dapper root
When a prof won’t let you take grad algebra you just email them the pdf
#book-recommendations
sudden kindle
pdf of what
gray gazelle
u think if i had solved all of the problems in pugh's book
including the meme ones and the 3 stars
i'd have been able to skip analysis
marble solar
I used Pugh problems to prepare for my second quarter honors real analysis final
It didn't work
I got bodied hard
timber mesa
d&f anime filler list
pale scarab
How long has that taken you including typing them up.? That's pretty impressive though
static crest
I did all of groups in < 30 days (644/974 of the exercises)
then my semester started, so it took me about another 30ish days to do the rings exercises (166/974 of the exercises) (I do have to mention that the average rings exercise was much harder than the average groups exercise; the average rings exercise took about 3x more space to write)
then I took a break for about a month while my midterms and stuff were going on
and I've been slowly going through the modules exercises, which make up the rest
but I'm probably not gonna do much in it until summer break starts
sudden granite
where does set theory discussion go 😳
oh this is book discussion
rip
unfortunately chill doesnt exist for me
sudden granite
k
willow pecan
sudden granite
thanks
gray gazelle
unfortunately chill doesnt exist for me
how did this happen?
sudden granite
i asked for the change since if i continued sending gifs in chill i would have been banned
this was months ago tho
willow pecan
sudden granite
i should probably ask mniip for chill again but it is kind of a waste of time
gritty apex
How many are there
gray gazelle
prolly see Gelfand's algebra
long bear
Dan Saracino makes a good cappuccino
gritty apex
prolly see Gelfand's algebra
This looks like kids book
gray gazelle
then lang's basic math ?
prolly see this once
gray gazelle
gritty apex
Why they can't make one proper book for all algebra
gritty apex
Contemporary Abstract Algebra
Its color. I like color
gray gazelle
gray gazelle
mostly red
gritty apex
It's not that stalin
long bear
in ours hearts it is
gritty apex
Good fonts nice
gray gazelle
were you looking for an abstract algebra text ?
gritty apex
Pre algebra, elementary algebra, abstract algebra, linear algebra.
gritty apex
Linear algebra
long bear
No but like
You should start with pre algebra and elementary algebra if you haven't established them
gritty apex
You should start with pre algebra and elementary algebra if you haven't establis...
I know that.
What's a abstract algebra even used for
long bear
for linear algebra, I will recommend to you what an old sage from distant lands once recommended me, Linear Algebra by Insel, Friedberg and Spence
gray gazelle
the canonical linear algebra recommendations are friedberg, or axler, or hoffman-kunze
gritty apex
No colour
broken meadow
tterra
broken meadow
we learned the definition of characteristic polynomial in linear algebra
i am excited
gray gazelle
note that the roots of the characteristic polynomial are precisely the eigenvalues
broken meadow
i think it's cool that it works regardless of the basis
yes exactly that is also very cool
gray gazelle
very important too
broken meadow
:3
gray gazelle
some things you care about are e.g. the characteristic polynomial splitting into linear factors
also fun fact
gritty apex
What the hell is universal algebra
gray gazelle
the constant term is the determinant, and the linear term is the trace!
gray gazelle
What the hell is universal algebra
the precursor to interuniversal algebra
gray gazelle
no prove it
gray gazelle
ah
gray gazelle
the constant term is the determinant, and the linear term is the trace!
show this
broken meadow
oh
gray gazelle
by splitting i mean
broken meadow
oh
gray gazelle
you can write it as a product of things that look like x - c
gray gazelle
for example, if the field were the complex numbers, it would always split like that
but e.g. x^2 + 1, the characteristic polynomial of 90 degree counterclockwise rotation on R^2, does not split like that
gray gazelle
one reason you care about this is because if your operator is diagonalizable, then you split
broken meadow
o
gray gazelle
("split" in algebra means expressible as a product of linear factors)
broken meadow
right
gritty apex
You should start with pre algebra and elementary algebra if you haven't establis...
Is there anything else to these other than Khan academy
gray gazelle
more generally your operator admits a jordan canonical form if and only if its characteristic polynomial splits
but
that comes later
long bear
On youtube
gray gazelle
now here's the big fact about characteristic polynomials
gray gazelle
the really big fact about characteristic polynomials
gray gazelle
if A is a matrix or an operator, and p(x) is its characteristic polynomial, then p(A) is the zero operator
(ask me if you dont know what p(A) means)
broken meadow
what
long bear
(he does math, not only chem)
broken meadow
what is A
broken meadow
uh
gray gazelle
whose characteristic polynomial we're interested in
broken meadow
how did u put A in place of x
long bear
the other one is called professor leonard
If you have money to spare, the best one is a site called "math and science"
I don't have the moneys unfortunately
but he puts up trial lessons on yt
they are goo
good
gray gazelle
if $p(x) = a_nx^n + \cdots + a_1x + a_0$ is any polynomial with coefficients in the field $F$, and $A$ is a square matrix with entries from $F$, then we define $p(A)$ to be the linear operator $$p(A) := a_n A^n + \cdots + a_1A + a_0 I,$$ where $I$ is the identity matrix
hasty eagleBOT
(T*Terra, dqⁱ ∧ dpᵢ)
long bear
https://www.youtube.com/user/professorleonard57 https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA
@gritty apex
gray gazelle
if p(x) is the characteristic polynomial of A, then the operator p(A) is identically zero. this is known as the cayley-hamilton theorem
long bear
both have playlists
broken meadow
and then i was like
long bear
broken meadow
"uh"
long bear
Prealgebra playlist
broken meadow
now i am less "uh" and more "hmm"
gray gazelle
there's a cute fake proof of it as follows:
p(x) = det(A - xI) by definition
p(A) = det(A - AI) = det(A - A) = det(0) = 0
broken meadow
kek
gritty apex
<@!792598153118613514>
Got it. Why haven't anyone cataloged these properly and sequentially in books. The math is scattered here and there in multiple books
broken meadow
so later i have to figure out how to correctly do it
gray gazelle
the proofs i know of involve decomposition into cyclic subspaces
you'll probably learn it
gray gazelle
anyways metal those are the main important facts about characteristic polynomials
don't forget em
broken meadow
okay
long bear
that are specific to these areas
You could even
just pick up a hs math book
and learn from that
broken meadow
idk what a cyclic subspace is ultra 😭 we only learned about... idk the generic subspaces
long bear
I'm not sure what the hs books in America/international are
gray gazelle
broken meadow
feel like these terms being reused might count for something
broken meadow
:hmm:
gray gazelle
here "cyclic" refers to cyclic as a module over the polynomial ring F[x], whereas cyclic in the case of (abelian) groups refers to cyclicity as Z-modules
gritty apex
Is early transcendals good book for calculus by Stewart @long bear
long bear
I like uh
whats it called
George Simmons
Calculus with Analytic Geometry
I think it's called
broken meadow
i see ultra
the iterative application of T on v seems kinda similar to how cyclic group is generated by a generator element
but it seems different
because you said we take the span of the set
i will have to think on this
maybe it has to do with T being linear
ah
hmmmmmm
this is thinky time
so what if i chose to start with T(v) in place of v
and repeated application of T from there
it's still
"cyclic" right
meaning i still will find v in the subspace
hmmmm
kind of like Z versus Z_n ?
