Overview

ECE 103 introduces first-year engineering students to basic concepts of discrete mathematics. Through this course, we will gain familiarity with mathematical ideas of relevance to engineering on a rigorous footing. Along the way, we will develop facility in logical reasoning and analytical thinking. Topics we plan to cover are

• Proofs, mathematical induction, recursion

• Efficient exponentiation and multiplication

• Greatest common divisor, Euclid algorithm

• Prime numbers, modular arithmetic, Fermat Little theorem

• Public-key cryptography, RSA

• Counting, the binomial theorem, elementary probability theory

• Generating random numbers with their factorisation

• Elementary graph theory: connectivity, trees, planarity

• De Bruijn sequences and Gray codes

Text Book

Discrete Mathematics for Engineers
Course Notes for ECE 103
Department of Combinatorics and Optimization
University of Waterloo
Spring 2010 edition

The notes are available at the Campus bookstore (SCH) and costs around $20 + tax.

These may be supplemented with additional lecture notes, which will be posted on the course website.

NOTE: There is no substitute for attending the lectures.

Grading

Homework	weekly (9 in all)	10% (best 7 out of 9)
Quizzes	weekly (9 in all)	10% (best 7 out of 9)
Midterm	Wed, June 16, 2010	30%
Final	Thu, August 5, 2010	50%

Homework

There will be nine graded homework assignments in all. You are encouraged to complete all of them. The best seven of these will be counted towards your final mark in the course, to allow for emergencies such as illness.

A homework is due every Monday, except on May 3, May 24, June 14, and July 5. It will be posted on the web at least five days in advance. The homework will be based on the material covered in class until the preceding Wednesday. Each assignment will consist of four to five questions. You are required to attempt all of them. The homework will be collected by your TA at the end of the tutorial on the due date. Late submissions will not be accepted. Graded homework will be returned to you in the next tutorial.

You should be able to solve most of the problems in the homework on your own if you have understood the lectures. However you can expect an odd question that will require additional thought. You may work on the homework in small groups (and are encouraged to do so, in case of difficulty). You may also consult your TA or the instructor during their office hours and tutorials. However, you should write up the solutions on your own and mention all sources of help, including the people you consulted, or the internet.

Solutions will be posted on the web after the due date.

NOTE: For privacy reasons, please include a cover sheet with each assignment. On the cover sheet, write the assignment number, your name, your student ID number, your tutorial number, and acknowledgements of help. Do not write any solutions on the cover sheet. On the remaining pages with your solutions, please include the assignment number, your student ID number, and your tutorial number, but do not write your name or acknowledgments. The cover sheet will be detached before your assignment is returned. Assignments will only be returned to the student to whom it belongs.

Tutorials and quizzes

From May 10, there will be a tutorial every Monday (except on the university holiday on May 24) running for roughly two hours.

The first hour and twenty minutes of the tutorials will be open for a discussion of the homework and a review of the lectures. You are encouraged to approach the TAs with any difficulty you face in the lectures and homework during this time.

During the last half hour of the tutorial, there will be a quiz (except on May 3, May 24, June 14, and July 5), which each of you is required to complete on your own, possibly with our help. The problems assigned in the quiz will be of similar difficulty to the ones in the homework, and will test the same material. You are free to consult the text, your notes, or us for the quiz. However, you are not allowed to discuss the problems with your classmates.

The homework and quiz will be collected at the end of the tutorial and returned to you in the next tutorial, after grading. Solutions to the quizzes will be posted on this web page on the next day.

There will be nine quizzes in all. The best seven of these will be counted towards your final mark in the course, to allow for emergencies such as illness.

Office hours

The instructors will make themselves available to help you with the course every week (see section on instructors above). You are advised to see us during that time (or approach the TA during the tutorial) if you have any difficulty with the lectures, homework, or any other aspect of the course. Please use email only in special circumstances. We may not be able to answer all your email queries individually.

Avoidance of academic offenses

Students are expected to know what constitutes academic integrity, to avoid committing academic offenses, and to take responsibility for their actions. Students who are unsure whether an action constitutes an offense, or who need help in learning how to avoid offenses (e.g., plagiarism, cheating) or about rules for group work/collaboration should seek guidance from the course professor, TA, academic advisor, or the Undergraduate Associate Dean. The Office of Academic Integrity at the University of Waterloo maintains a website with a number of items of interest to students. In particular the pages on Academic Integrity for students provide various examples as well as a tutorial on the subject. For information on categories of offenses and types of penalties, students should refer to Policy #71, Student Discipline. Students who believe that they have been wrongfully or unjustly penalized have the right to grieve; refer to Policy #70, Student Petitions and Grievances, as well as Policy #72, Student Appeals.

Students that need special help are accommodated

The Office for Persons with Disabilities (OPD), located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the OPD at the beginning of each academic term.

Additional information

For more information on the first-year engineering program in general, please see the First Year Engineering website.

Feedback

Please pass on your comments, criticism, and opinions on the course to us; these are always welcome. You may choose to do this through your class representatives, or you may directly write or speak to us.