# A레벨_Further Mathematics(AS)_Decision 1 > A레벨

## 과정소개

교재 : edexcel / 수강기간 : 30일

Decision Mathematics 1

Decision Mathematics 1 gives a brief
overview of the field of discrete mathematics and some of the foundational
problems that developed the field. These ideas later developed into the field
of Computer Science, and here we look at the algorithms that were formulated to
solve some of these initial problems.

**Chapter 1: Algorithms**

The concept of an algorithm is introduced,
and the flow chart formulation of problem solving is presented. The chapter
then looks at the following algorithms: the bubble sort and quick sort for
sorting lists into order; the binary search algorithm to find items within
ordered lists; and the First-fit, First-fit decreasing and Full Bin algorithms
for solving the basic bin packing problem.

**Chapter 2: Graphs and Networks**

In this chapter we develop the language of
Graph Theory necessary to allow us to formulate the problems we are going to
solve. This area of Mathematics was developed simultaneously in different
languages leading to more than one naming conventions. We then look at the ways
we can use matrices to represent graphs.

**Chapter 3: Algorithms on Graphs**

The problem of finding minimum spanning
trees for a network is solved using two distinct algorithms: Prim’s algorithm
and Kruskal’s algorithm. The nearest neighbour algorithm is introduced, which
helps find short paths connecting all nodes. Finally, the problem of finding
the shortest path through a network is addressed using Dijkstra’s algorithm.

**Chapter 4: Route Inspection**

The concept of Eulerian and semi-Eulerian
graphs are introduced, and how they affect circuits containing every arc
exactly once. We then take on the famous ‘Chinese Postman Problem’ of finding
the shortest path travelling every arc of a network using the route inspection
algorithm, and considered the two cases where our start and end points are
either the same or different.

**Chapter 5: The Travelling Salesman Problem**

The travelling salesman problem involves
finding the shortest tour that visits every node once. It is divided between
the classical problem, where each vertex must be visited only once, and the
practical problem where vertices can be visited more than once. Using a
combination of the nearest neighbour algorithm and minimum spanning trees,
upper and lower bounds are found to constraint the solution to this problem.

**Chapter 6: Critical Path Analysis**

Dependency tables and activity networks are
introduced, and the idea of using dummy arcs to carry dependence is used. Next
critical activities are identified using early/late times, and the float of
activities are calculated. We use Gantt charts to represent all the activities
and their times, and use this information to create scheduling diagrams for
either a fixed or variable number of workers.

**Chapter 7: Linear Programming**

Using the idea of decision variables and
constraints, we reduce complex problems down to their fundamental variables. By
carefully plotting the constraints on a graph, we use multiple methods to find
the optimal solution to these problems, involving the case where integer valued
solutions are required.

## 강의목록

- 19 강의
- 02:44:58

- 1. Algorithms 1-1 00:06:34
- 2. Algorithms 1-2 00:10:30
- 3. Algorithms 1-3 00:07:34
- 4. Algorithms 1-4 00:05:46
- 5. Algorithms 1-5 00:06:13
- 6. Graphs and Networks 2-1 00:07:54
- 7. Graphs and Networks 2-2 00:05:11
- 8. Algorithms on Graphs 3-1 00:13:18
- 9. Algorithms on Graphs 3-2 00:08:10
- 10. Algorithms on Graphs 3-3 00:10:18
- 11. Route Inspection 4-1 00:09:52
- 12. The Travelling Salesman Problem 5-1 00:11:10
- 13. The Travelling Salesman Problem 5-2 00:09:38
- 14. Critical Path Analysis 6-1 00:06:26
- 15. Critical Path Analysis 6-2 00:08:02
- 16. Critical Path Analysis 6-3 00:07:39
- 17. Critical Path Analysis 6-4 00:08:00
- 18. Linear Programming 7-1 00:10:45
- 19. Linear Programming 7-2 00:11:58