This course considers applications of mathematics to political science. Five major topics will be covered: a model of escalatory behavior, game-theoretic models of international conflict, yes-no voting systems, political power, and social choice. For each model presented, the implications of the model as well as the limitations of the model will be discussed. Students will be actively involved in the modeling process. There is no particular mathematical prerequisite for this course though we will do some algebraic computations from time to time and discuss deductive proofs of some of the main results. Prerequisite: eligibility for Q courses.

A course for students who intend to take calculus and need to acquire the necessary skills in algebra and trigonometry. The concept of function is stressed, with particular attention given to linear, quadratic, general polynomial, trigonometric, exponential, and logarithmic functions. Graphing in the Cartesian plane and developing the trigonometric functions as circular functions are included. This class makes extensive use of the TI-82 graphing calculator. Prerequisites: eligibility for Q courses, satisfactory performance on precalculus entrance exam.

An introduction to the basic ideas of differentiation and integration in one variable. Topics include limits, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications. Prerequisite: background in precalculus mathematics.

An introduction to the basic ideas of differentiation and integration in one variable. Topics include limits, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications. Prerequisite: background in precalculus mathematics.

This course will start with a review of definite integration and introduce several important techniques of integration. Several applications of the definite integral will be discussed. To begin the study of multivariable calculus we will discuss the basic geometry of vectors in two and three dimensional Euclidean space. From there the topics covered will include: graphs of multivariable functions including contour maps, partial differentiation and the gradient, the chain rule, multiple integration, and change of variables. Prerequisite: Mathematics 111 or permission of the instructor.

This course introduces students to the methodology of mathematical proof. The logic of compound and quantified statements, mathematical induction, and basic set theory including functions and cardinality are covered. Topics from foundational mathematics are developed to provide students with an opportunity to apply proof techniques. Prerequisites: permission of the instructor.

An introduction to modern abstract algebraic systems. The structures of groups, rings, and fields are studied together with the homomorphisms of these objects. Topics include equivalence relations, finite groups, group actions, integral domains, polynomial rings, and finite fields. Prerequisite: Mathematics 331 or permission of the instructor.

An introduction to the classical methods of solving ordinary and partial differential equations, including such topics as: description of some equations arising in the physical sciences, Laplace transforms, matrix methods, Fourier series. Prerequisite: Mathematics 331, or permission of the instructor.

An introduction to the rigorous study of functions of real variables. Topics include the topology of Euclidean spaces, continuity, convergence, and the Riemann integral. Proofs will be emphasized. Prerequisites: Mathematics 231 or permission of the instructor.