3 Key skills assessment units
Numerical and mathematical skills are used to describe and tackle a wide range of problems. These key skills are about understanding when particular techniques should be used, how to carry them out accurately and which techniques should be applied in particular situations. Developing your numerical, graphical and algebraic skills means being able to plan how you are going to use your skills over a period of time, monitoring your progress and then reviewing your approach. In developing and assess
Author(s): The Open University

2 Sources of help
Numerical and mathematical skills are used to describe and tackle a wide range of problems. These key skills are about understanding when particular techniques should be used, how to carry them out accurately and which techniques should be applied in particular situations. Developing your numerical, graphical and algebraic skills means being able to plan how you are going to use your skills over a period of time, monitoring your progress and then reviewing your approach. In developing and assess
Author(s): The Open University

Numerical and mathematical skills are used to describe and tackle a wide range of problems. These key skills are about understanding when particular techniques should be used, how to carry them out accurately and which techniques should be applied in particular situations. Developing your numerical, graphical and algebraic skills means being able to plan how you are going to use your skills over a period of time, monitoring your progress and then reviewing your approach. In developing and assess
Author(s): The Open University

Brain-Computer Interfaces
science, technology, neuroscience, medicine, electrical engineering, bioengineering, neural prostheses, brain, nervous system, neurological disease, injury, spinal cord, electrical signal, neuron, mathematical algorithm, chips, computer, motor cortex, ele
Author(s): No creator set

Asymmetric Information
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Author(s): No creator set

6 Solutions to the exercises
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

1 Symmetry in two dimensions
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

8.7 Luminosity functions
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

8.6 Line spectra: Activity 8 Quasar redshifts
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

8.5 Line spectra: Activity 7 Colours and broad lines
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

8.3 Line spectra: ions and spectral lines
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

8.1 Continuum spectra
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

7.9 Compton scattering
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

7.8 Example 2 and questions
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University

7.5 Emission from spiralling electrons: synchrotron radiation
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Author(s): The Open University