Given positive integers and , the -th Macaulay representation of is an expression for as a sum of binomial coefficients: Here, is a uniquely determined, strictly increasing sequence of nonnegative integers known as the Macaulay coefficients. For any two positive integers and , is less than if and only if the sequence of Macaulay coefficients for comes before the sequence of Macaulay coefficients for in lexicographic order. Macaulay coefficients are also known as the combinatorial number system. (Wikipedia).
Determine Rational or Irrational Numbers (Square Roots and Decimals Only)
This video explains how to determine if a given number is rational or irrational.
From playlist Functions
Ex 1: Find the Inverse of a Function
This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Determining Inverse Functions
Ex: Find the Inverse of a Rational Function
This video explains how to find the inverse of a rational function with x in both the numerator and denominator. Site: http://mathispower4u.com Blog: http://mathispower4u.com
From playlist Determining Inverse Functions
(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
Sparse resultants in differential and difference algebra: an overview
From playlist Workshop on Model Theory, Differential/Difference Algebra, and Applications
Ex 2: Find the Inverse of a Function
This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Determining Inverse Functions
Ex: Determine a Real, Imaginary, and Complex Number
This video explains how decide if a number is best described by the set of real, imaginary, or complex numbers. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Performing Operations with Complex Numbers
Bhargav Bhatt - Prismatic cohomology and applications: Kodaira vanishing
February 21, 2022 - This is the third in a series of three Minerva Lectures. Prismatic cohomology is a recently discovered cohomology theory for algebraic varieties over p-adically complete rings. In these lectures, I will give an introduction to this notion with an emphasis on applicatio
From playlist Minerva Lectures - Bhargav Bhatt
Rewrite a number from scientific notation when it is smaller that
👉 Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu
From playlist How to Convert Scientific Notation to a Number
Jennifer WILSON - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 3
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Alfred Noël - Molien Series and a Recent Theorem of Kostant
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
R. Lazarsfeld: The Equations Defining Projective Varieties. Part 3.2
The lecture was held within the framework of the Junior Hausdorff Trimester Program Algebraic Geometry. (14.1.2014)
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Reflections: Science and Religion, Natural and Unnatural
Dwight H. Terry Lectureship October 26, 2006 Reflections: Science and Religion, Natural and Unnatural Barbara Herrnstein Smith is Braxton Craven Professor of Comparative Literature and English and director of the Center for Interdisciplinary Studies in Science and Cultural Theory at
From playlist Terry Lectures
Yang-Hui He (6/16/21): Universes as Bigdata: from Geometry, to Physics, to Machine-Learning
We briefly overview how historically string theory led theoretical physics first to algebraic/differential geometry, and then to computational geometry, and now to data science. Using the Calabi-Yau landscape - accumulated by the collaboration of physicists, mathematicians and computer sci
From playlist AATRN 2021
Commutative algebra 60: Regular local rings
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define regular local rings as the local rings whose dimension is equal to the dimension of their cotangent space. We give s
From playlist Commutative algebra
Nonlinear algebra, Lecture 5: "Nullstellensätze ", by Bernd Sturmfels
This is the fifth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Hilbert’s Nullstellensatz is a classical result from 1890, which offers a characterization of the set of all polynomials that vanish on a given v
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Y. André - Perfectoid Cohen-Macaulay rings and homological aspects of commutative algebra...
Y. André - Perfectoid Cohen-Macaulay rings and homological aspects of commutative algebra in mixed characteristic The homological turn in commutative algebra due to Auslander and Serre was pushed forward by Peskine and Szpiro with a systematic use of the Frobenius functor, which led to ti
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Math tutorial for writing the inverse of a rational function
👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the
From playlist Find the Inverse of a Function