In geometry, a valuation is a finitely additive function on a collection of admissible subsets of a fixed set with values in an abelian semigroup. For example, the Lebesgue measure is a valuation on finite unions of convex bodies (that is, non-empty compact convex sets) of Euclidean space Other examples of valuations on finite unions of convex bodies are the surface area, the mean width, and the Euler characteristic. In the geometric setting, often continuity (or smoothness) conditions are imposed on valuations, but there are also purely discrete facets of the theory. In fact, the concept of valuation has its origin in the dissection theory of polytopes and in particular Hilbert's third problem, which has grown into a rich theory, heavily reliant on advanced tools from abstract algebra. (Wikipedia).
Absolute versus relative measurements in geometry | Rational Geometry Math Foundations 134
In science and ordinary life, the distinction between absolute and relative measurements is very useful. It turns out that in mathematics this is also an important distinction. We must be prepared that some aspects of mathematics are more naturally measured relatively, rather than absolute
From playlist Math Foundations
Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Math 101 091117 Introduction to Analysis 05 Absolute Value
Absolute value: definition. Notion of distance. Properties of the absolute value: proofs. Triangle inequality
From playlist Course 6: Introduction to Analysis (Fall 2017)
I still don't get it evaluating expressions
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
What is the difference between finite and infinite sequences
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What are the formulas for arithmetic and geometric sequences
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Tropical Geometry - Lecture 3 - Fields and Varieties | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We review valuation rings. We give a few examples of discrete and non-discrete valuation rings, and give a brief sketch of how non-discrete valuation rings us
From playlist Algebraic geometry II: Schemes
Geometry of tropical varieties with a view toward applications (Lecture 1) by Omid Amini
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
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Tropical Geometry - Lecture 5 - Fundamental Theorem | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Johannes Nicaise: The non-archimedean SYZ fibration and Igusa zeta functions - part 1/3
Abstract: The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its
From playlist Algebraic and Complex Geometry
Optimization and Tropical Combinatorics (Lecture 4) 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: 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)
Tropical Geometry - Lecture 4 - Gröbner Bases and Tropical Bases | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Interaction between singularity theory and the minimal model program – Chenyang Xu – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.5 Interaction between singularity theory and the minimal model program Chenyang Xu Abstract: We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and p
From playlist Algebraic & Complex Geometry
Schemes 23: Valuations and separation
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We state a condition for morphisms of schemes to be separated in therms of discrete valuation rings, and apply this to the line with two origins and the proje
From playlist Algebraic geometry II: Schemes
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Tropical Geometry - Lecture 12 - Geometric Tropicalization | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels