book-recommendations

[fervent lava]

If not, Calculus and Analysis in Euclidean Space by Jerry Shurman is a rigorous multivariable calculus book that has the necessary linear algebra in it. If yes, people in this server have recommended folland advanced calculus, calculus on manifold by spivak.

If your not looking for rigor, paul online math notes has a calculus 3 course or the multivariable chapters in https://www.whitman.edu/mathematics/multivariable/multivariable.pdf.

That link above is similar to Stewart's calculus book but it's more suitable for self study.

[willow crown]

is it just me but I feel like spivak is overrated

I don't really get what all the buzz is about

like why does the section on real sequences only come up at the end?

[restive falcon]

because they aren't as relevant until you start doing proper analysis

[willow crown]

but it is an analysis textbook?

you wouldn't study the definition of continuity in a first course on calculus

[flint forge]

It’s not an analysis textbook in any sense.

[flint forge]

It would either be a hard first course or a reasonable second course in calculus

For example someone might take AP calc in highschool and then take a spivak based class in college.

This was pretty common at my undergrad

[karmic thorn]

Same at my uni, although the course wasn't strictly based on Spivak. Incoming students had taken calculus in school, while the calculus course in first year was a precursor to analysis with some formal definitions and proofs.

[left surge]

Any well regarded books on probability?

[sage python]

Measure theoretic or no?

For measure theoretic Durrett seems to be the standard and it's p good

[hearty steppe]

What is the difference between Resnick and Durrett

[halcyon hornet]

Is it Friendly actually?

[stray veldt]

yeah

its intended for a non mathematical audience

very much focused on exploration

[halcyon hornet]

Woah.

It works well with non Calculus prerequisites and is Not very rigorous but still covers elementary number Theory Well and makes it strong?

@stray veldt.

[halcyon hornet]

Left.

Me hanging.

[stray veldt]

i dont know what "makes it strong" means

it has no calculus prereq

its a nice book, i havent read it fully

it approaches number theory in a way similar to what fermat would have done

[hasty turret]

Loads of advanced math have no calculus requirements

Algebraic number theory is almost completely calc free

Topology is calc free

[heady ember]

Set theory / logic too i think

[hasty turret]

Yea, Anything that doesn't have anything to do with analysis is calc free

Also analysis night be considered calc free?

[heady ember]

[hasty turret]

I mean calculus is technically calc free

[heady ember]

Isn't analysis calculus but more pure math

[hasty turret]

Because you can learn calc without knowing calc

[stray veldt]

[hasty turret]

I am completely lost on what calc free means

[stray veldt]

did you do any algebraic nt

[hasty turret]

Well,No

[heady ember]

[stray veldt]

you will find that you need complex analysis

"need"

[heady ember]

Very nice

[stray veldt]

if you want to do interesting things

[hasty turret]

Ok,makes sense

[stray veldt]

lots of arithmetical data is encoded in certain zeta and L functions

[hasty turret]

But I don't get why you can't just bypass calc and just start complex

[heady ember]

[hasty turret]

You just need to learn the definitions

And visualise the functions

[lapis sundial]

You need calculus to do many things w complex analysis

[heady ember]

Potatyc, im going to guess this is ryc

Ok im wrong

Its not chalk bird

[lapis sundial]

I mean most of the major theorems in complex analysis involve integrals for starters

[hasty turret]

True,You can just look up definitions tho

Which is exactly why I am confused about "calculus free"

What does calculus mean exactly

Lesser analysis? Tricks from analysis engineers borrowed?

[heady ember]

I'd guess you probably will be very confused if you don't at least know the prereqs / basics like what's an integral

If you try to learn analysis without calc

[hasty turret]

Do spivak then

Spivak is more calculus than analysis whatever that means

[gray gazelle]

Recommend me an interesting book with topology flavour (no AT)

[halcyon hornet]

Boy Boy worth a try.

[halcyon hornet]

Well but Analysis and Abstract Algebra and Linear Algebra and stuff.

[halcyon hornet]

Bahahahha.

[halcyon hornet]

BAHAHAA.

[halcyon hornet]

Yes I am needy I Need Mathematics Knowledge And Wealth.

[halcyon hornet]

Tell Me about them sensei.

[halcyon hornet]

I Like yours words funny man.

Sheesh the book Loch Suggested Is worth simping on

.

OH GOD ON LOOKING THIS BOOK IT SEEMS SO PERFECT LIKE.

AAAA I Want it now.

@stray veldt Can I DM?

[stray veldt]

[iron granite]

What book did he suggest?

[gray gazelle]

hey folks, I'm looking for a book or any other resources to familiarize myself with the type theory and main studies that are done in that area, any recommendation ?

[karmic thorn]

This might be relevant:

[gray gazelle]

thanks friend, I'm looking for something to help me get started and find my path, right now i'm a bit clueless. Also i'm interested to understand it from the mathematics side of it rather than programming side

[shell geyser]

Am looking forward to a calculus/linear algebra-based introductory probability and statistics textbook. Certainly no measure theory. I'm currently looking at Walpole's "Probability & Statistics for Engineers & Scientists" but I'm worried it might be a bit light on theory. Notably, it lacks a proof of the central limit theorem and also doesn't cover much on joint distributions.

[proper lotus]

How does probabilitycourse.com compare?

Because it's quite good

If that is too little stats you might want to try PSU's STAT 414 and 415, their notes are online

[shell geyser]

I went to have a look and it seems pretty neat. Thanks for the recommendation. I'll skim through it and see if I like it.

[karmic thorn]

You might be able to find certain lecture notes online, but I'm not familiar with any.

[hallow oriole]

anyone have any low prereq group theory books?

[hallow oriole]

also, does anyone have a decent e-reader?

[stray veldt]

good ones with larger screens are pretty expensive

i like the ones by onyx boox, since they run android and you get a pretty good digital pen to annotate pdfs with

[barren cloud]

I own a kobo clara hd

[sturdy sail]

So, I will start studying a bit of homological algebra this semester. I am currently thinking about reading either the book by Hilton-Stammbach or the one by Rotman. Has some of you read any of these books? What is your general opinion on them? Also, are there any books on this book you would recommend?

I know Weibel (iirc) has tons of mistakes throughout the book, so I am trying to avoid picking this one for a first course on homological algebra.

[cursive orbit]

most introductory abstract algebra textbooks should have an introduction to the number theory needed for group theory

[oblique beacon]

Hi, I was wondering if working through "Discrete Mathematics with Applications" by Susanna S. Epp would teach me proofs?

Because I have a discrete math class coming up and maybe I can kill two birds with one stone? Or would going through a different book be better to get a basic grasp of proofs?

[stray veldt]

the book seems to teach standard "intro proofs" stuff

[oblique beacon]

@stray veldt so you think its sufficient for the basics then? I'll do that

[stray veldt]

i checked the pdf

its very thorough

like the first 500 pages are intro proofs

you can find shorter intros if you want, but you definitely dont need any additional stuff

[oblique beacon]

looks good

I have have time

thanks loch

[grand thistle]

hmm right

but

i just looked at the table of contents of artin and dummit/foote and they don't seem to have it?

could you recommend a book which does?

[cursive orbit]

dummit and foote definitely has it

in "Preliminaries"

[grand thistle]

oh right my bad

i didnt look at that, i just skipped to see the actual chapters sorry

thank you

[primal mica]

I was wondering if anyone had a good recommendation for a first course in statistics and a second course in statistics.

