Instructor: Mike Zabrocki Office: TEL 2028 Telephone: 4167362100 x33980 Email: web page: http://garsia.math.yorku.ca/~zabrocki 

Date  Section  Notes 
Feb 2/09  Cat Ladies  REMEMBER: class is in Ross 525! 
Feb 9/09  Apple Pi  HW 7 due 
Feb 18/09  Cat Ladies  (Note: Wed) make up date for Fall, Quiz 3, HW 8 due 
March 9/09  Apple Pi  First day of 'winter' term for us 
March 16/09  Cat Ladies  ninth homework assignment due 
March 23/09  Apple Pi  tenth homework assignment due, talk about projects 
March 30/09  Cat Ladies  Quiz 4 
April 6/09  Apple Pi  project descriptions are due in person/by email BEFORE this date 
April 13/09  Cat Ladies  twelfth homework assignment due (and by 12th, I mean 11th) 
April 20/09  Apple Pi  Quiz 5 
April 27/09  Cat Ladies  thirteenth hw assignment due (12th) 
May 4/09  Apple Pi  fourteenth assignment due (13th) 
May 11/09  Cat Ladies  Project Presentations 
May 20/09  Apple Pi  (Note: Wed) Make up day for Winter, Quiz 6 
Holidays and Important dates:  


Tutor: Dorota Mazur : dorota@yorku.ca
Class: Ross 525 from 7:309pm
Tutorials: The class has been divided into two groups and will meet
in alternate weeks. Those that are in Tutorial 1 are now Cat Ladies and
Tutorial 2 is Apple Pi. The list of who should attend which tutorial is
below (I will update it after a week or so).
If you are confused about how you became a Cat Lady or an Apple Pi please
ask your classmates (they are to blame).
Cat Ladies and Apple Pi will meet in South Ross 525.
Note that I switched the class meetings after the first day because
September 29 is when Rosh Hashanah begins and it is listed on the
Important dates
only as a footnote. Since we won't meet the lecture at 7:30 that evening
it is better if we don't meet the tutorials either.
Cat Ladies 
Apple Pi 
Patryk Ambrozy Nadine Mohammed Ata Munim Jonathan Weltman Mithika Jegasothy Robert Jordan Phu Liem Reuben Weltman Shaofang Xu Katryna Sa Weiyang Shi Claudia Diaconescu Irena Dikushin Reynaldo Isip LeeAnn Attong Brett Bridges Alvin Chou Kajethra Umathevan Iru Shah 
Zakir Khoja Marlon Walker Huyanh Tran Sanjam Suri Ji hyun Kim Bianca Zeppa Lei Zhao Naamah Jacobs Sunhye Lee Diana Malandrino Adil Durrani Jimmy Lim Natasha Lunardo Darek Dufaj Victoria Panthaky Jason Larabee Divya Na Brant Nanton Ranindupal Singh Adil Durrani 
Text: John Mason with Leone Burton and Kaye Stacey,
Thinking Mathematically.
Gary Chartrand, Albert D. Polimeni, Ping Zhang,
Mathematical proofs : a transition to advanced mathematics
Statement of Purpose: This is a critical skills course. Here are some questions to consider.
Just what are the objects which you consider when you do mathematics? What is meant by the fraction one half? How does it represent a ratio? How does it represent a quantity? Are these conceptions different? Can you reconcile them?
How would you describe a triangle to someone (for example a blind person) who has never seen one.
How would you describe a circle?
What conventional conceptions do you have which inform your own thinking about these and other mathematical objects?What is meant by a proof? How you convince yourself, and how do you convince others that an answer is correct? What are the conventions for presenting concise mathematical proofs? How well does the presentation reflect the means by which a particular mathematical discovery was made? What does it mean for an ordinary language argument (mathematical or otherwise) to be valid? What is a counterexample? How does one make conjectures and how does one go about trying to assess whether they are correct?
It is pretty easy to convince oneself or others of the correctness of answers which seem intuitively correct. What is much harder is to convince when answers while correct are counterintuitive. An example some of you may have seen is the "Monty Hall Problem".Can you learn problem solving? Most of the problems you solved in High School were done mechanically or by mimicking solutions to similar problems in the textbook? What means are available to deal with problems which are genuinely novel?
The text, "Thinking Mathematically" by John Mason has a rich selection of problems for consideration. Most require minimal technical background but almost all require hard thinking. Mason suggests a way of working strongly grounded in self awareness both in terms of what you are doing, and how you feel while doing it.Are there techniques which extend your problem solving and proving capabilities? You will learn about combinatorial proofs which are arguments based on the analysis of situations rather the manipulation of formulas.
You will learn about recursive methods and mathematical induction as a tool in calculations and in proofs.
You will learn to use representations from other branches of mathematics (for example, geometric models to solve probability problems) to help obtain answers.
You will learn to present proofs and explanations which are concise and logically correct.
Participation  Based on attendance and convener presentation  10% 
Individual Investigation and Writing Assignments  Normally one each week  30 % 
Group Investigation Project  Winter term  15% 
Quizzes  3 Fall, 3 Winter  15% 
Final Examination  Winter examination period  30% 
Here are some sample quiz question types: