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Advanced Mathematical MethodsPowerPoint Presentation

Advanced Mathematical Methods

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Advanced Mathematical Methods. COMP3006 Introduction to the course. Introduction. 2 sections Maths-Dr. Karen Page & Statistics –Dr. Simon Prince Maths until reading week. Course contact details. All communication concerning this course will be done via the email list.

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Introduction

- 2 sections
- Maths-Dr. Karen Page & Statistics –Dr. Simon Prince
- Maths until reading week

Course contact details

- All communication concerning this course will be done via the email list.
- Please join by sending an email with
Subject: join

- to [email protected]
- Information also on the websites:
http://www.cs.ucl.ac.uk/staff/K.Page/maths.html

http://www.cs.ucl.ac.uk/staff/S.Prince/3006.htm

Lectures and examples classes

- Check the website for timetable changes
- Until reading week:
lectures Thurs 9-10, MPEB 1.04

Fri 9-10, MPEB 1.13

Fri 12-1, MPEB 1.13

examples class Thurs 10-11, MPEB 1.04 (with Dr. Ged Ridgway); starting 12th October

Coursework

- 85% exam
- 15% coursework
- Maths coursework= average of homework grades

Homework

- I’ll set several exercises per lecture
- To help pass exam you should try to do all of these before the exam
- 2 per lecture = 6 per week are mandatory for coursework
- You will get credit for serious attempts
- Bring solutions for the week to the next examples class, attach coursework coversheet (http://www.cs.ucl.ac.uk/teaching/cwsheet.htm)
- I will attend examples classes to mark your work (for undergraduates only)

Notes

- Handouts will be partial copies of overheads
- They will contain spaces which you’ll need to fill

Useful books

- Axler “Linear algebra done right” 2nd edition (Springer)
- Boas “Mathematical methods in the physical sciences” 2nd edition (Wiley)
- **Bourne and Kendall “Vector analysis and Cartesian tensors” 3rd edition (Chapman and Hall)
- ***Kreyszig “Advanced Engineering Mathematics” 8th edition (Wiley)
- Pinkus and Zafrany "Fourier Series and Integral Transforms" 1st edition (Cambridge University Press)
- **Any books in the Schaum series on relevant topics

Motivation- Section 1 mathematics

Syllabus consists of two areas:

- Linear algebra & calculus
These build on courses B45 & B46 and are designed to give a general education in mathematics which will be useful for further courses in fourth year :

intelligent systems

machine vision and virtual environments

many other useful applications: financial world, game theory in economics, bioinformatics, mathematical and computational biology

Black-scholes’ stochastic differential equation

Bioinformatics:

Sequence comparison and microarray expression matrices

Topics

- Week 1: Basic topics in linear algebra, Gaussian elimination, complex numbers, eigenvalues and eigenvectors (easy stuff)
- Week 2: Differential vector calculus, including method of steepest descents
- Week 3: Integral vector calculus- Green’s theorem, Divergence theorem, Stokes’ theorem
- Week 4: Fourier series (complex), Fourier transforms, Laplace transforms

Topics

- Week 5: Further linear algebra- Gram-Schmidt, special complex matrices, orthogonal diagonalisation, spectral decomposition, singular values decomposition
- Note: The 2nd lecture will be on complex numbers. If you haven’t done this before, try to do lots of exercises (you’ll need to be familiar with this for later lectures)

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