GATE Syllabus for Data Science

Probability and Statistics for GATE DA syllabus

• Counting (permutation and combinations) 
• Probability axioms
• Sample space 
• Events 
• 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, uniform, exponential, Poisson, normal, standard normal, t-distribution, chi-squared distributions, cumulative distribution function, 
• Conditional PDF, Central limit theorem, confidence interval, z-test, t-test, chi-squared test.

Linear Algebra for GATE exam for GATE DA syllabus

• Vector space, subspaces 
• Linear dependence and independence of vectors 
• Matrices, projection matrix, orthogonal matrix, idempotent matrix, partition matrix and their properties, 
• 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 for GATE DA syllabus

• Functions of a single variable, 
• Limit 
• Continuity and differentiability 
• Taylor series 
• Maxima and minima 
• Optimization involving a single variable.

Programming, Data Structures and Algorithms for GATE DA syllabus

• Programming in Python 
• Basic data structures: 
  • Stacks 
  • Queues Linked lists 
  • Trees 
  • Hash tables 
• Search algorithms: 
  • Linear search and binary search, 
• Basic sorting algorithms: 
  • Selection sort 
  • Bubble sort 
  • Insertion sort 
• Divide and conquer: 
  • Mergesort 
  • Quicksort 
• Introduction to graph theory 
• Basic graph algorithms: traversals and shortest path.

Database Management and Warehousing for GATE DA syllabus

• ER-model, 
• Relational model: 
  • Relational algebra 
  • Tuple calculus 
• SQL 
• Integrity constraints 
• Normal form 
• File organization 
• Indexing
• Data types 
• Data transformation such as normalization, discretization, sampling, compression 
• Data warehouse modelling: schema for multidimensional data models, concept hierarchies, 
• Measures: categorization and computations.

Machine Learning for GATE DA syllabus

• 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
  • K-means/k-medoid 
  • Hierarchical clustering 
  • Top-down 
  • Bottom-up: 
  • Single-linkage 
  • Multiple-linkage 
  • Dimensionality reduction, 
  • Principal component analysis.

AI for GATE DA syllabus

• Search: 
  • Informed 
  • Uninformed 
  • Adversarial 
• Logic 
• Propositional 
• Predicate 
• Reasoning under uncertainty topics — 
  • Conditional independence representation 
  • Exact inference through variable elimination
  • Approximate inference through sampling.