algebra does use some theorems from NT but like
#book-recommendations
quick hornet
you dont really need a deep understanding of the number theory to use those theorems
stray veldt
number theory was the motivation for a lot of algebra after all
motivation is always nice
quick hornet
that's true
stray veldt
well, tbf, not sure what you consider "more" algebra
hearty steppe
Like diving into stuff like Algebraic Topology
manic turret
can anybody tell me the best books for undergraduate probability and statistics
flat osprey
@manic turret depends neffew
Casella & Berger is the standard
But it's pretty dry
I used Rice in undergrad and it went ok
sterile pelican
I remember Feller’s introduction to probability theory and its applications was one I used in uni only we used only volume 1 I think
flat osprey
Feller is good if you're only worried about probability
sage python
@flat osprey What if I'm worried both about probability and the fact that there's a venomous snake in my room?
gray gazelle
3 birds 1 stone because now you won't have to worry about Nassim Taleb sneaking through your chimney on Black Tuesday and calling you an imbecile
mossy flume
I need an intro to proofs recommendation
this semester there is no textbook for my section
the teacher is just providing notes and video lectures
but a text might be nice
velvet briar
That open logic book in #books-old looks fantastic
mossy flume
this is what they used last semester for the honors section
Textbook: Paul Sally, "Tools of the Trade: Introduction to Advanced Mathematics" (2008).
Syllabus: Chapters 1-4 of Sally (in the order 1,3,4,2)
open logic?
gray gazelle
why didn't i know of this before
mossy flume
should I use that?
mossy flume
is that a intro to proofs book?
velvet briar
It's intro-esque
mossy flume
hm
quartz pawn
Its a math logic book but you could use it as that
velvet briar
It has easy proofs in it
quartz pawn
The first few chapters
mossy flume
what about like intro proofs in general? I would like a textbook for that
would baby rudin be overkill?
like the first couple chapters
gray gazelle
velleman is one recommendation that i make a lot
very hand holdy compared to this logic text and rudin though (not a bad thing)
i would not recommend learning proofs from rudin
mossy flume
gotcha
velvet briar
I also like Fraleigh's abstract algebra for very easy proofs
mossy flume
How To Prove It - Velleman?
velvet briar
If you want to learn abstract algebra along side haha
mossy flume
that one?
gray gazelle
yeah that one
gray gazelle
you can learn proofs while learning other things
velvet briar
Yaya but the book has very easy proofs, so you can learn both at once
No point if you think you'll never take abstract of course
gray gazelle
i think you will find a good chunk of that in velleman, minus the second to last and last points
mossy flume
Hm ok
velvet briar
Interesting that the "real numbers" section is an intro to real analysis
mossy flume
Real Analysis is a different class
I take that like first semester sophomore year
This class is just "fundamental mathamatics" which is hella vague
I'm just calling it intro to proofs cause that's all I can really tell it is
velvet briar
Oh cool, it's an "everything" class
gray gazelle
i think it'd be hard to find a textbook that does all of this
you'd need to use multiple
mossy flume
but I've seen previous semesters have textbooks
Textbook: Paul Sally, "Tools of the Trade: Introduction to Advanced Mathematics" (2008).
Syllabus: Chapters 1-4 of Sally (in the order 1,3,4,2)
this is what the class used last semester (albeit different prof)
should I just get that? Or just Velleman
velvet briar
We could give you textbooks for each part
gray gazelle
It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups.
well look at that
mossy flume
what's that?
gray gazelle
excerpt from a description of the book i found
mossy flume
the Sally book?
gray gazelle
yes
mossy flume
I probably should have looked that up lol
ok cool
so it does seem to be an everything book
it's just that I've never heard of that book so I came here to ask
gray gazelle
im going to check on libgen
gray gazelle
i couldn't find a copy on libgen
flint forge
ok that table of contents is fine
mossy flume
I mean @velvet briar was saying maybe recommend a bunch of different books
gray gazelle
bct in chapter 5
intro proofs course
mossy flume
like I said idk anything I'm baby freshman
flint forge
i mean intro to proofs is a meme
you can do serious math in a first class
plus i doubt theyd get through this entire text
you could spend a full semester on the topics in ch5
hearty steppe
Haven’t heard of Paul Sally’s book
Velleman has been good for me for the most part
quartz pawn
You don't really need intro to proofs but it's a good first class.Like the stuff in intro to proofs can probably taught within two weeks of the class lol. Stuff like propostional logic , quantifiers set theory and stuff.
flat osprey
I feel like intro to proofs isn't really needed as a class
quartz pawn
Yea
flat osprey
It's something you just sorta pick up on the streets
quartz pawn
I think there should be time dedicated to it but it doesn't have to be a full semester.
soft terrace
my college used its discrete math course to do intro to proofs
gray gazelle
my uni just assumed you knew all the "intro proof stuff" beforehand or would pick it up during the first few weeks
there is an intro to proofs course, but the math majors typically don't take it
soft terrace
i met a bunch of students in my college that said they learned proofs in high school
but then again i met a student taking calc 3 at 16 yo too
sage python
@mossy flume oh god
Sally
My lawd
That book is something
@flint forge that book was how they taught a block of math 159 I think
(The class that people who didn't do honors calc take before analysis)
mossy flume
@sage python is that a good oh god or a bad oh god
i met a bunch of students in my college that said they learned proofs in high school
@soft terrace
I wish my HS had proofs. I had basic "proofs" like "show the magnitude of a cross product of 2 2D-vectors is the same as the area of the parallelogram formed by the two vectors" and also "show that the gradient is always parallel to the level curve"
but these were only in the calc 3 class that I took senior year which had like 20 kids out of the 2600-ish in my HS
broken meadow
man
placid leaf
I am enrolling in BSc with Data Science as my major.
The classes will start from first week of 2021. I wanted to get some headstart.
Which one should I read:
- An Introduction to Statistical Learning
by Gareth M. James, Daniela Witten, Trevor Hastie, Robert Tibshirani
or
- The Elements of Statistical Learning
by Jerome H. Friedman, Robert Tibshirani, and Trevor Hastie
or if I should start with something else
pls @ me
gray gazelle
authors?
placid leaf
@gray gazelle I updated the original message with author names
ah found it, the 2nd book is more advanced, so I am going with the 1st
still I want to know what books you folks would recommend
tame sluice
fathom monolith
i would prolly just start with calculus tbh
sage python
Bit of a bad oh god lol, I do not like Sally for the most part
hearty steppe
Is sally silly?
long bear
Sally is salty
mossy flume
ok so it looks like I'll look at the Telleman book for extra reference I guess
silent pond
i am looking for a book on coordinate geometry which deals into more detailed theory/proofs then some usual plane geometry books
sterile pelican
The only one I could think of is Euclid's Elements
though the best book I learn geometry from is probably Lang's Geometry and Coexter's Geometry revisited
long bear
I mean
This is more synthetic geometry
but uh
the foundations of geometry
by hilbert
has been a fun read
sterile pelican
I never read Hilbert's book
long bear
He has two
That relate to gometry
Geometry and the imagination
and The foundations of geometry
sterile pelican
compared to Euclid's Elements it is not as dry, yes?
The amount of postulates and axioms in that book bothered me and I never get to finish it
long bear
i've never read euclids elements
The foundations of geometry is a uh, alternative to that then
fair tundra
Has anyone ever read 'The Artist and the Mathematician'? I just finished it. It's about Nicolas Bourbaki and his publications/ventures in Pure Mathematics the 1930's. Not a technical book, but wonderful nonetheless.
wooden sparrow
Isn't Nicholas bourbaki a pseudoname for a group of French math students?
quick hornet
not students, top researchers
they used it as a pen name to publish a series of french textbooks
hasty turret
Does the book exist?
wooden sparrow
@quick hornet thanks
prisma snow
Am i going to be killed for discovering the truth?
fair tundra
The first rule of discussion XIPs existence is
...we don't talk about XIP's existence
hasty turret
...we don't talk about XIP
@fair tundra Is that a psuedoname for PIXar?
fair tundra
You're not not on the right track
wooden sparrow
Yeah Xip is slang for Pixar for arabs
fair tundra
Would you be willing to fill out a survey to rate your interaction with @fair tundra-bot today?
flat osprey
Gpt 4
fair tundra
Available 2023 with 17 trillion parameters
wooden sparrow
marble solar
So I've read apostol's analytic number theory, do you guys have a direction to go into after that?
sage python
@marble solar are you interested at all in automorphic forms?
Or getting into the area? That's kinda my style of analytic number theory
marble solar
Yeah, I'm open
sage python
So the sorta first case of this business is called Tate's thesis
He recasts the business with the Riemann zeta function, specifically its meromorphic continuation and functional equation, as following from Fourier analysis on the adeles
And he generalizes it quite a bit
marble solar
Alrighty I'll dig around
sage python
The book I'm reading for automorphic forms is Goldfeld-Hundley, which only works over Q rather than number fields in general like Tate
Has the advantage that you don't need background in algebraic number theory
Chapter 1 is background on p-adics, adeles, and the Haar integral and Fourier transform on those guys. Then chapter 2 is a case of Tate's thesis
There's another book just by Goldfeld which has a less adeles and more Lie theory and analysis take on automorphic forms, especially Maass forms
And another possibility is learning about holomorphic modular forms. Diamond-Shurman is good for that
Finally Ramakrishnan-Valenza is good if you want Tate's thesis in its full glory, on number fields. Contains all the background algebraic number theory
serene crater
Did someone read 'Finite-Dimensional Vector Spaces'?
quartz pawn
There are a couple of books called that. You mean by Halmos? Not I.
serene crater
Ah yes
serene crater
I read it
@flat osprey What is your opinion on the book?
gray gazelle
any music theory book recommendations from like math point of view
hearty steppe
dm @torn crypt
torn crypt
They focus on weird things, have janky pacing, reinvent the wheel, and have sometimes questionable content
But uh
There’s Mazzola’s Topos of Music, there’s some geometry of music guy but idk, there’s Agustín’s Computational Counterpoint Worlds
gray gazelle
have you read any of those
gray gazelle
ok so ure saying there isnt a good book on the topic and topics dogshit overall
torn crypt
Janky bad notation
long bear
music 
gray gazelle
c4t do you know other people?
long bear
XD
hearty steppe
no I think Dir is the only person on the whole server interested in the math behind music theory
torn crypt
Agustin’s is fine but bad notation & janky writing
gray gazelle
And not even Dir likes it
torn crypt
There’s a weird neuro section, and a janky section on a plugin
gray gazelle
youre blocked by everyone probably
long bear
Can you react?
torn crypt
Mazzola has better writing, still bad notation sometimes, but reinvents the wheel painfully for some typing stuff
gray gazelle
yes
long bear
Then react to a message please.
gray gazelle
no
long bear
gottem
hearty steppe
theres probably a lot of room for innovation in the math behind music theory but the incentive doesn't seem to be there
gray gazelle
ok dir how mch do u know and whre from did u learn
long bear
Dir are you a musician?
gray gazelle
and how much math did you know when u were srudying it
long bear
beggers can't be choosers
torn crypt
@gray gazelle topos of music might be your best bet, but it’s a bit weird in how it’s 4 volumes
long bear
torn crypt
Also idk how much I know
long bear
long bear
what kinda math?
torn crypt
@long bear I’m not really
gray gazelle
Lmao it's 1310 pages long
torn crypt
I did music before but like kinda dropped off
long bear
fair enough
torn crypt
@hearty steppe basically
torn crypt
Also a lot of it is forcefully generalizing & strapping math to it I think
As someone who’s looked into this stuff: math music theory really has no reason to exist beyond some minor connections to music software and morbid curiosity
gray gazelle
ok so not worth the time?
torn crypt
Yeah basically
gray gazelle
thanks
torn crypt
Unless you’re just curious or are trying to connect it to software stuff
I mean a lot of pure math kinda feels like people asking “ok but what if not”
But this is just “huh can I model this with XYZ”
torn crypt
Yeah like ok buddy sure
gray gazelle
Oh and ofc algebraic topology
gray gazelle
Idk just looking over the contents section
Now I'm really intruiged what they're doing
torn crypt
I could understand a bit of generalizing like orbifolds for some geometric stuff, or categories for some algebraic stuff
But like
Ok why do I need a topos
gray gazelle
For grothendieck universes 
torn crypt
Does it fall out naturally or are you forcing it?
If its forced then its worthless
And these topoi are in the same book as the janky counterpoint models that are questionable at best
High key mazzola’s counterpoint thing is garbage
It was like
<50% on the money or smth
torn crypt
And ironically was about symmetry but threw away the (dis)cantus symmetry
So like
@gray gazelle yeah screw his janky type stuff
I never got around to reading topos of music tbh
It just reeked of “this is not right”
Also am lazy
gray gazelle
It does look like a prof flexing all of his knowledge about math
torn crypt
Highkey
torn crypt
It definitely feels like the “morbid curiosity” justification
Why? Idk felt like it
Imagine using @ as a symbol tho
Like why tho
gray gazelle
Oh lol he does
flat osprey
@serene crater it's very good!
