Class Log
Numbers refer to sections of the textbook "An introduction to mathematical thinking" by W. Gilbert and S. Vanstone.
Monday 4/30/13. Review problems.
Friday 4/27/13. Review problems.
Wednesday 4/25/13. The fundamental theorem of algebra (continued).
Monday 4/23/13. The fundamental theorem of algebra (8.8).
Friday 4/20/12. Complex conjugation (8.3,8.4). The complex exponential function. DeMoivre's theorem (8.6).
Wednesday 4/18/12. Discussion of Midterm 2 solutions.
Tuesday 4/17/12. Complex numbers: Geometric interpretation of multiplication (8.5), roots of unity (8.7).
Monday 4/16/12. No class (Patriots' day).
Friday 4/13/12. Complex numbers: Definition and basic properties (8.1,8.2,8.3). Euler's formula.
Wednesday 4/11/12. Review of functions and cardinality.
Monday 4/9/12. Review of congruence and equivalence relations.
Friday 4/6/12. A union of countably many countable sets is countable. Examples: The set of algebraic numbers is countable, the set of finite subsets of the set of positive integers is countable.
Wednesday 4/4/12. The power set of a set X is ``strictly larger'' than X. A union of two countable sets is countable.
Monday 4/2/12. The set of rational numbers is countable, The set of real numbers is not countable (6.6). Algebraic and transcendental numbers.
Friday 3/30/12. Cardinality (continued), Countable sets. (6.6)
Wednesday 3/28/12. Examples of injective and surjective functions from calculus (6.5). Cardinality (6.6).
Monday 3/26/12. Injective and Surjective functions (6.5).
Friday 3/16/12. Inverse functions (6.4,6.5).
Wednesday 3/14/12. Chapter 6. Functions. The graph of a function. Composition of functions.
Monday 3/12/12. Chapter 5. Rational numbers, real numbers, and decimal expansions.
Friday 3/9/12. Equivalence relations (continued).
Wednesday 3/7/12. Equivalence relations (continued).
Monday 3/5/12. 3.3 Equivalence relations.
Friday 3/2/12. Solving equations modulo m (3.5,3.6).
Wednesday 2/29/12. 3.7 The Euler phi function and the Euler-Fermat theorem.
Monday 2/27/12. 3.5 Linear congruences and 3.6 The Chinese Remainder theorem.
Friday 2/24/12. 3.2 Divisibility tests and 3.4 Fermat's little theorem.
Wednesday 2/22/12. 3.1 Congruence.
Monday 2/20/12. No class (Presidents' day).
Friday 2/17/12. 2.5 Prime numbers (continued).
Wednesday 2/15/12. 2.5 Prime numbers.
Monday 2/13/12. 2.3 Linear Diophantine equations.
Friday 2/10/12. 2.2 The Euclidean algorithm (continued).
Wednesday 2/8/12. 2.1 The Division algorithm and 2.2 The Euclidean algorithm.
Monday 2/6/12. 4.3 The Binomial theorem (continued).
Friday 2/3/12. 4.3 The Binomial theorem.
Wednesday 2/1/12. 4.1 Mathematical Induction (continued).
Monday 1/30/12. 1.5 Proofs (continued) and 4.1 Mathematical Induction.
Friday 1/27/12. 1.4 Quantifiers (continued) and 1.5 Proofs.
Wednesday 1/25/12. 1.3 Sets and 1.4 Quantifiers.
Monday 1/23/12. 1.1 The Language of mathematics and 1.2 Logic.