Current Teaching

Integration techniques. L'Hôpital's Rule. Improper integrals. Partial derivatives. Infinite sequences and series, power series. First-order differential equations, with applications.

Systems of linear equations and matrices. Determinants. Vector spaces. Inner product spaces. Eigenvalues and eigenvectors.

Limits, continuity, differentiability, rules of differentiation. Absolute and relative extrema, inflection points, asymptotes, curve sketching. Applied max/min problems, related rates. Definite and indefinite integrals, Fundamental Theorem of Integral Calculus. Areas, volumes. Transcendental functions (trigonometric, logarithmic, hyperbolic and their inverses).

This course covers the fundamentals of discrete mathematics with a focus on proof methods. Topics include: propositional and predicate logic, notation for modern algebra, naive set theory, relations, functions and proof techniques.

Systems of linear equations, matrices determinants, vectors, geometry, linear transformations, linear independence, basis, dimension, eigenvalues and eigenvectors, complex numbers, applications.

Implicit functions and differentiation. Related rates, concavity, inflection points and asymptotics. Optimization. L'Hôpital's rule. Applications of integration. Techniques of integration. Vectors: geometric and analytic descriptions; dot product, orthogonality and projection; cross product; lines and planes in 3-space.

Limits and continuity. Differentiation with applications. Newton-Raphson method. Integration; the Fundamental Theorem of Calculus.

This course is a continuation of Discrete Mathematics I. Topics include: recursion, induction, introduction to number theory including modular arithmetic and graph theory (time permitting).

Sets and relations, proposition and predicate logic, functions and sequences, elementary number theory, mathematical reasoning, combinatorics, graphs and trees, finite-state machines, Boolean algebra.

The syntax and semantics of propositional and predicate logic. Applications to program specification and verification. Optional topics include set theory and induction using the formal logical language of the first part of the course.

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.