It maybe shouldn't be your first exposure to linear algebra, and if it is there should be someone to whom you can ask questions
torn crypt
50/50
Honestly: I’d believe it if I was told it was mathgen if I didn’t know he had bad naming sense
I’ve skimmed some of it
So like
I actually can’t tell
I’d have to really read it a bit to try and figure out his bad technobabble from his jargon wizardry
I know the A-addressed part refers somehow to his messed up type foundation
I don’t remember what half of those words mean
gray gazelle
I think this book is directed at graduates
quartz pawn
Yea alot of books like that are not really practical suff. It's like you said just showing you can do it because.
quartz pawn
Music : A mathematical offering is one that my professor should be and it's really readable.
torn crypt
It’s incomprehensible without reading the prior chapters since his bad naming
But iirc it’s like
Ok glue these together like how manifolds glue together R^n subsets
gg that’s it
like ok why did I need so many layers
you’re not working in foundations here, you can use words that already exist
I can’t just skim it because of that, but I don’t want to read it either because I know it’s not that impressive
This is how it feels like
Looks incomprehensible and ultimately meaningless
Even my tiny scribbles & collected ramblings could be considered slightly interesting as an idea at best
and I’m pretty sure it’s not best case
gray gazelle
I think I changed my mind. It's just not an elementary book. The author uses the entire framework of mathematics to formally analyse music
gray gazelle
It's interesting I think
torn crypt
There’s some philosophical something or another at the start of volume 1
Iirc
but like sure ok pick one
math or rambly music theory
please
I don’t wanna go back and forth, mix your motivation in with the exposition of the math bruv
gray gazelle
I think it's less about the music and more about the topoi
torn crypt
Too bad the math isn’t that great either iirc
Since it’s all kinda music directed, it’s all probably janky or otherwise hard to translate to normal
If it’s even worth
I remember seeing one theorem that got a whole section in one of the math music books (I think Agustín’s?) was something like
ok yeah there’s always a successor such that you’re never cornered
Wow sounds nice
Whoops it’s in a very much so finite collection, you could definitely brute force it
So why did this get a section
Also it was like, <12! by some significant margin iirc?
Idk I forget
Anyhow it seemed strange to me
long bear
Do you guys think uh Langs three books on algebra is good enough to get a good grasp on the subject?
hasty turret
Should be.
quartz pawn
Have y'all tried Lang's book on differentiable manifolds?
midnight oracle
re: the music theory discussion: I think the geometry of musical chords by dmitri tymoczko is decent because theres fairly reasonable geometric intuition behind it. He also uses an orbifold approach to model chords.
one would have to translate his papers into clean maths as he's not a mathematician but the idea is definitely reasonable.
one idea i had when reading his stuff is that one could think of a cadence, say I-IV-V-I, as a loop on the orbifold he proposes, so investigating the fundamental/(co)homology groups might produce some musically relevant invariants
civic carbon
You will either love or hate Lang's writing. I'm in the latter category. I wince slightly when I realize a Lang book is the right reference for something I have to look up.
serene crater
It maybe shouldn't be your first exposure to linear algebra, and if it is there should be someone to whom you can ask questions
@flat osprey Thanks, I'm curreently
reading the book and i really like it thus far
Luckily, I can ask people if I need help
stone belfry
math pleb here. In this stack overflow question (https://math.stackexchange.com/questions/1359770/why-does-the-division-algorithm-work-for-converting-between-number-bases), what kind of response does the top commenter use? I know he is using some kind of generalized function that explains any base to base conversion but what is it called specifically, and how the hell do you read it? Is that what you would call a proof?
What books should I read to understand that kind of language
For instance, how do you read this? It looks like gibberish to me. Any book recommendations? https://media.discordapp.net/attachments/359052581022203914/747576233126002738/unknown.png
gray gazelle
Probably how to prove it
Some analysis books will also treat n-nary notation if you are familiar with proofs
But this is basic notation so preferably refer to the first one
stone belfry
Thanks guys!
hearty steppe
I remember using Rosen, decent book
hollow current
yes, i learned intro to discrete math by it
hasty turret
Is concrete math by knuth good?
hearty steppe
I think just picking a discrete math book up just kinda gives you some surface knowledge of some math topics that dabble into finite mathematics
It’s good but it has limitations. If you want to specialize in a topic area, discrete math books won’t be enough
hasty turret
How do you get good,then?
hearty steppe
Start with proofs and dive into linear and abstract algebra
That’s my strategy rn lol
delicate anchor
@hasty turret so what i found to be kinda the fastest method
for me, a lowly peasant in a small town
was to do a number of things out of opportunity, and a couple by brute choice
- i took a course in discrete maths using Rosen's textbook. you can do this without the course, but the course will help a lot
- i got trained by the putnam guide for a semester, 1-2 hours a week and worked separately on competition problems to practice
- i went through everything on khan academy up through diff eqs and covered some gaps with paul's online math notes
- baby rudin
- axler for linear algebra
- i gave terry tao's solving mathematical problems a quick read
- bert mendelson's intro to topology
hasty turret
How is all of this related to discrete math?
hasty turret
Yes
delicate anchor
yeah, just rosen for that
and then a walk through combinatorics or whatever that book was
yeah miklos bona
or perhaps on whatever is interesting to you. there are a lot of subfields
there's graph theory, cryptography, etc
obsidian valley
is that a guide to mathematical maturity
hasty turret
Yes,ig
pulsar aurora
Concrete mathematics is not bad, but Knuth and friends wrote it as a companion piece for Knuth's Art of Computer Programming so it is focused more on algorithm analysis.
old matrix
hey guys, which book is better to start with the preparation for pre rmo [PRMO]? Excursion In Mathematics (or) Challenge and Thrill of Pre-College Mathematics [PRMO is an Indian mathematics exam]
any Indians here?
hasty turret
Prmo is very different from the other math Olympiads
It's closer to an exam like jee,than to a MO
You have to practice doing questions fast,instead of learning theory
hasty turret
I didn't use any books,so I don't know
If you prepare for jee,the theory should be sufficient
old matrix
But I am a class 10 student
hasty turret
Are you familiar with combinatorics,Algebra and geometry?
