Mathematics
Bachelor of Arts in Liberal Arts
Mathematics encompasses an area of human endeavor that aids our grasp, construction, and conveyance of notions such as quantity, ratio, change, measure, value, and space and time—all basic and integral to the human experience. This statement arguably rings truer than ever today, as much of our communication, information exchange, and transactions flow over the digital highway, which is built on and most readily described by discrete mathematics. Therefore, DRBU students study mathematics as part of an integrated liberal arts curriculum and not as a separate specialty. In addition to gaining college-level mathematical skills, such as constructing geometric and analytic proofs and applying simple calculus operations, students will get to look into and reflect on one of the main human processes for gaining knowledge.
In this strand, students will read and prepare demonstrations on assigned materials, including selected primary texts, study guides, and supplements. Live demonstrations not only allow students to work through the materials, but also to think about how to communicate their rationales and insights to others. Demonstrations also bring students closer to the thinking and learning processes the authors of primary texts went through in struggling to advance new human knowledge.
Finally, developing in students the propensity to raise and ponder important questions and providing them with the learning tools to explore and address those questions are central to DRBU’s educational goals. The main activities of the Mathematics strand—reading the primary texts, performing demonstrations, and engaging in discussions around the materials—serve this central objective well by inviting students to explore and reflect on some of life’s deeper questions: What constitutes knowledge and what meaning does it have? How is such knowledge acquired? What assumptions, if any, are such knowledge contingent upon? Is the scope of knowledge limited? If so, what are the limits?
The Mathematics strand of DRBU’s Bachelor of Arts in Liberal Arts program comprises two consecutive semesters in the junior year. Students will begin the first semester with “A point is that which has no part” from Euclid’s Elements and proceed to work through much of the thirteen books of this Greek classic on geometry. The second semester follows the transition from algebra to geometry through the study of Conics by Apollonius and Geometry by Descartes. Students learn to leverage their skills in geometry to further develop their understanding of the fundamental properties of curves generated from cutting an oblique circular cone. This study provides the tools for understanding Descartes’ algebraic description of geometry and lays the foundation for modern mathematics in general and calculus in particular.
A second transition takes place from figures and spaces to motions and changes. The second portion of the semester is devoted to reading Newton’s Principia Mathematica. Attention is focused on sections of the Principia devoted to Newton’s construction of calculus using geometric methods. Readings from the Principia are supplemented with writings from Taylor, Euler, and Leibniz. Here, students are introduced to calculus from both geometrical and analytical approaches. They also develop skills in applying some simple calculus techniques. The year concludes with the reading of Dedekind’s writings on numbers theory, an area that allows students to reflect on the nature of numbers and their structural and symbolic significance in the contemporary world.