# Syllabus

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## Prerequisites

Calculus of Several Variables (18.02); Differential Equations (18.03) or Honors Differential Equations (18.034)

## Overview

This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, integration (roughly the first eight chapters of the textbook).

This course is CI-M (Communication Intensive in Major), so there will be required writing assignments and oral presentations. In the first half of the course, there will be periodic (short) writing assignments due in the recitations. The main writing assignment for the second half of the course is a paper, written in LaTeX, that has been revised twice, on a topic closely related to the material in 18.100. For example, one could start with one or more exercises in the text related to a common topic (e.g., Baire's theorem, the Cantor set, Cauchy sequences, conditionally convergent series, the Riemann zeta function etc.). Then, the subject can be developed by consulting some other reference (e.g., a short note or article in the *American Mathematical Monthly*, or a section in some other book). The final paper should be approximately 5 pages long. The writing should be aimed at a typical MIT math major, and it should reflect your own understanding of the subject. There will also be some oral presentations in recitation.

## Text

Rudin, Walter. *Principles of Mathematical Analysis.* 3rd ed. New York, NY: McGraw-Hill, Inc., 1976. ISBN: 007054235X.

## Exams

There will be two 90-minute in-class quizzes and one three-hour final exam.

## Homework

There will be 9 graded homeworks. You may discuss the homework problems with other students, but the final write-up should be entirely your own, and based on your own understanding.

## Grading

ACTIVITIES | PERCENTAGES |
---|---|

Final Exam | 25% |

Quizzes | 25% |

Homework | 25% |

CI-M | 25% |