Mathematical proofs | Elementary mathematics
In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain theorems, like the prime number theorem, could only be proved by invoking "higher" mathematical theorems or techniques. However, as time progresses, many of these results have also been subsequently reproven using only elementary techniques. While there is generally no consensus as to what counts as elementary, the term is nevertheless a common part of the mathematical jargon. An elementary proof is not necessarily simple, in the sense of being easy to understand or trivial. In fact, some elementary proofs can be quite complicated — and this is especially true when a statement of notable importance is involved. (Wikipedia).
Prove that there is a prime number between n and n!
A simple number theory proof problem regarding prime number distribution: Prove that there is a prime number between n and n! Please Like, Share and Subscribe!
From playlist Elementary Number Theory
Introduction to Indirect Proof
This video introduces indirect proof and proves one basic algebraic and one basic geometric indirect proof. Complete Video List: http://mathispower4u.yolasite.com/
From playlist Relationships with Triangles
Introduction to Direct Proofs: If n is even, then n squared is even
This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Mathematical Induction - Inequalities (1 of 4: General pointers)
More resources available at www.misterwootube.com
From playlist Introduction to Proof by Mathematical Induction
Last review for Introduction to Higher Mathematics (Proofs)
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Equivalence relations -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Number Theory - Fundamental Theorem of Arithmetic
Fundamental Theorem of Arithmetic and Proof. Building Block of further mathematics. Very important theorem in number theory and mathematics.
From playlist Proofs
In this first video in our mathematical proof series, (the slightly injured) Ben discusses direct proofs and shows two examples.
From playlist Basics: Proofs
AN ELEMENTARY PROOF OF BERTRAND'S POSTULATE! Special #SoMe1
I love when a deep result in mathematics is provable only with elementary techniques, like basic knowledge of combinatorics and arithmetic. In this video I will present the queen of this proofs, namely the Erdős' proof of the Bertrand's postulate, which states that it is always possible to
From playlist Summer of Math Exposition Youtube Videos
Nima Rasekh - Every Elementary Higher Topos has a Natural Number Object
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/NimaSlidesToposesOnline.pdf One key aspect of elementary topos theory is the existence of a natural number object. W
From playlist Toposes online
Math 060 Linear Algebra 092017 Properties of Determinants
Recall statement of theorem on interaction of elementary row operations and the determinant. Rephrasal of theorem as det(EA) = det(E)det(A) for elementary matrices E. Proof of third part: first "wrong cofactor lemma"; then use lemma to finish proof. Corollary: A is invertible if and onl
From playlist Course 4: Linear Algebra (Fall 2017)
Linear Algebra 14TBD: An Application of the Product Property of the Determinant
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications
Groups with bounded generation: properties and examples - Andrei S. Rapinchuk
Arithmetic Groups Topic: Groups with bounded generation: properties and examples Speaker: Andrei S. Rapinchuk Affiliation: University of Virginia Date: October 20, 2021 After surveying some important consequences of the property of bounded generation (BG) dealing with SS-rigidity, the co
From playlist Mathematics
The Complexity of Multilinear Averages - Frederick Manners
Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory Topic: The Complexity of Multilinear Averages Speaker: Frederick Manners Affiliation: Von Neumann Fellow, School of Mathematics Date: February 28, 2023 A central question in additive combinatorics is to determine wh
From playlist Mathematics
Math 060 091117 Multiplicative Inverses, Elementary Matrices
Multiplicative inverses: definition, examples, uniqueness of. Inverse of a product. Exercise. Invertible matrices and the solution set of a linear system. Elementary row operations correspond to elementary matrices.
From playlist Course 4: Linear Algebra (Fall 2017)
Mikhail Gromov - 1/4 Old, New and Unknown around Scalar Curvature
Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove
From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature
Elliptic Curves: Good books to get started
A few books for getting started in the subject of Elliptic Curves, each with a different perspective. I give detailed overviews and my personal take on each book. 0:00 Intro 0:41 McKean and Moll, Elliptic Curves: Function Theory, Geometry, Arithmetic 10:14 Silverman, The Arithmetic of El
From playlist Math
Linear Algebra 14TBD: Complete Proof of the Product Property of the Determinant
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications
We present updates to the automated geometric functionality of the Wolfram Language introduced in Version 12 and display new functionality for automated geometric reasoning.
From playlist Wolfram Technology Conference 2021
Learning to write an algebraic proof
👉 Learn how to write an algebraic proof. Algebraic proofs are used to help students understand how to write formal proofs where we have a statement and a reason. In the case of an algebraic proof the statement will be the operations used to solve an algebraic equation and the reason will
From playlist Parallel Lines and a Transversal