Maths for Computing

Unit 11: Maths for Computing

Unit code D/615/1635
Unit level 4
Credit value 15

Introduction

In 1837 English mathematicians Charles Babbage and Ada Lovelace collaboratively described a machine that could perform arithmetical operations and store data within memory units. This design of their ‘Analytical Engine’ is the first representation of modern, general-purpose computer technology. Although modern computers have advanced far beyond Babbage and Lovelace’s initial proposal, they are still fundamentally relying on mathematics for their design and operation.

This unit introduces students to the mathematical principles and theory that underpin the computing curriculum. Through a series of case studies, scenarios and task-based assessments students will explore number theory within a variety of scenarios; use applicable probability theory; apply geometrical and vector methodology; and finally evaluate problems concerning differential and integral calculus.

Among the topics included in this unit are: prime number theory, sequences and series, probability theory, geometry, differential calculus and integral calculus.

On successful completion of this unit students will be able to gain confidence with the relevant mathematics needed within other computing units. As a result they will develop skills such as communication literacy, critical thinking, analysis, reasoning and interpretation, which are crucial for gaining employment and developing academic competence.

Essential Content

LO1: Use applied number theory in practical computing scenarios

  • Number theory:
  • Converting between number bases (Denary, Binary, Octal, Duodecimal and Hexadecimal).
  • Prime numbers, Pythagorean triples and Mersenne primes.
  • Greatest common divisors and least common multiples.
  • Modular arithmetic operations.
 
  • Sequences and series:
  • Expressing a sequence recursively.
  • Arithmetic and geometric progression theory and application.
  • Summation of series and the sum to infinity.

LO2: Analyse events using probability theory and probability distributions programming

  • Probability theory:
  • Calculating conditional probability from independent trials.
  • Random variables and the expectation of events.
  • Applying probability calculations to hashing and load balancing.
 
  • Probability distributions:
  • Discrete probability distribution of the binomial distribution.
  • Continuous probability distribution of the normal (Gaussian) distribution.

LO3: Determine solutions of graphical examples using geometry and vector methods

  • Geometry:
  • Cartesian co-ordinate systems in two dimensions.
  • Representing lines and simple shapes using co-ordinates.
  • The co-ordinate system used in programming output device.
 
  • Vectors:
  • Introducing vector concepts.
  • Cartesian and polar representations of a vector.
  • Scaling shapes described by vector co-ordinates.

LO4: Evaluate problems concerning differential and integral calculus

  • Differential calculus:
  • Introduction to methods for differentiating mathematical functions.
  • The use of stationary points to determine maxima and minima.
  • Using differentiation to assess rate of change in a quantity.
 
  • Integral calculus:
  • Introducing definite and indefinite integration for known functions.
  • Using integration to determine the area under a curve.
  • Formulating models of exponential growth and decay using integration methods.