Mathematical Economics

Mathematical economics is the application of mathematical methods to represent economic theory and analyze economic problems. By translating economic concepts—such as utility, production, and market equilibrium—into formal models using calculus, matrix algebra, and optimization techniques, this approach provides a rigorous and precise language for economic analysis. It moves beyond intuitive or verbal arguments to allow for the formal derivation of testable hypotheses, the systematic analysis of complex interdependencies, and the study of economic dynamics, thereby forming the foundational framework for much of modern economic theory and econometrics.

1. Introduction to Mathematical Economics
   1. The Nature of Mathematical Economics
      1. Definition and Scope of Mathematical Economics
      2. Historical Development of Mathematical Methods in Economics
      3. Mathematical vs. Non-mathematical Economics
         1. Advantages of Mathematical Approaches
         2. Limitations and Critiques
      4. Mathematical Economics vs. Econometrics
         1. Distinction in Methods and Objectives
         2. Complementary Roles in Economic Analysis
   2. The Use of Mathematical Models
      1. Purpose and Role of Models in Economics
      2. Ingredients of a Mathematical Model
         1. Variables
            1. Endogenous Variables
            2. Exogenous Variables
            3. Stock vs. Flow Variables
         2. Constants and Parameters
            1. Economic Interpretation of Parameters
            2. Structural vs. Reduced-Form Parameters
         3. Equations and Identities
            1. Behavioral Equations
            2. Definitional Identities
            3. Equilibrium Conditions
      3. Model Construction Process
         1. Abstraction and Simplification
         2. Specification of Functional Forms
         3. Validation and Testing
   3. Mathematical Foundations
      1. The Real Number System
         1. Properties of Real Numbers
         2. Intervals and Inequalities
         3. Absolute Value and Distance
      2. Set Theory
         1. Basic Set Concepts
            1. Sets and Elements
            2. Subsets and Supersets
            3. Universal Set and Empty Set
            4. Cardinality
         2. Set Operations
            1. Union
            2. Intersection
            3. Complement
            4. Difference
            5. Cartesian Product
         3. Relations and Functions
            1. Definition of Relations
            2. Properties of Relations
               1. Reflexivity
               2. Symmetry
               3. Transitivity
            3. Definition of Functions
            4. Domain and Range
            5. Types of Functions
               1. One-to-One Functions
               2. Onto Functions
               3. Inverse Functions
               4. Composite Functions