Instructor | Dr. Mark Comerford |
Office | Lippitt 102 F |
Phone | 874 5984 |
mcomerford@math.uri.edu | |
Office Hours |
Tuesday 2 - 4 pm or by appointment |
Texts | Russell A. Gordon Real Analysis - A First Course (Second Edition), ISBN-10 0201437279
Theodore W. Gamelin,
Robert Everist Greene
Bert Mendelson |
Prerequisites | Mth 243 or equivalent |
Lectures and Homework Problems
Section | Problems |
0.1 Mathematical Logic | Homework 1 |
0.2 Sets and Functions | |
0.3 Mathematical Induction | |
1.1 Real Numbers | 10, 11, 14 |
I Metric Spaces | 2.2: 4 |
1.2 Absolute Value, Intervals and Inequalities | 8, 17, 21 | I Open and Closed Sets, Neighbourhoods | 2.4: 6 |
1.3 The Completeness Axiom | 6, 19, 21 |
II Density and Sequences in Metric Spaces | TBA |
1.4 Countable and Uncountable Sets | 9, 5, 8 |
1.5 Real-Valued Functions | |
2.1 Convergent Sequences | 5, 9 |
III Cauchy Sequences | II, III Problems |
2.2 Monotone and Cauchy Sequences | 2, 27 (27 is extra credit) |
2.3 Subsequences | 12 |
IV Limits, Continuity | TBA |
2.4 Supplementary Exercises | 18 |
3.1 The Limit of a Function | 10, 27 |
3.2 Continuous Functions | 10 |
3.3 Intermediate and Extreme Values | 7, 23 |
3.4 Uniform Continuity | 4, 5 |
3.5 Monotone Functions | |
3.6 Supplementary Exercises | IV Completeness, the Contraction Mapping Principle |
Completeness Problems |
4.1 The Derivative of a Function | 3 |
4.2 The Mean Value Theorem | 10 |
4.3 Further Topics on Differentiation | |
4.4 Supplementary Exercises |
Here is a link to Theorems 4.30 and 4.31 at the end of the course whose proofs we did not have time to cover in class.
A list of the theorems whose proofs you need to know for the final can be found here.
Exams
Midterm | 3 - 4:15pm, Wednesday October 16 Lippitt 204 |
Final | 3 - 6pm, Friday December 13 Lippitt 204 |
Evaluation
Homework | 40% |
Midterm | 25% |
Final | 35% |
Course Description
This course is an introduction to the wonderful world of real numbers, real analysis and topology. The course is self-contained and so no initial knowledge of real analysis is required. However, familiarity with calculus concepts up to and including math 243 (multivariable calculus) is essential and math 307 (Introduction to Mathematical Rigor) is highly desirable. In real analysis we will cover the material in the first four chapters of Gordon's book up to differentiation and the mean value theorem while in topology we will cover the basic results on metric spaces.
In addition to covering the course material, there will be strong emphasis on mathematical rigor and mastering techniques of proof. This is reflected in the rather large percentage of the overall grade which is given over to homework which will be assigned weekly.
In addition to homework, there will be one midterm (provisional date Monday October 15) and a final. The material covered in the exams will be partly based on the homework, but there is also some expectation that there will be unseen problems. In addition, you may be asked to give proofs of theorems covered in class and you will be given in advance a list of those theorems which are examinable.
Goals and Objectives
The goals of the course are to have you develop the skills of working with real numbers, limits, continuity and differentiability.
At the conclusion of this semester you should be able to:
Special Accommodations
Students who need special accomodations and who have documentation from Disability Services should make arrangements with me as soon as possible. Students should conact Disability Services for Students, Office of Student Life, 330 Memorial Union, 874-2098.