At the beginning of the 20th century, the German mathematician David Hilbert (1862–1943) advocated an ambitious program to formulate a system of axioms and rules of inference that would encompass all ...

In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus. In the Limit Laws video, we introduce the limit laws and discuss how to ...

Calculus has a formidable reputation as being difficult and/or unpleasant, but it doesn’t have to be. Bringing humor and a sense of play to the topic can go a long way toward demystifying it. That’s ...

For four decades, a quiet boundary in pure mathematics kept a powerful theorem locked inside the safe world of finite quantities. Now a new result known as Sebestyen’s theorem has pushed that boundary ...

Concepts covered in this course include: standard functions and their graphs, limits, continuity, tangents, derivatives, the definite integral, and the fundamental theorem of calculus. Formulas for ...