Sources: Real-life Math

Math 131a: Real Analysis

Real analysis is a rigorous study of the (hopefully familiar) objects from calculus: the real numbers, functions, limits, continuity, derivatives, sequences, series, and integrals. While you are likely quite familiar with computing with these objects, this course will focus on developing the theoretical foundation for the definitions, theorems, formulas, and algorithms that you are used to usin...

MATH 3001 Real Analysis

This is a study of metric spaces, a subject originally initiated by Maurice Fréchet in 1906 and subsequently developed by Hausdorff, Riesz, and ultimately Banach. The original motivation behind the theory idea was to extend the notion of convergence from the real and complex field to more abstract spaces. The idea of the metric was used by Fréchet to induce a topology on the space and later thi...

Math 321: Real Variables Ii

Annoucements • Office = MATH 221 (Directly above the Mathematics Department Office.) • Email = [email protected] • Text = “Baby Rudin” – Principles of Mathematical Analysis 3/e by Walter Rudin • Course Website = “http://www.math.ubc.ca/∼feldman/m321/” • Topics: – Riemann-Stieltjes integral (§6) – Sequences & Series of functions (§7) – Power Series, Special Functions, Fourier Series (§8) – Ano...

Math 140: Foundations of Real Analysis

Math 535: Real Groups Lecture Notes