Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Tutorial
Module Offerings
5100MATHS-SEP-CTY
Aims
To further the study of mathematical methods in the areas of multidimensional calculus such as partial differentiation and multiple integration and applications, together with elements of discrete mathematics such as linear programming, difference equations, graph theory & networks, game theory, etc.
Learning Outcomes
1.
Integrate and differentiate functions of several (two) variables.
2.
Apply calculus of several (two) variables in relevant problem scenarios.
3.
Model, solve and analyse problems involving the use of: difference equations, game theory, graph theory, and linear programming.
Module Content
Outline Syllabus:Partial differentiation: Taylor series, unconstrained and constrained optimisation with Lagrange multipliers. Hessians and convexity/concavity.
Integration of functions of two variables: Iterated integration, change of order in integration, transformation to polar coordinates.
Difference equations: Modelling discrete time problems. Solution to difference equations (simple analytical problems). Applications: e.g. population growth, amortization.
Graphs: Graphs as models, directed graphs, graphs and matrices; trees, planarity. Shortest paths: 'Greedy algorithms', Dijkstra's algorithm. Spanning trees: Prim's algorithm, Kruskal's algorithm. Hamiltonian paths & cycles: Travelling Salesperson problem. Eulerian paths and circuits: Chinese postman problem. Fleury's algorithm. Linear Programming: graphical and algebraic methods.
Game Theory: Nash Equilibria, Saddle points, Mixed Strategies, Types of game situation e.g. Prisoner's Dilemma, Hawk Dove.
Module Overview:
This module continues to build on mathematical methods and elements of discrete/finite mathematics which have increasing application in science, engineering and business decision making.
This module continues to build on mathematical methods and elements of discrete/finite mathematics which have increasing application in science, engineering and business decision making.
Additional Information:This module continues to build on mathematical methods and elements of discrete/finite mathematics which have increasing application in science, engineering and business decision making. This module lays the foundations for further
study at level 6.