# Tag Info

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### How/when is calculus used in Computer Science?

I can think of a few courses that would need Calculus, directly. I have used bold face for the usually obligatory disciplines for a Computer Science degree, and italics for the usually optional ones. ...

### How/when is calculus used in Computer Science?

This is somewhat obscure, but calculus turns up in algebraic data types. For any given type, the type of its one-hole contexts is the derivative of that type. See this excellent talk for an overview ...

### How/when is calculus used in Computer Science?

Numerical Methods. There exist cumbersome calculus problems that are unique to specific applications, and they need solutions faster than a human can practically solve without a program. Someone has ...

### How/when is calculus used in Computer Science?

Automation - Similar to robotics, automation can require quantifying a lot of human behavior. Calculations - Finding solutions to proofs often requires calculus. Visualizations - Utilizing ...

### What is the meaning of $O(m+n)$?

Part 1 I'm going to do something I decided I wouldn't do: try to nutshell my research on this topic. I'll go over on how the algorithmic O-notation must be defined, why it is probably not what you've ...
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### How/when is calculus used in Computer Science?

Many people already provided applications in CS. But sometimes you'll find Calculus when you least expect: Regular-expression derivatives reexamined If you know automata this pdf might be worth ...

### Can someone explain why there are two summations here?

And why are they exactly the same? I showed a math professor and he thinks they're labelled wrong but couldn't figure it out. I don't even get why there are two. When in doubt, check the book's ...
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### What is the depth of recursion if we split an array into $\log_2(n)$ with each recursive call?

Let $f(n) = n/\log n$, and denote by $g(n)$ the number of applications of $f$ it takes to get $n$ below some arbitrary constant. On the one hand, $f^{(t)}(n) \geq n/\log^t n$, and so  g(n) \geq \...
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### Abs(sum of differences of elements in a sorted array) = array.Max()-array.Min() Why?

If you picture these as distances along a road, it should be very intuitive. If (for example) you start at kilometer #7, then proceed through kilometers #45, #81, and #97, then the distances you ...

### How/when is calculus used in Computer Science?

Some more specific examples: Calculus is used to derive the delta rule, which is what allows some types of neural networks to 'learn'. Calculus can be used to compute the Fourier transform of an ...
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### Do formulas involving fewer repetitions of variables give higher numerical precision?

First, I want to say that it is not the case in general that an algorithm that minimizes the number of uses of the inputs is more accurate, at least for IEEE 754 floating point. For example, ...

### How/when is calculus used in Computer Science?

To these other excellent answers I add this point: rigor in testing. In creating test cases for some applications I have had to make use of calculus to predict expected running times, memory sizes, ...

### How/when is calculus used in Computer Science?

Calculus -- the integral portion -- is used directly in CS as a foundation for thinking about summation. If you work through any portion of Knuth's Concrete Mathematics section on summation, you will ...

### Hash function to hash 6-digit positive integers

A hash table usually uses two different things: One, a hash function that maps an item to a hash code (with the requirement that equal items are mapped to equal hash codes), and two, a function that ...

### Why do Computers use Hex Number System at assembly language?

The simplest reason is that, the computer does not see this, it only sees the binary. This really just aids the programer. Binary is a mess to look at, octal does not usually work since an octal ...

### Trigonometry in computer science

Interpolation. If by computer science you include numerical computing, any why the hell not, you often use trig functions in interpolation. Sometimes you have a sampled version of a function, say a ...
A hash function cannot avoid collisions when the size $M$ of the hash table is smaller than the size of the universal set $U$ that you are hashing. This is a consequence of the compression step. In ...