Real Analysis (NEW)

What is a real number? Why are there “more” real numbers than rational numbers when both sets of numbers are infinite? If a sequence does not blow up to infinity, does this mean that it must eventually converge? Is there a function that is continuous everywhere but nowhere differentiable? What is the relationship between continuity and integrability? Real Analysis answers these questions and many more. This course revisits familiar topics, such as real numbers, sequences, series, topology in the real line, limits, continuity, and integrals, but studies them in a mathematically rigorous way. It can be the first exposure of students to abstract mathematics, where graphical, numerical, and intuitive arguments are replaced by rigorous mathematical proofs.