Department of Mathematics & Statistics
Basic Algebra I
- Sept. 1-Sept 3:
Overview of the course. Sets,
relations, and functions.
Induction. Number systems
including complex numbers. Equivalence relations.
- Sept 8-Sept 10: (Chapter 1)
Arithmetic in Z. The division algorithm.
The Euclidean algorithm and gcd's.
- Sept 13-Sept 17: (Chapter 1)
Fundamental theorem of arithmetic.
- Sept 20-Sept 24: (Chapter 2)
Congruences. Modular arithmetic. Finite fields.
- Sept 27-Oct 1: (Chapter 3)
Rings. Definitions and basic examples. Isomorphisms and homomorphisms.
- Oct 4-Oct 8: (Chapter 4)
Arithmetic in polynomial rings. Division algorithm and
- Oct 11-Oct 15: (Chapter 5)
Congruences in polynomial rings. More on finite fields.
- Oct 18-Oct 22:
Review of the material, and midterm test (to be
given, in-class, on Friday October 22.)
- Oct 25-Oct 29: (Chapter 6)
Ideals and quotient rings.
- Nov 1-Nov 5: (Chapter 9)
Integral Domains. Unique factorization in number rings. Application to
- Nov 8-Nov 12: (Chapter 9)
More on rings, Integral domains, and quadratic integers.
- Nov 15-Nov 19: (Sections 7.1 -7.5)
Group theory. Definition and basic examples. Subgroups,
isomorphism and homomorphism. Lagrange's theorem.
- Nov 22-Nov 26: (Sections 7.6-7.9)
More group theory. Normal subgroups, quotients, and homomorphisms.
- Nov 29-Dec 3:
Review of the material.