Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Mathematics of Optimization: How to do Things Faster
 
Steven J. Miller :  Williams College, Williamstown, MA
Mathematics of Optimization: How to do Things Faster
Hardcover ISBN:  978-1-4704-4114-2
Product Code:  AMSTEXT/30
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-4342-9
Product Code:  AMSTEXT/30.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-1-4704-4114-2
eBook: ISBN:  978-1-4704-4342-9
Product Code:  AMSTEXT/30.B
List Price: $160.00 $122.50
MAA Member Price: $144.00 $110.25
AMS Member Price: $128.00 $98.00
Add to cart
Mathematics of Optimization: How to do Things Faster
Click above image for expanded view
Mathematics of Optimization: How to do Things Faster
Steven J. Miller :  Williams College, Williamstown, MA
Hardcover ISBN:  978-1-4704-4114-2
Product Code:  AMSTEXT/30
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-4342-9
Product Code:  AMSTEXT/30.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-1-4704-4114-2
eBook ISBN:  978-1-4704-4342-9
Product Code:  AMSTEXT/30.B
List Price: $160.00 $122.50
MAA Member Price: $144.00 $110.25
AMS Member Price: $128.00 $98.00
Add to cart
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 30; 2017; 327 pp
    MSC: Primary 46; 65; 90; 97; 58; 11; 68

    Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the “why” and the “how” in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.
    Readership

