|Catalog Description:|| This introductory course covers concepts from combinatorics to probability and statistics. Special emphasis is on the application of these concepts toward discovery of bioengineering principles from experimental observations and large-scale data as well as the design of experiments. Topics in combinatorics include (a) permutations and selections, (b) the binomial theorem and Vandermonde's identity, and (c) combinatorial proofs, with applications to (d) genome rearrangements, and (e) the traveling salesman problem (TSP). Topics in probability include (a) the law of addition and the law of multiplication, (b) independence and exclusiveness of observations, (c) conditional probability and Bayes' theorem, with applications to (d) Mendel's laws of heredity, and (e) the discovery of genetic linkage. Topics in statistics include (a) the hypergeometric probability distribution and (b) the p-value, with applications to (c) high-throughput biotechnologies, such as DNA sequencing and microarray hybridization. Additional topics include (a) the binomial probability distribution, and the limits of (b) the Poisson distribution and (c) the normal distribution, (d) estimation of mean, variance and correlation, with applications to (e) simulations and sampling of probability distributions, (f) the Luria–Delbrück experiments on bacterial sensitivity and resistance to viruses, and (f) Einstein's theory of random walk and Perrin's experiments on the Brownian motion.
Skills gained include (a) proving mathematical theorems, (b) programming numerical and symbolic computations in Mathematica, (c) design of algorithms, (d) flowchart construction, (e) analysis of articles in scientific journals, and (f) analysis of patents. Activities toward gaining these skills include (a) designing experiments, (b) learning-by-doing in-class problem solving, (c) guest lectures on applications of statistics to current research, (d) seminars and conferences on campus, (e) conference reports, and (f) end-of-class celebration.
100% grade = 60% assignments, 30% quizzes, 10% class participation; assignments and quizzes require cover page (-10%), and accepted up to two days late (-10%/day); class attendance is required.|