620-142 Mathematics B First Semester, 2008

Subject Objectives

On completion of this subject, students should:

Comprehend:

• the concepts of modular arithmetic;
• the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
• the concepts of abstract vector spaces and inner product spaces;
• the uses and properties of linear transformations;
• the role of eigenvalues and eigenvectors in the study of such mappings.

Have developed the ability to:

• do calculations in the integers modulo n;
• find coordinates and matrices to represent vectors and linear transformations;
• find eigenvalues, eigenvectors and diagonal forms of matrices;
• change coordinate systems to simplify problems involving vector spaces and linear transformations.

Appreciate:

• the use of modular arithmetic and linear algebra in cryptography and coding theory;
• the role of linear algebra to find invariants and bring out the underlying geometry in problems;
• the use of the software package Matlab as a tool for mathematics.

In addition to learning specific technical skills that will assist you in your future careers in science, engineering, commerce, education or elsewhere, you will have the opportunity to develop in this subject, generic skills that will assist you whatever your future career path.