A friendly introduction to real analysis.
We are developing an online beginner's course (based on MATH 131A/131B at UCLA1).
Join Howard for Office Hours each week. We use this time for tutoring real analysis students.
We post animated videos introducing concepts in real analysis and math research.
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Even when sequences do not converge, useful information can, in some instances, be gleaned from them by looking at their upper and lower limits (also known as limit superior and limit inferior). This graphic shows how these terms relate.#realanalysis #iteachmath #matheducation pic.twitter.com/kpHgrtFwvQ
— Typal Academy (@TypalAcademy) April 15, 2024
The diameter of a set is the least upper bound on the distance between pairs of points in the set. This graphic shows why the diameter of two overlapping sets is bounded above by the sum of the diameters of the individual sets.#realanalysis #iteachmath #matheducation pic.twitter.com/OHuRLcqbyr
— Typal Academy (@TypalAcademy) April 12, 2024
To show a set is open, we often proceed by picking an arbitrary element in the set and showing a ball around that point is also in the set. This graphic illustrates the intuition for proving the set {x : x_1 > x_2} in the plane is open. #realanalysis #iteachmath #matheducation pic.twitter.com/VxVmySS47X
— Typal Academy (@TypalAcademy) April 4, 2024
A limit point of a set can be defined by saying each ball about the point contains a distinct point that is in the set. How does this relate to "limit" in the name? Here's one way to see the connection.#realanalysis #iteachmath #matheducation pic.twitter.com/hT8L66D4Dn
— Typal Academy (@TypalAcademy) July 26, 2023
We are happy to share a mini-lesson on sequence convergence, which shows how to write a direct proof from the definition of convergence. #realanalysis #uclamathhttps://t.co/OtjOE5Dt0B
— Typal Academy (@TypalAcademy) July 17, 2023
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Course evaluations from time as a teaching assistant for 131 can be found here: 2017F evals, 2018W evals, 2018S-2A evals, and 2018S-5A evals. ↩