reccomendation for set theory?

[remote sparrow]

👻

#book-recommendations message

there is also halmos, which treats it in a naive way

[inland elm]

i like halmos a lot

[heady ember]

Do you want to learn set theory for the sake of set theory or for other stuff?

[steep spade]

okay

[steep spade]

I want to learn for probability and linear algebra

[fierce hedge]

just you just need to know some very basic set theory which the books will already have in first chapter

[grand thistle]

you wont need a whole book on it then

i agree with numbpy

just look at the first chapter of ur probability or linalg book

you should be fine

[steep spade]

oh 👌

[chrome yacht]

maybe Simon's comprehensive course in analysis part 1? it looks very conversational but i don't know if it is any good

[gray gazelle]

mhm

[gray gazelle]

alr thanks for the suggestion

[wispy root]

Any books for trig?

Understandable to a 15yr old

[safe wyvern]

SL Loney
Any standard high school math book?

[mystic orbit]

not a book but I suggest khan academy

it's likely better than any book you might find

especially if you're not used to learning from books

[wispy root]

Thanks chmoneky and aplha

[onyx cobalt]

[mystic orbit]

I'm not chmonkey

I'm his enemy

[onyx cobalt]

now u are

[mystic orbit]

I'm not chmonkey

[stuck zephyr]

[rigid barn]

Whoever fights chmonkey should see to it that in the process he does not become chmonkey. And if you gaze long enough into a server, the server will gaze back into you.

[rigid barn]

You won't find stuff about trans/alg numbers or Hamel bases (basis of R as a Q-VS) in an analysis book. Try Niven's "Irrational Numbers" for the former, iirc the prerequisites are minimal. IDK any books that touch on Hamel bases, maybe some functional analysis ones do. For a construction of the reals and some of their cool properties (e.g. unique complete ordered field) see Ebbinghaus' "Numbers".

[dapper root]

[stuck zephyr]

[tender river]

chmonkeying goes to Chmonkey Thread #1061337023413244018 message

[green estuary]

Thank you for these suggestions, they are exactly what I was looking for!

[rigid barn]

de nada

[safe wyvern]

Glad to help!

[gray gazelle]

Is there a book I can find about Trigonometry and Calculus?

[charred abyss]

Stewart's Precalculus and Calculus.

Although you don't need one, i've found it quite useful to have a graphing calculator while learning Calculus

[gray gazelle]

Thank you!

I need it for advanced reading

[dim condor]

Any good geometry book ? Level should around stuff like ioqm , amc10-12

[marsh lodge]

Any great books for calculus 2 and calculus 3 separately?

[astral pumice]

Ping me

[pliant stream]

see chapter 1 of grimmett and stirzaker

[sick root]

Any recommendations for introduction to topological groups ?

[rigid barn]

chapter 1 of Fourier Analysis on Number Fields is dedicated to TG and the Haar measure

Stroppel's Locally Compact Groups

Deitmar's A First Course on Harmonic Analysis

[sick root]

thank you for your recommendations

btw i want to start reading about polish groups but i have no idea about toological groups so i am thinking i should start from that, right ?

[rigid barn]

idk what polish groups are, i assume it's TG that are polish spaces?

so i'd say yes

[sick root]

exactly

thanks again

[molten pendant]

are there any easier, more friendlier books on topology other than munkres?

or maybe i should just try harder?

[remote sparrow]

Topology without Tears by morris

gamelin as well

[narrow relic]

What part are you having trouble with?

[hexed basin]

any book recommendations for functional equations ??

[junior drum]

Any platform recomendaton for learning trigonometry,calculus,logrithm,vector ;

and many more topics

[dim sierra]

Khan Academy

[junior drum]

because i am currently in lower grade but had a huge intrest in learning concept from higher classes

and preparing for IIT-JEe

[junior drum]

thanks bro

[orchid mortar]

Gamelin has topo?

[crimson leaf]

Probably Gamelin and Greene the dover book

[deep summit]

David summit abstract algebra has the maximum topics covered right ?? Do you recommend it to a beginner in pure maths ?

If no then what is the best abstract algebra books u recommend but it should cover all topics.

[pliant stream]

this requirement doesn't make any sense

[deep summit]

Half knowledge is a dangerous thing

[fierce hedge]

all topics?? Unless you mean all topics taught in usual algebra courses then yes DnF is enough

[pliant stream]

again this requirement makes no sense

not to mention college course often skips through significant parts of a text

[fierce hedge]

yeaah, I'd recommend to tally with some algebra course otherwise it'd a huge time commitment

[sleek canyon]

any book recommendations for the more applied side of maths? like statistics and data??

[pliant stream]

what do u want to do with statistics

statistical theory? machine learning? machine learning theory? applied stats?

biostats? epidimeolgy? econometrics? etc.

[sleek canyon]

machine learning or applied stats would be cool, but if you have any of the others, that would also be very useful

[pliant stream]

for machine learning, kevin murphy's book

for applied stats, idk

[pliant stream]

also check out https://www.nowpublishers.com/MAL and related series, though this is mostly academia stuff

[deep summit]

Yes we should have a code word for that, all topics asked in usual real analysis courses, do you know a book for ATAIU real analysis courses aswell ?

[pliant stream]

literally ANY real analysis book lol

as said before, courses skip through books

[sleek canyon]

thank you !!

