Questions about the relation of (subfields of) computer science to the relevant mathematical foundations and their application.
Questions tagged [mathematical-foundations]
135 questions
219
votes
32 answers
Why is writing down mathematical proofs more fault-proof than writing computer code?
I have noticed that I find it far easier to write down mathematical proofs without making any mistakes, than to write down a computer program without bugs.
It seems that this is something more widespread than just my experience. Most people make…
user56834
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39
votes
3 answers
What exactly is a logic?
An apology might be in due for asking another question about prerequisites, but I was confused about the starting points.
I have come across various terms such as "Modal Logic", "Temporal logic", "First -order Logic", "Second order Logic" and…
Sheldon Kripke
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35
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11 answers
Why is data in computer science considered to be discrete?
I understand that "structure" of data is totally dependent on Boolean Algebra, but:
Why is data considered to be a discrete mathematical entity rather than a continuous one?
Related to this:
What are the drawbacks, or invariants, that are…
evil_potato
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25
votes
2 answers
Do any programming languages use general recursive functions as their basis?
This is a naïve and, therefore, possibly malformed question, so apologies in advance!
My view is that a Turing Machine can be seen as the computational basis for procedural/imperative programming languages. Similarly, the lambda calculus is the…
Xophmeister
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15
votes
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
votes
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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15
votes
6 answers
What parts of linear algebra are used in computer science?
I've been reading Linear Algebra and its Applications to help understand computer science material (mainly machine learning), but I'm concerned that a lot of the information isn't useful to CS. For example, knowing how to efficiently solve systems…
Kelmikra
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15
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3 answers
Shannon Entropy of 0.922, 3 Distinct Values
Given a string of values $AAAAAAAABC$, the Shannon Entropy in log base $2$ comes to $0.922$. From what I understand, in base $2$ the Shannon Entropy rounded up is the minimum number of bits in binary to represent a single one of the values.
Taken…
Sean C
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14
votes
5 answers
What is the difference between $\log^2(n)$, $\log(n)^2$, $(\log n)^2$, $\log (n^2)$ and $\log \log n$?
In research articles (e.g. this one's abstract), I often see the complexity of an algorithm expressed using a somewhat ambiguous notation:
$\log^2(n) = ?$
$\log(n)^2 = ?$
$(\log n)^2 = (\log(n)) \times (\log(n))$
$\log(n^2) =…
Suzanne Soy
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12
votes
1 answer
Monad in Haskell programming vs. Monad in category theory
I have a question about concept of monad used in Haskell programming
and category theory in math.
Recall in Haskell a monad consists of following components:
A type constructor that defines for each underlying type how the
corresponding monad type…
user267839
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11
votes
2 answers
Mathematical conjectures equivalent to the halting of a Turing machine
This question is about whether every mathematical theorem can be reduced to the question of whether a single Turing machine halts. In particular, I'm interested in conjectures that are currently unproven.
For example: Wikipedia says that it's…
N. Virgo
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10
votes
3 answers
Resources for studying the mathematical foundations of machine learning, for someone from a math/physics background
I am a soon-to-be physics graduate student with a background in theoretical and experimental cosmology. In my work, I've often found myself applying machine learning models and techniques for the purposes of performing data analysis tasks. I, as…
10GeV
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10
votes
4 answers
Could Gödel’s incompleteness theorem be circumvented with a quine?
As you all probably know, Gödel’s incompleteness theorem states, that it will never be possible for mathematics to prove its own correctness.
Mainly because that proof would be part of mathematics too, and hence need proving itself. And that leads…
anon
10
votes
2 answers
What are the implications of Homotopy Type Theory?
I've recently come across the topic of homotopy type theory and I'm interested to learn more. I have a very limited background in type theory.
Can anyone tell me, in functional programming terms or through practical examples, how exactly is HoTT…
thoughtpolice
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9
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2 answers
What are Markov chains?
I'm currently reading some papers about Markov chain lumping and I'm failing to see the difference between a Markov chain and a plain directed weighted graph.
For example in the article Optimal state-space lumping in Markov chains they provide the…
Bakuriu
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