so stupid
#book-recommendations
gray gazelle
tribal kernel
Worst I’ve had is a physics professor encouraged the class not to buy the international edition because if was missing a chapter and some exercises
Had a math professor who said he didn’t know anything about international versions
I think he was talking about Hoffman and Kunze cause it wasn’t in print anymore except for the international edition
But dang that engineering professor is dumb
sleek python
wtf some profs are so greedy
It's only a us thing from what I've heard, we don't have profs act like that here
tribal kernel
I even had a professor who wrote the book for that course and she provided it for free
sleek python
Same, had a language teacher provide us with a free pdf of her book
flint forge
Whats the best reference (not learning) book for linear algebra
sage python
Dummit and Foote
robust palm
does anyone know where to get solutions to royden's real analysis?
gray gazelle
from your brain
fast portal
What is the best reference for Diff Eq
gray gazelle
what do you want to learn about them? How to solve them or more like analysis of ODEs?
prisma snow
Idc about what he wants, but I'd like a reference for the analysis of ODEs. Please @ me if someone recommends something.
gray gazelle
ODEs Basics and Beyond by Schaeffer,Cain
prisma snow
Thanks
gray gazelle
required basic analysis knowledge and being comfortable with linear algebra
prisma snow
Should be fine
slender dragon
Dummit and Foote
@sage python
Perfect book
upper ruin
Hi guys, do you have tcwag book?
valid moth
@flint forge I think HK is pretty short
Although I haven't read it so I can't really say
robust palm
from your brain
@gray gazelle I wasn't asking for myself, but for a friend who's taking a functional analysis course where that is one of the texts used
gray gazelle
from their brain
robust palm
I'm not a big fan of the text from the bit I've looked at, probably more because of the old style typesetting (using epsilon for $\in$)
hasty eagleBOT
mathew_soto78:
robust palm
and not so much because of the actual presentation
valid moth
Can you even learn functional analysis if you are not first functional yourself 😎
valid moth
this is why you consume caffeine in the morning
gray gazelle
2 cups a day, any less and i can't work well
robust palm
how dare you assume I can be functional
valid moth
I'm going to go ahead and assume you can be type theoretic actually
robust palm
@gray gazelle thanks for the link!
radiant basalt
I'm currently trying out the lectures of Schuller of the Geometric Anatomy series, and I'd like to ask, does anyone know some books that I should supplement it with, for practicing problems ? Or should I go for things individually, like Munkres for Topology, and similarly individual books for other topics ? If so, then I'd like recommendations for Differential Geometry
tribal kernel
For diff geometry recommendations, Lee’s introduction to smooth manifolds and Riemannian manifolds are great books. Spivak also has a good series on calculus on manifolds and differential geometry series, Do Carmo’s book is also good
velvet briar
I loved Tu's diff geo and more people should talk about it imo. Throw that on the pile
gray gazelle
tu's diffgeo is brilliant
i've read his an introduction to manifolds pretty thoroughly, except for the derham chapter, and i thought it was superb
i'm taking a course in riemannian geometry right now and i think that his Differential Geometry - Connections, Curvature, and Characteristic Classes is also very well written
they are good books
i always check that or lee when i need clarification on something do carmo skips over
tribal kernel
I have not heard of this one. Perhaps I will look it up
marble solar
Not reading spivak for everything manifolds
Only spivak's comprehensive introduction is allowed
tribal kernel
Yes and you must read all 2000+ pages
radiant basalt
Thanks for the recommendations guys, I'll be checking them out!
tribal kernel
Btw I'm recommending diff geometry books, but I'm not familiar with the text you referenced so these may not be necessary. Whatever the case, the books are good in case you do need more geometry in your life 🙂
radiant basalt
ahh Thank you! and yeah there's quite a chance of encountering a lot of Geometry in my life haha
fast portal
what do you want to learn about them? How to solve them or more like analysis of ODEs?
@gray gazelle solve them
gray gazelle
Wolfram alpha
fast portal
Not learning mind you
It is more like I want a reference
The book I learned it from sucks as a reference
gray gazelle
Wolfram alpha
slender dragon
Apostol Book is good
fast portal
slender dragon
Apostol Calculus Vol 2
fast portal
For Diff Eq?
slender dragon
Yes
It have two sections on Differential Equations
You can see too, Boyce Di Prima Differential Equations book
fast portal
Thanks I will give them both a look
near adder
I used this for my DE course
Same as enigsis mentioned
I found to be pretty nice, last chapters on PDE's and sturm-louville theory. Very last sections on singular SL as well
fast portal
The latter has some really worrying reviews on amazon 
waxen elbow
hello; any good probability book for a first course that goes a bit deep ?
slender dragon
The latter has some really worrying reviews on amazon :Sweat:
@fast portal
Let me see it
fast portal
@slender dragon
hasty turret
You could always libgen it and check for yourself
marble solar
@fast portal Boyce and DiPrima is a classic reference for elementary ODEs
I don't know an analyst who doesn't have it on their shelf
It does a lot of things really nicely, like picard's iteration
hearty steppe
Boyce Di Prima is ok
I like Nagle Saff Snider better
Especially for its breadth of exercises
gray gazelle
When I try to translate sentencial logic to english sentences I alway translate with a word by word conversion. Sometimes it works. Sometimes it does not. When should I not do it?
I was on the wrong place. I am going to ask in another channel
hearty steppe
try Paul's online notes (look up on google) and Professor Leonard youtube channel
I used James Stewart for problem sets
granite heath
I won these from a math contest
broken meadow
cool pencil
granite heath
Haha thanks
pine igloo
I won these from a math contest
@granite heath congrats😃
the "Challenging Problems in Geometry" is a nice book
strange osprey
Do you guys like dover publication's books on math?
strange osprey
This is like all the math books https://store.doverpublications.com/by-subject-mathematics.html
runic hatch
they dont seem bad
gray gazelle
cheap book good
strange osprey
Haha Ikr
hearty steppe
I mean like legal free
I don’t think it was project Gutenberg
But that’s one lol
stray veldt
actually quite the opposite
project gutenberg has mostly books with expired copyrights
but the legality still depends on where you live
because copyright laws do
timber mesa
also SpringerLink if your uni is affiliated
wooden sparrow
Can we use sci-hub to unlock Springer books from paywall?
cunning lark
That would be pirating?
hasty turret
flint forge
@sage python (or anyone else)
is there a good modern text on rep theory of finite groups
i feel like fulton harris is missing some stuff
sage python
Idk how modern Serre is but it's good for finite groups especially
flint forge
is either written in latex
sage python
Wait Ultra isn't Ginzo's book like
Prelude to geometric Langlands?
Lmao
http://www-math.mit.edu/~etingof/reprbook.pdf this doesn't focus on finite groups but it's got some stuff
Serre's typesetting is nice, not sure if it's exactly latex but it's clean to read
marble solar
Welcome to MIT how may I help you
radiant basalt
What was that free books URL
@hearty steppe
I created this list of websites with some research, these provide ebooks for free and some are illegal.
