MOAC Worksheets
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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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