## A First Course in Discrete MathematicsDiscrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules. |

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### Contents

I | 1 |

II | 2 |

III | 3 |

IV | 6 |

V | 10 |

VI | 13 |

VII | 19 |

VIII | 23 |

XXVIII | 94 |

XXIX | 96 |

XXX | 99 |

XXXI | 107 |

XXXII | 112 |

XXXIII | 113 |

XXXIV | 114 |

XXXV | 115 |

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### Common terms and phrases

1-factorisation 1-factors adjacent affine plane arranged auxiliary equation binary sequences bipartite graphs bipartite tournament block contains choose codewords coefficients consider construct corresponding Deduce denote the number diagonal discrete mathematics disjoint edge colouring entries Euler's eulerian circuit Example Exercise exists four colours FPP of order given gives graph G graph of Figure Gray code greedy algorithm groups Hadamard matrix hamiltonian cycle hamiltonian graph incidence matrix inclusion-exclusion principle induction latin square league schedule Lemma magic square matrix of order memory wheel minimum modp MOLS of order non-zero Note number of edges number of solutions obtain odd number orthogonal partition permutation Petersen graph planar plane graph plane of order play problem Proof properties recurrence relation result round routes sequences of length seven-point plane Show shown in Figure Similarly spanning tree square of order subgraph subsets Suppose Theorem vertex degree

### References to this book

Shortest Connectivity: An Introduction with Applications in Phylogeny Dietmar Cieslik Limited preview - 2004 |