This worksheet can be used as an in-class group worksheet or as a prequel to the lecture on this section.  Students will describe each of the theorems introduced and give an example to show how it is used.  After completion, discussion should include examples of finding zeros and how these theorems are helpful in the process.

This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.

This course will introduce you to the Western philosophical tradition through the study of thinkers such as Plato, Aristotle, Descartes, Cavendish, Hume, and Kant. You’ll grapple with questions that have been significant to philosophy from its beginnings: Questions about the nature of the mind, the existence of God, the foundations of knowledge, and the good life. You’ll also observe changes of intellectual outlook over time, and the effect of scientific, religious, and political concerns on the development of philosophical ideas.

This subject surveys main currents of European cultural and intellectual history in the modern period. Such a foundation course is central to the humanities in Europe. The curriculum introduces a set of ideas and arguments that have played a formative role in European cultural history, and acquaints them with some exemplars of critical thought. Among the topics to be considered: the critique of religion, the promise of independence, the advance of capitalism, the temptations of Marxism, the origins of totalitarianism, and the dialects of enlightenment. In addition to texts, we will also discuss pieces of art, incl. paintings and film.

A series of lectures delivered by Peter Millican to first-year philosophy students at the University of Oxford. The lectures comprise of the 8-week General Philosophy course, delivered to first year undergraduates. These lectures aim to provide a thorough introduction to many philosophical topics and to get students and others interested in thinking about key areas of philosophy. Taking a chronological view of the history of philosophy, each lecture is split into 3 or 4 sections which outline a particular philosophical problem and how different philosophers have attempted to resolve the issue. Individuals interested in the 'big' questions about life such as how we perceive the world, who we are in the world and whether we are free to act will find this series informative, comprehensive and accessible.

This course is an introduction to epistemology: the theory of knowledge. We will focus on skepticism—that is, the thesis that we know nothing at all—and we will survey a range of skeptical arguments and responses to skepticism.

This subject traces the evolution of ideas about nature, and how best to study and explain natural phenomena, beginning in ancient times and continuing through the Middle Ages and the Renaissance. A central theme of the subject is the intertwining of conceptual and institutional relations within diverse areas of inquiry: cosmology, natural history, physics, mathematics, and medicine.