Overview

Indicative content includes:

Semester 1

• Introduce and use Graphs and Digraphs
• Apply Greedy Algorithms to various graphs
• Look at the fundamental of Sets and how to use them
• Learn to build Venn Diagrams
• Gain the concepts of Boolean algebra and Karnaugh maps to solve logic problems
• Use Lists in relation to algorithms
• Apply the use of Binary Trees for given problems
• Write Linear Difference Equations for various situations
• Gain a foundation in Differentiation both in theory and application.

Semester 2

PART 1. MATRICES 1. Matrices. Definition. Notations. Vector-row and vector-column. Main diagonal of a matrix. Diagonal and square matrices. Symmetric matrix. Identity matrix. Transpose. 2. Operations on matrices. Addition. Multiplication by a scalar. Commutativity of addition. Matrix multiplication. 3. Linear transformations in 2D. Reflections and projections. Contractions, expansions and shear. Rotation matrix. 4. Concept of inverse of a matrix and its use for solving n linear equations with n unknowns. Examples. Inverse of a 2-by-2 matrix. “Express-and-substitute” method for solving 2 simultaneous equations. Matrix method.

PART 2. 2D and 3D SPACES 5. Vectors. Basic definitions and notations. Addition and subtraction. Multiplication by a scalar. Magnitude. Unit vector. Position vector. Coordinate decomposition. 6. Scalar product of vectors. Orthogonality. Euclidean distance between 2 points in the n-dimensional space. 7. Lines in 2D. Generic equation in 2D. Line between two points in 2D. Points on the same/different sides of a line in 2D. 8. Intersection of lines in 2D. Solving by using matrix inverse. Special cases. 9. Planes and lines in 3D. Generic equations. Line between 2 points in 3D. Intersection of a line and a plane in 3D. Plane defined by 3 points in 3D. 10. Special cases of lines and planes in 2D and 3D. Lines parallel to the coordinate axes in 2D. Planes parallel to xy-plane, yz-plan and xz-plane, and parallel to the coordinate axes. 11. Circles and spheres. Generic equations. Intersection between a circle and a line in 2D. Points inside and outside circles and spheres. 12. Vector orthogonal to a line in 2D. Normal and unit normal vector for a line between 2 points. 13. Orthogonality between vector and line/vector and plane. Finding the unit normal vectors for lines and planes given by their generic equations. 14. Collinearity between vectors. Vectors parallel to lines/planes

PART 3. PROBABILITY 15. Counting rule. Permutations. n-factorial. Binomial coefficients. Combinations. 16. Sample space. Elementary events. Compound events. Equiprobable and non-equiprobable elementary events. Probability and its properties. 17. Contingency tables. Joint, marginal and conditional probabilities.

Assessment Strategy

-threshold -Equivalent to 40%.Uses key areas of theory or knowledge to meet the Learning Outcomes of the module. Is able to formulate an appropriate solution to accurately solve tasks and questions. Can identify individual aspects, but lacks an awareness of links between them and the wider contexts. Outputs can be understood, but lack structure and/or coherence.

-good -Equivalent to the range 60%-69%.Is able to analyse a task or problem to decide which aspects of theory and knowledge to apply. Solutions are of a workable quality, demonstrating understanding of underlying principles. Major themes can be linked appropriately but may not be able to extend this to individual aspects. Outputs are readily understood, with an appropriate structure but may lack sophistication.

-excellent -Equivalent to the range 70%+.Assemble critically evaluated, relevent areas of knowledge and theory to constuct professional-level solutions to tasks and questions presented. Is able to cross-link themes and aspects to draw considered conclusions. Presents outputs in a cohesive, accurate, and efficient manner.

Learning Outcomes

• Apply elementary algebra.

• Calculate probabilities for elementary and compound events.

• Perform basic matrix and vector operations.

• Understand graph and digraph problems and algorithms for solving them.

• Understand polynomial functions, and their derivatives.