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Many believe mathematics is only about calculations, formulas,
numbers, and strange letters. But mathematics is much more than
just crunching numbers or manipulating symbols. Mathematics is
about discovering patterns, uncovering hidden structures, finding
counterexamples, and thinking logically. Mathematics is a way of
thinking. It is an activity that is both highly creative and
challenging. This book offers an introduction to mathematical
reasoning for beginning university or college students, providing a
solid foundation for further study in mathematics, computer
science, and related disciplines. Written in a manner that directly
conveys the sense of excitement and discovery at the heart of doing
science, its 25 short and visually appealing chapters cover the
basics of set theory, logic, proof methods, combinatorics, graph
theory, and much more. In the book you will, among other things,
find answers to: What is a proof? What is a counterexample? What
does it mean to say that something follows logically from a set of
premises? What does it mean to abstract over something? How can
knowledge and information be represented and used in calculations?
What is the connection between Morse code and Fibonacci numbers?
Why could it take billions of years to solve Hanoi's Tower? Logical
Methods is especially appropriate for students encountering such
concepts for the very first time. Designed to ease the transition
to a university or college level study of mathematics or computer
science, it also provides an accessible and fascinating gateway to
logical thinking for students of all disciplines.
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