For background: I'm a graduate physics student and I've done a few semesters of quantum, as well as undergrad thermal physics and soon to start a thermodynamics of materials course.

I feel fairly comfortable with mathematics, but I just feel I have a lot of holes in my knowledge when it comes to statistics.

[warm glen]

for your first course i can recommend OpenIntro stats which is free on their website

[sleek python]

Casella and Berger's Statistical Inference is a classic and covers most of the basics. If you want a quick overview of a lot of topics there's All of Statistics from Wasserman but I don't recommend it as a primary textbook to study/learn from.

[solar anvil]

Does anyone know any good books on computational geometry?

[brittle breach]

think it might help you in the New World ?

[heady ember]

Btw loch also has created his own intro to proofs, 50 pgs, which you can find under pinned either in #book-recommendations or #proofs-and-logic I think

[frosty girder]

they do

artin does have it

well not like an intro to nt stuff, but still there is modular arithmetic

[grand thistle]

oh shit it does

bruh they both have it nvm

[frosty girder]

yeah lol

i dont shill artin for nothing

😌

[grand thistle]

bruh what the whole 14 week course is literally just the second chapter of artin

a watered down version

[frosty girder]

which course is this

[runic hatch]

Is this like high school

[grand thistle]

im trying to take a course over the summer

and i chose

a group theory course

[frosty girder]

Ooo

[grand thistle]

from aops

[frosty girder]

i see

[grand thistle]

i can't take any college level classes like LA or anything bc the only formal class ive taken and will have credit for is high school geometry...

[grand thistle]

yeah

[hallow oriole]

low means calc and set theory

alternatively i'd be fine with books for the prereqs of a better group theory book

[hearty steppe]

You won’t need a low level Calc class to get through Pinter I don’t think.

I’m going through Pinter right now and it doesn’t seem to be using any calculus yet

And I don’t really expect it to cuz calculus is analysis territory

It may use things like sums and stuff that you have seen in calculus but calculus is all about functions and representing their behaviors the representations being some form of algebraic manipulation involved when we map domains to ranges

But you don’t really get that kind of abstraction in good depth until you get to analysis. I feel like the non rigorous Calc classes are just more memorizing things with mostly basic algebraic manipulation

[restive falcon]

algebra by artin

always

[hallow oriole]

hmmmm looks good

plus the literal first link of it i clicked was the full book

sooooooo that's pretty cool

[hearty steppe]

It’s not necessarily a first course in abstract algebra…

[restive falcon]

it literally is

[hearty steppe]

Compared to Pinter it’s like a second look

[gusty smelt]

pinters book is like

lower than a first look at abstract algebra type of course lol

anyhow yeah artin is good

dami has a good rant on all the popular books

this

[hearty steppe]

Why would it be lower than a first look?

I guess you are comparing to a college level course and the content covered?

[gusty smelt]

yeah

[hearty steppe]

Oh ok gotcha

[gusty smelt]

i mean depends on college ig

[hearty steppe]

But Pinter has a lot in it

Over 30 chapters

[gusty smelt]

oh i must be thinking of another book

gillian?

[hearty steppe]

Even covers galois

Idk I heard Gillian can be hard

[gusty smelt]

yeah the main thing is you are not gonna see a lot of the side topics in any book all covered in class

[hearty steppe]

Oh your thinking of Fraleigh

I am not going thru Fraleigh

[gusty smelt]

but what artin has as its "main content" chapters will be covered

[hearty steppe]

But I skimmed it and it is very watered down

Fraleigh I remember peaking at that and I felt quite underwhelmed compared to Pinter in hindsight looking back

[plain barn]

anyone knows a good book about linear algebra?
my knowledge context:
I know a little bit about dot products, I know what a matrix is and uhh, I know how to add them

that's pretty much it

[hallow oriole]

someone's probably going to rec Linear Algebra Done Right or Linear Algebra Done Wrong so i'll just do it first

😎

[plain barn]

thx

[plain barn]

this one?

[hallow oriole]

yeah

there's also Linear Algebra and its Applications

by strang

i think

which is (apparently) good for self-study

[plain barn]

idk is this "applications" like, applied mathematics?

like, not applied to just problem solving, but to other things?

[restive falcon]

what book would you suggest for the grad real analysis required for narasimhan/schlag

[hallow oriole]

just scrolling through the pdf i wouldn't say it's got much in the way of applied maths lmao

[plain barn]

sure

[restive falcon]

I've heard this book is bad
and that friedberg-insel-spence is better

[plain barn]

I'm between reading linear algebra done wrong and linear algebra and its applications

[hallow oriole]

i mean

[restive falcon]

i myself would recommend algebra by artin if you're more familiar with proof-based maths

[hallow oriole]

why not both

[hallow oriole]

both are free online officially and easily, afaict

you can pick and choose

if a book explains something one way that you prefer, take that and abandon the rest

[plain barn]

I am

[restive falcon]

then artin is great

it goes into other areas of algebra as well

like group theory and ring theory

but it contains all the linear algebra from a general first course as well

[plain barn]

so I think I'll go to this one

I'm interested on these topics as well

[restive falcon]

good idea

[hallow oriole]

wait

the artin book has that too?

huh

that's pretty cool

oh, and it has galois theory

oh fuck me this book is a lot more than i thought

[restive falcon]

can anyone answer this

[gusty smelt]

hmm looking at it seems like a standard book on complex analysis will probs do

like honestly when you do riemann surface you dont need to remember that much of complex analysis

[restive falcon]

wait
complex analysis for complex analysis?

[gusty smelt]

oh this book is your first intro to complex analysis?

lol sorry it looks like a second course to me

[restive falcon]

no I'm not doing it now

just for future

[gusty smelt]

i would not recommend it for a first course

it basically looks like riemann surfaces and things that are like relevant to it

rather than just complex analysis

if that makes sense

[restive falcon]

hm

[gusty smelt]

A concise course in complex
analysis and Riemann surfaces
Wilhelm Schlag

this one right

[sage python]

Schlag Complex is probably in principle "doable" for a first course in complex analysis in the sense of, he doesn't assume prior background in the subject

But you need to know some differential geometry, algebraic topology, and real analysis before going into it

And most people do a first course in complex analysis before they reach the point in their mathematical careers where they're ready for Schlag

[restive falcon]

I'll probably do all of those first

though

through self study

[sage python]

Narasimhan only requires the real analysis bit

For that material I'd say first 19 chapters of "Real Analysis for Graduate Students" by Richard Bass is good

[gusty smelt]

i mean even if u do the others first just looking at it i feel like you should do a different first course in Comp anal first

like the first 3 chapters dont seem sufficient to me for the basic complex analysis stuff

[sage python]

Hmm, which points do you think it misses?

[gusty smelt]

i mean im just looking at the index and i dont see anything about the like, integration theorems and the build ups to it and etc ig

also its 58 pages for the first 3 chapters and they move to like, riemann surfaces

which idk i dont this is necessarily sufficient for this stuff?

[sage python]

1.6 is Cauchy theorems

[fervent lava]

What would be the complex analysis book to do after someone finishes baby rudin?

[gusty smelt]

oh right winding number hmm makes sense

[sage python]

Honestly I think most complex analysis books are wayyyyy too drawn out lol

[restive falcon]

if i do like
algtop, diffgeom and some grad real analysis first

would schlag be good

[sage python]

Probably fine

[gusty smelt]

dami might say yes and he may be right, but id reccomend instead to do like, say something like gamelin first, a more standard complex analysis book, and then a book on riemann surfaces

[sage python]

Narasimhan is a good intermediate

[fervent lava]

What are the opinions for stein complex analysis?

