Continuity, limits, and the derivative for algebraic, trigonometric, logarithmic, exponential, and inverse functions. Applications to physics, chemistry, and engineering. Prerequisites: high school algebra, plane geometry, trigonometry, and analytic geometry. Honors section available first semester. (Gen.Ed. R2) [Note: Because this course presupposes knowledge of basic math skills, it will satisfy the R1 requirement upon successful completion.]
Continuity, limits, and the derivative for algebraic, trigonometric, logarithmic, exponential, and inverse functions. Applications to physics, chemistry, and engineering. Prerequisites: high school algebra, plane geometry, trigonometry, and analytic geometry. Honors section available first semester. (Gen.Ed. R2) [Note: Because this course presupposes knowledge of basic math skills, it will satisfy the R1 requirement upon successful completion.]
One-semester review of manipulative algebra, introduction to functions, some topics in analytic geometry, and that portion of trigonometry needed for calculus. Prerequisite: MATH 011 or Placement Exam Part A score above 15. Students with a weak background should take the two-semester sequence MATH 101-102. (Gen.Ed. R1)
This course is based on the first examination of the Society of Actuaries. Its content is largely dependent on that examination. Presently, it covers: calculus of a single variable (integration, differentiation, infinite series, Taylor's series etc.); calculus of several variables (Jacobians, Lagrange multipliers, double and triple integrals, etc.); probability Theory (discrete and continuous distributions, conditional probability and expectations, Bayes' rule, joint distributions, moment generating functions, the central limit theorem, etc.) The problems are drawn from old SOA examinations and most will have an insurance industry emphasis. Much of the material is a review of several courses, but this review is extensive and probably exceeds most interested students' backgrounds.
Foundational material in mathematical finance. Course covers interest rates, annuities, bonds, forwards, futures, options and other derivative securites. (Basis of actuarial exam in financial math exam fm/2).
This course provides an introduction to systems of differential equations and dynamical systems, as well as chaotic dynamics, while providing a significant set of connections with phenomena modeled through these approaches in Physics, Chemistry, and Biology. From the mathematical perspective, geometric and analytical methods of describing the behavior of solutions will be developed and illustrated in the context of low-dimensional systems, including behavior near fixed points and periodic orbits, phase portraits, Lyapunov stability, Hamiltonian systems, bifurcation phenomena, and chaotic dynamics. From the applied perspective, numerous specific applications will be touched upon ranging from the laser to the synchronization of fireflies, and from the outbreaks of insects to chemical reactions or even prototypical models of love affairs. In addition to the theoretical component, a self-contained computational component towards addressing these systems will be developed with the assistance of MATLAB (and wherever relevant Mathematica). However, no prior knowledge of these packages will be assumed.