Prerequisites:
Graduate standing,
Undergraduates with permission of the instructor.
Audience:
Core mathematics course. Beginning graduate students in mathematics. Interested
students in engineering. Well motivated
senior undergraduate mathematics majors.
Date | Posted Notes | Topics | Sections | Homework |
9/24/01 | Lecture One | Review of Advanced Calculus | 2.1,2.2,2.3,2.4,2.5 | Homework One |
10/1/01 | Lecture Two | Topology of the Reals | 2.5,2.6,2.7 | Comments on Homework One |
10/15/01 | Lecture Three | Topology of Reals; Lebesgue Measure | 2.6, 3.1, 3.2 | Homework Two |
10/22/01 | Lecture Four | Measure Theory | 3.2,3.3,3.4 | Comments on Homework Two |
10/29/01 | Lecture Five | Measurable Functions | 3.4,3.5,3.6 | Homework Three |
11/05/01 | Lecture Six | Lebesgue Integral | 4.1,4.2 | Comments on Homework Three |
11/12/01 | Lecture Seven | Convergence Theorems | 4.2,4.3,4.4 | Homework Four |
11/19/01 | Lecture Eight | Differentiation | 5.1,5.2,5.3 | Comments on Homework Four |
11/26/01 | Lecture Nine | Hausdorff Measures | Hand-Out | Homework Five |
12/03/01 | Lecture Ten | Fractal Dimension | Hand-Out | Comments on Homework Five |
12/10/01 | Review Material | Final |
Role of Course in the Graduate Curriculum:
This course gives an introduction to measure theory and integration.
These topics are essential for a deeper understanding of probability theory
and stochastic processes as well as approximation theory.
Course Goals:
Grading:
There will be four or five homework assignments. The questions illustrate the logical structure of the material, theorem proving, and computations.
Homework is worth 80% of the letter grade. The final examination is worth 20% of the grade. The final will have a take-home portion as well as an in-class part.
If a homework cannot be completed because of sickness or business travel, then the student should contact the instructor before the due date. There will be a special assignment available at the end of the term to make up any missed homeworks.
Letter grades will be given on the scale: 85% or better A, 70% -85% B, 55%-70% C, and so on.
Attendance:
Academic Honesty
The university's Academic Honesty policy is in effect for this course.
Please read Section 11: "Academic Honesty" in the Drexel University Student Handbook
to make sure you are familiar with this policy.
An electronic version of the Student Handbook appears on the 1998 Drexel CD.
You may visit the university's student handbook.