Mathematical Explorations with MATLAB is designed for the type of mathematics usually encountered in first-year university courses. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain fluency with MATLAB; no starting knowledge is assumed. A variety of topics are covered such as matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations. The book is divided into three parts. Part One comprises a very elementary 'hands-on' introduction to the features of MATLAB, followed by a series of methods chapters. Part Two contains a variety of projects, which build on earlier ideas. Part Three contains a number of 'Modelling Projects' in which the reader is invited to employ some of the skills developed in Part One.