School of Mathematics and Statistics

University of Plymouth

Mathematics Support Materials

About This Project:

The aim of this project is to produce a library of portable, interactive, web based support packages to help students learn various mathematical ideas and techniques and to support classroom teaching. The packages are in Adobe's Portable Document Format (PDF). These packages will introduce the mathematical ideas and their rules. The packages will use the linking capabilities of PDF files to generate exercises and quizzes and so allow the students to test their understanding of the material with immediate feedback. We will also use our backgrounds in science to construct smaller support packages to show applications of mathematics in science and engineering.

To view the files, you will need the latest (free) version of Acrobat Reader: Acrobat Reader 5.0. Essentially, though, all you need to know is that any text or symbol in green is a link. However, detailed instructions about how to use the packages can be found here.

The Packages:

Note that the packages may be either worked through on line or downloaded and used on any computer. They are compact enough to fit on a floppy disk.

Basic Algebra:

Brackets	Simple Equations	Factorising
Fractions	Inequalities	Simultaneous Equations
Powers	Logarithms	Quadratic Equations
Algebraic Fractions	Complex Numbers	Functions
Binary Numbers 1	Binary Numbers 2

Graphs:

Straight Line Graphs

Quadratic Functions

Log-Log Plots

Trigonometry:

Trigonometry 1

Calculus:

Introduction to Differentiation	Maxima and Minima	The Product and Quotient Rules
The Chain Rule	Indefinite Integration	Definite Integrals
Partial Differentiation

Vectors:

Vectors

Matrices and Determinants:

Introduction to Matrices	Multiplying Matrices	Determinants 1
Determinants 2

Vector Calculus:

Gradients and Directional Derivatives

Divergence and Curl

The Laplacian

Logic and Proof:

Proof by Induction

Series Tests

Truth Tables and Boolean Algebra

Units:

Units	Converting Units	Electrical Units
Dimensional Analysis

Applications:

Forces	Waves	Lenses
Pressure	Chemistry	Simple Circuits
Power in DC Circuits	AC Systems and Phasors	Boolean Algebra and Logic Gates
Quantum Theory

Click here to post your feedback or comments on the packages

The Software:

Since HTML, the language of the web, is poorly suited to mathematical formulae, this project uses LaTeX and PDF. LaTeX is a variant of TeX, which is the world standard for typesetting mathematics. It produces professional quality output which is universally accepted by scientific publishing companies. We use LaTeX to produce PDF (portable document format) output which can be put on the web. These PDF files are read using the freely available and widely distributed Adobe Acrobat Reader.

These packages were produced using LaTeX. This was then converted into PDF files. The LaTeX code makes much use of various packages which have been developed by D.P. Story. Some information about TeX and LaTeX can be found here.

Acknowledgements:

We are grateful to David McMullan for discussions on many aspects of this work and thank Arsen Khvedelidze for his help. We thank HEFCE for funding our work as part of the PPLATO FDTL4 project and our colleagues in PPLATO for useful discussions. We are also grateful to the Higher Education Academy Engineering Subject Centre for funding us via a Mini-Project grant in collaboration with Frank Hamer and LTSN Physical Sciences for a development project grant, in collaboration with Simon Belt, and for the opportunity to present these ideas at various workshops.

Martin Lavelle | Robin Horan

School of Mathematics and Statistics, The University of Plymouth, Plymouth, PL4 8AA, UK