Mathematics 3819 Modern Computer Algebra

General Information

• Course goals: This course is an introduction to basic algebraic algorithms that are useful for computer algebra systems and their applications. More specifically, operations like multiplication, division, greatest common divisors and factorization are studied over several domains including the ring of integers, finite fields, polynomial rings, and quotient rings. The basic tools considered include modular arithmetic, discrete Fourier transform, Chinese remainder theorem and Newton iteration. Several applications to cryptography, including the Advanced Encryption Standard (AES), the RSA cryptosystem, the Diffie-Hellman key exchange and Shamir's secret sharing scheme are also considered.
• Prerequisities: MATH 2108 or MATH 3101 or MATH 2100, or permission of the School.
  Mathematical maturity is recommended. At least one undergraduate abstract algebra course may be useful; undergraduate courses in discrete mathematics and in data structures could be helpful.
• Tentative lecture schedule (html file) as of August 2016 (before classes start).
• Textbook: Modern Computer Algebra by Joachim von zur Gathen and Jurgen Gerhard, 3rd edition, Cambridge University Press, 2013.
  We also use CryptoSchool by Joachim von zur Gathen, Springer, 2015.
• Language: for the implementations in the assignments any of Maple, C, Java or SAGE can be used.
• Classes begin: Wednesday, September 7, 2016.
  Classes end: Friday, December 9, 2016.
  Fall break: October 24-28, 2016.
• Evaluation: There will be two assignments and a midterm test for a total of 50% of the mark. The tentative schedule of assignments is below.

  Assignment	Hand-out Date	Due Date	Worth
  1	September 28	October 19	15%
  2	November 2	November 23	15%

  In addition to the two assignments there is a midterm test on Wednesday November 16, 2016 worth 20% of the final mark. Term mark is 50% and final examination is 50%.
  Important: to pass the course you need at least 30% in term marks (equivalent to 15% out of the 50% of the total marks corresponding to the assignments and midterm test).
  

• Withdrawal: The last day for withdrawal from the course without academic penalties is the last day of classes.
• Academic Accommodation:
You may need special arrangements to meet your academic obligations during the term. For an accommodation request the processes are as follows:
• Pregnancy and Student Parental Leave: write to me with any requests for academic accommodation during the first two weeks of class, or as soon as possible after the need for accommodation is known to exist. For more details see the Parental Leave Guide.
• Academic Accommodations for Students with Disabilities: The Paul Menton Centre for Students with Disabilities (PMC) provides services to students with Learning Disabilities (LD), psychiatric/mental health disabilities, Attention Deficit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders (ASD), chronic medical conditions, and impairments in mobility, hearing, and vision. If you have a disability requiring academic accommodations in this course, please contact PMC at 613-520-6608 or pmc@carleton.ca for a formal evaluation. If you are already registered with the PMC, contact your PMC coordinator to send me your Letter of Accommodation at the beginning of the term, and no later than two weeks before the first in-class scheduled test or exam requiring accommodation (if applicable). After requesting accommodation from PMC, meet with me to ensure accommodation arrangements are made. Please consult the PMC website for the deadline to request accommodations for the formally-scheduled exam (if applicable).
• Religious obligation: write to me with any requests for academic accommodation during the first two weeks of class, or as soon as possible after the need for accommodation is known to exist. For more details see the Religious Observation Guide.

Contact Information: