MAT 127A: Real Analysis (Fall 2019), CRN 48776 (A01), 48777 (A02)

     Finals week information:

Final Exam Time and Place: Wednesday, Dec. 11, 10:30am-12:30pm, in 168 Hoagland, the room where our class meets. Bring a pencil and your university ID!

Review Session: Tue., Dec. 10, 1:10-3pm, 204 Art.

Regular OH: Monday, December 9, 1:10-2pm, at my office (3210 Math). There will be no other regular OH during Finals week.

Administrative OH: Tuesday, Dec. 10, 12:10-1pm, at my office (3210 Math). I will not answer questions about the class material during this OH, but we can talk about any other questions or concerns. You need to let me know of any special circumstances by 1pm on December 10.

Material covered on the final: sup and inf, max and min, completeness axiom and consequences, definition of limit of a sequence, algebraic and order limit theorems, monotone sequences and their convergence, subsequences, Bolzano-Weierstrass, infinite limits, limsup, liminf, Cauchy criterion, convergence of infinite series (definition, absolute convergence, conditional convergence, algebraic and order theorems, various tests for convergence), alternating series, rearrangements, geometric series, p-series, open sets, closed sets, accumulation (limit) points, isolated points, interior points, boundary points, closure of a set, compact sets (definition, Heine-Borel, open covers), connected sets, limit of a function, continuous functions, uniform continuity, continuous functions on compact sets, intermediate value theorem, monotone functions.

Study tips: Understand all examples we did in the lectures and in discussions. You also need to know how to solve homework problems and problems from the first two midterms. Solving the practice final problems on your own is a good to test of your preparation.