Modular forms | Complex analysis | Hyperbolic geometry | Conformal mappings | Automorphic forms | Spherical geometry
In complex analysis, the Schwarz triangle function or Schwarz s-function is a function that conformally maps the upper half plane to a triangle in the upper half plane having lines or circular arcs for edges. The target triangle is not necessarily a Schwarz triangle, although that is the most mathematically interesting case. When that triangle is a non-overlapping Schwarz triangle, i.e. a Möbius triangle, the inverse of the Schwarz triangle function is a single-valued automorphic function for that triangle's triangle group. More specifically, it is a modular function. (Wikipedia).
The Schwarz Lemma -- Complex Analysis
Part 1 -- The Maximum Principle: https://youtu.be/T_Msrljdtm4 Part 3 -- Liouville's theorem: https://www.youtube.com/watch?v=fLnRDhhzWKQ In today's video, we want to take a look at the Schwarz lemma — this is a monumental result in the subject of one complex variable, and has lead to many
From playlist Complex Analysis
Some identities involving the Riemann-Zeta function.
After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming
What are bounded functions and how do you determine the boundness
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.
From playlist Determining Inverse Functions
Ex 1: Determine a Derivative using The Chain Rule
This video provides an example of how to determine the derivative using a chain rule. Complete Video List: http://www.mathispower4u.com
From playlist Differentiation Using the Chain Rule
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Norms in inner product spaces. Othogonality. The Cauchy-Schwarz Inequality. The Triangle Inequality. The Parallelogram Equality.
From playlist Linear Algebra Done Right
17. Graph limits IV: inequalities between subgraph densities
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Among all graphs with a given edge density, which graph h
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Graph norms and Erdos-Simonovits-Sidorenko's conjecture - Hamed Hatami
Conference on Graphs and Analysis Hamed Hatami June 8, 2012 More videos on http://video.ias.edu
From playlist Mathematics
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Mod-01 Lec-07 Cauchy Schwaz Inequality and Orthogonal Sets
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Mod-01 Lec-06 Introduction to Inner Product Spaces
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Complex Analysis (Advanced) -- The Schwarz Lemma
A talk I gave concerning my recent results on the Schwarz Lemma in Kähler and non-Kähler geometry. The talk details the classical Schwarz Lemma and discusses André Bloch. This is part 1 of a multi-part series. Part 1 -- https://youtu.be/AWqeIPMNhoA Part 2 -- https://youtu.be/hd7-iio77kc P
From playlist Complex Analysis
Topology of Norms Defined by Systems of Linear forms - Pooya Hatami
Pooya Hatami University of Chicago May 7, 2012 Gowers' uniformity norms are defined by average of a function over specific sets of linear forms. We study norms that are similarly defined by a system of linear forms. We prove that for bounded complex functions over FnpFpn, each such norm is
From playlist Mathematics
Complex Analysis (Advanced) -- The Schwarz--Pick Lemma -- The First Divide
Excerpt from a talk I gave concerning my recent results on the Schwarz Lemma in Kähler and non-Kähler geometry. The talk details the classical Schwarz Lemma and discusses André Bloch. This is part 5 of a multi-part series. Part 1 -- https://youtu.be/AWqeIPMNhoA Part 2 -- https://youtu.be/
From playlist Complex Analysis
Ex: Determine Function Values from the Graph of a Function (Cubic)
This video explains how to determine function values from the graph of a function. http://mathispower4u.com
From playlist The Properties of Functions
11. Pseudorandom graphs I: quasirandomness
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao discusses a classic result of Chung, Graham, a
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019