nice...
ty for explaining all this ultra
i must go now though
it is late
:3
charred carbon
Hey guys, I needed your help for buying a Calculus book. I have confusion between Spivak Or Apostol Vol 1 . Which do you think is better suited? BTW I am in 10th grade
gray gazelle
find copies of them on the internet and see which one you like more before you go spending money
charred carbon
Oh you mean the PDFs?
charred carbon
You Know Who
gray gazelle
lib***
prisma snow
Lyou iknow bwho
long bear
I like how uh
gray gazelle
you missed an asterisk, "library"
gray gazelle
abhay reminds me of Alex
charred carbon
I am not joking@long bear
long bear
Nor am I
gray gazelle
you missed an asterisk, "library"
informal name 
long bear
you are truely a member of the top 0.0000000000000001% of Rick and Morty watchers
gritty apex
What's wrong with Rick and morty
long bear
Nothing
gray gazelle
everything
charred carbon
@long bear I had added that so that you all can get an idea and would be able to give better recommendations based on my level
prisma snow
😂 he wasn't saying you're lying if you say you learn calculus in grade 10. He meant its weird for you to say that as if you are trying to flex. I disagreed though, because you could have just wanted a book that suits your level, but now that you assume people wouldn't believe you're that smart, it feels like a flex
long bear
Sure.
gritty apex
everything
So you must be fan of spongebob
hasty turret
SpongeBob viewers are probably smarter than Rick and Morty fans
gray gazelle
ok ill take it back. im sorry
charred carbon
😂 he wasn't saying you're lying if you say you learn calculus in grade 10. He m...
Damn, I will make sure now that I don't mention that again when asking for recommendation
long bear
😂 he wasn't saying you're lying if you say you learn calculus in grade 10. He m...
Hannibal Lecter perception 100 I see
prisma snow
Damn, I will make sure now that I don't mention that again when asking for recom...
No, like I said, I didn't think so. Damon is just dumb so he gets jealous easily.
long bear
Yes
hasty turret
Yea
prisma snow
Just don't be like "I'm not lying, I'm really smart enough to do calculus"
gray gazelle
nobody is smart enough to do calculus
long bear
No, like I said, I didn't think so. Damon is just dumb so he gets jealous easily...
😢 Don't give me reality checks like this
prisma snow
So you must be fan of spongebob
Bad at multi, but god tier at roasting
hollow current
yes because he is in 5th
gritty apex
Who is flexing here
hollow current
your mom
gray gazelle
long bear
gritty apex
My disappointment is immeasurable and my day is ruined
wheat nymph
does anyone have "Transition to college mathematics and statistics" textbook?
compact snow
Yeah, for new books, I'd get a Calculus BC prep book on Amazon for $15. Of course, check the stars and reviews (and number of reviewers). Those books are focused and fluff free. Then get a textbook if you want the full, mostly skipped, experience.
For being cheap, ditto but borrow from your public library.
Fair enough. In minor defense, the AP is a very popular test and you'll be as prepared as a lot of other people going into college.
prisma snow
Just watch the blue brown guy and do geometric calculus so you can be confused about how to differentiate 1/x
compact snow
awww.
I need to watch more youtube lol.
I'm thinking of making "proofville" where you can grow math postulates (animals) and math definitions (plants) to make dishes.
gray gazelle
I'm thinking of making "proofville" where you can grow math postulates (animals)...
huh?
compact snow
I'd just follow Euclid's Elements.
The point isn't to make the computer check if something is true. The point is there'd be a database of combines that "means something," unknown to the user, to math people.
prisma snow
I take one statement of the definition of compact, one statement of the Heine Borel theorem, and I get one dish of confusion.
compact snow
Eh, like all things, if done well, it'd be cool.
Like grow Apples and Bananas (variables A, B) and mix it with Adder oil to get A+B or with mega-adder oil to get AB or excellent-adder oil to get A^B or extreme-adder oil to get B^A.
That kind of silliness.
Two zephyrs (n in Z) mixed with excellent adder oil and one pinch of mint (-1) would be 2^n - 1. 🙂
karmic thorn
Sounds interesting.
raw pawn
Can anyone recommend me the best introductory text to logic?
winter acorn
Can anyone recommend me the best introductory text to logic?
how to prove it by vellerman 
fast portal
velleman*
winter acorn
hollow current
@raw pawn hammack book of proof
gray gazelle
Guys is it weird that I would rather answer questions here than to do my math homework?
stray veldt
your brain prefers easier tasks
gray gazelle
not if your homework is all about circles
marble solar
Hey guys, I needed your help for buying a Calculus book. I have confusion betwee...
