Discrete Mathematics

CS 107 Spring 2013

Instructor Information

Name Numan Sheikh Email numan@gift.edu.pk

Room #: Faculty Room, EE Dept, First Floor Website: http://numangift.wordpress.com

Course Information

Class Days & Timings Monday: 13:40-14:55 (Room G-2) & Location Tuesday: 13:40-14:55 (Room G-4) Batch Spring 2012

Course Description

This is an introductory course in Discrete Mathematics oriented toward Computer Science. The main areas covered in the course are: Fundamental Concepts of Mathematics, Logic, Sets and Proofs, Functions, Relations, Combinatorics and Graph Theory, Number Theory, Modular Arithmetic and basic Algorithmic Analysis.

Objectives

On completion of this course, students will be able to explain and apply the basic methods of discrete (non-continuous) mathematics in Computer Science. They will be able to use these methods in basic programming courses as well as subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems. In particular, students will be able to:

Reason mathematically about basic data types and structures (such as numbers, sets, graphs, and trees) used in computer algorithms and systems; distinguish rigorous definitions and conclusions from merely plausible ones; synthesize elementary proofs, especially proofs by induction.

Model and analyze computational processes using analytic and combinatorial methods.

Apply principles of discrete probability to calculate probabilities and expectations of simple random processes.

Work in small teams to accomplish all the objectives above.

Required Text(s)

Lecture Notes from OCW will form the official text and the course outlines for this course. They are taken from the Spring 2005 offering of Mathematics for CS course at MIT OCW website.

MIT OCW Lecture Notes (6.042J / 18.062J Mathematics for Computer Science, Fall 2005), which will be posted on the website regularly.

You may also want to get hold of one or more of the following books as they also cover the material in a nice way.

B. Kolman, R. C. Busby and S. C. Ross, Discrete Mathematical Structures.

Kenneth H. Rosen, Discrete Mathematics and Its Applications.

Susanna S. Epp, Discrete Mathematics with Applications.

Policies

General Policies Attendance is expected and failure to attend regularly will have an adverse impact on your grade. 100%

attendance is strongly recommended for this course.

Almost all the assignments will be followed by a quiz related to the assignment, and will be part of the assignment grade.

We may have extra Quizzes that can be announced or un-announced.

Interactive class sessions are preferred. Therefore, class participation will be much appreciated.

Students must retain copies of all quizzes, assignments and exams, submitted in paper form or electronically. Grade changes will not be made without proof of submission of all relevant work.

Academic Dishonesty Academic dishonesty will not be tolerated. Copying materials from other sources (your peers, books, internet) without proper referencing and acknowledge of the source is a serious offense and will be dealt with severely.

Assignments • You are required to submit the homework as an individual; however, you may team up with one student in class

to understand and solve the problem, but you may not share your final submission. You will be graded also on degree of active, prepared participation, rather than problem-solving success only. In case you decide to team up with an individual for an assignment, you have to mention that on the cover page of your assignment submission. (Some of the assignments may be Individual assignments. In this case it will be mentioned with the announcement of the assignment).

• Assignments are important and deadlines will be strictly adhered to. • You will have two slip days for submission of your assignments.

Each assignment has a due date and a due time, which will be posted on the course web page. “Slip days" are given to you to give some flexibility with the assignment deadlines. Each person starts the term with two slip days, which can be used to push back assignment deadlines.

• Slip days work as follows:

Pushing an assignment deadline back by one day (24 hours) costs each person one slip day. Even one minute delay will cost you a slip day.

Partial slip days are not allowed, e.g., it is not possible to use part of a slip day to push a deadline back by 6 hours.

Slip days are not transferable from one student to another.

Assignments that are submitted late (with no slip days to cover them) will not be accepted and will receive a mark of 0%.

Assignments are normally due at noon on Thursday. Doing the problem sets is, for most students, the best way to master the course material. Problem sets will count for up to 30% of the final grade. Solutions to the problem sets will be provided immediately after the due date. You can use the two slip days and mention it on the cover page. If you have used your slip days, late problem sets will not be accepted. The first page of each problem set has a cover page for use when you submit the problem set. Complete the information called for on the cover page and attach it as the first page of your submission. Be sure to complete the full collaboration statement on the cover page:

"One the group members worked on this assignment and no help was taken from internet-sources of other people",

or "I collaborated on this assignment with (student in class), got help from (people other than collaborators and course staff), and referred to (citations to sources other than the class material from this term)".

No problem set will be given credit until it has a collaboration statement. Submissions which are unduly hard to follow (or illegible) will get little credit even if the solutions are "correct".

Grading

There will be five in-class quizzes, a Midterm Exam and a Final exam. Grades for the course will be based on the following weighting: Assignments 20% Quizzes 25% Midterm 20% Final Exam 35%

Lecture Schedule

3 Weeks Sets and Logic 2 Weeks Proof Techniques, Induction, Contradiction

Mid-Term I 3 Weeks Combinatorics, Counting, pigeonhole principle 1 Week Number Theory, GCD Algorithm 1 Week Recurrence, Tower of Hanoi

Mid-Term II 4 Weeks Graphs,Trees, Eulerian Graphs, Hamiltonian Graphs, Coloring, Planarity

and Euler's formula, BFS/DFS 1 Week Big Oh and other asymptotic notations

Final Exam