1. Semester: I
2. Number of Credits: 4

Module 1: Elements of logic
Necessary and sufficient conditions, theorems and proofs (direct, contrapositive); elements of set theory, relations and functions, vectors in Rn , open and closed sets in Rn, convex sets in Rn  and their properties, bounded sets, compact sets; continuity, sequences, convergent and bounded sequences in Rn,  Weierstrass Theorem, Brouwer’s Fixed Point Theorem, concave and quasi concave functions

Module 2: Introduction to Integral and Differential Calculus
Rules of differentiation, transcendental functions, total and partial derivatives, Young’s Theorem, Euler’s Theorem, homogeneous functions; integration: definite and indefinite integrals, integration by parts

Module 3: Introduction to Matrices
Types of matrices, operations on matrices, determinants, eigen values and eigen vectors, quadratic forms: definite and semi-definite forms, economic applications (primal and dual in LPP), elementary differential and difference equations

Module 4: Static Optimization
First and second order conditions for local interior optima, (Unconstrained local global theorem), concavity and uniqueness, sufficient conditions for unique global optima, constrained optimization with Lagrange multipliers, second order conditions, sufficient conditions for optima with equality constraints, inequality constraints, Kuhn Tucker conditions, Envelope Theorem, duality, calculus of variations and the Euler equation, Elements of dynamic optimization: the Hamiltonian