Research Methodology and Techniques in Mathematics

Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Typically, the study of math is divided into two major pure mathematics or applied mathematics. Pure mathematical research involves significant mathematical exploration and the creation of original mathematics. Pure mathematics seeks to develop mathematical knowledge for its own sake rather than for any immediate practical use. Applied mathematics seeks to expand mathematical techniques for use in science and other fields or to use techniques in other fields to make contributions to the field of mathematics. Boundaries between pure mathematics and applied mathematics do not always exist. Research in the area of mathematics education has flourished over the past two decades. The book "Research Methodology and Techniques in Mathematics" is the most comprehensive and up-to-date survey of the best research, new developments, and critical conflicts and controversies in mathematics. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.