This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
The Cantor Set, one of the most important sets in mathematics. Come and see why it’s so important, enjoy! Cantor Intersection Theorem https://youtu.be/PybSLopesaE Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel: youtube.c
From playlist Topology
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
Complete metric space: example & proof
This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.
From playlist Mathematical analysis and applications
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
Some Small Ideas in Math: A Set of Measure Zero Versus a Set of First Category (Meager Sets)
There are a ton of different ways to define what it means for a set to be "small". Here, we will focusing on the difference between a set of measure zero versus a set of first category by using examples to demonstrate that they are different sizing methods. Depending on the context of the
From playlist The New CHALKboard
G. Walsh - Boundaries of Kleinian groups
We study the problem of classifying Kleinian groups via the topology of their limit sets. In particular, we are interested in one-ended convex-cocompact Kleinian groups where each piece in the JSJ decomposition is a free group, and we describe interesting examples in this situation. In ce
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
MAE5790-23 Fractals and the geometry of strange attractors
Analogy to making pastry. The geometry underlying chaos: Stretching, folding, and reinjection of phase space. The same process generates the fractal microstructure of strange attractors. Rössler attractor. Visualizing a strange attractor as an "infinite complex of surfaces" (in the words o
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
Real Analysis Ep 17: The Cantor Set
Episode 17 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about the Cantor set. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.fairfie
From playlist Math 3371 (Real analysis) Fall 2020
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Group actions on 1-manifolds: A list of very concrete open questions – Andrés Navas – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.8 Group actions on 1-manifolds: A list of very concrete open questions Andrés Navas Abstract: Over the last four decades, group actions on manifolds have deserved much attention by people coming from different fields
From playlist Dynamical Systems and ODE
A. Wright - Mirzakhani's work on Earthquakes (Part 1)
We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The s
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Professor Adrian Moore journeys through philosophical thought on infinity over the last two and a half thousand years. This comes from a BBC radio series. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE 00:00 Horror of the I
From playlist Logic & Philosophy of Mathematics
Danny Calegari: Big Mapping Class Groups - lecture 3
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h
From playlist Topology
Danny Calegari: Big Mapping Class Groups - lecture 1
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h
From playlist Topology
MAST30026 Lecture 2: Examples of spaces (Part 1)
I started with the definition of a metric space, we briefly discussed the example of Euclidean space (proofs next time) and then I started to explain a few natural metrics on the circle. Lecture notes: http://therisingsea.org/notes/mast30026/lecture2.pdf The class webpage: http://therisin
From playlist MAST30026 Metric and Hilbert spaces