In mathematical logic, Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature of Skolem arithmetic contains only the multiplication operation and equality, omitting the addition operation entirely. Skolem arithmetic is weaker than Peano arithmetic, which includes both addition and multiplication operations. Unlike Peano arithmetic, Skolem arithmetic is a decidable theory. This means it is possible to effectively determine, for any sentence in the language of Skolem arithmetic, whether that sentence is provable from the axioms of Skolem arithmetic. The asymptotic running-time computational complexity of this decision problem is triply exponential. (Wikipedia).
Discrete Math - 4.1.2 Modular Arithmetic
Introduction to modular arithmetic including several proofs of theorems along with some computation. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Automated Theorem Proving and Axiomatic Mathematics
Jonathan Gorard
From playlist Wolfram Technology Conference 2019
Live CEOing Ep 263: Predicate Logic Theorem Proving in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Predicate Logic Theorem Proving in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Regularity and non-standard models of arithmetic #PaCE1
Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems
From playlist Logic
Logic 2 - First-order Logic | Stanford CS221: AI (Autumn 2019)
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3bg9F0C Topics: First-order Logic Percy Liang, Associate Professor & Dorsa Sadigh, Assistant Professor - Stanford University http://onlinehub.stanford.edu/ Associa
From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2019
Tim Steger: Construction of lattices defining fake projective planes - lecture 3
Recording during the meeting "Ball Quotient Surfaces and Lattices " the February 26, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Ma
From playlist Algebraic and Complex Geometry
Distinguished Visitor Lecture Series Finding randomness Theodore A. Slaman University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
Abraham Robinson’s legacy in model theory and (...) - L. Van den Dries - Workshop 3 - CEB T1 2018
Lou Van den Dries (University of Illinois, Urbana) / 27.03.2018 Abraham Robinson’s legacy in model theory and its applications ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHe
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Lajos Hajdu: Skolem’s conjecture and exponential Diophantine equations
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 24, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Calculus 1.5 Inverse Functions and Logarithms
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Foundations S2 - Seminar 4 - Lower Lowenheim-Skolem
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this lecture Will proves the lower Lowenheim-Skolem theorem. The webpage for this seminar is https://metauni.org/foundations/ You can join this seminar from anywhere, on any device, at https://www.
From playlist Foundations seminar
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
(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
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
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
Every Cube is an Arithmetic Sum (visual proof without words)
This is a short, animated (wordless) visual proof demonstrating that every cube can be written as the sum of an arithmetic progression involving the triangular numbers T_n, which are the sum of the first n positive integers. #manim #proofwithoutwords #math #mathshorts #mathvideo #mtbos
From playlist Finite Sums
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Units in a Ring (Abstract Algebra)
The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar
From playlist Abstract Algebra