## Course Learning Outcomes:

The course hones and upgrades the mathematical skills acquired in school and paves the way for our next course Mathematical Methods for Economics-II. Collectively, the two papers provide the mathematical foundations necessary for further study of a variety of disciplines including economics, statistics, computer science, finance and data analytics. The analytical tools introduced in this course have applications wherever optimisation techniques are used in business decision-making. These tools are necessary for anyone seeking employment as an analyst in the corporate world. The course additionally makes the student more logical in making or refuting arguments. Course Modules:

## Preliminaries:

Logic and proof techniques; sets and set operations; relations; functions and their properties; number systems

## Functions of one real variable:

Graphs; elementary types of functions: quadratic, polynomial, power, exponential, logarithmic; sequences and series: convergence, algebraic properties and applications; Continuous functions: characterisations, properties with respect to various operations and applications; Differentiable functions: characterisations, properties with respect to various operations and applications; Second and higher order derivatives: properties and applications  ### Single Variable Optimization:

Geometric properties of functions: convex functions, their characterisations and applications; local and global optima: geometric and calculus-based characterisations, and applications.

## Linear Algebra:

Vector spaces: algebraic and geometric properties, scalar products, norms, orthogonality; linear transformations: properties, matrix representations and elementary operations; systems of linear equations: properties of their solution sets; determinants: characterization, properties and applications. NOTE: The above modules give a rough idea about the topics covered in our Mathematical Methods for Economics-1 course. Students will be given modules as per their respective Universities outline after prior discussion