Decision and Discrete Mathematics: Maths for Decision-Making in Business and Industry

by Hardwick, Ian

• ISBN13: 9781898563273
• ISBN10: 1898563276
• Edition: 2nd
• Format: Paperback
• Copyright: 1996-09-01
• Publisher: Woodhead Pub Ltd

Summary

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.

Table of Contents

Preface	vii	(1)
Acknowledgements	vii
Chapter 1 An introduction to networks	1	(16)
1.1 Terminology
1.2 Investigations
1.3 Minimum connector problem
1.4 Chinese postman problem
1.5 Travelling salesman problem
1.6 Notes
Chapter 2 Recursion	17	(4)
2.1 Definition
2.2 Investigation
2.3 Divisibility
2.4 Highest common factors
2.5 Notes
Chapter 3 Shortest route	21	(10)
3.1 Investigations
3.2 Dijkstra's algorithm
3.3 Delays at nodes
3.4 Chinese postman problem
3.5 Arcs with negative values
3.6 Notes
Chapter 4 Dynamic programming	31	(14)
4.1 Investigations
4.2 The method of dynamic programming
4.3 Applications of dynamic programming
4.4 Notes
Chapter 5 Flows in networks	45	(18)
5.1 Investigations
5.2 Terminology
5.3 Cutsets
5.4 Maximum flow, minimum cut theorem
5.5 Cutsets in directed networks
5.6 Restrictions on nodes
5.7 Several sources and/or sinks
5.8 Flow augmentation system
5.9 Networks with arcs having lower capacities
5.10 Notes
Chapter 6 Critical path analysis	63	(19)
6.1 Activity on arc: investigations
6.2 Activity on arc: definitions and conventions
6.3 Activity on arc: procedure
6.4 Activity on node: investigations
6.5 Definitions and conventions
6.6 Activity on node: procedure
6.7 Activity on node: total float
6.8 Activity on arc: total float
6.9 Gantt charts
6.10 Resource levelling
6.11 Notes
Chapter 7 Linear programming (graphical)	82	(10)
7.1 Investigation
7.2 Graphical representation
7.3 Drawing the objective function
7.4 Notes
Chapter 8 Linear programming: simplex method	92	(15)
8.1 Investigation
8.2 Simplex method
8.3 The simplex tableau
8.4 XXX constraints
8.5 Three dimensions
8.6 Minimisation problems
8.7 Notes
Chapter 9 The transportation problem	107	(14)
9.1 Investigations
9.2 The transportation array
9.3 Maximisation problems
9.4 Unbalanced problems
9.5 Non-unique optimal solutions
9.6 Degeneracy
9.7 Notes
Chapter 10 Matching and assignment problems	121	(19)
10.1 Investigations
10.2 Hall's marriage theorem
10.3 Matching improvement algorithm
10.4 Investigations
10.5 Hungarian algorithm
10.6 Impossible assignments
10.7 Maximising problems
10.8 Non-unique solutions
10.9 Unbalanced problems
10.10 Notes
Chapter 11 Game theory	140	(16)
11.1 Investigation
11.2 The minimax theory
11.3 What is a zero-sum game?
11.4 Stable solutions
11.5 Row and column domination
11.6 Expectation = expected pay-off
11.7 Minimax mixed strategy
11.8 Games with known values
11.9 Using linear programming
11.10 Miscellaneous exercises
11.11 Notes
Chapter 12 Recurrence relations	156	(21)
12.1 What is a recurrence relation?
12.2 Investigations
12.3 First order linear equations
12.4 Complementary functions and particular solutions
12.5 Inhomogeneous u(n+1) = au(n) + XXX(n)
12.6 Inhomogeneous: a = 1
12.7 Second order linear
12.8 Second order homogeneous
12.9 Summary
12.10 Miscellaneous exercises
12.11 Notes
Chapter 13 Simulation	177	(7)
13.1 Introduction
13.2 Random numbers
13.3 Use of random numbers
13.4 Notes
Chapter 14 Iterative processes	184	(15)
14.1 Introduction
14.2 Investigation
14.3 Convergent sequences
14.4 Graphical representation
14.5 Roots of polynomials
14.6 Interval bisection
14.7 Problems with interval bisection
14.8 Iteration formula v interval bisection
14.9 Hero's method for square roots
14.10 Notes
Chapter 15 Sorting and packing	199	(17)
15.1 Investigation
15.2 Sorting
15.3 Bubble sorting
15.4 Shuttle sort
15.5 Shell sort
15.6 Quick sort (super-pointer version)
15.7 First half of sort program
15.8 (Bin) packing
15.9 Packing algorithms
15.10 Notes
Chapter 16 Algorithms	216	(12)
16.1 What is an algorithm?
16.2 Investigations
16.3 Simple algorithms
16.4 The efficiency of algorithms
16.5 Use of recurrence relations
16.6 Notes
Glossary	228	(2)
Answers	230	(24)
Index	254