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.
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.
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