Hilbert's seventeenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression of positive definite rational functions as sums of quotients of squares. The original question may be reformulated as: * Given a multivariate polynomial that takes only non-negative values over the reals, can it be represented as a sum of squares of rational functions? Hilbert's question can be restricted to homogeneous polynomials of even degree, since a polynomial of odd degree changes sign, and the homogenization of a polynomial takes only nonnegative values if and only if the same is true for the polynomial. (Wikipedia).
C56 Continuation of previous problem
Adding a bit more depth to the previous problem.
From playlist Differential Equations
A first example problem solving a linear, second-order, homogeneous, ODE with variable coefficients around a regular singular point.
From playlist Differential Equations
B25 Example problem solving for a Bernoulli equation
See how to solve a Bernoulli equation.
From playlist Differential Equations
13F Example Problems for Euclidean n Space
Some example problems in Euclidean n-Space.
From playlist Linear Algebra
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
C52 Introduction to nonlinear DEs
A first look at nonlinear differential equations. In this first video examples are shown of equations that still have explicit solutions.
From playlist Differential Equations
C47 Example problem solving a Cauchy Euler equation
The last problem solved in this section, before we move on to another technique for linear differential equations.
From playlist Differential Equations
C49 Example problem solving a system of linear DEs Part 1
Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.
From playlist Differential Equations
Infinity: The Science of Endless
"The infinite! No other question has ever moved so profoundly the spirit of man," said David Hilbert, one of the most influential mathematicians of the 19th century. A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity stil
From playlist Explore the World Science Festival
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 1) by Greg Blekherman
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 2) by Greg Blekherman
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Optimization and Tropical Combinatorics (Lecture 1) by Michael Joswig
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Optimization and Tropical Combinatorics (Lecture 2) by Michael Joswig
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME 27 June 2022 to 08 July 2022 VENUE Madhava Lecture Hall and Online Algebraic geometry is the stud
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Tropical Quantum Field Theory, Mirror Polyvector Fields and Multiplicities... by Helge Ruddat
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE 27 June 2022 to 08 July 2022 VENUE Madhava Lecture Hall and Online Algebraic geometry is the study of s
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Quantum Geometry of Matroids by Dhruv Ranganathan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Unentscheidbare Probleme in der Mathematik
Prof. Dr. Dr. Katrin Tent, Mathematikerin von der Universität Münster und derzeit Gastwissenschaftlerin am Hausdorff Research Institute for Mathematics (HIM) der Universität Bonn, sprach im 200. Jahr des Bestehens der Bonner Alma Mater über "Unterschjeidbare Probleme in der Mathematik":
From playlist Hausdorff Center goes public
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 4) by Greg Blekherman
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study o
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
C60 Example problem involving free damped motion
Example problem using a linear differential equation to solve for damped harmonic motion.
From playlist Differential Equations
Early Modern England: Politics, Religion, and Society under the Tudors and Stuarts (HIST 251) In this lecture Professor Wrightson examines the problem of order in early modern society, focusing on crimes of violence and upon property crime. In examining violence, he notes the existence
From playlist Early Modern England with Keith E. Wrightson