Like at CSULB, math 233 intro to proofs is notoriously crazy because students have to come up with their own proofs with very little guidance
#book-recommendations
marble solar
civic carbon
There is an alternative universe where I designed that course I think haha
marble solar
A certain Algebraist there is very stringent on how he grades, and often leads math majors leaving the major
civic carbon
almost every imaginable proof will feel creative to an intro to proof student.
marble solar
civic carbon
and a lot of it for me is to just spend a month doing variations on the same handful of proof methods. Just iterating and practicing.
gray gazelle
Most of us would lol
marble solar
I would've dropped out of math if my professor didn't spend a year making me memorize proofs. I would've failed out of UCLA
civic carbon
I once accidentally put a proof on a test of a proposition from the book, and students noticed and decided it was a good idea to memorize every proof from the book
marble solar
I yield, I am not a good mathematician. I am sloppy, I am slow, I cannot calculate accurately, and I often have very vague notions
gray gazelle
I don't think any of those are good markers
civic carbon
I would say that math grows most when a diverse set of minds work on it.
marble solar
I completely agree with that zeta, but I believe that if you don't have an existing study/support structure built in, the best thing you can do is create a model for students to master
civic carbon
A mix of stubborn slow and sloppy fast people, for example.
gray gazelle
Sloppy fast probably means intuitively active people
Stubborn slow as in rigorous and precise?
marble solar
I feel that
marble solar
Blair recently taught the 233 @civic carbon, he used a really interesting book
gray gazelle
Answer this in #math-discussion
civic carbon
I would say taht my strength as a mathematician is that I will give up a line of reasoning almost immediately if it seems unfruitful. However, if everyone was like me, we would never have made class field theory.
marble solar
Number, Space, and the Structures of Mathematics by Scott Taylor. A review copy of the text is
available for free at this site: http://web.colby.edu/sataylor/numberspacestructure/
gray gazelle
I can spend a lot of time (at my level) on such ideas
I feel like when things will get more abstract I'll lose that skill
civic carbon
When I teach it now, about 25% of the course is cultural. What do mathematicians actually do? Why do they do it? What is even the point of pure math? There are a combination of readings, youtube videos, etc including e.g. Mathematician's Apology.
(There will never be an opportunity to make students read A Mathematician's Apology that I will not take)
gray gazelle
That good huh
civic carbon
it's thoughtprovoking
marble solar
Have you read Bill Thurston's on Proofs and Progress?
civic carbon
plus I get to say "you're allowed to say you think the author is a jackass"
gray gazelle
It's been a while since I read a fun math book tbh
marble solar
Thurston has written a few, but Proofs and Progress is an essay
civic carbon
I have not, it sounds interesting!
marble solar
It's like 7 pages, I highly recommend it
It talks about how mathematicians conceptualize proofs, how learning is about cultural interactions, how much more is conveyed by non-verbal communication
or even inflection/tone
civic carbon
I think it is really underemphasized how little of math is actually proofs.
marble solar
Bill Thurston spent years working on accessibility of mathematics for younger people trying to convince them of that fact zeta
I don't even think I like proofs that much, I think I just enjoy the social/cultural aspects of math
civic carbon
my current video is about Euler's non-proof that zeta(2)=pi^2/6, so I've been meditating on that a lot
marble solar
civic carbon
I am already reading it haha
Is the article that this is in response to also worth reading?
I love any chance I have to have students read mathematicians passionately disagreeing
gray gazelle
Did you guys read the one on Dota ?
marble solar
I haven't read the article he's responding to
gray gazelle
marble solar
But it's rather short, so I'd imagine it's worth reading if it spurred this caliber of a response
civic carbon
I see the idea that "The thing about math is that there is always a singular correct answer" unquestioned way too much
marble solar
I also agree with that. Did you see the research where psychologists gave students faulty calculators
For calculations that were moderately difficult, but something they could still do by hand accurately fairly quickly
And all the students went with the calculators anyway
@civic carbon This essay by Thurston convinced my friend to quit becoming an Actuary and to pursue pure math
gray gazelle
It has convinced me to quit pure physics and pursue adulterated physics
Jan is reaching ultimate troll status
gray gazelle
I can focus for exactly 0 seconds at a time
So your attention span is a goal for me
marble solar
Sounds reasonable
I think the point is as you sophisticate you re-learn/re-shape those foundational tools to something more than it ever was
sage python
Yeah tbf there are parts of math with too few people to even have a social aspect
e.g. continuous logic
<3
valid moth
by being scholze
weary nymph
Anyone have experience with How to Prove it (A structured approach) by Daniel J. Velleman?
I am once again stuck with set theory proofs, the very first one in Halmos's Naive Set Theory to be specific, so I figured out I should go to the roots of my problem with set proofs
hollow current
@long anchor worked with it as i remember
weary nymph
These are the kind of proofs I want to be dealing with
how does that compare to what hammack does?
soap is it a free book
https://www.people.vcu.edu/~rhammack/BookOfProof/ this looks legit
hasty eagleBOT
Commander Vimes:
hollow current
lmao
weary nymph
if a homie releases his book under a CC license I'd rather get it from his link
weary nymph
@long anchor did you engulf the whole thing or it's possible to freely check any of the chapters for their corresponding proof instructions?
long anchor
@weary nymph uhh i mean if u know logic already it should be pretty easy to read the main proof techniques
theres like a chapters dedicated to each technique
and there probably is a chapter dependency chart in the first few pages
night knot
How's "Invitation to Discrete Mathematics" by Matousek?
