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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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Advanced mathematical methods

Advanced Mathematical Methods

COMP3006

Introduction to the course


Introduction
Introduction

  • 2 sections

  • Maths-Dr. Karen Page & Statistics –Dr. Simon Prince

  • Maths until reading week


Course contact details
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 3006-request@cs.ucl.ac.uk

  • 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
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
Coursework

  • 85% exam

  • 15% coursework

  • Maths coursework= average of homework grades


Homework
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
Notes

  • Handouts will be partial copies of overheads

  • They will contain spaces which you’ll need to fill


Useful books
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
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


Advanced mathematical methods

Option pricing:

Black-scholes’ stochastic differential equation

Bioinformatics:

Sequence comparison and microarray expression matrices


Topics
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


Topics1
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)