Further Maths Lesssons

I will use this page to keep you up to post the presentations used in each lesson. You will receive log-in details for the Further Maths resources online which can be found here.

If you need any help with the homework or have any questions about D1 or any of your other maths modules then either email or call me and I will get back to you as quickly as possible.

A spreadsheet showing completed homeworks may be found here. Please check it and complete any homeworks that you have not yet handed in to me.

Decision 1

Lesson 7

This week you were introduced to Linear Programming. After a review of linear inequalities, we looked at the formulation of linear programming problems

The presentations about formulation of problems and sketching inequalites are here:

Notes, examples and answers are here:

WEEK 7 HOMEWORK

This weeks homework is to complete questions 4,5 and 7 from exercise 6A. You should also sketch the inequalities and label the feasible region in each case.

Lesson 6

We continued work on Activity-on-arc diagrams by looking at Gantt or cascade charts, which show the times that each activity may start and finish and the total float on each activity. Activity with float may be delayed without affecting the minimum completion time of the project. We also looked at how many workers it might take to complete a project.

The presentations about Cascade charts and scheduling diagrams are here:

Notes and examples are here:

WEEK 6 HOMEWORK

Lesson 5

In this lesson you were introduced to activity-on-arc diagrams and the associated precedence tables. We studied how to analyse activity on arc diagram by performing a forward and backward passs to calculate early event times and latest event times and hence the critical activities.

The presentations used in class are:

Notes and examples are here:

WEEK 5 HOMEWORK

Lesson 4

In this lesson we studied matchings in bi-partite graphs. The matching improvement algorithm can be used to improve an initial matching.

You were given the following notes and worked examples:

WEEK 4 HOMEWORK

Lesson 3

In this lesson we studied route inspection problems otherwise known as the Chinese postman problem. The ides is that we want to start at a vertex traverse every arc at least once and then return to the starting vertex.

Presentation for the route inspection problem.
The more adventurous among you might also want to check out this presentation where there are six odd vertices in the network!

You were also given the following notes and worked examples:

Route Inspection notes
Notes from the Further Maths support Network (in places these refer to the textbook, but don't worry if you don't have access to this, they are still useful)
Route Inspection definitions examples and solutions
Route Inspection examples and solutions (***there was a missing weight from one of the arcs in question 3, which has now been corrected***)

WEEK 3 HOMEWORK

Lesson 2

We covered Prim's algorithm on a table (distance matrix) and Dijksta's algorithm to find the shortest path between two vertices in a network. The presentations used are found here:

You were also given the following notes and worked examples:

Prim's algorithm on a table notes
Prim's algorithm on a table: examples and solutions (***note that there was an error in Q1 in the sheet handed out in class, this version is correct***)
Dijkstra's algorithm notes
Dijkstra's algorithm: examples and solutions

WEEK 2 HOMEWORK

Lesson 1

With Luciano, you covered the definitions we will use in Graph theory using this presentation The following resources were handed out:

Glossary of graph definitions
An activity using graph definitions: you can use this for practice

You also covered Prim's and Kruskal's algorithms to find the minimal spanning tree of a network. The presentation for these two algorithms is here.

WEEK 1 HOMEWORK