Quantitative reasoning can assist the study of systems that are impractical to approach using word models alone. The curriculum on the physics tutorials web page is important for this kind of inquiry. These materials overlap heavily with core requirements at science-technology schools (i.e. see requirements at Caltech and Harvey Mudd College).
Deterministic dynamical systems and stochastic dynamical systems
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Stochastic statics and equilibrium systems
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As these topics are first introduced, individual lectures will focus either on math accompanied by only relatively elementary physical models or instead on physics accompanied by only very basic math. I hear that bad things happen when students start out taking calculus and calculus-based physics at the same time. Familiarity with these topics eventually allows us to describe how experimental data and theory are compared. Even though physicists and biologists share vocabulary: hypothesis, statistical significance, or test, recognizing differences in the ways these words are used can facilitate interaction between these disciplines. After introductory math and physics become separately comfortable, we can combine them to do interesting things like discuss how quantum indeterminism is distinct from deterministic chaos.
The math tutorials at Harvey Mudd College might be helpful for reviewing pre-algebra, algebra, and calculus. Fred Safier's Schaum's Outline of Precalculus, 2nd ed contains practice problems. If, for entertainment purposes, you wish to make your hair stand on end, you can browse through Edward Barbeau's Mathematical Fallacies, Flaws, and Flimflam. For syllabi and textbook recommendations in related areas, please feel free to browse the HMC physics course descriptions and math course descriptions. If you find this material interesting, you might also enjoy the q-Bio summer school at LANL, Bill Bialek's graduate course Biophysics: Searching for Principles, or the course HMC Math 118/119 Mathematical Biology. You can even major in mathematical and computational biology.
Mathematics
Ronald E. Larson, Robert P. Hostetler, and Bruce H. Edwards, Calculus of a Single Variable: Early Transcendental Functions, Boston: Houghton Mifflin, 1999.
Susan J. Colley, Vector Calculus, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2002.
David C. Lay, Linear Algebra and its Applications, 2nd ed update. Reading, Massachusetts: Addison-Wesley, 2000.
William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 7th ed. New York: John Wiley & Sons, 2001. ** Unlike (apparently) a bunch of reviewers of Amazon.com, I enjoyed htis textbook, though the current edition is unnecessarily expensive. There is no need for it to cost $156.66. Buy it used!
Steven H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books: Cambridge, MA, 1994. * This is much less expensive than Boyce and DiPrima. Please see Chapter 5, 6, 7, 9, and 10, particularly pp. 123-159, 196-199, 301-304, 353-357, 398-407
Analysis of statistical distributions
John R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd ed. Sausalito: University Science Books, 1997. * This is a quick reference for basic uncertainty propagation, but I feel it has too much in the way of equations passed down from heaven.
Philip R. Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. Boston: McGraw-Hill, 1992. ** I prefer this handbook; it goes into a bit more detail than the Taylor error analysis book.
Non-calculus physics
John D. Cutnell and Kenneth W. Johnson, Physics. Hoboken, NJ: Wiley. * You don't need to get the current $150 version. I just can't find the citation for the older version I used in 1999.
F. Bueche, Principles of Physics, 4th ed. New York: McGraw-Hill, 1982. ** This is an alternative if you can't find the Cutnell.
Additional physics
Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. W. H. Freeman: New York, 1980. * Read this for chapters 1, 2, 3, and 4