Basic Maths: 40%

• Set theory:Venn diagram, set operations, mathematical induction, functions and relations
• Algebra and linear algebra: Logarithms, Binomials, Inequalities, Theory-of-equations, Matrices, Basics of limit, continuity, differentiation, integration, series and sequences and their convergence
• Combinatorics: Sum and product rules, permutation, combination, recurrence relations, pigeon-hole principle, principle of inclusion and exclusion
• Probability and statistics: basic notion of probability, discrete and continuous probability distributions, binomial, Poisson and normal distributions, conditional probability and Bayes theorem

Basics of Programming: 30%

(The student should be familiar with the basic concepts of programming and should be able to write programs involving the following concepts in any one of the following languages: C, C++, Java, Python, MATLAB)

• Variables, datatypes, assignments, expressions
• Conditional constructs and iteration (loops)
• Function or method call, recursion, recursive decomposition of a problem
• Parameter passing mechanism, scope, binding, pointers
• Arrays, lists, stacks, queues, binary tree, binary search tree
• Basics of searching and sorting
• Graph and its representation and traversal

Artificial-Intelligence and Machine-Learning (Basics + Applied): 20%

(The student should be familiar with the basic concepts of Artificial Intelligence and Machine Learning)

• Binary classification
• Multi-class classification
• Regression
• linear models
• SVMs
  
• Decision-trees
• Neural networks
• Clustering
• k-means

Writing Skills: 10%

The student should be able to write essay-type articles on research-related topics.