Probably Spivak's Calculus is better for your tastes
marble solar
not if your homework is all about circles
Circles are hard
willow pecan
Yes
vague mason
Gauss Jordan
gray gazelle
LLL
gray gazelle
Circles are hard
no like basic circles.
For example an inscribed angle of a circle is one half the measure of the intercepted arc
its just memorization on what is inscribed and intercepted means
worldly basalt
Coordinate geometry FTW
pale scarab
Hey guys, I needed your help for buying a Calculus book. I have confusion betwee...
Khan academy is good for high school calculus. If you want to go deeper after learning the basics from khan pick up a analysis book. I used understanding analysis by abbott in undergrad and found it to be quite easy to read and is one of the only textbboks I was actually able to do all the problems since it doesn't have a ton. All solutions are available for that book which makes it nice for self study also.
gray gazelle
+1 for abott .
Another one (especially if you like diagrams) to consider is Mathematical Analysis I & II by Claudio Canuto.
static crest
gray gazelle
Yeah , wasn't aware. Though the review that gave it 2 stars is beyond me. Others rated it fairly decent idk
I like the text , i know that haha.
Nvm. some here (@Lerath2) also mentioned the text being 'awful' in a way. #math-discussion message
Welp lol
lmao
narrow echo
timber mesa
two types of people
obsidian valley
the correct answer in my case is just to do [any algebra book]
marble rock
do AM ring theory
obsidian valley
but i do appreciate the fight people have over whether i should be doing d&f or not
marble rock
solve alot of exercises
broken meadow
Not gallian
i am learning that the book is pretty much good for first courses in algebra lmfao
marble rock
start now
marble rock
do it now
warped cedar
gray gazelle
Wow, it seems like a new mod every day
broken meadow
it is linear algebra for me tonight 😌
ember pivot
:O
pale scarab
cs majors who do abstract algebra
Its like stewarts calc book but for algebra. Its not that bad just the problems sets are repetitive and not that difficult and it kinda stays surface level. That said its very approachable and easy to read. I did nearlly every problem for the chapters we did in my undergrad class. Later when I tried to do some d&f problems I realized i don't really know that much.
hasty turret
I don't get why d&f is so polarizing.
Just do your own proofs if you think the proofs are too wordy
hearty steppe
Not gallian
I thought gallian is supposed to be hard
broken meadow
it is hard if you have a smooth brain like me :3
i am in mild pain
but suffering is good
quick hornet
sage python
D&F's in a weird spot, I get why it's polarizing
Since people have different priorities
If you want a book that's rather easy, has good exercises, and is complete
D&F is perfect
But it's written as if you're a child and a lot of people just get bored
The problem with Drunknarwhal's point is that if you just say "Oh why don't you just substitute for where the book lacks" then there's literally no reason to use any book over any other book lmao
But for a lot of people having cleaner exposition is a case for e.g. Jacobson over D&F
slow wraith
timid vector
im pretty much set on Fraleigh fwiw
fraleigh is nice
although the homology chapters went right over my head
narrow oyster
any thoughts on Gallians Abstract Algebra
(8th edition gallian contemporary abstract algebra)
a teacher I dont really like is gonna be teaching this next spring, I think I can deal with her if the book is decent
hasty turret
gray gazelle
looks weird jan niku
hasty turret
tbh, It's not that bad
narrow oyster
idk its bad because the teacher is shit
i have her now for analysis with a shit book
my plan was to learn entirely from the book and not go to class at all
idk DD two downvotes
that looks pretty bad to me
gray gazelle
looks like a book made for kids
narrow oyster
LOL IT DOES
its typeset like a prealgebra book wtf
ugh also its a bunch of application stuff
ppl who took the class said they skipped all of the applied stuff though
so why even use this book
gray gazelle
maybe deal with the author or sth lol
narrow oyster
i think i already did df up to like chapter 3 of this tho
so that might help
i could just start that again over summer and take this course as a not 100% paying attention or trying thing
gray gazelle
you probably already learned 70% of that course jan niku
static crest
I thought gallian is supposed to be hard
it's about the easiest algebra tb to exist
narrow oyster
fug
static crest
I'm personally a big hater of gallian
I hate the notation, it's exposition somehow dumbs things down even more than d&f
gray gazelle
do df jan niku
static crest
it's excessively wordy, but doesn't even cover half the content
static crest
the exercises are also turbo boring
narrow oyster
ill just use a different book
static crest
and not really a challenge whatsoever
narrow oyster
i cannot take another class like this analysis one
i think ill just drop out at that point
static crest
the best part of d&f, no matter what anyone's opinion on the exposition is
is that the exercises are actually 10/10
hasty turret
The exercises
static crest
for the most part (just ignore sections 4.5, 6.2 and 9.6, only sections with garbage exercises)
narrow oyster
take a subject and excise from it any sort of abstraction or complicated creative thought
hasty turret
When it's not computing grobner bases/Sylow groups/whatever
narrow oyster
turn into idk tutor said formalism fetish or something
but im also dk anything 😄
idk i remember the exercises being really enlightening in that book
but i didnt make it very far
but they were enjoyable and tested your understanding of the material and it wasnt just flip back through the chapter and find X definition and rewrite it
like this analysis book is
static crest
ya, that's kinda what gallian exercises feel like
just flip through the chapter
find relevant theorem
and the answer is "immediate from theorem xyz"
90% of the time
flint forge
ch14 exercises suck as well
viral oracle
Hey, I know that this belongs to the EE server but since i´ve got no responses there (not even in the physics server), I hoped that someone there may be able to help me out, here is my question: "Hey guys, I wanted to ask if someone have by any chance some papers or resources (best in pdf), which are focused on more in-depth usage of complex numbers in circuit analysis. I am thinking about this topic as topic of my thesis so I want to find some resources. Thanks.". Any help would be highly appreciated.
silk quartz
viral oracle
Google gave me this
<http://www.its.caltech.edu/~jpelab/phys1cp/AC%20Circuits%20...