    Undergraduate and graduate students interested in learning and teaching optimization and operation research.
  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Acknowledgements
    • Preface
    • Course Outlines
    • Part 1 . Classical Algorithms
    • Chapter 1. Efficient Multiplication, I
    • 1.1. Introduction
    • 1.2. Babylonian Multiplication
    • 1.3. Horner’s Algorithm
    • 1.4. Fast Multiplication
    • 1.5. Strassen’s Algorithm
    • 1.6. Eigenvalues, Eigenvectors and the Fibonacci Numbers
    • 1.7. Exercises
    • Chapter 2. Efficient Multiplication, II
    • 2.1. Binomial Coefficients
    • 2.2. Pascal’s Triangle
    • 2.3. Dimension
    • 2.4. From the Pascal to the Sierpinski Triangle
    • 2.5. The Euclidean Algorithm
    • 2.6. Exercises
    • Part 2 . Introduction to Linear Programming
    • Chapter 3. Introduction to Linear Programming
    • 3.1. Linear Algebra
    • 3.2. Finding Solutions
    • 3.3. Calculus Review: Local versus Global
    • 3.4. An Introduction to the Diet Problem
    • 3.5. Solving the Diet Problem
    • 3.6. Applications of the Diet Problem
    • 3.7. Exercises
    • Chapter 4. The Canonical Linear Programming Problem
    • 4.1. Real Analysis Review
    • 4.2. Canonical Forms and Quadratic Equations
    • 4.3. Canonical Forms in Linear Programming: Statement
    • 4.4. Canonical Forms in Linear Programming: Conversion
    • 4.5. The Diet Problem: Round 2
    • 4.6. A Short Theoretical Aside: Strict Inequalities
    • 4.7. Canonical is Not Always Best
    • 4.8. The Oil Problem
    • 4.9. Exercises
    • Chapter 5. Symmetries and Dualities
    • 5.1. Tic-Tac-Toe and a Chess Problem
    • 5.2. Duality and Linear Programming
    • 5.3. Appendix: Fun Versions of Tic-Tac-Toe
    • 5.4. Exercises
    • Chapter 6. Basic Feasible and Basic Optimal Solutions
    • 6.1. Review of Linear Independence
    • 6.2. Basic Feasible and Basic Optimal Solutions
    • 6.3. Properties of Basic Feasible Solutions
    • 6.4. Optimal and Basic Optimal Solutions
    • 6.5. Efficiency and Euclid’s Prime Theorem
    • 6.6. Exercises
    • Chapter 7. The Simplex Method
    • 7.1. The Simplex Method: Preliminary Assumptions
    • 7.2. The Simplex Method: Statement
    • 7.3. Phase II implies Phase I
    • 7.4. Phase II of the Simplex Method
    • 7.5. Run-time of the Simplex Method
    • 7.6. Efficient Sorting
    • 7.7. Exercises
    • Part 3 . Advanced Linear Programming
    • Chapter 8. Integer Programming
    • 8.1. The Movie Theater Problem
    • 8.2. Binary Indicator Variables
    • 8.3. Logical Statements
    • 8.4. Truncation, Extrema and Absolute Values
    • 8.5. Linearizing Quadratic Expressions
    • 8.6. The Law of the Hammer and Sudoku
    • 8.7. Bus Route Example
    • 8.8. Exercises
    • Chapter 9. Integer Optimization
    • 9.1. Maximizing a Product
    • 9.2. The Knapsack Problem
    • 9.3. Solving Integer Programs: Branch and Bound
    • 9.4. Exercises
    • Chapter 10. Multi-Objective and Quadratic Programming
    • 10.1. Multi-Objective Linear Programming
    • 10.2. Quadratic Programming
    • 10.3. Example: Quadratic Objective Function
    • 10.4. Removing Quadratic (and Higher Order) Terms in Constraints
    • 10.5. Summary
    • 10.6. Exercises
    • Chapter 11. The Traveling Salesman Problem
    • 11.1. Integer Linear Programming Version of the TSP
    • 11.2. Greedy Algorithm to the TSP
    • 11.3. The Insertion Algorithm
    • 11.4. Sub-problems Method
    • 11.5. Exercises
    • Chapter 12. Introduction to Stochastic Linear Programming
    • 12.1. Deterministic and Stochastic Oil Problems
    • 12.2. Expected Value approach
    • 12.3. Recourse Approach
    • 12.4. Probabilistic Constraints
    • 12.5. Exercises
    • Part 4 . Fixed Point Theorems
    • Chapter 13. Introduction to Fixed Point Theorems
    • 13.1. Definitions and Uses
    • 13.2. Examples
    • 13.3. Real Analysis Preliminaries
    • 13.4. One-Dimensional Fixed Point Theorem
    • 13.5. Newton’s Method versus Divide and Conquer
    • 13.6. Equivalent Regions and Fixed Points
    • 13.7. Exercises
    • Chapter 14. Contraction Maps
    • 14.1. Definitions
    • 14.2. Fixed Points of Contraction Maps
    • 14.3. Introduction to Differential Equations
    • 14.4. Real Analysis Review
    • 14.5. First Order Differential Equations Theorem
    • 14.6. Examples of Picard’s Iteration Method
    • 14.7. Exercises
    • Chapter 15. Sperner’s Lemma
    • 15.1. Statement of Sperner’s Lemma
    • 15.2. Proof Strategies for Sperner’s Lemma
    • 15.3. Proof of Sperner’s Lemma
    • 15.4. Rental Harmony
    • 15.5. Exercises
    • Chapter 16. Brouwer’s Fixed Point Theorem
    • 16.1. Bolzano-Weierstrass Theorem
    • 16.2. Barycentric Coordinates
    • 16.3. Preliminaries for Brouwer’s Fixed Point Theorem
    • 16.4. Proof of Brouwer’s Fixed Point Theorem
    • 16.5. Nash Equilibrium
    • 16.6. Exercises
    • Part 5 . Advanced Topics
    • Chapter 17. Gale-Shapley Algorithm
    • 17.1. Introduction
    • 17.2. Three Parties
    • 17.3. Gale-Shapley Algorithm
    • 17.4. Generalization
    • 17.5. Applications
    • 17.6. Exercises
    • Chapter 18. Interpolating Functions
    • 18.1. Lagrange Interpolation
    • 18.2. Interpolation Error
    • 18.3. Chebyshev Polynomials and Interpolation
    • 18.4. Splines
    • 18.5. Exercises
    • Chapter 19. The Four Color Problem
    • 19.1. A Brief History
    • 19.2. Preliminaries
    • 19.3. Birkhoff and the Modern Proof
    • 19.4. Appel-Haken Proof
    • 19.5. Computational Improvements
    • 19.6. Exercises
    • Chapter 20. The Kepler Conjecture
    • 20.1. Introduction
    • 20.2. Sphere Packing
    • 20.3. Challenges in Proving the Kepler Conjecture
    • 20.4. Local Density Inequalities
    • 20.5. Computer-Aided Proof
    • 20.6. Exercises
    • Bibliography
    • Index
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     

    • I think that this book offers a vast and useful outline of many mathematical problems arising from the common ground of optimization theory and operations research. Surely it can be useful and of interest to advanced undergraduates and beginning graduate students concerned with applications of mathematics to optimization problems and related fields.
      Giorgio Giorgi, Mathematical Reviews

