# Discrete Mathematics with Algorithms

by

## M. O. Albertson and J. P. Hutchinson

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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