MATHEMATICAL REASONING

WHY THIS BOOK WAS CREATED

This textbook is prepared as a college level program designed to satisfy the mathematics graduation requirement for liberal arts majors. The primary goal of the program is for students to develop a mathematical lens through which to view the world and gain deeper understanding of environmental, economic, social, and political issues. It is this author’s belief that the emphasis in this learning experience should be more about the construction of arguments and the interpretation of real data and less about the computation of numbers. (As a prerequisite for this course, students should be proficient with high school algebra). Throughout this course, thoughtful attention to reasoning processes will develop the habits of mind that allow students to effectively use mathematics in their academic, professional, and personal lives.

In particular, this course will target the development of these primary habits:

  • How to ask probing questions
  • How to identify underlying assumptions
  • How to gather and organize real data
  • How to reach and support a conclusion

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DEFINITE POSSIBILITIES

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WHY THIS BOOK WAS WRITTEN

Too many people have the wrong impression of mathematics. Math classes and textbooks are typically burdened by decontextualized and algorithmic exercises that seem irrelevant to one's life. In contrast, this progressive book offers a fresh perspective -- a highly pragmatic and philosophical approach to mathematical reasoning, while forming a new theory of subjective rationalism. There are three ways in which we filter the reality of the world around us -- subjectively, objectively, and with uncertainty. Accordingly, this book begins with a study of social choice mathematics and the variables of decision making. Next, it examines formal logic and an objective search for truth. The second chapter includes inductive and deductive reasoning, and the principles of argumentation from a mathematical perspective. The third chapter contains a comprehensive introduction to probability -- including simple, compound, conditional, and binomial probabilities. The book concludes with an entertaining exploration of game theory, integrating key concepts from throughout the book. Written with a purpose -- featuring recurring themes of social justice and interconnected content, this book cultivates the tools that enable a reader to construct a more sophisticated lens through which to view the world.