## Curriculum

We aim to share the beauty of mathematics with our students: The notion that mathematics can be interesting and even fun is espoused and readily accepted. Beyond the regular classroom instruction, mathematics is presented via games, competitions, investigations, art, music, special projects, and computer-based activities. While some applications to areas such as art, science and finance are presented to help the students learn and enjoy the material, no special time is taken to justify or enhance mathematics through the teaching of other subjects.

As a result of the program, students come to view mathematics as a sense-making activity at which they themselves are quite capable. While the content provided is typically focused on typical middle school fare, the approach is through the relationship of that content to higher mathematics. For example, common fractions are addressed in the context of topics such as infinite series or fractals. When prime numbers are presented, the Goldbach Conjecture is discussed. Thus, the debate over teaching basics or providing enrichment is sidestepped. Both are essential.

The Real Numbers: This course covers the whole numbers, the Integers, fractions, mixed number and decimals. Students learn the meaning and representations of the Real numbers, their relationships to one another and the overall nature of the Real Number systems as consisting of both the Rational and the Irrational numbers.

Discovery Mathematics: This course covers advanced topics in Mathematics with a Socratic teaching approach. Each student is encouraged to explore Mathematics in collaboration with his/her fellow students, formulating his/her own theories and eventually coming to significant mathematical discoveries. The standard first year course investigates the concepts of partial sums and limits.

The Operations on the Real Numbers: This course covers the main operations on the Real Numbers of addition, subtraction, multiplication and division. Students learn the meaning of these operations, their properties, how to compute them and most importantly, how to apply them in the real world.

Discovery Mathematics: This course covers additional advanced topics in Mathematics with a Socratic teaching approach. Each student is encouraged to explore Mathematics in collaboration with his/her fellow students, formulating his/her own theories and eventually coming to significant mathematical discoveries. A second year course might investigate graph theory, number theory, game theory, social choice, or probability.

Algebra I/Algebra II: Each student takes one of these courses based on previous Mathematics background and their performance on a placement exam. The topics covered in Algebra I and Algebra II are the standard topics including algebraic expressions, equations, graphing, inequalities, generalized exponents and problem-solving.

Logic: This course covers propositions, logical connectives, truth tables, logical equivalences and the validity of arguments. Students learn the basics of logical thinking in a formal way.

Proof: This course covers the meaning of Mathematical proof and the basic methods and processes involved in constructing and writing proofs. Students learn how to put together logical arguments and communicate them effectively to others. The Mathematics involved is wide ranging and proofs in other fields, such as Law, are presented.

The Foundations of Advanced Mathematics: This course covers the central mathematical concepts of sets, equivalence relations and functions. The Mathematics is abstract but powerful and the course culminates with an exploration of the notion of Infinity.

# Interested in teaching one of these courses?

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