Credit: (3-2)4

Content: Logic. Relations and Functions. Matrices and determinants. Inverse of a matrix, matrix polynomials, Cayley-Hamilton theorem. Systems of linear equations, parametric solutions. Counting: principle of inclusion, exclusion, pigeonhole principle. Mathematical induction, recursive relations. Permutations, combinations. Discrete probability. Graphs.

Goals: The goal of this course is to reacquaint the student with some basic mathematical concepts (sets, functions, matrices, combinatorics, probability) and through problem solving show how these concepts are treated in a discrete or a finite setting.

Course Outline:

• (Week 1) Sets. Operations on sets.
• (Week 1) Functions. Relations.
• (Week 1) Matrices. Operations. Inverse.Determinant.
• (Week 1) Matrix polynomials. Echelon form of a matrix.
• (Weeks 2) Systems of linear equations.
• (Weeks 2) Mathematical induction and recurrence relations.
• (Week 1) Pigeonhole principle. Basic counting rules.
• (Week 1) Permutations and combinations.
• (Week 1) Combinations with repetition.
• (Week 1) Inclusion-exclusion principle
• (Week 1) Discrete probability

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