Questions about the relation of (subfields of) computer science to the relevant mathematical foundations and their application.
Questions tagged [mathematical-foundations]
132 questions
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1 answer
Mathematics topics or fields that increase computer programming proficiency?
Generally computer programmers who are mathematicians or have mathematics background are very good in terms of algorithms and computer programming in general.
What I am not saying:
Mathematics is needed to be a good computer programmer.
Mathematics…
Charitoo
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15
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6 answers
What precisely differentiates Computer Science from Mathematics in theoretical context?
I am a university level student of Computer Science having a great passion to study Mathematics. I have a firm belief that Computer Science or Theoretical Computer Science is a direct branch of Mathematics and Logic and also of the opinion that a…
Maxood
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7
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2 answers
Minor Mistake in Computability, Complexity, and Languages?
In the book Computability, Complexity, and Languages (2nd edition), Martin Davis writes in chapter 1 (Preliminaries), section 2 (Functions):
A partial function on a set $S$ is simply a function whose domain is a subset of $S$. An example of a…
Good Night Nerd Pride
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1 answer
Why is addition in GF(2^8) the same as XOR?
I get the impression it has to do with either some quirk involved with limiting to 2^8 or that I'm misunderstanding what addition can be within the context of a finite field, but I'm not quite sure why it's described as 'addition' in the literature…
0x777C
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2
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1 answer
What is discrete mathematics and why am I learning about it?
I started computer science in university. And we started learning about Discrete and it's mathematics which is completely based on logic, which I understand. however, how is predicates, sets, proofs are related to computers ? I want to know the…
hameed
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2
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1 answer
Equivalence relations with $\cap$, $\cup$ and $\circ$
I have the relations $E_1$ and $E_2$.
A reflexive, symmetric and transitive property shows that two relations are equivalent to each other. I need to prove if this is true for the following
a) $E_1 ∩ E_2$
b) $E_1 ∪ E_2$
c) $E_1 ∘ E_2$
I found out…
LSR
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2
votes
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What is a mod b if a < b?
So when you are decrypting an encryption with modular arithmetic, I know the modulus operator (%) gives the remainder of a/b, but what if a is less than b?
For example, 5%2 is 1, since the answer is 2 remainder 1. But for something like 2%9, how do…
user17137
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1 answer
Why is this mapping from binary to natural numbers surjective?
In my Lecture we came across something of importance for the Church-Turing-Thesis and i noticed one particular function, which confused me.
Function:
Let $bin(x)$ be the injective binary extension without leading zeros. It is not surjective because…
Mark Lauer
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1
vote
1 answer
How to understand the probablistic analysis of skiplist?
I've been studying the skiplist analysis from the open data structures book here:
Open Data Structures
I've understood the first 3 lemma's, (after looking at how they use indicator variables in the section 1.3.4 of the book).
However, Lemma 4.4…
siebenheaven
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vote
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How much calculus do you actually use (not counting use of a graphing calculator)?
I'm wondering if it's worth it to pursue some deep study into calculus. Already, I have some familiarity with derivatives, limits, and integrals. Though, I also have a graphing calculator that's helped me in high school and college a algebra.
moonman239
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1
vote
2 answers
"Mathematical Physics"'s equivalent for Computer Science
Mathematical Physics is a well defined scientific fields that deals with the application of mathematics , mathematical tools , and mathematical methods in the theories and the problems of physics.
Is there a well defined scientific field that deals…
Jhdoe
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0
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0 answers
What is the underlying structure of problems?
We all the time write and talk about mathematical problems in plain English. For example, we define "the traveling salesman problem". But what is the actual, underlying structure of a "mathematical problem"? Can arbitrary mathematical problems be…
MaiaVictor
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1 answer
Is a zero matrix nilpotent matrix?
Let a matrix $A=0$. Can I say $A$ is nilpotent? I am asking if the zero matrix is nilpotent or not.
Nilpotent means that $A^k = 0$ for some $k$ that is a non-negative integer. When $k = 1$, $A^k = A = 0$. Does this idea support that a zero matrix is…
0
votes
1 answer
How do you convert bits into a different alphabet?
I have forgotten how to do this. How do I figure out what the requirements are for a 128-bit string using a certain alphabet?
That is to say, I want to generate a UUID (128-bit) value, using only the 10 numbers for the alphabet. How many numbers do…
Lance
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0
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1 answer
How are Complex Numbers and Complex Analysis used in CS?
The world is 3D and data of it is usually (as far as I know) represented and processed with real numbers. I've seen very few cases where complex numbers are used in programming and none when it comes to processing anything that doesn't explicitly…
ChocolateOverflow
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