Thanks, I´ve actually read that one before 😄
silk quartz
So what do you mean when you say "more in-depth usage"?
viral oracle
It´s kinda hard to explain, the topic itself is not that hard (its just some circuit analysis with application of complex numbers) but all the texts are pretty straight forward and usually provide like "general overview", but I am trying to find something which would provide like in-depth take on every major topic from this field (so they will start from complex numbers operations, definitions, theorems and then take a look on its usage in circuit analysis). That is also the reason why I want to do the thesis on this topic, there is not that much good resources on this (especially in my language). So I guess that I will just do more research and use the existing shorter resources. Thanks anyway.
blazing wyvern
Westergren and Rade's Handbook of mathematics has just a few reviews but the publishing company is Springer, if anyone here has it by chance, would you recommend it?
silk quartz
I mean, complex numbers in circuit analysis can go pretty deep, especially when you start looking at feedback and stability.
This can get into complex analysis territory.
And there's a whole field of complex dynamical systems.
static crest
ya, a lot of the complex number in circuit analysis usage starts veering into pure control theory really
especially when you have like transistor analog circuits
that's a specific thing you can look into, analog circuits, for a lot of complex analysis usage
silk quartz
But usually, the focus here is on the circuit behavior. The mathematical infrastructure is built just well enough to understand the electronics.
And by the time most students reach these topics, they're pretty comfortable with the basics of complex numbers.
viral oracle
And by the time most students reach these topics, they're pretty comfortable wit...
Yeah, I want to study theoretical physics or mathematical physics after high school, so I wanted to take rather deeper look into the math behind it.
silk quartz
Honestly, the math isn't -all- that complicated. Complex Analysis will take you a long ways.
viral oracle
Honestly, the math isn't -all- that complicated. Complex Analysis will take you ...
I believe so, but this I will have to do at uni, which is kinda long away 😄 but anyways, thanks for help, this widen my knowledge
storm sleet
Any good books on Riemann surfaces from a number theoretic perspective?
Or algebraic geometric
vale wing
hi, anyone encountered a number theory books that covers negative number modulo and congruence in detail? For instance, when does a == -a (mod 1000).
stray veldt
pretty much every number theory book?
stray veldt
i have never seen a definition of congruence that only does positive numbers
hasty eagleBOT
derivada.schwarziana
timber mesa
try starting a discussion in #elementary-number-theory
sage python
@storm sleet this might not be exactly what you're looking for but
There's a book I've been meaning to read
"Galois Groups and Fundamental Groups" by Szamuely
obsidian valley
just based off the desc and author does anyone have thoughts on this book: https://www.amazon.ca/Model-Theory-Beginners-15-Lectures/dp/1848903618/ref=sr_1_1?dchild=1&keywords=9781848903616&linkCode=qs&qid=1616624546&s=books&sr=1-1
storm sleet
Isn't Chang the normally recommended book?
storm sleet
Or Hodge if the person recommending dislikes you - This is a joke
storm sleet
I say this mostly in jest
I haven't read hodges but I've heard its incredibly dense. I'm trying to make my way through Chang myself
obsidian valley
I have yet to force myself to do the necessary algebra to read C&K lol
storm sleet
sorry I thought you meant Jesse 😅
Yeah Ch 1 was a bit tricky bc I wasn't paying close enough attention I think
I'm simultaneously trying to teach myself logic and algebraic geometry/algebraic number theory as an undergrad
gray gazelle
why is model theory = algebraic geometry - fields
lol
what are you danning me for
i just heard jan say it at some point
so universal algebra + logic + fields = algebraic geometry
marble rock
omg really wanna learn logic i read some enderton was so cool
and model theory
cool col
marble rock
over air
sudden kindle
yes
marble rock
haha winter is over
no model theory haha
sorry
serious: was wondering are these fields of math ( model theory , logic etc ) strong when thinking about other fields
like do they have applications
or are they just meant to serve as a foundation of math
and thats it
sudden kindle
they have applications
marble rock
where
sudden kindle
no i didnt
ripe granite
like do they have applications
ben shapiro debates
sudden kindle
they have applications
From the post above. these are some applications
In fact some of the most striking successes of model theory have been theorems about the existence of solutions of equations over fields. Examples are the work of Ax, Kochen and Ershov on Artin's conjecture in 1965, and the proof of the Mordell-Lang conjecture for function fields by Hrushovski in 1993.
fossil island
thought i'd share this
Roman did a whole lecture series on lin alg
pretty based
timber mesa
haven't checked it out but yes, he does have an active channel and seems dedicated to it
active-ish
storm sleet
So theorems are polynomials ?
gray gazelle
as expected of my algebra prof's advisor
prisma snow
Does lax do that? I think not. Lax trash. 
No, but I will now quickly before I start my actual work!
Chapter 2 is duality lol wut
prisma snow
I don't like the formatting...
prisma snow
@gray gazelle send me yours 😂
sudden kindle
of chapter 2
karmic thorn
Yeah, you guys got the OCR version or sth
I got such a copy for Jacobson
Futile attempts to fix the typesetting
storm sleet
oh god the dover ebook of Jacobson has unbearable OCR issues
karmic thorn
Yeah lmao
daring palm
hasty turret
Ask the Olympiad server
karmic thorn
Invite link in #old-network .
hidden sparrow
long story short: I have math anxiety due to bad early experiences, but now as an adult I'm trying to overcome it because it's extremely beautiful and empowering. Finished some statistics / R courses and looking to move on to linear algebra and calculus. At the same time I still have this anxiety and lack of confidence. Any books you can recommend that could help me build that confidence up, or just develop more intuition? Even if it's something not practical, but beautiful and approachable for a knob like me. I'm very much not a natural and I rarely get wtf is going on until I see a geometric representation
fast portal
Why is peter lax so overwhelmingly favored by you
prisma snow
I think he must be attractive or something
fast portal
If that was true you would be simping too
prisma snow
I can't even be mad, because true
karmic thorn
Tech boomer MoonBears
prisma snow
Damn, I simp Lax now too
karmic thorn
hasty turret
What it didn't send a photo
Discord must have thought that was nsfw
sudden kindle
long story short: I have math anxiety due to bad early experiences, but now as a...
