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What is the relation between geometry and arithmetic? How can we model the motion of the heavenly bodies? What roles do diagrams and imagination play in a demonstrative proof? What is the structure of good reasoning? Can there be mathematics of the infinite and the infinitesimal? Are there multiple geometries? Students study original and influential works of mathematics, demonstrating hundreds of theorems to one another in class, and inquiring into the foundations of geometry, mathematical physics, logic, number theory, set theory, algebra, analysis, multi-variable calculus, differential equations, and astronomy.

Books and More

Apollonius Conics

Nicolaus Copernicus On the Revolutions of the Spheres

Richard Dedekind Essays on the Theory of Numbers

René Descartes Geometry, Rules for the Direction of the Mind

Euclid Elements

Leonhard Euler Essays

Leibniz A New Method for Maxima and Minima, On Recondite Geometry

Nikolai Lobachevsky Theory of Parallels

Isaac Newton Principia

Nicomachus Arithmetic

Blaise Pascal Generation of Conic Sections

Ptolemy Almagest

François Viète Introduction to the Analytical Art

René Descartes Rules for the Direction of the Mind and Optics, Scientific Revolution

Albert Einstein

Gottlob Frege The Foundations of Arithmetic

Jacob Klein Greek Mathematical Thought and the Origin of Algebra

Ernst Mach The Science of Mechanics

C. S. Peirce Selected papers

Bertrand Russell An Introduction to Mathematical Philosophy

Alan Turing On Computable Numbers with an Application to the Entscheidungs Problem

Action in Classical and Modern Physics, from Leibniz to Feynman

Computation: Feynman, Leibniz, Lovelace, Turing, Peirce, and Searle

The Fundamental Theorem of Algebra

Meter and Form in English Poetry

Readings in the Origins of Algebra

Quantum Phenomena

Computer Programming

Abstract Algebra

Set Theory

Multivariable Calculus

Coding: It's Not Greek!

The information presented is for illustration purposes only and may not reflect the current reading list and preceptorial and study group offerings. Works listed are studied at one or both campuses, although not always in their entirety.

Senior Essay

Relating Space and Geometry: The Necessity of Spatial Experience in Association with Multiple Versions of Geometry

Senior Essay

Close Your Eyes and Learn Geometry: Embracing Radical Ideas in Lobachevskian Geometry

Senior Essay

Turning the World Inside-Out: Why the Newtonian Theory of Planetary Motion Supersedes the Ptolemaic

Senior Essay

Imaginary Geometry and Our Understanding of Space

Senior Essay

Outer Spaces Inner Intuitions – How Proofs Shape our Relation to Mathematics in Euclid and Lobachevsky

Senior Essay

Necessity, Contingency, and Freedom: An Analysis of Leibniz’s World Through the Lens of Computer Science

Senior Essay

Number, Perception and Continuity

Senior Essay

Structures of Mathematical Thought: An Essay on Kant’s Philosophy of the Mathematical Mind

Senior Essay

Hume’s Empirical Mathematics

Senior Essay

The Role of Beauty in Science as Seen in the Einstein, Podolsky, and Rosen Paper and Responses to it Within the Context of Quantum Theory

Senior Essay

Mind the Gap: The Philosophical Implications of the Divide of Logic and Intuition in Lobachevski

Senior Essay

What is a Curve? A Search for Continuity in Leibniz’s Calculus