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Advanced Mathematical Methods COMP3006 Introduction to the course

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

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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.uk3006-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

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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

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

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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 ) http://www.cs.ucl.ac.uk/teaching/cwsheet.htm I will attend examples classes to mark your work (for undergraduates only)

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

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Useful books 1.Axler “Linear algebra done right” 2nd edition (Springer) 2.Boas “Mathematical methods in the physical sciences” 2nd edition (Wiley) 3.**Bourne and Kendall “Vector analysis and Cartesian tensors” 3rd edition (Chapman and Hall) 4.***Kreyszig “Advanced Engineering Mathematics” 8th edition (Wiley) 5.Pinkus and Zafrany "Fourier Series and Integral Transforms" 1st edition (Cambridge University Press) 6.**Any books in the Schaum series on relevant topics

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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

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Option pricing : Black-scholes’ stochastic differential equation Bioinformatics: Sequence comparison and microarray expression matrices

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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

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Topics Week 5: Further linear algebra- Gram- Schmidt, special complex matrices, orthogonal diagonalisation, spectral decomposition, singular values decomposition Note: The 2 nd 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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Down to business…

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