[sleek canyon]

oh okay tysm

really helpful

:)

[pliant stream]

for applied stats, you also have bayesian stuff from like gelman and his books

[sleek canyon]

ohhh okay sounds good thanksss

[pliant stream]

and there's stat foundations of data science, not sure how applied it is though

[sleek canyon]

are there any books in general youd recommend for a mathematician

oohh

[deep summit]

I was thinking about abott or bartle, abott seems more expressive but it leaves a lot of work for readers, and as a self learner i would not know if my proofs are right sitting at home, soo bartle seems better

[sleek canyon]

im interested in data science so that could be cool

[pliant stream]

elements of stat learning is somehow the classic, but it's written in 2003 so SUPER outdated

[sleek canyon]

so far ive only read fermats last theorem

[pliant stream]

u mean like

[deep summit]

There is funny book on history of goldbach conjecture

[pliant stream]

any analysis book will cover the contents of a first semester analysis course

[deep summit]

Which book do u recommend

[pliant stream]

strichartz way of analysis is an OK book

[deep summit]

How come book of 2003 is outdated but david abstract algebra of 1963 is still recommended

[pliant stream]

1. I have no idea what david abstract algebra is 2) they are different fields

[crimson leaf]

He's referring to D&F

[deep summit]

Dummit

[crimson leaf]

But as Andrew said different fields and different audiences

[smoky sandal]

May I know wt's a gd reference for learning p-adic analysis?

[hollow shore]

can you share with me your homework psets assigned from silverman's aa text? I plan to work through the book.

[sacred turret]

Is anyone here familiar with the book Discrete Mathematics and its Applications by Kenneth H. Rosen? The book has many different editions, and I wondered if it mattered which edition I would buy. Are the solutions to the exercises also included?

[charred abyss]

Solutions would be online if not already in the book, but I believe solutions are included, yes.

[daring lake]

Lang covers a lot but it's quite terse. D&F is much more nicer, I used it for groups, rings and fields.

[charred abyss]

Artin.

[remote sparrow]

abbott wrote a partial solutions guide and there is an unofficial complete solutions guide online

[pliant stream]

https://www.amazon.com/Brownian-Martingales-Analysis-Wadsworth-Mathematics/dp/0534030653

good book

[charred abyss]

Are you memeing?

[quick hornet]

why are you replying to a post i sent 2 years ago

i guess the answer is yes

but

???

[tardy oasis]

Same

[junior isle]

Is friedberg insel and Spence better than Hoffman kunze???

I'm learning about the computations aka RREF, but then after vector spaces are introduced It seems like a waste to keep reading an introductory book like hefferon If i already know the computations and have some math maturity

Any thoughts?

[rustic grove]

If what you are saying is that you are learning linear algebra for the first time, I would suggest you keep an 'introductory book' for reference as the matrix approach to linear algebra is very useful in applied mathematics and for this reason is usually someones first experience with the subject. If you wish to use a more rigorous book like either of the ones you mentioned, I personally prefer Insel and Spence. It has more exercises that have a wide range in difficulty from computational problems to harder proofs. They both cover similar material...

[junior isle]

Do they really cover the same? It seems from the table of contents that hoffman and kunze has more stuff, like Jordan forms and polynomials

[pliant stream]

meh...what you should read depends on your interests really

don't read an entire book on lin alg just because

[rustic grove]

I believe Spence has a chapter titled 'Canonical forms', which covers this

[mystic orbit]

is this a meme?

[analog lava]

the rising sea by ravi vakil seems a friendly and nice intro

what prereqs does it require?

[acoustic imp]

What is your background? A sure-fire way of gauging this kind of thing is to simply throw yourself into the deep end; it will be apparent rather quickly if you are ready for it or not.

[analog lava]

idk if the hungerford algebra is enough

i know basic point-set topology

basic real analysis , super basic little commutative algebra

and very very little diff geo

not even diff geo more diff topology ( manifolds )

[junior isle]

Just because?

[narrow relic]

What's "nlab"?

[sturdy shore]

a website

[humble walrus]

is there some cutoff to how long ago we can reply to posts? 🤨

[finite gale]

use common sense

[toxic stone]

Australian Signpost Mathematics New South Wales 10 (5.1-5.3) Teacher Companion, 1st edition<- this book got a pdf?

Tried looking on google, couldn't find it

[limpid rose]

Hey guys does anyone know about a cool recreational math book?

Something for long train rides

[hollow shore]

you can check out gardner's logic puzzle books

[covert bane]

To Mock a Mockingbird by Smullyan is nice

[wicked thunder]

Imagine necroposting

[safe barn]

No but it’s usually pointless and unnecessary to do so, especially if it’s so long ago that the person who sent the message forgot the details of their message

[brisk rapids]

I'm learning real analysis from Bartle but is there a book that can help condense the calculus you'd need to know for a UG physics course?

[gray gazelle]

what are some good books for Algebra 1?

[chrome yacht]

you might wanna take a look at schroder's analysis book if you need something concise

[gray gazelle]

Actually is Paul

's Online Notes any good?

[brisk rapids]

Okay

[tardy oasis]

Haven't used his notes for algebra, I used them for calculus sometimes, but they are good. Not sure how they are if that's all you're using, probably best to use a textbook in addition, but they have good exercises and good explanations of stuff if you get stuck

[errant heath]

Are there any books for proper note taking, specifically for math books?

[vestal comet]

A good question

[mossy flume]

it's such a personal preference type thing

I don't think a book would help

[remote sparrow]

don't take notes

[mystic orbit]

it'd be so funny if such a book actually exists

[wicked fractal]

Actually a good question

[errant heath]

Why?

[mystic orbit]

coz it's such a niche subject

and any book on it would likely cover more info about it then anyone would need in a lifetime

[wraith edge]

obsidian techniques might

[finite gale]

there are people who don't need to take notes at all, and there are people who write down a couple important notes to keep in mind while reading

i think this also dependent a bit of how much reading you've done in the past as well

and/or what you are reading and how much time you have and/or how much you need to retain

but obviously, you shouldn't write down everything you see

but for reading some textbook, i find it nice to try to understand some of the motivation behind things then for important statements, write them down and try to prove them myself while reading a little at a time for hints as needed; though of course this is not very feasible to do for every statement one comes across

[flint hill]

Do you have any books suggested for abstract algebra? If yes, please state the name of the book out.

