In mathematics, specifically in number theory, the extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n) is a non-decreasing function that is ultimately positive and we say that m is a minimal order for f. Similarly if M(n) is a non-decreasing function that is ultimately positive and we say that M is a maximal order for f. Here, and denote the limit inferior and limit superior, respectively. The subject was first studied systematically by Ramanujan starting in 1915. (Wikipedia).
Absolute Extrema of Functions of Two Variables
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From playlist Functions of Several Variables - Calculus
Theory of numbers: Multiplicative functions
This lecture is part of an online undergraduate course on the theory of numbers. Multiplicative functions are functions such that f(mn)=f(m)f(n) whenever m and n are coprime. We discuss some examples, such as the number of divisors, the sum of the divisors, and Euler's totient function.
From playlist Theory of numbers
Ex: Function and Inverse Function Values Using a Table
This video explains how to determine function values and inverse function values using the table of values of a function. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Determining Inverse Functions
Arithmetic statistics over number fields and function fields - Alexei Entin
Alexei Entin Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Ex: Function Arithmetic - Determine Function Values from a Table
This video explains how to find the sum, difference, product, and quotient of two functions using the graphs of the two functions. Site: http://mathispower4u.com
From playlist The Properties of Functions
Ex: Function Arithmetic - Determine Function Values from a Graph
This video explains how to find the sum, difference, product, and quotient of two functions using the graphs of the two functions. Site: http://mathispower4u.com
From playlist The Properties of 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
Ex 2: Find Sum, Difference, Product, and Quotient of Functions (Function Arithmetic)
This video provides 4 examples of how to find the sum, difference, product and quotient of functions. The domain is also given. Site: http://mathispower4u.com
From playlist The Properties of 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
Salma Kuhlmann: Real closed fields and models of Peano arithmetic
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 SPECIAL 7th European congress of Mathematics Berlin 2016.
Linear equations in smooth numbers - Lilian Matthiesen
Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for
From playlist Mathematics
Garnet Chan - Arithmetic tensor networks and integration - IPAM at UCLA
Recorded 26 January 2022. Garnet Chan of the California Institute of Technology presents "Arithmetic tensor networks and integration" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: I will discuss how to perform arithmetic with tensor networks and the consequences for the in
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Prasad's volume formula and its applications by Mikhail Belolipetsky
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
OVERKILL | an obvious inequality
We prove an "obvious" compound inequality of four numbers by first establishing the harmonic-geometric-arithmetic-quadratic mean inequality. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website
From playlist Overkill | Solving simple problems with overpowered math.
Ananth Shankar, Picard ranks of K3 surfaces and the Hecke orbit conjecture
VaNTAGe Seminar, November 23, 2021
From playlist Complex multiplication and reduction of curves and abelian varieties
Foundations - Seminar 9 - Gödel's incompleteness theorem Part 1
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Will Troiani starts the proof of Gödel's incompleteness theorem. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecati
From playlist Foundations seminar
The Complexity of the Non-commutative Determinant - Srikanth Srinivasan
The Complexity of the Non-commutative Determinant Srikanth Srinivasan Institute for Advanced Study October 11, 2010 I will talk about the computational complexity of computing the noncommutative determinant. In contrast to the case of commutative algebras, we know of (virtually) no efficie
From playlist Mathematics
Geordie Williamson: Geometric Representation Theory and the Geometric Satake Equivalence
MSI Virtual Colloquium: Geometric Representation Theory and the Geometric Satake Equivalence Geordie Williamson (University of Sydney) During this colloquium Geordie will explain in very broad terms, what the Langlands correspondence is and why people care about it. He will then explain i
From playlist Geordie Williamson: Representation theory and the Geometric Satake
Ex 2: Function Arithmetic - Add, Subtract, Multiply, and Divide with Fractional Inputs
This video provides several examples of how to add, subtract, multiply, and divide function values. Site: http://mathispower4u.com
From playlist The Properties of Functions