**General Info:**

- Time: Mo We 5:30PM--6:45PM
- Classroom: SCC 1304
- CRN: 41820

**Prerequisites**: MAT 211
and MAT 271 with grade C or better.

**Textbook**: Introduction to
Analysis by Maxwell Rosenlicht ISBN-13: 9780486650388 Dover
Publications

**References**

- Basic Analysis: Introduction to Real Analysis by Lebl. It was used as the textbook by Dr. Jennings.
- Elementary Analysis: The Theory of Calculus by Kenneth A.Ross. This is one of the books that I learnt the subject from.
- Introduction to Real Analysis by Robert G. Bartle and Donald R. Sherbert. I have used this as the textbook when I was visiting the National University of Singapore.
- Mathematical Analysis (A straightfoward approach) by K.G.Binmore it explains many of the topics at a more leisure place.

There are also a few classic analysis books listed in "Suggestions for Further Reading" of our textbook. If you want to go further, read Rudin and Royden's books. (both have newer editions).

**Syllabus**: The system
of real numbers, metric spaces, continuous functions and differential
functions. This roughly corresponds to Chapter 2, 3 and 4 of the textbook.

**Course Management**:
BlackBoard

**LaTeX:** is a modern typesetting system for mathematics and
more. Visit The LaTeX Project
for more information.

Overleaf is a web-base service (has free option) that allows you to use LaTeX without installing it on your machine. ShareLaTeX is another one. And these services are going to merge.

**Homework:** can earn you up to 5 extra-credit points. To
earn them you need to present homework problems in class and typeset them
in LaTeX.

**Test: **

- Test 1 (25 pts), on Chapter 2, (9/20)
- Test 2 (25 pts), on Chapter 3, (11/01)
- Test 3 (25 pts), on Chapter 4, (12/04)
- Final Exam (25 pts+5 extra credits), accumulative, (Dec 13) 5:30pm--7:30pm.

**Grading Scheme**:

A | A- | B+ | B | B- |

100--93 | 92--89 | 88--84 | 83--79 | 78--74 |

C+ | C | C- | D+ | D |

73--69 | 68--64 | 63--59 | 58--54 | 53--50 |

**Schedule Outline**:
Chapter 2,3 and 4. There are roughly 85 pages of materials.

**Tentative Schedule**

08-21 | The field properties | 08-23 | Order |
---|---|---|---|

08-28 | The least upper bound property | 08-30 | The least upper bound property |

09-04 | Labor Day | 09-06 | Existence of square roots |

09-11 | discussion | 09-13 | discussion |

09-18 | discussion | 09-20 | Test 1 |

09-25 | Metric Spaces | 09-27 | Open and Closed sets |

10-02 | Open and Closed Sets | 10-04 | Convergent sequences |

10-09 | Completeness | 10-11 | Completeness |

10-16 | Compactness | 10-18 | Compactness |

10-23 | Connectedness | 10-25 | discussion |

10-30 | discussion | 11-01 | Test 2 |

11-06 | Definition of continuity | 11-08 | Continuity and Limits |

11-13 | Continuity of Rational operations | 11-15 | Continuous functions on a compact space |

11-20 | Continuous functions on a compact space | 11-22 | Continuous functions on a connected space |

11-27 | discussion | 11-29 | discussion |

12-04 | Test 3 |

**Learning Outcomes**: Please
refer to this
Expected Outcomes section.

**Other Policies**: For
policies on academic integrity, accommodation for students with
disabilities, due dates and make-up work and various other topics,
please consult this page .