[remote sparrow]

there do exist books which people recommend for abstract algebra

true statement

[tardy oasis]

Dummit and Foote is a typical reference

Also it's in one of the pins

[remote sparrow]

is this a graduate or undergrad class

[flint hill]

ug

grad book is fine as well

[remote sparrow]

are you an honors or regular student

[flint hill]

I'm just a freshman starting next few weeks

[remote sparrow]

judson or pinter

[flint hill]

I finished baby Rudin until chapter 8

and did some real analysis

[remote sparrow]

dummit and foote is ok too

[flint hill]

books

okay, thanks

Is your profile from Hyouka

[remote sparrow]

yes

[wicked fractal]

Book recommendations for algebraic topology

[fierce hedge]

Hatcher is the default recommendation, there's Bradon which is harder and does manifolds also. I've heard good things about Hudson Sato but this is not a textbook, more of a intuition provider I'd say.

(I haven't used any of them beyond few pages so I can't vouch for any of them)

[gray gazelle]

does anyone know any quality books about algebra 1

[valid monolith]

Any of these covers what you are looking for? Algebra 1 bumfel
Algebra 2 bumfel
A new algebra 1 bernad child
A new algebra 2 bernard child
Higher algebra hall and knight
Higher algebra bernard child

[slim bramble]

That's how I take notes.
1-Read the chapter.
2-As you read note down the formal stuff: like definitions, theorems, properties, etc. basically anything that you'll need to remember when solving problems on your own.
3-As you solve the problems write down interesting problems to remember them: problems that are fun, hard, or Insightful; this way you can retain something interesting to talk about in conversations about your topic or discussions
4-Save your notes, so that you can use them as a reference.

*you really don't need to worry much about retaining information from the chapter, if you solve enough problems. it'll stick, and for the future you have your notes as a reference

*make your notes nice and tidy. take care of your handwriting and learn some pretty fonts. I use spencerian font personally. it makes writing fast and fun.

[upbeat vine]

This is how I take notes.
1- Start with the chapter.
2- Write down the definition and preferably some examples. Ensure that the examples aren't taking up space (if you use a note-taking app, enlarge and place examples in a mind-map form).
3- Go ahead and write down the theorem. Read the proof (or a step of a proof) once and then try to recreate the proof in Latex. Once the proof is completed, take a screenshot and resize the proof and paste it in front of the theorem. This ensures the proof doesn't take away the space and is easily viewable.
Mind map any additional remarks regarding the claims so that they don't clutter and are easily viewable upon zooming in.
4- Connect your theorems and corollaries with any additional arrows for faster viewing.

This is how they end up looking:

[wicked yew]

Can someone recommend me a good book for math newbie like me that teaches trigonometry, algebra, & geometry to help me understand calculus? Thanks I really feel like I'm the dumbest person wanting to bang my head t wall I haven't even frickin got a correct answer even frickin once I feel very stupid

[rustic grove]

Can someone please list some books that can take you from no abstract algebra to a high level. I take it this year and would like to have some resources ready 🙂

[heady ember]

look in pinned

[slim bramble]

@upbeat vine @errant heath This may be interesting to you I recently discovered "cornell note taking" you can look it up online pretty useful at retaining info from a fast pace source like lectures or when you want to read textbooks pretty fast and also be efficient. i used it for philosophy books and found them useful

[upbeat vine]

I have seen that before: I think it might work for more prose-styled disciplines, the structure doesn't really make sense for math.

[molten pendant]

does hubbard hubbard's vector calculus require analysis as prerequisite?

or can I just dive into that book with calc 1~2 experience on the level of stewart

[sterile pelican]

I uhh read the section like a novel then write some examples in some parts I don’t get, then do the exercises while navigating back on the definitions, steps and theorems when needed :^)

[slim bramble]

agreed

[gray gazelle]

what are some good books for highschool algebra? (alg 1 and 2)

[mystic orbit]

no a book but khan academy is golden

[gray gazelle]

Okay. Can I use Khan Academy and Paul's Online Notes? Or do you think Khan Academy is good enough.

[mystic orbit]

you can use both if you want ig

I dunno if one has anything that the other doesn't tbh

nah, I'm pretty sure khan academy has all you need

[gray gazelle]

okay

for just algebra 1 and 2?

does it have precalculus there too?

Or do u recommend reading

[errant heath]

peep through this: https://openstax.org/details/books/elementary-algebra-2e

[gray gazelle]

whats this

[errant heath]

openstax has a ton of free online books.

This is for Elementary Algebra.

[gray gazelle]

Okay. Thanks.

so, elementary algebra is what? alg 1?

[errant heath]

hmm. I don't remember.

Are you taking a algebra class soon?

[gray gazelle]

yeah

never the less these are new topics for me

most of them at least

so i appreaciate it

[errant heath]

For sure.

[errant heath]

I have two I can send you.

Also, I would check this out: https://www.amazon.com/Intermediate-algebra-college-students-Leithold/dp/0023696001

I think you can get the PDF online. It's got more rigor than other Algebra books.

Just so you know, if you want to do pre-calc, you'll need trig.

From openstax: https://openstax.org/details/books/precalculus-2e
From Stewart: https://www.amazon.com/Precalculus-Mathematics-Calculus-James-Stewart/dp/0840068077

More Challenging book: https://www.amazon.com/Before-Calculus-Functions-Analytic-Geometry/dp/0673469115

[gray gazelle]

Does James Stewart have any Algebra books (Algebra 1 and 2)? I hear he is a great author

or does he only make books in the "calculus field"

[chrome yacht]

i don't know what algebra 1 and 2 are but james stewart does have a book titled College Algebra it seems

that is over 800 pages, a much shorter book would be algebra by gelfand https://books.google.com.np/books/about/Algebra.html?id=Z9z7iliyFD0C&redir_esc=y

[gray gazelle]

it seems to cover very little

I would like to know if anyone has any books about Algebra 1? or maybe a book combined of Algebra 1 and 2

lmk

[rancid hollow]

Any book recommendations to get more practice with problems like this? https://math.stackexchange.com/questions/2397182/point-in-triangle-with-maximum-distance-from-vertices

I had to look up how to prove this for a problem in Dumbo and Feet 🙃

But thats an abstract algebra book it has no lessons or practice problems for geometry

[fierce hedge]

most likely olympiad books on geometry, maybe check aops books

[gray gazelle]

does anyone know any good books about Algebra 1 and 2? Individual books or combined doesn't matter

[rancid hollow]

Bet ty

[gray gazelle]

it would even work if you we're to send some sort of combination such as Algebra and Trigonometry i dont mind

but I would appreciate if it included Algebra 1

[maiden quarry]

anyone know any good books just for recreational reading? I read the math book by Clifford Pickover and thought it was interesting, but I'd like something more in-depth and concentrated

[pliant stream]

Fourier analysis by stein and shakarchi

[weary cape]

https://openstax.org/books/elementary-algebra/pages/1-introduction

[gray gazelle]

is this algebra 1 and 2?

