Courses and content Designed

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Students are introduced the category of sets, groups, rings, metric spaces, and topological spaces. Emphasis is placed on reasoning behind the choice of morphisms in each category. The class then introduces the notion of functor by way of the Fundamental Group, then expose students to some contravariant functors. Continuing with Algebraic Topology, we use covering spaces to introduce products and coproducts, initial and final object.

Students are introduced to the algebra and geometry of the complex plane, including the roots of unity in exponential form. Polynomials and Rational Functions are introduced as mappings of the Riemann Sphere, with a special emphasis on Moebius Transformations. The Cauchy-Riemann equations help students connect conservative vector fields and analytic functions. The students are exposed to all of the elementary complex functions and major theorems.

Students are introduced to the algebraic and geometric interpretation of vectors, vector operations, dot product, and cross product. This is followed by the study of calculus on vector-valued functions, including parametrization by arc length, curvature and torsion, and the TNB frame. Students, then, study calculus of multivariable functions, including LaGrange Multipliers and Integration. We finish with calculus on multivariable, vector-valued functions, including Green's and Stoke's Theorem.

 Students begin with vector spaces over the real numbers and the geometry of linear transformations along with their matrix representations. This includes the study of general vector spaces, linear transformations, and matrices with respect to various bases. Topics also include solutions to systems of equations using matrix reduction, geometric and algebraic interpretations of determinants, characteristic polynomials, eigenspaces, differential equations and Markov Chains.

We begin with the basic ideas of counting in each civilization, base representations, and early methods of computing. The first half of this course is dedicated to studying mathematical contributions from Mesopotamia, Egypt, Greece, China, India, and the Islamic World. The second half of this course focuses on the mathematical contributions  from women and mathematical feuds - Tartaglia and Cardano, Newton and Leibniz, Descartes and Fermat, Cauchy and Gauss - and we can't forget - Galois.

 This course covers the material found in a traditional Calculus book.  The lessons emphasize understanding the reasoning behind the definitions and informal/formal proofs of propositions. Each Calculus concept is interpreted algebraically, numerically, and graphically.  This course includes AP Prep  materials.

During my 10 years as leader of the American Math Competition Club at BASIS Scottsdale, I wrote a curriculum supporting the mathematics needed to perform well on the AMC 12, AIME, and USAMO.  The lessons I authored are categorized by topics and include relevant AMC 12 and AIME problems. As an additional resource, I used some AOPS content to support my lessons.