Maybe Proofs from the BOOK
Or Paul Lockhart Measurement
narrow talon
Needham’s visual complex analysis? Maybe after calc
marble solar
Needham’s visual complex analysis? Maybe after calc
probably after calc 3 at the very least
It would help to be done with linear algebra & differential equations
So that some finer points of complex make more sense
sage python
Tbh I think you shouldn't touch multivariable calculus until linear algebra
Linear algebra and single variable calc can be done independently
willow pecan
On the other hand, multivariable calc some say is best done after linear algebra
marble solar
The correct way is the reverse order you took them in
That's what my math prof said
willow pecan
marble solar
He'd also say, if you're a math major you can do both at the same time
If that's too much for you, then don't major in math
willow pecan
There is something to be said for a class that teaches them in a well integrated way
marble solar
TBH California CCs are better at lower division education than UCs/CSUs
(Well at least the one I was at)
storm sleet
Tbh I think you shouldn't touch multivariable calculus until linear algebra
wait, are you suggesting we wait to teach calculus involving vectors and matrices until people learn vectors an matrices?
Thats insane!
marble solar
The advantage of going to a UC right away is getting into upper division early or getting REUs
willow pecan
Almost certainly
UCs have some good instructors, but CCs definitely have more of a teaching focus
marble solar
I have a feeling if I went to a UC right away
I would have failed out
I wasn't mature enough, nor did I know enough to succeed. The support network I got in CC is why I'm in academic math now
storm sleet
Its kinda insane that at some European universities they start with real analysis
I would've dropped a math program had they asked me for that
marble solar
It's not at like a Rudin level or anything
It's usually a little watered down, like Courant's
Unless you're at like Oxbridge or something
or an ENS
storm sleet
Even so, its a lot to ask for that level of maturity. My college saves it till junior year and we use Abbot
narrow talon
Lol, some Russian friends took analysis in high school
marble solar
My CC did calculus out of spivak, and we proved a lot of what you'd do in junior year analysis
narrow talon
One dude in particular who’s super down to earth but insane mathematically
marble solar
epsilon-delta to uniform convergence
storm sleet
I did our schools undergrad analysis sequence when I was a freshman, so I was 2 years ahead, and only had taken 1 proofs course
marble solar
The CC program ended on Calculus on Manifolds via spivak
storm sleet
Taking an intro to abstract algebra, analysis, and a second term of linear at the same time, all when the pandemic just started was a trip
marble solar
Taking an intro to abstract algebra, analysis, and a second term of linear at th...
well you get good at writing problem sets up quickly lol
I saw my profs intro to proof class exam once
storm sleet
How to get good at TeX step 1:
marble solar
It looked painfully easy, but the avg was super low
willow pecan
But at least at Berkeley, the department has started to place more emphasis on teaching
There are now two tenured teaching professors
storm sleet
Oregon State is nice and chill, but lacks depth in some areas
Like, we don't have any algebraic geometry, and have 5 classes in algebra between undergrad and grad
tbf we're mostly an applied college, so we have a ton of numerics courses
willow pecan
But doesn't OSU have good number theory?
storm sleet
We have 2 number theory courses as far as I know
The undergrad computational course, and the rarely taught grad courses
willow pecan
I see
storm sleet
Which is unfortunate as someone who's interested in it
willow pecan
I got this impression because of the Corvallis proceedings
Where most of the modern theory of automorphic forms and representations was written down
storm sleet
Oh? I didn't know lol
Could've fooled me. We have like 2 number theorists and like 12 geometers it feels like, so our priorities must've shifted
Engineering college go brr
sage python
@marble solar so a typical calc 3 class can be done concurrently with a linear algebra class
marble solar
I'm aware of that lol
sage python
And there's probably an argument that if you're overwhelmed by just the math that's not a good look
But
I think calc 3 shouldn't be taught the way it is
Which is why I'm hard in favor of linear algebra first and teaching calc 3 in a non-stupid way
willow pecan
I see
marble solar
They used to run it that way at Dartmouth
but the pass rates were higher the other way round
So if you do calc 3 then linear algebra, dartmouth found
The pass rates were higher
🤷♂️ g
sage python
I mean pass rates aren't something to be maximized in themselves
marble solar
🤷♂️
marble solar
I mean pass rates aren't something to be maximized in themselves
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
sage python
Maybe at generic places but Dartmouth has the reputation to be like
Yeah if you failed fuck you, you failed
Hold that L
Obv you don't wanna go out of your way to fail people or something but
If doing things the right way makes it a bit tougher and some people can't meet the standards
That's what the grade reflects
hidden sparrow
Thanks for the suggestions I'll take a gander
willow pecan
Also worked on the Manhattan project
gray gazelle
It would have been epic if Cahn was married to the original instructor. Then you could say he cucked his job and his wife
pale scarab
It's usually a little watered down, like Courant's
Thats not what ive heard but Ive only talked to some german/french grads. The undergrad experience in Europe seems to be a lot more advanced then the states.
