The admission test will consist of three parts. The first two parts, `Mathematics’ and `Computer Programming’, are to be attempted by all candidates. The third part has multiple modules. A candidate must select the  most relevant module to his/her area of interest and attempt only one module. If a candidate finds two modules related to his research area, he should attempt the one module he/she  can get a better score.

Course contents are adapted from the HEC curriculum.

Section 1- Mathematics

Total Questions: 20 Questions

Linear Algebra: Algebra of linear transformations and matrices, determinants, rank, systems of equations, vector spaces, orthogonal transformations, linear dependence, linear Independence and bases, eigenvalues and eigenvectors, characteristic equations, Inner product space and quadratic forms.

Discrete Structures: Mathematical reasoning, propositional and predicate logic, rules of inference, proof by induction, proof by contraposition, proof by contradiction, proof by implication, set theory, relations, equivalence relations and partitions, partial orderings, recurrence relations, functions, mappings, function composition, inverse functions, recursive functions, number theory, sequences, series, counting, inclusion and exclusion principle, pigeonhole principle, permutations and combinations, elements of graph theory, planar graphs, graph coloring, euler graph, hamiltonian path, rooted trees, traversals.

Calculus and Analytic Geometry:

Differential calculus; Concept and idea of differentiation, Geometrical and Physical meaning of derivatives, Rules of differentiation, Rates of change, Tangents and Normals lines, Chain rule, implicit differentiation, linear approximation,; Extreme value functions, Mean value theorems, Maxima and Minima of a function for single-variable, Integral calculus; Concept and idea of Integration, Indefinite Integrals, Techniques of integration, Definite Integrals,Applications of Integration; Area under the curve, Analytical Geometry; Straight lines in R3, Equations for planes.

Numerical Computing: Error Analysis, Solution of Non-Linear Equations (Bisection Method / Method of Iteration / Newton Raphson Method / Secant Method), Solution of Linear System of Equations (Gaussian Elimination Method/ Gauss–Jordon Elimination Method / Gauss–Seidel Iteration Method), Operators,  Interpolation, Numerical Integration.

Section 2 – Computer Programming

Total Questions: 30 Questions

Data Structure and Algorithms: Abstract data types, Stack (linked lists and array implementations), Recursion and analyzing recursive algorithms, divide and conquer algorithms, Sorting algorithms (selection, insertion, merge, quick, bubble, heap, shell, radix, bucket), queue (linked and array implementations of queues), linked list & its various types, sorted linked list, searching an unsorted array, binary search for sorted arrays, hashing and indexing, open addressing and chaining, trees and tree traversals, binary search trees, heaps, M-way trees, balanced trees, graphs, breadth-first and depth-first traversal, topological order, shortest path, adjacency matrix and adjacency list implementations, memory management and garbage collection.

Design and Analysis of Algorithms: Analysis on nature of input and size of input Asymptotic notations; Big-O, Big Ω, Big Θ, little-o, little-ω, Sorting Algorithm analysis, loop invariants, Recursion and recurrence relations; Algorithm Design Techniques, Brute Force Approach, Divide-and-conquer approach; Merge, Quick Sort, Greedy approach; Dynamic programming, Search trees; Heaps; Hashing; Graph algorithms, shortest paths, sparse graphs, String matching; Introduction to complexity classes;

Object Oriented Programming: introduction to object oriented programming concepts, classes, objects, data encapsulation, constructors, destructors, access modifiers, const vs non-const functions, static data members & functions, function overloading, operator overloading, identification of classes and their relationships, composition, aggregation, inheritance, multiple inheritance, polymorphism, abstract classes and interfaces, generic programming concepts, function & class templates, standard template library, exception handling.

Section 3 – Select one most appropriate module related to your area of interest.

Total Questions: 25 Questions

Module A- Machine Learning and AI

 Artificial Intelligence: Introduction, basic concepts of AI, Problem Solving by Searching (Informed searching(Best-First Search, A*, Heuristics), Uninformed searching(BFS, DFS, UCS, IDS), Local searching(Simulated Annealing, Hill Climbing), Constraint Satisfaction Problems; Adversarial Search (Min-max algorithm, Alpha-beta pruning), Learning (Unsupervised learning, Supervised learning)

Machine Learning: machine learning and statistical pattern recognition.

