Announcements:

syllabus available below: follow the links

Description of the class

A presentation of fundamental tools required in advanced computer science, including topics such as propositional and first-order logic, topological properties of networks, managing tasks in parallel systems using graphs as well as modeling, simulation and queueing processes.

Objectives: syllabus available here

The objective of this course is to present the essential mathematical aspects of computer science. As any scientific discipline, computer science requires mathematical tools to formalize concepts, to abstract objects and to model events. Therefore, we will present the mathematical tools that any graduate student should be familiar with, and master well enough to be able to use them in her/his field of choice.

Sets, ordered sets, and functions

Propositional logic, 1st order logic, higher-order logics

Review of Induction, recursion
Applications to algorithm analysis, program termination proofs

This class will meet every MW, from 1:30 to 2:50pm, in room 321. For more details about the class: a tentative schedule

week #1: Brief introduction to logic, and notations.

week #2: Proofs and induction

week #3: Proofs and induction; inductive definition of sets and functions

week #4: Sets and functions

week #5: Sets and functions; operations and relations (quiz #1)

week #6: Reviews and exercises

week #7: Midterm #1; logic: propositional logic

week #8: Propositional logic
SPRING BREAK

week #9: Propositional logic; Predicate logic

week #10: Predicate logic

week #11: Predicate logic

week #12: Predicate logic

week #13: Predicate logic

week #14: Other kinds of logic, Constraint programming

week #15: Presentation of the projects

week #16: Final exam

As far as assignments and exams , there will be:

reading assignments, and homework assignments (randomly checked);

(announced and un-announced) quizzes throughout the semester;

2 mid-terms (cf. syllabus for schedule);

1 final exam.

Exams / Quizzes:

Quizzes: 1, 2, 3,

Midterm 1: 1,

Material for the class:

Lecture notes:

Lecture notes on sets / functions / cardinality / operations / relations: here

Lecture notes on induction: here

Lecture notes on ordered sets: here
Exercises given in class:

homework to be turned in on Wed. March, 28th: here

Exercises given in class in past semesters:

Exercises on sets / functions / cardinality / operations / relations: here

Exercises on induction: here

Additional exercises reviewed at the Saturday extra session (9/24): here

Exercises on first-order logic: 1, 2

Quizzes and Exams from past semesters:

quiz #1, solution

quiz #2, solution

quiz #3, solution

quiz #4, solution

midterm #1, solution

Martine Ceberio

Last modified: Mon Mar 26 18:52:38 MST 2007