willow pecan
I think that the undergrad experience in the US is much more flexible
You can easily make it very advanced
storm sleet
Math is one of the more flexible ones too afaik
At least at my college, though my CS department has been lenient with allowing me to take grad courses as replacements for undergrad
willow pecan
For my applied math undergrad, literally every single major requirement can be waived and replaced by something else
storm sleet
We have a set of required classes, but most of them are fairly logical (intro to analysis, linear algebra, intro to abstract algebra) but after that, its whatever you want
willow pecan
Ah we also have required classes but those are "required" and can be waived
storm sleet
If you can convince the advisors, they'll let you into the grad courses too. Few friends of mine are taking our grad algebra sequence and have taken our algebraic topology
narrow talon
I think that the undergrad experience in the US is much more flexible
Totally depends
sudden kindle
Depends on the resources available at your institution
narrow talon
A local uni which would’ve been way cheaper for me is super strict on courses
Not so much on what you can actually do if you really fight it I guess, but grad courses are off limits until senior year
sudden kindle
That's whack
gray gazelle
That just sounds like a meme school
storm sleet
Thats really wacc
narrow talon
Largely because they expect far less of their students, and if you don’t do functional analysis there’s nothing for you at the research level
narrow talon
That just sounds like a meme school
Their agriculture department is great tho
warm glen
Their agriculture department is great tho <:sully:651816820122189834>
davis?
willow pecan
marble solar
davis?
Davis is one of the best schools for 3 manifold Topology
I don't know if the professors are accepting students
willow pecan
Davis also has some people in pdes
ripe granite
Davis also has some people on PEDs
willow pecan
warm glen
Davis is one of the best schools for 3 manifold Topology
nice, i never considered figuring out which schools would be best for really specific topics like that, id always just look at which ones are best for the broad subjects like topology, number theory, etc
wonder what super specific topics ucsd is good for, that's where im at
ripe granite
doesnt sd have a few people doing AG?
marble solar
wonder what super specific topics ucsd is good for, that's where im at
They have some good analysts and PDE people; I've heard they have some good AG people
They have a very good knot theorist
ripe granite
Kedlaya is at SD
marble solar
Justin Roberts, knots knotes
If you're looking for undergrad research, knots is a good entry
I hear Roberts is a great mentor to young students
warm glen
oh yea we have mckernan for AG
sage python
Ah yeah Kedlaya's supposed to be beast
warm glen
roberts was my linear algebra professor haha
kedlaya's sort of a legend in competition math right?
ofc a leader in arithmetic geometry too
ripe granite
Zhouli Xu also seems to be doing cool stuff
I think I know someone heading to ucsd to work with him
warm glen
ahh yea he's new too, came at like the beginning of this school year i think
i forgot completely that zelmanov is here too, the fields medalist
marble solar
roberts was my linear algebra professor haha
Tell him you're interested in his knotes
I wonder if Roberts read my application and my letters
warm glen
Tell him you're interested in his knotes
good idea
is low dimensional topology what ur interested in/researching in?
marble solar
is low dimensional topology what ur interested in/researching in?
I've done some Surface level research in LDT
I've actually applied to do my PhD under Roberts
marble solar
Hrm. I'm probably not going this cycle
I applied a few months ago, but now I have an actual job
I kinda like the money
warm glen
understandable
it's still possible since im only a 2nd yr
hope admissions go well for ya
hearty steppe
MoonBears have you considered working on a blog and doing collab work with other university students?
thats where I am at rn
like literally reference everything your doing on a blog
and make sure you solidify your contacts you work with so people can't say your a fraud
like I kinda feel like your applying for these prestigious programs with little to show for extracurricular activity youve been focusing on since you last finished college
but I mean, I got a lot of work to do myself if I want to get into a good grad program in the future. So its like... me saying something like that is like someone else coming at me being like "well you better make sure you practice what you preach" lol
@marble solar
I think im going to seriously pick up the pace when I get my CPAP machine and actually can get some decent REM sleep. I really hope that helps. My productivity levels are still scaling lower and lower each week ever so slightly.
Least I feel like I'm not getting the most out of every day I try to get anything done. It takes several hours to start my day. Some days just feel like meh and its so hard to focus and get anything done.
marble solar
I mean I have a published paper and am working on a second one
hearty steppe
ahh ok. Maybe my hunch is correct. You don't have much extracurricular experience for these prestigious programs. They are extremely demanding. They seriously want people to stand out in what they've done before they applied to their programs.
So I mean, try to apply to the programs you want to get into when you've got more to show for
idk. Also probably trying to network with professors in the department you would be in would go a long way?
marble solar
You'd think right
hearty steppe
see if you can collab with those professors
I remember that I think Metal or some other mod mentioned doing reading groups with faculty and other students
marble solar
I literally got rejected from a school I applied to where my mentor was at
hearty steppe
are you apart of any collegiate organizations?
gray gazelle
are you a grad student at a prestigious program cat
hearty steppe
nah
marble solar
The department head even told me it's just because I wasn't in state for Irvine
marble solar
He told me I'll be a good candidate for a future cycle
Yes
Yes it is
I might apply for math ed
hearty steppe
My way of thinking is if you didn't make the cut, you have to have that much more to show next time around
marble solar
Cuz it's easier and my application would body then
Them* yes I have a second paper coming out this fall
ripe granite
oh what? wtf thats retarded
this is not ok
hearty steppe
and honestly I don't know how to measure that exactly tbh with you
trying to get into a good program may involve a lot of luck
despite what you do
marble solar
Well I can get more publications and try more connections
The area I moved to has a person in my research network
hearty steppe
yea I agree @ripe granite
marble solar
And I can apply to her school
ripe granite
then why did you say it?
gray gazelle
lol
hearty steppe
huh I thought that the reasoning that Moon got rejected was retarded
thats what I said
????