LIST OF WEBSITES TO FIND FREE EBOOKS
sudden kindle
yeah I've been using this calculus text this past semester for my recitation
hearty steppe
you should be fine with Ross
I haven't had to use Ross as of yet but I glimpsed thru it and it is very nicely structured.
so if your struggling with probability, that might be all you need
main stump
Anyone know any books how math was discovered, what is math. How did geometry come to be
Etc etc
A book that is for a senior high schooler not some super crazy shit i wont be able to read lol
granite sluice
@main stump Biographies can be an interesting source of that kind of information, among other things. Andre Weil wrote an interesting autobiography.
smoky surge
honestly ross is super boring
but maybe introductory probabilty theory is in general
granite sluice
Algorithms books are good for intro probability theory, but its usually immediately applied to something interesting
smoky surge
it was almost information overload but i was also going through it alone
yea i think its more trying to learn a ton of distributions i felt like i had to memorize the formulas for all of them and all expect values/variance
i might have gone about it the wrong way
i think when i redo it im going to use a universitys course to try and get a bettersense of how to go through it
granite sluice
yea i think its more trying to learn a ton of distributions i felt like i had to memorize the formulas for all of them and all expect values/variance
@smoky surge yeah this is probably not necessary, although it doesn't hurt. imo its more important to understand how and why the different probability distributions relate to each other, and what constructions they are used for, than to remember all the normalizing constants and moments and so on.
But being able to calculate accurately with them is a non-trivial and useful skill.
So it's probably learning that will pay off.
hearty steppe
I think probability is interesting. Stats however can bore me after a while, especially without much context
karmic thorn
Can anyone suggest alternatives to Coxeter's Intro. to Geometry? I need a physical copy and it's not available(at a reasonable price) at my place.
radiant basalt
Ahh... I'd say print it and get it turned into a book, that'd be super cheap. I have a printer at my home and I've printed and stitched several books myself. But Coxeter is a good book. The alternative to that might be EGMO (assuming you're asking this for Olympiads) but that's also going to be costly I believe.
karmic thorn
Nah, not olympiad stuff.
More like analytic geometry, eventually leading to some advanced stuff.
heavy garden
karmic thorn
Mine arrived 6 months ago and I'm still at page 56 
lost fjord
lol
It took it quite a while to get here
since it had to be shipped all the way from india apparently
karmic thorn
The red hardcover?
lost fjord
yes
karmic thorn
Ah yes, that one's printed in India. It's inexpensive as hell though.
karmic thorn
Ye, the quality of print is neat.
karmic thorn
Maybe shipping did that, but it's the inside that matters haha
lost fjord
I'd send a pic but my ipad is dead
karmic thorn
Lmao
karmic thorn
It's a great book, especially if you're learning on your own.
lost fjord
yeah that's why I chose it
I can't do super advanced anal books for I feel that I am no where near that level
(ie rudin)
karmic thorn
Definitely a good call. I should hasten up a little bit though lmao.
Yeah, Rudin doesn't seem great for a first read.
hasty turret
Baby rudin doesn't seem that bad
lost fjord
Here it is
karmic thorn
Looks the same although I admit the edges are a bit too worn out.
Maybe, the only time I looked at Rudin was midway in HS so I might've found it to be terse back then.
limpid gazelle
Tao's analysis is so slow
hearty steppe
Baby rudin is not a beginners analysis book, that’s for sure.
I dunno how anyone with very little formal math experience can read through it
gray gazelle
When does real analysis come into picture? Like when does one get into it
I have done some ODE things recently and I'm confused about the next step now
Like Laplace transform non homogenous DEs etc etc in ODE
karmic thorn
You can get started with Tao. Actually, analysis is more about writing proofs than getting computations done(as is the general emphasis in calculus). But nevertheless you'll develop a much better appreciation for the underlying mechanism of calculus, and beyond.
gray gazelle
I see
So should I like get started with it now
I'm asking this because I have little background in linear alg
worldly basalt
If your focus is jee then no
karmic thorn
Lin.Alg. isn't necessary until the chapter on differentiation on severable variable kicks in
And you could start with lin. alg. first if you like
Strang/Lay might be good starting point
And then get into analysis
gray gazelle
Great. Thanks alot Ted !
karmic thorn
No worries :)
hearty steppe
Real analysis is great when your doing Research or new cutting edge level work where you need math rigor. It’s not all that common in engineering if you do corporate level work unless you work in R&D or if you work with a strictly R&D organization or you are in academia
Like if for some reason you need abstract algebra knowledge involving stuff like groups or rings
Or topology
If you don’t plan on doing R&D intensive work or strictly research, I don’t think that level of math is necessary
Even stuff that requires some level of complex analysis, I’m sure it is recommended to have at least a semester’s worth of real analysis under your belt
quartz pawn
Yea if you''re doing research then you have to know real analysis.
It's the only way you'll know for sure whehter or not the conclusions that you're making are logically valid.
gray gazelle
On the subject of Laplace transforms, integrals like the Bromwich integral frequently show up in control theory engineering and a few other subjects so complex analysis is also going to be good to learn
hearty steppe
I mean especially if you really want to focus on independent research (like me) you should at the very least learn a semester of real analysis
shut grail
When you start getting further into metrics and functional analysis, you do use advanced linear algebra, so I think regular fundamental linear algebra with a first semester in real analysis should be all that’s necessary
hearty steppe
Depends on what your doing
But I mean a semester of real analysis seems to be the consensus around here. I’ll know for myself when I get there.
You should at least be able to pick up more without much trouble as you go
quartz pawn
Yea you need to have a solid basis in LA to do multidimensional real and func anal
Best to have it down so you're not having to keep going back and review it
gray gazelle
mvc or functional analysis without linear algebra sounds like a terrible idea
sage python
So honestly honestly? Functional analysis doesn't rely thaaat hard on finite dimensional linear algebra
Or at least what I've seen of it
gray gazelle
b-but muh matrices
sage python
Because nothing transfers over
If anything half your time is spent unlearning things
"Oh yeah so we have a sequence on the unit ball let's take a convergent... motherfucker"
gray gazelle
👀
granite sluice
At least some of functional amounts to 'what conditions do we impose so that the finite dimensional intuition works?' From that angle, knowing LA is important.
I mean, for instance, that notions of convexity and orthogonality work more or less as you'd expect in Hilbert spaces.
There are things that don't work, but the general strategy of 'decompose into orthogonal pieces, apply pythagorean theorem' is valid.
Related is thinking of conditional expectation as an orthogonal projector in a Hilbert space of random variables -- that gives a lot of intuition for conditioning via the finite dimensional intuition.
I guess because it's visual?
