In the 19th Century, though, mathematics expanded to include mathematical or symbolic logic, and therefore came to be viewed increasingly as the science of relations or of portraying necessary conclusions. The history of mathematics is approximately as old as humanity itself. Since antiquity, mathematics has been ultimate to developments in science, engineering, and philosophy. It has grown from simple measurement and calculation, and the methodical study of the shapes and motions of physical matters, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today. Mathematics displays much more robustness in its devotion to concepts and theories than do other sciences. These days history of mathematics is a powerful tool for a disseminating an understanding of mathematics. We look at history as a way of motivating the learner to see the significance of the area being studied. We consider to history as a route to help the learner understand the path of development to a mathematical concept or process. With the history of mathematics, students will come to know that mathematics and science is a work of all civilizations and teachers will find more confidence in teaching. In this book, topics are introduced in their historical contexts will assist students to better gain and appreciate the mathematical ideas involved. It covers number theory, calculus/analysis, and several historically oriented courses and includes chapters on simple groups and combinatorics, and some topics, including the Poincare conjecture. It presents new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years. This is not intended as a comprehensive and definitive guide to all of mathematics, but as an easy-to-use summary of the major mathematicians and the developments of mathematical thought over the centuries. This is intended to introduce some of the major thinkers and some of the most important advances in mathematics.