    • I started reading "Mathematics of Optimization: How to do Things Faster" without a significant background in optimization, linear programming, or operations research. Hence, I really did not know what to expect from the book. I was pleasantly surprised to find the book to be so much fun to work through. The writing is upbeat, entertaining and enlightening and the mathematics is varied, interesting, and inspiring...I am really impressed by "Mathematics of Optimization," and I would love to teach a course based on this book just in order to spend more time going through it myself...I think that the book is unique and should be relevant and of interest to advanced undergraduate and beginning graduate students in pure and applied mathematics and some closely related areas.
      Jason M. Graham, 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
Pure and Applied Undergraduate Texts
Volume: 30; 2017; 327 pp
MSC: Primary 46; 65; 90; 97; 58; 11; 68

Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the “why” and the “how” in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.
Readership

Undergraduate and graduate students interested in learning and teaching optimization and operation research.
  • Cover
  • Title page
  • Contents
  • Acknowledgements
  • Preface
  • Course Outlines
  • Part 1 . Classical Algorithms
  • Chapter 1. Efficient Multiplication, I
  • 1.1. Introduction
  • 1.2. Babylonian Multiplication
  • 1.3. Horner’s Algorithm
  • 1.4. Fast Multiplication
  • 1.5. Strassen’s Algorithm
  • 1.6. Eigenvalues, Eigenvectors and the Fibonacci Numbers
  • 1.7. Exercises
  • Chapter 2. Efficient Multiplication, II
  • 2.1. Binomial Coefficients
  • 2.2. Pascal’s Triangle
  • 2.3. Dimension
  • 2.4. From the Pascal to the Sierpinski Triangle
  • 2.5. The Euclidean Algorithm
  • 2.6. Exercises
  • Part 2 . Introduction to Linear Programming
  • Chapter 3. Introduction to Linear Programming
  • 3.1. Linear Algebra
  • 3.2. Finding Solutions
  • 3.3. Calculus Review: Local versus Global
  • 3.4. An Introduction to the Diet Problem
  • 3.5. Solving the Diet Problem
  • 3.6. Applications of the Diet Problem
  • 3.7. Exercises
  • Chapter 4. The Canonical Linear Programming Problem
  • 4.1. Real Analysis Review
  • 4.2. Canonical Forms and Quadratic Equations
  • 4.3. Canonical Forms in Linear Programming: Statement
  • 4.4. Canonical Forms in Linear Programming: Conversion
  • 4.5. The Diet Problem: Round 2
  • 4.6. A Short Theoretical Aside: Strict Inequalities
  • 4.7. Canonical is Not Always Best
  • 4.8. The Oil Problem
  • 4.9. Exercises
  • Chapter 5. Symmetries and Dualities
  • 5.1. Tic-Tac-Toe and a Chess Problem
  • 5.2. Duality and Linear Programming
  • 5.3. Appendix: Fun Versions of Tic-Tac-Toe
  • 5.4. Exercises
  • Chapter 6. Basic Feasible and Basic Optimal Solutions
  • 6.1. Review of Linear Independence
  • 6.2. Basic Feasible and Basic Optimal Solutions
  • 6.3. Properties of Basic Feasible Solutions
  • 6.4. Optimal and Basic Optimal Solutions
  • 6.5. Efficiency and Euclid’s Prime Theorem
  • 6.6. Exercises
  • Chapter 7. The Simplex Method
  • 7.1. The Simplex Method: Preliminary Assumptions
  • 7.2. The Simplex Method: Statement
  • 7.3. Phase II implies Phase I
  • 7.4. Phase II of the Simplex Method
  • 7.5. Run-time of the Simplex Method
  • 7.6. Efficient Sorting
  • 7.7. Exercises
  • Part 3 . Advanced Linear Programming
  • Chapter 8. Integer Programming
  • 8.1. The Movie Theater Problem
  • 8.2. Binary Indicator Variables
  • 8.3. Logical Statements
  • 8.4. Truncation, Extrema and Absolute Values
  • 8.5. Linearizing Quadratic Expressions
  • 8.6. The Law of the Hammer and Sudoku
  • 8.7. Bus Route Example
  • 8.8. Exercises
  • Chapter 9. Integer Optimization
  • 9.1. Maximizing a Product
  • 9.2. The Knapsack Problem
  • 9.3. Solving Integer Programs: Branch and Bound
  • 9.4. Exercises
  • Chapter 10. Multi-Objective and Quadratic Programming
  • 10.1. Multi-Objective Linear Programming
