Math 424: Honors Real Analysis

Fall 2017


Instructor: Florin Boca

Office: 371 Altgeld Hall

Phone: 244-9928

E-mail: fboca at illinois dot edu


Textbooks:

  • Maxwell Rosenlicht, Introduction to Analysis, Dover, 1986, electronic resource
  • Kenneth R. Davidson and Allan P. Donsig, Real Analysis and Applications: Theory in Practice, Springer 2010, electronic resource

  • Course description: A rigorous treatment of basic real analysis via metric spaces recommended for those who intend to pursue programs heavily dependent upon graduate level Mathematics. Metric space topics include continuity, compactness, completeness, connectedness and uniform convergence. Analysis topics include the theory of differentiation, Riemann-Darboux integration, sequences and series of functions, and interchange of limiting operations. As part of the honors sequence, this course will be rigorous and abstract. 3 undergraduate hours. No graduate credit. Credit is not given for both Math 424 and either Math 444 or Math 447. Approved for honors grading. Prerequisite: An honors section of MATH 347 or an honors section of MATH 416, and consent of the department.


    Syllabus:

  • The real number system
  • Metric spaces
  • Continuous functions
  • Differentiation and Riemann integration
  • Interchange of limit operations

  • Lectures: MWF 2:00-2:50, 443 Altgeld Hall

    Office hours: Monday 3:30-4:30, Thursday 5:00-6:00


    Grading policy: Comprehensive final exam: 35%; Best two midterm scores (out of three tests): 40%; Homework and quizzes: 20%; Class participation: 5%.


    Midterm exams calendar: M1: Wed Sep 27, M2: Wed Oct 25, M3: Wed Nov 29.

    Final exam: 8:00-11:00 am, Friday, Dec 15, 443 Altgeld Hall


    Last modified: August 27, 2017