Real Analysis

Math 112 - Harvard University - Spring 2002
MWF 12:00-1:00, Science Center 507
Instructor: Curtis T McMullen

Required Text: Marsden and Hoffman, Elementary Classical Analysis, 2nd edition, Freeman, 1993.
Click here for a list of corrections to the text.
For more about learning to write mathematical proofs, see: Daniel Solow, How to Read and Do Proofs.

Prerequisites: Multivariable calculus (Math 21a,b or 23a,b) and the ability to write proofs (or concurrent enrollment in Math 102). Not to be taken in addition to Math 25a,b or 55a,b. This course is not offered pass/fail.

Topics. This course will cover the rigorous foundations of analysis and calculus. Topics may include:
  • Set Theory and the Real Numbers
  • Topology of Euclidean Space
  • Compact and Connected Sets
  • Continuous Maps
  • Uniform Convergence
  • Differentiable Maps
  • Implicit Functions
  • Measure Theory and Integration
Reading and Lectures. Please read the book before coming to class! Students are responsible for all topics covered in the readings and lectures. Lectures may go beyond the reading, and not every topic in the reading will be covered in class.

Grades. Grades will be based on homework and quizzes (40%), the midterm (20%) and the final (40%).

Homework. Homework will be assigned every week. Late homework will not be accepted. Collaboration between students is encouraged, but you must write your own solutions, understand them and give credit to your collaborators.

30 Jan (W) First class
18 Feb (M) President's day
11 March (M) In-class midterm
25-29 Mar (M-F) Spring recess
3 May (F) Last class
4-15 May (Sa-W) Reading period
6-8 May (M-W) Take-home final exam

Course home page: