# MS/PhD

**Source**: https://wsai.iitm.ac.in/admissions/ms-phd-admissions/
**Parent**: https://wsai.iitm.ac.in/

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## MS/PhD

For those passionate about research and innovation, our advanced degree programs offer opportunities to delve into cutting-edge research in AI and data science, guided by our expert faculty.

The School of Data Science and AI at IIT Madras offers MS/PhD programmes in a variety of areas. We welcome applicants from diverse departments with an applied interest in AI/ML, as well as students from EE/CS/AI departments who are interested in fundamental research areas in AI/ML.

[Apply Now](https://research.iitm.ac.in/)

### Written Test Syllabus

The written test will have two parts: **Theory** (objective questions: MCQ, Fill in the blanks, True/False) and **Python Coding** (problems requiring you to write code in Basic Python).

#### Probability and Statistics

- Counting (permutation and combinations)
- Independent events, mutually exclusive events
- Marginal, conditional and joint probability
- Bayes Theorem
- Conditional expectation and variance
- Mean, median, mode and standard deviation
- Correlation, and covariance
- Random variables, discrete random variables and probability mass functions
- Uniform, Bernoulli, binomial distribution
- Continuous random variables and probability
- Distribution function, cumulative distribution function, Conditional PDF
- Uniform, exponential, Poisson, normal, standard normal, t-distribution
- Chi-squared distributions
- Central limit theorem
- Confidence interval
- Z-test, t-test, chi-squared test

#### Linear Algebra

- Vector space, subspaces
- Linear dependence and independence of vectors
- Matrices, projection matrix, orthogonal matrix, idempotent matrix, partition matrix
- Quadratic forms
- Systems of linear equations and solutions
- Gaussian elimination
- Eigenvalues and eigenvectors
- Determinant, rank, nullity
- Projections
- LU decomposition, singular value decomposition

#### Calculus and Optimization

- Functions of a single variable
- Limit, continuity and differentiability
- Taylor series
- Maxima and minima
- Optimization involving a single variable

#### Python Coding

You will be given coding tasks that you need to complete and execute by writing Python scripts. You will need to know the following:

- Basic Python syntax - comments, variables, basic data types
- Operators and Control Flow - If/else, for, while, range, break, continue, pass
- Functions - How to define and use them
- Lists/Arrays, Tuples, and associated methods

### Interview Topics

For those who qualify after the written test for the online interview, questions from the following additional topics may be asked:

#### Machine Learning

- Supervised Learning regression and classification problems
- Simple linear regression
- Multiple linear regression
- Ridge regression
- Logistic regression
- K-nearest neighbour
- Naive Bayes classifier
- Linear discriminant analysis
- Support vector machine
- Decision trees
- Bias-variance trade-off
- Cross-validation methods such as leave-one-out (LOO) cross-validation, k-folds cross-validation, multi-layer perceptron, feed-forward neural network
- Unsupervised Learning: clustering algorithms

#### Artificial Intelligence

- Search: informed, uninformed, adversarial
- Logic: Propositional Logic, Predicate Logic
- Reasoning under Uncertainty Topics
- Conditional Independence Representation
- Exact Inference through Variable Elimination
- Approximate Inference through Sampling

**Note for PhD Applicants:** You may also be asked questions from specialized topics during the interview. You can select a topic from Deep Learning, NLP, Vision, RL, or Time-Series modeling depending on your interest and background.

### Sample Question Papers

Download sample question papers to prepare for the written test. The GATE DA (Data Science and AI) model question paper is also a good reference, as our test is structured in a similar fashion.

#### DSAI MS/PhD Sample Question Paper

Practice questions for the written test

[Download](https://wsai.iitm.ac.in/pdf/DSAI-MS_PhD-SampleQuestionPaper.pdf)

#### GATE DA Sample Question Paper

Data Science and AI model question paper

[Download](https://wsai.iitm.ac.in/pdf/DA-GATE-Sample.pdf)

#### DA 2024 GATE Question Paper

Official GATE 2024 question paper

[Download](https://wsai.iitm.ac.in/pdf/DA24S1.pdf)