| Edition |
Fourth edition. |
| Description |
xxii, 884, 40, 3, 14 pages : illustrations (some color) ; 24 cm |
| Note |
Includes index. |
| Contents |
pt. I. Management sciences -- 1. Street networks -- Euler circuits -- Finding Euler circuits -- Circuits with reused edges -- Circuits with more complications -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 2. Visiting vertices -- Hamiltonian circuits -- Fundamental principle of counting -- Traveling salesman problem -- Strategies for solving the traveling salesman problem -- Nearest-neighbor algorithm -- Sorted-edges algorithm -- Minimum-cost spanning trees -- Kruskal's algorithm -- Critical path analysis -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 3. Planning and scheduling -- Scheduling tasks -- Assumption and goals -- List-processing algorithm -- When is a schedule optimal? -- Strange happenings -- Critical-path schedules -- Independent tasks -- Decreasing-time lists -- Bin packing -- Bin-packing heuristics -- Decreasing-time heuristics -- Cryptography -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 4. Linear programming -- Mixture problems -- Mixture problems having one resource -- One product and one resource : making skateboards -- Common features of mixture problems -- Two products and one resource : skateboards and dolls, part 1 -- Mixture charts -- Resource constraints -- Graphing the constraints to form the feasible region -- Finding the optimal production policy -- General shape of feasible regions -- The role of the profit formula : skateboards and dolls, part 2 -- Setting minimum quantities for products : skateboards and dolls, part 3 -- Drawing a feasible region when there are nonzero minimum constraints -- Finding corner points of a feasible region having nonzero minimums -- Evaluating the profit formula at the corners of a feasible region with nonzero minimums -- Summary of the pictorial method -- Mixture problems having two resources -- Two products and two resources : skateboards and dolls, part 4 -- The corner point principle -- Linear programming, the wider picture -- Characteristics of linear programming algorithms -- The simplex method -- An alternative to the simplex method -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- |
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pt. II. Statistics : the science of data -- 5. Producing data -- Sampling -- Bad sampling methods -- Simple random samples -- Statistical estimation -- Experiments -- Randomized comparative experiments -- Statistical evidence -- Statistics in practice -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 6. Describing data -- Exploring data -- Displaying distributions -- Describing center : median and mean -- Describing spread : the five-number summary -- Describing spread : the standard deviation -- Displaying relations between two variables -- Regression lines -- Exploring data on several variables -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 7. Probability : the mathematics of chance -- What is probability? -- Probability models -- Equally likely outcomes -- The mean of a random phenomenon -- Sampling distributions -- Normal distributions -- The shape of normal curves -- The 68-95-99.7 rule -- The central limit theorem -- Applying the central limit theorem -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 8. Statistical interference -- Estimating a population proportion -- Confidence intervals -- Estimating a population mean -- Statistical process control -- The perils of data analysis -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- |
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pt. III. Coding information -- 9. Identification numbers -- The ZIP code -- Bar codes -- ZIP code bar code -- The UPC bar code -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 10. Transmitting information -- Binary codes -- Encoding with parity-check sums -- Data compression -- Cryptography -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- |
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pt. IV. Social choice and decision making -- 11. Social choice : the impossible dream -- Elections with only two alternatives -- Elections with three or more alternatives : procedures and problems -- Plurality voting and the Condorcet winner criterion -- The Borda count and independence of irrelevant alternatives -- Sequential pairwise voting and the Pareto condition -- The Hare system and monotonicity -- Summary -- Insurmountable difficulties : from paradox to impossibility -- The voting paradox of Condorcet -- Manipulability -- Impossibility -- A better approach? : approval voting -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 12. Weighted voting systems -- How weighted voting works -- Notation for weighted voting -- The Banzhaf power index -- Computing the Banzhaf power index -- How to count combinations -- Equivalent voting systems -- Finding the weights -- The Shapley-Shubik power index -- How to compute the Shapley-Shubik power index -- Comparison of the Banzhaf and Shapley-Shubik indices -- Systems with large numbers of voters -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 13. Fair division -- The adjusted winner divorce procedure -- The Knaster inheritance procedure -- Divide-and-choose -- Cake-division schemes : proportionality -- Cake-division schemes : the problem of envy -- Applying the trimming procedure to indivisible goods -- Dividing up the chores -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 14. Apportionment -- The apportionment problem -- The Hamilton method -- Paradoxes of the Hamilton method -- Divisor methods -- The Jefferson method -- The Webster method -- The Hill-Huntington method -- Which divisor method is best? -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 15. Game theory : the mathematics of competition -- Two-person total-conflict games : pure strategies -- Two-person total-conflict games : mixed strategies -- A flawed approach -- A better idea -- Partial-conflict games -- Larger games -- Using game theory -- Solving matrix games -- Practical applications -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 16. Theory of moves : a dynamic approach to games -- Game theory revisited -- Rules of TOM -- Interpreting TOM -- Cyclic games and moving power -- Return to prisoners' dilemma and chicken -- Larger games -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- |
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pt. V. On size and shape -- 17. Growth and form -- Geometric similarity -- The language of growth, enlargement, and decrease -- Numerical similarity -- Measuring length, area, volume, and weight -- U.S. customary system -- Metric system -- Converting between systems -- Scaling real objects -- Sorry, no King Kongs -- Solving the problem of scale -- Falls, dives, jumps, and flights -- Keeping cool (and warm) -- Similarity and growth -- Conclusion -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 18. Geometric growth -- Geometric growth and financial models -- The mathematics of geometric growth -- Arithmetic growth -- A limit to compounding -- A model for accumulation -- Exponential decay -- Growth models for biological growth -- Limitations on biological growth -- Nonrenewable resources -- Renewable resources -- Reproduction curves -- Sustained-yield harvesting -- Considerations from economics -- Why eliminate a renewable resource? -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 19. New geometries for a new universe -- Euclidean geometry -- Elliptic geometry -- Hyperbolic geometry -- Models for hyperbolic geometry -- The theory of relativity -- General relativity -- Relativity and length contraction -- Which geometry is true? -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 20. Symmetry and patterns -- Fibonacci numbers -- The golden ratio -- Balance in symmetry -- Rigid motions -- Preserving the pattern -- Analyzing patterns -- Strip patterns -- Symmetry groups -- Notation for patterns -- Imperfect patterns -- Further possibilities -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- 21. Tilings -- Regular polygons -- Regular tilings -- Tilings with irregular polygons -- M.C. Escher and tilings -- Tilings by translations -- Tilings by translations and half-turns -- Further considerations -- Nonperiodic tilings -- The Penrose tilings -- Quasicrystals and Barlow's law -- Review vocabulary -- Suggested readings -- Exercises -- Writing projects -- Answers to odd-numbered exercises. |
| Subject |
Mathematics.
|
| Added Author |
Consortium for Mathematics and Its Applications (U.S.)
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| ISBN |
0716728419 |
|
9780716728412 |
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