Eric Zaslow

Abstract

This book serves a course designed to teach first-year college students to try to answer topical, real-life questions using numerical analysis, or quantitative reasoning. The goal is to develop a student’s ability to make carefully reasoned, quantitative arguments utilizing basic mathematical skills. Quantitative reasoning is universally important in all scholarship, and to drive this point home we have chosen motivating questions from a variety of real-world concerns and a host of academic disciplines. These arguments form the core of the book, and are buttressed by skills developed in the appendices. We hope that the topics we explore along the way are both stimulating and fun for the reader. In many cases, a reliable answer to the questions we pose would require a major effort by an academic researcher. Our aim is not perfection,1 but to familiarize ourselves with the methods and practices of structured, numerical arguments. The pieces of these arguments are usually “simple” aspects of mathematics or statistics. We assume a familiarity but not a facility with these skills. The appendices offer brief reviews of the essential concepts and hints to their use, but the real focus is the application of these skills to answering the questions posed. The pedagogy comes through the extensive worked examples in the text. Much of the discussion concerns the tasks of creating a wellposed question, gathering reliable research, constructing a model and recognizing its underlying assumptions and limitations. Many themes and techniques are repeated in multiple chapters, although there is a general progression in mathematical sophistication over the course of the book as the topics become more scientific. We view scientific exploration as no different from any field of inquiry, and make no attempt to separate it out. The book adopts a narrative style, an intentional contrast from the math-first approach of many curricula. Answering a variety of questions in essentially the same way should help the student get comfortable with the process of “thinking in numbers.” While individual mathematical skills may be practiced and mastered, it is the coherent assembly of these skills that quantitative reasoning demands. Professors often expect this ability in their students, and aspects of quantitative reasoning are treated in economics, statistics and mathematics courses. But few university or high-school curricula have courses dedicated to this purpose: this book is a one-stop shop for the reader to review or learn basic mathematical skills while learning how to apply them to multi-step arguments in a quantitative way. The appendices serve to remind and instruct the reader in the necessary mathematical areas, such as algebra, functions, graphs, probability and statistics. Readers should be careful to read mathematics