valid moth
it's always how is "invitation to discrete mathematics by matousek"
never why is "invitation to discrete mathematics by matousek"
smoky surge
When y’all are reading through a chapter of it’s something more applied do y’all make sure you understand it 100 percent on the first read around or if you get a bit confused do you keep reading an come back
flint forge
i rarely ever understand anything 100% ever
at least on a first pass
i think its okay to get some big ideas together, try some exercises, go back if you find out you dont actually know whats going on
etc
smoky surge
thanks appreciate the advice
hearty steppe
Yea I mean I think re-reading and not sticking to one book for perspective is important
smoky surge
ok thanks sometimes i feel bad when i need multiple resources
hearty steppe
Multiple resources should be encouraged
And thinking about how you want to apply what you learn is important
Over time conceptual fluency should help with creativity
smoky surge
👍
open storm
Hi
Just saw this channel haha
What do you guys recommend for a good euclidean geometry textbook that's pretty rigorous
marble solar
Euclid's elements
wooden sparrow
In a numberphile video, that guy says it's next to Bible in something I don't remember
Euclid's mama must be proud :')
marble solar
Most printed books
wooden sparrow
Ohh
marble solar
In the world is 1) Bible, 2) Euclid's Elements
wooden sparrow
That needs a switcheroo
north spire
What do you guys recommend for a good euclidean geometry textbook that's pretty rigorous
@open storm My second semester course recommends Foundations of Geometry by Borsuk and Szmielew. I've worked through some of it and it's nice.
It's a modern treatment of the subject so you'll probably like it
wooden sparrow
No! I like to study Elements sitting by ye tree, dipping thy Greek bread into thy wine
gray gazelle
if you arent studying euclidean geometry using only one of these things then you're doing it wrong 
velvet briar
No wonder I can't understand it
I could never squeeze the shapes into the holes. My shapes just had too many damn corners. I think they sold me a broken one
wooden sparrow
Or a rat bit it's edges
limpid gazelle
Wait all these holes are the same up to homeomorphism so any block can fit in any hole
slender sphinx
acoustic pelican
Simply define the outside with the variable called inside and now all the blocks are in the inside. 
gray gazelle
so
who here has read both baby rudin and tao's first anal
maybe not cover to cover
but >100 pages of each
and done the exercises in those pages
marble solar
YA
gray gazelle
did you finish either one
weary nymph
@long anchor what logic book have you used before getting into Book of Proof
gray gazelle
@marble solar
marble solar
I used Rudin in my classes, and reviewed using Tao's
I prefer rudin over Tao, and I don't like Rudin
hollow current
for analysis Zorich for me looks extremely good
marble solar
My favorite is probably PUgh
Tao spends too much time doing the foundational stuff
integers, rationals, axiom of choice, etc.
gray gazelle
@marble solar lmao
why did you use it if you didn't like either
i mean you used tao for review
if you liked it even less? lol
sage python
I glanced through Pugh at some point, and my impression is that the way it does topology is... a bit awkward
marble solar
It does it from an analytic point of view
sage python
But I'd wager it does multivariable calculus better than Rudin
marble solar
It does everything better, except for the chapter 2
And that's up to taste, either abstract topology or analysis topology
because the exercises are fantastic
sage python
Eh, idk I'm semi-inclined to say that Rudin's take is just better™️
On topology at least
marble solar
again, up to taste
For multivariable, I do prefer spivak's calculus on Manifolds. Though some ppl think it's a little old
sage python
It's probably a bit presumptuous to say that the alternative taste is kinda worse but somehow... I think there's something you lose by just mixing sequences and open sets and just kinda doing stuff out there
And I'm not sure what you gain
Vs having it a bit more... "partitioned off" so to speak. But yeah idk how Pugh's material that's analogous to Rudin 5-7 is treated, I do think Rudin 7 is extremely difficult to beat but it's possible Pugh does it
I think I've told you this before but at some point I'd prefer that people just didn't bother with Riemann integration on R^n. It feels like a mess
marble solar
I think it helps, the proof of Fubini's theorem is rather simple
sage python
In particular I've heard change of variables is a nightmare
sage python
Looking it up in Shifrin at least it seems kinda bad
hollow current
@sage python why i googled shifrin and got this
marble solar
Spivak's ain't bad
gray gazelle
Any book that focuses on vector calculus, including(div, grad, curl, coordinate transformation, orthogonal and curvilinear coordinates) deeply (undergrad or grad level)?
gray gazelle
div , grad curl and all that book is like technical
its gonna be hard to get into unless you have some ocntext in multivariable function and stuff arldy
marble solar
he said any level
gray gazelle
I'm gonna give that book a try but is it good on coordinate transformations?
main flax
what are the differences between lang's and axler linear algebra?
main flax
he has an undergra linear algebra
civic carbon
Axler is a very good and readable writer (who happened to choose an incredibly arrogant/obnoxious title for his book) where as Lang is just arrogant.
Your style preferences will vary, but for me Lang's writing is always last in my list of things to refer to.
(He has a book on everything)
main flax
can you explain on the arrogant part lol, am curious
i never read his book before and i thought reading his linear algebra might prepare me (in terms of his writing style) when i eventually get to his grad algebra book
sudden kindle
Axler is very readable
velvet briar
Have never read Lang, can concur Axler is a very good book
velvet briar
Other than the determinant stuff yeah
Read Ladr, know what the determinant is from other sources
flint forge
Or just read ladw
dapper root
Is there actually a point to picking up a linear algebra specific book?
I have one I had to pick up for a class I took my freshman year, but it didn’t even go as in-depth as the linear algebra in Dummit & Foote goes
I’ve never really felt like my linear algebra was lacking to the point I couldn’t do the stuff I’ve had to do, and I’ve only learnt linear algebra from D&F and Aluffi for the most part
flint forge
I think it depends how much linalg you do
Like its more relevant for some fields than others
And least the in depth stuff
main flax
hm alright, i'll try axler
ebon bloom
Has anyone read Lang’s calculus books? Any opinions?
gray gazelle
Anyone have a source for Discrete Dynamical Systems: Theory and Applications by Sandfeur? It's a recommended source in Lay Linear Algebra, it's only a few dollars for a HC on Amazon, but I wanted to take a look at a digital copy before buying. I already checked Libgen.