[azure ridge]

gravitational pull of the sun

[slender cargo]

I'm at chapter 10 of Spivak's Calculus now for self-study. This book is weirdly becoming easier as I progress through it. Also was definitely the right choice versus Abbott since I had not taken calculus in forever

[wicked fractal]

Thanks. I'll take a look at them.

[flat jackal]

is there a best book for proof writing?

I’ve looked at a few such as the one by Jay Cummings and Gary but there isn’t really many problems

a book with a lot of problems that isn’t too overwhelming too read would be good❤️

[gray gazelle]

Any suggestions for a text on Measure Theory?

heard Folland is quite good but it seems to be overkill for what i need

Algebra 1 as in high school algebra?

[remote sparrow]

axler has a free one online

the masters program at my school uses it

[gray gazelle]

I see

any other suggestions?

[remote sparrow]

there are some more suggestions in pins

[gray gazelle]

ah

thanks

[remote sparrow]

of note is bass, which is also free online

there is a hard copy available on amazon but bass is no longer providing the latest edition there

however, it's easy to work around this if you upload the pdf for lulu to print

schilling is not free, but he has a full solutions manual available for free on his website

[junior isle]

Hammack has a lot

At least i thought so

[sterile pelican]

A book I read before was Gelfand's Algebra, and his Functions & Graphs book followed by Serge Lang's Basic Mathematics

[sterile pelican]

Velleman is a good book since he goes deeply on proof writing

[prisma loom]

By any chance, good friend, might you be willing to share a full-resolution version of thy profile picture?

[slim kestrel]

hi everybody ^^ Im going to uni next month and I'll study macroeconomics, microeconomics and advanced math in English (Im living in a non English-spea country). Any recommendations for books related to these? Thanks a lot!

[primal glade]

Any online book recommendations to be proficient in maths?
Like High School level...
I like: algebra, geometry, proofs, etc

[wispy bison]

have you looked in #books-old

[primal glade]

No, I didn't.
Thankssss
Can you recommend me?

[wispy bison]

no, I don’t know that many books

[primal glade]

okay I'll choose 1

okay

This is like a lower level :/. I have already studied them.

[grand thistle]

lang basic mathematics

[tender river]

i don't get it

[primal glade]

?

[tender river]

you asked for a high school level book and that book even order group linked (judson abstract algebra) is a uni level and somehow you have already studied that?

[primal glade]

That's univ level?

[grand thistle]

yea

[primal glade]

It looks like grade-7/8

[mellow wren]

wat lol

have you opened up judson?

[primal glade]

p.s. I read only the first few pages 💀.
It had some quadratic equations and set theory.

[tender river]

since when did they start teaching permutation groups and lagrange's theorem to 7th and 8th graders

[primal glade]

bruh, he deleted the link of that book

Idk if you meant books from #books-old.

[mellow wren]

http://abstract.ups.edu/aata/aata.html

[primal glade]

yes

[tender river]

this was the book even order linked http://abstract.ups.edu/aata/aata.html

[primal glade]

yes

but isn't that simple maths book?

[mellow wren]

look at like chapter 3

[grand thistle]

do you know what a group is

[primal glade]

OMG, I didn't check the book. Just the contents of the first 3 pages.
I thought the book was over.

Cryptography (cryptocurrency is based on it.)
Is actual math topic 💀? Like frrrr

[primal glade]

It's like a matrix

[tender river]

#book-recommendations message try this book

[jovial parrot]

hello pika

[shadow hedge]

Is chapter 3 (Counting) from the book of proofs by hammock important? I am currently struggling with the second part of this chapter mainly binomial theorem, counting multisets, pigeonhole principle and combinatorial proofs. I am reading this book to prepare for my bachelors which starts with real analysis. Can I skip this part for now or is it important later on?

[empty junco]

that all sounds unavoidable

[dapper root]

Supremely important

[shadow hedge]

So should I be able to do every exercise?

[empty junco]

uh

well maybe idk how hard they are

[subtle fractal]

any suggestions for a book that contains problems with legendre symbol

[narrow relic]

I read a lot of Schilling and liked it. It starts with abstract measures from the beginning

[empty junco]

sto loved schilling

shoutout to sto

[narrow relic]

Who is that?

[empty junco]

some guy

[narrow relic]

Okay.

[remote sparrow]

intro real analysis, afaik, doesn't really use a lot of those combinatorial techniques

you can skip this chapter for now if you're struggling, but come back to it later

[remote sparrow]

the only books i know of that contain problems with the legendre symbol are elementary number theory textbooks, which introduce it as a tool to develop quadratic reciprocity

dudley or burton are examples of such texts

[grim wolf]

Recommendations for books\online resources for learning geometric algebra?????????

