# Questions tagged [mathematical-foundations]

Questions about the relation of (subfields of) computer science to the relevant mathematical foundations and their application.

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### How does the forget layer of an LSTM work?

Can someone explain the mathematical intuition behind the forget layer of an LSTM? So as far as I understand it, the cell state is essentially long term memory embedding (correct me if I'm wrong), ...
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### How are Complex Numbers and Complex Analysis used in CS? [closed]

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 ...
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### Integer-array indexing (e.g. numpy.take) as function composition: where can I find more resources?

For context, one of Numpy's features is that an an array of integers can be passed as an index to an array, and this selects values at all of the specified positions, in any order with possible ...
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### What are the other language models of computation similar to lambda calculus?

I hope this question makes sense, but I was wondering if there are other models of computation similar to lambda calculus that you can use to build up axiomatic mathematical and logical fundamentals ...
1k views

### How does a computer interpret real numbers?

I understand that the modern day digital computer works on the binary number system. I can also get, that the binary representation can be converted to rational numbers. But I want to know how does ...
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### Can we see all of mathematics as an attempt to simplify computations?

This is a rather strong claim, and therefore likely to be incorrect, but hear me out. Firstly, when I talk of “computations”, I mean this in a broader sense than normally used, because I am including ...
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### If you can have cyclic base types, or if they need to be infinite types

I am confused how to properly think about classes of classes. Basically, you can have a dog "filo" which is an instance of the dog "class". But the dog class is itself not an instanceof of "animal", ...
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### How to represent a map data structure mathematically

Wondering how to represent a map object such as the following mathematically: var foo = { a: 10, b: 'bar', c: true } You could say that it was a function ...
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### 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", "...
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### Should I go for computer science or maths? [closed]

I am in 11th grade. The only subject which I love the most is solving alegebraic equations and questions related to it. I enjoy doing trigonometry but hate the part of proving theorems. I opted ...
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### Compute growth of function [closed]

Suppose that $p>0$ and $n>0$ is a natural number. How do I prove that $$\sum_{k=1}^n k^p = 1^p + 2^p + \dots +n^p \sim \frac{1}{p+1}n^{p+1}=\Theta(n^{p+1})$$ for $n \rightarrow \infty$?
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### Mathematical proofs implemented purely by Lambda Calculus

I've seen often stated that Lambda Calculus can be used for mathematical proofing but I haven't yet seen any example how it is actually used for the task. Is there a simple example, lambda ...
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### Why algorithms calculating non-tirivial zeros can't be used as proofs of Riemann Hypothesis?

Recently I was reading again this propositions as types paper by Philip Wadler: http://homepages.inf.ed.ac.uk/wadler/papers/propositions-as-types/propositions-as-types.pdf It gives an impression, ...
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### 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 ...
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### Soft Question: Looking for resources on computation over reals

As the title suggests, I want to take a look at resources (books, lectures or papers) that are available (free or paid) on computation over reals. Thanks in advance!
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### 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 ...
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### How does maths consistency impacts on computer science?

Lot of mathematicians have made several efforts to answer the question : are mathematics consistent ? Although we haven't yet had a proof of consistency, and surely we will never (Gödel second theorem)...
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### Set theory and computer science

It's said that in Zermelo–Fraenkel set theory (ZFC) one can develop all of mathematics. How about computer science? Is it possible to define algorithms as a first step? More specifically, how to ...
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### Is there a formalization of the computational model for quantum computers?

There are several equivalent computation models, each capable of simulating each other. For example, the lambda calculus or the SKI calculus which are based on rewriting, Cardelli's object calculus, ...
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### Mathematical equivalent of reduce()?

filter() in functional programming can be thought of as being analogous to an equation that filters the range of the variable. map() can be through of as a function mapping domain to codomain. ...
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### Mathematics topics or fields that increase computer programming proficiency? [closed]

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 ...
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### Tight bound on the number of divisors of n

The inner loop of this pseudocode runs only for the divisors of n for i=1 to n: if(n%i==0): for j=1 to n: Do something in constant time If I ...
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### How do you represent LISP as mathematical / logical model?

I asked this in stackoverflow, but the question probably fits here better. This question arose from the objection that LISP is regarded as a functional language with some simple principles, namely ...
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### Examples of continuations in pure mathematics [closed]

I am not a computer scientist and have no knowledge of programming. However, I wondered continuations occur as natural and interesting mathematical structures, perhaps as algebraic or type theoretic ...
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### magnetic Disk Calculation

A magnetic disk has 1000 cylinders, 10 tracks per cylinder, 128 sectors per track, ...
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### how long will it take to execute a ten-stage pipeline

Suppose you design a computer with a ten-stage Pipeline to execute one instruction, with each stage taking 5nsec A)how long ...
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### Can cognitive architectures (CLARION, SOAR, ACT-R) be used for creative mathematical reasoning?

Can cognitive architectures (CLARION, SOAR, ACT-R, others) be used for creative mathematical reasoning? As far as I understand, then it is the best to encode formal mathematical knowledge in the ...
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### What is the name of this type of function composition?

If standard function composition is defined as: (define compose { (B → C) → (A → B) → (A → C) } F G -> (λ X (F (G X)))) What type of ...
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### 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: ...
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### Trouble understanding Break-Even Point for upgrade

Null, Linda; Lobur, Julia: The Essentials of Computer Organization and Architecture, Jones&Bartlett Learning 2006, Ch. 7 Ex 2: Suppose the daytime processing load consists of 60% CPU activity ...
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### Proof by mathematical induction

Before we start, my textbook declares lgn as base two. I only have one question, how did log2 become n (both highlighted in yellow in the picture)? Is it because log2 = 1, which is too small to even ...
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### Pre-requisite knowledge before diving into algorithms

I'm having some difficulty trying to follow what the authors of some of the more highly recommended books on algorithms. I ran into the same problem when trying out some online courses. My goal is to ...
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### 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 ...