Exploring Mathematics with CAS Assistance : Topics in Geometry, Algebra, Univariate Calculus, and Probability

Exploring Mathematics with CAS Assistance is designed as a textbook for an innovative mathematics major course in using a computer algebra system (CAS) to investigate, explore, and apply mathematical ideas and techniques in problem solving. The book is designed modularly with student investigations and projects in number theory, geometry, algebra, single variable calculus, and probability. The goal is to provoke an inquiry mindset in students and to arm them with the CAS tools to investigate low entry, open ended questions in a variety of mathematical arenas. Because of the modular design, the individual chapters could also be used selectively to design student projects in a number of upper division mathematics courses. These projects could, in fact, lead into undergraduate research projects. The existence of powerful computer algebra systems has changed the way mathematicians perform research; this book enables instructors to put some of those new methods and approaches into their undergraduate instruction. Prerequisites include a basic working knowledge of discrete mathematics and single variable calculus. Programming experience and some basic familiarity with elementary probability and statistics are beneficial but not required. The book takes a software agnostic approach and emphasizes algorithmic structure of solution methods by systematically providing their step by step verbal descriptions or suitable pseudocode that can be implemented in any CAS.