Discrete Mathematics with Algorithms

M. O. Albertson and J. P. Hutchinson

Downloadable Version

Chapters 1 through 8, as well as the Solutions to Questions and the Index, are available here in .pdf format. There are 12 files, named and with contents as listed below:

File One (pdf): Sets and Algorithms: An Introduction (Chapter 1, pp. 1 - 40)
- 1.1: Introduction
- 1.2: Binary Arithmetic and the Magic Trick Revisited
- 1.3: Algorithms
- 1.4: Between Decimal and Binary
- 1.5: Set Theory and the Magic Trick
- 1.6: Pictures of Sets
- 1.7: Subsets
- 1.8: Set Cardinality and Counting
File Two (pdf): Sets and Algorithms: An Introduction (Chapter 1, pp. 41 - 63), Arithmetic (Chapter 2, pp. 65 - 87.)
- 1.9: Functions
- 1.10: Boolean Functions and Boolean Algebra
- 1.11: A Look Back
- 2.1: Introduction
- 2.2: Exponentiation, A First Look
- 2.3: Induction
- 2.4: Three Inductive Proofs
File Three (pdf): Arithmetic (Chapter 2, pp. 88 - 126), Arithmetic of Sets ( Chapter 3, pp. 127 - 142)
- 2.5: Exponentiation Revisited
- 2.6: How Good is Fast Exponentiation?
- 2.7: How Logarithms Grow
- 2.8: The "Big Oh" Notation
- 2.9: 2^n does not equal O(p(n)): Proof by Contradiction
- 2.10: Good and Bad Algorithms
- 2.11: Another Look Back
- 3.1: Introduction
- 3.2: Binomial Coefficients
File Four (pdf): Arithmetic of Sets (Chapter 3, pp. 143 - 180)
- 3.3: Subsets of Sets
- 3.4: Permutations
- 3.5: An Application of Permutations: The Game of Mastermind
- 3.6: The Binomial Theorem
- 3.7: Important Subsets
File Five (pdf): Number Theory (Chapter 4, pp. 181 - 238)
- 4.1: Greatest Common Divisors
- 4.2: Another Look at Complexities
- 4.3: The Euclidean Algorithm
- 4.4: Fibonacci Numbers
- 4.5: The Complexity of the Euclidean Algorithm
- 4.6: Congruences and Equivalence Relations
- 4.7: An Application: Public Key Encryption Schemes
- 4.8: The Dividends
File Six (pdf): Graph Theory (Chapter 5, pp. 239 - 282)
- 5.1: Building the LAN
- 5.2: Graphs
- 5.3: Trees and the LAN
- 5.4: A Good Minimum-Weight Spanning Tree Algorithm
- 5.5: An Ode to Greed
- 5.6: Graphical Highlights
File Seven (pdf): Searching and Sorting (Chapter 6, pp. 283-338)
- 6.1: Introduction: Record Keeping
- 6.2: Searching a Sorted File
- 6.3: Sorting a File
- 6.4: Search Trees
- 6.5: Lower Bounds on Sorting
- 6.6: Recursion
- 6.7: MERGESORT
- 6.8: Sorting It All Out
File Eight (pdf): Recurrence Relations (Chapter 7, pp. 339 - 388)
- 7.1: Beginnings of Sequences
- 7.2: Iteration and Induction
- 7.3: Linear Homogeneous Recurrence Relations with Constant Coefficients
- 7.4: LHRRWCCs with Multiple Roots: More About Rabbits
- 7.5: Divide-and-Conquer Recurrence Relations
- 7.6: Recurring Thoughts
File Nine (pdf): More Graph Theory (Chapter 8, pp. 389 - 449)
- 8.1: Minimum-Distance Trees
- 8.2: Eulerian Cycles
- 8.3: Hamiltonian Cycles
- 8.4: Minimum-Weight Hamiltonian Cycles
- 8.5: Graph Coloring and an Application to Storage Allocation
File Ten (pdf): Solutions to Questions in Chapters 1 - 3
File Eleven (pdf): Solutions to Questions in Chapters 4 - 6 (4.2)
File Twelve (pdf): Solutions to Questions in Chapters 6 (4.3) - 8, and book Index

This material is posted on my web page with permission from John Wiley and Sons.

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This page was automatically updated on 9 December 2002