PMAT 12212: Mathematics for Computing II

Course code  :  PMAT 12212

Title               :  Mathematics for Computing II

Pre-requisites :  PMAT 11212

Learning Outcomes:

Upon successful completion of the course unit, the student should be able to:

1. demonstrate knowledge in matrices
2. solve systems of linear equations
3. compute eigenvectors and eigenvalues
4. solve real world problems using counting techniques
5. demonstrate knowledge in basic graph theory.

Course Contents:

Matrices :

• Matrix notations, Algebra of matrices, Inverse of a matrix, Elementary row operations and calculation of inverse matrix, Determinant of a matrix, Minor and cofactor, Properties of determinants, Adjoint of a matrix and calculation of inverse matrix.

Systems of Linear Equations : 

• Matrix form of a system of equations and conditions for unique solutions, augmented matrix and echelon form, Conditions for existence of a unique solution, infinitely many solutions and no-solution.

Vector Spaces: 

• Linear Independence, Basis and Rank, Linear Mappings, Eigenvalues and Eigenvectors.

Counting Techniques: 

• Factorial notation, Sum rule and product rule, Pigeonhole principle, Permutations and combinations, Binomial expansion.

Graphs:

• Graph notation and basic definitions, Complete and bipartite graphs, Euler and Hamiltonian circuits, Directed and undirected graphs, Planar graphs, Graph colouring, Trees and their basic properties.

Method of Teaching and Learning : Lectures, interactive classroom sessions, and case discussions 

Assessment : End of course unit examination, group assignment, mid-term examination, class attendance

Recommended Reading:

1. Johnsonbaugh, R. (8th Ed., 2017). Discrete Mathematics, Pearson.
2. Rosen, K.H. & Krithivasan, K. (7th Ed., 2011). Discrete Mathematics and Its Applications,
McGraw-Hill.
3. Kreyzig, E. (8th Ed., 2006). Advanced Engineering Mathematics, Wiley Student Edition.
4. Susanna, S. E. (2010). Discrete Mathematics with Applications, Cengage Learning.
5. Larson, R. & Falvo, D. (6th Ed., 2009). Elementary Linear Algebra, Houghton Mifflin Harcout
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