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Session One (June 20 - July 9), ages 13-15
This course is for those who delight in solving challenging math problems, and who would like to further develop their skills for this purpose. Problem solving is the activity of the mathematician, and logical reasoning is the framework for this activity. Here we will give an introductory course in logic, drawing from examples outside of mathematics, but focusing on the use of logic within mathematics. Students will learn formal notions of familiar logical methods and then see how their formal understanding can be used directly to help solve mathematical problems. But logical reasoning is not all there is to problem solving. Good problem solving skills include ingenuity, creativity, and the ability to apply a variety of strategies and techniques. In this course, students will be taught fundamental tools and standard techniques for problem solving, and they will be given the opportunity to develop their mathematical ingenuity through practice on problems in a range of difficulty. The mathematical subject areas that the problems will be drawn from include set theory, number theory, and combinatorics - none of which will require more background than algebra.
Prerequisite: Completion of an algebra course.
Session One (June 20 - July 16), ages 14-16 Note: This is a 4 week session
This course is designed to prepare students for AP calculus in the Fall. Topics include algebra, trigonometry, analytic geometry, analysis of functions, and other foundational material required for the study of calculus. During this intensive course, students will cover material that is ordinarily covered in a one-semester high-school course.
Prerequisites: Courses in geometry and intermediate algebra at the high-school level.
Session Two (July 11 - July 30), ages 14-16
This course introduces bright students to geometry while building problem-solving abilities and logical-reasoning skills. Geometry plays an important role throughout the sciences, as well as in art, architecture, computer graphics, and all fields of engineering. In addition to teaching students proofs in geometry, this course will use a variety of methods to develop geometric intuitions and understanding, for example through the visual exploration of geometry and by carrying out geometric constructions. This course will use state-of-the-art computer tools to explore geometric concepts and investigate geometric properties. Applications of geometry will be presented throughout the course to help students appreciate the true importance of this subject.
Prerequisite: Students should have familiarity with algebra.
Session Two (July 11 - July 30), ages 14-16
A course description for this course will be available in January.
Prerequisite: A course in intermediate algebra (algebra II).
Inquiries concerning the Summer Institutes should be sent to epgy@infokids.com.hk.