The Mathematical Expanse: Excursions into the Enduring Questions

Transforms your perspective of mathematics! Extend your understanding of geometric topics by investigating dimensions, fractals, topological equivalence, and other geometries. Develop your reasoning skills through identifying deception in statistics, discriminating between cause and correlation, evaluating various voting methods, and exploring chaos theory. Refine your understanding of numbers and systems through studying prime, figurate, vampire, narcissistic, powerful, abundant, and transcendental numbers. [**Note: there are two versions of this book. Read below for more details.] After studying each mathematical topic, we will consider how the topic informs our answers to questions like: Who are we? What is the nature of reality? How do we know if something is true? What is good? What is beautiful? These questions and their related sub-questions have been part of the human experience from the dawn of human history. Considering how mathematics helps to inform these questions provides for a deeper, more meaningful understanding of mathematics. This book is ideal for: - Anyone interested in extending his or her own understanding of the scope and depth of mathematics - An undergraduate “Mathematics for Liberal Arts” course - A half-year high school senior mathematics elective for students Each section features: - Introductory exercises that prompt the reader to recall relevant information or skills - Concept development sections that explain the mathematics for even the math-phobic student - Content sections that connect the mathematics to literature, art, music, science, and other subjects - A “Something to Consider” section that asks the reader to think about related enduring questions - “Covering the Reading” questions that help to process the text - “Problems” that require the reader to research and consider the topic more thoroughly [**You may wish to consider the parallel book titled "Mathematical Explorations for the Christian Thinker." That book addresses the same enduring questions in mathematics but from an explicitly Christian perspective]

Jason VanBilliard has been professionally involved in the field of mathematics education since 1997. His experiences include teaching middle school and high school mathematics, teaching mathematics and pedagogy courses at the undergraduate and graduate levels, serving as a private consultant and a consultant for College Board, working for Educational Testing Service in a variety of contexts, and presenting at local and regional mathematics education conferences. Jason holds a B.S. in 7-12 Mathematics Education and a B.S. in Bible from Cairn University in Langhorne, PA, a M.A. in Mathematics from West Chester University in West Chester, PA, and an Ed.D. in Curriculum, Instruction, and Technology in Mathematics Education from Temple University in Philadelphia, PA.