Math Refresher for Scientists and Engineers
Chapter One
ALGEBRA
Many practical applications of advanced mathematics assume the practitioner is
fluent in the language of algebra. This review of algebra includes a succinct discussion
of sets and groups, as well as a presentation of basic operations with both real
and complex numbers. Although much of this material may appear to be elementary
to the reader, its presentation here establishes a common terminology and notation
for later sections.
1.1 ALGEBRAIC AXIOMS
Sets
A set is a collection of objects. The objects are called elements or members of the set.
Example: The expression "a and b belong to the set A" can be written a,
b [member of] A, where a, b are elements or members of set A.
Let iff be the abbreviation for "if and only if." Two sets A, B are equal iff they have
the same members. In other words, sets A, B satisfy the equality A = B iff set A has
the same members as set B.
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