NVM, it was 8 dollars with shipping and had good reviews so I just bought it.
gray gazelle
Beautiful
main flax
if it's not on libgen it's not worth getting 
hearty steppe
i mean thats debatable
wooden sparrow
@main flax lot of AOPS books aren't on libgen
sage python
Corollary
main flax
hahaha
valid moth
One book that I've recently realized is a great introduction to Mahāyāna Buddhism is the first volume (the second is a restricted text, I think, so I'm pretty sure one needs a lineage-holding teacher's permission for it
TIL they have OCR technology in buddhist monasteries
main flax
a book worth getting i see
echo brook
hey, im new to math (serious math) and I am trying to self-study because I am already done school and don't really wanna go back for an undergrad. This is my current "study" plan. If anyone has any feedback (ie order of phases or recommendations on books/other courses to go through) i would greatly appreciate it. Most of them are MIT OCW, I am using MIT OCW to just get the books they used, not for the video lectures.
Courses/Books in a phase are done in parallel:
Phase 1:
Calculus by Michael Spivek | MIT 18.05: Introduction to Probability and Statistics
Phase 2:
MIT 18.02: Multivariable Calculus | Book of Proofs by Richard Hammack
Phase 3:
MIT 18.03: Differential Equations | MIT 18.200: Discrete Math
Phase 4:
MIT 18.06: Linear Algebra | MIT 18.600: Probability and Random Variables
Phase 5:
MIT 18.100: Analysis | MIT 18.650: Fundamental of Statistics
Phase 6:
MIT 18.700: Linear Algebra Done Right | MIT 18.211: Combinatorial Analysis
so you are a college grad?
or...
high school grad who doesn't plan on going to uni?
echo brook
college grad, Software Engineering (aka project management with some coding). trying to switch careers
sturdy sail
That doesn't look bad for a starting point
You said you intended to focus more on probability and statistics, right?
After that you could study topics concerning these things more.
In order to specialize your knowledge
So in phase 7 or something you could start studying measure theory, then stochastic processes, stochastic/Itô Calculus, Brownian Motion and etc.
Probability theory is a very broad subject
echo brook
sounds good @sturdy sail ill prolly ask for more guidance when I get closer
thank you
north spire
@echo brook If you're starting with Calculus by Spivak, then it's somewhat pointless to use "Book of Proofs" in Phase 2. That's supposed to be one of the intro to proofs texts that you supposedly read before doing analysis.
Not sure what you mean by "get the books they used" but doing 18.06's Linear Algebra is pointless. If you manage to work through Spivak, then just start doing linear algebra as taught from LADR or Klaus Janich's book.
echo brook
I intend to do analysis in phase 5 which is why I want to go through book of proofs.
And by "get the books they used" I mean that the MIT courses often follow a required textbook and thats the one I intend to follow.
And I wanted to do 18.06 because it covers specific topics that I find interesting (PCA, SVD, and some other cool applications). I know it overlaps with LADR but i am in no rush.
north spire
Right but I'm telling you that if you're going through Spivak's Calculus (or any of the equivalent calculus books written by Courant, Silverman, Apostol), then going through Book of Proofs is useless.
Okay, I shouldn't say "useless". You could still learn things from it if you really wanted to. Like, some set theory is good to have since you'll be using that a lot and maybe some basic logic. But it's better to use that as a supplement to Spivak's text (such that you can go back to it when you're confused by Spivak).
Spivak's Calculus (or equivalent) teaches you how to do proofs so it's useless to work through that text. Once you're done with calculus, you can just jump straight into analysis. The treatment of certain topics will be a bit different in analysis but spivak will prepare you for that.
The flavour of 18.06 is very different from that of spivak's calculus. You won't see many proofs and it'll be more computational. Basically, your plan seems kind of weird to me and doesn't really make sense if you want to do serious math
Like, you can watch, idk, the 18.06 videos alongside doing LADR or LADW or Klaus Janich's book or whatever other abstract introductory linear algebra text you choose to work with. They can help you with the computational side of things but it's a bit of a waste of time to treat them entirely separately
echo brook
oh i didnt know Spivek covered proofs (the table of contents didnt indicate it so I assumed it didnt)
pure minnow
look man proofs are literally just ideas
spivak will be fine
and most proof books just wank off for several chapters anyways
echo brook
ok sounds good. ill prolly drop 18.06 and book of proofs then
north spire
I mean, i don't see anything wrong with using it as a supplement if you find spivak really hard at first. But, like, it's kind of dumb to do it after spivak
And when it comes to multivariable calculus and differential equations, if you're already going to use the calculus text by Spivak, then you might as well use rigorous textbooks for multivariable calculus and DEs. You can definitely use the videos as supplements, that's not a problem at all. But it's kind of a waste of time to treat them separately.
echo brook
for sure, that makes sense. I'll ask for those books once im done phase 1. do you have any thoughts about the statistics courses. Im thinking of dropping 18.05 (theres no textbook just lecture slides so prolly not that fruitful)
north spire
I haven't done anything formally with probability and statistics (might actually organize a reading course on that). At my uni, you are encouraged to take probability and statistics after 3 courses in analysis
echo brook
oh....
north spire
Look up ETH's first year and second year course curriculum for their math degree. That should give you a good sense of what you should be focusing on
Generally speaking, you start out with analysis and linear algebra, which slowly goes into abstract algebra from the 2nd semester onwards (at my uni, anyways). Then, you can start doing other courses like statistics and whatnot
echo brook
aight, ill follow the same framework
thanks for putting things into perspective @north spire
north spire
Sure
I mean, you don't have to follow what I said
Read what you enjoy, honestly. Going the MIT route isn't really wrong. It's just that I wouldn't go that route personally.
echo brook
I picked MIT mainly because it was the first resource that I found that outlined somewhat of a roadmap.
