Unit 23 Mathematics for Software Development

·       Aim

To provide learners with an understanding of the underlying mathematical concepts that support the diverse fields supported by software engineers.

·       Unit abstract

This unit is an introduction to some of the mathematical concepts and techniques that will be required by software engineers. To develop the mathematical skills necessary for software engineering learners must gain a range of mathematical skills, which are often applied in the creation of coded solutions to everyday problems.

The unit will allow the learner to appreciate and prepare for the more advanced concepts of mathematics required in relation to software engineering.

Learners taking this unit will explore areas of mathematics that are used to support programming. It will cover conditional statements, graphics and gaming (geometry and vectors), relationships in databases, the calling of methods (or procedures), matrices in the handling of arrays, large datasets and mapping, statistics, calculus and set theory.

·       Learning outcomes

On successful completion of this unit a learner will:

1. Understand core mathematical skills for software engineers
2. Understand the application of algebraic concepts
3. Be able to apply the fundamentals of formal methods
4. Be able to apply statistical techniques to analyse data.

Unit content

1         Understand core mathematical skills for software engineers

Algebra: basic notation and rules of algebra; multiplication and factorisation of algebraic expressions involving brackets, algebraic equations and simultaneous linear equations, quadratic equations involving real roots

Geometry: types and properties of triangles, Pythagoras’ Theorem, geometric properties of a circle; trigonometry: eg sine, cosine and tangent functions, angular measure

Vectors: representation of a vector by a straight line, equal and parallel vectors, magnitude of a vector, vector addition and subtraction, scalar multiplication, linear transformations, rotations, reflections, translations, inverse transformations, axioms of a vector space

2         Understand the application of algebraic concepts

Relations: domain, range, Cartesian product, universal relation, empty relation, inverse relation, reflexive, symmetric and transitive properties, equivalence relations

Matrices: addition and subtraction, scalar multiplication, matrix multiplication, properties of addition and multiplication of matrices, transpose of a matrix, determinant, identify matrix, inverse of a matrix, condition for a matrix to be singular, solution of simultaneous linear equations

Application in programming: use of variables and operators, using mathematics based commands, arrays, conditional statements, pseudo code, demonstration code

3         Be able to apply the fundamentals of formal methods

Sets: definitions of set and element, representation of sets using Venn diagrams, universal and empty sets, finite and infinite sets, N, Z and R, operations on sets, subsets, notation, predicates; laws of set theory; idempotent, associative, commutative, distributive, identity, involution, complement, De Morgan’s laws

Propositional calculus: simple and compound propositions, conjunction, disjunction, negation, implication and bi-implication, truth tables, validity, principle of mathematical induction, logical argument and deductive proof

Boolean laws of propositional calculus: idempotent, associative, commutative, distributive, identity, involution, complement, De Morgan’s Laws

4         Be able to apply statistical techniques to analyse data

Techniques: frequency distribution, mean, median, variance, deviation, correlation probability, factorial notation, permutations and combinations, laws of probability, conditional probability, Bayesian Networks

Learning outcomes and assessment criteria

Learning outcomes   On successful completion of this unit a learner will:	Assessment criteria for pass   The learner can:
LO1 Understand core mathematical skills for software engineers	design a programming solution to a given algebraic problemdesign a programming solution to a given geometric problemimplement code that presents a range of vectors
LO2 Understand the application of algebraic concepts	explain how relations link to technologies used in programmingdesign a programming solution to solve a given matrix manipulation
LO3 Be able to apply the fundamentals of formal methods	discuss the application of set theory in computingdesign a programming solution to a given propositional calculus problem
LO4 Be able to apply statistical techniques to analyse data	4.1 design a programming solution to solve a given statistical analysis technique.

Guidance

Links to National Occupational Standards, other BTEC units, other BTEC qualifications and other relevant units and qualifications

The learning outcomes associated with this unit are closely linked with:

Level 3	Level 4	Level 5
Unit 6: Software Design and Development	Unit 18: Procedural Programming	Unit 35: Web Applications Development
Unit 14: Event Driven Programming	Unit 19: Object Oriented Programming	Unit 39: Computer Games Design Development
Unit 15: Object Oriented Programming	Unit 20: Event Driven Programming Solutions	Unit 40: Distributed Software Applications
Unit 16: Procedural Programming	Unit 21: Software Applications Testing	Unit 41: Programming in Java
Unit 26: Mathematics for IT Practitioners	Unit 22: Office Solutions Development	Unit 42: Programming in .NET

This unit has links to the Level 4 and Level 5 National Occupational Standards for IT and Telecoms Professionals, particularly the areas of competence of:

• Software Development.