hasty turret
You should be fine
old matrix
Ohh okay
velvet shuttle
hey guys, which book is better to start with the preparation for pre rmo [PRMO]? Excursion In Mathematics (or) Challenge and Thrill of Pre-College Mathematics [PRMO is an Indian mathematics exam]
@old matrix well it depends ig
Many people Ik cleared even rmo with just the help of one of these books
Excursion is like a problem book
C&T has more theory
Take a good look at both of these books and decide for yourself
Because if you are past a certain level you cant go wrong either way
gray gazelle
@old matrix For theory, C&T, although there are also good books on specific topics
David M Burton - Elementary Number Theory
Schaum's Outline of Combinatorics
Modern Geometry - Clement Durrell (This one is hard to find in India)/College Geometry by Howard Eves
Also Arthur Engel's Problem Solving Strategies, Titu Andreescu's books are essential
The geometry books are fairly advanced and you must be good with the basics first. Use your school books or you can also check A School Geometry by HS Hall
hidden abyss
nah these arent really olympiad books, so wont be the best way for preparing for them
problems solving tactics is the best book, then there are other specific subject books i can recomment, but tbh most of your preparation should be in solving problems
sage python
They're kinda different though
Lee is more technical stuff on smooth manifolds
GP is more stuff like degree and intersection number
sage python
Probably my third favorite class in undergrad
quartz pawn
I was gonna use daminark's recommenation by John Lee I think instead of Munkres but I had heard of Pollack
just wanted to know what the sentiments were here in discord.
gray gazelle
munkres' analysis on manifolds?
or does munkres have a differential topology book
analysis on manifolds is more of an advanced calculus book imo
quartz pawn
Munkres topology
Namely because they are two different books. One is Gen Top one is more Diff Top
long bear
doesn't munkres include some algebraic topology in his gen topology book
gray gazelle
in the second half yes
sage python
So Munkres Topology is half point-set and then half pi_1/covering spaces. Then he has an algebraic topology book that just does homology I think, not too common. And I think he even has a difftop book that literally nobody uses, no idea what's in it. Then there's "Analysis on Manifolds" lol.
Lee has a trio, Topological Manifolds is at the level of Munkres Topology but with a better topic selection. Smooth Manifolds follows that up, it's about the very technical aspects of manifold theory. Riemannian Manifolds is diffgeo.
Guillemin-Pollack doesn't really talk about the technical side of manifold theory, it does as little as it needs to and somewhat informally (everything is a submanifold of R^n, not even sure if he gives a completely formal definition of orientability?), but then it does material Lee doesn't, like intersection numbers and degree. The main overlap is differential forms
So yeah the only two books among these that I think directly compare are Lee ITM and Munkres Topology
valid moth
what's ITM
quartz pawn
Introduction to Topological Manifolds
valid moth
who asked tho
hollow current
boreal mirage
how about tu's an introduction to manifolds?
gray gazelle
who asked tho
Evil
gray gazelle
tu's an introduction to manifolds is very well written and it's an easy book, so if you want to get "up to speed" on smooth manifold theory it's not a bad choice
gray gazelle
does anyone want to read rudin with me? (discuss the chapter contents and exercises and stuff in order to understand)
dm me if interested
gray gazelle
hmm
hearty steppe
Read Rudin later, not when your starting to learn Analysis imo
hidden abyss
lol i learnt calculus from rudin
gray gazelle
When I took calc3 we used open stax and Div, Grad, Curl, and all that. I kind of want to revisit vector calculus from a more applied perspective now that I've taken linear algebra. Are there any good books that have a lot of real world examples of vec caalc that use linear algebra?
gray gazelle
But I am a class 10 student
@old matrix I dont think you need to give prmo
you can directly give RMO
because you are in grade 10
If I remember correctly, PRMO is for grade 7 and below who wish to qualify for RMO
delicate anchor
i cant learn analysis from anything but rudin
everybody else covers like half the material if even that much
and in three times the length
hearty steppe
I don't understand, what other analysis books have you tried? I like Abbott, Schroder, and Apostol better than Rudin
delicate anchor
i tried abbott and had to stop
tried apostol
was a lil nicer
still had to stop once rudin came in and i understood.
hearty steppe
how did you not like Abbott lol he is incredibly easy to follow
compared to Rudin and Apostol
delicate anchor
rudin was fine
pretty straightforward reading
there were 2 proofs that had these arbitrary formulations and a couple that needed some thought for a few minutes
but
it was pretty clear where rudin was going and what he was doing, felt productive to read
vs abbott where it just felt unsubstantial
obv this is subject to subjectivism
hearty steppe
I disagree. Rudin is very compact and dense, making it hard to follow the proofs line by line.
whatever floats your boat man
delicate anchor
hm
i didnt have that experience
but i really
really appreciate your use of the terms compact and dense
gray gazelle
limpid gazelle
hearty steppe
your the only person I'll probably remember saying Rudin is easier than Abbott. I'll never understand that lol
Abbott is definitely one of the easiest books on analysis to read imo and I am pretty sure there are even easier books that cover less depth, but at least help build you to read the harder books.
Abbott is probably the easiest that covers the most depth of material per volume
delicate anchor
idk maybe it's just that rudin captures my attention better
i like working through it due to the format
hearty steppe
I mean I find the format appealing but I feel like my current understanding of proofs and analysis is not mature enough to really appreciate the density of rudin
delicate anchor
i can see how some might find it harder
hm
i see
i had some experience with proofs beforehand due to training for the putnam
that may contribute
idk what the normal exposure to proofs is going into it
sterile pelican
There is a nice little book called "Introduction to Mathematical Thinking" by Keith Devlin that can help get you started in proofs
If you want to go in a comprehensive depth into proofs there is Chartand, Polimeni and Zhang's book of "Mathematical Proofs" that I always recommend here, alternatively Hammack is a good book too and is far cheaper (and is free online).
quartz pawn
Chartrand probs the best intro proof books I've seen.
sterile pelican
Agreed but the pricing is a huge turnoff to most
sterile pelican
Though one thing unrelated of this entire chat is I highly recommend J.C. Burkill's book as "A First Course in Mathematical Analysis" I find it a better alternative to Spivak's Calculus if you studied from books like Lang's "Short Calculus".
quartz pawn
Not only does it give you a pretty comprehensive overview of proof methods but it gives you some well known proofs in a variety of areas in math. So you get a flavor for proving stuff and a diverse set of areas.
