Topics Covered

NOTE: The topics and the schedule below are subject to change.

(1) Chapter 0: compound statements, negation, logical connectives (AND, OR, IF THEN . implies, IFF . if and only if), negation of statements with and, or, if then, iff, contrapositive, converse; existential and universal quantifiers, negation of statements containing such quantifiers, proof techniques: direct proof, by counterexample, by contrapositive, by contradiction, by cases, proof of iff, proof of .the following are equivalent..

(2) Section 5.1: the weak form of the Principle of Mathematical induction.

(3) Sections 1.1 and 1.2: truth tables, propositions, logical equivalence.

(4) Mon, Sep 18, 06: Section 1.2 continued.

(5) Tues, Sep 19, 06: Section 1.3: logical arguments (resolution proofs).

(6) Wed, Sep 20, 06: Section 1.3 continued.

(7) Fri, Sep 22, 06: Quiz; Sections 2.1 and 2.2: Sequences, multisets, sets and operations on them

(8) Mon, Sep 25, 06: Sections 2.1 and 2.2 continued.

(9) Tues, Sep 26, 06: Sections 2.1 and 2.2 continued.

(10) Wed, Sep 27, 06: Sections 2.1 and 2.2 continued.

(11) Fri, Sep 29, 06: Section 2.3, 2.4, and 2.5: Binary relations: reflexive, symmetric, antisymmetric.

(12) Mon, Oct 2, 06: Binary relations continued; equivalence relations, partial orders; equivalence classes; partitions.

(13) Tues, Oct 3, 06: Continued.

(14) Wed, Oct 4, 06: Continued; comparable and incomparable elements; total orders; representation of a binary relation as a matrix and as a diagraph; notation for equivalence relations and partial orders.

(15) Mon, Oct 9, 06: Functions (Chapter 3); domain, target; range; image of an element/set; preimage of an element/set; preimage of the image of a set; image of the preimage of a set.

(16) Tues, Oct 10, 06: Functions continued.

(17) Wed, Oct 11, 06: Functions continued; one-to-one (injective) functions.

(18) Fri, Oct 12, 06: Exam I.

(19) Mon, Oct 15, 06: Functions continued; onto (surjective) functions; bijective (one-to-one correspondence) functions; cardinality of finite and infinite sets; the cardinality of the set of Natural Numbers.

(20) Tues, Oct 16, 06: Functions continued; composition and inverse.

(21) Wed, Oct 17, 06: Cardinality, countable, countably infinite, uncountable, (functions from/to higher dimensions not covered)

(22) Fri, Oct 19, 06: countable/uncountable continued.

(23) Mon, Oct 22, 06: Number Theory (Chapter 4): divides, quotients, remainder, how to find them, related theorems.

(24) Tues, Oct 23, 06: Section 4.2: greatest common divisor, writing gcd(a,b) as a linear combination of a and b.

(25) Wed, Oct 24, 06: Section 4.2 continued: the least common multiple, exercises, Section 4.3: prime numbers.

(26) Fri, Oct 26, 06: Quiz, 4.3 continued, Section 4.4.

(27) Mon, Oct 29, 06: 4.4 continued.

(28) Tues, Oct 30, 06: Finish Chapter 4.

(29) Wed, Nov 1, 06: Continued.

(30) Fri, Nov 3, 06: Section 6.1 (principles of inclusion and exclusion).

(31) Mon, Nov 6, 06: Section 6.2 (addition and multiplication principles).

(32) Tues, Nov 7, 06: Section 7.1 (permutations).

(33) Wed, Nov 8, 06: Section 7.2 (combinations).

(34) Fri, Nov 10, 06: Section 7.5 (repetitions).

(35) Mon, Nov 13, 06: Continued., begin.

(36) Tues, Nov 14, 06: Section 7.6 (derangements), begin 6.3 ().

(37) Wed, Nov 15, 06: Section 6.3 (the Pigeonhole Principle).

(38) Fri, Nov 17, 06: Exam II.

(39) Mon, Nov 27, 06: Binomial Theorem.

(40) Tues, Nov 28, 06: Binomial Theorem.

(41) Wed, Nov 29, 06: Matrices: definitions of row vectors, column vectors, square matrices, zero matrix, other topics.

(42) Fri, Dec 1, 06: Solution of Exam II; matrices and linear systems of equations.

(43) Mon, Dec 4, 06: Addition, subtraction, and scalar multiplication of matrices and vectors, dot/inner product of vectors, multiplication of matrices.

(44) Tues, Dec 5, 06: Powers of matrices, transpose, and special matrices.

(45) Wed, Dec 6, 06: Determinants, cofactors, adjoints.

(46) Fri, Dec 8, 06: More.

(47) Mon, Dec 11, 06: Matrix Inverse, using the inverse to solve linear systems.

(48) Tues, Dec 12, 06: More.

(49) Wed, Dec 13, 06: Linear Transformations.

(50) Fri, Dec 15, 06: Quiz, More about linear transformations.

Left:

· Circular, asymmetric relations, Hasse diagrams?

· Strong form of Math. Induction.

· Multinomial theorem.