Division (mathematics) | Articles containing proofs
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder exist and are unique, under some conditions. Because of this uniqueness, Euclidean division is often considered without referring to any method of computation, and without explicitly computing the quotient and the remainder. The methods of computation are called integer division algorithms, the best known of which being long division. Euclidean division, and algorithms to compute it, are fundamental for many questions concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, and modular arithmetic, for which only remainders are considered. The operation consisting of computing only the remainder is called the modulo operation, and is used often in both mathematics and computer science. (Wikipedia).
In this video we look at some formal definitions of polynomial division.
From playlist Polynomial Functions
13C Norm and Distance in Euclidean n Space
Norm and distance in Euclidean n-Space.
From playlist Linear Algebra
Solving Equations Using Multiplication or Division
This video is about Solving Equations with Multiplication and Division
From playlist Equations and Inequalities
Examples: Division by a Decimal with a Repeating Quotient
This video provides two examples of division by a decimal in which the quotient is a repeating decimal. Complete video list: http://www.mathispower4u.com
From playlist Multiplying and Dividing with Decimals
Dividing by a number is the same thing as multiplying by a reciprocal. This concept is particularly applicable when dividing by a fraction. Several examples are worked out and explained. From chapter 2 of the Algebra 1 course by Derek Owens
From playlist Algebra 1 Chapter 2 (Selected Videos)
Rings and modules 4 Unique factorization
This lecture is part of an online course on rings and modules. We discuss unique factorization in rings, showing the implications (Integers) implies (Euclidean domain) implies (Principal ideal domain) implies (Unique factorization domain). We give a few examples to illustrate these implic
From playlist Rings and modules
Abstract Algebra | A PID that is not a Euclidean Domain
We present an example of a principal ideal domain that is not a Euclidean domain. We follow the outline described in Dummit and Foote. In particular, we show that an integral domain D is a PID if and only if it has a Dedekind-Hasse Norm and that every Euclidean domain has a universal side
From playlist Abstract Algebra
Ring Theory: We define Euclidean domains as integral domains with a division algorithm. We show that euclidean domains are PIDs and UFDs, and that Euclidean domains allow for the Euclidean algorithm and Bezout's Identity.
From playlist Abstract Algebra
Existence Of Maximal Ideals - Feb 05, 2021- Rings and Modules
In this video we show using the axiom of choice that rings have maximal ideals.
From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]
Lecture 8. PIDs and Euclidean domains
From playlist Abstract Algebra 2
RNT2.5.1. Euclidean Algorithm for Z/3[x]
Ring Theory: Let f(x)=x^5+2x^3+2x^2 + x+2 and g(x)=x^4+2x^3+2x^2 be polynomials over Z/3. Use the Euclidean algorithm to find gcd(f,g), find the prime factorizations of f and g, and find coefficients for Bezout's Identity in this case. We also find a field in which f(x) factors into l
From playlist Abstract Algebra
The Euclidean Algorithm: How and Why, Visually
We explain the Euclidean algorithm to compute the gcd, using visual intuition. You'll never forget it once you see the how and why. Then we write it out formally and do an example. This is part of a playlist on GCDs and the Euclidean algorithm: https://www.youtube.com/playlist?list=PLrm
From playlist GCDs and Euclidean algorithm
In this video, you’ll learn more about dividing numbers. Visit https://www.gcflearnfree.org/multiplicationdivision/introduction-to-division/1/ for our interactive text-based lesson. This video includes information on: • Writing division expressions • Solving division problems • Remainders
From playlist Math Basics
Abstract Algebra | Introduction to Euclidean Domains
We give the definition of a Euclidean domain, provide some examples including the Gaussian Integers Z[i], and prove that every Euclidean domain is a principal ideal domain (PID). Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.mi
From playlist Abstract Algebra
Could this be the foundation of Number Theory? The Euclidean Algorithm visualized
The Euclidean Algorithm might just be the most fundamental idea in all of Number Theory. In this video I introduce the Euclidean Algorithm, taking inspiration from Martin H. Weissman's An Illustrated Theory of Numbers. You can find Martin's book here: http://illustratedtheoryofnumbers.co
From playlist Summer of Math Exposition Youtube Videos
From playlist Complex Multiplication
The Euclidean Algorithm -- Number Theory 5
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Number Theory v2