Analysis III: Basic Properties of Riemann Integration - Lecture 1

Explore the fundamental properties of Riemann integration in this first-year Oxford Mathematics student lecture. Delve into the intricacies of proving familiar concepts, such as how the integral of a sum of two functions equals the sum of their individual integrals. Begin with a brief recap of the previous lecture on defining Riemann integration before diving into the main content. Learn how these seemingly straightforward properties require substantial mathematical work to prove, serving as an excellent introduction to the complexities of Riemann integration. Gain valuable insights into the rigorous mathematical thinking required at the university level, and understand how this lecture fits into the broader context of Oxford's mathematics curriculum, which includes tutorials and problem-solving sessions to reinforce learning.