Number Theory | Congruence Modulo n -- Definition and Examples
We define the notion of congruence modulo n among the integers. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Congruence Modulo n Arithmetic Properties: Equivalent Relation
This video explains the properties of congruence modulo which makes it an equivalent relation. mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
In this video we continue discussing congruences and, in particular, we discuss solutions of linear congruences. The content of this video corresponds to Section 4.4 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/
From playlist Number Theory and Geometry
Number Theory | Some properties of integer congruence.
We examine some basic properties of congruence modulo n among the integers.
From playlist Modular Arithmetic and Linear Congruences
Number Theory | Linear Congruences Proposition 2
We give the proof of a proposition regarding the number of solutions of a linear congruence. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Number Theory | Congruence and Equivalence Classes
We prove the congruence modulo n is an equivalence relation on the set of integers and describe the equivalence classes.
From playlist Modular Arithmetic and Linear Congruences
Multiplicative order of a congruence class
In this video we introduce the concept of multiplicative order and we prove several properties and go over some examples. The content of this video corresponds to Section 8.1 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-
From playlist Number Theory and Geometry
Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
Peter Sarnak: Integral points on Markoff type cubic surfaces and dynamics
Abstract: Cubic surfaces in affine three space tend to have few integral points .However certain cubics such as x3+y3+z3=m, may have many such points but very little is known. We discuss these questions for Markoff type surfaces: x2+y2+z2−x⋅y⋅z=m for which a (nonlinear) descent allows for
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Number Theory | When does a linear congruence have a solution??
We give the proof of a proposition regarding linear congruences and their solvability. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
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
Richard Taylor "Reciprocity Laws" [2012]
Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu
From playlist Number Theory
A Short Course in Algebra and Number Theory - Fermat's little theorem and primes
To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the fifth lectur
From playlist A Short Course in Algebra and Number Theory
Great Abstract Algebra Book for Beginners (Covers Unique Topics)
This is considered a beginner abstract algebra book but it is quite different from other books. I used this book as a reference mainly for symmetry groups but it does contain other unique topics which you don't find in other books. Also the order in which the topics are discussed is differ
From playlist Cool Math Stuff
Lecture 7 - Relative Primality
This is Lecture 7 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2007.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Thin Matrix Groups - a brief survey of some aspects - Peter Sarnak
Speaker: Peter Sarnak (Princeton/IAS) Title: Thin Matrix Groups - a brief survey of some aspects More videos on http://video.ias.edu
From playlist Mathematics
A First Undergraduate Course in Abstract Algebra
This is an older book on Abstract Algebra. It is called A First Undergraduate Course in Abstract Algebra and it was written by Hillman and Alexanderson. Here is one version https://amzn.to/3ISQLNH Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (the
From playlist Book Reviews
George Boxer: Construction of torsion Galois representations
Find 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, bibliographies,
From playlist Algebraic and Complex Geometry
Theory of numbers: Congruences: Introduction
This lecture is part of an online undergraduate course on the theory of numbers. This lecture introduces congruences. We give some examples of using congruences to study the problem of which integers can be written as a sum of 2 or 3 squares or 3 cubes. For the other lectures in the
From playlist Theory of numbers