MATH 5510

MATH 5510 3.00, A, Fall 2018, Cross-listed with Education, GS/EDUC 5832 3.00.
Topics in Mathematics for Teachers
  • Days: Mondays
  • Time: 6:00 p.m– 9:00 p.m
  • Place: Vari Hall (VH). See the campus map.
  • Room:-1158
  • Office hours: by appointment, (DB or known as Tel building) 2036
  • Email: vnika@yorku.ca
  • Course Webpage: We will post course information, announcements and homework assignments on https://moodle.yorku.ca/. You are expected to check this webpage weekly.

Course Description:

Subsets and binomial coefficients- subsets, subsets of fixed size, properties of binomial coefficients, the Binomial Theorem, further properties of binomial coefficients, partitions and permutations - partitions: Bell numbers and Stirling numbers, permutations: cycle decomposition and Stirling numbers. We will introduce recurrence relations and generating functions, the principle of inclusion and exclusion (PIE). We will introduce various well-known problems in areas such as the system of distinct representatives, Latin squares, Steiner triple system, projective planes, linear codes, and Hamming codes, graphs and graphs colouring, etc.

Through studying these objects, we will learn proof techniques and construction methods used in combinatorics. More importantly, we will see the interplay among these three beautiful areas in combinatorics.

Prerequisite: Background in linear algebra.

Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.

Evaluation: Graded work will include

  • Autobiography: 5%
  • 5 Regular assignments (assignment 2-6): 40%
  • Participation in class measured by attendance and associated with class work: 10%
  • Reports on peers’ Presentations: 10%
  • Final Project (Oral presentations and written projects): 30%
  • Final Assignment: Reflections on the course and learning: 5%

Reference Resources: Combinatorics: Topics, Techniques and Algorithms by Peter Cameron

Tentative Schedule: The following schedule is tentative, it will get more accurate as the semester progresses.

Nr Date Lecture Topics Assessment/Evaluation
1 Sept.10th,, 2018 Organized counting, permutations, Pascal's triangle
2 Sept.17th, 2018 Subsets, Binomial Coefficients, Partitions, and Permutations Assignment #1 (Autobiography) Due date: Sept. 23rd 2018
3 Sept.24th, 2018 Recurrence Relations
4 Oct.1st, 2018 Generating Functions Assignment #2 (Subsets, Partitions, Permutations)
Oct. 8th, 2018  - No Class (Thanksgiving)
5 Oct.15th, 2018 The Principle of Inclusion and Exclusion (PIE) Assignment #3 (Recurrence Relations, Generating Functions)
6 Oct. 22nd, 2018 Systems of distinct representatives
7 Oct.29th, 2018 Latin Squares Assignment #4 (PIE, System of Distinct Representative)
8 Nov.5th, 2018 Steiner triple systems
9 Nov.12th, 2018 Error Coding Assignment #5 (Latin Squares, Steiner Triple System)
10 Nov.19th, 2018 Graphs and Graph Colouring
11 Nov.26th,, 2018 Work on final project Assignment #6 (Error Coding, Graphs and Graph Colouring)
12 Dec.3rd, 2018  

Final Project Presentations

 
  • Presentations: 15%
  • Peer Presentation Reports:10%
  • Reflection paper: 5%
  • Written paper: 15%- due on Dec.10th

University Important Dates:

  • First class: Sept. 10, 2018
  • Fall reading week (no classes, University open) Oct. 6-12, 2018
  • Thanksgiving Day-University closed: Oct 8, 2018
  • The last date to submit fall term work:  TBA
  • Fall classes end: Dec. 4, 2018
  • Last lecture of fall term: Dec. 3, 2018
  • Fall Study Day (no classes; University open): Dec. 5, 2018
  • Fall examinations: Dec. 6 - 21, 2018
  • Last date to enroll without my permission: Set.18, 2018
  • Last date to enroll with my permission: Oct. 2, 2018
  • Last date to drop the course without receiving a grade: Nov. 9, 2018
  • Course Withdrawal Period (withdraw from a course and receive a grade of “W” on transcript): Nov.10-Dec.4. 2018

Attendance: If you do miss a class, it is your responsibility to find out what was covered and whether any important announcement was made. Class participation is strongly encouraged. You can participate both by asking some questions and by answering others. Please don’t hesitate to ask for clarification.

Academic Honesty: Students are responsible for familiarizing themselves with policies regarding academic honesty as set out by the Senate of York University. Please Cheating and/or impersonation is dealt with severely. Please read the Senate Policy on Academic Honesty (which can be found in the University Policies and Regulations section of the York University Undergraduate Programs Calendar. http://secretariat-policies.info.yorku.ca/policies/academic-honesty-senate-policy-on/.

Note: Work below a B+ may be returned to be redone.  Work below B will definitely be returned for a rewrite.  All assignments may be rewritten – a chance to keep learning! At this stage (masters), it is essential that students work to the corresponding standards of mathematical thinking and presentation.  In professional mathematics, it is common for journals to require a rewrite of a mathematical paper.  It seems appropriate to require the same from master students!

Also – you will be using material from multiple sources: colleagues, the class, the internet.  It is essential that you both cite the sources and that you show your own understanding of the material you choose to present!  Otherwise, it is considered plagiarism.  If you are not certain how to cite sources – please ask.