Geometrical mathematics involves many topics other than traditional Euclidean geometry. This course explores various topics from semester to semester and may include some, but not all of the following: symmetry, groups, frieze and wallpaper patterns, graphs, surfaces, knots, and higher dimensions.

Prerequisite: eligibility for Q courses and a willingness to explore new ideas and construct convincing arguments is a necessity.

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 course, 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.

See above.

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 will provide an overview of one of the oldest and most beautiful areas of mathematics. It is ideal for any student who wants a taste of mathematics outside of the calculus sequence. Topics may include: number puzzles, prime numbers, congruences, quadratic reciprocity, sums of squares, Diophantine equations, cryptography, coding theory, and continued fractions.

Prerequisite: precalculus or permission of the instructor.

This course is both an introduction to ordinary differential equations as well as the final course in our three-semester Calculus sequence. The course is organized around methods for solving ordinary differential equations, and incorporates ideas from Calculus as needed (such as sequences and series). Topics include first and second order differential equations, Laplace transforms and series solutions.

Prerequisite: Math 111 and Math 114, 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 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.

Graph theory is a branch of mathematics that has applications in areas ranging from operations research to biology. This course is a survey of the theory and applications of graphs. Topics will be chosen from among connectivity, trees, Hamiltonian and Eulerian paths and cycles; isomorphism and reconstructability; planarity, coloring, color-critical graphs and the four-color theorem; intersection graphs, vertex and edge domination; matchings and network flows, matroids and their relationship with optimization, and random graphs. Several applications of graph theory will be discussed in depth.

Prerequisites: Math 231 or permission of the instructor.