Review of Foundations of Logic and Mathematics Applications to Computer Science and Cryptography

摘要

Chapter 0 - Boolean Algebraic Logic An introduction to this chapter explains the use of mathematics and logical reasoning used for several millennia. The need for logic, mathematics and computing is justified. Its use can be traced to ancient civilizations in Babylonia, China and India. Its use includes calculation of taxes, dates of astronomical events such as eclipses and change of seasons. Terms of logic are introduced, such as hypothesis, conclusion, implication, converse and contrapositive The concept of an empty set is defined. A table lists the alphabets for logic and set theory. For example the symbols for empty set, "belongs to", "equals", "for each", "there exists" are listed. The section on well formed formulae defines an atomic formula; infix, prefix and postfix notation are differentiated. Other sections in the chapter include tautologies and contradictions, proofs by tautologies, proofs by contradictions, synthesis of logical formulae and synthesis by Karnaugh's tables.