Course Overview
Mathematics originated in the distant past as our ancestors tried
to understand the world around them.
First, we will survey the role that problems and problem-solving
have played in the historical development of mathematics.
In Lecture 1 we will cover Mesopotomian and
Egyptian mathematics. The appropriate section in
Math 629 can be
found here
We will then go over the basic elements of problem solving:
- Models
- Abstraction
- Conjectures
- Hypotheses
- Proofs (Heuristic, Rigorous)
- Generalizations
We will be covering material from chapters 8-13 of
the manuscript
Survey of Mathematical Problems, by
Professors H. Boas and S. Geller.
In the remainder of the course we will focus on both historically
significant problems, basic or fundamental problems, as well as some open problems,
in a selection of the following areas:
- Algebra
- Algorithms and Complexity
- Calculus of Variations
- Complex Analysis
- Differential Equations
- Proofs, Logic, Foundations and Paradoxes
- Real Analysis
Students will select 2 or 3 of these topics, in consultation with the
instructor. The student will then
- Identify several historically important problems, which affected the
development of the mathematical area.
- Construct a web page summarizing the student's research.
- 2 or three basic/fundamental problems will be given to the student.
The solution of these will then be graded by the instructor.
- Students will have the option to given either a take home final exam,
or a final project.