The aim of this book is to bring students of economics and finance who have only an introductory background in mathematics up to a quite advanced level in the subject, thus preparing them for the core mathematical demands of econometrics, economic theory, quantitative finance and mathematical economics, which they are likely to encounter in their final-year courses and beyond. The level of the book will also be useful for those embarking on the first year of their graduate studies in Business, Economics or Finance. The book also serves as an introduction to quantitative economics and finance for mathematics students at undergraduate level and above. In recent years, mathematics graduates have been increasingly expected to have skills in practical subjects such as economics and finance, just as economics graduates have been expected to have an increasingly strong grounding in mathematics. The authors avoid the pitfalls of many texts that become too theoretical. The use of mathematical methods in the real world is never lost sight of and quantitative analysis is brought to bear on a variety of topics including foreign exchange rates and other macro level issues.
Part 1: Mathematics Introduction 1. Systems of Linear Equations and Matrices 2. Determinants 3. Elgenvalues and Elgenvectors 4. Conic Sections, Quadratic Forms and Definite Matrices 5. Vectors and Vector Spaces 6. Linear Transformations 7. Foundations for Vector Calculus 8. Difference Equations 9. Vector Calculus 10. Convexity and Optimization Part 2: Applications 11. Macroeconomic Applications 12. Single-Period Choice Under Certainty 13. Probability Theory 14. Quadratic Programming and Econometric Applications 15. Multi-Period Choice Under Certainty 16. Single-Period Choice Under Uncertainty 17. Portfolio Theory. Bibliography. Index
