In this new, 6th edition of Foundation Maths, guided by user feedback, we have included in many of the chapters a number of challenge exercises. These exercises are intentionally demanding and require a considerable depth of understanding. Solutions to these exercises can be found at www.pearsoned.co.uk/croft. A further set of test and assignment exercises is given at the end of each chapter. These are provided so that the tutor can set regular assignments or tests throughout the course. Solutions to these are not provided. Feedback from students who have used earlier editions of this book indicates that they have found the style and pace of the book helpful in their study of mathematics at university.
In order to keep the size of the book reasonable we have endeavoured to include topics which we think are most important, cause the most problems for students, and have the widest applicability. We have startedthe book with materials on arithmetic including whole numbers, fractions and decimals. This is followed by several chapters which gradually introduce important and commonly used topics in algebra. There follows chapters on sets, number bases and logic, collectively known as discrete mathematics. The remaining chapters introduce functions, trigonometry, vectors, matrices, complex numbers, statistics, probability and calculus. These will be found useful in the courses previously listed.
The best strategy for those using the book would be to read through each section, carefully studying all of the worked examples and solutions. Many of these solutions develop important results needed later in the book. It is then a good idea to cover up the solution and try to work the example again independently. It is only by doing the calculation that the necessary techniques will be mastered. At the end of each section the self-assessment questions should be attempted. If these cannot be answered then the previous few pages should be worked through again in order to find the answers in the text, before checking with answers given at the back of the book. Finally, the exercises should be attempted and, again, answers should be checked regularly with those given at the back of the book. This edition is enhanced by video clips (see www.pearsoned.co.uk/croft) in which we, the authors, work through some algebraic examples and exercises taken from the book, pointing out techniques and key points. The icon next to an exercise signifies that there is a corresponding video clip.
In conclusion, remember that learning mathematics takes time and effort. Carrying out a large number of exercises allows the student to experience a greater variety of problems, thus building up expertise and confidence. Armed with these the student will be able to tackle more unfamiliar and demanding problems that arise in other aspects of their course. We hope that you find Foundation Maths useful and wish you the very best of luck.
Anthony Croft, Robert Davison 2016
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