An inverse function is a second function which undoes the work of the first one. In this unit we describe two methods for finding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

This paper by ROSS CUTHBERT and HELEN MACGILLIVRAY discusses analysis of data on initiatives to improve retention rates on engineering degree programmes at Queensland University of Technology in Australia. The paper was presented at Delta 07 - the Southern Hemisphere Symposium on Undergraduate Mathematics Teaching. The Mathematics Access Centre at QUT offers optional extra support and examination workshops. The paper reports that students accessing these are nearly twice as likely to complete the course as the whole cohort, and half as likely to discontinue engineering.

Recruitment to post-graduate mathematics programmes and to lecturer positions in mathematics departments in UK universities has become dominated by international students and staff. Although mathematics is generally regarded as ‘the universal language’, the reality is that different countries have very different cultures when it comes to the teaching and learning of mathematics. There are significant variations in the pre-university mathematical experience, in terms of the curriculum content, learning styles, levels of abstraction, and assessment methods. Even within the UK, a considerable number of pre-higher education mathematics qualifications are available and, it is not always clear what mathematics can be expected when students commence their degree programmes. With increasing numbers of international students and academic staff in UK HE, the scene is becoming more complicated. Students enter degree courses with a wide range of backgrounds and bring with them very different experiences. At the same time, academic staff, having experienced different education systems, may have some unrealistic expectations from their students. With an HEA Teaching Development Grant (Individual Scheme 2012 -2013), this research by Aiping Xu, Coventry University has investigated the mathematical cultures of a range of the main international suppliers (of students and staff) to UK HE mathematics departments. Using semi-structured interviews and online questionnaires, personal experiences of academic staff who have studied or taught more than two educational systems have been drawn upon. Some examinations have also been studied in detail.

In this unit, we explain what it means for a function to tend to infinity, to minus infinity, or to a real limit, as x tends to infinity or to minus infinity. We also explain what it means for a function to tend to a real limit as x tends to a given real number. In each case, we give an example of a function that does not tend to a limit at all. (Mathtutor Video Tutorial) The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

In this unit, we recall what is meant by a simple sequence, and introduce infinite sequences. We explain what it means for two sequences to be the same, and what is meant by the n-th term of a sequence. We also investigate the behaviour of infinite sequences, and see that they might tend to plus or minus infinity, or to a real limit, or behave in some other way. (Mathtutor Video Tutorial) The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Some of the most important functions are linear. This unit describes how to recognize a linear function, and how to find the slope and the y-intercept of its graph. (Mathtutor Video Tutorial) The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.