sterile pelican
I think the best part of Chartand's book is the introductory chapters as it helps motivate the methods seamlessly, which I think many books failed to capture as a first exposure to proofs
another great thing is it has a review chapter
quartz pawn
I think Chartrand and Zhang are good writers we used their book in my discrete math class and its good too. Just good expositors overall
sterile pelican
though like I said it is quite costly, probably the most expensive one in my collection, so I suggest either you borrow or buy it 2nd hand
I use this book a lot to review some concepts so for me it is a must have
quartz pawn
the 4th edition of the book is relatively cheap
it's like 60 books.
but we have libgen.
so yea lol
sterile pelican
curious, may I ask what is libgen? I don't have that during my uni life before
valid moth
kisama
quartz pawn
sterile pelican
Ohh
long bear
https://libgen.is/ is a mirror
placid leaf
Functions that fail horizontal line test, don't have an inverse. The invertible functions are those that are strictly increasing or decreasing.
according to this $f(x)=x^2$ is not invertible
hasty eagleBOT
Greed:
gray gazelle
wrong channel
pulsar dome
Is there a book where I can learn more bout Arrow's Theorem and voting theory???
gray gazelle
ask questions like that in one of the pre-uni channels or one of the questions channels
pulsar dome
@gray gazelle is voting theory pre-uni????
gray gazelle
I was talking to greed
quartz pawn
Jameperezmon there are a plethora of books on social choice theory
This may not be the best place to ask for book recommendations on that type of stuff though.
You might be better looking off at https://discord.gg/HMjASv
or maybe https://discord.gg/FMrzyQ
@pulsar dome people at those places will probably have more to say on that type of stuff.
long bear
pulsar dome
@quartz pawn thanks!!
quartz pawn
granite sluice
Is there a book where I can learn more bout Arrow's Theorem and voting theory???
@pulsar dome I really liked this master's thesis: https://eprints.illc.uva.nl/953/1/MoL-2015-12.text.pdf ... it does use more machinery than strictly necessary (there is a combinatorial proof of arrows theorem out there), but since I think fourier analysis and boolean functions are cool I like this.
flat osprey
Does anyone have any references for stochastic processes? In particular I am interested in a finite time average of a signal with 1/f noise applied
delicate anchor
want a book on stats in general. i havent taken a probabilities course
flat osprey
@delicate anchor what is your math background
No undergraduate probability: Rice
Undergraduate probability: Casella & Berger
delicate anchor
i have a very strange background. i skimmed wasserman and thought it approachable, if concise
thanks, i'll check out both of those
trim narwhal
Is spivak beginner friendly?
pulsar aurora
no.
sterile pelican
I find it difficult to follow as a first exposure to Calculus, I used Lang's Short Calculus instead
then I head straight to Mathematical Proofs by Chartand
brittle latch
what about folland?
gray gazelle
i don't think folland has a single variable calculus book
if you mean his "advanced calculus" then yeah it's somewhat beginner friendly. you'd have to be somewhat comfortable in reading proofs to get through it though, which can be considered a beginner thing by some
dapper root
I used it for my first analysis book
Don’t recommend it if you don’t know calculus
Like yes, you could do it and it is self-contained in that respect, but yikes. I feel like doing a calculus course gives you more serious chops for doing complicated symbolic pushing around
brittle latch
im pretty familiar with calc already
took two years of calc in hs and a semester in college but im rusty and want to brush up so i was thinking about doing folland but ive never just read straight from a textbook
gray gazelle
for single variable, I really liked OpenStax(written in part by the GOAT Gilbert Strang) and I also used Anton, Bivens, and Davis's Early Transcendentals, especially for calc 2. For multi I used OpenStax to get a easy intro and followed it with Div, Grad, Curl and all that for a better intuition.
If you're looking for beginner friendly, openStax is pretty great, very informal, and you don't even have to pirate it.
hearty steppe
I remember Gilbert Strang’s linear algebra lectures and texts pretty much made me cringe back when I was still in school
gray gazelle
I always thought his prerecorded OCW stuff was pretty good, maybe not the most informative, but definately motivating.
limpid gazelle
libgen
gray gazelle
☝️
wooden sparrow
Is Gilbert strang a good author?
flat osprey
Yes
wooden sparrow
Nice
waxen elbow
hello, did someone read "All of Statistics: A Concise Course in Statistical Inference " by Wasserman ?
gray gazelle
I wanted a categorical approach to algebra and I found Algebra 0 by aluffi, I was wondering if anyone else has taken a look it it.
quick hornet
aluffi's text is... weird
its written for a target audience of students learning abstract algbera for the first time
rather than a "revisit" from a more categorical angle
now you can still probably get something out of it if you fall into the latter class of people, but meh
aluffi's writing is really fluffy and not in a good way
like if you're familiar with dummit and foote
d&f is fluffy and dry but most of the fluff feels like it has a reason to be there
aluffi is like that but with less substance?
and aluffi's exercises are like
super bad
so if youre gonna use aluffi definitely supplement it with another text, at least for the exercises
that said, the categorical approach to abstract algebra is interesting pedagogically
i do feel like aluffi's approach just introduces it too early
but i dont mind it in principle
and perhaps it could work with better execution
quartz pawn
Well now I know what not to use.
quick hornet
that said i am more negative on aluffi than most people
there are plenty of users in this server who like it
and plenty who share my opinion
its a somewhat controversial text
i think the categorical approach has potential but i think straight-up starting with categories is too ambitious
introducing some category theoretical concepts after a few chapters in an intro algebra text is an interesting idea though, and could potentially work
but honestly i feel like you only really start getting your "money's worth" out of categorical intuition once you get to alg top or w/e
like
if you dont understand adjunction, you cant possibly understand why category theory's actually important/helpful
but maybe thats just my bias
that said my #1 recommendation with this stuff is always
"give the first chapter or two a skim"
especially intro algebra texts since people tend to have very strong opinions about them
myself included
like for example, I really quite like dummit & foote despite the fluff, but its the text I learned out of, so I'm probably super biased
and a lot of people in this server dislike it
gray gazelle
I haven't taken abstract algebra yet, but I have been watching Bartosz's lectures, and reading nlab and applied category theory. I have a pretty light knowledge of algebra from the stuff I've flipped through.
quick hornet
well aluffi is certainly better than nlab lmao
gray gazelle
I'd say that I probably know more about category theory than I do about algebra
quartz pawn
I've read a bit out of dummit and foote and i decided I'm going to use it along with Artin. By fluff you mean unneccessary exposition, I kind of like that to an extent. Comprehensiveness is nice.
