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BASICS OF MATHEMATICS AND STATISTICS
The objective of this course is to give conceptual exposure of essential contents of mathematics and statistics to students
Linear equations, functions: slopes-intercepts, forms of two-variable linear equations; constructing linear models in biological systems; quadratic equations (solving, graphing, features of, interpreting quadratic models etc.), introduction to polynomials, graphs of binomials and polynomials; Symmetry of polynomial functions
Basics of trigonometric functions, Pythagorean theory, graphing and constructing sinusoidal functions, imaginary numbers, complex numbers, adding-subtracting-multiplying complex numbers, basics of vectors, introduction to matrices.
Differential calculus (limits, derivatives), integral calculus (integrals, sequences and series etc.).
Population dynamics; oscillations, circadian rhythms, developmental patterns, symmetry in biological systems, fractal geometries, size-limits & scaling in biology, modeling chemical reaction networks and metabolic networks.
Probability: counting, conditional probability, discrete and continuous random variables, mean, standard deviation and standard error, Populations and samples, expectation, parametric tests of statistical significance (student t test, F test and ANOVA), nonparametric hypothesis tests (chi square test), linear regression and correlation, factorial experiment design.
● Stroud, K. A., & Booth, D. J. (2009). Foundation Mathematics. New York, NY: Palgrave Macmillan.
● Aitken, M., Broadhursts, B., & Haldky, S. (2009) Mathematics for Biological Scientists. Garland Science.
● Billingsley, P. (1986). Probability and Measure. New York: Wiley.
● Rosner, B. (2000). Fundamentals of Biostatistics. Boston, MA: Duxbury Press.
● Daniel, W. W. (1987). Biostatistics, a Foundation for Analysis in the Health Sciences. New York: Wiley.
● Biostatistics: A Foundation for Analysis in Health Sciences, (11th edition), W W Daniel, John Wiley and Sons Inc., 2018.
● Statistical Methods, S. P. Gupta, 43rd Edition, Sultan Chand, 2014
● Fundamentals of Biostatistics, Khan and Khanum, Shiba Khan, Ukaaz /BSP books India, 2018
● Seymour Lipschutz, Linear Algebra, McGraw Hill, 2018
● Ramachandra Rao and Bhimasankaram, Linear Algebra, Second Edition, Hindustan Book Agency, 2017.
● J. N. Kapur, Mathematical Modelling, New Age international ltd., 2015.
● M. Ray and G.C. Sharma, Differential Calculus, Shivalal Agarwal & Co. Agra, 2010
● Statistical Methods in Biology Norman T. J. Bailey,3rd edition, Cambridge University Press, 2000
● Practical statistics for Experimental Biologists, A C Swardlaw, 2nd edition, John Wiley and sons Inc., 2000
● Biostatistics: Basic Concepts and Methodology for the Health Sciences, 10ed, ISV. Wiley 2019
