Peter J. Littig
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.
This course will cover the historical and theoretical development of various number systems, including the natural numbers, the integers, the rational numbers, the real numbers, and the complex numbers. An investigation of polynomials and their roots will be a highlight of the course. As time permits, we will also cover more "exotic" systems such as the quaternions, the octonions, and the Gaussian integers.
Student learning goals
Define and give explicit constructions of several important number systems.
Describe the historical origins of these number systems.
Use precise mathematical language to communicate ideas and demonstrate proofs of basic propositions.
Learn the axioms for a mathematical field, and apply them in specific examples.
Perform mathematical computations to solve problems.
General method of instruction
Interactive lectures, small group work, and student presentations.
There are no official requirements beyond the university's general entrance requirements. Students should be prepared, however, to learn and work with new and challenging mathematical concepts and methods. Students should also be curious about mathematics and mathematical thinking.
Class assignments and grading
Students will receive regular homework assignments, including both reading assignments and problem sets. Problem sets will involve mathematical computations and introductory-level proofs.
There will be several quizzes spaced throughout the quarter, as well as a midterm exam and a final exam.
Student grades are based on exam performance, HW effort, and in-class participation.