Mathematics 414
Analysis II

University of Illinois at Chicago
Spring, 2008

  • General course description: Analysis is the branch of mathematics which includes the theoretical side of calculus. This course is a follow-up to Math 313, an introductory course which emphasizes building the subject up from the foundations. You should either have taken Math 313 or have an equivalent background in rigorous, theoretical mathematics. As in Math 313, the emphasis will be on proving everything that is stated. The main topics in the course will be uniform convergence, existence and uniqueness for solutions to ordinary differential equations, and Fourier series. Along the way we will touch on the theory of metric spaces and the geometry of inner product spaces. We will begin the course with a closer study of absolute convergence of series than the one undertaken in Math 313, with an emphasis on the differences between absolute and conditional convergence. Before each exam I will give a detailed list of topics that you are expected to know about.

  • Reading: There will be NO TEXTBOOK. All the material you are expected to know (apart from background from Math 313) will be covered in the lectures. Those who would like to do outside reading, especially to make up for gaps in their preparation, should see me for recommendations.

  • Homework: Problems will be assigned roughly once a week, and solutions will be due roughly a week after the problems are assigned. For problems that have been assigned so far, and solutions to problems for which the due date has passed, click here.

  • Exams and grades: Tentatively, I am planning to give a one-hour midterm and a final. The first hour exam may be given in the seventh or eighth week. Grades will be based on the homework (35%), midterm (25%), and final (40%).