Mathematics

This relies on a multi-year and well-integrated study, beginning in middle school and ending by the 10th or 11th grade of the core subjects of Algebra, Trigonometry, Geometry, and Calculus. This is bedrock material; as necessary for a citizenry informed of the many scientific and technological issues which impact the nation as it is for students’ future studies.

AMSA and its foundational charter were specifically constructed to address the comparatively poor preparation of American students for what is to come later. There is a sharp qualitative leap in what is typically asked of students as they move from high school to their mathematically based college coursework, and to thrive in such programs is a very different proposition from admission. It is one of our important aims that, to the best of their ability, our students are prepared to succeed in whatever path taken in study and life. To this end we have developed a variety of courses as capstone to the mathematics curriculum. These courses include Calculus at Honors and AP levels, Multivariable Calculus, Linear Algebra with Differential Equations, Statistics at Honors and AP levels, topics via Independent Study, and Accounting/Financial Math. These are at the first and second year college level, and offer our junior and senior students the opportunity to gain familiarity and competence with important notions, methods, and styles of mathematical reasoning. They also offer the sustained practice needed to reinforce and extend skills in useful techniques and applications. It is the faculty’s conviction that AMSA students are thus offered a preparation for scientific and other technical fields which is rarely matched among American public schools.

It is here, more than anywhere else that Thurston’s statement speaks to us. In learning and in teaching, the weight of experience makes it clear that to understand mathematical ideas takes both sustained hard thought and a measure of inspiration. While memory, competence with routine calculations, and clarity on algorithms have a significant role to play, to really grasp the material, to know things inside out, asks the student to question, to critique, and to demand justification from the teacher and from themselves. Isaac Newton remarked that the true understanding of a thing did not come unless he could create it for himself from first principles. The faculty is acutely aware of how much is demanded for the attainment of such genuine understanding, and is dedicated to achieving an educational culture which makes it possible for our students to think imaginatively, to probe alternatives and to view ideas from a variety of perspectives.

Today the beauty and power of math underpins all of the sciences and is increasingly important in the humanities. Under construction are courses that will permit students to apply mathematics to research problems that link to the other departments. It is envisioned that beyond the traditional areas of Chemistry and Physics, areas which students may also profitably explore this connection include History, Art, Biology, and Computer Science. It is the goal of the faculty to give insight into the range and unifying power of mathematical thought and to provide our students with the knowledge and means to intelligently enter into its varied uses.

Our faculty is held to the highest standards and is dedicated to the advancement of their own learning, be it in mathematics or in pedagogical methodology or in the wider arts of education. They evaluate their own work and that of their colleagues, and reflect with honesty on what runs fair and what requires rethinking. Intellectual honesty is a keynote and our faculty consistently strives for the attainment and the sharing of the best possible practices that will lead to the success of AMSA’s students. Ultimately, any faculty that is to seek the best from its students must offer the best from itself.