Syllabus

This course in elementary number theory will cover most of the material in the first nine chapters of the text with possibly a few side excursions. The goals of this course include learning the beautiful theorems of elementary number theory, growing in the ability to read, understand, and write proofs, and developing skills in problem solving and logical thinking. We begin by learning mathematical induction and the well-ordering principle, two important and equivalent proof tools. Divisibility theory and the solution of Diophantine equations, and the Fundamental Theorem of Arithmetic lay the foundation for all later work. The theory of congruences simplify our work with linear equations, and we work toward the solution of quadratic equations by proving the Quadratic Reciprocity Law. Our journey will be highlighted by Fermat's Little Theorem, Wilson's Theorem, Arithmetic Functions, the Mobius Inversion Formula, Euler's Theorem applied to Cryptography, and the Theory of Indices.

Requirements

Your grade in the course will be based on 600 possible points. There will be three one-hour exams given during the semester, each covering about four weeks of work. Each one-hour exam will be worth 100 points. Homework will be collected and graded regularly. The total of all graded homework will be worth 100 points. The comprehensive final exam given at the end of the course will be worth 200 points. Clarity of thought and expression are important both on homework assignments and on exam solutions. This course will be challenging, but rewarding because hard work, perserverance, and attention to detail will usually be rewarded with success. Working in teams is valuable, but independent thinking is essential.

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Created 01/02/2003. Last modified 01/02/2003. Email to ekh@wfu.edu