## Math 444. Elementary Real Analysis

Instructor Syllabus

**Text:** R. B. Bartle and D. R. Sherbert, * Introduction to Real Analysis,* *4th Edition*, John Wiley & Sons

Chapter | Class Hours | |

1. | Preliminaries (Treat Sections 1.1, 1.2 lightly. Cover Section 1.3.) |
3 |

2. | The Real Numbers (Sections 2.1, 2.2 should be covered quickly, with emphasis placed on 2.3 and 2.4. The discussion of decimals in 2.5 can be omitted.) |
5 |

3. | Sequences (Section 3.6 can be omitted.) |
9 |

4. | Limits (Omit Section 4-3) |
3 |

5. | Continuous Functions (Omit Sections 5.5 and 5.6. Omit approximation in (p. 140-144) Section 5.4) |
6 |

6. | Differentiation (Omit Sections 6.3, 6.4.) |
3 |

7. | The Riemann Integral (Omit Section 7.4) |
6 |

8. | Sequences of Functions (Cover 8.1 and as much of 8.2 as time permits.) |
4 |

Leeway and Exams | 4 | |

Total | 43 |

This course is an introduction to ε - δ analysis on the real line for students who do not plan graduate study in mathematics. (Those students should take Math 447.) The students do not have much experience in writing proofs, and they will need practice in doing so. They should leave the course not only with a basic understanding of the fundamental concepts of real analysis, but also an improved ability at reading and writing mathematical arguments. Regular homework is an important aspect of the course.

Revised 11/18/10