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Mathematics

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.

Reading List

Archimedes 鈥淥n the Equilibrium of Planes,鈥 鈥淥n Floating Bodies鈥

Aristotle Poetics, Physics, Metaphysics, Nicomachaen Ethics, On Generation and Corruption, Politics, Parts of Animals, Generation of Animals

Amedeo Avogadro "Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies鈥

Claude Berthollet 鈥淓xcerpt from Essai de Statique Chimique鈥

Joseph Black 鈥淓xtracts from Lectures on the Elements of Chemistry鈥

Stanislao Cannizzaro 鈥淟etter to Professor S. De Luca鈥

John Dalton 鈥淓xtracts from A New System of Chemical Philosophy鈥

Hans Driesch 鈥淭he Science and Philosophy of the Organism鈥

Euclid Elements

Daniel Fahrenheit 鈥淭he Fahrenheit Scale鈥

Joseph-Louis Gay-Lussac 鈥淥n the Expansion of Gases by Heat,鈥 鈥淢emoir on the Combination of Gaseous Substances with Each Other鈥

William Harvey On The Motion of the Heart and Blood in Animals

Antoine Lavoisier Elements of Chemistry

Lucretius On the Nature of Things

Edme Mariotte Essays

Dmitri Mendeleev 鈥淭he Periodic Law of the Chemical Elements鈥

Nicomachus Arithmetic

Blaise Pascal Treatise on the Equilibrium of Liquids

J.L. Proust 鈥淓xcerpt from Sur Les Oxidations Metalliques鈥

Ptolemy Almagest

Hans Spemann 鈥淭he Organizer-Effect in Embryonic Development鈥 (Nobel Lecture 1935), 鈥淓mbryonic Development and Induction鈥

J. J. Thomson 鈥淓xtracts from System of Chemistry鈥

Rudolf Virchow 鈥淐ellular Pathology Lectures鈥

Apollonius Conics

Aristotle De Anima, On Interpretation, Prior Analytics, Categories

Francis Bacon Novum Organum

Nicolaus Copernicus On the Revolution of the Heavenly Spheres

Ren茅 Descartes Geometry, Discourse on Method

Johannes Kepler Astronomia Nova

Blaise Pascal Generation of Conic Sections

Ptolemy Almagest

Fran莽ois Vi猫te Introduction to the Analytical Art

Andr茅-Marie Amp猫re Essays

Daniel Bernoulli 鈥淥n the Vibrating String鈥

Charles-Augustin Coulomb 鈥淓xcerpts from Coulomb鈥檚 M茅moires sur l鈥櫭﹍ectricit茅 et le magn茅tisme鈥

Richard Dedekind Essay on the Theory of Numbers

Ren茅 Descartes Meditations, Rules for the Direction of the Mind

Leonhard Euler 鈥淩emarks on the Preceding Papers by Mr. Bernoulli鈥

Michael Faraday 鈥淓xperimental Researches in Electricity鈥

Benjamin Franklin 鈥淓xcerpt from several letters to Peter Collinson on the nature of electricity鈥

Galileo Galilei Two New Sciences

William Gilbert 鈥淒e Magnete鈥

David Hume Treatise on Human Nature

Christiaan Huygens Treatise on Light, On the Movement of Bodies by Impact

Gottfried Wilhelm Leibniz Monadology, Discourse on Metaphysics, Principles of Nature and Grace, Essays

James Clerk Maxwell 鈥淥n Faraday鈥檚 Lines of Force.鈥 鈥淥n Physical Lines of Force,鈥 鈥淎 Dynamical Theory of the Electromagnetic Field鈥

Isaac Newton Principia Mathematica

Jean-Antoine Nollet 鈥淥bservations on Several New Electrical Phenomena鈥

Hans Christian 脴rsted 鈥淓xperiments concerning the efficacy of electric conflict on the magnetic needle鈥

Brook Taylor 鈥淥n the motion of the stretched string鈥

Alessandro Volta 鈥淥n the Electricity excited by the mere contact of conducting substances of different kinds鈥

Thomas Young 鈥淥n the Nature of Light and Colors鈥

Niels Bohr 鈥淥n the Spectrum of Hydrogen鈥

Theodor Boveri Essays

Louisde Broglie 鈥淢atter Waves鈥

Charles Darwin Origin of Species

Albert Einstein 鈥淩elativity,鈥 鈥淥n the Electrodynamics of Moving Bodies,鈥 鈥淥n the Influence of Gravitation on the Propagation of Light,鈥 鈥淭he Foundation of the General Theory of Relativity,鈥 鈥淒oes the Inertia of a Body Depend upon its Energy Content?鈥

Michael Faraday 鈥淥n the Absolute Quantity of Electricity Associated with the Particles or Atoms of Matter鈥

Fran莽ois Jacob & Jacques Monod Essays

George Beadle & Edward Tatum Essays

G. H. Hardy 鈥淢endelian Proportions in a Mixed Population鈥

Georg Hegel Phenomenology of Mind

Werner Karl Heisenberg 鈥淐ritique of the Physical Concepts of the Particle Picture鈥

Edmund Husserl Crisis of the European Sciences

James Watson & Francis Crick Essays

Jean-Baptiste Lamarck 鈥淶oological Philosophy鈥

Nikolai Lobachevsky Theory of Parallels

Gregor Mendel 鈥淓xperiments with Plant Hybridization鈥

Robert Andrews Millikan 鈥淭he Electron鈥

Hermann Minkowski 鈥淪pace and Time鈥

Thomas Morgan 鈥淓volution and Genetics,鈥 鈥淭he Chromosomes and Mendel's Two Laws,鈥 鈥淭he Linkage Groups and the Chromosomes,鈥 鈥淪ex-Linked Inheritance,鈥 鈥淐rossing-Over鈥

Max Planck 鈥淭he Quantum Hypothesis鈥

Ernest Rutherford 鈥淭he Scattering of 伪 & 尾 Particles by Matter and the Structure of the Atom鈥

Erwin Schr枚dinger 鈥淔our Lectures of Wave Mechanics鈥擣irst Lecture鈥

Joel Sussman Essays

Walter Sutton Essays

J. J. Thomson 鈥淐athode Rays鈥

Albert Einstein Essays

Richard Feynman QED

G. H. Hardy A Course of Pure Mathematics

Georg Hegel Philosophy of Nature

Bertrand Russell An Introduction to Mathematical Philosophy

Computation

Computing Technology and Human Society

Neuroscience Mathematics and Natural Science

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

Rousseau on Civil Society: Two Provocative and Troubling Accounts

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

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

Senior Essay

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

Senior Essay

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

Senior Essay

Number, Perception and Continuity

Senior Essay

Imaginary Geometry and Our Understanding of Space

Senior Essay

Hume鈥檚 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鈥檚 Calculus