[weak fox]

Hi gang,
I recently studied Multivariable Calculus and Vector Calculus, and completed the adequate resources provided,
But, I feel I don't have enough practice as the assignments had very few problems.
Can anyone please direct me to books/assignment which I can solve.
Thanks

[broken meadow]

Look for any calculus book by Stewart or by Thomas

I cannot provide these books to you myself because piracy is against TOS

so i would do some googling

[remote sparrow]

https://www.amazon.com/Calculus-Multiple-Variables-Essential-Workbook/dp/1941691374

[remote sparrow]

https://home.csulb.edu/~tgao/TEACH/2010F/M485/syll485.pdf

i found a professor using this book

[crimson leaf]

I actually ended up getting a book one of my professors strongly recommend and it's written by a friend of his it seems pretty good so far. "Linear Programming with Matlab" we're kind of doing a directed study this semester too now which is cool

[remote sparrow]

👍

[gray gazelle]

what are some good books regarding Algebra 1 and 2 (highschool algebra)?

[wispy bison]

#discussion message

[valid monolith]

@numbpy Algebra 1 bumfel
Algebra 2 bumfel
A new algebra 1 bernad child
A new algebra 2 bernard child
Higher algebra hall and knight
Higher algebra bernard child

[subtle fractal]

Could anyone recommend me good books about complex numbers(it would be nice if it has problems ranging from basic to olyimpiad level)

[gray gazelle]

Hey i want a book that covers math from grade 1 to college
I am in bca degree program
I had mathematics in school but
I was not good i would like to study everything from basic to advance

[valid monolith]

Is grade 1 what year old?

[stuck agate]

whats your age?

[gray gazelle]

basically elementary subjects to college subjects

1. im not sure if they have one huge book

2. I do not know the contents of a college course

but I would assume you want to start with preAlgebra?

because im sure everyone know arithmetic

meaning

simple arithmetic

[valid monolith]

That's what i was thinking

[gray gazelle]

i think "grade 1" is exaggerated

[valid monolith]

That's why i asked what year is grade one

[gray gazelle]

prealgebra is where you should start

everything before that is fairly simple

[valid monolith]

Because could be either 1 or 1 or hs

[gray gazelle]

I think a middle school to college course

middle school (depending on where you're from) normally covers prealgebra

[valid monolith]

Yeah

[gray gazelle]

maybe late elementary

so

hm

one second

[stuck agate]

@gray gazelle

[gray gazelle]

Because, personally, I didn't read prealgebra much

I read like one AoPS book

about prealgebra and got it over with

[valid monolith]

You are right, i was just confused because generally in year 1 you just learn to count

[gray gazelle]

it was painful trying to read the same things

though there was some useful information

though aops is normally good for competition

i really like it

I like "The Basics and Beyond Series"

I would recommend giving it a try because it has a lot of information

so AoPS is really good in that field

if you're looking for a more strict curriculum inside a book

and want prealgebra maybe

hmmmmmmm

[valid monolith]

I have seen some books titled pre algebra but don't know anything else about it

[gray gazelle]

yeah I say go for PreAlgebra by AoPS

but considering you want to learn college mathematics

it will probably bore you

[valid monolith]

I mean is pre algebra, don't know to what extent the expectation of a college experience holds

[gray gazelle]

Gelfand's Algebra is pretty standard

and Serge Lang's Basic Mathematics

I got these books recommended to me and they're pretty standard

[valid monolith]

Oh i liked basic mathematics

[gray gazelle]

so this is getting passed down

But start with Gelfand's Algebra

or any other Algebra 1 book

Gelfand's Algebra is solid but there are other books

Serge Lang's Basic Mathematics is golden

but don't just depend on these two books

if you're serious about this you'll have to read more then this

well i mean

not for prealgebrs

in general

[valid monolith]

I left a list of elementary algebra books above

[gray gazelle]

considering you also want to learn other subjects

oh yea

thx

[valid monolith]

I personally bought a new algebra one and is good the rest are avaliable online for free

[gray gazelle]

if you want to read about Geometry i think Euclidean Geometry in Mathematical Olympiads is pretty good

but I'm not sure about the level of that book

[valid monolith]

Yeah

[gray gazelle]

Sullivan's Algebra and Trigonometry is solid for PreCalculus

but there's probably better picks

[gray gazelle]

are you saying you want like a book that covers all these subjects in one'

because there is probably such a thing

but it doesn't widely explain

the topics

[valid monolith]

You could do pre calc by separating the topics, as opposite as looking for pre calc books

[gray gazelle]

unless it has like 4000 pages

[gray gazelle]

that also works yea

it's probably better that way'

[valid monolith]

There is one book that comes to mind but i still don't think it does it... I'll try to remember the name

It's a russian book originally i think

[gray gazelle]

because if the book is specifically for precalc it may not cover everything you want to know

[valid monolith]

Yeah

[gray gazelle]

regardless

i dont think you want a huge book

it wont cover everything you desire

you'd be missing out

i suggest taking your time studying mathematics

idk

that's my approach more or less

[gray gazelle]

Hey sorry for the late response
But i just need something that gives a brief intro to things.
Because i gave first sem exams and i feel like i have forgotten everything ,and i would like to practice some questions.

[junior isle]

What do guys think about Jay Cummings analysis book

[heady ember]

#❓how-to-get-help

[keen depot]

Hey everyone, I was wondering if any of you would recommend reading Wittgenstein's Lectures on the Foundations of Mathematics.

I am quite familiar with Wittgenstein's work in philosophy of language, but since philosophy of mathematics fascinates me as well (already read Frege and Russel, and I'm quite familiar with Leibniz, whom I'd call some of the main figures of this branch).

My doubt lies in the fact that Wittgenstein was not a mathematician (something he points out at the beginning of the book, at which I had a look). I don't want to get into the book but get very little substance out of it

[gray gazelle]

Intro to Everything?

or like algebra and calculus and stuff

When you say this I think of Algebra to Calculus or Algebra, Calculus, Linear Algebra, Abstract Algebra, Discrete Mathematics, Proof Writing, Real Analysis, Complex Analysis, Probability, Statistics, Number Theory, Algebraic Geometry, Topology/Algebraic Topology, Numerical Analysis, Dynamical Systems, Combinatorials, etc.

like all of math>

I mean

There is one called All The Mathematics You Missed but it's quite advanced

All The Mathematics You Missed [But Need To Know For Graduate School] is good

by Garrity

when you say a "brief introduction"

check the video the math sorcerer made on youtube for the contents

but im not sure since you say "Grade 1"

[tacit niche]

I'm taking a course in automata theory next sem, but my proof skills are really weak. I already took discrete math, but we didn't have a textbook and we didn't cover proofs too much. Do you guys have any website/book/etc. recommendations to improve?

