This is an experimental video where I give answers to the (mostly) mathematical questions asked by viewers.

This lecture is part of an online undergraduate course on complex analysis. This is the first lecture, and gives a quick overview of some of the topics that might be covered, such as Cauchy's theorem, analytic continuation, the Riemann zeta function, and the Mandelbrot set. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN

This is the first part of a 3-part talk on p-adic numbers for advanced high school students. It is part of a series organized by the Berkeley mathematics circle. We define the 10-adic integers, which are similar to ordinary integers except their decimal expansion can be infinitely long. We show that one can do addition, multiplication, and subtraction with them. However they have some problems because it is possible for two nonzero 10adic integers to have zero product. We will see how to fix this in the next video. Links related to the video: Berkeley math circle: https://mathcircle.berkeley.edu/ Handout for talk: https://drive.google.com/file/d/1-UUjAqOIPK-PWUElAXWTdXJZVq7LFGAe Part 2 of talk: https://youtu.be/PeM5Hp0gWf4 Part 3 of talk: https://youtu.be/FWE3mA2otTU Further reading: Borevich and Shafarevich, Number theory, chapter 1.3 (advanced) J.-P. Serre, A course in arithmetic, chapter II (more advanced) N. Koblitz, p-adic numbers, p-adic functions, and zeta functions (very advanced, for anyone who is really ambitious)