  • 10.2. Quadratic Programming
  • 10.3. Example: Quadratic Objective Function
  • 10.4. Removing Quadratic (and Higher Order) Terms in Constraints
  • 10.5. Summary
  • 10.6. Exercises
  • Chapter 11. The Traveling Salesman Problem
  • 11.1. Integer Linear Programming Version of the TSP
  • 11.2. Greedy Algorithm to the TSP
  • 11.3. The Insertion Algorithm
  • 11.4. Sub-problems Method
  • 11.5. Exercises
  • Chapter 12. Introduction to Stochastic Linear Programming
  • 12.1. Deterministic and Stochastic Oil Problems
  • 12.2. Expected Value approach
  • 12.3. Recourse Approach
  • 12.4. Probabilistic Constraints
  • 12.5. Exercises
  • Part 4 . Fixed Point Theorems
  • Chapter 13. Introduction to Fixed Point Theorems
  • 13.1. Definitions and Uses
  • 13.2. Examples
  • 13.3. Real Analysis Preliminaries
  • 13.4. One-Dimensional Fixed Point Theorem
  • 13.5. Newton’s Method versus Divide and Conquer
  • 13.6. Equivalent Regions and Fixed Points
  • 13.7. Exercises
  • Chapter 14. Contraction Maps
  • 14.1. Definitions
  • 14.2. Fixed Points of Contraction Maps
  • 14.3. Introduction to Differential Equations
  • 14.4. Real Analysis Review
  • 14.5. First Order Differential Equations Theorem
  • 14.6. Examples of Picard’s Iteration Method
  • 14.7. Exercises
  • Chapter 15. Sperner’s Lemma
  • 15.1. Statement of Sperner’s Lemma
  • 15.2. Proof Strategies for Sperner’s Lemma
  • 15.3. Proof of Sperner’s Lemma
  • 15.4. Rental Harmony
  • 15.5. Exercises
  • Chapter 16. Brouwer’s Fixed Point Theorem
  • 16.1. Bolzano-Weierstrass Theorem
  • 16.2. Barycentric Coordinates
  • 16.3. Preliminaries for Brouwer’s Fixed Point Theorem
  • 16.4. Proof of Brouwer’s Fixed Point Theorem
  • 16.5. Nash Equilibrium
  • 16.6. Exercises
  • Part 5 . Advanced Topics
  • Chapter 17. Gale-Shapley Algorithm
  • 17.1. Introduction
  • 17.2. Three Parties
  • 17.3. Gale-Shapley Algorithm
  • 17.4. Generalization
  • 17.5. Applications
  • 17.6. Exercises
  • Chapter 18. Interpolating Functions
  • 18.1. Lagrange Interpolation
  • 18.2. Interpolation Error
  • 18.3. Chebyshev Polynomials and Interpolation
  • 18.4. Splines
  • 18.5. Exercises
  • Chapter 19. The Four Color Problem
  • 19.1. A Brief History
  • 19.2. Preliminaries
  • 19.3. Birkhoff and the Modern Proof
  • 19.4. Appel-Haken Proof
  • 19.5. Computational Improvements
  • 19.6. Exercises
  • Chapter 20. The Kepler Conjecture
  • 20.1. Introduction
  • 20.2. Sphere Packing
  • 20.3. Challenges in Proving the Kepler Conjecture
  • 20.4. Local Density Inequalities
  • 20.5. Computer-Aided Proof
  • 20.6. Exercises
  • Bibliography
  • Index
  • Back Cover

  • I think that this book offers a vast and useful outline of many mathematical problems arising from the common ground of optimization theory and operations research. Surely it can be useful and of interest to advanced undergraduates and beginning graduate students concerned with applications of mathematics to optimization problems and related fields.
    Giorgio Giorgi, Mathematical Reviews

  • I started reading "Mathematics of Optimization: How to do Things Faster" without a significant background in optimization, linear programming, or operations research. Hence, I really did not know what to expect from the book. I was pleasantly surprised to find the book to be so much fun to work through. The writing is upbeat, entertaining and enlightening and the mathematics is varied, interesting, and inspiring...I am really impressed by "Mathematics of Optimization," and I would love to teach a course based on this book just in order to spend more time going through it myself...I think that the book is unique and should be relevant and of interest to advanced undergraduate and beginning graduate students in pure and applied mathematics and some closely related areas.
    Jason M. Graham, 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
You may be interested in...
Powered by MathJax
Please select which format for which you are requesting permissions.