quick hornet
(as a source to learn out of that is)
gray gazelle
that's why I was looking for something with that approach
quick hornet
(nlab is fantastic as a reference)
well if you're really keen on the category theory stuff and want to look at it from that angle
quartz pawn
You have an opinon on Advanced Modern Algebra by Rotman
quick hornet
aluffi is a good text for that
i'd certainly supplement it with another text for exercises though
since aluffi's exercises are super softball
quartz pawn
I was wondering what's a good text in graduate algebra
gray gazelle
What would you suggest for exercises?
quick hornet
well as i said, i learned out of dummit & foote so im biased, but i think its exercises are quite nice (although there's a lot of them so it can sometimes be hard to filter out to the ones that actually present a concept worth thinking about)
lang's exercises are quite good (both in his undergrad and grad algebra text)
i dont really have anything else i can recommend personally but I'd imagine artin, jacobson, etc have good ones
at least, they're popular texts that i havent heard people complain about
but again, i dont have personal experience
lang's best exercise tbh
gray gazelle
lol, I like it.
wooden sparrow
lang's best exercise tbh
@quick hornet is that real?
quick hornet
yes.
sterile pelican
I am starting with Herstein's Topics in Algebra and I like it so far
valid moth
kisama
mint shore
Good day follows
Is there something good series for self learner?
I'm not looking for some 'fastest way'
I'm looking for some digging way that reads to real understand.
Cause I'm not student and I feel almost math that I learned in schools feels useless.
I'm trying to learn math again for real fun.
Any opinions welcome
🙂
sterile pelican
What kind of topics are you hoping to learn?
mint shore
Oh I wish all of them from kindergarten to university
That's why I mentioned 'series'
It's gonna be need few years but why not?
sterile pelican
kindergarten seems impractical for your level, are you a high school student?
A good book during my struggles with mathematics, at the highschool level, was Gelfand's books which are Algebra and Graphs & Functions
Then I followed it with Lang's Short Calculus
mint shore
Sounds good
and I'm not student
I'm just one of ordinary man who live as developer.
I just really looking for fun of math
sterile pelican
After Lang you want to do some higher level maths, if you want, I would learn some proofs for that so Chartand's "Mathematical Proofs" was my personal favourite but Hammack's "Book of Proof" is another good one
mint shore
Oh okay
sterile pelican
algebra sadly doesn't have a dover edition
mint shore
Huh... Seems only paper opinion available
sterile pelican
Oh yes I uhh own physical copies of my books
there should be a pdf somewhere though
sterile pelican
Yup
I don't find calculus very engaging imho so I wanted a short book to get it over with, it is far better to invest on learning proofs and higher level maths afterwards
dapper root
Namington is that real?
@wooden sparrow only in the first and second edition, the third and most current edition (which is the one I own) has actual exercises
Sorry for inadvertent ping Namington 😔
hexed pollen
does anyone have a good statistics/probability book that they would recommend?
just simple to understand
fathom monolith
A couple textbooks I ordered just arrived. I got the Ian Stewart book with the topological dog picture and I’m so excited to read it
I bought it after seeing the meme. Idk if it’s good or not, but there’s no way I don’t enjoy it
quartz pawn
@fathom monolith
pulsar aurora
Well, inform us if the meme was worth it.
crystal spade
Books/videos/websites for GCSES higher maths that covers all the topics with good tips
marble rock
what happens if i read real and complex analysis by rudin
without knowning any analysis without reading baby rudin
nvm i just read the contents
stray veldt
lol
maiden stratus
just search your topic on youtube?
there's videos on every gcse further maths topic
wooden sparrow
is the book How To Solve It by polya worth buying?
brittle latch
has anyone read A Programmer's Introduction to Mathematics
rain marsh
no
minor steeple
Can anyone recommend any good articles about benfords law? Please @ me if you reply:) thanks so much!
hearty steppe
I plan on taking a look at it at some point
granite sluice
Can anyone recommend any good articles about benfords law? Please @ me if you reply:) thanks so much!
@minor steeple https://en.wikipedia.org/wiki/Benford's_law ( math wikipedia is generally excellent )
minor steeple
Thank you!
trim narwhal
Is Stewart's Calculus beginner friendly?
hearty steppe
It’s fine for doing problem sets
Use Professor Leonard Youtube channel along with it and you should be fine
trim narwhal
Ok thanks
gray gazelle
(bit of a repost) Anyone have suggestions on calculus books for a second look at vector calculus that emphasizes it's connection to linear algebra and applications? I've already gone through OpenStax and Schey, so I think I have a good foundation but I'd like to see more examples and LA mixed in.
brittle marsh
hey does anyone know any good books regarding number theory?
quartz pawn
Andrew Granville recently came out with a number theory Number Theory : A MasterClass and I think it's great.
some of the problmes are pretty challenging though.
stray veldt
ireland rosen is the standard recommendation
brittle marsh
well, I am currently going through real anylasis and, I plan to study number theory soon for myself
slender sphinx
definitely second ireland rosen
sage python
Kasar's Photon, if you know a bit of algebra then Ireland-Rosen is a common recommendation, also Serre's Course in Arithmetic
For elementary stuff I like Weil's Number Theory for Beginners
drowsy pewter
has anyone read undergrad text in math for multivar calc? I liked the lin algebra not sure if theres something better for a refresh
marble rock
is there an algebraic geometry textbook taht is self contained
other than varieties and algorithms one
limpid gazelle
What's a good book on measure theory
Also @frigid comet what's your opinion on this?
sage python
"Real Analysis for Graduate Students" by Richard Bass is my favorite
limpid gazelle
Alright thank you I'll look into that
marble solar
@marble rock there's Algebraic Curves by Fulton, which is a precursor to the big boys
It's pretty self contained, even introducing the basic commutative algebra that you need
marble solar
Yeah no worries, that should be mostly smooth sailing until chapters 5/6
marble rock
finite robin
Anyone have tips in finding people who have textbooks that are willing to sell? I'm not talking about on Discord.
Maybe there are people that have these books I'm looking for.
stray veldt
have you tried abebooks
finite robin
Yeah but this book is pretty expensive, 100$ lowest price
hasty turret
libgen?
hidden abyss
yea lol
finite robin
Sadly need a hard copy, I can't study well with an online pdf on a computer screen due to slight epilepsy issues
I might have to suck it up and pay the 100$ if I can't find a hard copy cheaper
stray veldt
buy an e reader
flint forge
Have you tried reddit
finite robin
How would that work though?
flint forge
“Hi does anyone have book for sale”
hasty turret
Sadly need a hard copy, I can't study well with an online pdf on a computer screen due to slight epilepsy issues
@finite robin Have you tried dark mode?
finite robin
But....hmmmm, I mean I could do that but that just seems weird
@finite robin Have you tried dark mode?