Graphical models (full Bayes, Naïve Bayes), Decision trees for classification & regression for both categorical & numerical data, Ensemble methods, Random forests, Boosting (Adaboost and Xgboost), Stacking;

Supervised learning:Four Components of Machine Learning Algorithm:  Hypothesis, Loss Functions, Derivatives and Optimization Algorithms, Gradient Descent, Stochastic Gradient Descent, Linear Regression, Nonlinear Regression, Perceptron, Support vector machines, Kernel Methods, Logistic Regression, Softmax, Neural networks;

Unsupervised learning: K-means, Density Based Clustering Methods (DBSCAN, etc.), Gaussian mixture models, EM algorithm, etc.

Misc : Reinforcement learning;Tuning model complexity; Bias-Variance Tradeoff;Grid Search, Random Search; Evaluation Metrics; Reporting predictive  performance

Deep Learning: Linear / non-linear classification, , linear regression, logistic regression, Neural Networks (Soft max, momentum, Regularization, Gradient Descent & Stochastic Gradient Descent (SGD), activation functions, neural net architecture, representational power), Back propagation, Building Neural Networks (loss functions, weight initialization, regularization, dropout, batch normalization), Convolutional Neural Networks (CNN)  (Convolutional and Pooling Layers), Popular CNN based architectures and their reasoning, Recognition Tasks (Localization, Detection, Segmentation, etc.), Transfer Learning and Fine-tuning, Deep Learning for  Natural Language Processing (NLP), Learning word and sentence embedding (word2vec), Introduction to recurrent networks (RNNs, LSTMS, GRU).

 Module B- Data Science

 Big Data Analytics: Basic big data concepts and definitions, Understanding of Hadoop ecosystems including Yarn, Hive, HBases, Spark, Zookeeper, Impala and Map Reduce, SQL and No-SQL Databases, Dimensional Data Modeling, Data Warehousing,  Basic concepts of cloud computing and service models, Understanding of important public cloud platforms and their key services, data lakes, ETL vs ELT, Other key concepts about big data and cloud computing

 Database Management: Introduction to advanced data models such as object relational, object-oriented. File organization concepts, Transactional processing, and Concurrency control techniques, Recovery techniques, Query processing and optimization, Database Programming, Integrity and security, Database Administration, Physical database design and tuning, Distributed database systems, Emerging research trends in database systems.

 Database Systems: Basic database concepts, Database approach vs file based system, database architecture, three-level schema architecture, data independence, relational data model, attributes, schemas, tuples, domains, relation instances, keys of relations, integrity constraints, relational algebra, selection, projection, Cartesian product, types of joins, normalization, functional dependencies, normal forms, entity relationship model, entity sets, attributes, relationship, entity-relationship diagrams, Structured Query Language (SQL), Joins and sub-queries in SQL, Grouping and aggregation in SQL, concurrency control, database backup and recovery, indexes, NoSQL systems.

 Data science tools and techniques: Data Preprocessing: feature selection/elimination/construction, dimensionality reduction: SVD, PCA, data mining challenges and potential solution, Datasets types and properties, Similarly and distance metrics,  Classification models: Decision Tree, Beyesian models, KNNs, Bagging, Boosting and ensemble models, NNs, etc., Frequent itemsets and association rule mining,  Sequential Pattern Mining, Clustering,  Recommender systems.

Information Retrieval: Push, pull, querying, browsing, Probability ranking principle, Bag of words representation, Vector space model, Term frequency, Document frequency and inverse document frequency, BM25, Inverted index and postings, Evaluation methodologies, Statistical and unigram language models, query likelihood, Maximum likelihood estimate, Relevance, Relevance feedback, Pseudo-relevance feedback, Implicit feedback, Rocchio feedback, Scalability and efficiency, Spams, Crawlers, focused crawling, and incremental crawling, PageRanks and HITS, Link analysis: Personalized PageRank, Hubs and Authorities, and Trust Rank.

Module D- Remote Sensing and GIS

Remote Sensing fundamentals: Basics of EM radiation, wave-matter interaction, EM spectrum, and characteristics of wave propagation (reflection, refraction, scattering, reflectance, albedo, polarization, etc.)

