Book of Proof

Book of Proof by Richard Hammack.

Important for topic maps research and also captures an important distinction that is sometimes overlooked in topic maps.

From the Introduction:

This is a book about how to prove theorems.

Until this point in your education, you may have regarded mathematics as being a primarily computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers.

But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the Fundamental Theorem of Calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others
of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm.

This book will initiate you into an esoteric world. You will learn to understand and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

Quite legitimately there are topic map activities that are concerned with the efficient application and processing of particular ways to identify subjects and to determine when subject sameness has occurred.

It is equally legitimate to investigate how subject identity is viewed in different domains and the nature of data structures that can best represent those views.

Either one without the other is incomplete.

For those walking on the theoretical side of the street, I think this volume will prove to be quite valuable.

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