Theorems about prime numbers | Articles containing proofs | Uniqueness theorems | Factorization
In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. For example, The theorem says two things about this example: first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product. The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, ). This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique; for example, This theorem generalizes to other algebraic structures, in particular to polynomial rings over a field. These structures are called unique factorization domains. (Wikipedia).
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
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217
Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin
From playlist Math Foundations
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra and some additional notes about how roots of polynomials and complex numbers are related to each other.
From playlist Modern Algebra
Theory of numbers: Fundamental theorem of arithmetic
This lecture is part of an online undergraduate course on the theory of numbers. We use Euclid's algorithm to prove the fundamental theorem of arithmetic, that every positive number is a product of primes in an essentially unique way. We then use this to prove Euler's product formula fo
From playlist Theory of numbers
Number Theory | Fundamental Theorem of Arithmetic
We give a proof of the Fundamental Theorem of Arithmetic. http://www.michael-penn.net
From playlist Number Theory
First Fundamental Theorem of Calculus Calculus 1 AB
I introduce and define the First Fundamental Theorem of Calculus. I finish by working through 4 examples involving Polynomials, Quotients, Radicals, Absolute Value Function, and Trigonometric Functions. Check out http://www.ProfRobBob.com, there you will find my lessons organized by clas
From playlist Calculus
Calculus: The Fundamental Theorem of Calculus
This is the second of two videos discussing Section 5.3 from Briggs/Cochran Calculus. In this section, I discuss both parts of the Fundamental Theorem of Calculus. I briefly discuss why the theorem is true, and work through several examples applying the theorem.
From playlist Calculus
The Primes are Infinite | MathBits
How many prime numbers are there? Quite a few. #MathBits MathBits playlist: https://www.youtube.com/playlist?list=PLztBpqftvzxXC3ow93HXIKx_yHyk5GXCE "Court Gavel - Judge's Gavel - Courtroom" by weiss_paarz_photos is licensed under CC BY-SA 2.0 ★DONATE★ ◆ Support Wrath of Math on Patre
From playlist MathBits
Grothendieck Pairs and Profinite Rigidity - Martin Bridson
Arithmetic Groups Topic: Grothendieck Pairs and Profinite Rigidity Speaker: Martin Bridson Affiliation: Oxford University Date: January 26, 2022 If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling t
From playlist Mathematics
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
Fun with finite covers of 3-manifolds - Nathan Dunfield
https://www.math.ias.edu/seminars/abstract?event=47565
From playlist Members Seminar
Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups
24th Workshop in Geometric Topology, Calvin College, June 29, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Asymptotic invariants of locally symmetric spaces – Tsachik Gelander – ICM2018
Lie Theory and Generalizations Invited Lecture 7.4 Asymptotic invariants of locally symmetric spaces Tsachik Gelander Abstract: The complexity of a locally symmetric space M is controlled by its volume. This phenomena can be measured by studying the growth of topological, geometric, alge
From playlist Lie Theory and Generalizations
Philosophy of Mathematics & Frege (Dummett 1994)
Michael Dummett gives a talk on Frege and the philosophy of mathematics. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE Another good introduction to the philosophy of mathematics: https://www.youtube.com/watch?v=XyXWnGFKTkg
From playlist Logic & Philosophy of Mathematics
Amir Mohammadi: Finitary analysis in homogeneous spaces and applications
Abstract: Rigidity phenomena in homogeneous dynamics have been extensively studied over the past few decades with several striking results and applications. In this talk, we will give an overview of recent activities related to quantitative aspect of the analysis in this context; we will a
From playlist Number Theory Down Under 9
Fundamental Theorem of Calculus (1 of 5: Considering COVID-19)
More resources available at www.misterwootube.com
From playlist Integral Calculus