\documentclass{article}
\usepackage{latexsym}
\author{Geoff Smith}
\title{Introductory Mathematics: Algebra and Analysis}
\author{G.~C.~Smith}
\begin{document}
\maketitle

\noindent {\bf Preface} \hfill {v}\\ \\
{\bf 1. Sets, Functions and Relations} \hfill {1}\\
{1.1} Sets\hfill{1}\\
{1.2} Subsets\hfill{2}\\
{1.3} Well-known Sets\hfill{3}\\
{1.4} Rationals, Reals and Pictures\hfill{6}\\
{1.5} Set Operations\hfill{8}\\
{1.6} Sets of Sets\hfill{11}\\
{1.7} Paradox\hfill{14}\\
{1.8} Set-theoretic Constructions\hfill{15}\\
{1.9} Notation\hfill{16}\\
{1.10} Venn Diagrams\hfill{17}\\
{1.11} Quantifiers and Negation\hfill{19}\\
{1.12} Informal Description of Maps\hfill{21}\\
{1.13} Injective, Surjective and Bijective Maps\hfill{22}\\
{1.14} Composition of Maps\hfill{23}\\
{1.15} Graphs and Respectability Reclaimed\hfill{29}\\
{1.16} Characterizing Bijections\hfill{30}\\
{1.17} Sets of Maps\hfill{31}\\
{1.18} Relations\hfill{31}\\
{1.19} Intervals\hfill{37}\\ \\ 
{\bf 2. Proof}\hfill{39}\\
{2.1} Induction\hfill{39}\\
{2.2} Complete Induction\hfill{43}\\
{2.3} Counter-examples and Contradictions\hfill{47}\\
{2.4} Method of Descent\hfill{50}\\
{2.5} Style\hfill{53}\\
{2.6} Implication\hfill{54}\\
{2.7} Double Implication\hfill{54}\\
{2.8} The Master Plan\hfill{56}\\
\eject
\noindent {\bf 3. Complex Numbers and Related Functions}\hfill{57}\\ 
{3.1} Motivation\hfill{57}\\
{3.2} Creating the Complex Numbers\hfill{62}\\
{3.3} A Geometric Interpretation\hfill{70}\\
{3.4} Sine, Cosine and Polar Form\hfill{76}\\
{3.5} $e$\hfill{80}\\
{3.6} Hyperbolic Sine and Hyperbolic Cosine\hfill{85}\\
{3.7} Integration Tricks\hfill{88}\\
{3.8} Extracting Roots and Raising to Powers\hfill{89}\\
{3.9} Logarithm\hfill{90}\\
{3.10} Power Series\hfill{92}\\ \\
\noindent {\bf 4. Vectors and Matrices}\hfill{95}\\
{4.1} Row Vectors\hfill{95}\\
{4.2} Higher Dimensions\hfill{97}\\
{4.3} Vector Laws\hfill{98}\\
{4.4} Lengths and Angles\hfill{98}\\
{4.5} Position Vectors\hfill{103}\\
{4.6} Matrix Operations\hfill{104}\\
{4.7} Laws of Matrix Algebra\hfill{106}\\
{4.8} Identity Matrices and Inverses\hfill{108}\\
{4.9} Determinants\hfill{110}\\
{4.10} Geometry of Determinants\hfill{119}\\
{4.11} Linear Independence\hfill{120}\\
{4.12} Vector Spaces\hfill{121}\\
{4.13} Transposition\hfill{123}\\ \\
\noindent {\bf 5. Group Theory}\hfill{125}\\ 
{5.1} Permutations\hfill{125}\\
{5.2} Inverse Permutations\hfill{130}\\
{5.3} The Algebra of Permutations\hfill{131}\\
{5.4} The Order of a Permutation\hfill{133}\\
{5.5} Permutation Groups\hfill{135}\\
{5.6} Abstract Groups\hfill{136}\\
{5.7} Subgroups\hfill{142}\\
{5.8} Cosets\hfill{143}\\
{5.9} Cyclic Groups\hfill{146}\\
{5.10} Isomorphism\hfill{148}\\
{5.11} Homomorphism\hfill{151}\\ 
\eject 
\noindent {\bf 6. Sequences and Series}\hfill{153}\\ 
{6.1} Denary and Decimal Sequences\hfill{153}\\
{6.2} The Real Numbers\hfill{156}\\
{6.3} Notation for Sequences\hfill{158}\\
{6.4} Limits of Sequences\hfill{160}\\
{6.5} The Completeness Axiom\hfill{169}\\
{6.6} Limits of Sequences Revisited\hfill{170}\\
{6.7} Series\hfill{174}\\ \\ 
\noindent {7. Mathematical Analysis}\hfill{181}\\ 
{7.1} Continuity\hfill{181}\\ 
{7.2} Limits\hfill{194}\\ \\ 
\noindent {\bf 8. Creating the Real Numbers}\hfill{197}\\ 
{8.1} Dedekind's Construction\hfill{197}\\
{8.2} Construction via Cauchy Sequences\hfill{199}\\
{8.3} A Sting in the Tail: $p$-adic numbers\hfill{202}\\ \\
\noindent {\bf Further Reading}\hfill{204}\\ \\
\noindent {\bf Solutions}\hfill{205}\\ \\ 
\noindent {\bf Index}\hfill{213}
\end{document}