😐
Some of the pathologies of infinite dimensional space can also be seen as 'pathologies in high dimensional space and let n -> infinity.' Finite dimensional Euclidean space is weird for large dimension.
I prefer to think of conditional expectations as giving a bimodule structure.
@sweet lotus What do you mean?
(Also rep theory is another situation where the compact group/ infinite dimensional theory works the same way as the finite dimensional/ finite group setting, provided you have the right hypothesis. Finiteness just lets you build intuition and avoid technicalities.)
(Although matrix coefficients are maybe not emphasized in the finite group setting in the way that they might be to make transitioning to infinite dimensional case easier.)
What is B(H)?
oh, borel field?
My knowledge of infinite dimensional rep theory mostly stops at the representation theroy of SO(n) -- pretty much everything I think about is finite anyway.
Yeah. Usually for calculation I use matrix coefficients anyway.
Given a conditional expectation E on a subalgebra M of B(H) onto a subsubalgebra N, you have that E(axb)=aE(x)b for all a,b in N and x in M.
@sweet lotus Is this a quantum probability thing?
(Guessing mainly as I know vaguely that RVs are replaced by operators, or something like that.)
soft terrace
does quantum probability have cool applications?
hearty steppe
Probably with anything quantum related I’d imagine.
Quantum physics, quantum chemistry, quantum biology, etc
It would however apply to quantum level mechanics?
So it may not really matter on classical level interactions
I think most people confuse that quantum is better than classical or it’s just a whole different level. The deal here is, it depends on what scale your measuring at. If you are going for sub-molecular, then it matters. Otherwise no
So subcellular interactions in the case of quantum biology as an example, submolecular regarding quantum chemistry, and sub atomic particle regarding physics?
You need to be familiar with concepts ranging from complex Bayesian inference, non-locality, etc?
smoky surge
it sounds cool
hearty steppe
Yea I think quantum is really only necessary for molecular level stuff
Quantum computing is a bit different tho compared to other fields of quantum sciences
gray gazelle
Any book recommendation for algebraic numbers?
sudden kindle
Number Fields by Marcus
gray gazelle
@sudden kindle idk, seems like Marcus doesn't even define algebraic numbers, I think I need something easier
sudden kindle
it does tho
gray gazelle
which page
sudden kindle
ok this books kinda assumes you have seen field thoery / galois theory before
gray gazelle
told you homie
sudden kindle
This book might be better without the algebra background
I. Stewart and D. Tall, Algebraic Number Theory and Fermat's Last Theorem
It actually looks like a great brook from the TOC, i havnt read it tho
Its funny because the language of algebra was not available to the pioneers of algebraic number theory, but instead created by them in order to serve the needs of the new theory they were creating
broken meadow
!
marble solar
Algebraic, not Analytic
Look at these theory builders heh
They can't even solve problems kek
In all seriousness, that looks pretty cool
molten wave
ok triangle inequality man
marble solar
I hope I become a tenure track professor
I'll bash algebra every week, then I'll inevitably have to use it for something
I'll tell all my students to keep it quiet and don't let anyone know
hasty turret
How would a bash of analysis look like?
marble solar
You just saw it
'triangle inequality'
In algebra, the methods follow from the definitions. In analysis, the methods follow from pure pain supplemented with triangle inequality
marble solar
Both of which are an over simplification
(But I'll still knock algebra every chance I get, as my professors did before I)
sage python
The disadvantage of doing everything is that you can't knock anything
Honestly I should choose one side and act like I'm conquering the other side
broken meadow
do nothing, and you can knock everything
tight crag
As a logician both algebra and analysis suck
broken meadow
so my take is that math sucks
tight crag
jk I love both of them
sage python
"All the interesting work in analysis is being subsumed by my algebra work tbh"
hasty turret
Isn't logic algebra?
steel viper
monkaS
hearty steppe
I mean what else is it going to be subsumed by and what does subsumed mean
broken meadow
subsumed i think means to like
be put under
or sth liek that
oh
it means more to absorb or encapsulate
interesting
hearty steppe
I think analytical proof writing is general what analysis involves?
Other than that I guess mostly algebra
molten wave
@tight crag on a scale from jan to logician where would you place yourself
tight crag
Logician
hollow peak
I think analytical proof writing is general what analysis involves?
@hearty steppe what does this mean
tribal kernel
Start with let ε>0
twilit wraith
worldly basalt
Express your thoughts in not book section
gray gazelle
Well listen
Books can be idelogized as math
Cuz math books
See!!!
They equalize the same traits!
livid ermine
it seems pretty interesting
broken meadow
lol
tribal kernel
I haven't read any of this but the idea is cool
timber mesa
have anyone looked at the infinitely large napkin project?
it's fun if you want a quick overview of some things in mathematics, though I haven't ever used it (nor its exercises) as a serious study tool
cunning lark
Suppose I'd like to get a good introduction into probability and statistics, which doesn't make me hate it even more than I already do, which book would I read?
gray gazelle
Casella/Berger
granite sluice
Suppose I'd like to get a good introduction into probability and statistics, which doesn't make me hate it even more than I already do, which book would I read?
@cunning lark Rethinking statistics is pretty friendly. Without knowing more about your level its hard to answer.
cunning lark
I still have to pass an kinda introductory university exam in probability/statistics. It's kinda the bane of my existence
granite sluice
@cunning lark I mean, Statistical Rethinking by Richard McElreath
crystal kraken
I wanna start Real Analysis. Which book should i refer that would make my foundations strong but will also (gradually) advance me to higher levels?
worldly basalt
Demidovich
gray gazelle
make my foundations strong
you can't go wrong with rudin here but be warned it's not easy at all
maybe pugh?
pugh has an insane number of exercises and they can get pretty challenging ive heard
||especially the meme ones||
crystal kraken
okay i'll look up all three and try to decide which to go for. Thanks godfather, TTerra.
@gray gazelle by rudin, you mean 'Principles of Mathematical Analysis', right?
dapper root
Yeah the first one
There’s 3 rudins and that’s the first one aka baby rudin I believe
hasty turret
(just google baby rudin)
crystal kraken
So principles of mathematical analysis: baby rudin
Real and complex analysis: teenage rudin??
Functional analysis: adult rudin??
hasty turret
Baby,papa , grandpa
crystal kraken
Ohhk. That's weird but ok.
gray gazelle
Getting ****ed by grandpa rudin 
dapper root
Is papa rudin measure theory?
crystal kraken
Getting ****ed by grandpa rudin
That sounds SO weird without context.
gray gazelle
Is papa rudin measure theory?
first few chps are
hasty turret
That sounds SO weird without context.
That's the point
desert chasm
Hey I'm a ug electrical engineer in my 3rd year, looking for a good book on probability
I loved visual complex analysis so if I could get a recommendation like that book, I'd be very appreciative
If not that's cool too
tribal kernel
I wanna start Real Analysis. Which book should i refer that would make my foundations strong but will also (gradually) advance me to higher levels?
