New York University 4 credits Math
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: Minimum grades of A- in MATH-UA 123 or MATH-UA 133 and MATH-UA 140 or minimum grades of B+ in MATH-UA 129 and MATH-UA 148.
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