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.

1. History of Pythagoras' theorem
2. History of Pythagoras' Theorem II
3. History of Greek Geometry I
4. History of Greek Geometry II
5. History of Greek Number Theory
6. History of Greek Number Theory II
7. Infinity in Greek Mathematics
8. History of Number Theory and Algebra in Asia
9. History of Number Theory and Algebra in Asia II
10. History of Polynomial Equations
11. History of Polynomial Equations II
12. History of Analytic Geometry and the Continuum
13. History of Analytic Geometry and the Continuum II
14. History of Projective Geometry
15. History of Calculus
16. History of Infinite series
17. Mechanics and the Solar System
18. History of Non-Euclidean Geometry
19. The Number Theory Revival
20. Mechanics and Curves
21. Complex Numbers and Algebra
22. History of Differential Geometry
23. History of Topology
24. Hypercomplex Numbers
25. History of Complex Numbers and Curves
26. History of Group Theory
27. History of Galois Theory I
28. History of Galois Theory II
29. History of Algebraic Number Theory and Rings I
30. History of Algebraic Number Theory and Rings II
31. Simple groups, Lie groups, and the Search for Symmetry I
32. Simple groups, Lie groups, and the Search for Symmetry II

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.