Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.
Dividing polynomials with remainders
Using polynomial expressions and factoring polynomials.
Evaluating a polynomial at a given value
Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept
Terms coefficients and exponents in a polynomial
Simply a polynomial
Using the inverse of a matrix to solve a system of equations.
Understanding and solving matrices.
Using matrices to figure out if some combination of 2 vectors can create a 3rd vector
Using Gauss-Jordan elimination to invert a 3x3 matrix.
Inverting a 3x3 matrix
When and why you can't invert a matrix.
And another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form
Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
Solving a system of linear equations by putting an augmented matrix into reduced row echelon form
Another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form
Calculator for Natural Logarithms
Log-a-what? No, this tutorial is about neither chopped wood nor music (actually logarithms do have applications in music), but it is fascinating nonetheless. You know how to take an exponent. Now you can think about what exponent you have to raise a numbe
This book has seven chapters. Chapter one provides several basic notions to make this book self-contained. Chapter two introduces neutrosophic groups and neutrosophic N-groups and gives several examples. The third chapter deals with neutrosophic semigroups and neutrosophic N-semigroups, giving several interesting results. Chapter four introduces neutrosophic loops and neutrosophic N-loops. Chapter five just introduces the concept of neutrosophic groupoids and neutrosophi...
1.1 Groups, N-group and their basic Properties
It is a well-known fact that groups are the only algebraic structures with a single binary operation that is mathematically so perfect that an introduction of a richer structure within it is impossible. Now we proceed on to define a group.
DEFINITION 1.1.1: A non empty set of elements G is said to form a group if in G there is defined a binary operation, called the product and denoted by '•' such that
The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem.
1.2 Definition of Fuzzy Cognitive Maps
In this section we recall the notion of Fuzzy Cognitive Maps (FCMs), which was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices.
DEFINITION 1.2.1: An FCM is a directed graph ...