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Discrete Mathematics
 
Martin Aigner :  Freie Universität Berlin, Berlin, Germany
Discrete Mathematics
Discrete Mathematics
Softcover ISBN:  978-1-4704-7063-0
Product Code:  DISCMAT.S
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
eBook ISBN:  978-1-4704-1138-1
Product Code:  DISCMAT.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-1-4704-7063-0
eBook: ISBN:  978-1-4704-1138-1
Product Code:  DISCMAT.S.B
List Price: $140.00 $107.50
MAA Member Price: $126.00 $96.75
AMS Member Price: $112.00 $86.00
Add to cart
Discrete Mathematics
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Discrete Mathematics
Discrete Mathematics
Martin Aigner :  Freie Universität Berlin, Berlin, Germany
Softcover ISBN:  978-1-4704-7063-0
Product Code:  DISCMAT.S
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
eBook ISBN:  978-1-4704-1138-1
Product Code:  DISCMAT.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-1-4704-7063-0
eBook ISBN:  978-1-4704-1138-1
Product Code:  DISCMAT.S.B
List Price: $140.00 $107.50
MAA Member Price: $126.00 $96.75
AMS Member Price: $112.00 $86.00
Add to cart
  • Book Details
     
     
    2007; 388 pp
    MSC: Primary 05; 06; 11; 90; 94;

    The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level.

    Praise for the German edition…

    This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics.

    —Konrad Engel for MathSciNet

    Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Günter M. Ziegler has been an international success with translations into 12 languages.
    Readership

    Undergraduates and graduate students interested in discrete mathematics, algorithms, and combinatorics.
  • Table of Contents
     
     
    • Cover
    • Title
    • Copyright
    • Contents
    • Prefaces
    • Part 1. Counting
    • Chapter 1. Fundamentals
    • §1.1. Elementary Counting Principles
    • §1.2. The Fundamental Counting Coefficients
    • §1.3. Permutations
    • §1.4. Recurrence Equations
    • §1.5. Discrete Probability
    • §1.6. Existence Theorems
    • Exercises for Chapter 1
    • Chapter 2. Summation
    • §2.1. Direct Methods
    • §2.2. The Calculus of Finite Differences
    • §2.3. Inversion
    • §2.4. Inclusion-Exclusion
    • Exercises for Chapter 2
    • Chapter 3. Generating Functions
    • §3.1. Definitions and Examples
    • §3.2. Solving Recurrences
    • §3.3. Generating Functions of Exponential Type
    • Exercises for Chapter 3
    • Chapter 4. Counting Patterns
    • §4.1. Symmetries
    • §4.2. Statement of the Problem
    • §4.3. Patterns and the Cycle Indicator
    • §4.4. Polya's Theorem
    • Exercises for Chapter 4
    • Chapter 5. Asymptotic Analysis
    • §5.1. The Growth of Functions
    • §5.2. Order of Magnitude of Recurrence Relations
    • §5.3. Running Times of Algorithms
    • Exercises for Chapter 5
    • Bibliography for Part 1
    • Bibliography for Part 1
    • Part 2.Graphs and Algorithms
    • Chapter 6. Graphs
    • §6.1. Definitions and Examples
    • §6.2. Representation of Graphs
    • §6.3. Paths and Circuits
    • §6.4. Directed Graphs
    • Exercises for Chapter 6
    • Chapter 7. Trees
    • §7.1. What Is a Tree?
    • §7.2. Breadth- First and Depth-First Search
    • §7.3. Minimal Spanning Trees
    • §7.4. The Shortest Path in a Graph
    • Exercises for Chapter 7
    • Chapter 8. Matchings and Networks
    • §8.1. Matchings in Bipartite Graphs
    • §8.2. Construction of Optimal Matchings
    • §8.3. Flows in Networks
    • §8.4. Eulerian Graphs and the Traveling Salesman Problem
    • §8.5. The Complexity Classes P and NP
    • Exercises for Chapter 8
    • Chapter 9. Searching and Sorting
    • §9.1. Search Problems and Decision Trees
    • §9.2. The Fundamental Theorem of Search Theory
    • §9.3. Sorting Lists
    • §9.4. Binary Search Trees
    • Exercises for Chapter 9
    • Chapter 10. General Optimization Methods
    • §10.1. Backtracking
    • §10.2. Dynamic Programming
    • §10.3. The Greedy Algorithm
    • Exercises for Chapter 10
    • Bibliography for Part 2
    • Bibliography for Part 2
    • Part 3. Algebraic Systems
    • Chapter 11. Boolean Algebras
    • §11.1. Definition and Properties
    • §11.2. Propositional Logic and Boolean Functions
    • §11.3. Logical Nets
    • §11.4. Boolean Lattices, Orders, and Hypergraphs
    • Exercises for Chapter 11
    • Chapter 12. Modular Arithmetic
    • §12.1. Calculating with Congruences
    • §12.2. Finite Fields
    • §12.3. Latin Squares
    • §12.4. Combinatorial Designs
    • Exercises for Chapter 12
    • Chapter 13. Coding
    • §13.1. Statement of the Problem
    • §13.2. Source Encoding
    • §13.3. Error Detection and Correction
    • §13.4. Linear Codes
    • §13.5. Cyclic Codes
    • Exercises for Chapter 13
    • Chapter 14. Cryptography
    • §14.1. Cryptosystems
    • §14.2. Linear Shift Registers
    • §14.3. Public- Key Cryptosystems
    • §14.4. Zero-Knowledge Protocols
    • Exercises for Chapter 14
    • Chapter 15. Linear Optimization
    • §15.1. Examples and Definitions
    • §15.2. Duality
    • §15.3. The Fundamental Theorem of Linear Optimization
    • §15.4. Admissible Solutions and Optimal Solutions
    • §15.5. The Simplex Algorithm
    • §15.6. Integer Linear Optimization
    • Exercises for Chapter 15
    • Bibliography for Part 3
    • Solutions to Selected Exercises
    • Index
    • A
    • B
    • C
    • D
    • E
    • F
    • G
    • H
    • I
    • J
    • K
    • L
    • M
    • N
    • O
    • P
    • Q
    • R
    • S
    • T
    • U
    • V
    • W
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     

    • Aigner offers a very enjoyable review of discrete mathematics at the graduate level.
      Choice Reviews

    • This book gives a leisurely and clear exposition of the main topics of discrete mathematics.
      Allen Stenger for MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2007; 388 pp
MSC: Primary 05; 06; 11; 90; 94;

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level.

