| Course Schedule |
| Notes: These topics are meant to correspond, but only roughly, to class meetings. Pace and content may be modified at the discretion of the class. |
| Week 1 |
The Integers - The whole numbers, positive, negative and zero. Basic properties. Examples. |
| Week 2 |
The Relation of Divisibility and the Division Algorithm. Bases for the number system (Decimal, Binary, etc.). Examples. |
| Week 3 |
Primes, Greatest Common Divisors and Factorization. Irrational Numbers. Examples. |
| Week 4 |
Gauss and the Notion of Congruence. Fermat and Euler. Public Key Encryption. Examples. |
| Week 5 |
Polynomials - Basic properties. Examples. |
| Week 6 |
Divisibility and the Division Algorithm for Polynomials. Examples. |
| Week 7 |
Greatest Common Divisors. Factorization. The Remainder Theorem. Roots and Factors. Partial Fractions. Examples. |
| Week 8 |
Finding Roots. Creating Roots. The Methods of Hero and Newton. Cauchy. Solutions in Radicals. Examples. |
| Week 9 |
Algebraic Numbers. Transcendental Numbers. Notions of Galois Theory. A glimpse of algebraic number theory. Examples. |
| Week 10 |
Summary and Applications. Casting out nines. Decimal Representation of Fractions. Gaussian Integers. Pythagorean Triples. |
| Week 11 |
Some Geometry - Rigid Motions in the Plane. Similarities. Congruence and Similarity of geometric figures. Examples. |
| Week 12 |
The Group of Isometries. Its structure and the Classification of Isometries. Examples. |
| Week 13 |
Applications - The Conic Sections. Wallpaper Patterns. Foundations of Trigonometry. |
