These exercise sheets are meant to provide a quick introduction to the main ideas, principles and results of various key topics for students following the multi-disciplinary MSc/PhD programme in the MOAC Doctoral Training Centre. For an in-depth, more rigourous treatment, the student should consult a textbook (see recommended texts below); the worksheets provide a study aid to these books.

• Worksheet 1 - Differentiation and Integration
• Worksheet 2 - Vectors and Matrices
• Worksheet 3 - Probability
• Worksheet 4 - Dynamical systems
• Worksheet 5 - Inferential Statistics
• Worksheet 6 - Optimization
• Worksheet 7 - Fourier Series, Fourier Transform and Sampling
• Worksheet 8 - Principal Component Analysis and Clustering
• Worksheet 9 - Modelling methodology

Recommended Texts

Basic Mathematics
L. Bostock, F.S. Chandler   Mathematics: The Core Course for A-Level (Nelson Thornes)

Calculus
K. E. Hirst   Calculus of One Variable (Springer SUMS)

Linear Algebra
David C. Lay   Linear Algebra and Its Applications (Addison-Wesley)
T.S. Blyth, E.F. Robertson   Basic Linear Algebra (Springer SUMS)

Differential Equations and Dynamical Systems
James C. Robinson   An Introduction to Ordinary Differential Equations (Cambridge Texts in Applied Mathematics)
Ferdinand Verhulst   Nonlinear Differential Equations and Dynamical Systems (Springer)
Morris W. Hirsch, Stephen Smale, Robert Devaney    Differential Equations, Dynamical Systems and an Introduction to Chaos (Academic Press)
David J Logan    Applied Partial Differential Equations (Springer)
David J Logan    A First Course in Differential Equations (Springer)

Numerical Analysis
Richard Burden, J. Douglas Faires   Numerical Analysis (Brooks Cole)
Arieh Iserles    A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics)

Mathematical Statistics
Lee J. Bain, Max Engelhardt   Introduction to Probability and Mathematical Statistics (Duxbury Classic Series))

Stochastic Processes
Zdzislaw Brzezniak, Tomasz Zastawniak   Basic Stochastic Processes: A Course Through Exercises (Springer SUMS)

Complex Analysis
Tristan Needham    Visual Complex Analysis (Oxford University Press)

Mathematical Biology
Christopher Fall, Eric S. Marland, John M. Wagner, John J. Tyson    Computational Cell Biology (Springer)
James Keener, James Sneyd   Mathematical Physiology (Springer)

Bioinformatics
W.J. Ewens, G. Grant    Statistical Methods in Bioinformatics: An Introduction (Springer)
Dan Krane, Michael Raymer   Fundamental Concepts of Bioinformatics (Benjamin Cummings)

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See also Hugo's MOAC Worksheets page on his personal homepage.

Prepared by:

Hugo van den Berg