[flint forge]

I think you have to learn alg top, homotopy theory, stable homotopy theory, computational homological algebra, and then infinity categories first

Then you’d be ready for some complex analysis

[gusty smelt]

this is wrong dont listen to him

obv you need spectral sequences

in there

b4 complex analysis

[flint forge]

And at least a few weeks of generalized homology theory

[restive falcon]

i think this is trolling

[gusty smelt]

also ill say one thing allison, that it might be useful to like

do riemann surfaces before the full diff geo stuff

i think riemann surfaces is a very gentle intro to geo

atleast it was for me

[flint forge]

I honestly think like

I should try to learn geometry in the mG style

At some point

I just don’t have time

And it’s not relevant

[gusty smelt]

which is maybe why im not a fan of diff geo-> comp anal

[flint forge]

:/

[gusty smelt]

this depends on perspective ig, so riemann surfaces are super structured and also n=2 case right

so things are by and large easier to do on these

and then when you get to general manifolds its like

"ah so i am weakening this"

other people might like it the opposite way

where they learn the general theory and then see this specail case as a strenghtening

[restive falcon]

my intro real analysis book does manifolds

[gusty smelt]

oh last 4 ch seem nice

but might be nice to see in a diff manifold book in all of the details ig

[flint forge]

I feel like one should learn topological manifolds first

But maybe that’s my bias

[grand thistle]

what book is that

[restive falcon]

would this be enough before lile
schlag

[gusty smelt]

i mean right i think you want like, AT b4 diff geo too imo max

thats how my school does it

[restive falcon]

browder
mathematical analysis: an introduction

[flint forge]

Oh

Okay

Yeah then I agree

That’s how uchi does it

[gusty smelt]

like first chapter of hatcher atleast

[flint forge]

I think you want

PD

At least

[gusty smelt]

PD?

[flint forge]

Loin are duality

Poincare

[gusty smelt]

on poincare duality

oh*

[flint forge]

I think it’s nice to see the completely topological proof first

[gusty smelt]

right see it in derham and also in singular ig is nice

[restive falcon]

oh should i do algebraic topology before that section then

[gusty smelt]

but my school also does 1 ch of hatcher per semester

[flint forge]

I think a lot of people teaching really structured manifold stuff

[gusty smelt]

so

lol

[flint forge]

Tend to use machinery you just don’t need

And that messes w intuition

Like assuming stuff is smooth when you really don’t need it

[restive falcon]

like do first 10 chapters of browder
rotman algtop
last 4 chapters of browder

[gusty smelt]

i wouldnt say it messes with intuition but i do think AT will help there

but also going upto PD in any AT book will take a while

so i understand if someone wants to like

learn some manifolds first

[restive falcon]

I'm gonna finish it for riehl anyway

[flint forge]

What is browser

Browser

Fuck

[gusty smelt]

lol

also fuck im running late for class gg

gtg

[restive falcon]

probably will do riehl before getting into diffgeom stuff

[flint forge]

One thing I will say is like

There’s no reason to plan much of this ahead of time

You really only need to know where you’re headed next

[restive falcon]

there is a need

[gusty smelt]

yeah i always make a plan like this and it turns out there was like

10% of the plan that stayed the same

lol

[restive falcon]

because otherwise i get completely offtrack and do nothing

[gusty smelt]

it is comforting to do tho ig

[restive falcon]

at least i have some structure

[grand thistle]

i swear i spend 80% of my time making plans and 20% studying

[restive falcon]

[current plan]
finish artin up to modules (probably skip a few sections on fields to get back to for galois theory)
browder up to ch10
hatcher's notes
rotman topology
riehl category theory
browder chapters 11-14
grad real analysis
schlag complex analysis
differential geometry

this may change

probably will change in fact

[fluid skiff]

is there some sort of book reading clubs here for the above mentioned mathematics books

[restive falcon]

I'm sure you could set one up with people who are interested

[flint forge]

Many have tried

Few succeeded

[fluid skiff]

well I want to learn automorphic forms and I have some knowledge about introductory analytic number theory

therefore I am going through books that come up my way

and the list is quite huge

[flint forge]

It is hard to organize a reading group for a single book

It is basically impossible to do for more than one

[fluid skiff]

well we could all share what books we have read/interested in and then we make groups for individual channel based on book names

like I can start with Introduction to analytic number theory by Tom Apostol

[sage python]

Oh Browder yeah that's what I mentioned

[restive falcon]

yeah

[grand thistle]

mine is
finish apostol calc til i’m done with sequences and series
abbott understanding analysis
(i’ll probably be doing a group theory course along w this)
hoffman kunze linalg
mendelson topology
munkres analysis on manifolds
a bit of artin algebra
lee topological, smooth and reimann manifolds series (supplemented by renteln manifolds tensors and forms and hatcher maybe)

idk if i need more prerequisites i’ll do it along the way ig

oh wait i forgot

i think i’ll do the lebesgue integral and fourier series chapter in apostol or rudin sometime after abbott and before munkres

[frosty girder]

[frosty girder]

[grand thistle]

heh i organized it in chronological order

added some books too

[stray veldt]

i didnt read this many books during my whole undergrad

[grand thistle]

100% not gonna go through like half of these i just like looking at textbooks full of symbols and things i dont understand

[gray gazelle]

@grand thistle What book you have on abstract algebra?

[grand thistle]

artin's algebra

[gray gazelle]

Thx

[shell geyser]

What a mood.

[smoky zephyr]

same honestly lol

[frosty girder]

i hope to go through many of these

and many more

oof

[mystic orbit]

my plan:
hubberd
rudin/artin
...

those are the only writers I know

[frosty girder]

my list is actually kinda long as well

[smoky zephyr]

my list is basically just random books

most of which i will definitely not read

[frosty girder]

sadge

[mystic orbit]

based

[halcyon garden]

Jacobson is stinky poo, too much English and the proofs are all clogged up with words

[runic hatch]

I have like 30 books on my to-read list

[frosty girder]

same ab

[gray gazelle]

same

[smoky zephyr]

yeah totally just do every single proof in symbols without using words, how bad could it be

[halcyon garden]

But like theres a balance, the amount of words make it an eyesore for me personally, I'm sure it's useful for a few folks

[iron granite]

Any good higher math exposition books?

[shy compass]

is hatcher's notes the same thing as the book "algebraic topology"?

[halcyon garden]

Tbh the real issue I have is the unreadability of the pdf due to bad alignment and all the words make it tiresome to read

[smoky zephyr]

pretty sure it’s just the brief notes on point set topology

[halcyon garden]

Plus the LaTex rendering is blurry for some reason, fine Jacobson might be good... but my Jacobson is terrible

[smoky zephyr]

[iron granite]

Have you tried ZL*b?

[halcyon garden]

Ye

[iron granite]

You need Basic Algebra 1, right?

[gray gazelle]

any book that goes in depth on simple concepts like proof for the FOIL method, deriving formulas for volume, area of cone, pyramid ect ect

[cursive orbit]

The scanned pdf is much better

Or it might be a DjVu

[gray gazelle]

i need this because i realized in school they just made me memorize and now lately i actually got to udnerstanding stuff and want to see if i missed out on something before moving on to more advanced stuff

[frosty girder]

lara alcock has nice books

[cursive orbit]

Those for volume and area can probably be found in calculus textbooks. For something that presents a more rigorous approach to algebra, maybe Lang's basic mathematics?