Orbital mechanics & map projections: Optical sensing, Radiometers, Scatterometers and Radar imaging, Spaceborne hyperspectral and multispectral sensors (principles of imaging & related issues),

Synthetic aperture radar:  basics & applications, Basic ideas related to scatterometry/altimetry/GNSS-based sensing/reflectometry

GIS: Image enhancement and Visualisations, Fundamentals of GIS platforms, Interpolations, filtering, basic data types, spatial databases, mapping servers, Datum, projections, rasters, vector data, etc.

Module E: Programming languages and Formal software engineering

Automata and computability theory:

Regular expressions, non/deterministic finite automata, language acceptance, push-down automata, chomsky normal form, context free/sensitive grammars, non/deterministic turing machines, complexity classes, P vs NP,  NP-completeness, decidability.

Compiler construction:

Scanner, lexical analyzer, recursive descent parsing, factoring, LR parsing, earley parsing, type checking, semantic analysis, attribute grammars, code generation, register scheduling.

Semantics, logic and proof:

First order logic, propositional logic, free vs bound variables, substitutions,  skolemization, unification, resolution theorem proving, operational/denotational semantics, binary decision diagrams (BDDs), invariants

Advanced:

Static analysis, dataflow analysis, lattices, liveness, reaching definition, available expression analysis, constant propagation, constant folding.

Module E- Computer Hardware/Software Security

 Artificial Intelligence: Introduction, basic concepts of AI, Problem Solving by Searching (Informed searching(Best-First Search, A*, Heuristics), Uninformed searching(BFS, DFS, UCS, IDS), Local searching(Simulated Annealing, Hill Climbing), Constraint Satisfaction Problems; Adversarial Search (Min-max algorithm, Alpha-beta pruning), Learning (Unsupervised learning, Supervised learning)

Machine Learning: machine learning and statistical pattern recognition. Graphical models (full Bayes, Naïve Bayes), Decision trees for classification & regression for both categorical & numerical data, Ensemble methods, Random forests, Boosting (Adaboost and Xgboost), Stacking; Supervised learning: Loss Functions, Derivatives and Optimization Algorithms, Gradient Descent, Stochastic Gradient Descent, Linear Regression, Nonlinear Regression, Perceptron, Support vector machines, Kernel Methods, Logistic Regression, Softmax, Neural networks; Unsupervised learning: K-means, Density Based Clustering Methods (DBSCAN, etc.), Gaussian mixture models, EM algorithm, etc. Misc : Reinforcement learning;Tuning model complexity; Bias-Variance Tradeoff;Grid Search, Random Search; Evaluation Metrics; Reporting predictive  performance , Linear / non-linear classification, , linear regression, logistic regression, Neural Networks (Soft max, momentum, Regularization, Gradient Descent & Stochastic Gradient Descent (SGD), activation functions, neural net architecture, representational power), Building Neural Networks (loss functions, weight initialization, regularization, dropout, batch normalization), Convolutional Neural Networks (CNN)  (Convolutional and Pooling Layers), Popular CNN based architectures and their reasoning,

Computer Architecture:

Basic digital design, Digital logic design (DLD), Pipelining, ISA, Microarchitecture, Branch predictors, speculative execution, datapath, sequential logic, data coherency & consistency, CISC architecture, RISC architecture, RISC V, Embedded Device – UART, SPI, I2C, JTAG, Software and Cloud components– Firmware of the device

Cyber Security: Basic security concepts, Information security terminology, Malware classifications, Types of malware. Server side web applications attacks. Cross-site scripting, SQL Injection, Cross-site request forgery, Planning and policy, Network protocols and service models. Transport layer security, Network layer security, Wireless security, Cloud & IoT security, microarchitectural attacks, side channels, side channel attacks, covert channels, covert channel attacks, randomization, obfuscation, denial of service (DOS) attacks, Requirement and Basic Properties, Main Challenges, Confidentiality, Integrity, Availability, Non-Repudiation, IoT Architectures (Device, Cloud, Gateway, Backend, Applications), Security Classification & Access Control, Data classification (Public and Private), Privacy issues, Authentication and Authorization, Data Integrity, Web Based Attacks and Implementation, Sniffing, Phishing, DNS Hijacking, Pharming, Defacement etc., Cryptology Cipher –Symmetric Key Algorithms (AES and DES), Asymmetric Key Algorithm (RSA) Attacks– Dictionary and Brute Force, Lookup Tables, Reverse Lookup Tables, Rainbow Tables, Attack Surface and Threat Assessment