Competitive Mathematics for High School Students

Course Description

Description

This course is a very challenging problem-solving course for students who have participated in the AMC and are eager to take their skills to the next level.

In one part of the course, general problem-solving techniques are introduced, such as:

• the pigeon hole principle
• invariance principle
• extremal principle
• induction principle
• systematic checking

Some of these general problem-solving paradigms enjoy applicability outside of mathematics. In the other part of the course, these metholds are discussed in specific mathematical contexts such as:

• number theory
• combinatorics, sequences
• polynomials

In tackling non-routine problems whose solutions are not immediate, students are encouraged to approach problems from different angles. A further goal of this course is to improve a student's ability to write proofs.

Students attend weekly whiteboard sessions to discuss challenging problems.

Materials Needed

There is a textbook purchase required for this course:

The Art of Problem Solving, Volume 2: and Beyond, by Rusczyk and Lehoczky, 7th Ed. www.artofproblemsolving.com

ISBN: 978-0-9773045-8-5

A graphing calculator is recommended, such as:

• TI-83 PLUS
  
• TI-84 PLUS

List of Topics

There are eleven weeks of topics and one week for the final exam. Click here to view all 11 topics along with sample problems:

Competitive Math Syllabus

Whiteboard Session Times

All whiteboard session times will be held on Tuesdays at the following times:

• Session 1: 9:00 pm - 10:00 pm EST
• Session 2: 10:00 pm - 11:00 pm EST

Instructor will attempt to accommodate student preferences.

Whiteboard Demo

Click on the image below to view the Whiteboard demo:

System Requirements

All CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer). This course does not require Adobe Flash. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course uses an online mathematical whiteboard for individual or group discussions with the instructor. The whiteboard web site requires cookies, popup windows, and the Java Runtime Environment. (Note: iOS & Android devices cannot run Java applets.)