[gray gazelle]

Thanks I will take a look into it

[restive falcon]

no it's his pointset notes

[fiery pine]

hey guys, can somebody provide me book to brush up highschool / uni level math

I am planning to apply uni sometimes this year; and I haven't brushed up for the past +10 years in my life

[restive falcon]

probably sth like stewart or thomas for calculus

[fiery pine]

@restive falcon ?

[restive falcon]

and an elementary linear algebra book maybe
but that will probably be covered in uni

[restive falcon]

yep

[fiery pine]

I can actually provide the course syllabus

[marble solar]

Stewart is a terrible calculus book

[restive falcon]

oh

[marble solar]

Thomas' Calculus book is much better

Stewart doesn't even cover inverse function theorem

Instead does an implicit differentiation trick to get around it

[marble solar]

Is that following stewart

Yeah see how it doesn't have Inverse function theorem

That means you're following stewart

[fiery pine]

Unfortunately I am not sure about it

I got from the uni website

that I am planning to apply

[marble solar]

That's an outline for stewart

It's an ok book

I have to teach my study group out of it for Calculus

[fiery pine]

Thomas' Calculus, by Joel Hass?

You are referring this one, right?

[marble solar]

There's a University Calculus one

[fiery pine]

This one is high school?

[restive falcon]

pearson
for-profit exam board

[marble solar]

That's the current(?) one

This is the one I learned from

It was pretty decent

I'm really not a fan of Stewart. The more I use it the more I hate it

[fiery pine]

I can give a try this book; my main objective is just to get my math at high school level again

within 5 months

[winged meadow]

I'm searching for a introductory book about Category Theory, with exercises if possible, that is not to fast or to harsh for a person with near zero experience in the domain

[winged meadow]

Oh, and if someone knows a good book about linear differential equations for someone who 1) hates doing it and 2) don't understand anything; that could help me 1) understand them 2) Maybe like them (that's optional), it would be awesome

[restive falcon]

the book I've heard is best is Riehl's Category Theory in Context

[winged meadow]

I'll take a look, thanks a lot

[winged meadow]

(I'm still looking for this)

[flint forge]

What does “the domain” mean

Like category theory or math or algebra-flavored stuff?

[winged meadow]

Category Theory

[flint forge]

Oh then riehl is a great choice

[gray jungle]

what do you think of kelley general topology?

[gray gazelle]

Book recommendations on how to improve my mathematical logic?

[wicked panther]

Books recommendations on differential equations

[blazing canopy]

at what level, and about ordinary, partial, linear, nonlinear, applied, numerical, ...?

[wicked panther]

Uhh I’m not totally sure.. but it’s after multi variable calculus.. I’ll see and tell if i find out more information on it

[blazing canopy]

OK, then you probably want an introductory book on ordinary differential equations

Unfortunately I do not have a recommendation for that kind of book, but it's important to note that differential equation is a vast field.

So if you are trying to study it for a course, you'll need to target specifically whatever your course is trying to cover, as there aren't any clear standards.

[wicked panther]

I honestly didn’t realize it was so broad, I’ll try to ask my professor about what field the class covers

Thank you for the help mr chipmunk

[blazing canopy]

A differential equation is any equation involving derivatives, so that is an incredibly broad range of equations.

[frosty girder]

also i think it would depend if ur DE class is proof based or a cookbook class (where you just learn how to solve some specific types of DEs and not much about why or how these methods work)

[agile jay]

Hey uh can anyone recommend books on introductory linear algebra

[gray gazelle]

Any book recommendationd on math logic?

[restive falcon]

I've heard good things about enderton

[frosty girder]

Friedberg, Insel and spencer is great

and LADW is pretty good i have heard

[agile jay]

I see, ty I'll have a look

https://www.amazon.co.uk/dp/9353432995/ref=cm_sw_r_apan_i_7G10QNC9PA0B9TRDW07K

This one looks good

[frosty girder]

[candid sedge]

can someone recommend me a book for coordinate geometry

i'm done with school lvl coordinate

so need a good book for competitive exams

[gray gazelle]

This i buy in online shop

[frosty girder]

which exam

[candid sedge]

i just want a book which can at the very least prepare me fully for Jee Mains ( indian exam )

its a tough exam so i need one which has good theory

[frosty girder]

another jee peasant

😔

u dont need much theory for mains

for geometry u need to do questions

[candid sedge]

not that i want to perform very well in mains

idc about it

i just want to learn it so a theory packed book would suffice

[frosty girder]

see the formulae from here https://drive.google.com/file/d/1YaG8E_79_NqnmERI62iycapgkFSHNLVP/view

[candid sedge]

i was just giving the standard for the book

[frosty girder]

sl loney is insane if u need something like that

[frosty girder]

what do you want to do, if u dont mind telling?

[candid sedge]

idk

not sure

one thing im sure of is that i cant qualify mains this year with the prep ive done

so i'll just try getting better at what i like

[candid sedge]

ive heard that name

i'll try it thanks

[frosty girder]

u probably can

qualifying isnt particularly hard from what i understand

[normal sandal]

Cap

[frosty girder]

[candid sedge]

i started integration from IA Maron last week

good book

[hollow shore]

challenge and thrill has a pretty good coverage of analytic geometry

[candid sedge]

but just solving integrals would lead me nowhere

[frosty girder]

i never did a book on integration and i never want to

[frosty girder]

true

[candid sedge]

so i'll try coordinate geometry for a while

[frosty girder]

80+ theorems in a single chapter 😵‍💫

[hollow shore]

😵‍💫

[candid sedge]

so should i try SL Lonely for now ?

[frosty girder]

u can

[hollow shore]

It's a dated book lmao

[frosty girder]

~~if u want to qualify mains, that is just qualify it, that needs 90ish out of 300 marks, which i think is doable)

[frosty girder]

doesnt mean its bad

it has a ton of theory

[candid sedge]

i'll try getting like, 150 marks in the next attempt

but that's as far as i can go

will try for Bitsat

and other exams available here

[frosty girder]

if u have the patience, try grinding chem

[normal sandal]

I have to give JEE 😢

[frosty girder]

u do too wordslinger?

same

😢

[normal sandal]

I might not

I have no aspirations to a Btech nor am I good at PCM

[frosty girder]

i mean, u can get into iisc or iiser

[normal sandal]

Going in just to fail seems counterproductive

[frosty girder]

understandable

[normal sandal]

I hope I get into my dream school 😢

[frosty girder]

thats what im hoping 😢

[willow relic]

does anyone know of any good books on mathematical bio?

[hearty steppe]

Not quite like what you’ll find for actual math books. I’ll have to get back to you on that one. I don’t want to suggest anything that is just insufficient in both breath and depth. Currently, that’s mostly how I feel about math bio books in the current state of things.

They’re more like “here’s some equations we are using that fit the pattern of data we collect from labs and clinical studies”

Take it from me and go through the pins and learn math the real way.

I suppose overall they could be ok if they match the project or research context your working with.

Focus on getting through Casella and Berger and try to get to Evans (I have not made it to Evans yet). Evans is a partial Diff Eq text that is considered GTM (graduate texts in math) level.

I am also gona try to make some headway through Brin & Stuck’s Dynamical Systems book at some point. Biology is a bunch of convoluted dynamical systems orchestrating together and eachother really so I suggest that text as well.

Oh and you probably want some foundational background in math to work through a text like Casella and Berger

Essentially you need to be good at statistics/probability, have intuition for Diff Eq on an abstract level, and then if you can handle more, be able to deconstruct complex systems

If you can do all of those things, there may be hope for you to do work in astrobiology

[proper lotus]

What book is Evans?

[hearty steppe]

His partial Diff Eq book

I’m still working thru Casella and Berger and that book will take me a minute.

So my motivated interest in the topology + measure theory route is to really develop a unique angle of approach to get through this mix of content

Biology is the hardest of the sciences other than literally studying outer space and subatomic particle interactions

There’s a reason why a lot of mathematicians and physicists avoid biology. It’s either too hard, or the opportunity for them isn’t there

Right now I’m not quite doing biology research. I’m doing cognitive science focused research

My actual molecular biology research is sort of sitting on the back burner

I think I’ll be able to use it in the AGI project I’m involved in however at some point

[pale scarab]

Anyone have some favorite books from MIR? I was looking at some of the old geometry books and the problems are really high quality. I wonder if any of you know of some other good problem books in the old soviet style outside of geometry.

[karmic thorn]

Not math but the 9(?) volume A Course in Theoretical Physics by Landau and Lifschitz was published by Mir originally.

[hallow oriole]

does anyone have the solution list for Book of Proof?

i've been working my way thru the exercises and i'm fairly confident i have everything correct but would like to check

[willow relic]

Astrobiology?

[willow relic]

what sort of background is expected? I've got the regular undergrad background in ODE/PDE, probstat, and analysis

[willow relic]

Not doing any research or a project, I'm just trying to get a look at the field

[hearty steppe]

Go through The books I mentioned if your interested in being a mathematician that studies biology

[willow relic]

Perfect. I'll check them out

[hearty steppe]

Because that’s the road I’m taking

[willow relic]

I've seen a couple things that make it seem like you can apply sort of

"economics" concepts and theory to mathmatical biology in some ways?

w/population models and stuff yeah?

[hearty steppe]

Biology is the hardest science. Don’t assume that abstract mathematics doesn’t have its place

Correct

[willow relic]

No I absolutely agree with you.

[hearty steppe]

Biology has a lot of working economy intuition

[willow relic]

I have a background in economics, and I'm sort of sick of the field in general, but I'd like to find a place to apply some of the things I've learned

I'm also doing some research in game theory which seems adjacent. It just seems like a field that exists at an intersection of a lot of the things I'm interested in, but I never gave it much thought until recently because I "didn't like biology when I took it in high school" but all I remember learning about is the cell cycle anyways

[hearty steppe]

I would suggest you also study chemistry and physics to the point you have a comfortable foundation

[willow relic]

makes sense

[hearty steppe]

I probably don’t have the best foundation myself but it’s manageable and I can use math to reinforce it better overtime

[willow relic]

Yep, I'm probably in a similar place to you. I have an ok math background for an undergrad but could always be better

I have a book called "Mathematical Biology: An introduction" by J.D Murray, if that means anything to you

[hearty steppe]

I’ve got it archived. Again it’s more or less another reference book for using mostly statistical inference methods that have worked in clinical settings

The intuition of the methods aren’t really given much depth at all. So you don’t have much to go off of without going through a text like Casella and Berger

Labs are not always clinical settings but they usually are

[willow relic]

C&B looks neat. I've already seen some of the stuff in there across various mathematical statistics/econometrics/stochastics courses but I'm also seeing a lot of things I've never really seen before

[hearty steppe]

Try to see if you can breeze through it. There’s way harder books getting into stochastic processes and measure theory

Even probability

[willow relic]

I'm in a first year PhD course on Stochastic Processes and MCMC right now. It's rough

[hearty steppe]

Haha I bet

[willow relic]

me, a junior in undergrad, when the professor says "you're a math PhD student, right?"

[hearty steppe]

So you got a taste of the difficulty at least

[willow relic]

Yeah. I have an ok(?) grade in the class right now but we haven't gotten our first midterms back so we'll see how that one turns out

I'm happy I'm taking it but wow it's a tough class compared to all my undergrad stuff

[hearty steppe]

I think the main issue is that the way the material is presented in the “math bio” books is mainly designed for statisticians that are working with biological data.

This doesn’t mean the statisticians have a foundation in understanding biology to a certain degree which I feel hurts their credibility in the long run.

Also not every statistician is a go hard mathematician statistician I would assume.

So when your going through those types of books instead of books designed to present the mathematics as intuitively as necessary, a lot of abstraction you want to gauge is actually hidden from you

So in this kind of area of work, you really want to focus on go hard in math or physics, in my honest opinion

If you can do both, great. I don’t have the convenience to REALLY do both so I’m focusing on math. Physics is too much speculative jargon for me to sift through to manage a proper balance of the two and compared to how math is structured and going through physics texts is a different experience than going through math texts.

There’s a reason why “applied mathematics” is a thing. Cuz there is opportunities for people that didn’t get a chance to become math savants and commit to the field out of purity at an early age (I am saying this part as an absurd generalization for the humor points). But it’s almost impossible to get into a pure field now a days unless you are showing talent at a really young age.

[primal mica]

Does anyone know a book fairly similar to this one?

I’ve picked it up from the library but I won’t have time to thoroughly work through it before I graduate and move on to somewhere else. Seems semi-difficult to find this exact volume, and I’m not really familiar with other books on ODEs of similar content

[sudden kindle]

any books that prove the Chebotaerev density theorem?

I'm looking for books that have applications of L functions to arithmetic problems, in particular Chebotaerev density theorem

[runic hatch]

Differential dynamical systems by JD Meiss covers somewhat similar material and in a more straightforward fashion

[primal mica]

Thank you, kindly. I will look into it :)

[halcyon garden]

I take offense at this paragraph. I believe you are saying this due to the dearth of faculty positions. But can you truly say that most faculties who have made a meaningful contribution were guided into math at an early age? This is not the case from my observation at my university, I know a few professors who are some of the best mathematicians in my country and are a big deal in their fields who weren't brought into this field at a young age. Even the fresh hires at my uni definitely have profiles that don't require you to be a savant to have. Please don't undo the work of all the people doing outreach by making statements that would discourage the people who discovered the joy of math at a later age. I acknowledge your point of the fac positions being very few but this is also the case for applied departments when you adjust it for the supply, there will be people who were introduced to computing at such an early age that they would be gods at debugging and optimizing.

Sorry for the wall of text.

"If you don't have incredible intuition, you build it from scratch with examples, like me" - A top tier mathematician at my school who has like a billion pubs at annals of mathematics

[hearty steppe]

It’s going to be nearly impossible to do work in a pure field even if you study math.

I study theoretical mathematics is what I’m saying because I believe it’s the only real way to study math even if what you do is applied focused. Don’t skimp out on the theory and doing the exercise problems in the theory books! That’s where you should be spending most of your time as a mathematician at least.

