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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