I'll follow your suggestions and branch off if I find something interesting.
north spire
Yea
That's a good way of approaching it. Nothing's really stopping you from learning other things if you're really interested
It might be hard if you don't have prerequisites but there's nothing wrong with exploring a bit if you're self-studying
hot prism
does anyone have a good pdf on number thoery
all the ones i see is either too easy or too complicated
valid moth
what's your background
hot prism
Year 10 highschool kid
valid moth
and what is your motivation to study this
hot prism
exam
valid moth
competition math?
hot prism
ye
valid moth
try aops
hot prism
I am in india, and it is called the PRMO
valid moth
is that the regional round
hot prism
ye
valid moth
look at what i linked i suppose
wooden sparrow
@hot prism I'm from India too
hot prism
sup bro
hot prism
the exam, the topic, or the book?
hearty steppe
What is LADW
hot prism
Well, you can answer all of it with the class 7 syllabus alone, but learning other things will cut down on time
CBSE class 10
wooden sparrow
Ohh
hot prism
and from looking at past papers, there is not a single question on complex numbers
But algebra, number theory, are the big guys
wooden sparrow
@hot prism look at last 3-4 years papers
wooden sparrow
Could you find any papers involving complex numbers?
hot prism
no
north spire
What is LADW
@hearty steppe Linear Algebra Done Wrong by Sergei Treil
wooden sparrow
@hot prism pirate AOPS books from libgen or/and z library
wooden sparrow
You bought it?
hot prism
the book?
wooden sparrow
No, the exam
hot prism
Just search PRMO past papers and it comes up
wooden sparrow
Okayy
gray gazelle
im partial to folland's advanced calculus
it has a nice coverage of topics
and he introduces all of the necessary topology (rather quickly, but oh well)
gray gazelle
cant quite comment on the last few chapters (fourier series) but the first 5 are super good
dapper root
The Fourier stuff is alright
I think it’s a good presentation but I didn’t get any of it tbh
I like that Folland usually introduces the single variable stuff then like 2 sentences later generalizes it to R^n
gray gazelle
gotta motivate it somehow
dapper root
The only part it’s kind of lack luster on is stuff R^n -> R^m
Like he touches upon the derivative being a matrix and stuff
But you pretty much only deal with stuff R^n -> R or R -> R^n
But that’s most of analysis anyway until way later
gray gazelle
the inverse function theorem is also kinda ignored
gray gazelle
nvm, it's in there
dapper root
He touches on that and implicit for like an entire section
valid moth
smh doing calc 3 before ISM
gray gazelle
and asks for the converse as an exercise
wooden wigeon
i’m back
gray gazelle
folland is super nice for a theory-calculation mix imo, but if you want raw theory just open spivak (or munkres if you want to move at a snails pace)
wooden wigeon
so you said folland?
gray gazelle
yeah
dapper root
Depends on what you want tho
Are you looking for jjst like I know the basic idea
Or a really rigorous treatment
wooden wigeon
it’s just a calc 3 class
dapper root
Like college?
gray gazelle
i will always give overkill book recs :)
dapper root
If you want like super seat of your pants just rough idea can do the calculations idc why it works
Your course text is probably fine
Like Stewart
wooden wigeon
let me see what shitty book they use
dapper root
If you want a rigorous but not overkill I think Spivak
wooden wigeon
it is stewart
dapper root
Yeah I used that
valid moth
do you also recommend 10th graders looking to learn elementary number theory for math comps look at a course in arithmetic?
dapper root
Idk anything about NT
gray gazelle
how is spivak not overkill but folland is?
dapper root
Because Folland is pretty much analysis and Spivak still is not calculusy
Does Spivak cover topology?
gray gazelle
are you referencing calculus on manifolds?
wooden wigeon
yeah multi variable
valid moth
i recommend ISM
gray gazelle
bruh
dapper root
Arch pls no
wooden wigeon
why does this class say that we have essay assignments
gray gazelle
calc 3
essay
valid moth
because you have essay assignments
wooden wigeon
for math??
dapper root
So I’m gonna be honest like this is a math focused discord so I might get flamed
But I think like
wooden wigeon
ESSAY?
dapper root
Stewart is fine if you’re just trying to be an engineer or CS or whatever
If you want to be a mathematician do something else, or maybe even not
wooden wigeon
yeah cs major
dapper root
I used Stewart and later on did the material rigorously
wooden wigeon
but like i want to know my shit
valid moth
im not even sure what stewart is so lol
shadow nebula
why is essay one letter away from easy
dapper root
Also I can see why you’d have an essay
wooden wigeon
why?
dapper root
Err, I had a paper for my diff eq
Idk if essay means like ESSAY or a paper, but it covered some application
wooden wigeon
“Frequent essay assignments in which students are required to utilize deductive logic and critical thinking skills to write mathematical proofs, explanations, and verifications in paragraph form”
gray gazelle
this sounds like a regular assignment
dapper root
that sounds like maybe it just means a proof
valid moth
gray gazelle
||take a proof and call it an essay so you don't scare people||
valid moth
that one time max got an A- on an english paper, when his prof remarked he had very clear and rigorous logical structure but nothing much of substance was being said
wooden wigeon
i hate english
valid moth
y
valid moth
in what sense
wooden wigeon
too much brain needed
dapper root
Maybe look into Apostol?
valid moth
is this why you decided to study cs
wooden wigeon
hard to come up with ideas
gray gazelle
...and math doesn't need brain?
valid moth
lol
shadow nebula
wooden wigeon
not much
dapper root
Lol
valid moth
wooden wigeon
the stuff i’m doing doesn’t
gray gazelle
math doesn't need brain
not much
legendary take
dapper root
You’ve unknowingly pissed off a lot of people
wooden wigeon
yup
dapper root
But I can sort of understand your position
wooden wigeon
how so
dapper root
If you’re good at math and have only seen calculus
gray gazelle
i get your position too, im just memeing
wooden wigeon
yeah i’ve only seen calculus
dapper root
I see how you could come to that co clusion
wooden wigeon
i don’t see how calculus is hard
dapper root
Like I was in the same place, but a lot of us do way more than calculus so
weary nymph
how is English hard
dapper root
It rubs a lot of people the wrong way lmao
wooden wigeon
but matrices are hard
weary nymph
it's a ton easier than any language I know
dapper root
I think they mean
wooden wigeon
i’m talking about english class..
