Faculty of Graduate Studies MATH 5220 Problem Solving II, Summer 2015
Course Description:
This course aims to further develop the problemsolving techniques begun in 5210. These include exploring symmetries and generalizations, the pigeonhole principle, strong induction, recursion methods, inequalities, and applications of calculus. We will cover material ranging from combinatorics, elementary number theory, the summation of series, calculus of a real variable, basic complex numbers, geometry, and basic algebra. Some emphasis will be on solving problems appearing in mathematical contests such as national and international mathematical Olympiads and the Putnam competition. Last but not least, this course will explore the design of a Canadian competition for mathematical modeling.
The marks will be base on inclass work, assignments and a group based project.
 Course Times: Tuesdays and Thursdays, 6:00 p.m. to 9:00 p.m.
 Dates: May 19, 2015, to June 25, 2015
 Location: N638 Ross Building
 Instructors website: http://math.blog.yorku.ca/
 Course Moodle Site: http://webct.math.yorku.ca/course/view.php?id=XX
 Prerequisites: The formal prerequisite for this course is MATH 5220 Problem Solving I.
Course Objectives:
 Explain the different types of mathematical propositions.
 Explain basic algebraic concepts of factorization, equations, and fundamentals structures such as groups, rings, and fields.
 Apply number theory and combinatorics to solving arithmetic problems
 Explain complex numbers.
 Apply basic summation formulas.
 Explore the continuous, differentiable, and integrable functions in R
 Explore various types of inequalities and several techniques for solving them
 Explain common techniques for solving problems in Euclidean geometry.
 Design a mathematical modeling competition framework for Canadian high schools.
Expectations: You are expected to:
 join in a group, work regularly in class and some group work outside of class
 prepare and present some material in class, and in the written project
In addition, you are encouraged to use the resources of the Internet to track information and discussions about problemsolving see the course website for a link to problemsolving sites. You may be required to sign onto one of these lists, for a few weeks, and comment on the potential of such lists as a resource.
Text: Loren C. Larson, Problemsolving through problems, Springer 2006.
Reference Text: Newman, Donald J. A Problem Seminar. Problem books in mathematics. New York, NY: SpringerVerlag, 1982.
Other materials: We will make use of the following materials:
 The Centre for Education in Mathematics and Computing: http://www.cemc.uwaterloo.ca/
 Putnam archive: http://kskedlaya.org/putnamarchive/
 The William Lowell Putnam Mathematical Competition: http://math.scu.edu/putnam/index.html
 High School Mathematical Contest in Modeling (HiMCM), http://www.comap.com/highschool/contests/himcm/instructions.html
Attendance: attendance is required at all classes. Attendance will be taken at the beginning and end of each class.
Evaluation: There will be weekly homework assignment on each mathematical topic, due the week after it is assigned, mainly from the textbook, and a final project. Late assignment will be penalized at 5% per class. Graded work will include
Assignments  50% 
Participation  20% 
Project  30% 
Total  100% 
Topic Outline:
Nr  Date  Topic  Reading  Assignment 
1  May 19^{th}, 2015  Combinatorics & Probability  
2  May 21^{st}, 2015  Pigeonhole Principle and Strong Induction  Chapter 2  Assig1 
3  May 26^{th}, 2015  Pigeonhole Principle and Strong Induction  Chapter 2  
4  May 28^{th}, 2015  Number theory  Chapter 3  Assig2 
5  June 2^{nd}, 2015  Number theory  Chapter 3  
6  June 4^{th}, 2015  Algebra  Chapter 4  Assig3 
7  June 9th, 2015  Summation of series  Chapter 5  Project midpoint check 
8  June 11^{th}, 2015  Inequalities  Chapter 7  Assig4 
9  June 16^{th}, 2016  Geometry  Chapter 8  
10  June 18^{th}, 2015  Geometry  Chapter 8  Assig5 
11  June 23^{rd}, 2015  Real Analyses  Chapter 6  Assig6 
12  June 25^{th}, 2015  Project presentation: Mathematical Modeling Competition  Project Written Component: Due 
Evaluation Standards for Graduate Student Work.
Level Standard to be achieved for performance at the specified level
A+ 

A 

A 

B+ 

B 

C 

Each piece of written work is expected to include:
 Your current problemsolving questions and/or ongoing dialog on your previous questions.
 Failure to include this will result in a deduction of one level (point) in the grade for the assignment.
Note: Work below a B+ may be returned to be redone. At this stage (Graduate work), 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 graduate 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.
Assignment Submissions, and Lateness Penalties
Assignments may be submitted in class (or no later than midnight) by email on their due dates. Assignments received later than the due date will be penalized 5% per class. Exceptions to the lateness penalty for valid reasons such as illness, compassionate grounds, etc., will be considered by the Course Director only when supported by written documentation (e.g., a doctor’s letter).
Academic Honesty
Students are responsible for familiarizing themselves with policies regarding academic honesty as set out by the Senate of York University. 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://secretariatpolicies.info.yorku.ca/policies/academichonestysenatepolicyon/
Cheating and/or impersonation are dealt with severely.
InClass Behaviour: All cell phones and pagers are to be turned off during lectures.