Several complex variables | Riemann surfaces | Theta functions | Elliptic functions | Analytic functions
In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function. In the abstract theory this quasiperiodicity comes from the cohomology class of a line bundle on a complex torus, a condition of descent. One interpretation of theta functions when dealing with the heat equation is that "a theta function is a special function that describes the evolution of temperature on a segment domain subject to certain boundary conditions". Throughout this article, should be interpreted as (in order to resolve issues of choice of branch). (Wikipedia).
Daniele Agostini - Curves and theta functions: algebra, geometry & physics
Riemann’s theta function is a central object throughout mathematics, from algebraic geometry to number theory, and from mathematical physics to statistics and cryptography. One of my long term projects is to develop a program to study and connect the various aspects - geometric, computatio
From playlist Research Spotlight
Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function
In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL
From playlist Etale Theta
Calculus - Find the limit of a function using epsilon and delta
This video shows how to use epsilon and delta to prove that the limit of a function is a certain value. This particular video uses a linear function to highlight the process and make it easier to understand. Later videos take care of more complicated functions and using epsilon and delta
From playlist Calculus
Big-Theta Practice - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Introduction to Big-Theta Notation
This video introduces Big-Theta notation. http://mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Trig Functions on the Unit Circle
How do these 6 trigonometric functions fit together on the unit circle? Downloadable copy for your refridgerator: http://bit.ly/YT-TrigFunctions
From playlist Trigonometry
PreCalculus - Trigonometry (6 of 54) The Trigonometry Function: Sine Explained
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the trigonometry function: What is the sine of an angle?
From playlist Michel van Biezen: Pre-Calculus 6-9 - Trigonometry Review
The Terminal Side of Theta is given by 3x + 5y = 0, find the Six Trig Function Values of theta
The Terminal Side of Theta is given by 3x + 5y = 0, find the Six Trig Function Values of theta If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer T
From playlist Trigonometric Functions and Fundamental Identities
Lecture 01-02 Linear regression with one variable
Machine Learning by Andrew Ng [Coursera] 0105 Model representation 0106 Cost function 0107 Cost function intuition I 0108 Cost function intuition II 0109 Gradient descent 0110 Gradient descent intuition 0111 Gradient descent for linear regression 0112 What's next
From playlist Machine Learning by Professor Andrew Ng
Introduction to Probability and Statistics 131B. Lecture 10.
UCI Math 131B: Introduction to Probability and Statistics (Summer 2013) Lec 10. Introduction to Probability and Statistics View the complete course: http://ocw.uci.edu/courses/math_131b_introduction_to_probability_and_statistics.html Instructor: Michael C. Cranston, Ph.D. License: Creativ
From playlist Introduction to Probability and Statistics 131B
Tensor Calculus 3b: Change of Coordinates
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Stanford CS229: Machine Learning | Summer 2019 | Lecture 4 - Linear Regression
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Go0j18 Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
Stanford CS229: Machine Learning | Summer 2019 | Lecture 5 - Perceptron and Logistic Regression
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Eb7jw6 Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
Stanford EE104: Introduction to Machine Learning | 2020 | Lecture 7 - constant predictors
Professor Sanjay Lall Electrical Engineering To follow along with the course schedule and syllabus, visit: http://ee104.stanford.edu To view all online courses and programs offered by Stanford, visit: https://online.stanford.edu/
From playlist Stanford EE104: Introduction to Machine Learning Full Course
undergraduate machine learning 26: Optimization
Introduction to optimization: gradient descent and Newton's method. The slides are available here: http://www.cs.ubc.ca/~nando/340-2012/lectures.php This course was taught in 2012 at UBC by Nando de Freitas
From playlist undergraduate machine learning at UBC 2012
(ML 16.11) The likelihood is nondecreasing under EM (part 1)
We show that in EM, the likelihood of the data (under the sequence of estimates produced by the algorithm) is nondecreasing.
From playlist Machine Learning
Machine Learning by Andrew Ng [Coursera] 0308 The problem of overfitting 0309 Cost function 0310 Regularized linear regression 0311 Regularized logistic regression
From playlist Machine Learning by Professor Andrew Ng
Modular forms: Theta functions in higher dimensions
This lecture is part of an online graduate course on modular forms. We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors
From playlist Modular forms
22. Generalized Linear Models (cont.)
MIT 18.650 Statistics for Applications, Fall 2016 View the complete course: http://ocw.mit.edu/18-650F16 Instructor: Philippe Rigollet In this lecture, Prof. Rigollet talked about log-likelihood function, link function, and canonical link, etc. License: Creative Commons BY-NC-SA More inf
From playlist MIT 18.650 Statistics for Applications, Fall 2016