I want to be able to do these
>Solve mathematical puzzles.
>Prove mathematical theorems
>Able to do computation using combinatorics and permutation without trouble. Like I have hard time doing round dining table problems.
I have forgotten whatever topics I need to study to be able to develop skills in solving above types of problems. What is best sequence of topics I should study from basic to complex ones.
I guess most of us wants to do this.
>how to prove theorems
you need a full math undergrad
the start is real analysis and linear algebra
I am CS major.
I can know real analysis is needed but what is in linear algebra.Its just vectors and matrices.
it would be wise to approach math in a more humble manner. linear algebra is relatively simple but not nearly as much as they make it look for non math majors. it is a very nice topic and you need to be able to use its tools very well for higher topics. using the correct book goes a long way, try Hoffman & Kunze
while I'm recommending books you can use Tao Analysis I for analysis
But nobody answered my question. I guess you all are confused too. Meanwhile I am looking through all maths topics that are required to develop skills I mentioned.
what kind of puzzles do you want to solve? "prove theorems" means you want to learn math and I already told you what you should do.
>Hoffman & Kunze
My first linear algebra book was Howard Anton's elements of linear algebra.I don't know why it has 3-4 star ratings in Amazon but I could understand very clearly.
Like these I forgot what topic of maths was it.
>pigeonhole principle states that if n items are put into m containers, with n > m
unrigorous linear algebra for non mathematicians is to serious linear algebra as calculus is to analysis
that doesn't mean it's bad or you won't understand - I'm sure you know how to use the FTC for example but have no clue what it really means or how to prove it
that's combinatorics
you might not be interested in math, but just in elementary discrete mathematics. there's a decent class with a book in that at ocw.mit.edu
FTC. I remember I understood it well not just apply it for solving problems.
I guess you are not acquainted with more abstract maths.
Since my background was engineering my course had more application of maths. Calculus, Complex numbers, vectors, matrices, basic probability, basic set theory, basic graph theory, basic discrete maths(set theory was here I guess and so was logic, proposition)
I didn't have any more abstract maths.
Like say I used mathematical induction to solve problems but never knew why it worked.
You mean combinatorics includes discrete maths or the other way round?
combinatorics is a big, rich, proper field
"elementary discrete mathematics" means a special, elementary (low on theory) set of topics which might be useful to CS majors
which book?
>it's just vectors and matrices
It's the complete opposite actually, you are missing the entire geometric intuition of abstract/linear algebra watch this short video to see what I'm talking about youtube.com
As for your other problems the only way to learn is to solve problems, lot's and lot's of math problems. Get Concrete Math and just solve away. Get the book 'The Art & Craft of Problem Solving' by Zeitz. Keep doing combinatorics in Knuth's books until you get it
So I guess these are books in order i need to study.
By Knuth you mean Art of computer programming?
It is a nightmare for me. I thought of keeping it for next life.
I wonder if even 1000 people in America has fully read and understood at most 70% of that crazy Knuth wrote in his book
set theory is good to know, and you surely must learn it eventually if you're serious about math, but it might seem dry to you and make you lose interest rather quickly
I'd really suggest starting with intuition / application heavy topics like real analysis and linear algebra. there's a reason I recommend Tao, it has a chapter on set theory
by the way
>I guess you are not acquainted with more abstract maths.
fuck off you retarded CS baboon
the Art of computer programming series is not meant to be used as a reading / learning textbook. it's an encyclopedic reference
...
this is useless for general math, in particular for combinatorics
>CS baboon
Sadly I am CS graduate with programming skills.
I earn more than $80k
No offence to maths students but you have to be extremely intelligent to earn money in maths business which you obviously aren't.
Put your maths degree in your ass and die solving millennium problems.
lmao that's what I get for trying to help you
good luck being a retarded code monkey all your life and never knowing shit about anything
>math business
kek
Thanks I will skip this but would read first 1-2 chapters just to get to know.
You started first for calling me baboon
False, there is exercises for a reason, and Knuth specifically tells you in the preface it's not a reference since the field is so gigantic now it would be impossible to have one reference for all of computer science.
It's not that difficult, I've done vol 1 through 4, and am currently reading 4B 'mathematical preliminaries' and his Satisfiability fascicle. It's the exact same shit you would learn in any introductory CS class except there are an absolutely ridiculous amount of exercises and research problems per section (with fully worked out solutions available in the book for problems that are known to be solved). The books look large, but remember a lot of the pages are review material (if you already know the prelims) and exercises/answers to exercises.
Another myth of TAOCP is people who know nothing claim Vol 2 random numbers is "out of date" when in fact, everybody still uses those tests for randomness including theoretical cryptographers building FPGAs as a test bench for cryptanalysis.
Another myth is "But there's no red/black trees!" there is, in Vol 3, and Splay trees.
tl;dr don't listen to anybody's 2bits on TAOCP unless they have actually read it.
The statement below is false.
The statement above is true.
Wow so you are among 1000 some people in US to understand that.
You must be working for DARPA
