Elementary arithmetic | Mathematical concepts | Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not. For example, −4, 0, 82 are even because By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any even number is 0, 2, 4, 6, or 8. The same idea will work using any even base. In particular, a number expressed in the binary numeral system is odd if its last digit is 1; and it is even if its last digit is 0. In an odd base, the number is even according to the sum of its digits—it is even if and only if the sum of its digits is even. (Wikipedia).
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
Concavity and Parametric Equations Example
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Concavity and Parametric Equations Example. We find the open t-intervals on which the graph of the parametric equations is concave upward and concave downward.
From playlist Calculus
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Now that we understand division, we can talk about divisibility. A number is divisible by another if their quotient is a whole number. The smaller number is a factor of the larger one, but are there numbers with no factors at all? There's some pretty surprising stuff in this one! Watch th
From playlist Mathematics (All Of It)
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Linearity is crucial throughout mathematics. In this video, I demonstrate the linearity of linear differential equations and explain why it can be useful. This video is the first precursor to our discussion of homogeneous differential equations.
From playlist Differential Equations
The "tangent plane" of the graph of a function is, well, a two-dimensional plane that is tangent to this graph. Here you can see what that looks like.
From playlist Multivariable calculus
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This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
11_6_1 Contours and Tangents to Contours Part 1
A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.
From playlist Advanced Calculus / Multivariable Calculus
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We present some basics of divisibility from elementary number theory.
From playlist Divisibility and the Euclidean Algorithm
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Integers vary wildly in how "divisible" they are. One way to measure divisibility is to add all the divisors. This leads to 3 categories of whole numbers: abundant, deficient, and perfect numbers. We show there are an infinite number of abundant and deficient numbers, and then talk abou
From playlist Number Theory
Constraints on classical Gravitational Scattering amplitudes (Lecture 3) by Shiraz Minwalla
RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lectures
From playlist Recent Developments in S-matrix Theory (Online)
Priya Natarajan: The Politics of Equality
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From playlist The MacMillan Report
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Welcome to Financial Mathematics. In the second video of lesson 8 we consider some necessary conditions for the absence of arbitrage on the market. For example we discuss the Put-Call Parity, and the impossibility of having two (or more) risk-free assets. Topics: 00:00 Welcome 03:55 Uniq
From playlist Financial Mathematics
Proving conditional statements -- Proof Writing 10
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From playlist Proof Writing
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Interest rate parity (IRP) anticipates depreciation (appreciation) by the currency with the higher (lower) interest rate to maintain equilibrium (i.e., investor indifference). In equilibrium, 100*exp[r(b)*T]*F(0) = 100*S(0)*exp[r(q)*T] where r(b) is the base currency's interest rate and r(
From playlist Financial Markets and Products: Intro to Derivatives (FRM Topic 3, Hull Ch 1-7)
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From playlist Financial Options Theory with Mathematica
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From playlist Non-Hermitian Physics - PHHQP XVIII
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From playlist Combinatorics
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From playlist Hydrodynamics and fluctuations - microscopic approaches in condensed matter systems (ONLINE) 2021
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From playlist Multivariable calculus
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Gave an introduction to complexity the
From playlist MIT 18.404J Theory of Computation, Fall 2020