Foundational Mathematics for Tertiary Students

Aim and Significance of the Book Foundational mathematics with applications in R computer software was written to fill the gap between a hitherto traditional mathematics and a quest to have a mathematical text that blends mathematical concepts with software applications. This is the contemporary way. In a fast-growing digital and information technology world, solving mathematical problems with calculators, and sometimes manually, is uninspiring and time-wasting, especially in a big data era. Today, data characteristics are many and huge, requiring practitioners to acquire computer programming skills needed for solving mathematical problems associated with such data. Apart from saving time, it helps to accomplish many tasks at a faster rate thereby creating space for development in other areas of life. In addition, deploying software applications to solving complex integral functions, for example, allows for more accurate results, better than what would have been obtained using other approximation methods. Another advantage of applying software applications to mathematical problem solving is in the area of graphing. Computer software applications provide powerful graphical manoeuvres and features that allow for multiple graphing that provides better visualisation and interpretation. To this end, the book offers to ginger the interest of early tertiary students who would have to take mathematical courses as part of their programme structure. Often, such students may not be mainstream mathematics students; hence, their interest is mostly low. Having a book that introduces them to computer applications of mathematical concepts would ordinarily be interesting. By so doing, the reported fear for mathematics would be allayed thereby helping ameliorate the usual failure associated with the subject. One significant contribution of this book would be the interest it is expected to generate and the associated implication on teaching of mathematics. It is apparent that the advent of this book would add another dimension to the teaching of mathematics in most tertiary settings, with significant emphasis on computer software application to concepts taught in class. This dimension, hitherto, was non-existing in some tertiary jurisdictions. In a nutshell, it’s expected that foundational mathematics with software applications in R would impart tertiary students quite significantly by whipping up better interest in mathematical practices. Key Features of This Book The book consists of seven chapters, covering topics in set theory, number systems and inequalities, functions and algebra as well as exponential and logarithmic functions. The rest are differential and integral calculus and differential equations. At the beginning of each chapter, one will find general objectives. These are smart objectives on the particular chapter to help readers assess knowledge acquired after reading through the chapter. There are a total of 127 worked examples and 54 trials, whose answers are provided immediately beneath the questions. Apart from the R applications to problems, solutions to examples are systematically arranged so that the ordinary student can follow without assistance. Overview of the R Computer Software Environment R is an environment that allows the user to interact with the computer using commands and receiving feed backs. It’s a programming language created in New Zealand in 1991 by Ross Ihaka and Robert Gentleman. It’s very powerful for statistical computing and graphics. The first R version, 1.0.0, was released in the year 2000. Managed by the R Development Core Team, R can be obtained from the Comprehensive R Archive Network (CRAN) web site, http://cran.r-project.org/. Apart from the fact that R is free (which may not be entirely true, because you need internet access to have full knowledge of R), its major advantage is the fact that is a programming language. What this means is that, before one executes a command successfully, then the individual might have a good understanding of what to do and what to expect. Codes or commands are typed after the prompt (>). Note that there are functions needed to execute certain tasks in R, but do not come with standard R installation. They are called “packages”. Packages are also available on the CRAN website. R is case sensitive, and to add comments to command lines, precede comments by the comment operator # and use the navigation keys ( , , ) to navigate through written commands line. Constant practice is required when one wishes to get used to R.