John’s, we consider mathematics an integral part of our understanding of the human intellect and of the world.The mathematics tutorial seeks to give students an insight into the fundamental nature and intention of mathematics and into the kind of reasoning that proceeds systematically from definitions and principles to necessary conclusions.
He was also known to have made up his own theories, but most of them were based on the works of his predecessors. The contents of this book are still used in schools today.
“All those who have written histories bring to this point their account of the development of this science. Some of Euclid’s other works include Data, On Divisions of Figures, Phaenomina, Optics, Surface Loci, Porisms, Conics, Book of Fallacies, and Elements of Muic.
The rest of the year is devoted to studying the conic sections as presented by Apollonius, followed by the study of Descartes’s , one of the foundational works of modern mathematics.
Thinking through the differences between the Cartesian and ancient approaches occasions further reflection on the nature of mathematical objects and our efforts to understand them.
Euclid, “The most prominent mathematician of antiquity”(Euclid of Alexandria) lived in Alexandria, Egypt was born around 325 B. He never moved from Alexandria, he traveled, but he never lived any other place besides Alexandria.
There is another written document that states that Euclid was born in Megara.Tutorials meet three times a week, with one tutor and 13 to 16 students.The study of mathematics begins with Euclid’s , concentrating primarily on the geometrical books, but also giving some attention to Euclid’s treatment of number and to the relation between number and magnitude.Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. Only the first four of his other books survived till this day.He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. The rest were either lost, burned, or stolen by thieves.Then, after he was done teaching, he wrote his best work, The Elements, which is “one of the most beautiful and influential works of science in the history of mankind.” (Joyce, Elements, Intro.1996-8) It was based on the works of mathematicians that came before him, who he had much respect for, and his own thoughts and theories.The study of Euclid introduces students to a reasoned proof that articulates its presuppositions and proceeds by demonstration.The last eight weeks of the year are devoted to Ptolemy’s also gives rise to questions that will recur over the four years, such as: What is meant by “giving an account” of how such bodies move?During their four years at the college, all undergraduates study pure mathematics and the foundations of mathematical physics and astronomy.They develop rigor in thinking and appreciation of a reasoned account, as well as the spirit of inquiry the college attempts to cultivate across the curriculum.