Text(s)/Materials:

Rusczyk & Lehoczky, (1996) The Art Of Problem Solving, Vol 1 & 2, Norman OK, Mu-Alpha,Theta. Reference Text: Larson, (1983). Problem Solving Through Problems. New York. Springer-Verlag

Course Description:

Advanced Problem Solving is designed to offer our most talented students an opportunity to explore in more detail a diversity of areas of undergraduate mathematics and problem solving techniques. Topics are selected from such areas as: Algebra, Geometry, Number Theory, Trigonometry, Combinatorics, and Probability. Many students take this course in order to increase their problem solving skills for math competition, including the AMC and AIME.

Teaching and Learning Methodology and Philosophy:

We attempt to view past learning in new contexts and from new points of view in order to strengthen and broaden understanding of previously learned topics and to add new approaches to student's problem solving. Cognitive skills developed through advanced exploration of mathematics can extend to other disciplines. Much of the learning is expected to take place through problems designed as stepping stones to concept development. Students can exercise creativity, intuition and imagination while analyzing, evaluating and integrating information. The course emphasizes individual and group explorations, discussions, and problem solving. Verbal and written communication are stressed. There is an emphasis on making connections between and among topics in the various areas in mathematics. Ideas and concepts are introduced in class, through the textbooks, and exploration proceeds as directed by class interaction. Formulas, processes, and "mental gymnastics" techniques are illustrated and students are given the opportunity to explore and practice them. Sharing of student ideas and methods is encouraged throughout our work. Regular attendance is essential, since it is not possible to recreate the spontaneous class discoveries and catalytic involvement.

Student Expectations:

All students are expected to
• be involved in class discussions and explorations
• spend time in preparation, reading and individual exploration outside of class
• explore independently and in small groups
• make a contribution to class exploration through extensions and connections
• maintain a notebook of their work, to include notes, homework problems (solved with complete work), assessments, and other work they have created.

Assessment Practices, Procedures, and Processes:

Students may be evaluated through varied assessments, both group and individual.
Grades are determined by taking into account some of the following:
• Classroom participation, involvement, and contributions to exploration.
• "Take Home" problem sets which include both the use of concepts generated in class and independent, open ended investigation.
• In class, group and individual quizzes and exams. (Curved relative to difficulty of problems.)
• Individual (and group) research projects, reports, and portfolios
• Self evaluation by the student with reflection on: contributions made to the success of the class, sharing of ideas both outside of class and within, and level of involvement.

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