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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.

### 1. Logic and Proof

Abstract
Most languages follow some grammatical rules in order to convey ideas clearly. Mathematics written in English of course has to follow these rules. Moreover, the ideas have to obey logical rules to be meaningful.
Kam Yu

### 2. Sets and Relations

Abstract
The language of sets is an important tool in defining mathematical objects. In this chapter we review and study set theory from an intuitive and heuristic approach.
Kam Yu

Abstract
Let S be a set.
Kam Yu

### 4. Linear Algebra

Abstract
Linear algebra is the starting point of multivariate analysis, due to its analytical and computational simplicity. In many economic applications, a linear model is often adequate.
Kam Yu

### 5. Vector Calculus

Abstract
In this chapter we introduce multivariate differential calculus, which is an important tool in economic modelling. Concepts developed in the previous chapters are applied to the Euclidean space, which is both a metric space and a normed vector space.
Kam Yu

### 6. Convex Analysis

Abstract
Models in economic analysis often assume sets or functions are convex. These convexity properties make solutions of optimization problem analytically convenient.
Kam Yu

### 7. Optimization

Abstract
In economics we frequently have to find the points that maximize or minimize a differentiable functional f(x, θ).
Kam Yu

### 8. Probability

Abstract
Most graduate level econometrics textbooks require the readers to have some background in intermediate level mathematical probability and statistics. A lot of students, however, took business and economic statistics and then econometric courses in the undergraduate program.
Kam Yu

### 9. Dynamic Modelling

Abstract
In this chapter we extend economic modelling to include the time dimension. Dynamic modelling is the essence of macroeconomic theory. Our discussions provide the basic ingredients of the so-called dynamic general equilibrium model.
Kam Yu