This fall, I am teaching History of Mathematics, Real Analysis I, and PreCalculus II: Trigonometry.
History of Mathematics
Historical development of various areas in mathematics and important figures in mathematics from ancient to modern times.
Real Analysis I
Introduction to real analysis. The main topics of single-variable calculus-convergence, continuity, differentiation, and series as they are applied and extended in advanced settings with emphasis on precise statements and rigorous proofs. Structure of the real numbers, open and closed sets. Integration, metric spaces, and other topics and applications as time allows.
PreCalculus II: Trigonometry
Angles and their measures; trigonometric functions; the circular functions of trigonometry; graphs of sine, cosine, tangent, cosecant, secant, and cotangent functions; algebra of trigonometric functions; inverse trigonometric functions; solving problems with trigonometry; analytic trigonometry; fundamental trig identities; proving trigonometric identities; sum and difference identities; multiple-angle identities; the Law of Sines; the Law of Cosines.