The course introduces discrete structures and techniques for computing. Sets. Graphs and trees. Functions: properties, recursive definitions, solving recurrences. Relations: properties, equivalence, partial order. Proof techniques, inductive proof. Counting techniques and discrete probability. The course, which is the first term of the two term sequence, aims at conveying those skills in discrete mathematics that are used in the study and practice of computer science. The entire course is theoretical material (discrete mathematics).
The course is delivered by traditional weekly or by-weekly lectures with homework, midterms and final. Homeworks mimics the exams and is reviewed during the lectures nearly every week. Attendance is not required. Whenever possible lectures are recorded and become available on-line.
Percentages are approximate.
- Simple proof techniques - 5%
- Discrete structures (set, sequences, graph, trees) - 20%
- Functions, Function properties, Ciphers - 10%
- Countability, Inductively defined sets, Recursion - 10%
- Binary relations, Equivalence, Ordering - 15%
- Mathematical induction - 5%
- Summations and close forms - 5%
- Permutations and combinations - 10%
- Discrete probability - 10%
- Recurrence relations - 5%
- Analysis of algorithms, Rates of growth - 5%
The course landing page provides more detailed information. It links individual items of information about each aspect of this course, including the schedule of lectures, homework and exams, contact points, office hours, textbook, basis for grade, objectives, homework and exams procedures, slides, answered and unanswered exam-like questions, disability resources, current grades, recorded lectures, and student evaluations.