A Primer of Mathematical Analysis and the Foundations of Computation

<p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>This book is a different approach to teaching the foundations of mathematical analysis and of computation. The main idea is to delay the use of formal definitions which are definitions that nobody can understand without working with them. The approach of this book is to employ the history of mathematics to first develop fundamental concepts of mathematical analysis and the theory of computation and to only introduce formal definitions after the concepts are understood by the students.</span></p><p><br></p><p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>The historical order clarifies what analysis is really about and also why the theory of computation came about. The book provides students with a broader background involving for instance glimpses of cardinal arithmetic predicate logic background as well as the importance of a sound theory of the infinitesimal (which is in essence the foundations of mathematics and computation).</span></p><p><br></p><p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>There is a wealth of exercises and numerous graphical illustrations which give an experienced instructor lots of possibilities to select a stimulating course with a broader background. Even for just browsing by general readers this book presents stories insights and mathematical theories covering a window of ancient times to the present.</span></p><p><br></p><p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>The book is self explanatory and self sufficient so any staff member in the departments of mathematics or computer science can teach this course.</span></p><p><br></p><p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>This book will give the students the right techniques and skills to work with mathematical analysis and the theory of computation and to go on further to study more advanced courses on the subject.</span></p>