Mathematical Economics

1. Front Matter

   Pages i-xiii

   PDF

2. Logic and Proof

   • Kam Yu

   Pages 1-17

3. Sets and Relations

   • Kam Yu

   Pages 19-42

4. Basic Topology

   • Kam Yu

   Pages 43-63

5. Linear Algebra

   • Kam Yu

   Pages 65-99

6. Vector Calculus

   • Kam Yu

   Pages 101-118

7. Convex Analysis

   • Kam Yu

   Pages 119-133

8. Optimization

   • Kam Yu

   Pages 135-152

9. Probability

   • Kam Yu

   Pages 153-176

10. Dynamic Modelling

    • Kam Yu

    Pages 177-206

11. Back Matter

    Pages 207-214

    PDF

This textbook provides a one-semester introduction to mathematical economics for first year graduate and senior undergraduate students. Intended to fill the gap between typical liberal arts curriculum and the rigorous mathematical modeling of graduate study in economics, this text provides a concise introduction to the mathematics needed for core microeconomics, macroeconomics, and econometrics courses. Chapters 1 through 5 builds students’ skills in formal proof, axiomatic treatment of linear algebra, and elementary vector differentiation. Chapters 6 and 7 present the basic tools needed for microeconomic analysis. Chapter 8 provides a quick introduction to (or review of) probability theory. Chapter 9 introduces dynamic modeling, applicable in advanced macroeconomics courses. The materials assume prerequisites in undergraduate calculus and linear algebra. Each chapter includes in-text exercises and a solutions manual, making this text ideal for self-study.

• mathematical economics
• static optimization
• dynamical system
• dynamic optimization
• dynamic modelling

“Even though the book is aimed at serving as a single semester course, it is sufficiently rich in its contents. This makes it stand out from other similar titles. … Sufficient references have been included for those desirous of delving deeper into the mathematical fundamentals of economics. The book has been written with a lot of caution, brevity and wisdom; and is worth every penny spent on it.” (Firdous Ahmad Mala, Journal of Economics, Vol. 136, 2022)

“This book by Prof. Kam Yu is an interesting addition to the literature on the basic mathematical tools for economic analysis (more specifically, for neoclassical economics). It covers a wide range of topics, ranging from topology to probability theory, going through linear algebra, optimization theory and dynamic programming. Its strength lies in a large number of examples and exercises. In that sense, it is useful for junior andsenior college students.” (Fernando Tohmé, zbMATH 1471.91005, 2021)

• Lakehead University, Thunder Bay, Canada

  Kam Yu

​Kam Yu studied engineering, mathematics, and economics in Hong Kong, the UK, and Canada. He teaches economics at Lakehead University, where he received a teaching award in 2016. His primary research interest is in the area of social and economic measurement.

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