Praise for the German edition…

This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics.

—Konrad Engel for MathSciNet

Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Günter M. Ziegler has been an international success with translations into 12 languages.
Readership

Undergraduates and graduate students interested in discrete mathematics, algorithms, and combinatorics.
  • Cover
  • Title
  • Copyright
  • Contents
  • Prefaces
  • Part 1. Counting
  • Chapter 1. Fundamentals
  • §1.1. Elementary Counting Principles
  • §1.2. The Fundamental Counting Coefficients
  • §1.3. Permutations
  • §1.4. Recurrence Equations
  • §1.5. Discrete Probability
  • §1.6. Existence Theorems
  • Exercises for Chapter 1
  • Chapter 2. Summation
  • §2.1. Direct Methods
  • §2.2. The Calculus of Finite Differences
  • §2.3. Inversion
  • §2.4. Inclusion-Exclusion
  • Exercises for Chapter 2
  • Chapter 3. Generating Functions
  • §3.1. Definitions and Examples
  • §3.2. Solving Recurrences
  • §3.3. Generating Functions of Exponential Type
  • Exercises for Chapter 3
  • Chapter 4. Counting Patterns
  • §4.1. Symmetries
  • §4.2. Statement of the Problem
  • §4.3. Patterns and the Cycle Indicator
  • §4.4. Polya's Theorem
  • Exercises for Chapter 4
  • Chapter 5. Asymptotic Analysis
  • §5.1. The Growth of Functions
  • §5.2. Order of Magnitude of Recurrence Relations
  • §5.3. Running Times of Algorithms
  • Exercises for Chapter 5
  • Bibliography for Part 1
  • Bibliography for Part 1
  • Part 2.Graphs and Algorithms
  • Chapter 6. Graphs
  • §6.1. Definitions and Examples
  • §6.2. Representation of Graphs
  • §6.3. Paths and Circuits
  • §6.4. Directed Graphs
  • Exercises for Chapter 6
  • Chapter 7. Trees
  • §7.1. What Is a Tree?
  • §7.2. Breadth- First and Depth-First Search
  • §7.3. Minimal Spanning Trees
  • §7.4. The Shortest Path in a Graph
  • Exercises for Chapter 7
  • Chapter 8. Matchings and Networks
  • §8.1. Matchings in Bipartite Graphs
  • §8.2. Construction of Optimal Matchings
  • §8.3. Flows in Networks
  • §8.4. Eulerian Graphs and the Traveling Salesman Problem
  • §8.5. The Complexity Classes P and NP
  • Exercises for Chapter 8
  • Chapter 9. Searching and Sorting
  • §9.1. Search Problems and Decision Trees
  • §9.2. The Fundamental Theorem of Search Theory
  • §9.3. Sorting Lists
  • §9.4. Binary Search Trees
  • Exercises for Chapter 9
  • Chapter 10. General Optimization Methods
  • §10.1. Backtracking
  • §10.2. Dynamic Programming
  • §10.3. The Greedy Algorithm
  • Exercises for Chapter 10
  • Bibliography for Part 2
  • Bibliography for Part 2
  • Part 3. Algebraic Systems
  • Chapter 11. Boolean Algebras
  • §11.1. Definition and Properties
  • §11.2. Propositional Logic and Boolean Functions
  • §11.3. Logical Nets
  • §11.4. Boolean Lattices, Orders, and Hypergraphs
  • Exercises for Chapter 11
  • Chapter 12. Modular Arithmetic
  • §12.1. Calculating with Congruences
  • §12.2. Finite Fields
  • §12.3. Latin Squares
  • §12.4. Combinatorial Designs
  • Exercises for Chapter 12
  • Chapter 13. Coding
  • §13.1. Statement of the Problem
  • §13.2. Source Encoding
  • §13.3. Error Detection and Correction
  • §13.4. Linear Codes
  • §13.5. Cyclic Codes
  • Exercises for Chapter 13
  • Chapter 14. Cryptography
  • §14.1. Cryptosystems
  • §14.2. Linear Shift Registers
  • §14.3. Public- Key Cryptosystems
  • §14.4. Zero-Knowledge Protocols
  • Exercises for Chapter 14
  • Chapter 15. Linear Optimization
  • §15.1. Examples and Definitions
  • §15.2. Duality
  • §15.3. The Fundamental Theorem of Linear Optimization
  • §15.4. Admissible Solutions and Optimal Solutions
  • §15.5. The Simplex Algorithm
  • §15.6. Integer Linear Optimization
  • Exercises for Chapter 15
  • Bibliography for Part 3
  • Solutions to Selected Exercises
  • Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
  • K
  • L
  • M
  • N
  • O
  • P
  • Q
  • R
  • S
  • T
  • U
  • V
  • W
  • Back Cover

  • Aigner offers a very enjoyable review of discrete mathematics at the graduate level.
    Choice Reviews

  • This book gives a leisurely and clear exposition of the main topics of discrete mathematics.
    Allen Stenger for MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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