Start with a classical analysis book, not with Rudin. I personally enjoy Marsden and Hoffman
Rudin is an awful book for foundations lol
Bartle and Sherbert is also a good book and it takes it fairly slow.
gray gazelle
stop calling it foundations
severe ridge
Why ^
karmic thorn
Foundations is an entirely different branch of mathematics.
crystal kraken
Rudin is an awful book for foundations lol
@tribal kernel TTera suggested otherwise. Ahhhh, i am confused.
severe ridge
Lol ohhhhh yes
crystal kraken
Bartle and Sherbert is also a good book and it takes it fairly slow.
Nah, idt i have enough time to take it slow
crystal kraken
karmic thorn
Sherbert isn't as slow as Tao I guess.
But Tao/Pugh are top tier for an introduction to analysis as far as I've read these two.
severe ridge
Rudin is one of the recommended books but it’s too fast compared to marden and hoffman?
tribal kernel
Rudin just assumed this isn’t the first analysis book right? It’s pretty difficult too
crystal kraken
Ok everyone, i need help. Pls suggest which book would you have wanted your first analysis book to be?
flint forge
no
rudin is meant to be a first book in analysis
it is a very good book if you are okay with the terrible type setting
tribal kernel
Marsden and Hoffman was my second analysis book, but it was very clear, and we used it for the multi variable sections in it. It has comprehensive sections on single and multi variable analysis and it works it’s way all the way up to elementary Fourier analysis and differential equations
gray gazelle
Königsberger is best 
red stream
What about Understanding Analysis by Stephen Abbott
That's what I have been working through
tribal kernel
I think that book is actually pretty great too. Very systematic and clear
red stream
Yea it works well for me
gray gazelle
Does anyone have any experience uploading to libgen?
red stream
gray gazelle
I indexed a djvu book but cba to register/upload/seed etc.
tribal kernel
Rudin’s books require a lot of mathematical maturity. Lots of experience with proofs and prerequisite knowledge with his later books. They may be good for teaching a course or a second look at the subject to recognize the elegance of the subject, but I wouldn’t recommend it for a first analysis experience. Either classical or modern.
gray gazelle
huh
From what little I've read of Principles of Mathematical Analysis it seems very beginner friendly
Having a look at the titles, I'd assume you're meant to read them all in release order 🤔
flint forge
From what little I've read of Principles of Mathematical Analysis it seems very beginner friendly
@gray gazelle this is a hot take lmfao
Rudin’s books require a lot of mathematical maturity. Lots of experience with proofs and prerequisite knowledge with his later books. They may be good for teaching a course or a second look at the subject to recognize the elegance of the subject, but I wouldn’t recommend it for a first analysis experience. Either classical or modern.
@tribal kernel his first book is useable but i agree there is likely a better choice for a first pass
timber mesa
Does anyone have any experience uploading to libgen?
@gray gazelle it's easy, you don't need to register but there's a pass somewhere in the forums. DM me if you want
gray gazelle
@flint forge why do you say that?
steel viper
gray gazelle
@timber mesa aight
steel viper
its ok to use rudin when youve just been putting off analysis for like 6 months though right
flint forge
its a good book but its not 'very beginner friendly'
in the sense that something like Pinter is
its ok to use rudin when youve just been putting off analysis for like 6 months though right
@steel viper try 4 years
steel viper
chad
gray gazelle
Well I've only read the first 2 chapters or so, and iirc it only ever used naive set theory
flint forge
i mean i can write a book that is incredibly hard with few prerequisites
steel viper
hatcher has no prerequisites if you intuit
gray gazelle
i mean i can write a book that is incredibly hard with few prerequisites
Ye... I think Jackson's Electrodynamics is supposed to have close to no prerequisites
(Other than 1000000IQ)
quartz pawn
Rudin's book has a good solutions manual on amazon for free.
dense wren
why buy a solution manual when you can make your own
tribal kernel
That reminds me of what my old electromagnetism professor used to say
The perfect electromagnetism text would start with Maxwells equations on page one, and the rest of the book is blank pages for students to derive the consequences
karmic thorn
You're welcome.
crystal kraken
you did nothing, ted.
karmic thorn
I didn't add to your burden of books, for which I deserve to be thanked.
crystal kraken
crystal kraken
@lost fjord not cool 
valid moth
@tribal kernel That's still suboptimal. The optimal ED text would start with a blank page for students to derive maxwells equations and then the rest of the book would be blank pages as well for them to derive the consequences
tribal kernel
Lol would the book also contain the empirical data from which Maxwell proposed such laws?
tribal kernel
Lol I'm in that gang too
cyan canopy
What are the differences between classical and modern analysis?
tribal kernel
New book idea: come up with a new set of maxwell's equations and derive the consequences of those laws
What are the differences between classical and modern analysis?
@cyan canopy Usually it's whether or not measure theory is considered or not. Do we consider functions as just being by themselves (classical) or do we consider functions up to equivalence classes and try to consider the properties of spaces of functions (modern)?
cyan canopy
So most early university courses fall into classical analysis?
tribal kernel
Usually yeah. In early classes we like to consider functions that have nicer properties like continuity, but considering functions as equivalence classes lets us ignore parts of functions where it may be inconvenient. This gives us lots of advantages for a general theory of functions
gray gazelle
In which analysis class do you study non continuous functions 
Well except for integration
tribal kernel
Well yeah that's sort of the example that motivates a lot of it
But eventually you start studying modern PDEs which may or may not have totally continuous/differentiable solutions
gray gazelle
Your pfp is scaring me rn ngl 
tribal kernel
Lol yeah it haunts more than a few people's nightmares
Doug Walker + Squidward is a combo made in hell
gray gazelle
But eventually you start studying modern PDEs which may or may not have totally continuous/differentiable solutions
Fair, I haven't done much with PDEs yet
hearty steppe
I think I'm going to go ahead and recommend this book for people learning Linear Algebra for the first time or haven't touched it in years.
https://www.amazon.com/Elementary-Algebra-Classics-Advanced-Mathematics/dp/013468947X
the explanations are pretty nice overall and plenty of examples to work through the exercises. Also a nice chunk of exercises per section
I will say it doesn't replace the experience you'll get learning Linear Algebra more rigorously, like with Janich, Lang, Hoffman-Kunze, or other books. But at least this will ease you into those.
tribal kernel
Ooh that sounds like a good experience. My first book was Hoffman and Kunze and I do like it but it was maybe not a great first book
hearty steppe
hoffman-kunze is def more advanced
dense wren
what do you all think of axler's linear algebra book?
molten wave
hoffman-kunze is very good at pointing the connections between concepts
I've recently had a cursory read of hoffman-kunze and like I realized I knew all the concepts and none of the connections
tribal kernel
Those more difficult books are usually good at that. Not good for a first read but really illuminating for a second attempt at a subject.