Fields are becoming so interconnected now outside and inside math that most of what mathematicians will be doing is computer science or data science related as well

[halcyon garden]

Brb in 12 years to prove you wrong

[hearty steppe]

I hope you do

My point is it’s very unlikely you’ll be doing pure math research for your entire career

Maybe around your prime you might have a shot

At some point you are probably gona work in the industry or with a team of programmers

[halcyon garden]

Maybe, but I find it hard to fathom how someone doing analytic number theory or algebraic geometry would do applied work, but sure they can contribute tangentially

[hearty steppe]

Cryptography and data science are very involved with mathematical intuition

It’s certainly not as difficult as the purity of the subjects you study but there is room there

The idea is you can use your insight to deconstruct problems outside of math

And you can use that as a stepping stone to do research in your area that’s more lined up with the purity of the subject if that’s what matters to you, but I think it’s important to be open minded about the odds weighed against wanting to stick to one route and not be open about how interdisciplinary routes can actually maximize your studies

It’s like me being stubborn about having to get into grad program when I should be open to the possibility that maybe that won’t work out and that shouldn’t demotivate my studies

[blazing canopy]

It seems like you're viewing pure mathematics as something that can only be studied by the privileged few, and everybody else must do applied research, but I know for a fact there are many mathematicians who are neither superstars nor geniuses in early life who study pure mathematics

[hearty steppe]

No you can study pure math but it’s hard to contribute new things

I am probably wording it terribly but I think the approach should be, study from the pure books and if you get a chance definitely contribute

But everything is so interconnected now with computer science and data science

[blazing canopy]

You might not contribute to something that revolutionizes the field, but I simply know many colleagues, friends, etc, who just study small niche problems in pure mathematics and are able to receive some small amount of funding for it

[hearty steppe]

Wdym

How do I learn more about this?

[runic hatch]

I think they’re saying that it’s arguably harder to work in pure compared to applied? I also don’t know enough to have my own opinion on that

[hearty steppe]

Correct

You can study pure and work in applied

I’m pretty sure anyway, since that’s what I’m trying to do

[blazing canopy]

There are certainly some low-hanging fruit in applied math, but my experience would not suggest that it is intrinsically more difficult to do pure research

There are some big problems in pure mathematics that are impossibly difficult to tackle, but the average mathematician is not working on those things

[hearty steppe]

Anyway I’m sorry for ramping up a storm. I really meant to say that it’s important to be open to working in applied if you can’t find work in pure math

Working and studying are two different things?

Right?

Lol

[blazing canopy]

I'm speaking as a professional mathematician, so those are the same at that level. You work on the things you are studying.

[hearty steppe]

But many applied mathematicians study from pure math books clearly

[blazing canopy]

OK, but that is a different meaning of the word. It is common for a mathematician to say "I'm interesting in studying problems concerning..."

meaning that these are the problems that they are working on in their research

[hearty steppe]

Oh studying problems vs studying a whole subject you mean

So like you would look into the problem but you can also get insight from a subject text

[blazing canopy]

Well, either way, I mean for the two to be the same, in my above statements. I understand that they can mean different things in other contexts.

I'm just saying that, in my experience, it is not intrinsically more difficult to work/research in a pure field than an applied one.

[hearty steppe]

Yea well I didn’t mean to mix things up earlier. I think it’s important to kinda be mindful that we should be open minded about how we choose to explore math and the potential to use it for work?

[blazing canopy]

In fact, in my experience, there is actually a lot of scrutiny put on applied mathematical research because the metrics for what constitutes a worthwhile application can be a little more demanding, or discerning.

[hearty steppe]

I would be curious to learn more about perspective on how people study math, whether they go through pure math books and do some or most of the exercises. Especially how they prioritize their time when they also do work which may not really relate to what they study directly.

[blazing canopy]

Scrutiny that does not exist in pure mathematics, that is. For example, study of certain numerical algorithms can be heavily scrutinized if it does not translate to real-world computational performance gains, compared with existing algorithms.

At the graduate level, you can still learn a lot by just reading from books. But later on, it is difficult because usually most fields move fast enough that books have not yet been written.

[hearty steppe]

I am also noticing there are many glorified engineers out there that think they understand mathematics but don’t really study mathematics, at least like some of us do going through the pure texts.

[hearty steppe]

This sounds a bit scary but also exciting.

Also “numerical algorithms” is kind of a loaded term here? I’m sure some people are thinking of algorithms involving numerical methods.

[blazing canopy]

I do not understand your question/statement.

[hearty steppe]

What exactly would you consider a numerical algorithm as it seems like a loaded statement. If it’s even a complex computation, it can still qualify as a numerical algorithm. When I mean numerical methods, I’m talking about context limited to “numerical methods” level and themes books.

[hasty turret]

How often do applied mathematicians just work as engineers

It feels there are some parts of engineering that are just nice math

[blazing canopy]

This is all just semantics I guess. You can count whatever you like as a "numerical algorithm", it is not perfectly defined. Same with the meaning of "applied mathematician" or "engineer".

[sage python]

Bredon cohomology wants to know your location

[mossy python]

does anyone know a good linear algebra book for dummies?

[grand thistle]

i think linear algebra done wrong is really good

im using it rn

by treil

[mossy python]

ohh!

would it be suitable for

like

a

10th grader?

[grand thistle]

I mean as long as u have some mathematical maturity

I’m in 9th grade

[runic hatch]

you can always crack open the book and try reading the first few pages

[grand thistle]

i recommend familiarity with proofs

a lot of the exercises tell u to prove stuff

[runic hatch]

for linear algebra done wrong specifically it's available online for free right

[mossy python]

asking this for my brother, but yeah he's pretty decent

[mossy python]

oh

[grand thistle]

i like how much the book covers as well

[runic hatch]

ye it's a pretty comprehensive book

[gray gazelle]

there is as well a book called "Linear Algebra for dummies"

[grand thistle]

it has all the normal stuff + some more advanced spectral theory and some multilinear (tensor) stuff

[mossy python]

ohhh icic

got that book!

sergei triel right?

[grand thistle]

i dont think they meant linear algebra for dummies literally

[grand thistle]

yeah

thats the one

[mossy python]

there is one

lol

with that exact name

the "for dummies" series

[grand thistle]

yeah ik but im pretty sure those aren't really that comprehensive

but idk

[mossy python]

oh

[grand thistle]

ive never read one of those

except for one about minecraft when i was like 7

[mossy python]

linear algebra done wrong, this seems better though

[mossy python]

there's one for everything..?

damn

lol

[runic hatch]

yeah I think LADW is probably better

[mossy python]

aight, thanks guys!

[grand thistle]

no problem

[wicked trout]

Looking for the most rigorous set theory book ever.

[hasty turret]

Don't

[wicked trout]

Why

I feel this itch

[hasty turret]

It's very niche tbh

If you are qualified enough,yea go ahead ig

[wicked trout]

Ofc I am not qualified

But curious

[hasty turret]

I guess Principia mathematica counts

[proper lotus]

I don't even know enough math to know what is 'rigorous set theory.'
Does https://en.wikipedia.org/wiki/Naive_Set_Theory_(book) count

[quick hornet]

https://arxiv.org/abs/1305.3835

[wicked trout]

Thanks for that. I've found the formalized axioms for proof solvers

[proper lotus]

Ah yes it's #foundations

[wicked trout]

But too hardcore to grasp

[hasty turret]

They can't too hardcore

The problem might be you might be misunderstanding your problem

[wicked trout]

It can be

But i'm shooting blind

[hasty turret]

What do your axioms look like

[wicked trout]

Maybe something will stick

I mean I read this old USSR book which has 5 axioms and some formula

[quick hornet]

if you struggle to understand the axioms used by proof assistants, i doubt 'most rigorous' is what you want

[wicked trout]

and they say its obvious that you can derrive this from these

[quick hornet]

halmos is indeed probably a good req for you

[wicked trout]

i cannot see the connection

so i go dive into other sources

[quick hornet]

it does miss 1 axiom but w/e

[wicked trout]

to get deeper intuition

[proper lotus]

I feel like you're looking for intuition and mistaking this lack of intuition for lack of rigour

[wicked trout]

aint it the same?

