Fall 2023

Math 112: Real Analysis

Instructor: Salim Tayou

E-mail: tayou@math.harvard.edu, Office: Science Center 238.

Schedule:

• Meeting times: Monday-Wednesday 09:00 AM-10:15 AM.
• Room: NW B101.
• First/last meeting: Wednesday, September 6th/ Monday, December 4th, 2023.
• Office hours: See Canvas or by appointment, in Science Center 238.

Syllabus:

This class is an introduction to mathematical analysis and the theory behind calculus. I am planning to talk about the following topics: the real numbers, completeness, cardinality, sequences and series, monotone convergence, Bolzano-Weierstrass, topology of the real numbers, limits of functions, continuous functions, intermediate value theorem, the derivative of a function, mean value theorem, Taylor’s theorem, the Riemann integral and its properties, fundamental theorem of calculus, sequences and series of functions, uniform convergence, power series and Taylor series, Weierstrass approximation theorem. Additional topics may include: special functions (exponential and logarithmic functions, trigonometric functions), Fourier series, the Gamma function, and an introduction to functions of several variables

Textbooks:

• Walter Rudin, "Principles of Mathematical Analysis" (3rd edition).
• Stephen Abbott, "Understanding Analysis" (2nd edition).

Prerequisites:

Math 19a/b or 21a/b and an ability to write proofs or concurrent enrollment in Mathematics 101 (or an equivalent background in mathematics).

Grading:

Homework will be assigned weekly. The solutions can either be scanned or typed and uploaded on Canvas. Homework will count for 70% of the final grade. Late homework can only be accepted under special circumstances. Collaborative work on homework is accepted but you must write your own solution as well as the names of the collaborators. There will be a midterm and a final exam, which will count for 30% of the grade.