Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

Prerequisites

18.02 Multivariable Calculus; 18.03 Differential Equations; or 18.034 Honors Differential Equations

Description

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.

The three options for 18.100:

• Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.
• Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.
• Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.

Textbook

Rudin, Walter. Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics). 3rd ed. McGraw-Hill, 1976. ISBN: 9780070542358.

Other Recommended Readings

Apostol, Tom M. Mathematical Analysis. 2nd ed. Pearson Education, 1974. ISBN: 9780201002881.

Spivak, Michael. Calculus. 4th ed. Publish or Perish, 2008. ISBN: 9780914098911.

Grading Policy

Note: In order to pass the course, you do have to satisfy the minimum requirements for the CI recitations, including attendance.