Of course but the computer still produces the light that causes issues
flint forge
Whats weird about it
stray veldt
honestly, you can get an e-reader for less than 100 bucks and never have that problem again
flint forge
Can those read arbitrary pdfs
stray veldt
ofc the standard kindle is a bit small, but if you are willing to pay more you can get a bigger one
hasty turret
Probably
stray veldt
yes
finite robin
I will consider that, but it's still has light which is a problem
stray veldt
i use the boox nova pro and its in many aspects superior to real books
finite robin
That's actually a great idea
flint forge
It doesnt have light
hasty turret
So,How are you typing these? Are you uncomfortable,rn?
stray veldt
essentially yes
finite robin
So,How are you typing these? Are you uncomfortable,rn?
I modified my phone to be extremely dark and it's not close to my face. When studying on a computer, I sadly have to be closer and this has caused issues
Darker than lowest brightness
hasty turret
I guess, you could do the same with an e reader
stray veldt
my e-reader runs android btw and i could technically run discord on it
finite robin
E-reader might be the best solutions, will spend a day at least asking around
Thank You
stray veldt
the tech is steadily improving
response time is still "bad"
as soon as prices drop i will buy a bigger digital paper thing
just for being able to carry essentially an infinite stack of paper with you at all times in addition to all the books/research papers and your annotations on them
marble solar
PandaMan, I've found a lot of gems at local used bookshops
Or used booksales, especially ones at college campus'
finite robin
I would love to go on an adventure, but I dont think I'm gonna find people doing book sales during this time lol
marble solar
Yeah, things are pretty bad right now
torpid plank
What are your favorite books on graduate complex analysis?
I'd like something that starts with quickly covering the basic stuff (assuming I've studied them but would like to be reminded), then goes to more interesting things
torpid plank
Thanks, it does look very nice
marble solar
No don't use stein and shakarchi
It has great exercises, but some of the treatment of integration is done rather poorly
I think the Gold standard is Ahlfors
I personally am a huge fan of Donald Marshall's book, but it does have its detractors
If you're familiar with grad real, Rudin is another option
valid moth
narasimhan
hearty steppe
You mean Narayan?
I haven’t checked out Narayan yet. There’s also Bartle
I guess that’s real analysis tho
Bartle is kinda a short soft intro it looks like, kinda like Aubrey and Alcock
delicate anchor
isnt ahlfors undergrad level?
civic carbon
I like Stein and Shakarchi, but it depends what material you're looking to learn. Complex analysis is a big subject
and their text is definitely focused on the analysis side more than the geometry side.
but they have a very good treatment of entire functions and product theorems
but no coverage of things like branch covers (I think?)
like all books that try to prove the prime number theorem, I hate their proof of the prime number theorem
(for some reason every book wants to find the proof that uses the least possible technology instead of the proof that it seems plausible any human being would have ever found)
karmic thorn
Stupid me bought Stein and Sakarchi in 11th grade, thinking complex analysis concerned the elementary treatment of complex numbers. Ended up closing the book forever after reading "...rotation composed with a dilation is homothety in C.."
civic carbon
When I want to look up something in complex analysis, or understand something, I grab Gamelin or Stein/Shakarchi
For an "undergrad book" Gamelin has a lot of stuff in it, and is certainly the first place I ever understood that I should be thinking of these analytic number theory tricks in terms of laplace transforms
balmy hare
agreed
marble solar
I believe Ahlfors to be at the graduate level
valid moth
what about narasimhan
sage python
Narasimhan is the one I've heard is real good
But it's very firmly grad level in the sense of, it has heavier prereqs than many books
marble solar
What kind of pre reqs?
sage python
Like it pulls some measure theory/Hilbert spaces for sure, maybe or maybe not some algebraic topology?
burnt cobalt
Hi
I am really interested in statistics but I do not really know where to start, is there a place to go? My knowledge in maths isn´t deeper than algebra
And basic algebra
Just basic algebra, I wanted to say
slender sphinx
Do you know calculus? I would focus on your background first before going deeper
quick hornet
there are sources out there that are approachable without calculus.
i don't like them.
quick hornet
the foundations of statistics are based on calculus
but many places offer a statistics course that sort of glosses over this detail
giving formulas and tables and stuff to let you skip the actual calculus-ing
quick hornet
i personally dont like this approach so i dont really have recommendations for it
quick hornet
lol
quartz pawn
Lol he's memeing
quick hornet
thats a joke
quick hornet
the "standard" for introductory computational calculus at north american schools is Stewart
its so popular that everyone and their mother has an opinion on it
some people love it, some hate it
personally i think it does a competent enough job
but theres a lot of other options
quartz pawn
Its all good. They're math and memes specific to this server; you'll get them once u get more into the culture
And Stewart is standard
quick hornet
https://openstax.org/ has free calculus textbooks
broken meadow
stewart is cool and fine
quick hornet
also a stats textbook fwiw (which doesnt require calculus)
burnt cobalt
What should I know about math before getting into it?
hasty turret
What about amann escher?
broken meadow
brush up on precalculus topics
i think stewart textbooks have some kind of preliminary chapter
to check ur knowledge
otherwise you can use like
idk
khan academy
burnt cobalt
Oh, my knowledge in math comes mostly from Baldor books, I don´t know if you know them, I feel like they are good
So, I'll go with Stewart
broken meadow
cool
burnt cobalt
Thank you!
quick hornet
by the way
textbooks are fucking expensive
if you dont mind slightly breaking a law no one enforces
libgen
burnt cobalt
Really where I live textbooks almost don't exist, i'm from Venezuela
Also we can't buy anything with our credit cards so slightly broken laws aren't that bad
quick hornet
get either "calculus" or "calculus: early transcendentals"
there isnt much of a difference between the two
the latter just introduces transcendental functions (exponentials/logarithms) earlier in the text
technically "before" they can be rigorously defined
for pedagogical reasons (a lot of students see these functions in high school, so it makes sense to discuss them earlier)
burnt cobalt
Alright, is it the one which has the introductory chapters?
quick hornet
they both should
burnt cobalt
Thank you
Wish me luck, it's the first time I'm gonna get into autodidactical math
I have never studied without a teacher but here we go
Thank you!
limpid gazelle
Who has the pdf of the book "Modern Geometries Non-Euclidean Projective and Discrete Geometry" please share it with me
Thanks
trim narwhal
is better stewart or spivak for start calculus?
restive raptor
Depends what you want out of a calculus book
trim narwhal
what do you mean?
restive raptor
exactly what I said
the two are very different approaches to calculus
it depends on why you're doing it, and how much you enjoy math, and how much you want to learn
and what you want to learn
karmic thorn
If you want rigour and want to deeply understand calculus, choose Spivak. If you want an application-based, less-theory approach, choose Stewart/Thomas.
Question: If anyone has watched Tadashi Tokieda's Topology & Geometry lecture series at AIMS, can you suggest a good book for reference? There is no reading list provided, and I'm not sure what exactly to look out for since I know almost nothing about topology.
I checked out Topology Without Tears, and although it seems understandable, it doesn't seem to connect well with geometric aspects of topology (Tadashi starts off this series with deformations and stuff)
Would you suggest any readings as prerequisites?
Well, since you made the point it's non-standard, I suppose there isn't likely a book which supplements them
So I would like something that can clarify the prereqs for me at the very least
tropic lion
So I'm hoping to self-study abstract algebra and I already have a book and I'm wondering if it's good enough
karmic thorn
Okay 🙂
tropic lion
John R. Drubin's mondern algebra
karmic thorn
So I'm hoping to self-study abstract algebra and I already have a book and I'm wondering if it's good enough
@tropic lion Is it Judson or Pinter? :p
tropic lion
5th edition
karmic thorn
Never heard of this one. But I like Judson and Pinter.
Point-set topology is general topology, right?
hasty turret
What is the difference between a self study text and a normal one?
hasty turret
Can't you just learn from any non bad book?
karmic thorn
Self study texts are usually less rigorous but pedagogically sound, I guess
karmic thorn
Is Abstract Algebra a strict prerequisite for Algebraic Topology? I have some idea about groups, but not in much depth.
Yeah, at least I'm clear on the axioms for groups, rings and fields.
I'll have to study the action bit.
steel viper
hi magician
karmic thorn
Not much, just started off with Terry's Analysis 1
dapper root
If you only want to talk about the fundamental group
then I guess, but if you want to do more serious stuff you need to be able to do homology and stuff
steel viper
tropic lion
What's differential topology?
steel viper
what if topology but smooth
tropic lion
Is it anything like differential geo?
karmic thorn
So I guess I'll first focus on Analysis/Abstract Algebra, then jump to Topology
dapper root
You can learn point-set separately
and learning point-set topology is a boon to Analysis
IMO
steel viper
the virgin learning from rudin vs the chad learning from bredon
karmic thorn
It seemed fairly accessible when I studied the basics from Topology Without Tears, although it's fairly abstract
dapper root
Yeah later on you really want to be able to make use of compactness + connectedness
Altho I guess if you know that one theorem
which says closed + bounded = compactness (the topological defn) then you can get away without really knowing topology
but also idk if Tao is at a level you want to reduce from infinite to finite by taking open covers or w/e
karmic thorn
Ummm so should I go for Analysis, or Point-Set Topology first?
dapper root
I say analysis
karmic thorn
I think I have heard that Topology without Tears is not that good?
Doesn't look like a neat text, but I guess it's atleast not imprecise.
dapper root
but you can just do both IMO, learning just some really basic point-set is easy
and won't take long
steel viper
i did point set with like 0 analysis beforehand other than spivak and everything but like metrization was okay
based jan
tropic lion
also what do y'all think of someone doing complex analysis before real analysis?
dapper root
KingArthur I think dumb
karmic thorn
Okay, so I should work through a standard text like Munkres and Tao in parallel?
dapper root
IMO
tropic lion
hehehe
steel viper
lol
dapper root
You won't appreciate the beauty of how nice complex analysis is
tropic lion
I mean I can self study real anal
dapper root
Also less memyey
tropic lion
before complex anal
dapper root
if you haven't done real anal before I assume you haven't seen proofs
basically lmfao
karmic thorn
I have
karmic thorn
I've been working through some abstract math lately, so I can frame proofs, although it takes crazy long
tropic lion
I know I'm talking more about classes than books now but you guys seem pretty smart so that's why
dapper root
so that's why what?
hasty turret
Technically, You could develop the rest,knowing only the definition of a group
karmic thorn
I see. Well, I'll just follow the typical college sequence then. Analysis/Abstract Algebra, then some Linear Algebra/Multivar Calc and then advanced analysis(Rudin type)
hasty turret
Yea, Definitely not realistic
karmic thorn
Ah he's an applied mathematician
He's a brilliant teacher!!!
Yeah
He works mostly in mathematical physics
But I read somewhere he's in applied math too
quartz pawn
I mean its applied in a sense lol
steel viper
develop the rest of what lmao
karmic thorn
I don't know, I think mathematical physics is just a sub-branch of applied maths lol
steel viper
mathematical physics is a branch of pure math because it is useless 🙂
karmic thorn
And not all of mathematical physics is dynamical systems either?
Yeah, I guess physicists work with Gauge Theory and stuff too
(I don't even know what it is, by the way)
hasty turret
Classical mech is the only real physics
@gray gazelle wdym
karmic thorn
Classical Mechanics is mathematically sophisticated compared to Quantum Mechanics
Physicists say so; problems in classical mechanics require much more mathematical machinery than quantum mechanics
So if you really want to do this lecture series asap, you need analysis more than algebra
Point taken
Certainly. The first few lectures have been dedicated to building intuition, it seems.
I'm guessing the math behind those Mobius strips would be tedious
But I'm a fan of his teaching methodology
That alone seems to be a good motivation to learn
Unmotivated teachers can drain a subject of its beauty
Well, once I enter college I'll have to relearn this stuff anyway
I'm just getting myself used to abstract maths, so that I don't have to struggle with understanding the why of maths once I'm seriously pursuing it in a formal setting
karmic thorn
I did jump to category theory XDD
steel viper
ew
karmic thorn
Quickly realised it was a disaster
steel viper
its not even that its impossible its just that theres no point
steel viper
karmic thorn
Yeah, that's what I meant
It's too terse for someone just starting off with real maths
tight crag
Math people are ultra homogeneous
steel viper
yes slim that's what i was referring to
@sweet lotus now we are all checks notes ...you?
karmic thorn
But Analysis seems fairly accessible to me now
karmic thorn
So does Abstract Algebra