## AppendixANotation

The following table defines the notation used in this book. Page numbers or references refer to the first appearance of each symbol.

Symbol Description Location
$$a \in A$$ $$a$$ is in the set $$A$$ Paragraph
$${\mathbb N}$$ the natural numbers Paragraph
$${\mathbb Z}$$ the integers Paragraph
$${\mathbb Q}$$ the rational numbers Paragraph
$${\mathbb R}$$ the real numbers Paragraph
$${\mathbb C}$$ the complex numbers Paragraph
$$A \subset B$$ $$A$$ is a subset of $$B$$ Paragraph
$$\emptyset$$ the empty set Paragraph
$$A \cup B$$ the union of sets $$A$$ and $$B$$ Paragraph
$$A \cap B$$ the intersection of sets $$A$$ and $$B$$ Paragraph
$$A'$$ complement of the set $$A$$ Paragraph
$$A \setminus B$$ difference between sets $$A$$ and $$B$$ Paragraph
$$A \times B$$ Cartesian product of sets $$A$$ and $$B$$ Paragraph
$$A^n$$ $$A \times \cdots \times A$$ ($$n$$ times) Paragraph
$$id$$ identity mapping Paragraph
$$f^{-1}$$ inverse of the function $$f$$ Paragraph
$$a \equiv b \pmod{n}$$ $$a$$ is congruent to $$b$$ modulo $$n$$ Example 1.2.30
$$n!$$ $$n$$ factorial Example 2.1.4
$$\binom{n}{k}$$ binomial coefficient $$n!/(k!(n-k)!)$$ Example 2.1.4
$$a \mid b$$ $$a$$ divides $$b$$ Paragraph
$$\gcd(a, b)$$ greatest common divisor of $$a$$ and $$b$$ Paragraph
$$\mathcal P(X)$$ power set of $$X$$ Exercise 2.4.12
$$\lcm(m,n)$$ the least common multiple of $$m$$ and $$n$$ Exercise 2.4.23
$$\mathbb Z_n$$ the integers modulo $$n$$ Paragraph
$$U(n)$$ group of units in $$\mathbb Z_n$$ Example 3.2.4
$$\mathbb M_n(\mathbb R)$$ the $$n \times n$$ matrices with entries in $$\mathbb R$$ Example 3.2.7
$$\det A$$ the determinant of $$A$$ Example 3.2.7
$$GL_n(\mathbb R)$$ the general linear group Example 3.2.7
$$Q_8$$ the group of quaternions Example 3.2.8
$$\mathbb C^*$$ the multiplicative group of complex numbers Example 3.2.9
$$|G|$$ the order of a group Paragraph
$$\mathbb R^*$$ the multiplicative group of real numbers Example 3.3.1
$$\mathbb Q^*$$ the multiplicative group of rational numbers Example 3.3.1
$$SL_n(\mathbb R)$$ the special linear group Example 3.3.3
$$Z(G)$$ the center of a group Exercise 3.5.48
$$\langle a \rangle$$ cyclic group generated by $$a$$ Theorem 4.1.3
$$|a|$$ the order of an element $$a$$ Paragraph
$$\cis \theta$$ $$\cos \theta + i \sin \theta$$ Paragraph
$$\mathbb T$$ the circle group Paragraph