The Helix Summer Science Institutes, July 2015
Discover Mathematics behind Fractals Summer Course
Course Description:
Fractals are everywhere. You can find them in our lungs, kidneys, and blood vessels, flowers, plant, trees, terrain, rhythm of the heart, clouds, mountains, in the wilderness of nature. Today, fractals are used in medical research, in the movies, wireless communications, biology, computer graphics and games. In this course, students will learn about the fascinating concept of fractals, discover the mathematics behind them, and write iterative algorithms to create breathtaking computer graphics by using fractals. Students will be presented with background and mathematical foundations used in creating different types of fractals. Lectures will be interactive and lead to very interesting hands-on exercises that involve knowledge of Math and Computer Science. Major topics include Calculus, Geometry, Algebra and Transformations, 3D graphics, and Computer Programming.
MATH 5220 Problem Solving II
This course aims to further develop the problem solving 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, 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 based on in-class work, assignments, and a group 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
Text:
Loren C. Larson, Problem solving through problems, Springer 2006.
Reference Text:
- Titu Andreescu and Razvan Gelca, Putnam and Beyond, Springer, 2007.
- Titu Andreescu and Razvan Gelca, Mathematical Olympiad Challenges, Second edition, Birkhäuser, 2009.
- Newman, Donald J. A Problem Seminar. Problem books in mathematics. New York, NY: Springer-Verlag, 1982.
