Lecture Description
We now move to the Golden age of European mathematics: the period 1500-1900, in this course on the History of Mathematics. We discuss hurdles that the Europeans faced before this time and how they emerged, with the help of Arab algebra and translations of Greek works, to harness the Hindu-Arabic number system and a host of novel symbols including Vieta's new use of letters to represent unknowns to tackle new problems. Quadratic equations had been solved by almost all earlier mathematical civilizations; cubic equations was a natural step, taken by Tartaglia and Cardano and others. Tartaglia also discovered a formula for the volume of a tetrahedron, and Vieta a trigonometric way of solving cubics.
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.