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Decision and discrete mathematics: Maths for decision-making in business and industry

I Hardwick, The Spode Group

Explores key concepts and fundamental algorithms, and also relates decision mathematics to real-life situations for lower-division undergraduates and two-year technical program students.
Choice

Compact and precise, explains decision maths concepts, operational research, electronics. Clear explanations of algorithms, plentiful examples, diagrams, self study questions with answers, examination standard questions.
Focus: Teachers in Business Education

 - clear explanations of algorithms and all concepts
 - plentiful worked examples, clear diagrams
 - many exercises (with answers for self-study)
 - exam-standard questions

This text offers a complete coverage in the Decision Mathematics module, also known as Discrete Mathematics, of the syllabuses of English A-level examination boards. it is a rewritten and modern version of Decision Mathematics (published by Ellis Horwood Ltd in 1986 for The Spode Group, so well known for its development of innovative mathematics teaching). It is also a suitable text for foundation and first year undergraduate courses in qualitative studies or operational research, or for access courses for students needing strengthening in mathematics, or for students who are moving into mathematics from another subject discipline.

Compact and concise, it reflects the combined teaching skills and experience of its authors who know exactly what mathematics must be learnt at the readership level today. The text is built up in modular fashion, explaining concepts used in decision mathematics and related operational research, and electronics. It emphasises an understanding of techniques and algorithms, which it relates to real life situations and working problems that will apply throughout future working careers.

ISBN 1 898563 27 6
ISBN-13: 978 1 898563 27 3
January 1996
264 pages  242 x 169mm  paperback  
£30.00 / US$50.00 / €35.00

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About the author

Ian Hardwick, The Spode Group

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Contents

An introduction to networks
 - Terminology
 - Investigations
 - Minimum connector problem
 - Chinese postman problem
 - Travelling salesman problem
 - Notes

Recursion
 - Definition
 - Investigation
 - Divisibility
 - Highest common factors
 - Notes

Shortest route
 - Investigations
 - Dijkstra’s algorithm
 - Delays at nodes
 - Chinese postman problem
 - Arcs with negative values
 - Notes

Dynamic Programming
 - Investigations
 - The method of dynamic programming
 - Applications of dynamic programming
 - Notes

Flows in network
 - Investigations
 - Terminology
 - Cutsets
 - Maximum flow, minimum Cut theorem
 - Cutsets in directed networks
 - Restrictions on nodes
 - Several sources and/or sinks
 - Flow augmentation system
 - Networks with arcs having lower capacities
 - Notes

Critical path analysis
 - Activity on arc: investigations
 - Activity on arc: definitions and conventions
 - Activity on arc: procedure
 - Activity on node: investigations
 - Definitions and conventions
 - Activity on node: procedure
 - Activity on node: total float
 - Activity on arc: total float
 - Gantt charts
 - Resource levelling
 - Notes

Linear programming: Graphical
 - Investigation
 - Graphical representation
 - Drawing the objective function
 - Notes

Linear programming: Simplex method
 - Investigation
 - Simplex method
 - The simplex tableau
 - Constraints
 - Three dimensions
 - Minimisation problems
 - Notes

The transportation problem
 - Investigations
 - The transportation array
 - Maximisation problems
 - Unbalanced problems
 - Non-unique optimal solutions
 - Degeneracy
 - Notes

Matching and assignment problems
 - Investigations
 - Hall’s marriage theorem
 - Matching improvement algorithm
 - Investigations
 - Hungarian algorithm
 - Impossible assignments
 - Maximising problems
 - Non-unique solutions
 - Unbalanced problems
 - Notes

Game theory
 - Investigation
 - The minimax theory
 - What is a zero-sum game?
 - Stable solutions
 - Row and column domination
 - Expectation = expected pay-off
 - Minimax mixed strategy
 - Games with known values
 - Using linear programming
 - Miscellaneous exercises
 - Notes

Recurrence relations
 - What is a recurrence relation?
 - Investigations
 - First order linear equations
 - Complementary functions and particular solutions
 - Inhomogeneous u,, = au - 2k”
 - Inhomogeneous: a = I
 - Second order linear
 - Second order homogeneous
 - Summary
 - Miscellaneous exercises
 - Notes

Simulation
 - Introduction
 - Random numbers
 - Use of random numbers
 - Notes

Iterative processes
 - Introduction
 - Investigation
 - Convergent sequences
 - Graphical representation
 - Roots of polynomials
 - Interval bisection
 - Problems with interval bisection
 - Iteration formula v interval bisection
 - Hero’s method for square roots
 - Notes

Sorting and packing
 - Investigation
 - Sorting
 - Bubble sorting
 - Shuttle sort
 - Shell sort
 - Quick sort (super--pointer version)
 - First half of sort program
 - (Bin) packing
 - Packing algorithms
 - Notes

Algorithms
 - What is an algorithm?
 - Investigations
 - Simple algorithms
 - The efficiency of algorithms
 - Use of recurrence relations
 - Notes

Glossary

Answers