History of Modern Mathematics

Mathematics is a vital field of study in today's modern worldbut it has its roots in the ancient world. The evolution of mathematics is as an ever-increasing series of abstractions, one that begins with the simplest counting systems, evolves into numeral systems, and expands from there. The major disciplines within mathematics sprang from the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs created the broad subdivisions of mathematics into the studies of quantity, structure, space, and change. Mathematics is an evergrowing field, but the mathematical discoveries of the past help the student to better understand the maths they study today.Selected Contents: Introduction; Theory of Numbers; Irrational and Transcendent Numbers; Complex Numbers; Quaternions and Ausdehnungslehre; Theory of Equations; Substitutions and Groups; Determinants; Quantics; Calculus; Differential Equations; Infinite Series; Theory of Functions; Probabilities and Least Squares; Analytic Geometry; Modern Geometry; Elementary Geometry and Trigonometry; Non-Euclidean Geometry; Appendix I: Important Figures in the History of Mathematics; Appendix II: A Timeline of Mathematics; Appendix III: Ancient Mathematics; Appendix IV: Indian Mathematics; Index