[gray gazelle]

for proofs?

[tacit niche]

yeah, mostly

[gray gazelle]

I really like How to prove it: A structured approach by Velleman

you don't really need that much of a background

in proofs

and the author explains the contents very well

[tacit niche]

Thank you so much!

[gray gazelle]

sure

[gray gazelle]

Definitely check out Sipser’s Theory of Computation once you’re done. It’s a great read

[lime sapphire]

a concise introduction to pure mathematics by liebeck

[gray gazelle]

does anyone have any good books in mind for alg 1/2

whar

[atomic moat]

@urban summit
https://drive.google.com/file/d/1qc8sIXPUzg758Kr5swr6DBMi_EZt9ClU/view?usp=drivesdk

Can you press the link?

[urban summit]

Yes

Thank you for book

Forgot to tag @atomic moat

[atomic moat]

No worries
All the best on your journey

Can you download the file?

[urban summit]

Yes i can

[valid monolith]

@numbpy Algebra 1 bumfel
Algebra 2 bumfel
A new algebra 1 bernad child
A new algebra 2 bernard child
Higher algebra hall and knight
Higher algebra bernard child

[fallow cypress]

@obsidian valley I default to pinging you whenever wittgenstein is mentioned

[tardy oasis]

Also Higher Algebra by Jacob Lurie! jk

[gray gazelle]

a book for self help or self improvement I like is the Bible (Roman Catholic 73 books version) and the Gospels are a good starting place

[humble knot]

Hello, I want to find some books can help me with IMC, do you have some suggestions (rated, comment helpful for me)? Thank you very much, my email for docx, pdf,..: [e-mail]

[fierce hedge]

Email

[gray gazelle]

Serge Lang or Dummit and Foote for a graduate/3rd course in algebra?

anyone who has dipper their toes in both care to comment?

[upbeat vine]

People who read these read because they are written by Wittgenstein and not because they want some good intro to Foundation of Mathematics. I imagine this would be a good book to read about his thoughts on FoM, but if you are interested in how actual mathematicians approach FoM, you should look elsewhere.

[remote sparrow]

look in pins

[finite gale]

Lang is pretty good after a first course in algebra I'd say; though I'm not sure what you used in a second course of algebra

[remote sparrow]

depends on how thorough your first course was

if you're an honors student that used dummit and foote, lang might be okay. there are plenty of choices out there though

if you used a book like judson, pinter, saracino, beachy and blair, etc. then dummit and foote is probably the better next step

[karmic thorn]

Any recommendations for an accessible/introductory text (or lecture notes) on Lie groups? I'm taking a course on Lie algebras and I'd prefer to see some of the motivation underlying them first

[inland elm]

i don't know how helpful this is, but lee's intro to smooth manifolds, chapter 7, has a good amount of examples
he also talks about why we would want lie groups in the first place, and as is standard for lee, is very wordy

[sage python]

Do you know manifold theory chaiegenvalue?

Not much but basic stuff

If so try this: https://www.math.stonybrook.edu/~kirillov/mat552/liegroups.pdf

[karmic thorn]

Thanks, I'll take a look

[karmic thorn]

Thanks, do you have anything in mind that doesn't assume a knowledge of manifold theory though? I'd say my understanding is still mostly superficial

I'd be okay with down-to-Earth/classical diff geo of curves and surfaces though

[sage python]

"Lie Groups, Lie Algebras, and Representations" by Hall

[gray gazelle]

what are some good books about trigonometry

more introductory books preferably

[karmic thorn]

Thanks

[clever orchid]

Trigonometry by IM gelfand and Mark Saul

[gray gazelle]

ooh thanks

[subtle fractal]

any good books about trig

[inland elm]

you might have to scroll a bit far up, but some people were talking about that earlier

[gray gazelle]

someone pls recommend best motivational,thirilling book pls pls

[keen depot]

Yes, I don't doubt this. My intention is to read something that isn't just rhetorical rambling without substance. I have read about the foundations already, so I'm really curious to read something about some thoughts concerning them

[devout yew]

what books would you recomend for learning calculus?

[coral prawn]

what purpose are u learning calc for?

[wraith edge]

what is a good math book thats mostly for fun

that has outlandish ideas

like thinking of spaces without the points in it

[formal bronze]

What do you mean by this?

[lime vessel]

Pointless topology?

[tardy oasis]

Would you by chance be thinking of pointless topology? I'm not sure of any books on this topic, but you may find some by looking into locales and frames

[lime vessel]

Pointless indeed

[wraith edge]

i was watching a video about intuitionists logic

and the guy said that it leads to thinking of spaces without thinking of the points

i dont know what he meant

okay i found the video, its around the 47:10 mark he says about it https://youtu.be/21qPOReu4FI

also winning plays of your mathematical games seems like a fun book

something along those lines

[tardy oasis]

Constructivism

[tardy oasis]

Yeah pointless topology (locales) is what he meant

[rustic grove]

'Tensor calculus for physicists' or the start of a relativity book will have the material in (all be it condensed)

[pallid yew]

does anyone have any book reccomendations

[stuck zephyr]

For what topic?

[pallid yew]

idk really

i am in hs for context

idrk what to learn

[strange karma]

Someonmme can recommend me a book about linea algebra?

[stuck zephyr]

Are you done with precalc?

