Real Analysis III: MATH4001

Academic Year 2015-2016


General Information:

  • Instructor: Dr. Youness Lamzouri.
                           Office: N515 Ross Building.
                           Email: lamzouri@mathstat.yorku.ca.
                           Website: www.math.yorku.ca/~lamzouri.

  • Time and location : Monday, Wednesday and Friday 1:30-2:30 pm in VH 1020 (Vari Hall).

  • Office hours: Wednesdays and Fridays 11:30 am-12:30 pm, or by appointment.

  • Textbook: "Real Analysis" by N. L. Carothers. Cambridge University Press.

  • Course Description :

    This course aims to broaden and deepen the student's knowledge in real analysis. It provides an essential basis for further study in several mathematical areas including functional analysis, probability theory and harmonic analysis. The first part of the course covers the topology of metric spaces and normed vector spaces with the objective of generalizing several notions including continuity and limits to a more abstract setting. The second part serves as a transition from the discussion of abstract spaces to concrete spaces of functions including a study of the Riemann-Stieltjes integral and Fourier analysis. The third and last part of the course concerns Lebesgue measure and integration on the real line.


    Course Evaluation:

  • 20% Assignments : There will be four assignments counting for 5% each. Late assignments will not be accepted.

    Assignment 1 (Due Wednesday Oct 28, 2015 at the beginning of class).

    Assignment 2 (Due Monday December 7, 2015 at the beginning of class).

    Assignment 3 (Due Monday February 22, 2016 at the beginning of class).

    Assignment 4 (Due Wednesday April 6, 2016).

  • 45% Midterm exams: There will be three midterm exams counting for 15% each. Detailed exam syllabi will be posted about one week before each exam date. There will be no makeup midterms. If you miss a midterm exam and have a valid excuse (with an acceptable documentation), the exam weight will be transferred to the final exam. The Tentative dates for the midterms are:
             - First midterm exam: Monday November 2, 2015.
             - Second midterm exam: Monday December 7, 2015.
             - Third midterm exam: Monday February 22, 2016.

  • 35% Final Exam: The final exam will be comprehensive. It will be scheduled by the registrar for the April exam period.