That’s how I feel about Hatcher
marble solar
@cyan canopy many of the classical analysis/pde type problems are looking at explicit solutions to some equation
More of the modern techniques are properties of solutions to PDEs
I think one of the more recent ideas getting traction is Decoupling Theory
You can see Larry Guth's pdfs on that
cyan canopy
Hmm interesting
marble solar
that's at a decently high level though
astral mauve
wow free nitro emoji cool
marble rock
im almost done with single variable analysis
and i want to improve
i want a textbook that is spicy
hard
hard hitting with problems
goes into deep waters quickly
merciless
on group theory
something that will force me to improve
like a textbook that will end me
HARD
something that will teach me to slow down when reading
spicy advanced merciless
it can be on anything really other than group theory but its my fav thing in my math that i know
my background up till now : dummit foote algebra uptill galois theory , pugh real analysis uptill function spaces ( not finished yet ) , hoff man kunze uptill algebras and determinants , soon going to read topology a categorical approach
im not good though
velvet briar
A natural suggestion is Atyiah-Mcdonald
Which, I haven't gotten through myself so get going haha
marble rock
i did atiyah macdonald uptill modules and some localization
but i was advised to learn analysis first
velvet briar
Yeah it gets real freakin hard there and after
marble rock
and increase the 'maturity'
velvet briar
Analysis is a good idea before something like AM for sure
marble rock
yea
any notes
on isaac? @inland coral
on the textbook
isaac
prereqs , exercises etc
granite sluice
I've recently had a cursory read of hoffman-kunze and like I realized I knew all the concepts and none of the connections
@molten wave What was a surprising one?
molten wave
like how jordan decomposition follows from shit about characteristic polynomials
granite sluice
Interesting. I assume you mean something more than the fact that you can read off the characteristic polynomial from the jordan decomposition?
sage python
Well, I would guess it's more that the existence of Jordan decomp is related to char polys
timber mesa
what do you all think of axler's linear algebra book?
@dense wren could be a pet peeve of mine, but I think it's a really terse book and his avoidance of determinants is kind of dumb. There's better books for mathematicians and non-mathematicians alike. I like H&K and Jim Hefferon's book
granite sluice
Googling some vague memory lead me to this puzzle "Exercise 286 Classify the finite dimensional indecomposable representations of the 1-dimensional abelian complex Lie algebra. What does this have to do
with Jordan blocks of the Jordan normal form of a matrix?" ( https://math.berkeley.edu/~reb/courses/261/35.pdf )
So... that 1 dimensional lie algebra is just C, with the trivial bracket. So a representation is some matrix, presumably the one we are taking the JNF of.
I guess the point is that being indecomposable is the same being a Jordan block in some basis? (Well, specifically being irreducible means that there are no non-trivial invariant subspaces.) So decomposition into indecomposables is JNF?
It's not clear to me that irreducible is the same as being a Jordan block -- e.g. for nilpotent blocks there is a fixed subspace. Maybe if we require the matrix to be invertible?
granite sluice
But, yeah, part of the problem here is that Abelian lie algebras are not semi-simple, so you can't just invoke the decomposition theorem. Still this feels tantalizingly close to some nice insight about JNF.
velvet briar
Topology is pretty lit, go there if you want
velvet briar
Yeah that's not a bad combo
marble rock
i just want something hard than fun now
basically
99% my fate is decided to be a math major
and im going to have to take this shit srs
so
velvet briar
I'm back to AM then
marble rock
yea
gray gazelle
you need to know what a derivative is 
velvet briar
Should know topology actually, my bad
marble rock
thats it?
velvet briar
Still can probably hack it
marble rock
i know that
i think the faresrt ive been
is proving mean value
and read tyalor theorem
farest*
in analysis
velvet briar
And you should know some analysis, as analysis concepts are extended into manifolds
marble rock
how much
gray gazelle
familiarity with the inverse and implicit function theorems will help
marble rock
i dont know any multivariable
hearty steppe
So Kaynex do you think I should know some analysis before doing topology? Some people been saying I should just start reading Lee and Munkres
gray gazelle
you can read spivak for a quick and dirty intro to those theorems
(spivak's calculus on manifolds)
velvet briar
You probably don't need any multivariable
Well, maybe it would be good to know
Should at least understand Rudin ch.2 before hitting top imo
@hearty steppe
granite sluice
Okay, I found where I was confused -- the indecomposable representations are exactly those where the matrix can be represented as a Jordan block. Since the representation always decomposes into indecomposables (not irreducibles -- its not a semi-simple Lie algebra, so we can't invoke Weyl), we get the JNF.
So what classifies the indecomposables? I think this is now basically the usually proof of JNF. It's indecomposable iff it is a single Jordan block.
So, its a nice perspective on JNF, even if its not a pure thought proof. Maybe missing something though.
slender dragon
Should at least understand Rudin ch.2 before hitting top imo
@velvet briar
Chapter 2 on Metric Spaces, Chapter on Continuity and chapter on Functions Sequences
Those chapters have Metric Spaces
timber mesa
topology doesn't really have any prereqs per se (Munkres is self-contained) but you won't see the motivation for any of it before doing some analysis
crystal kraken
New book idea: come up with a new set of maxwell's equations and derive the consequences of those laws
@tribal kernel then why name the new set of equations as Maxwell's?
Name them 'Squidward's Equations' or something. Lol
tribal kernel
Best idea yet
calm crane
there are many formulations of maxwell equations if youre interested
easiest is jus start from lagrangian
gray gazelle
@marble rock yo homeboy you need multivar for that
How do you know topology of metric spaces without knowing multivar
i did for a bit
slender dragon
How do you know topology of metric spaces without knowing multivar
@gray gazelle
They don't relate, at least the basic of Metric Spaces
gray gazelle
Of course they relate, how do you make examples that are compelling?
slender dragon
I don't know, hahaha
I don't know a lot from Multivariable Calculus
But, I know a little of Metric Spacea
From Rudin
Chapter 2, Continuity and Sequence of Functions
gray gazelle
Rudin..
runic hatch
it is tougher to learn from compared to other books
slender dragon
Yes
gray gazelle
It's not awful, it's just not very good for learning the material for the first time
slender dragon
Of course, I can make the most difficult book in the world, a book only of theorems and "Proof. Left to the reader."