gray gazelle
it seems c4t confused the quotation with the referent
ripe granite
facepalm
gray gazelle
brofib is saying that saying "retarded" is not okay
marble solar
Hrmmm
marble solar
Anyways
hearty steppe
I forget some words are not acceptable mate
Also, the poor social intelligence I have doesn't help
marble solar
So yeah, I got rejected from a school that I'd have a phd advisor who would let me finish in sub 4 years
hearty steppe
like honestly my worst enemy is my social intelligence.
marble solar
I have an amazing application for math education research
hearty steppe
Its not very good at all.
hearty steppe
I've had problems with peer communication my entire life and it haunts me annoyingly. I just try to be less hard on myself every passing day
they let you do that in grad school?
marble solar
Uhhh
hearty steppe
just get into a program and then be like, I want to switch into this other program lol
marble solar
So the school I'm applying to in math ed
The funding comes from the math department
So all I'd have to do is convince some pure person to be my advisor
ripe granite
pure person 
marble solar
I'd stoop to AG if I had to
hearty steppe
anyway sorry about earlier Brofib
I always try to be diplomatic about anything I've done wrong if people point it out like a purple elephant in the room lol
I think virtual conferences are a flex
ripe granite
anyway sorry about earlier Brofib
you don't have to apologize to me
hearty steppe
not sure if you done them @marble solar
ripe granite
just try not to use the r-word
marble solar
I go to weekly research seminars and attend conferences regularly
marble solar
At least one conference every 3-4 months
When it was in person I tried to do all the local ones
Irvine, riverside, San Diego, etc.
Just trying to network my way in
marble solar
Most things you can think of to scheme your way in, networking, working on experience both professionally and academically, etc.
I've done
||the only thing I haven't tried is getting a good GPA||
hearty steppe
so the experience is going to be tricky for me cuz I hate corporate work and quite frankly, I want to do academic stuff. So I am working on my blog and collaborating with other university students from diff levels
im considering doing like nonprofit tutoring/teaching stuff
I just hate the industry tbh
and theres really nothing useful for me to do in the industry for what I want to focus on
marble solar
I hate the tutoring/math education stuff too
Russian school of math is a cool place to work
hearty steppe
other than bioinformatics to some degree, which I know im not well enough versed in to land a job yet
marble solar
I pissed my boss off though
hearty steppe
wdym you hate tutoring math education stuff
I don't hate it, I enjoy it but its not my passion
I find it rewarding cuz I'm helping other people learn
marble solar
I hate the companies
hearty steppe
oh...
marble solar
I hate how they market
I hate their profit incentives or how they train people
Like C2 educate
Or princeton review
I don't think profit is a bad thing in itself, I just don't like the whole salesman thing
Like just pay the money and your kids will learn
Why do you want some dumb youtube video
hearty steppe
god we really went off the rails on this chat. Nothing book related :\
gray gazelle
Can anyone suggest some good books to start learning calculus by myself, I do not want a book that just has some short text followed by a vague and unexplained example, but rather one that will go into detail and won't leave random bits out. Hopefully you understand what I mean. Thanks
hearty steppe
I used James Stewart while watching Professor Leonard's Youtube videos
gray gazelle
I used James Stewart while watching Professor Leonard's Youtube videos
ah alright, were his textbooks helpful overall?
hearty steppe
plenty of psets for elementary calc
crimson cipher
hello folks, I am interested in studying kreyszig's functional analysis given its prerequisites are minimal for applications and then later on studying a more in depth functional analysis text for proper theory once I gain more prerequisite knowledge. Is it a good idea or should I just wait and do a full on text later?
slow roost
I don't see what harm it could do
crimson cipher
On one hand I was thinking that I was wasting time because I would probably cover the same stuff later but on the other hand it isn't guaranteed I'll have the time to cover it in depth later
slow roost
well, any stuff you manage to learn from it now will be time saved later
wispy pebble
very cool ppl is a donator role
broken meadow
who ping
gray gazelle
potg did
raw pawn
Why is bertsekas intro to probability recommended so much? the book doesnt even have problem sectioms
sections
pearl imp
I was wondering if anyone uses the book "Linear Algebra and its Applications 5th ed." by Lay?
devout mist
Any recommendations for intro to finite group theory?
sudden kindle
Any recommendations for intro to finite group theory?
I like Dan Saracino's Abstract Algebra A first course
If you've never worked with groups before
thorn sedge
Guys, may i ask a book recommendation for linear algebra? Im 1st year math graduate, we learn vector spaces, linear maps, matrices, ortogonality, endomorphisms.. I look for a problem book, but that has proofs as problems. In my course i have a lot of proof problems i cannot find a suitable book that has that kind of problems, most are numerical or calculating problems. I would really appreciate ur help ❤️❤️
thorn sedge
I will look into it, thank u very much
gray gazelle
i just went off the "first year math grad" lol
sage python
Hoffman-Kunze is also a good (if old) proofsy LA book
@hasty turret what's wrong with it?
gray gazelle
klaus janich
and then ikramov for problems
just intuit the whole subject
i'm a janich fanboy
hasty turret
I saw a few proofs in lax. Seems like there are a few unnecessary steps
gray gazelle
also isn't roman advanced linear algebra?
hasty turret
interpreting why those steps are necessary is a big hassle
gray gazelle
also isn't roman advanced linear algebra?
yes, they said "first year math grad"
although he does go through the pre reqs but it is quite fast
oh yeah then absolutely roman
lmao
but vector spaces is an ug topic,is it not?
everything is an undergrad topic
i see
judging by that person's english he might not be asking precisely what he wants to
oof not that react
dense pewter
im pretty sure most people learn vector spaces at about the same time they learn about the elementary theory of heights
hasty turret
Ok,I haven't seen enough lax to judge it
gray gazelle
t. algebraist
sage python
Yeah that's why I said Lax, I heard that's what they use at NYU for first year grad students who might'vr had eh linear background. I think Hegel said that?
