Lecture Description
Calculus has its origins in the work of the ancient Greeks, particularly of Eudoxus and Archimedes, who were interested in volume problems, and to a lesser extent in tangents. In the 17th century the subject was widely expanded and developed in an algebraic way using also the coordinate geometry of Descartes. This is one of the most important developments in the history of mathematics. Calculus has two branches: the differential and integral calculus. The former arose from the study by Fermat of maxima and minima of functions via horizontal tangents. The integral calculus computes areas and volumes beyond the techniques of Archimedes. It was developed independently by Newton and Leibnitz, but others contributed too. Newton's focus was on power series, for which differentiation and integration can be done term by term using a formula of Cavalieri, and which gave remarkable new formulas for pi and the circular functions. He had a dynamic view of the subject, motivated in large part by physics. Leibnitz was more interested in closed forms, and introduced the notation which we use today. Both used infinitesimals, in the form of differentials.
Course Index
- History of Pythagoras' theorem
- History of Pythagoras' Theorem II
- History of Greek Geometry I
- History of Greek Geometry II
- History of Greek Number Theory
- History of Greek Number Theory II
- Infinity in Greek Mathematics
- History of Number Theory and Algebra in Asia
- History of Number Theory and Algebra in Asia II
- History of Polynomial Equations
- History of Polynomial Equations II
- History of Analytic Geometry and the Continuum
- History of Analytic Geometry and the Continuum II
- History of Projective Geometry
- History of Calculus
- History of Infinite series
- Mechanics and the Solar System
- History of Non-Euclidean Geometry
- The Number Theory Revival
- Mechanics and Curves
- Complex Numbers and Algebra
- History of Differential Geometry
- History of Topology
- Hypercomplex Numbers
- History of Complex Numbers and Curves
- History of Group Theory
- History of Galois Theory I
- History of Galois Theory II
- History of Algebraic Number Theory and Rings I
- History of Algebraic Number Theory and Rings II
- Simple groups, Lie groups, and the Search for Symmetry I
- Simple groups, Lie groups, and the Search for Symmetry II
Course Description
In this course, Prof. N.J. Wildberger from UNSW provides a great overview of the history of the development of mathematics. The course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed)Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology and hyperbolic geometry. This course is meant for a broad audience, not necessarily mathematics majors. All backgrounds are welcome to take the course and enjoy learning about the origins of mathematical ideas. Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. At UNSW, this is MATH3560 and GENS2005. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.