[stuck zephyr]

Intro to Linear Algebra by Gilbert Strang

[remote sparrow]

#book-recommendations message

[pallid yew]

i believe so. i've learnt like algebra, complex number things, proving things w/ trig identitys, single var differentiation, im learning integration, etc ig? we dont cover linear algebra at hs here so theres that maybe

[stuck zephyr]

You lesrn linear algebra in university

I'd say start with calc

[pallid yew]

like i can do https://www.nzqa.govt.nz/assets/scholarship/2022/93202-qbk-2022.pdf this stuff discluding the integration (also probably cant do 4c )

[stuck zephyr]

You jump from here #book-recommendations message

[pallid yew]

cool thank you

[pallid yew]

like single var?

[stuck zephyr]

Wait hold on that's multivariable calc

[stuck zephyr]

Integration are mostly start in calc I

You start learning integration from khan academy or Paul's notes

#book-recommendations message

[pallid yew]

ok

[strange karma]

can explain me how i can see the book

[remote sparrow]

what book are you talking about

[remote sparrow]

no

it's close to what's covered in abbott

or ross

rudin does metric spaces very early and uses this formalism throughout

cummings and abbott stick to the real line

it's not a bad idea to do baby rudin after cummings or abbott

however your goal doesn't necessarily need to be papa rudin

[loud cradle]

definitely a good idea to read about metric spaces somewhere before attempting adult rudin

[remote sparrow]

if you've got a firm grasp of cummings or abbott, you can try schilling or axler for measure theory

a high schooler studying this material is already above average

why does this goal need to be accomplished in high school? why not be a substantially prepared undergraduate

[gusty smelt]

Have u tried mit Primes

It gives research experience to highschoolers in math

I taught someone wh9 was doing this for rep theory

I wouldn’t worry too much about how much more you need for background

You will get the background as needed as part of the experience

Most high school kids are competition kids and don’t know much math, so it looks like they are selective bc these people get rejected

If you know advanced math then you will probs be fine

Just focus on your basics for now

Analysis algebra and topology

Yeah, alg top is more than expected, but I’d consider it integral ig

I think literally a first course in analysis, algebra and some,point set is more than anyone can ask of you if that makes sense

Like the primes ppl I knew had less than this

Eh if u want

Don’t try to tailor to an application

Study the math you want

Don’t specialize rn is my advice

so cold emailing profs is like

basically they will not even check half the times if it is not an instutitional email or someone they know

I think the basics will be enough if its coming from a highschooler to entice atleast some profs

My advice really is that this should be secondary: dont warp what math you learn around this

you have plenty of time to do many different things

dont rush

yes

Do math that sounds fun to you

not ones that you think will give you more chance with profs or w/e (for now atleast)

I think the best mathmeticians I know always did this, i.e take classes that sound fun or learn something that sounds fun

rather than have a solid plan. In their early years that is

[remote sparrow]

@gray gazelle i appreciate your ambition, but i worry you are being sucked into a misguided idea that you already need to be a ready-made scholar to be even worthy of becoming a researcher. your phd is supposed to be where you learn how to be a researcher. if you want to pursue research prior to a graduate degree, that's very commendable, but don't feel pressured to do so.

https://twitter.com/pengpeng_xiao/status/1625169701184716806

^ tweets like these are really awful

research is labor. doing all this stuff before even getting a funded phd or a part-time TA job is doing a lot of unpaid labor

being an academic is already a fraught and precarious position

[strange karma]

linear algebra

[remote sparrow]

i referenced multiple books in linear algebra in that post

can you specify which one

i already linked hefferon's website, which has the linear algebra book

[sage python]

I'm flattered

[formal bronze]

Does that tweet refer to PhD applicants in mathematics? Because the field wasn't specified there. And I think other fields generally expect more research experience from applicants than mathematics.

[remote sparrow]

no, but it should not matter. OP is an economist

[formal bronze]

Not saying the tweet wasn't 'awful' though

[rare stirrup]

Hey guys I wanted a book for a brief history of physics like 1-100 covering up every single Theory numerical and ya and book recommendation?

[molten pendant]

any good books on probability theory( that doesn't require analysis/ measure theory)?

i didn't like ross's book

[remote sparrow]

blitzstein and hwang

[wispy bison]

Where do you get this book?

[fierce hedge]

Pretty sure that's a joke cover

[rancid orbit]

Any recommendations for math books to read when feeling empty and lost?

[rancid orbit]

omg https://www.abebooks.com/9780321118219/Math-Sense-5-Five-Morrow-0321118219/plp

[fierce hedge]

No fucking way, I refuse to believe that it's a real

damn, it is real except the "cohomological part"

[paper tangle]

Any good problem books on topology (like that have theory as problems)

[coral prawn]

[rancid orbit]

Topology; a first course by Munkres

[paper tangle]

Why the laugh 💀

[coral prawn]

The stuff above u

Not Yr stuff

Have fun with topology!!!!

[paper tangle]

Do u know any other cause I ve had munkres this sem and it wasn't particularly a problem book

[rancid orbit]

I expected it, so here's for you "Problems in Topology" by V.V. Prasolov and A.B. Sossinsky

[paper tangle]

Thank you 🙏

[rancid orbit]

"Topology: A Collection of Problems" by L.A. Steen and J.A. Seebach

Exercises in Topology is a companion to Munkres' "Topology" book mentioned earlier. It provides additional exercises and solutions for further practice.
topoly: A collectoin of Problems, this book offers a collection of problems that complement the material covered in the counterexamples book.

[paper tangle]

Ah I see

Thank you so much again

[bronze hazel]

Hey, I’m looking for an entry-level calculus textbook that I would be able to use to prepare for 12th grade’s calculus classes in advance. Does anybody have recommendations?

[heady ember]

Not a book but try khan academy or Paul's online math notes

Both are legally free online

[torn crypt]

I remember getting rejected

[rain wren]

isnt that like half of ug or smth?

[grand thistle]

isnt that like first year stuff

[tardy oasis]

I too got rejected when I had that in high school

[grand thistle]

what would they look for in someone who's "researching" in high school

[rain wren]

real analysis is 3rd year in the us

[grand thistle]

like obviously not the edge cases like the guy who came up in quanta a few months ago who did like number theory research in high school

[rain wren]

ranal is first year in europe doe

[grand thistle]

but like more 'average' people like this i guess

[rain wren]

not really sure about the others, however

[rain wren]

"""average""""

[grand thistle]

lol wtf 💀 what are they learning for the two years before that

[rain wren]

like

calc 2

I dunno

[grand thistle]

oh wait i forgot the calculus sequence existed

[rain wren]

[paper tangle]

i couldnt find this book is it perhaps possible that i could get some hints on where to look

[crimson leaf]

Calc 1, Calc 2, Calc 3, linear algebra, intro to proofs, solving differential equations, maybe a calculus based probability course

[rancid orbit]

I'm so sorry. it was result of gpt and i found that,
V. Prasolov and A. Sossinsky, Knots, links, braids and 3-manifolds, Translations of Mathematical Monographs 154, American Mathematical Society, Providence, RI (1976).

Which means it's not a workbook

[torn crypt]

result of gpt

[paper tangle]

ah its ok

[deep field]

has anybody had experience with knapp's basic algebra?

[paper tangle]

yes

[deep field]

somebody mentioned the book here in discord and it looks interesting

[paper tangle]

it is

[deep field]

+its free

would you recommend the book for undergrad learning algebra for first time>

[paper tangle]

yes

imo

[rain wren]

ew

calc based probability

disgusting

[crimson leaf]

Yeah it's alright at the discrete part but the continuous part gets kind of boring up till clt imo

[crimson leaf]

Just so you know responses by chatgpt are banned

[coral prawn]

Lmfao

[coral prawn]

... wtf using gpt for math book reccs 💀

[fierce hedge]

The book is literally free, you can download it from the author's website

[fierce hedge]

Nope, I ran a study group using that and let's say it's not very beginner friendly, it's more of a upper ug book. Plus some of its notations are a bit unusual and it some topics like diagonalizability are left to much later. That said it has good problems and you can always pair it up with a friendlier book.

[fierce hedge]

In his innocence Bing does indeed sometime gives you links to the books.

[coral prawn]

D a m n

[fierce hedge]

Bing can even search movie torrents lmfao

[coral prawn]

LMFAO WHAT

Geez.. I should use bing when I can't find smth on lib- um, I meant, that totally legal site.

[fierce hedge]

Based Bing

[coral prawn]

NAAAAHHHHHHHHHH

IT ACTUALLY 😭

[mystic orbit]

LOLLL

[crimson leaf]

Bing and GPT both gave out valid Windows keys as well

[onyx cobalt]

LMAO

bing seems questionable sometimes

and bard is sassy and stubborn

[valid monolith]

That's awsome

[visual sedge]

any good higher level geometry books? i'm at the undergrad level, used to proofs, and my focus is in analysis but just want to do some geometry out of interest and for fun. just looking for something that won't be too easy.

[remote sparrow]

#book-recommendations message

[visual sedge]

thank you i'll check that out

[weary cape]

For some its 1st year. I will be doing real analysis my first year.

[prisma loom]

shifrin - differential geometry: a first course in curves and surfaces

[sage python]

I feel like Do Carmo is better than Shifrin for diffgeo

[solemn haven]

Recommendations for proof-based undergraduate linear algebra? I'd like to know if there are more books of the style of Hoffman's Linear Algebra 🙂

[remote sparrow]

look in pins

[fallow cypress]

linear algebra done wrong is easier than hoffman and kunze

[empty junco]

GOAT

[sage python]

Halmos and Shilov are the best choices it seems?

[empty junco]

idk what shilov is

piracy time

um

axler rolling in his grave

[sage python]

This bit feels a bit like a meme for sure. Though people who use it like it and it seems to cover a good bit

Also Axler is alive. And tbh let him roll with his bullshit...

[empty junco]

maybe he was alive

but this killed him

[empty junco]

hmm if shilov covers nothing numerical then I think it gets no diffed by halmos tbh

[sage python]

Does Halmos do numerical stuff?

[solemn haven]

Hmm, I was thinking about using three books for reference, but what do you guys think? Is Hoffman and Shilov enough?

[empty junco]

no but that was the only thing it was gonna lose out on

[ocean mulch]

I do have a copy of Lang's Linear Algebra

Although I've never read it, but I did open it a few times. I guess it's not bad? Can be a good primer

[sage python]

You don't need 3 books lol

[tender river]

good luck trying to finish one of them

[solemn haven]

Well, I'm trying to teach myself lol

[crimson leaf]

You need like one linear algebra book and it really doesn't matter that much which one you pick from Dami's list as long as you like it

Reading 3 is probably gonna lead to you reading none

[ocean mulch]

For low-level stuff like lin alg, esp if it's your first time, I'll say ditch books and follow a course (MIT one is a blessing, for example). You most likely just don't have the maturity to study from books yet.

[solemn haven]

I already had a more computation based course and have experience with proofs from stuyding set theory

[ocean mulch]

It's not about the skills, but the intuition. And there can be only so much said in a book. I always find explanation easier done on a blackboard

https://www.youtube.com/playlist?list=PL221E2BBF13BECF6C

This one is probably the most famous MIT online course

And for good reasons 😄 I heard it's extremely well done

[crimson leaf]

It's good but unless you haven't taken a linear algebra course before I don't think it will be much use

[ocean mulch]

https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D

or this one

[ocean mulch]

but ene haven't taken a lin alg course before 😄 that's why I say ditch books

[crimson leaf]

Ene has

They took a computational course just like this one

[ocean mulch]

I think this one is more proof-based, no?

idk, looks fancy 😄

Anyhow, might not be the best recommendation, but my point remains

[tender river]

how's lax?

[gusty smelt]

strang is very computation based. If you are a pure math person id say just read one of the many recommended book

[crimson leaf]

No

[viral halo]

a book on set theory?

[gusty smelt]

you dont need to like, deliberate too hard about which one