Dr. Thakur Prasad – författare

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables. The mathematical statements that describe relationships are expressed using algebraic terms, expressions, or equations. As it developed, algebra was extended to other non-numerical objects, like vectors, matrices or polynomials. Then, the structural properties of these non-numerical objects were abstracted to define algebraic structures like groups, ring, fields and algebras. This textbook presents a lucid and unified description of Abstract algebra at a level which can be easily understood by the students who posses reasonable mathematical aptitude and abstract reasoning. So that they can easily understand various mathematical concepts, techniques and tools needed for their course. Efforts have been made to explain such points in depth, so that students can follow the subject easily.

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and engineering. Confusingly, linear algebra is not actually an algebra in the technical sense of the word “algebra”. Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences. Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear ones. The aim of this book’s exposition is to help students develop from being successful at their present level, in classes where a majority of the members are interested mainly in applications in science or engineering, to being successful at the next level, that of serious students of the subject of mathematics itself.

In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A "graph" in this context is made up of "vertices" or "nodes" and lines called edges that connect them. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics. Graph theory is also widely used in sociology as a way, for example, to measure actors'' prestige or to explore diffusion mechanisms, notably through the use of social network analysis software. Under the umbrella of Social Network graphs there are many different types of graphs: Starting with the Acquaintanceship and Friendship Graphs, these graphs are useful for representing whether n people know each other. next there is the influence graph. This graph is used to model whether certain people can influence the behaviour of others. Finally there''s a collaboration graph which models whether two people work together in a particular way. The measure of an actors'' prestige mentioned above is an example of this, other popular examples include the Erdõs number and six degrees of separation. A useful book that covers all relevant information related to theory and application of Graph in easy language. Contents: Introduction; Reconstruction Conjecture; Ramsey Theory; Route Problems; Directed Acyclic Graphs; Algebraic Graph Theory; Bipartite Graph.