weary nymph
ohh
dapper root
Analyzing texts for literacy meaning etc
Presumably they’re a native English speaker
In which case the language is trivial lol
gray gazelle
||if math doesn't require a lot of brain why don't you become the next euler with that massive heap of grey matter?||
/s
dapper root
I’ve heard people mention Apostol tho for calculus
wooden wigeon
matrices are a different language when compared to calculus
dapper root
Has anyone ever used it?
wooden wigeon
the math i’m doing doesn’t require a lot of brain
but the math beyond engineering probably does
dapper root
Also various people on the internet recommended Hubbards Linear Algebra, Multivariable Calculus, and Differential forms
I can’t speak for it
But you’ll probably need linear algebra for CS too
So this might be a good option
gray gazelle
is linear algebra really necessary for super basic calc 3? actual question
gray gazelle
like i can't think of anywhere it seriously comes up if you remove a lot of the theory
wooden wigeon
no i told you my linear algebra class requires concurrent or completion of calc 3
i also have to do discrete math and probability theory
gray gazelle
that's why im asking if basic calc 3 requires linear algebra; im not sure what basic calc 3 entails precisely so im interested to see how much LA can be removed without destroying the math
dapper root
Okay I’m looking at what I think is a pdf of the table of contents
And it involves words like manifolds
So like
Idk about that
gray gazelle
dapper root
Maybe Apostol is a better choice
wooden wigeon
3d space
dapper root
Like I think you can definitely use manifold in a not crazy way
But I can’t look at the text itself
So
wooden wigeon
what does manifold mean?
dapper root
Uhhh
gray gazelle
generalization of curve and surface
dapper root
Locally looks like Euclidean space
So a good example
A sphere
Like if you’re an ant on a sphere
And can’t jump
It looks like 2D
You can move right, up, left, down
Or any combination of that
gray gazelle
||things look flat near you, the ant, so you naturally conclude that the earth is flat||
dapper root
So that’s a 2-manifold because locally it looks like 2D space
dapper root
So like if you want to generalize alculus
You take it to manifolds
Uh
You might never
Usually the first class which introduces manifolds in any meaningful way
Is a first year graduate course in math
At least in the US
So that’s why it’s a bit dicey to me that they include the word
wooden wigeon
I wanted to ask. What do people with math degrees do?
gray gazelle
no undergrad manifolds course?
dapper root
But like
wooden wigeon
like pure math
dapper root
Reading reviews
Idk, I don’t think they’re that common TTerra
Pure math has a lot of things
You can go industry and work at highly technical jobs
Or go academia and do researxh
I know only of the latter really since that’s my goals, but industry jobs do exist
And pay way more
gray gazelle
people with/wanting math degrees also have to deal with "oh, you're a math major? calculate 489594837e^π19737383838"
dapper root
Heh
wooden wigeon
i was going to do civil engineering but it sounded too boring
dapper root
I get “wow I hated math” way more
marble solar
Pure math, you mainly go do research mathematics or focus on teaching mathematics
dapper root
And I’m like “cool, I don’t care”
Yeah to parrot off what MoonBears said you usually are going to be doing research, but non-universities are interested in math researxh too
wooden wigeon
are the vectors in calc 3 the same as the ones in physics
dapper root
Eh
If your class is focused to like an average audience probably
But vector in math can mean way more
wooden wigeon
There’s a lot to math i don’t know about
dapper root
the class probably is taught to appeal to your intuition in which case they’ll probably tell you to imagine a vector as something in 3-space
gray gazelle
there is always a lot to math that everyone doesn't know about
there's too much shit to learn
marble solar
The direction and magnitude doesn't really tell you what algebraic operations you can do with vectors
wooden wigeon
I just want school to start
i forgot there was summer school so i didn’t sign up...
marble solar
fresh graduated
wooden wigeon
no just graduated
wooden wigeon
i couldn’t really do calc 3 yet because i didn’t get my ap scores till like 3 days ago
so couldn’t even sign up
wooden wigeon
yeah
marble solar
There's a book by Ted Shifrin on multivariable that covers more advanced stuff
But it might be geared towards math people rather than CS people
gray gazelle
if you aren't already, become acquainted with libgen
you'll save good money on textbooks
wooden wigeon
yeah i use libgen for my cs books
but online resources are way better for cs in my opinion
marble solar
I could never read CS books, it's such a mess
dapper root
Yeah I just dmed them about that
I just don’t know if publically talking about that site is frowned upon
Lmao
marble solar
They don't give a clear definition of anything
marble solar
I took one, and it was one too many
wooden wigeon
what’s wrong with cs?
dapper root
It could’ve been condensed
wooden wigeon
I prefer being taught without a textbook
marble solar
There's nothing wrong with CS, I just dislike programming
wooden wigeon
my calculus teacher didn’t use a textbook and he taught great
wooden wigeon
yeah a missing semi colon and your code doesn’t work
marble solar
Yeah things like that, or calling a wrong file name
wooden wigeon
but in math if you screw up once you have to do redo the whole problem..
marble solar
or doing whatever drives me up the wall
Math stops being computation oriented after a while
Usually there's a few approaches to a problem, and if you have a rough idea of where things are going you can kind of salvage your approach
I guess I think of it as "I'm the compiler", and I try to write out neat arguments
wooden wigeon
is this linear algebra book bad
H. Anton and C. Rorres. 2014. Elementary Linear Algebra, Applications Version, 11th edition. John Wiley & Sons, Inc., Hoboken, New Jersey.
