Students should be able (1) to define and explain concepts of a relation, a function, an open set, a compact set, a convex set and to graph simple functions, quadratic functions, polynomial functions, rational functions, exponential functions, and logarithmic functions, and to draw level curves for some commonly used functions in economics, (2) to identify some basic properties of a function such as monotonicity, continuity, and differentiability, convavity, convexity, quasi-concavity, quasi-convexity, homogeneity and homotheticity, (3) to perform matrix operations such as matrix addition and subtraction, matrix multiplication, and to compute determinants and inverses of matrices, (4) to analyze solutions to systems of linear equations and to solve systems of linear equations using the matrix inverse and Cramers rule, (5) to do differentiations for both one-variable and multi-variable functions using various differentiation rules (sum, difference, product, quotient, and chain rule), (6) to do comparative statics using implicit function theorems, (7) to identify and characterize extreme values of one-variable and multi-variable functions, (8) to solve static optimization problems with equality constraints using Lagrangean functions, (9) to solve static optimization problems with inequality constraints through Kuhn-Tucker method, (10) to analyze qualitative behaviours of systems of dynamic equations through stability analyses of equilibrium points (11) to solve dynamic optimization problems both in discrete time and continuous time