MAT3104: Functional Analysis

This is a pure mathematics course covering topics needed for physical, life and social science disciplines.  Topics covered include: Metric Spaces; Normed Spaces; Normed Linear Operators; Inner Product Spaces; and Fundamental Theorems of Functional Analysis and Applications.

Course Objectives   
On successful completion of this course unit, the learners should be able to: 

• Describe properties of normed linear spaces and construct examples of such spaces 
• Extend basic notions from calculus to metric spaces and normed vector spaces iii. State and prove theorems about finite dimensionality in normed vector spaces iv. State and prove the Cauchy-Swartz Inequality and apply it to the derivation of other inequalities 
• Define the concepts of Hilbert spaces and Banach Spaces 
• Describe the dual of a normed linear space 
• Apply orthonormality to Fourier series expansions of functions 

Expected Learning Outcome
This course unit is meant: 

• To discuss the basic competence in the concepts, principles, and procedures necessary to develop the learners’ habit of critical thinking and logical reasoning in pure Mathematics.  
• To encourage orderliness, speed and accuracy in the presentation of mathematics.  
• To help learners acquire the analytic skills of expression in proper mathematical language and using mathematical symbols correctly.  
• To provide instructions that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills.  
• To build a strong foundation in calculus of functions as preparation for subsequent courses in mathematics and other sciences.  
• To Lay a foundation for postgraduate study in pure Mathematics