Real Analysis II: MATH3001

Winter 2014


General Information:

  • Instructor: Dr. Youness Lamzouri.
                           Office: N515 Ross Building.
                           Email: lamzouri@mathstat.yorku.ca.
                           Website: www.math.yorku.ca/~lamzouri.
  • Lectures: Tuesdays and Thursdays, 5:30-7:00 pm, in ACE 007 (Accolade East).
  • Office hours: Tuesdays and Thursdays, 2:30-3:30 pm.
  • Textbook: "Principles of Mathematical Analysis" by Walter Rudin. McGraw-Hill, Third edition, 1976.

  • Course Description :

    This course is the second in a three course sequence in real analysis. It provides an essential background for a variety of higher level undergraduate and graduate courses including those in analysis, probability, geometry and topology. We will essentially cover Chapters 1-7 of the textbook. Covered topics include: Metric spaces, compact and complete spaces, numerical sequences and series, power series, continuity, differentiation, Taylor's theorem, Riemann integration, the Riemann-Stieljes integral, sequences and series of functions, uniform convergence and the Weierstrass approximation theorem.


    List of practice problems:

  • Week 1 (Jan 6-10): Pages 21-23 : 1, 2, 5, 11, 12.

  • Weeks 2 and 3 (Jan 13-24): Pages 43-46 : 5, 6, 7, 9, 10, 11.

  • Weeks 4 and 5 (Jan 27 - Feb 7): Pages 43-46 : 13, 14, 15, 16, 18, 22, 24, 29. Pages 78-82 : 1, 23, 24 a) and b).

  • Week 6 (Feb 10-14): Pages 78-82 : 4, 5, 6, 7, 14 a), b) and c), 16, 17.

  • Weeks 7 and 8 (Feb 24 - March 7): Pages 78-82: 9, 10, 13. Pages 98-102: 1, 2, 3, 4, 6, 8, 9, 11, 12.

  • Weeks 9 and 10 (March 10-21): Pages 98-102: 15, 17, 18, 19, 20. Pages 114-119: 1, 2, 4, 6, 11, 15, 22, 25. Pages 138-142: 2, 7, 8.

  • Weeks 11 and 12 (March 24 - April 4): Pages 138-142: 10, 11, 12, 15. Pages 165-171: 2, 3, 4, 5, 6, 7, 12, 23.


    Course Evaluation:

  • 20% Assignments : There will be two assignments counting for 10% each. Late assignments will not be accepted.

    Assignment 1 (Due Tuesday February 25, at the beginning of class).
    Solution to Assignment 1.

    Assignment 2 (Due Friday April 11).

  • 30% Midterm exam: The tentative date for the midterm exam is: Tuesday, February 25, 2014.
    Midterm syllabus: Chapters 1, 2, and Chapter 3 except the sections: Power series, Summation by parts, Addition and multiplication of series and rearrangements.
    There will be no makeup exam. If you miss the midterm exam and have a valid excuse (with an acceptable documentation), the exam weight will be transferred to the final exam.

    Here is the solution and marking scheme of the midterm exam.

  • 50% Final exam: The final exam will be comprehensive. It will be held on Friday April 11 from 7:00 to 10:00 pm in ACW205. Here is the syllabus for the final exam. I will hold extra office hours on Wednesday April 9, from 11:00 am-1:00 pm.