| Preface | p. xiii |
| Sets | p. 1 |
| Preliminaries | p. 1 |
| Algebra of Sets | p. 4 |
| Venn Diagrams | p. 9 |
| Power Set | p. 10 |
| Countable Sets | p. 11 |
| Some Special Maps (Functions | p. 17 |
| The characteristic function | p. 21 |
| Partitions of Sets | p. 22 |
| The Minset and Maxset Normal Forms | p. 24 |
| Multisets | p. 31 |
| Propositional Calculus and Logic | p. 41 |
| Propositions | p. 41 |
| Compositions of Propositions | p. 43 |
| Truth Tables and Applications | p. 45 |
| Some Further Applications of Logic | p. 55 |
| Functionally Complete Set of Connectives | p. 63 |
| The Connectives NAND and NOR | p. 64 |
| More on Sets | p. 69 |
| The Principle of Inclusion and Exclusion | p. 69 |
| The Pigeonhole Principle | p. 81 |
| Some typical applications of the pigeonhole principle | p. 82 |
| Binary Relations | p. 89 |
| Relations | p. 89 |
| Equivalence relations | p. 89 |
| Union, intersection and inverse of relations | p. 91 |
| Composition of relations | p. 93 |
| The matrix of a relation | p. 95 |
| Closure operations on relations | p. 98 |
| Some Counting Techniques | p. 107 |
| The Principle of Mathematical Induction | p. 107 |
| Strong Induction | p. 114 |
| Arithmetic, Geometric and Arithmetic-Geometric Series | p. 131 |
| Permutations and Combinations | p. 144 |
| Rules of product and sum | p. 144 |
| Permutations | p. 147 |
| The arrangements of objects that are not all distinct | p. 149 |
| Combinations | p. 152 |
| Generation of permutations and combinations | p. 156 |
| Recurrence Relations | p. 167 |
| Partial Fractions | p. 167 |
| Rational functions | p. 167 |
| Partial fractions | p. 168 |
| Procedure for resolving into partial fractions | p. 170 |
| Some solved examples | p. 173 |
| Recurrence Relations: Preliminaries | p. 180 |
| Homogeneous solutions | p. 183 |
| Particular solutions | p. 187 |
| Solution by the method of generating functions | p. 193 |
| Some typical examples | p. 197 |
| Recurrence relations reducible to linear recurrence relations | p. 205 |
| Partially Ordered Sets | p. 213 |
| Preliminaries | p. 213 |
| Hasse Diagrams | p. 216 |
| Chains and Antichains in Posets | p. 221 |
| Graphs | p. 241 |
| Preliminaries and Graph Terminology | p. 241 |
| Some typical examples | p. 261 |
| Paths and Circuits | p. 265 |
| Shortest Path in Weighted Graphs | p. 271 |
| Eulerian Paths and Circuits | p. 281 |
| Hamiltonian Paths and Circuits | p. 298 |
| Planar Graphs | p. 309 |
| Applications | p. 313 |
| Some further examples | p. 316 |
| Graph colouring | p. 319 |
| Matrix Representations of Graphs | p. 325 |
| Adjacency matrix | p. 325 |
| Trees | p. 343 |
| Introduction and Elementary Properties | p. 343 |
| Rooted Trees | p. 350 |
| Tree Searching or Traversing a Tree | p. 362 |
| Applications of Trees | p. 376 |
| Prefix codes | p. 376 |
| Binary search trees | p. 384 |
| On counting trees | p. 388 |
| Some further examples | p. 395 |
| Spanning Trees and Cut-Sets | p. 400 |
| Minimal/Minimum/Shortest Spanning Tree | p. 416 |
| Groups | p. 443 |
| Groups: Preliminaries | p. 443 |
| Subgroups | p. 449 |
| Lagrange's theorem | p. 451 |
| Quotient Groups | p. 455 |
| Symmetric Groups | p. 457 |
| Rings | p. 467 |
| Rings | p. 467 |
| Polynomial Rings | p. 470 |
| Quotient Rings and Homomorphisms | p. 474 |
| Fields and Vector Spaces | p. 481 |
| Fields | p. 481 |
| Field extensions and minimal polynomial | p. 484 |
| Characteristic of a field | p. 485 |
| Splitting field | p. 485 |
| Vector Spaces | p. 491 |
| Basis of a vector space | p. 494 |
| Subspaces and quotient spaces | p. 498 |
| Linear transformations | p. 504 |
| Lattices and Boolean Algebra | p. 509 |
| Lattices | p. 509 |
| Lattices as Algebraic Systems | p. 515 |
| Sublattices and Homomorphisms | p. 521 |
| Distributive and Modular Lattices | p. 525 |
| Complemented Lattices | p. 541 |
| Boolean Algebras | p. 545 |
| Boolean Polynomials and Boolean Functions | p. 554 |
| Switching (or Logical) Circuits | p. 567 |
| Matrices, Systems of Linear Equations and Eigen Values | p. 577 |
| Linear System of Equations | p. 577 |
| Rank of a matrix | p. 577 |
| Linear system of equations | p. 578 |
| Elementary Row Operations, Gaussian Elimination | p. 581 |
| Elementary row operations | p. 581 |
| Gaussian elimination in matrix form | p. 583 |
| Gaussian elimination method | p. 585 |
| Direct methods for the solution of linear system of equations | p. 591 |
| Method of factorization | p. 594 |
| Some additional examples | p. 598 |
| Eigen Values | p. 600 |
| Eigen values and eigen vectors | p. 603 |
| Bibliography | p. 613 |
| Index | p. 615 |
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