Math 190 (Mathematical Problem Solving)                                   Summer2006
              Instructor: Dr. Kin Y. Li
              Office: Room 3471           Office Phone: 2358 7420          e-mail address: makyli@ust.hk
              Office Hours: Mondays 3:00pm-4:00pm (or by appointments)
              Prerequisite: Advanced Level Pure Math
              Grade Scheme: Presentations (10%) and 2 Tests (45% each).
              Lecture Notes: Available from www.math.ust.hk/∼makyli/UG.html under Math 190
                   Selected articles of Mathematical Excalibur (www.math.ust.hk/excalibur)
              References: (Library Reserve for Math 190)
                  Arthur Engel, Problem-Solving Strategies, Springer-Verlag, 1998.
                  Loren Larson, Problem-Solving Through Problems, Springer-Verlag, 1983.
                  EdwardLozansky and Cecil Rousseau, Winning Solutions, Springer-Verlag, 1996.
                  Istvan Reiman, International Mathematical Olympiad 1959-1999, Wimbledon, 2001.
              Useful Websites:   www.kalva.demon.co.uk        www.unl.edu/amc
                   www.mathdb.org       www.mathlinks.ro
              Purposes of the Course: This is an enrichment course. We study materials that are
              covered in the curricula of special secondary schools (for gifted students) in other countries.
              It is hoped that the materials may be passed to future generations of secondary school
              students and a culture to enjoy deep mathematics can evolve.
                  This is also a challenging course. We push students to think about difficult problems.
              As rountine problems are labors of the hands, the difficult problems develop the mind
              to think maturely and critically. The problems we will look at came from many sources
              ranging from local to regional to global math competitions, such as the Hong Kong Math
              Olympiad (HKMO), Asia-Pacific Math Olympiad (APMO), International Mathematical
              Olympiad (IMO) and the William Lowell Putnam Math Competition (Putnam Exam).
              Course Descriptions: In the first part of the course, we will cover supplementary mate-
              rials to secondary school mathematics as well as some basic undergraduate mathematics
              that are often used in mathematical competitions. The topics include materials in algebra,
              geometry, number theory, combinatorics and mathematical games.
                  In the second part of the course, we will look at methods of proofs and problem
              solving techniques. These include proof by contradiction (indirect proof), mathemati-
              cal induction, infinite descent, false position, homothety, inversion, pigeonhole principle,
              invariants, monoinvariants, extremal principle and more.
              Reminders: Students are highly encouraged to come to office hours for consultations.
              All materials presented in lectures and tutorials as well as proper class conduct are the re-
              sponsibility of the students. The instructor reserves the right to make any changes
              to the course.