[hasty turret]

Ok,This is like a highschooler trying for the olympics because they want to get a good grade in gym class

[wicked trout]

you get the details you feel the big picture

[proper lotus]

Nami's the most qualified I think, and he says you should look at the Halmos book (the one linked)

[wicked trout]

haha, sounds right. maybe looking for inspiration for the lacking discipline at the moment.

[proper lotus]

So I would listen to Nami

[runic hatch]

For sure

[quick hornet]

if intuition and rigour were the same thing, all grade school classes would be replaced by homotopy type theory.

[wicked trout]

isnt it about the broken bureaucracy? system is just the way it is.

[hasty turret]

99% of mathematicians don't go beyond naive set theory in foundations pov I think

[quick hornet]

for some reason, kids find things like 'numbers' and 'adding' and 'pictures' more intuitive than 'types' and 'topoi' and 'infty-1 categories'

no clue how.

[wicked trout]

in school they avoid logic and proofs, you just rote memorize.

[hasty turret]

Unironically,types are actually intuitive tho

[wicked trout]

when i found that it excist it cured my childhood trauma of learning shit i dont get

[sage python]

The first thing we do when teaching kids addition is get them to unlearn types such as apples and oranges

[manic fox]

llol

[sage python]

To abstract 2apples + 2apples = 4apples and 2oranges + 2oranges = 4oranges

To statements like 2+2=4

[hasty turret]

Big math is against types

[quick hornet]

if youre truly ready for the most rigorous stuff you'd skip the textbooks and go to nlab

then read whatever nlab recommends

[frosty girder]

[quick hornet]

half-serious

[frosty girder]

[wicked trout]

brain will break, not smart enough, but what is nlab?

[manic fox]

nlab 🙏

[quick hornet]

nlab is responsible for that sticker

https://ncatlab.org/nlab/show/HomePage

[sage python]

lambdaman you should start from the basics but viewed properly

For example how well do you "understand" addition?

Like deep down. Why does carrying work the way it does?

Not rhetorical

[quick hornet]

'tis the will of the one God, praise be!

[sage python]

https://www.jstor.org/stable/pdf/3072368.pdf?casa_token=pxa43UZRCD0AAAAA:EWypocNuC8NoJ-O3LdLPY2BzdICerb36VRCl4_5WpzGKjPy3wPEBqz8cWdxIjIODpeG4c-Ir8hddDkwYm_xq5AdSthnDoFQgoZMYmP4-9v5qcAcNOnk

@wicked trout try this out

(Kinda joking, though it is unironically a good intro to what it covers)

[wicked trout]

abstract algebra and operations that is what comes from memory. function with two arguments

[frosty girder]

[wicked trout]

carrying what is it ? i know currying from lambda calculus

[sage python]

When you add two numbers and carry the 1

[wicked trout]

i could not explain it rigorously, the nature works that way just

[sage python]

Yeah I'm mostly kidding about that paper, it explains carrying using some ridiculously fancy shit lol

[wicked trout]

sometimes complex shit inspires to search deeper.

[hasty turret]

Now that I think about it,carrying is incredibly arbitrary and so is our way of adding things

[north heron]

hello, do you recommend any book for statistic and probability from 0 ? i'm doing basic mathematic from serge lang but there are not in it

i need to get good knowledge in that to start university in some months

( i got close to 0 knowledges in that right now )

if you know a french book is a plus, but i'm fine with english book too

[runic hatch]

I liked Statistics by Freedman, Pisani and Purves a lot

[north heron]

https://www.amazon.fr/Statistics-David-Freedman/dp/8130915871/ref=sr_1_1?__mk_fr_FR=ÅMÅŽÕÑ&crid=6972SQM3I9UD&keywords=Statistics+by+Freedman%2C+Pisani+and+Purves&qid=1648382709&sprefix=statistics+by+freedman%2C+pisani+and+purves+%2Caps%2C43&sr=8-1#customerReviews that one ?

[runic hatch]

yep, nice to see there's a french version too

[north heron]

thanks you

[north heron]

does it cover probability a lot too ?

[runic hatch]

yeah there's a fair bit of probability stuff too

later on, once you feel like you have a good grasp of basic stats/probability, I recommend Mathematical Statistics and Data Analysis by Rice

those two books should tide you over for most of undergraduate stats

[polar mango]

Any recomendation for calc 1 books?

[marble solar]

Spivak/Apostol/Courant are great, I'm partial to Spivak

If you want a more standard, Thomas' University Calculus is great

[sudden kindle]

I wanna learn number theoreeeee!!

https://tenor.com/view/meme-let-me-in-gif-15458934

[frosty girder]

i wanna learn mathsssss!!

[tardy walrus]

i wanna break free!

[honest trout]

Wsg cuh

[patent mango]

I've seen a book completely filled with proofs of Pythogorean theorem. I forgot it's name. Help!

[heady ember]

You just vaguely stated that the book has proof of Pysthagoras' Theorem

How do expect ppl to know what book are you talking about with that little detail

[rare apex]

I need a good introduction to game theory that includes studies on hirarcical cognitive reasoning. As little as math as possible would be good 👍

[flint forge]

Game theory is very mathematical idk how much you can get away with no math hahaha

(I would give a rec but all the game theory texts I know are basically math textbooks)

[rare apex]

That's cool what can you recommend?

[flint forge]

https://www.amazon.com/Introduction-Game-Theory-Martin-Osborne/dp/0195128958

I read a large part of this in undergrad and liked it

[rare apex]

Thx

[solemn mantle]

The Pythagorean Proposition https://www.amazon.com/Pythagorean-Proposition-Elisha-S-Loomis/dp/0873530365

[patent mango]

Exactly, thank you so much!!

[timber mesa]

in this case it's like, the one book dedicated to proofs of the Pythagorean thm

[rocky nebula]

can anyone recommend me a book on ODE?

[gray jungle]

what are the prerequisites to lee's introduction to topological manifolds ?

[blazing canopy]

What kind of ODE? At what level?

[timber mesa]

yeah are you looking for a theoretical/qualitative theory kind of book or just something that teaches you how to solve ODE

[slim peak]

Viorel Barbu,'s book entitled "Differential Equations"

[rocky nebula]

ODEs of any order and at a first level. I just learned the basics ODES on Howard Anton book of calculus

[rocky nebula]

I'd like both, but not too rigorous, I'm a physics student

[rocky nebula]

I'll take a look at it, tks

[slim peak]

It includes background from physics in the introduction

[rocky nebula]

great

[cinder tundra]

Anyone know any more recent books (preferably less rigorous, since I have that already) which covers much the same material as Mendelson's Introduction To Mathematical Logic?

Also, any good books which goes in depth into computability theory specifically would be nice too

[runic hatch]

If you understand everything in the appendix with a quick skim then you’re probably OK; some analysis knowledge also helps

[sudden kindle]

@slim nacelle have any book recs to learn about special vals of L funcs

[hallow oriole]

now that i think abt it this channel is prolly the place to post this

[slim nacelle]

Hmmm from what perspective?

[blazing canopy]

If you are able to find online copies of these books, there is nothing better than just looking at the first chapter of the book and you'll know immediately whether it seems like you have the prerequisites to read it

[slim nacelle]

This is a gargantuan topic

[hallow oriole]

i don't know how i didn't think of that

[sudden kindle]

I don't know. What perspectives are there? I'm looking for an introduction. I just know the analytic class number formula

[slim nacelle]

Rationality results, connections to Bloch-Kato and Beilinson’s conjectures, congruences, generalization to multiple L-values…

[sudden kindle]

Hm

[fluid skiff]

by any chance anyone has ebook for this https://lib.ugent.be/catalog/rug01:000005363

[fluid skiff]

seems like we are at similar stage

[frank lava]

Does anyone know a good book for learning 3D geometry? Like planes and such. Preferably with lots of problems.

