Explores the concept of number from an historical perspective and the modern mathematical perspective. Stresses the new properties of "'number"', starting with counting numbers and progressing to the concept of a field.
The concept of number will be studied from a historical perspective and the modern mathematical perspective. Starting with counting numbers and progressing to the concept of a field, the new properties of "number" will be stressed. As a capstone, modern error correcting codes of the digital highway will be constructed using the "arithmetic" and properties of finite fields.
The course will have two goals. First, the students will be exposed to a historical view of number to show how the modern concept of number came about. The second goal will be to develop the basic mathematical thinking of the students by stressing the properties of numbers and how these properties allow us to do our everyday "arithmetic".
Student learning goals
General method of instruction
Prerequisites are an honest intellectual curiosity and the willingness to work hard.
Class assignments and grading
The only way that students can learn to do mathematics is to try to do it. Therefore, there will be problems assigned along with the historical readings. The personal computer will be used in the course. Besides the homework problems, there will be three quizzes and a final project.