marble solar
Ehh it's hard to get a good linear algebra book at the lower division level
wooden wigeon
what about this DE book
William E. Boyce and Richard C. DiPrima. 2012. Elementary Differential Equations and Boundary Value, 10th edition. John Wiley & Sons, Inc., Hoboken, New Jersey
marble solar
Boyce and DiPrima is great
It's a classic reference. Most lower division linear algebra texts are equally bad
So I wouldn't worry about it
wooden wigeon
i just want to get a good grade
marble solar
It'll be mainly computation oriented
Row-reduce this matrix, what does that say about some linear space you're looking at
wooden wigeon
yeah i’m going to do a combined linear algebra and de class
marble solar
That's what I did Nelson
wooden wigeon
yeah so i can take another class
but i’d probably have to be on top of my game
probably a fast paced class
wooden wigeon
what i thought it would be easy for a math major
marble solar
I mean math courses are in general not easy, but I was missing a lot of pre-requisites
wooden wigeon
was it cc?
marble solar
Yeah
wooden wigeon
what are the pre reqs
marble solar
Well I was supposed to have calc 1
wooden wigeon
mine is just calc 3
marble solar
The calculus course I took was a little strange, and not computation focused. I had a hard time interpreting row-reduction and determinants
wooden wigeon
but row reductions aren’t a part of calculus
marble solar
I have an issue where if I don't understand on a conceptual level what I'm doing, then I can't perform, and the CC prof. I had was very particular
well the D.E. part certainly is
And I didn't understand what row-reduction meant
marble solar
Yeah, I failed 3 of 4 years of HS math
pulsar aurora
You can do linear algebra completely without calculus.
wooden wigeon
and you still wanted to be a math major?
pulsar aurora
Just calculus benefits from linear algebra
marble solar
I'm a stubborn one, Nelson
marble solar
I just finished my MS, and submitted a paper for publication
wooden wigeon
is it also at UCLA?
marble solar
No, I got the fuck out of there. I did my MS at CSULB
I had the option to do it at UCLA, but I wouldn't get funded for it. CSULB gave me 2 years of free tuition
The research I did was at UCI
wooden wigeon
is it merit based for the free tuition
marble solar
No, need-based
marble solar
Set you up for theory to do grad school. You use harder books like Rudin
And they give harder problem sets/exams
wooden wigeon
Yeah but no way i’m doing math!
i don’t like word problems
i don’t know how people can solve them so easily
marble solar
Practice
marble solar
My CC prof never assigned word problems. He said "Go get a bachelor's degree, and have someone pay you to teach them to do their word problems"
wooden wigeon
That’s not good
marble solar
Why isn't that good?
wooden wigeon
I think so
marble solar
I'm skeptical
wooden wigeon
Well you have to set up the equations
whereas you could just be handed the problem
marble solar
I mean, eventually when you get good enough at setting up the equations the word problems become trivial
Without ever having to explicitly practice word problems
marble solar
When I applied for tutoring jobs, I was given word problems at the white board in front of 3-4 people for the interview. I could solve them without doing 100 of them and stressing me out in Calculus
And that's not because "I'm so smart" it's just that when you do it long enough, you see through these kinds of things
wooden wigeon
were they calculus problems?
marble solar
Yeah
marble solar
It depends on what you're doing in CS
If you're modelling fluid flow
I'd imagine some math knowledge would be very helpful
wooden wigeon
i want to go into software engineering and then go make my own company
and code my own website
pulsar aurora
If you're just programming, yeah, algebra is about all you need. 😛 CS theory though, calculus becomes more important, I'm sure.
marble solar
Ok, well what kind of company do you want?
wooden wigeon
i haven’t thought that far
marble solar
That's ok, it's hit or miss on who needs what in industry
wooden wigeon
yeah in a couple of years things could be different
torn smelt
Ayo sorry for disturbing, anyone got a recommendation for a book covering Order Theory?
marble solar
I have a friend that dropped out of Uni at 17 to work for apple. Got laid off and started his own companies for years. He finally decided he wants to mine the moon and asteroids for rare minerals
wooden wigeon
you could do that legally?
marble solar
He went back to school, and is now starting his PhD in physics so he can get into the technical development
I mean, I'm sure where there's a will there's a way
wooden wigeon
is it worth it to drop out to work for apple
i assume it would be
because you get experience
marble solar
I mean he made money, then was able to run his own companies for 8-10 years before going back to school
wooden wigeon
just having apple on your resume could probably get you a job anywhere
marble solar
Yeah, although it's more known for being good in hardware and ok at software
pulsar aurora
Experience > education depending on the experience.
wooden wigeon
oh yea i forgot they made products...
wooden wigeon
yup
marble solar
since this is uhh book discussion
wooden wigeon
it was book discussion and then sidetracked
inner charm
does anyone know a good starting book for something like data analysis
wooden sparrow
just having apple on your resume could probably get you a job anywhere
@wooden wigeon can't get a job in medicine for reasons
dusky sigil
Which book would you suggest if I want to revisit complex analysis
gray gazelle
me irl
limpid gazelle
That statement is vacuously true
stray anchor
Hey, can anyone suggest me a book for basic arithmetic?
limpid gazelle
A Course in Arithmetic by Serre
stray anchor
Thanks @limpid gazelle . I'll check it out.
gray gazelle
You just ruined a life
stray anchor
Yeah, he did. I couldn't understand a word described in the contents.
gray gazelle
why does it have that name 
stray anchor
Any suggestion for a arithmetic book that a dumb guy like me can understand with a good amount of problems?
north spire
You shouldn't look down on yourself like that. I'm not sure if there are any books that might help with that but Khan academy should contain stuff for you to use
stray anchor
I tried Khan academy, it didn't have enough challenging problems I was looking for.
I'm trying brilliant app. But it only has problems other than the theory.
north spire
what do you mean problems other than the theory?