[heady ember]

[prime oak]

hey book recommendations on complex analysis/

[grand thistle]

schlag

[smoky zephyr]

the only reason i’m gonna use this is because it’s relatively short lol

[frosty girder]

use apostol

i will shill it till the end of time

[smoky zephyr]

@frosty girder i’m using rudin for single variable and munkres for multivariable

[frosty girder]

analysis?

but why rudin

[smoky zephyr]

because it’s short

[frosty girder]

its not beginner friendly

imo

[smoky zephyr]

[frosty girder]

its very terse

[smoky zephyr]

we will find out

[frosty girder]

i did already

i was gonna use it as well

i switched to apostol coz it was easier to read

[smoky zephyr]

i will find out

[frosty girder]

Sure llol

i mean, rudin is a classic

[smoky zephyr]

strad is using rudin and he isn’t dead yet

so how bad can it be

[woven forge]

i've done abbott before doing rudin

[frosty girder]

[woven forge]

its much smoother after that

[frosty girder]

yeah thats better

exactly

[woven forge]

also i recommend tao's analysis

its like modernised and friendlier version of rudin

[smoky zephyr]

well i have a few books on my list so worst case scenario, i’ll switch

[frosty girder]

i dont recc this for a few reasons

[frosty girder]

noice

[woven forge]

Measure, Integration & Real Analysis

has anyone seen this book by axler?

[smoky zephyr]

why

is it because it’s super slow

[frosty girder]

mind if i tell in like 30 mins or so?

gotta go

[smoky zephyr]

ok

[gray gazelle]

yes it's great it has picture of Axler's cat

[frosty girder]

there are like 4-5 reaons

[frosty girder]

based

[woven forge]

its cute

[frosty girder]

ping me in like 10 mins quantum

[smoky zephyr]

i will if i remember

[woven forge]

actually i have some questions regarding its prerequisites

[gray gazelle]

I like the approach a lot, although might be quite hard for first time real analysis learners

[woven forge]

the problem is i don't really know about multivariable analysis

such as implicit function theorrem

i'm quite struggling with the course currently

[gray gazelle]

also it has this picture

[smoky zephyr]

already love it

[smoky zephyr]

[woven forge]

This is a pretty good linear algebra book.

[surreal cargo]

you should look at tao's analysis 1

[karmic thorn]

🚫

[frosty girder]

[frosty girder]

ok im back

so problems with tao analaysis

Firstly, its too wordy, not in a good way, at times his explanations go pretty weird
the first chapter of the book is good at motivating analysis

but otherwise there isnt much good stuff in it

[vague basin]

is there anyone good at physic?

[frosty girder]

second, he spends 6 chapters of the first book covering things that should be done in one chapter at max

there are not many problems

and their is a lack of computational problems

all this makes for a pretty not good first experience

i think the book would be better as a reference of some sorts

also, he doesnt use metric spaces

which isnt the best thing

and spending 6 chapters constructing the reals is

[frosty girder]

what level of physics

[normal sandal]

Just use Rudin

[frosty girder]

dont use rudin

for a first go

[normal sandal]

Terrible as a first text though

[frosty girder]

i wont recc that

[frosty girder]

exactly

but brilliant as a reference for later on

U should ideally do a book with tons of problems

apostol for example, doesnt shy away from giving problems

his chapter on topology had 50 different exercises, many of which had parts

and the chapter on limits had more than 70 or so

u dont need to do all of them

but u should have the options to do many

[atomic hound]

a book that teaches all 2d/plane geometry!!!

and the cool geometry formulas

[woven forge]

https://www.amazon.com/Geometry-Enjoyment-Challenge-Richard-Rhoad/dp/0866099654

there is this book

but its pretty expensive so I suggest chekcing out libgen tbh

[marble solar]

Spivak Calc. on Manifolds gets you up to speed fast

[gray gazelle]

neee complex analysis book

rigor please

or challenging

[hollow peak]

stein and shakarchi

[gray gazelle]

how do you rate it?

[hollow peak]

rigorous and complete /10

sort of the standard

[gray gazelle]

what do you explore after?

can you go onto anything involving complex anal for most part

[hollow peak]

you can study riemann surfaces

[gray gazelle]

or is it a complete primer

yeah i wish i could lol

[hollow peak]

lol complex analysis gets significantly deeper than just a first course unfortunately

[gray gazelle]

atm i realized idk any non trivial examples of riemann manifolds

ig ill come back in a month or so asking for more

new goal is to become analysis god

mostly complex tho

[hollow peak]

it's quite the nontrivial path

you need a not insignificant amount of topology and geometry for complex stuff

[brittle breach]

@gray gazelle

[sage python]

Check pinned messages, I posted a review of a fair number of complex analysis books

[grand thistle]

how good r stein and shakarchi's other books

isn't their complex analysis textbook part of a 4 volume series

of fourier analysis, complex analysis, real analysis and measure theory, and functional analysis

[balmy phoenix]

boolean algebra and set theory involving power series for someone who is really struggling to manipulate sets?

[misty wyvern]

What is the worst complex analysis book

No rigor, makes wrong statements, completely trivial

[timber mesa]

sounds like you know the answer

[blazing canopy]

maybe a complex analysis book for toddlers?

[crystal lion]

I made some notes a while ago

[frosty girder]

and what book is that

[gray gazelle]

does this exist

[blazing canopy]

There's https://www.amazon.com/Bayesian-Probability-Babies-Chris-Ferrie/dp/1492680796 so I thought it might be plausible there's one for complex analysis as well

[runic hatch]

sadly it doesn't look like there's a complex analysis one in this series

[solid idol]

In need of, Short Book, Easy to Read, Topic - Set Theory not more than 15 Dollars

[karmic thorn]

What level of set theory?

[solid idol]

Level?

I wanna do Set Theory for Linear Algebra

[karmic thorn]

Okay, something like Hammack's Book of Proofs should be fine. You can find a free PDF on the author's webpage.

[solid idol]

Sure. Thanks!

[karmic thorn]

https://www.people.vcu.edu/~rhammack/BookOfProof/

[solid idol]

the book costs more than 15 dollars (Hardcopy)

Any other recommendations by any chance?

I am tight on budget.

Is Naive Set Theory by Paul R. Halmos Good? Found it for 5 Dollars is it worth?

[smoky zephyr]

@solid idol the pdf is legally available for free

do you need it to be a hardcopy?

[solid idol]

yeah but... i dont like reading pdfs

i need hardcopy

hardcopy is +15$

[runic hatch]

Halmos seems quite good for 5 dollars IMO

It should help you for lin alg and a bit beyond

[coral narwhal]

I don't think you need Halmos for intro Linear Algebra, but it is a good book so you should prolly get it :)

[frigid comet]

Yeah that's a great book. Halmos writes well in general.

[smoky zephyr]

halmos LA

[heady ember]

Just print it out?

[solid idol]

15$*

[solid idol]

how. book arent supposed to be just pages, they should be a cover.

[heady ember]

How does a cover make any difference

[solid idol]

it does

[heady ember]

[solid idol]

that will cost more money. to fix the printer at home

[heady ember]

Its not like the cover has important information anyway

[solid idol]

well. ig i will ask for some money. Thanks!