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Math & Stat Suggestions

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Math and Stat for Biologists

I am often asked by other faculty and students about potential math and stat courses for students to take. "What are the math/stat courses that are really needed to become a quantitative biologist"? My answer is found below. I also list my favorite textbooks and other resource for self-study. I personally believe beyond the required courses, one can study additional material by herself/himself with good textbooks (not any textbooks though!) because we are often interested in knowing how to use math and stat to understand biological processes rather than proving math is correct For graduate students, there is not much option but self-learning because these are undergraduate courses.

Required Math Courses

Calculus I & II

Calculus for Biology and Medicine by Claudia Neuhauser

Khan Academy (http://www.khanacademy.org/)
MIT (http://ocw.mit.edu/courses/#mathematics)

Linear Algebra

Linear Algebra and Its Applications by Gilbert Strang

Khan Academy (http://www.khanacademy.org/)
MIT (http://ocw.mit.edu/courses/#mathematics)

NOTE: Prerequisit for many stat courses
Must know for learning matrix population models

Introductory Differential Equations

Textbook: Any suggestion?

Khan Academy (http://www.khanacademy.org/)
MIT (http://ocw.mit.edu/courses/#mathematics)

Required Statistics Courses

Intro to Probability and Statistics Textbook: Mathematical Statistics and Data Analysis by John A. Rice
Linear Statistics Textbook: Any Suggestion?

Additional Math Topics

Calculus of Variation

Textbook: A Primer on the Calculus of Variations and Optimal Control Theory by Mike Mesterton-Gibbons

NOTE: If you are interested in opitimal control of natural resource management, this is an important topic. The textbook is relatively easy to read if you did well in the four math courses above.

Non-Linear Dynamics

Textbook: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering by Steven H. Strogatz

NOTE: You must be proficient on this topic if you want to be a theoretical ecologist.

Partial Differential Equations

Textbook: Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow

NOTE: This topic is important if you are interestred in spatial dynamics. Even if you are only interested in discrete space models, you should study this topic to avoid many common mistakes!

Numerical Analysis

Textbook: Any Suggestion?

NOTE: I personally think this should be a part of every math course. When I took the course (long time ago), I used the book by Cheney and Kincaid.

Stochastic Processes

Textbook: Discrete Stochastic Processes (Kluwer International Series in Engineering and Computer Science, 321) by Robert G. Gallager

Additional Reading:
Higham D.J. An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations. SIAM Review, 43(3): 525-546

NOTE: If you are interested in stochastic processes (pretty much every biological processes), you should study this topic.

Additional Stat Topics

Time Series Analysis Textbook: Time Series: A Biostatistical Introduction (Oxford Statistical Science Series, No. 5) by Peter J. Diggle
Multivariate Statistics Textbook: Applied Multivariate Statistical Analysis
by Dean W. Wichern
Non-Parametric Statistics Textbook: Practical Nonparametric Statistics, 3rd Edition by W. J. Conover
Bootstrap and other simulation-based statistics

Textbook: An Introduction to the Bootstrap by Bradley Efron, Robert J. Tibshirani

NOTE: Someone stole my book when I was moving to Texas. If you find a copy with my name, please return it to me! It is on page 101 (possibly written in Japanese)