Chapter 8: Applications to Computer Science

Question 1

Give examples from computer science where mathematical techniques are routinely employed

Answer 1

Precise language and predicate calculus to describe the spec for a program

Verify correctness using logic

Programming with logical formula in prolog

Solving optimisation problems with logic

Using expected value to calculate complexity

Calculating risk using probability and expected values

Complexity classes

Using the size of a set

Recursion

Recursively defined functions to work out complexity

Induction to prove properties of entities

Relations to express programming constructs

Vectors and matrices in graphs

Question 2

When is it useful to precisely define what we want code to do?

Answer 2

unexpected behaviour

Trying to determine behaviour of a language

Safety critical applications

Question 3

What applications have we seen in Chapter 2?

Answer 3

Properties of java operations, Properties of functions

Question 4

What applications have we seen in Chapter 4?

Answer 4

Bayesian Updating, using expected values to calculate complexities

Question 5

What applications have we seen in Chapter 6?

Answer 5

Code applications of recursion, Proof by induction that a recursive function has a property

Question 6

What applications have we seen in Chapter 7?

Answer 6

Calculating powers of a number in modular arithmetic