Computer LaboratoryComputer Science Tripos Syllabus - Continuous Mathematics

Continuous Mathematics
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## Continuous Mathematics

Lecturer: Dr R.J. Gibbens

No. of lectures: 4

This course is a prerequisite for Computer Graphics and Image Processing, Artificial Intelligence I, Artificial Intelligence II (Part II), Computer Vision (Part II), Information Theory and Coding (Part II), Quantum Computing (Part II), Digital Signal Processing (Part II).

Aims

The aims of this course are to review some key concepts and operations defined in continuous mathematics involving real and complex-valued functions. Focus is on the use and implementation of these notions as encountered in computer science.

Lectures

• Review of analysis. Limits, continuity and differentiability. Power series and transcendental functions. Taylor series. Complex variables.

• Fourier series. Introduction. General properties. Uses and applications.

• Basis functions and decompositions. Expansions and basis functions. Orthogonality, inner products and completeness. Useful expansion bases for functions.

• Representation of signals. Fourier transforms and their inverses: introduction and general properties. Uses and applications. Brief introduction to wavelet analysis and its comparison with Fourier analysis.

Objectives

At the end of the course students should

• understand how functions can be represented in terms of their projections onto basis functions

• be fluent in the use and properties of complex variables and power series

• grasp key properties and uses of Fourier analysis, transforms, and wavelets

Reference books

* Oppenheim, A.V. & Willsky, A.S. (1997). Signals and systems. Prentice-Hall.
Pinkus, A. & Zafrany, S. (1997). Fourier series and integral transforms. Cambridge University Press.
Stephenson, G. (1973). Mathematical methods for science students. Addison Wesley Longman.

Next: Data Structures and Algorithms Up: Michaelmas Term 2004: Part Previous: Computer Design   Contents
Christine Northeast
Wed Sep 8 11:57:14 BST 2004

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