Real numbers, topology of Euclidian space, integration, continuity, differentiability, sequences, and series of functions. Prerequisite: MATH 211. (Offered spring semester only.)

Herbert S. Gaskill and P.P. Narayanaswami, Element of Real Analysis, Prentice Hall 1998.

Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics

Students majoring in mathematics.

1. To develop a rigorous understanding of the real number system and its properties
2. To develop a rigorous understanding of real-valued functions with an emphasis on the properties of continuity, differentiability, and integrability
3. To develop a rigorous understanding of sequences and series.
4. To introduce students to graduate-level mathematics.
5. To develop an ability to state and prove theorems
6. To enhance the learning process by using technology as a tool to reinforce, expedite, and display mathematical concepts.

MATH 211 (Calculus III) or equivalent.

1. Properties of the real number system:  a) algebraic properties, b) order properties, c) completeness, d) absolute value, and e) countability.
2. Sequences: a) the limit of a sequence, b) limit theorems, c) Monotoneity, and d) the Cauchy criterion.
3. Limits and continuity: a) the limit of a function b) continuous functions, c) continuity on intervals, d) properties of continuous functions, and e) inverse functions.
4. Topological concepts:  a) open and closed sets, b) properties of closed sets, and c) uniform continuity.
5. Differentiation: a) the Mean Value Theorem, b) L'Hopital's rule, and c) Taylor's Theorem.
6. Integration: a) the Riemann integral, b) the Fundamental Theorem of Calculus, and c) the integral as a limit.

1. Modern classrooms (Frey 343-349) equipped with a computer teaching station and VCR.
2. Several computer labs (Frey 145, 166, and 245) equipped with appropriate software.
3. The mathematics reading room (Frey 351).
4. Student math resource people available Monday through Thursday nights in Frey 349 and 351.

Three one-hour lecture sessions per week with homework and exams.