Mathematics 190 - Syllabus - Fall 2006
Dr. Lawrence Fearnley
This is a required course on foundations for advanced mathematics which uses notes provided by the professor, plus references literature as appropriate.
The goal of the course is to communicate to students what constitutes mathematical rigor, how a mathematician develops the creativity to make new discoveries, and prove them to a level that would be required by the professional mathematician.
The following topics are included:
A. Mathematical Logic:
The Propositional Calculus
The Predicate Calculus
Set Theory
Axiom Systems
Hausdorff Maximality Principle
Gšdel's Theorems
B. Foundations of Principal Mathematical Subspecialties:
Group Theory
Topology
Analysis
C. Special attention is given to foundation theorems which help the student to successful subsequently in Advanced Calculus.
Structure of the Course
The method of teaching this course involves providing to the student a carefully structured sequence of axioms, definitions, and theorems which are designed to fit the needs of the student and are adjusted continuously to the rate of progress of the student. The university professor who pioneered this course structure, who has been called in the mathematical literature "the greatest math teacher ever," established the special benefits of this program by producing outstanding students, some of whom became presidents of the American Mathematical Society.
Grading
1. The conventional methods of evaluation, namely examinations and assignments, including a comprehensive final examination.
Plus
2. The student's achievements in proving theorems in class, with credit rewards on the basis of the number and difficulty of the problems solved by the student.