Department of Mathematics & Statistics
Basic Algebra I
- Sept. 2-Sept 9:
Overview of the course. Sets,
relations, and functions.
Induction. Number systems
including complex numbers. Equivalence relations.
- Sept 12-Sept 16: (Chapter 1)
Arithmetic in Z. The division algorithm.
The Euclidean algorithm and gcd's.
- Sept 19-Sept 23: (Chapter 1)
Fundamental theorem of arithmetic.
- Sept 26-Sept 30: (Chapter 2)
Congruences. Modular arithmetic. Finite fields.
- Oct 3-Oct 7: (Chapter 3)
Rings. Definitions and basic examples. Isomorphisms and homomorphisms.
- Oct 10-Oct 14: (Chapter 4)
Arithmetic in polynomial rings. Division algorithm and
- Oct 17-Oct 21: (Chapter 5)
Congruences in polynomial rings. More on finite fields.
- Oct 24-Oct 28:
Review of the material, and midterm test (to be
given, in-class, on Friday October 28.)
- Oct 31-Nov 4: (Chapter 6)
Ideals and quotient rings.
- Nov 7-Nov 11: (Chapter 6)
Ideals and quotient rings. Introduction to groups.
- Nov 14-Nov 18:
(Sections 7.1 -7.5)
Group theory. Definition and basic examples. Subgroups,
isomorphism and homomorphism. Lagrange's theorem.
- Nov 21-Nov 25:
More group theory. Normal subgroups, quotients, and homomorphisms.
- Nov 28-Dec 2:
Review of the material.
- Dec 5: Final exam.