For the first time and nevee
Never
gray gazelle
Those would rather appear in graduate texts where proofs really aren't difficult
slender dragon
Yes
cunning lark
Or in undergrad if the writer was lazy or it is reaaaally obvious
slender dragon
Rudin seems lazy sometimes
Well, that's not wrong, I think sometimes Dummit and Foote book does that
runic hatch
Rudin is more slick
crystal kraken
So many mixed reviews on Rudin
hasty turret
What do the negative reviews look like?
runic hatch
Pulled from Amazon
This one is pretty odd
like they say that rudin doesnt move away from the real case, but immediately contradicts themselves with the metric spaces comment
also apostol's analysis text is even more focused on the reals
unless they wanted rudin to also discuss complex stuff?
hasty turret
Do some constructions really lack rigour?
stray veldt
its not really contradictory
you can state a lot of theorems over general metric spaces
but just always work with the real numbers
runic hatch
ah fair
still odd though considering most introductory analysis texts predominantly work with reals
also is it better to introduce normed spaces compared to just focusing on metric spaces?
sage python
Normed spaces are probably the correct setting for analysis in a way but a lot of the "metric space theorems" that you'd need in a treatment of normed spaces have the same proof either way
In those cases I'd rather just see it done in metric spaces, sorta makes it clear what follows from what
valid moth
yeah
@sage python so here's my hot pedagogical take:
do away with intro real anal, just teach freshmen complex analysis; since R subset C this actually covers real anal anyways
timber mesa
imagine not following this book for multivar https://www.amazon.com/Differential-Calculus-Normed-Spaces-Analysis/
valid moth
here's the even hotter take
don't teach real or comp anal
just teach multivar
since C = R^2 multivar covers both
gray gazelle
Um
What about differentiability in ℂ
Complex analysis makes great use of the fact that ℂ is a complete field
do away with intro real anal, just teach freshmen complex analysis; since R subset C this actually covers real anal anyways
This also doesn't work since some theorems are very specific to ℝ. Consider for example monotone convergence or intermediate value theorem
Those two are very important to establish some of the results
Eh it's a shit take
valid moth
no no you see this is why you would also teach DEs at the same time
you get the complete comp anal experience
(it seems like you don't realize im joking N/U)
runic hatch
Just do everything in the most general setting possible
sage python
Nah the strat is to teach complex analysis by just teaching algebraic topology and then harmonic functions
The interpolation of the two is complex analysis
valid moth
no no just teach quaternionic analysis
sage python
Quaternions are a myth
flint forge
quaternions are a group
sage python
A finite one at that
valid moth
analyticity, holomorphy, harmonicity and conformality in the context of quaternions. Unlike the complex numbers and like the reals, the four notions do not coincide. nevermind
don't teach it
gray gazelle
(it seems like you don't realize im joking N/U)
@valid moth I did miss that completely
brittle latch
does anyone know of any opencourse lectures that use folland's calculus?
i wanna delve into the book but i like to have lectures to keep me company as well lol
(please @ me)
hollow peak
i think we shouldn't even bother teaching multivariable calculus, only differential forms and integration on manifolds
all the vector calc theorems are trivial corollaries 
tribal kernel
Technically true but you’ll piss off a lot of engineers lol
flint forge
why even teach single variable
all single variable theorems are trivial corollaries of multivariable ones
marble solar
Anyone have experience with Apostol's Dirichlet Series and Modular forms?
gray gazelle
wait how did that guy react in this channel
timber mesa
ᵉˣᶜᵉᵖᵗ ʷʰᵉⁿ ʸᵒᵘ ⁿᵉᵉᵈ ᵗʰᵉ ᶠᵃᶜᵗ ᵗʰᵃᵗ ᴿ ⁱˢ ᵃⁿ ᵒʳᵈᵉʳᵉᵈ ᶠⁱᵉˡᵈ ˡⁱᵏᵉ ᶠᵒʳ ᵗʰᵉ ⁱⁿᵗᵉʳᵐᵉᵈⁱᵃᵗᵉ ᵛᵃˡᵘᵉ ᵗʰᵉᵒʳᵉᵐ
livid ermine
have anyone here read aluffi algebra chapter zero?
wise crater
fuark any suggestions for algebraic topology textbooks?
tribal kernel
have anyone here read aluffi algebra chapter zero?
@livid ermine I’m using it in my algebra class rn
livid ermine
do you think its good? it looks kind of nice, but working with categories seems kind of strange that early, although I have heard arguments for it
tribal kernel
I personally like it and it’s probably good if you haven’t had an advanced course in algebra but you’ve seen the concepts before. I think the arguments are pretty clear for at least the first few chapters
dapper root
I like Aluffi a lot
I used it for my first exposure
If you commit to it and decide to just swallow some of the pills i.e. that category theory is actually useful it'll pay off in the long term
Also Aluffi isn't category theory heavy until the last two chapters, it simply uses the language from the start
tribal kernel
There are people here who really do t like that book but I like it more than most other algebra books
tight crag
It seems boring
dapper root
The most common critique I see is that "exercises are too easy" which I think is kind of bleh
Other textbooks are too dry for me
D&F and Lang are the other two I own and reading them is a slog
tribal kernel
Aluffi also has a sense of humor which is nice
I hear Lang is good but DF is really dry
Better as a reference text than for studying
dapper root
Lang is a reference
I don't like it
It's not really a textbook in my head it's like an encyclopedia
dapper root
D&F is definitely not a reference text IMO
it's used as a textbook a lot and isn't complete enough to be a reference text, maybe for like undergraduate algebra math
But Lang can be used as a reference even for stuff in a lot of different fields well into your graduate school life
tribal kernel
Yeah probably better for reference as an undergrad text
But my undergrad algebra was incredibly weak
One semester of undergrad algebra and it didn’t cover fundamental theorem of abelian groups, Sylow’s theorems, symmetric or dihedral groups except for the definition, alternating groups, direct products, Lagrange s theorem, PIDs, Jordan Holder, and most other things you’d expect to learn
We did, however, discuss some Galois theory, public key cryptography, and elliptic curve arithmetic
quick hornet
standard for whether a text is a good reference text:
does it have dedekind's modular law
(and preferably refer to it by name)
latent pulsar
so should I read linear algebra done right or linear algebra done wrong :yaw:
quick hornet
Linear Algebra Done Just Kinda Average
anyway, LADR is a fine text but axler's anti-determinant slant is... a bit extreme
even if i understand the desire to deemphasize them
latent pulsar
hmmm so many textbooks
livid ermine
i worked through the first 300 pages and i really liked it, but it might just be because the book itself is very nice
the formatting and all the hyperlinks i mean
timber mesa
LADW seems fine for a second reading of linalg, apparently it's written for an honors course and it has lots of explanation. It's also concise which is a plus for me
Hefferon's book has a ton of examples and things
LADR is kind of terse and I agree that kicking determinants to the very last chapter is dumb
I did linalg with Hoffman & Kunze's and I thought it was fine, I like how it mentions things about infinite-dimensional spaces sometimes
karmic thorn
I've started with Shafarevich's Linear Algebra and Geometry and it looks good, although there are no exercises which is a bit disappointing.
slender sphinx
@latent pulsar Hoffman-Kunze
raw herald
anyone know where I can find loads of material about taxicab geometry stuff? like taxicab metric Lp spaces etc.
flint forge
Tbh id just look into like lecture notes on the subject or smth
Im not sure how much you will find
tight crag
Maybe Burago Burago Ivanov has some stuff
sage python
I guess it partially depends on what angle you're looking at the material from. The analysis, the geometry, combinatorics of paths in a grid, etc
tight crag
I wrote a thing in the summer about how you can't embed a circle in taxi space
sage python
Ah you mentioned
tight crag
But I don't think I really used a source for that
Yeah there's definitely a lot of probability stuff on taxi space
And combinatorics
BBI should definitely have some stuff
From the metric geometry pov
That is, Burago Burago Ivanov a course in metric geometry
sage python
Someone should write a book titled "A Course in Coarse Geometry"
tight crag
A fine course in coarse geometry
sage python
God I do not want to do this research statement.