Hah Buncho
hasty turret
What is this "elementary theory of heights"? I know it's a mochizuki thing,but what does he mean by that?
willow pecan
Wouldn't we all like to know
There's also the theory of heights at the introductory graduate level
From some recent paper by Fosenko or something
sage python
You're asking about the meme or what the actual subject is about?
hasty turret
Wait,There is a subject dealing with "theory of heights"?
Or is that just part of IUTT or smt
tranquil ocean
prisma snow
@gray gazelle dami recommending lax too, what have you done to this server?
||Also, is drake going to die for insulting lax? ||
👀
That's why the spoilers
sage python
Lol I haven't read any of Lax I just know it's supposedly a "graduate introduction to linear algebra"
fast portal
Lax is now added to my collection.
also dami can we get another one of your megaposts about textbooks, but Differential Equations isntead of AA or CA
ripe granite
graduate linear algebra 
narrow talon
Lax is good for intuition on more advanced stuff
And yeah, it’s the grad text at NYU but it’s dependent on the prof whether they actually follow it
The applied profs tend to follow Lax, pure tend to loosely follow it with misc stuff from whatever field they’re in mixed in
As expected
fast portal
One may even say he is lax
sage python
graduate linear algebra <:hmmm:773801269532819466>
More like, "you're an incoming grad student who somehow doesn't know linear algebra"
sage python
also dami can we get another one of your megaposts about textbooks, but Differen...
Idk about differential equations books at all
marble solar
For an ODEs class Boyce and DiPrima seems to be pretty decent. The main thing you need is gobs and gobs of examples in ODEs, so even the schaum's outline helps a lot
For PDEs, skip any and all undergrad books, just go to Evans
willow pecan
PDEs really suffers a lot from intro pdes not being too hard and real pdes being very hard
Like
For heat/wave/Laplace, you can do separation of variables/Fourier series
But you moment you introduce the slightest nonlinearity, everything explodes into Sobolev spaces
broken meadow
More like, "you're an incoming grad student who somehow doesn't know linear alge...
How does that even happen
ripe granite
maybe I will understand some of those words after this quarter
broken meadow
i will take a babby intro to pde this spring i think :3
willow pecan
Sobolev spaces are Lp spaces where you keep track of the derivatives as well
Naturally this is important for pdes because you want your solutions to be differentiable
This ties into ideas of strong vs weak solutions
And whether or not solutions have sufficient regularity
mossy flume
I don't think I'm ever gonna take PDE lmao
willow pecan
PDEs are good
mossy flume
there are more interesting courses out there
willow pecan
I highly recommend them
mossy flume
I don't even wanna take diff eq
marble solar
PDEs at the undergrad level is kinda....not really that great
Instead you take complex analysis
mossy flume
maybe I'll throw baby PDE on at the end of senior year
yea I wanna take complex analysis
junior year
marble solar
Then you go into grad PDEs, and you're like holy shit
Complex Analysis is all about PDEs
mossy flume
i c
willow pecan
Complex analysis is all about a single pde
marble solar
Complex analysis is all about a single pde
My class covered more than one
🤷♂️
But then again I did 4 quarter ssoooo
mossy flume
Next sem I'm doing diff eq, real analysis, and differential geometry
should be a fun time
sage python
How does that even happen
Idk but again that's what people here say
ripe granite
complex analysis is all about gaining intuition to do AG
sage python
Complex analysis is just harmonic functions \cap algebraic topology
marble solar
Complex Analysis is all about preparing you to do harmonic analysis
ripe granite
ye do AG
sage python
Should I know Reznick?
mossy flume
He's apperently a big name in AG
and multiple people here have said "take an AG course with Reznick"
ripe granite
what kind of AG?
sage python
"The John and Harriet J. Absentminded Professor of Mathematics"
I already respect this guy
fast portal
Idk but again that's what people here say
My undergrad curriculum has 0 official LA class. It teaches all the necessary bytes in the other courses where they are required. So taking it becomes pointless.
marble solar
CSULB has no required upper division linear algebra course
Grad students there come out not learning diagonlizability, direct sums, etc.
willow pecan
fast portal
Mood
mossy flume
what kind of AG?
I mean there are 3 AG courses here
Intro to Algebraic Geometry
Modern Algebraic Geometry
Complex Algebraic Geometry
sage python
Dope
mossy flume
wtf I'm taking my first lin alg course and I'm doing diagonizability and direct sums and stuff
ripe granite
no I meant what kind of AG does Reznick do lol
mossy flume
oh idk
mossy flume
just alot of people have mentioned his name so I'm like 👀
marble solar
wtf I'm taking my first lin alg course and I'm doing diagonizability and direct ...
you usually cover it in Upper division linear algebra
mossy flume
I have to take graduate AA first tho so idk if I'll get to an AG course
sage python
Funny thing is the person at UIUC with a similar name who I know is Rezk 😛
Charles Rezk is very much a thing in algebraic topology
ripe granite
yes
mossy flume
Funny thing is the person at UIUC with a similar name who I know is Rezk 😛
I'll probably take honors Abstract Algebra with him in a year or so
ripe granite
nice!
mossy flume
you usually cover it in Upper division linear algebra
I mean I'm taking the highest level undergrad lin alg class offered here but it has no prior lin alg requirement
marble solar
RIP
ripe granite
I'll probably take honors Abstract Algebra with him in a year or so
so straight to E infinity rings eh
that would be pretty funny
mossy flume
lol
ripe granite
I mean I'm taking the highest level undergrad lin alg class offered here but it ...
I think there is no prereq here as well?
mossy flume
We offer 3 lin alg classes here
marble solar
I think there is no prereq here as well?
115A has a 33A pre-req
ripe granite
not enforced
marble solar
Not enforced for you
mossy flume
lower level computational lin alg, upper level computation lin alg, and then upper level proof based lin alg
hollow drum
115A has a 33A pre-req
Quarter semesters?
marble solar
semester quarters?
ripe granite
and you dont use 33A stuff at all