Mathematics for Social Scientists is offered throughout the six weeks with teaching scheduled daily before other courses. If taken in conjunction with another course, there is no extra charge. Christopher Saker is a Lecturer in the Department of Mathematical Sciences and the Manager of the Essex Further Mathematics Centre. His research interests lie in the combinatorics of words, particularly the study of unavoidable sets.

Course Objectives This course is intended for those with little recent mathematical experience but who are motivated to learn. The aim is to provide a service course in support of other Summer School courses (primarily in the analysis of quantitative data) by presenting a unified introduction to the mathematical ideas and techniques used in those courses. The structure of the course is arranged, firstly, to provide an introduction to the concepts and techniques for the practical side of the subject, and, secondly, to develop a more deeper understanding of the ways in which these concepts and techniques are connected. Summer School participants may take any one Part and/or all three Parts of the course, but anyone taking Parts 2 or 3 will be presumed to be familiar with the material covered in the preceding Parts.

Course Content Part 1 of the course is an introductory module which begins by reviewing the equations and graphs of straight lines and simple curves. It progresses to the study of functions such as trigonometric, logarithmic and exponential functions. The session concludes with an introduction to differentiation and some of its applications

Course Prerequisites Participants in the course should be familiar with the basic ideas of arithmetic and algebra (addition, subtraction, multiplication, division, use of brackets, positive, negative, fractional powers, and the solution of simple equations). Students should possess a basic scientific calculator.

Recommended Reading For a review of the concepts listed in the prerequisites we recommend the Algebra Refresher which can be found by following the revision booklets link from http://www.mathscentre.ac.uk/students.php. Note that the site also has learning resources available for these and other basic mathematical topics.

Additional Reading Haeussler, E.F., Paul, R.S., and, Wood, R. 2004. Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences. Prentice Hall. Recommendations for other textbooks will be made during the course.

Students entering the course should be familiar with the basic ideas of arithmetic and algebra (addition, subtraction, multiplication, division, use of brackets, positive negative and fractional powers, and the solution of simple equations) as described, for example, in Haeussler, E.F., Paul, R.S. and Wood,R., Mathematical Analysis for Business, Economics and the Life and Social Sciences, 11th ed., Pearson (pp. 2-19, 30-34 and 147-151). Students should possess a basic scientific calculator. Students may take any or all of the three Parts of the course, but anyone taking Parts 2 or 3 will be presumed to be familiar with the material covered in the preceding Parts.

Lecture 1: Gradients, equations and graphs of straight lines.

Lecture 2: Linear Regression.

Lecture 3: Graphs of quadratic functions, the solution of quadratic equations by completion of the square and by the formula.

Lecture 4: Exponential and Logarithmic functions.

Lectures 5: Radian measure and trigonometric functions.

Lectures 6 – 9: Differentiation.

Lectures 10: Curve sketching.

Reading list:

The book by Haeussler, Paul and Wood referred to above is an acceptable text for Sessions 1 and 2 of the course. Students may also find the following books useful, although it is not necessary to read them before the course: + * Arya,J.C. and Lardner,R.W., Mathematical Analysis for Business, Economics and the Life and Social Sciences, 4th ed., Pearson + * Booth, D.J. Foundation Mathematics. Addison Wesley + * Dowling, E.T. Introduction to Mathematical Economics. Schaum’s Outline Series. McGraw Hill. (This book contains many worked examples.) + * Black, J. and Bradley, J.F. Essential Mathematics for Economists. Wiley. + Chiang, A.C. Fundamental Methods of Mathematical Economics. McGraw Hill. * Croft, A. and Davison, R. Foundation Maths. Longman. * Green, P.E. Mathematical Tools for Applied Multivariate Analysis. Academic Press. + * Grossman, S.I. Elementary Linear Algebra. Wadsworth. * Mizrahi, A. and Sullivan, M. Mathematics, an Applied Approach. Wiley. * Nicholson, R.H. Mathematics for Business and Economics. McGraw Hill. * Page, S., Berry, J. and Hampson, H. Mathematics, a Second Start. Prentice Hall. * Smith, K.J. College Mathematics and Calculus. Brooks/Cole. * indicates that this book is in the Summer School Library + indicates that this book is in the University Library The list contains good books for people wanting to read around the topics we will be covering during the course but they are not required reading and will not be referred to directly in the lectures so purchasing them is entirely optional.

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