I think I'll grade today to procrastinate
And then Saturday/Sunday I'll do research statement
tight crag
I have to write a statement of interest for a fellowship today
sage python
And then Monday/Tuesday I'll study for probability
tight crag
It's only one page though
sage python
Ah nice. Yeah on my end I'm gonna implement some revisions on the personal statement, and then focus on the research statement, which is 2 pages
Though I'm gonna have to learn a bunch of stuff lol
sage python
Nerd
sudden kindle
@sage python are you appying to NSF GRFP
sage python
Yeah
tight crag
I have to talk about how much I love teaching
sudden kindle
same
sage python
What area are you thinking about for your research statement?
sudden kindle
im writing about average rank of elliptic curves
sage python
inb4 Langlands
sudden kindle
and how we can use computers to compute it
sage python
Ah that's good. More specific than my stuff was tbh
tight crag
Computers are good
gray gazelle
🤖
sudden kindle
@sage python your OG research statement was like what?
gray gazelle
Made up computers are great
sage python
Yeah looking through I just mumbled about how bounding ranks on elliptic curves builds eventually toward BSD
But I had no specific problem I knew of which was like
Ah yes this is something I could make progress on
I think that was one of the flaws of my app first time around tbh
gray gazelle
What are your issues with the Berkeley software distribution?
sage python
So yeah idk this time around I'm talking about subconvexity
gray gazelle
How hard can u bullshit these grant things? Like is it real mathematicians reviewing them?
sudden kindle
youre a secon year grad student right?
sage python
I'm kinda in this weird limbo where it's like, I already put a bunch of time in and I'm gonna put more in the research statement so I wanna do it, but I also don't wanna set my expectations too high because even so it's still a bit last minute and NSF is hard to get
Yeah I am
sudden kindle
yeah it takes a fuck ton of time to write these things
just to even figure out what to write
gray gazelle
time to bombard wojo with questions
timber mesa
How hard can u bullshit these grant things? Like is it real mathematicians reviewing them?
depends on the country but usually yes, there's some sort of scientific committee reviewing those
sage python
Lol idk if he's particularly deep into this area, he seems more arithmetic geometry ish
gray gazelle
Wojo does number theory as far as I know
sage python
Number theory means a lot of things
gray gazelle
But idk much number theory so there is that
sage python
You could be working on Tao style additive stuff, the Langlands program, arithmetic geometry
sage python
All the stuff in between, and obv each of these areas has its own subarea (e.g. Diophantine stuff vs Shimura varieties vs etc)
sudden kindle
yeah mathematicians will be reviewing your NSF GRFP proposal, you're submitting to the "algebra, number theory & combinatorics" area, so i assume there will be some people in that background, but they might be working in mathematics more generally. they're definitely mathematicians reviewing tho
sage python
Idk if his research area is perfectoid stuff but he's somewhat into the stuff, more generally I think he leans arithmetic geo
The stuff I'm talking about is more along the lines of analysis of automorphic forms
gray gazelle
I see I see
sudden kindle
its all included in the langlands problem 
gray gazelle
Although wojo probably still knows about that
sage python
I think he's got an idea of how automorphic forms work, I'm not sure exactly how much of what I'm writing is familiar to him though because it starts to get specialized to the "Unless you're doing something with it you're unlikely to know it" territory
sudden kindle
sloth you wanna write your research statement that is appreciable by non experts
gray gazelle
Yeah how about solving RH
sage python
Oh I mean it's appreciable I'm saying the subject matter of the paper more
sudden kindle
you have better luck getting a stable job and making a million dollars @gray gazelle
sage python
Like e.g. there's a particular bound on L-functions that you get out of playing with the trace formula
And using Walpsburger stuff
The plan is to get improved bounds
It seems like the first paper to ever do that was written in 1995 by Iwaniec and Sarnak
So it's specialized in that sense, but obv I won't just jump in and be like aight I assume when I say the word "convexity bound" you know exactly what that means
(esp because I don't even know 100% 100% what it means lol)
sudden kindle
yeah
sage python
So yeah arithmetic geometry people tend to be aware of this but this is kinda the analysis analysis side of automorphic forms
And I don't know how far they tend to look into it before it's like, yeah it's not that productive anymore
Unless you're doing Langlands and you have to know everything
🙃
timber mesa
valid moth
No no dami, the big brain strat is to do Langlands adjacent
You see someone told me this once
gray gazelle
sage python
Wonder who
sage python
Oh you should've said it more clearly the first time
You were slurring your words together
valid moth
Okay damoomer
Anyways if math fields were a graph what exactly would be the langlands adjacent ones
marble solar
Analytic NT is a field that's seen ups and downs
valid moth
Also what would be the radius of the graph
sage python
7
marble solar
PDE seems to always be a good field
valid moth
I see
gray gazelle
I feel like category theory has seen a lot of downs
sage python
N/U do you know what category theory research entails?
marble solar
I don't think cat theory has seen that many downs
hollow peak
yeah i'm applying for a grant to study the quotient rule
sage python
Like idk my impression is that you've got essentially no perspective on what category theory research looks like to make the claim that it has had ups or downs or anythings
Honestly it's mostly homotopy theory first off
And like... okay down since when? Do you think it had an explosion in the 80s and interest has since dwindled down? Or what?
gray gazelle
I was speaking of pre AG
valid moth
Is pre AG where you study prepresheafs
sage python
Like pre Grothendieck style AG?
marble solar
I think Category Theory is one of the hot fields right now
sage python
Since category theory as a notion came into being in the 40s I think
marble solar
Along with AG
There's a lot of really bright students going in there producing good results under great mathematicians
valid moth
Hmmmmm
category theory and ag
ct ag
isn't that like the dna letters
coincidence?
basically we are born to do cat theory and ag
sage python
So if i had to guess
marble solar
Analytic NT has died and resurrected and died and resurrected. Same thing with Knots
sage python
PDE is probably still the king in terms of volume of research
Moonbears which kinda analytic NT do you mean?
gray gazelle
Are there multiple analytic NT?