Brilliant has both problems and theory. It's not a great place to learn theory but it certainly contains many problems
slender sphinx
what basic arithmetic are you hoping to learn?
north spire
I found this under the "Basic Mathematics" category
Perhaps you should have a look at it
stray anchor
Okay
gray gazelle
Brilliant has both problems and theory. It's not a great place to learn theory but it certainly contains many problems
what do you mean not a great place to learn theory?
north spire
Well, if you want to learn calculus, for instance, it's better to learn it from a textbook and then use the wiki pages for further insight
gray gazelle
hmm
I've heard good things about the subscription requiring courses but I've never seen them
Meh
A book is definitely superior
Just solve a lot of exercises for the "brilliant" experience
I really like the wiki-style information pages they have but I think I see what you mean
not a way to learn calculus
I do like those
For revising stuff
yea
Very convinient
north spire
I've heard good things about the subscription requiring courses but I've never seen them
Those are actually quite good but they serve well as "problem courses"
not a way to learn calculus
Yeap
stray anchor
You've all been of great help. 
still kettle
Serre's Arithmetic is a great book lmao
A Course in Arithmetic by Serre
@limpid gazelle
Does anyone know a good text about Measure Theory? I was reading the first chapters of Rudin's real and complex analysis, but I want more
sage python
I like "Real Analysis for Graduate Students" by Bass
Folland is also a common recommendation which seems decent
valid moth
@still kettle I recommend this book for measure theory https://cdn.discordapp.com/attachments/342850939306246145/715418124496797738/1.jpg
gray gazelle
A very sophisticated piece of literature
still kettle
@still kettle I recommend this book for measure theory https://cdn.discordapp.com/attachments/342850939306246145/715418124496797738/1.jpg
@valid moth It seems a great and comprehensive text, but a bit too advanced for me
valid moth
ah, no worries, you can return to it in 15 years
tough holly
Hi everyone! I just finished typesetting my lecture notes from a first semester real analysis course at UW-Madison into LaTeX and thought I'd share it. Things covered include (but are not limited to) basic topology, sequences, and differentiation. I'd love for it to be in more hands than just mine, especially if learning will be online again for many students. Please feel free to give me feedback and share it with others, I hope it's a useful resource!
https://github.com/emmettgalles/math521
sage python
@tough holly eyyyy Madison fam
main flax
why you doxing yourself tho
gray gazelle
@tough holly thanks for sharing it!
quick hornet
Doxxing isn't an issue if you don't act like a shitlord
so youre saying i shouldn't link hopf in ags
darn
sage python
Link what?
split moon
@tough holly even more compactness 
potent jungle
Hey, what do you think about Calculus by Spivak vs Calculus by Stewart?
valid moth
the level of rigor varies
if you want to continue onto more pure math then try spivak
dapper root
Depends on what you want from life
valid moth
i want to retire at 35 magician
dapper root
If you want to do pure math you could also get away with Stewart
valid moth
should i do spivak or stewart
dapper root
It just means you’ll have to do your first “rigorous” course later
retire at 35 is definitely a Stewart thing
potent jungle
I actually prefer applied math than pure
dapper root
Okay
potent jungle
so applied = stewart, pure = spivak?
dapper root
Do you want a rigorous treatment
valid moth
ah in that case i recommend https://www.amazon.com/Introductory-Calculus-Infants-Omi-Inouye/dp/0987823914
dapper root
Bruh
Rigorous = Spivak
Easier, faster, idc about sweating all the details = Stewart
Also bruh is in reaction to what arch linked
potent jungle
I don't actually know what you mean about rigorous treatment
dapper root
Not to anything you said MzDay
Do you know what rigor is?
Like
Procing stufd
Probably up till now like
valid moth
be sure to also check out https://images-na.ssl-images-amazon.com/images/I/51m-6QB4V9L.jpg
dapper root
People told you stuff in math like
“This jjst works”
Maybe you know the rational root theorem?
valid moth
also are you a highschooler and if so what grade
potent jungle
Ok I am losing you both now lol
dapper root
Your math you’ve learnt till now
People have given you tools
And said “this is how it works”
potent jungle
alright
dapper root
And you just did computations
valid moth
to be honest if you are young or even if not there is a nonzero chance you don't know if you'd like actual pure math because you haven't been exposed to it yet
potent jungle
Oh I got you ok
valid moth
so you could always try spivak and see
dapper root
Stewart will be like that
Spivak is gonna be like
So this is why it works
Much more than Stewart
If you wanna go fast and don’t plan to do math
potent jungle
Ok so I guess Spivak it is in that case
valid moth
again are you a highschooler mz?
dapper root
But later on when I did my first “real” math course
It was like aaaaaaa hard how do I prove stuff
potent jungle
No, im 25
potent jungle
working with computer graphics and trying to learn math more extensively
valid moth
i see
potent jungle
I want to learn calculus basically for myself
dapper root
I’d say Spivak then
potent jungle
and of course continue on later
dapper root
If it’s for you
I think you’d want to see it done like really properly
Not some@half baked thing
Which like, is fine for most people IMO
If you said you’re an engineering student
And just want to study over the summer before classes
I’d have said Stewart if ya know what I mean?
potent jungle
Yeah I got you know lol
dapper root
👍
potent jungle
I guess Spivak is the way to go if I really want to learn
thank you both by the way!
really helped me
valid moth
wtf why do you capitalize imo
i thought u were talking about the actual IMO
lol
also np
valid moth
you mean P magician
dapper root
Like FYI
valid moth
wtf
dapper root
Idk man
potent jungle
😂
valid moth
is this your brain on being a 90s kid
valid moth
just go all caps to be safe
dapper root
TRUE I WILL ALWAYS CAPS AT ALL TIMES FOREVER
valid moth
CAPS LOCK IS CRUISE CONTROL FOR COOL
dapper root
M A Y B E E V E N D O T H I S
slender sphinx
wait why are you awake arch
dapper root
???
slender sphinx
👀
dapper root
,ti archysys#0631
hasty eagleBOT
No matching users found!
valid moth
ｗｈｙａｒｅ＊ｙｏｕ＊ａｗａｋｅｐｏｃｏ
dapper root
,ti archysys#0631
hasty eagleBOT
No matching users found!
