Lectures: 11.00am-12.15pm on Tuesdays, Thursdays, in CSIC 4122 except when a CSCAMM Workshop takes place in the CSIC building.

Office Hour: by appointment with preference for Tuesdays 3:30pm-4:30pm.

Assignments: Homework must be submitted on the date assigned. Homework must be prepared without consulting any other person. You may however consult any written reference. In this case you should cite the reference. Results taken from the reference should be (re)stated to the notation used in the course. Explanation should be given in complete English sentences. Written work must be legible and clear.

Description: MATH 631 Real Analysis II is the continuation of MATH 630 Real Analysis I. In particular it presents: Abstract measure and integration theory, metric spaces, Baire category theorem and uniform boundedness principle, Radon-Nikodym theorem, Riesz Representation theorem, Lebesgue decomposition, Banach and Hilbert Spaces, Banach-Steinhaus theorem, topological spaces, Arzela-Ascoli and Stone-Weierstrass theorems, compact sets and Tychonoff's theorem.

Prerequisite: MATH 630

Grading: 25% Homeworks ; 25% Mid-Term Exam ; 50% Final Exam

References: Required textbook: Barry Simon, Real Analysis, ISBN 978 14704 10995, AMS 2016. Recommended textbooks: John Benedetto, Wojciech Czaja, Integration and Modern Analysis, ISBN 978 0817 643 065, Birkhauser/Springer 2009. H.L. Royden and P.M. Fitzpatrick, Real Analysis, 4th Edition, Pearson 2010.