Acknowledgements
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Author(s): The Open University

Learning outcomes
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Author(s): The Open University

Acknowledgements
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

6 Solutions to the exercises
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

5 Curves from parameters
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

4 Hyperbolic functions
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

3 New graphs from old
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

2 Graph sketching
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

1 Real functions
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

Overview
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

Learning outcomes
Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.
Author(s): The Open University

Acknowledgements
We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video.
Author(s): The Open University

Learning outcomes
We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video.
Author(s): The Open University

Acknowledgements
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University

5.3 Powers
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University

5.2 Existence of roots
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University

5.1 Arithmetic with real numbers
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University

4.4 Further exercises
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University

4.3 Least Upper Bound Property
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University

4.2 Least upper and greatest lower bounds
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property.
Author(s): The Open University