Probability/stochastic processes:
G. Grimmett and D. Stirzaker, Probability and Random Processes, OUP, 2001
| Very nicely written book, covering both basic and advanced material |
Statistics:
L. Wasserman, All of Statistics, Springer, 2004
| Overly simplified but well-written introductory book |
Engineering mathematics:
G. Strang, Introduction to Applied Mathematics, Wellesley Cambridge Press, 1986
| Non-rigorous, intuition-oriented introduction and review of many topics in applied maths |
Analysis:
W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, 1976
Partial Differential Equations:
J. David Logan, Applied Partial Differential Equations, UTM, Springer, 1998
| Good introduction for non-mathematics students |
Linear Algebra:
R. Valenza, Linear algebra : An introduction to abstract mathematics, Springer-Verlag, 1993
| Introduction to linear algebra that also introduces basic group theory |
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Machine learning/applied statistics:
D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, 2003
| Excellent textbook, presenting both information theory and statistical learning. The focus is on the underlying algorithms. |
T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning, Springer, 2003
| Well-written introduction. Includes relatively recent topics such as SVMs and boosting. Doesn't discuss graphical models. |
M. Wainwright and M. Jordan, `Graphical models, exponential families, and variational inference,' Technical Report 649, Dept. of Statistics, UC Berkeley, 2003
Information theory:
T. Cover and J. Thomas, Elements of Information Theory, John Wiley, 1991
| Still the best introduction to information theory. Useful concepts such as entropy, mutual information and KL divergence are discussed right at the beginning. |
Optimisation:
D. Bertsekas, Nonlinear Programming, 2nd ed., Athena Scientific, 1999
D. Bertsekas, Convex Analysis and Optimization, Athena Scientific, 2003
Projective Geometry:
R. Hartley and A. Zisserman, Multiple View Geometry in computer vision, Cambridge Univ. Press, 2000
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