This book is written for students who arc prepared to make a first departure from the deeply worn path that leads from arithmetic to calculus in the typical mathematics curriculum. Because of its deliberate pace and emphasis on student readability as well as its treatment of engaging topics, this book is suitable for courses taught as several different levels.
Truth and Quantifiers.
Unlike propositions, we almost never talk about predicates being simply true or false. What is more important is the truth or fallacy of the proposition we get after substituting a value for the variable in a predicate. Hence, our discussion of the “truth” of predicates must include the set that these values come from. We will call this set the domain of the predicate, and we will never discuss the truth of predicates without making the domain clear.
Given a predicate and domain, the natural question to ask is, “Does the predicate become a true proposition when its variable is replaced by members of the domain?” The three most common answers to this question are always, sometimes, or never.
Contents.
1 Puzzles, Patterns, and Mathematical Language.
2 A Primer of Mathematical Writing.
3 Sets and Boolean Algebra.
4 Functions and Relations.
5 Combinatorics.
6 Probability.
7 Graphs and Trees.
A Rules of the Game.
В Matrices and Their Operations.
Selected Answers and Hints.
References and Further Reading.
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