Real Analysis Tutoring

 I offer tutoring for undergraduate real analysis, as well as graduate real analysis. These courses can go by several different course titles, so if your course is named Advanced Calculus, Modern Analysis, Measure Theory, or Functional Analysis, then feel free to reach out and inquire about more details. Meetings are available online and in-person.

Specific topics

I am familiar with all chapters from Rudin’s Principles of Mathematical Analysis except for 10 (integration of differential forms). I’m also familiar with chapters 1 through 8, then 13, 14, 17, 18, and 20 from Royden & Fitzpatrick’s Real Analysis (4th ed). Some of these topics include

• Properties of real and complex numbers

• Basic topology

• \(\varepsilon\)-N and \(\varepsilon\)-\(\delta\) definitions of limits, infinite sequences, series, and continuity

• Differentiation and integration

• Sequences and series of functions

• Types of convergence (pointwise, uniform)

• Exponential and trigonometric functions

• Functions of several variables

• Lebesgue measure and integration theory

• General measure spaces

• \(L^p\) spaces

• Convergence theorems (bounded convergence, monotone convergence, generalized Lebesgue dominated convergence)

• Abstract normed linear spaces

• Riesz representation and duality

• Product measures

Georgia Tech Course Listings

Below are the relevant course numbers at Georgia Tech for which I offer tutoring.