In this video, we discuss limits in ∞-categories. This is the second video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further informa
From playlist Higher Algebra
Complex polynomials and their factors | Linear Algebra MATH1141 | N J Wildberger
We look at the arithmetic of complex polynomials, prove both the Factor theorem and the Remainder theorem, and discuss the contentious "Fundamental theorem of Algebra" from a computational perspective. ************************ Screenshot PDFs for my videos are available at the website htt
From playlist Higher Linear Algebra
The matrix approach to systems of linear equations | Linear Algebra MATH1141 | N J Wildberger
We summarize the matrix approach to solving systems of linear equations involving augmented matrices and row reduction. We also study the consequences of linearity of themultiplication of a matrix and vector. ************************ Screenshot PDFs for my videos are available at the webs
From playlist Higher Linear Algebra
Regions in the complex plane | Linear Algebra MATH1141 | N J Wildberger
We show how the language of complex numbers and their polar forms allows us to describe certain regions of the complex plane. These are often given by inequalities involving either the modulus or argument of a complex number z. ************************ Screenshot PDFs for my videos are av
From playlist Higher Linear Algebra
The magic of matrix multiplication | Linear Algebra MATH1141 | N J Wildberger
We prove the crucial result that matrix multiplication is associative. Along the way we review summation notation and get practice with indices and ranges. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise over
From playlist Higher Linear Algebra
Euclidean spaces -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
The algebra of nxn matrices | Linear Algebra MATH1141 | N J Wildberger
We introduce the algebra of n by n matrices, concentrating on the 2 by 2 case. The zero and identity matrices are discussed, along with some special types. And we see how this is all a big extension of ordinary arithmetic. ************************ Screenshot PDFs for my videos are availab
From playlist Higher Linear Algebra
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
History of Geometry IV: The emergence of higher dimensions | Sociology and Pure Maths| NJ Wildberger
In this history of mathematics, the 19th century stands out as an especially important chapter in the story of geometry. One of the key developments here is the move to understanding and studying higher dimensions. Here we touch on some of these advances, with an aim to explaining: where d
From playlist Sociology and Pure Mathematics
Toward Higher Inductive Types - Michael Shulman
Michael Shulman University of California, San Diego; Member, School of Mathematics November 14, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
David Ben-Zvi: Geometric Langlands correspondence and topological field theory - Part 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Hodge theory and algebraic cycles - Phillip Griffiths
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Phillip Griffiths Institute for Advanced Study October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a f
From playlist Pierre Deligne 61st Birthday
Omer Bobrowski: Random Simplicial Complexes, Lecture I
A simplicial complex is a collection of vertices, edges, triangles, tetrahedra and higher dimensional simplexes glued together. In other words, it is a higher-dimensional generalization of a graph. In recent years there has been a growing effort in developing the theory of random simplicia
From playlist Workshop: High dimensional spatial random systems
Constructive Type Theory and Homotopy - Steve Awodey
Steve Awodey Institute for Advanced Study December 3, 2010 In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in
From playlist Mathematics
Taylor Dupuy | Spheres Packings in Hyperbolic Space
African Mathematics Seminar | 2 September 2020 Virtually hosted by the University of Nairobi Visit our webpage: https://sites.google.com/view/africa-math-seminar Sponsor: International Science Programme
From playlist Seminar Talks
From Coxeter Higher-Spin Theories to Strings and Tensor Models by Mikhail Vasiliev
ORGANIZERS : Pallab Basu, Avinash Dhar, Rajesh Gopakumar, R. Loganayagam, Gautam Mandal, Shiraz Minwalla, Suvrat Raju, Sandip Trivedi and Spenta Wadia DATE : 21 May 2018 to 02 June 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore In the past twenty years, the discovery of the AdS/C
From playlist AdS/CFT at 20 and Beyond
Vector and matrix forms for systems of linear equations | Linear Algebra MATH1141 | N J Wildberger
A system of linear equations may also be viewed in vector form, as an attempt to write one vector as a linear combination of other vectors. Or it more alternatively be viewed in matrix form. We discuss the matrix of coefficients, the vector of variables and the vector of constants. Puttin
From playlist Higher Linear Algebra
Tensionless AdS/CFT (Lecture 1) by Matthias Gaberdiel
PROGRAM KAVLI ASIAN WINTER SCHOOL (KAWS) ON STRINGS, PARTICLES AND COSMOLOGY (ONLINE) ORGANIZERS Francesco Benini (SISSA, Italy), Bartek Czech (Tsinghua University, China), Dongmin Gang (Seoul National University, South Korea), Sungjay Lee (Korea Institute for Advanced Study, South Korea
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022