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
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
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
Triangle Congruence (quick review)
More resources available at www.misterwootube.com
From playlist Further Properties of Geometrical Figures
Determining if Two Triangles are Congruent by Plotting Points
👉 Learn how to show whether two triangles are congruent from the coordinate (x-y) plane. Two or more triangles are said to be congruent if they have the same shape and size. To show whether two triangles whose points on the coordinate plane are given we first plot the points on the coordin
From playlist Congruent Triangles
Introduction to Congruent Triangles
Complete videos list: http://mathispower4u.yolasite.com/ This video will define congruent triangles and state the ways to prove two triangles are congruent.
From playlist Triangles and Congruence
Determining multiple missing values using congruent polygons
👉 Learn how to solve with similar polygons. Two polygons are said to be similar if the corresponding angles are congruent (equal). When two polygons are similar the corresponding sides are proportional. Knowledge of the length of the sides or the proportion of the side lengths of one of th
From playlist Congruent Polygons
CTNT 2022 - Wieferich Primes (by Keith Conrad)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures
Tim Steger: ​Construction of lattices defining fake projective planes - lecture 8
Recording during the meeting "Ball Quotient Surfaces and Lattices " the March 01, 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 Mathe
From playlist Algebraic and Complex Geometry
In this video we introduce Fermat's little theorem and give a proof using congruences. The content of this video corresponds to Section 7.2 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
Primes and Equations | Richard Taylor
Richard Taylor, Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/taylor One of the oldest subjects in mathematics is the study of Diophantine equations, i.e., the study of whole number (or fractional) solutions to polynomial equ
From playlist Mathematics
Angelica Babei - A family of $\phi$-congruence subgroups of the modular group
In this talk, we introduce families of subgroups of finite index in the modular group, generalizing the congruence subgroups. One source of such families is studying homomorphisms of the modular group into linear algebraic groups over finite fields. In particular, we examine a family of no
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Mathematics drop-in | Thursda 18th June | Ask questions for GCSE & A-level mathematics LIVE REVISION
If you need help with GCSE or A-level mathematics, drop in and ask a question!
From playlist Past livestreams
Identifying congruent parts between two polygons
👉 Learn how to solve with similar polygons. Two polygons are said to be similar if the corresponding angles are congruent (equal). When two polygons are similar the corresponding sides are proportional. Knowledge of the length of the sides or the proportion of the side lengths of one of th
From playlist Congruent Polygons
Level raising mod 2 and arbitrary 2-Selmer ranks - Chao Li
Chao Li Harvard University December 4, 2014 We prove a level raising mod p=2p=2 theorem for elliptic curves over â„šQ, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by explaining
From playlist Mathematics
Introduction to number theory lecture 9: Congruences
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 This lecture revies congruences, proves Fermat's theorem, and gives some applications of it
From playlist Introduction to number theory (Berkeley Math 115)
Prasad's work on the congruence subgroup problem by Andrei Rapinchuk
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)
Do you know the five tests for congruent triangles? In this video I explain congruence and go through some example problems. anime opening: https://www.youtube.com/watch?v=m1GIFsT5Yng
From playlist Geometry Revision
Some important facts about ≡ (mod n)
We prove some important facts about a very important equivalence relation on the integers -- congruence modulo n. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/micha
From playlist Proof Writing
What is the Definition of Congruent Triangles - Congruent Triangles
👉 Learn about congruent triangles theorems. Two or more triangles (or polygons) are said to be congruent if they have the same shape and size. There are many methods to determine whether two triangles are congruent. Some of the methods include: (1) The SSS (Side Side Side) congruency the
From playlist Congruent Triangles