Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Simplex: Implementation and Methods

Description

This lecture covers the implementation of the Simplex algorithm, including the creation of rational numbers, clausal forms, and the methods involved. It explains the process step by step, from defining constraints to solving linear equations.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Related concepts (14)

Rational number

In mathematics, a rational number is a number that can be expressed as the quotient or fraction \tfrac p q of two integers, a numerator p and a non-zero denominator q. For example, \tfrac{-3}{7} is a rational number, as is every integer (e.g., 5 = 5/1). The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by boldface Q, or blackboard bold \Q. A rational number is a real number.

Dyadic rational

In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number.

Construction of the real numbers

In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a mathematical structure that satisfies the definition. The article presents several such constructions. They are equivalent in the sense that, given the result of any two such constructions, there is a unique isomorphism of ordered field between them.

Gaussian rational

In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the Gaussian rational field, denoted Q(i), obtained by adjoining the imaginary number i to the field of rationals Q. The field of Gaussian rationals provides an example of an algebraic number field, which is both a quadratic field and a cyclotomic field (since i is a 4th root of unity).

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Related lectures (48)

Complex Numbers: Introduction and Operations

Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.

Linear Equations and Matrices

Introduces linear equations, matrices, systems of equations, and solution sets for 2 or 3 unknowns.

Method of Undetermined Coefficients

Explores the method of undetermined coefficients for solving non-homogeneous linear differential equations with constant coefficients.

Systems of Linear Equations and Matrices MOOC: Warm-up for EPFL MOOC: Learning to study science and engineering MOOC: Linear Algebra (Part 1)

Covers the definition and solution of linear equations with real coefficients in 2D and 3D space.

Linear Homogeneous Equations