Honors Analysis I

Catalog description

This is an introduction to the rigorous treatment of the foundations of real analysis in one variable. It is based entirely on proofs. Students are expected to know what a mathematical proof is and are also expected to be able to read a proof before taking this class. Topics include: properties of the real number system, sequences, continuous functions, topology of the real line, compactness, derivatives, the Riemann integral, sequences of functions, uniform convergence, infinite series and Fourier series. Additional topics may include: Lebesgue measure and integral on the real line, metric spaces, and analysis on metric spaces. | Prerequisites: A grade of A- or better in ( MA-UY 2114 or MA-UY 2514 ) and ( MA-UY 1044 or MA-UY 2034 or MA-UY 3054 ) and Junior level standing or above. Recommended: MA-UY 2514 Honors Calculus III and MA-UY 3054 Honors Linear Algebra with a grade of B+ or better. | Anti-Requisite: MA-UY 4614