Instructor:

Ashwin Nayak
Combinatorics and Optimization, U. Waterloo
and
Perimeter Institute for Theoretical Physics

Email:    anayak [at] math
Office:    MC 4034
Phone extension:    3601

Teaching Assistant:

Berkant Ustaoglu,        bustaoglu [at] math.uwaterloo.ca,        DC 3144,    x 7814
Combinatorics and Optimization, U. Waterloo

Outline

This course introduces first year undergraduate mathematics students to basic elements of algebra. The idea is to gain familiarity with concepts of fundamental importance on a rigorous footing.

The topics that we will cover are:

• Logic, proofs, mathematical induction
• Divisibility, primes, GCD
• Extended Euclidean algorithm, linear Diophantine equations
• Linear congruences, Fermat's little theorem, Chinese remainder theorem
• Public key cryptography, RSA, including fast exponentiation
• Complex numbers, the complex plane, polar representation
• De Moivre's theorem, Fundamental theorem of algebra
• Polynomials, factorization, roots, error-correcting codes
• Equations over finite fields, partial fractions

A weekly lecture schedule is available here.

Text book

An introduction to Mathematical Thinking: Algebra and Number Systems
W.J. Gilbert and S.A. Vanstone

This book is available at the university bookstore in South Campus Hall for $74.95 + tax.

The text is not a substitute for the lectures. The lectures may present the material covered in the text in a different manner, or deviate from it entirely. You are advised to take your own notes in class.

Homework problems will be generally be assigned from the exercises in the text.
 

Evaluation

The final mark in the course will be based on homework, unannounced quizzes conducted during the tutorials, one midterm, and the final exam. The weight given to the different components  is

1. Homework:    15%
2. Quizzes:          5%
3. Midterm:        30%
4. Final:              50%

Homework

There will be ten graded homework assignments in all. The best eight of these will be counted towards your final mark in the course.

There will be a homework assignment essentially every week, and will be posted on the web every Monday. The homework will be based on the material covered in class from that Monday to Friday. The homework will be due on the following Tuesday, before 1 pm, in Math drop box no. 5 outside MC 4066 (slot 10 A-L, slot 11 M-Z). 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 consult your TA or the instructor during their office hours or during the tutorial. You should write up the solutions on your own and mention all sources of help. Solutions will be posted on the web after the homework is collected.
 

Tutorials

From May 9 until July 25 (except May 23, Victoria Day), there will be a tutorial every Monday at 2:30 pm running for roughly one hour.

The tutorial 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 are facing in the lectures and homework during this time. The instructor may also be available during the tutorials for part of the time.

There will be a small number of unannounced quizzes during the tutorials, which each of you is required to complete on your own. The quizzes will be of 10 to 15 minute duration, and will be conducted at the end of the tutorial. It is your responsibility to be present for all the tutorials. The problem(s) assigned in the quiz will be of similar difficulty to the ones in the homework. You are free to consult the text, or your notes for the quiz. However, you are not allowed to discuss the problems with your classmates. The quizzes will be collected at the end of the tutorial and returned to you the next week after grading. Solutions to the quizzes will be posted on this web page on the next day.
 

Office hours

We will make ourselves available to help you with the course one hour every week (check here). You are advised to see us during that time (or 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.
 

Note on 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. For information on categories of offenses and types of penalties, students should refer to Policy #71, Student Academic Discipline. Students who believe that they have been wrongfully or unjustly penalized have the right to grieve; refer to Policy #70, Student Grievance.

Note for students with disabilities

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.

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 write directly to us. If you prefer not to reveal your identity, you could use an anonymous remailer, like this one, to send us email.