### Additional Information

#### Book Details

### Abstract

Edexcel's own course for the 2008 specification. Providing the best possible match to the specification, Edexcel AS and A Level Modular Mathematics DM2 motivates students by making maths easier to learn.

Completely re-written by chief examiners for the specification, it provides student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample past exam papers for thorough exam preparation, and regular review sections that help consolidate learning are included. Opportunities for stretch and challenge are presented throughout the course.

Also included is an interactive FREE LiveText CD-ROM, containing Solutionbank and Exam Cafe to support and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Book. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with chief examiner's commentary.

### Table of Contents

Section Title | Page | Action | Price |
---|---|---|---|

Cover | Cover | ||

Contents | ii | ||

About this book | iv | ||

Chapter 1: Transportation problems | 1 | ||

1.1: Terminology used in describing and modelling the transportation problem | 2 | ||

1.2: Finding an initial solution to the transportation problem | 3 | ||

1.3: Adapting the algorithm to deal with unbalanced transportation problems | 6 | ||

1.4: Knowing what is meant by a degenerate solution and how to manage such solutions | 7 | ||

1.5: Finding shadow costs | 10 | ||

1.6: Finding improvement indices and using these to find entering cells | 15 | ||

1.7: Using the stepping-stone method to obtain an improved solution | 17 | ||

1.8: Formulating a transport problem as a linear programming problem | 26 | ||

Summary of key points | 31 | ||

Chapter 2: Allocation (assignment) problems | 32 | ||

2.1: Reducing cost matrices | 33 | ||

2.2: Using the Hungarian algorithm to find a least cost allocation | 34 | ||

2.3: Adapting the algorithm to use a dummy location | 43 | ||

2.4: Adapting the algorithm to manage incomplete data | 44 | ||

2.5: Modifying the algorithm to deal with a maximum profit allocation | 48 | ||

2.6: Formulating allocation problems as linear programming problems | 52 | ||

Summary of key points | 59 | ||

Chapter 3: The travelling salesman problem | 61 | ||

3.1: Understanding the terminology used | 62 | ||

3.2: Knowing the difference between the classical and practical problems | 62 | ||

3.3: Converting a network into a complete network of least distances | 62 | ||

3.4: Using a minimum spanning tree method to find an upper bound | 67 | ||

3.5: Using a minimum spanning tree method to find a lower bound | 73 | ||

3.6: Using the nearest neighbour algorithm to find an upper bound | 78 | ||

Summary of key points | 86 | ||

Chapter 4: Further linear programming | 88 | ||

4.1: Formulating problems as linear programming problems | 89 | ||

4.2: Formulating problems as linear programming problems, using slack variables | 91 | ||

4.3: Understanding the simplex algorithm to solve maximising linear programming problems | 94 | ||

4.4: Solving maximising linear programming problems using simplex tableaux | 101 | ||

4.5: Using the simplex tableau method to solve maximising linear programming problems requiring integer solutions | 114 | ||

Summary of key points | 120 | ||

Review Exercise 1 | 121 | ||

Chapter 5: Game theory | 134 | ||

5.1: Knowing about two-person games and pay-off matrices | 135 | ||

5.2: Understanding what is meant by play safe strategies | 136 | ||

5.3: Understanding what is meant by a zero-sum game | 137 | ||

5.4: Determining the play safe strategy for each player | 137 | ||

5.5: Understanding what is meant by a stable solution (saddle point) | 138 | ||

5.6: Reducing a pay-off matrix using dominance arguments | 144 | ||

5.7: Determining the optimal mixed strategy for a game with no stable solution | 145 | ||

5.8: Determining the optimal mixed strategy for the player with two choices in a 2*3 or 3*2 game | 149 | ||

5.9: Determining the optimal mixed strategy for the player with three choices in a 2*3 or 3*2 game | 153 | ||

5.10: Converting 2*3, 3*2 and 3*3 games into linear programming problems | 153 | ||

Summary of key points | 164 | ||

Chapter 6: Network flows | 165 | ||

6.1: Knowing some of the terminology used in analysing flows through networks | 166 | ||

6.2: Understanding what is meant by a cut | 171 | ||

6.3: Finding an initial flow through a capacitated directed network | 178 | ||

6.4: Using the labelling procedure to find flow-augmenting routes to increase the flow through the network | 182 | ||

6.5: Confirming that a flow is maximal using the maximum flow minimum cut theorem | 193 | ||

6.6 Adapting the algorithm to deal with networks with multiple sources and/or sinks | 197 | ||

Summary of key points | 205 | ||

Chapter 7: Dynamic programming | 207 | ||

7.1 Understanding the terminology and principles of dynamic programming, including Bellmanâ€™s principle of optimality | 208 | ||

7.2 Using dynamic programming to solve maximum and minimum problems, presented in network form | 209 | ||

7.3 Using dynamic programming to solve minimax and maximin problems, presented in network form | 217 | ||

7.4 Using dynamic programming to solve maximum, minimum, minimax or maximin problems, presented in table form | 221 | ||

Summary of key points | 232 | ||

Review Exercise 2 | 233 | ||

Examination style paper | 241 | ||

Answers | 245 | ||

Index | 279 |