sage python
There are a lot of aspects to analytic NT
hollow peak
I didn't know additive had an analytic branch
marble solar
Producing great results
marble solar
There'll be a lull for like 2 decades
and then some guy hits something
and then all this interest in it again
valid moth
not sure, this doesn't look that hot to me
sage python
"Some guy"
You mean Tao
hollow peak
arch i think you're just jealous of not being able to do slick and beautiful math like ant
sage python
But yeah obv Langlands has fuckin snowballed
marble solar
analytic or algebraic archsys?
marble solar
NTY
sage python
Also I think there's a lot of stuff that's kinda Sarnak style
hollow peak
NTY
number theorY
sage python
I mean Langlands probably subsumes a lot of automorphic formsy type stuff
But yeah Sarnak lives on the very analytic side of that picture
I feel like that's gaining some traction now
valid moth
pro writing tip: replace 'subsumes' with 'vores'
sage python
Obv that's where I'm kinda set to go atm, my advisor Simon Marshall too. Akshay Venkatesh is a name there
sudden kindle
"I am an analytic number theorist, although my calculus students see me as more of a cleric. "
sage python
Hahaha, yeah
marble solar
I feel like an analytic NT calculus test would be like
"Prove euler summation's approximation"
"Prove abel summation, use dirichlet's test for convergence to prove that ___ converges"
etc. with all these O bounds
marble solar
I think Garnett told our Complex TA "Prove the prime number theorem in discussion section over these weeks"
I'd love to see it, I have my midterm
sage python
Lol looking through old Facebook messages one of the first things I see
"I want a ray which deletes analytic NT from my brain"
And tbh same that part of the class made me want to commit sudoku
valid moth
Lol
marble solar
Luckily we didn't have that part on our complex final, although he still managed to get us
On dirichlet's problem on riemann surfaces
valid moth
Were there any interesting questions on that final dami
sage python
Hard for questions about that kind of number theory to be interesting tbh
marble solar
I mean all you can do in complex is like Arithmetic progression or Prime Number Theorem
It's unlikely you have time for both
And most of those questions boil down to asymptotic estimates of the zeta function
i.e. Taylor series expand to O(1/x^2) apply MVT
sage python
Yeah I don't think I have any pictures of that test
marble solar
I twisted my ankle pretty hard right before this test. I was out for two weeks
First day back in the class I had this midterm. 75 and up ended up being an A
So I just squeaked it LOL
marble solar
No, he just wanted to cover the basics of everything we learned up until that point
The prof. is known for going very slowly
Through the material
His class was always strange, if you had an A going into the Final, you didn't have to do the Final
In general, I felt his exams were well written
Albeit usually very standard/straight-forward problems with very minimal partial credit
gray gazelle
Damn, I would love that class
marble solar
Yeah, he's a good educator. We ended up having a house party at his place
at the end of analytic NT
If you're in the state of CA he's teaching the same class again next semester
hollow peak
I will make the trek down to irvine for this sweet man
but first I have to write this terrible 1500 word paper about the bible
hearty steppe
is this a good syllabus to follow https://dspace.mit.edu/bitstream/handle/1721.1/74139/18-100b-fall-2006/contents/syllabus/index.htm
sage python
This is decent I think
valid moth
@hollow peak what sweet
must be pretty good candy if you're willing to walk to california for it
wooden geode
hi guys
does anyone have an opinion on halmos's naive set theory?
i started reading it today and i actually like it a lot
hearty steppe
@velvet briar I can't find that Applied Group Theory book you recommended?
hearty steppe
ty
hearty steppe
Sloth is there a better syllabus you can suggest for a first semester of material in Real Analysis?
sage python
I mean idk this is fairly standard?
Like obv you can adjust the timing based on what you want
tribal kernel
Honestly it looks pretty good except the equicontinuous and fundamental theorem of algebra. Wouldn’t really think of those as analysis 1 topics
hearty steppe
ok
timber mesa
I wish I'd learned equicontinuity earlier tbh
tribal kernel
I learned about it in my first semester of functional analysis. Can be pretty useful
soft terrace
we did equicontinuity in my class
runic hatch
besides alfohrs, what other books are good for complex analysis?
hollow peak
I hear rudin is good
runic hatch
oh right i can look into papa rudin now
tribal kernel
I use Schlag and it's alright
Assumes you know diff forms and good bit of other things first
sage python
s c h l a g
tribal kernel
Kinda sparse on details imo
dapper root
Fuck Schlag
valid moth
The books I hear recommended the most are
stein shakarchi
narasimhan
papa rudin
ahlfors
i forget the name of the last but iirc it starts with a g— ah gamelin or something
sudden kindle
Alfohrs is not a good book actually
gray gazelle
papa rudin
crystal kraken
I hear Rudin's books are good for reviewing. Terrible for starters.
dense wren
@crystal kraken I second that
tribal kernel
I agree too. They just require a lot of maturity in mathematics and the subjects they teach to be good on a first go
Maybe a good book for a class that's trying to give relatively advanced students an intro that shows the connections and high level structure in analysis
marble solar
@runic hatch Marshall's complex analysis
@sudden kindle ahlfors is an excellent text
For reading, Stein and Shakarchi is good for complex analysis
Exercises, but reading it is wonky in some places
marble solar
Ahlfors is lacking in exercises
Papa Rudin is just too slick for my tastes
We used like 4 books in my grad complex analysis class
gray gazelle
Hello. I have done each exercises on chapter 1.1 on how to prove it and it was not enough. where can I find more? I want only exercises. not courses.
karmic thorn
Book of Proof by Hammack is good.
gray gazelle
not that i have read the book, but why didnt u do the rest of how to prove it?
@karmic thorn yes but I definitely need only exercises. not more courses. I am already lost in many concepts. I do want to focus on my chapter.
karmic thorn
Well I suggested it for more exercises actually, the contents are more or less the same in two texts I guess
gray gazelle
@gray gazelle because I want to focus on this chapter because I have already go to 3.1 but I do many mistakes.
@karmic thorn what text?
karmic thorn
Book of Proof by Hammack and How to Prove It by Velleman.
gray gazelle
@karmic thorn can I do ONLY the exercises of book by proof?
karmic thorn
Sure why not, who's stopping you lmao.
If you have some gaps just give it a read, it's a concise book and you're not dealing with something very complicated here.
gray gazelle
@karmic thorn I want to do the minimum of proof to focus on cryptography and to make a project. once again I have to focus.
karmic thorn
Hmmm both the books constitute a bare minimum for proof writing honestly.
Other than that I don't have much of an idea why someone going into cryptography will need much familiarity with writing proofs.
gray gazelle
@karmic thorn I do not see any exercise on BOOK OF PROOF
the exercises are progressives
not easy to do with the first book
just write proofs for proof practice 
gray gazelle
@gray gazelle lol I am not even at the point that I can write proofs! I just learn proof structures. as I told I come back