Lectures: 12.30pm-1.45pm on Tuesdays, Thursdays, in CSIC 4122 except when a CSCAMM Workshop takes place in the CSIC building.

Office Hour: by appointment.

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 630 Real Analysis I is the graduate level course in mathematics that presents in a rigouros manner fundamental concepts in analysis: Lebesgue measure and the Lebesgue integral on R, differentiation of functions of bounded variation, absolute continuity and fundamental theorem of calculus, L^p spaces on R, Riesz-Fischer theorem, bounded linear functionals on L^p, measure and outer measure, Fubini's theorem.

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. Elliot H. Lieb, Michael Loss, Analysis, ISBN 978 08218 27833, 2nd Edition, AMS