valid moth
ｗｔｆ ｐｏｃｏ ｍｏｍｅｎｔ
dapper root
Wtf
valid moth
ｗｔｆ ｍａｇｉｃｉａｎ ｍｏｍｅｎｔ
dapper root
,ti archsys
hasty eagleBOT
The current time for Archsys is 06:56 AM (EDT) on Sun, 19/07/2020.
valid moth
ｉ ｊｕｓｔ ｗｏｋｅ ｕｐ ｖｅｒｙ ｅａｒｌｙ
shadow nebula
h i
valid moth
ｉｔ’ｓ ｎｏｔ ｔｈｅ ｓａｍｅ ｙｏｕ ｎｅｅｄ ｔｏ ｉｎｓｔａｌｌ ｊａｐａｎｅｓｅ ｉｎｐｕｔ
valid moth
no it isn't
all of my messages in full width alphanumeric from japanese keyboard are book titles though so relevant
dapper root
Ohhh arch I get what you are doing
That is so gross lol
I can’t do that since I’m on mobile
And I use a kana keyboard
valid moth
真的伤心
white pebble
ééé
shadow nebula
n o
valid moth
meiyou ni
white pebble
u need a shrine :x
cloud trench
heh, they are e-books
drowsy arrow
is reading a book recommended
i want to read a book but i dont know if it will necessary when i have khan academy which may sounds extremely arrogant
pulsar aurora
Read a book. I like reading textbooks over shit like Khan
Some textbooks provide more information or context than some video or web-series might provide.
cloud trench
is reading a book recommended
@drowsy arrow yes, book covers everything and then you can boil it down into a single page of important stuff
khan academy covers just a selective portion which may not be suitable
still umbra
Could anyone recommend a book for optimization? Don't know where to start tbh.
gray gazelle
Could anyone suggest me advanced number theory texts?
I have completed "An introduction to the Theory of Numbers" by GH Hardy and EM Wright
marble rock
velvet briar
If you've studied applied lin alg, then "Linear algebra done right" by Axler is a fantastic proof based linear algebra book
Linguistics?
wooden wigeon
lin alg is linear algebra
velvet briar
"Discrete mathematics" by Oscar Levin is an easy intro to sets and to logic, in case you're missing either. Pure needs both
"How to prove it" by Velleman is the common choice for people getting into proofs but you won't need it if you don't want to continue in pure
And all I've recommended are free pdfs online, don't rush to buy them if you don't want to haha
You're looking for applied? Have you done differential equations?
north spire
Problems in Mathematical Analysis by Demidovich is a good one
Linear Algebra Problems Book by Ikramov is also quite nice
Which parts of math have you done?
velvet briar
Paul's notes are the best source of differential eqs there is
https://tutorial.math.lamar.edu/classes/de/de.aspx
wooden wigeon
SomeT do you know any data structures and algorithm books?
north spire
"Pure mathematics" encompasses a lot of things
anyways, both problem books i recommended above are good if you want some nice practise
north spire
Yea that was the other book i was going to recommend
A Collection of Problems in a Course of Mathematical Analysis by Berman and Sneddon
wooden wigeon
Data Abstraction and Problem Solving With C++ by Frank Carrano
is that any good
how about python?
what’s a pearson book?
is that a company
java?
I thought matlab was for engineers
are prentice hall books good?
You know of any books on computer architecture and assembly language?
i could use library genesis and get the books for free
i said could
thanks for the help
i prefer online resources over textbooks
but i don’t think much people have videos on data structures and algorithms
i used corey schafer for python tutorials
but it’s the easiest language
I’m not sure whether i should do the java or c++ series of courses
in my school
usa
lisp?
never heard of it
the most common ones are python, any c, and java
most universities in my area teach in c++
i’m only looking for a job for a couple of years
i need a discrete math and linear algebra book too
me neither lol
i hate probability
drowsy arrow
does uh, anyone have a pre algebra book recommendation? im really indecisive when it comes to stuff like this
valid moth
@drowsy arrow try the AOPS one
drowsy arrow
thankies
solemn mantle
I feel like all the AOPS books are really solid for <12th grade
normal tinsel
Read the Bjarne s book (For c++)
acoustic ruin
Hi all, can anyone recommend a good book on cryptography?
I am new to the subject and looking for as practical approach as possible
civic carbon
"Modern Cryptography" by Mao is hands down my favorite Cryptography book
I find the narrative very compelling
acoustic ruin
Great thanks, do these have exercises as well?
civic carbon
I don't remember if Mao has exercises or not
gray gazelle
blahut has exercises
civic carbon
I should probably say the reason I like Mao is that it strikes a really nice balance between the practical side and the mathematical side, where as most texts seem to focus exclusively on one or the other.
gray gazelle
yeah Blahut is very math based
trim narwhal
Good book/course for learning Precalculus?
gray gazelle
does anybody have a pdf of artin's algebra that's clear
Libgen?
still kinda blurry
civic carbon
Yes
solemn mantle
Thanks
fast gull
what online forum is best for university level math help? my guess is stack exchange
but it doesn’t seem like it is helpful if you don’t know how to ask questions
or want to ask back and forth questions
north spire
but it doesn’t seem like it is helpful if you don’t know how to ask questions
@fast gull Then, it would seem that learning how to ask good questions would be the optimum way to move forward
But honestly, it's very nice. The people there tend to give very good feedback
north spire
Back and forth questions are allowed but try to maximize the space in the comments
Math Stackexchange
north spire
Usually if your discussions in the comments are very lengthy, the moderators will put those in chat. It won't be done immediately though so you can get your doubts clarified before they do that.
Generally, the best way to use it is to post your own attempt in as detailed a manner as possible. Like, if you're proving something, then just post your proof. If you think it's correct, then you just have to wait for confirmation of that. If you think it may not be correct, then you can add in a short statement at the end specifying what exactly it is about your proof that you find somewhat dubious.
delicate canopy
has anyone tried speed reading a math book?
or does it sound like absolute nonsense
pulsar aurora
Sounds dumb to do
delicate canopy
idk how people do that