Examination training mathematics and statistics for economists. Problems, hints, solutions. With the collaboration of Karl-Heinz Eger (Q931224)

The third edition of the book by Bernd Luderer has been published in 2008 (for the first ed. (1997) see Zbl 0869.00002). Its intention is to supply exercises and its solutions to enable the students to pass the undergraduate courses in statistics and mathematics for economists. The book is divided into three parts. Part~1 contains the exercises in the different fields, Part 2 puts some overview questions with respect to the material presented in the exercises, and the final Part 3 presents the solutions. The solutions for the exercises are very extensive and cover roughly 50\% of the book. The different fields dealt with origin mainly from the mathematics (3/4 of the chapters of Part~1), and one chapter is devoted to probability theory and the other to inferential statistics. The mathematical section starts with a chapter on linear algebra with linear equation systems using matrix notation. The two following chapters deal with elementary calculus for the cases of one or more independent variables. Linear optimization is mainly concerned with the explanation of the simplex methods, whereas financial mathematics employs formulas used in annuity calculations, compounded interests, to implement amortization schedules, and to calculate the possible profitability of an investment as well as its rate of return. Miscellaneous topics such as inequalities, set theory, and limits of numerical series are put together in chapter six of the book. The chapter on probability theory covers issues like random variables, central limit theorem, and random events. And under the header of statistics the author presents confidence intervals, testing a mean and a variance, and testing a probability. The exercises are comparable with respect to the degree and complexity of difficulty to similar courses at other universities and / or to related books on this subject. But it might be that the proportions between mathematics and statistics/probability theory are a little bit more balanced.