Ordinal numbers | Proof theory
In mathematics, 蠄0(惟蠅), widely known as Buchholz's ordinal, is a large countable ordinal that is used to measure the proof-theoretic strength of some mathematical systems. In particular, it is the proof theoretic ordinal of the subsystem -CA0 of second-order arithmetic; this is one of the "big five" subsystems studied in reverse mathematics (Simpson 1999). It is also the proof-theoretic ordinal of , the theory of finitely iterated inductive definitions, and of , a fragment of Kripke-Platek set theory extended by an axiom stating every set is contained in an admissible set. Buchholz's ordinal is also the order type of the segment bounded by in Buchholz's ordinal notation . Lastly, it can be expressed as the limit of the sequence: , , , ... (Wikipedia).
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
Determine if an Expression is a Polynomial
This video explains how to determine if an expression is a polynomial.
From playlist Introduction to Polynomials
Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
What is the definition of a monomial and polynomials with examples
馃憠 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials
My Twitter https://twitter.com/nessyhill | Instagram https://instagram.com/nessyhill Subscribe to BrainCraft! http://ow.ly/rt5IE I first heard about this story on RadioLab in their Elements episode: http://www.radiolab.org/story/elements/ It blew my mind. Go listen, it's an awesome col
From playlist Curious Stories
Selbstbewusste KI? | LaMDA | Ex Machina | KI in der Gesellschaft | Wissen Was @DoktorWhatson
Hat Googles Chat-System LaMDA wirklich ein Bewusstsein oder simuliert es ein Gespr盲ch einfach nur sehr gut? In den Medien ist der Chatbot derzeit ein gro脽es Thema. Im Science-Fiction-Film "Ex Machina" geht es um eine 盲hnliche Thematik: Ein Roboter mit extrem fortschrittlicher KI instrument
From playlist Filmbesprechungen | Wissenschaftler*innen reagieren
MAG - Lecture 7 - The Buchberger Criterion
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 7 we prove the Buchberger criterion, which allows us to recognise Grobner bases for ideals by looking at S-polynomials. The webpage for MAG is https://metauni.org/mag/. This video was recorded
From playlist MAG
Faulhaber's polynomials via Excel | Algebraic Calculus One | Anna Tomskova
Dr Anna Tomskova shows how Excel is a powerful tool for generating important mathematical sequences and objects -- in this case the Faulhaber polynomials that capture the sums of powers of natural numbers, and that contain the Bernoulli numbers as coefficients. Excel is not just oriented
From playlist Algebraic Calculus One
Solving Equations Foundation (GCSE 9-1 Maths)
Here is a short video on how to solve equations. Subscribe to the channel here: Like this video. Turn on Post Notifications
From playlist GCSE 9-1 MATHS All exam boards
Classify a polynomial then determining if it is a polynomial or not
馃憠 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
A Level Biology Revision "Structure and Properties of Starch Part 1"
In this video, we start looking at how glucose is stored in plant cells. First we explore why having a large concentration of glucose in a cell can present problems. We then look at the structure of one of the polysaccharides present in starch. This is called amylose. Image credit: Star
From playlist A Level Biology Biological Molecules
Summary for classifying polynomials
馃憠 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Labeling a polynomial based on the degree and number of terms
馃憠 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
CERIAS Security: Using process labels to obtain forensic and traceback information 5/5
Clip 5/5 Speaker: Florian Buchholz 路 Purdue University Much of the research in computer security, especially in digital forensics and intrusion detection, is concerned with retrieving and analyzing the information that is present on a system. In my talk I will analyze what kind of inf
From playlist The CERIAS Security Seminars 2005 (1)
CERIAS Security: Using process labels to obtain forensic and traceback information 4/5
Clip 4/5 Speaker: Florian Buchholz 路 Purdue University Much of the research in computer security, especially in digital forensics and intrusion detection, is concerned with retrieving and analyzing the information that is present on a system. In my talk I will analyze what kind of inf
From playlist The CERIAS Security Seminars 2005 (1)
CERIAS Security: Using process labels to obtain forensic and traceback information 2/5
Clip 2/5 Speaker: Florian Buchholz 路 Purdue University Much of the research in computer security, especially in digital forensics and intrusion detection, is concerned with retrieving and analyzing the information that is present on a system. In my talk I will analyze what kind of inf
From playlist The CERIAS Security Seminars 2005 (1)
CERIAS Security: Using process labels to obtain forensic and traceback information 1/5
Clip 1/5 Speaker: Florian Buchholz 路 Purdue University Much of the research in computer security, especially in digital forensics and intrusion detection, is concerned with retrieving and analyzing the information that is present on a system. In my talk I will analyze what kind of inf
From playlist The CERIAS Security Seminars 2005 (1)
CERIAS Security: Using process labels to obtain forensic and traceback information 3/5
Clip 3/5 Speaker: Florian Buchholz 路 Purdue University Much of the research in computer security, especially in digital forensics and intrusion detection, is concerned with retrieving and analyzing the information that is present on a system. In my talk I will analyze what kind of inf
From playlist The CERIAS Security Seminars 2005 (1)
Another Math of Infinity: Ordinals and "going past infinity"
As a follow up to the last video, here we introduce another math of infinity based on the thought experiment about infinite hotels from last time. Ordinals and well-orders in general give us a another way to think about infinite things; in terms of length and so in the context of ordinals
From playlist The CHALKboard 2022
Based on the operation learn how to classify a polynomial
馃憠 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Simplify First