Preface

“Fundamentals of Mathematics in Medical Sciences” is a book geared toward researchers and students in the medical field. The most significant mathematical issues needed for academic and research domains are attempted to be addressed simply. To make it easier for readers to understand these key ideas, complete solutions are given for all examples, exercises, and case studies.

The book claims to be more than just a list of topics. It introduces each topic as a component of a continuous stream of mathematical ideas that are clarified with simple examples and shows how useful mathematics is in medicine.

The concept of real-valued functions of one or more variables, their parts, and their geometric representation in the plane and in space are all thoroughly examined in the first section of this book. Understanding these ideas is necessary for understanding the following subjects.

The second section discusses Independent Probability, Conditional Probability, Bayes’ theorem, and the fundamental techniques of Parametric and Nonparametric Statistics.

Using correlation theory, the Least Squares approach, and their analytical validation for the general case of polynomial real-valued functions, the third section of the book focuses on recovering real-valued functions of one or more variables. This is similar to how the first section of the book was structured. The Discrete-Time Markov Chain Model and the Hidden Markov Model are both thoroughly examined in the final section, which is devoted to advanced multivariable analytic subjects. Following comprehension, the reader will find them to be of great use in research.

The appendix of this paper provides Fortran-90 programs, Python scripts, and Linux scripts for reproducing the offered information. According to the TIOBE programming community index, Fortran is utilized in scientific computing in addition to C and C++ on supercomputer platforms and High-Performance Computing clusters as of July 2022. The information offered here should prove helpful and motivating to readers who are interested in the principles of this subject.

The National Institute of Cardiology “Ignacio Ch´avez” and the Faculty of Sciences at the National Autonomous University of Mexico have to be thanked for giving instances and examples, respectively.