MOAC Worksheets

The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense. — Charles Darwin
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 PhD programme in the
MOAC Doctoral Training Centre. For an in-depth, more rigourous treatment, the student should consult a textbook (see recommended textbooks); the worksheets provide a study aid to these books.
Differentiation and Integration
Vectors and Matrices
Probability
Dynamics
Modelling methodology
Inferential Statistics
Optimization
Fourier Series, Fourier Transform and Sampling
Principal Component Analysis and Clustering

Resources

Basic Methods in Theoretical Biology
Analysis
Introduction to Modern Scientific Programming

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)
Quantum Mechanics & Statistical Physics
David J. Griffiths    Introduction to Quantum Mechanics (Prentice Hall)
David H. Trevena    Statistical Mechanics: An Introduction (Ellis Horwood)
J.R. Waldram    The Theory of Thermodynamics (Cambridge University Press)
Biochemistry & Metabolism
Jocelyn Dow, Gordon Lindsay, Jim Morrison    Biochemistry: Molecules, Cells and the Body (Prentice Hall)
J.G. Salway    Metabolism at a Glance (Blackwell)
Geoffrey M. Cooper    The Cell: A Molecular Approach (Sinauer)
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