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The study of con­tin­u­ous-time and dis­crete-time non­lin­ear dy­namic mod­els. Pro­vides ex­am­ples of chaotic be­hav­ior of so­lu­tions of some dy­namic sys­tems.

The study of continuous-time and discrete-time nonlinear dynamic models. Provides examples of chaotic behavior of solutions of some dynamic systems.

This course in­tro­duces the foun­da­tions of dis­crete math­e­mat­ics as they apply to com­puter sci­ence, fo­cus­ing on pro­vid­ing a solid the­o­ret­i­cal foun­da­tion for fur­ther work. Top­ics in­clude func­tions, re­la­tions, sets, sim­ple proof tech­niques, Boolean al­ge­bra, propo­si­tional logic, el­e­men­tary num­ber the­ory, writ­ing, an­a­lyz­ing and test­ing al­go­rithms.

This course introduces the foundations of discrete mathematics as they apply to computer science, focusing on providing a solid theoretical foundation for further work. Topics include functions, relations, sets, simple proof techniques, Boolean algebra, propositional logic, elementary number theory, writing, analyzing and testing algorithms.

Top­ics for the course in­clude sam­ple spaces and prob­a­bil­i­ties, dis­crete dis­tri­b­u­tions (Bi­no­mial, Neg­a­tive Bi­no­mial, Geo­met­ric, Hy­per­ge­o­met­ric, Pois­son, and Gamma), con­tin­u­ous dis­tri­b­u­tions (Uni­form, Nor­mal, Chi-squared), ex­pec­ta­tion and vari­ance, hy­poth­e­sis test­ing, in­ter­val es­ti­ma­tion and con­fi­dence in­ter­vals. There will be ex­ten­sive use of MS Excel and R, a sta­tis­ti­cal soft­ware pro­gram. At the end of the course, stu­dents should be able make mean­ing­ful con­nec­tions be­tween sta­tis­tics and other areas of study, in­clud­ing and so­cial sci­ences.

Topics for the course include sample spaces and probabilities, discrete distributions (Binomial, Negative Binomial, Geometric, Hypergeometric, Poisson, and Gamma), continuous distributions (Uniform, Normal, Chi-squared), expectation and variance, hypothesis testing, interval estimation and confidence intervals. There will be extensive use of MS Excel and R, a statistical software program. At the end of the course, students should be able make meaningful connections between statistics and other areas of study, including and social sciences.