mathematics tutorials
The Mathematics Tutorial will give you insight into the fundamental nature and purpose of mathematics. You'll develop the ability to take mathematical definitions and principles and use them to arrive at necessary conclusions. During your 4 years at Saint Mary's you'll study pure mathematics and learn the foundations of mathematical physics and astronomy.
Freshman Mathematics: Greek Mathematics, Geometry and Astronomy
You'll begin freshman year with Euclid's Elements, including the geometrical books, his treatment of number and the relation between number and magnitude. The geometrical understanding you acquire through Euclid will lead directly into exploration of Ptolemy's Almagest, primarily his theories on the movement of heavenly bodies. The questions you encounter during freshman year will inform your entire 4-year experience in the Mathematics Tutorial.
Sophomore Mathematics: Astronomy, Conic Sections, Transition to Modern Mathematics
Sophomore Mathematics examines 2 of the most fundamental transitions in the tradition of astronomy and mathematics. During the first term you'll continue your studies of Ptolemy, eventually moving on to Copernicus's revision of Ptolemy. The rest of the year is devoted to Apollonius' presentation of the conic sections, followed by Descartes' Geometry. By the end of sophomore year students must demonstrate proficiency in basic algebra.
Junior Mathematics: Calculus, Mathematic Theory
The Junior Mathematics Tutorial pursues questions about the continuity of motion, the infinite and the infinitesimal, and the development of calculus. The year begins with Decartes Geometry, moves on to Newton's Principia and overall creates a sweeping vision of the mechanical motions of the universe.
Senior Mathematics: Non-Euclidean Geometry, Relativity, Topics in Modern Mathematics
The first term of Senior Mathematics begins with non-Euclidean geometry and Lobachevsky's Geometrical Researches on the Theory of Parallels. In the second semester you'll study Einstein's special relativity and energy-mass papers. At the end of both terms each tutor leads inquiries into a range of specific topics, including general relativity, Poincaré, Kant on space and time, Einstein's Geometry and Experience or Hawking's Einstein's Dream.
