.png&w=1920&q=75)
INTEGRATED-M-SC in Mathematics at National Institute of Technology Patna
Patna, Bihar
.png&w=1920&q=75)
About the Specialization
What is Mathematics at National Institute of Technology Patna Patna?
This Integrated M.Sc Mathematics program at National Institute of Technology Patna focuses on providing a comprehensive understanding of pure and applied mathematics, along with essential computational and interdisciplinary skills. It is designed to foster analytical thinking, problem-solving abilities, and a strong foundation for advanced research or diverse industry roles. The curriculum blends theoretical rigor with practical applications relevant to the evolving Indian scientific and technological landscape, preparing students for high-demand careers.
Who Should Apply?
This program is ideal for high school graduates with a strong aptitude for mathematics and science, seeking a challenging five-year academic journey. It caters to those aspiring to careers in academia, research, data science, actuarial science, quantitative finance, and software development within India. It is also suitable for students aiming to pursue higher studies like Ph.D. in mathematical sciences or related fields.
Why Choose This Course?
Graduates of this program can expect diverse career paths in India, including roles as data scientists, quantitative analysts, software developers, educators, or researchers. Entry-level salaries typically range from INR 6-10 LPA, with experienced professionals earning significantly higher. The strong mathematical foundation also prepares them for competitive exams like UPSC, banking, and professional certifications in analytics or finance, contributing to significant growth trajectories in leading Indian and multinational companies.
Student Success Practices
Foundation Stage
Master Core Mathematical Concepts- (Semester 1-2)
Dedicate significant time to thoroughly understand fundamental concepts in calculus, discrete mathematics, linear algebra, and real analysis. Focus on building strong problem-solving skills by practicing a wide range of problems and proofs. Engage in peer study groups to clarify doubts and explore different approaches to complex problems.
Tools & Resources
Textbooks (e.g., NCERT, NPTEL videos), Online platforms like Khan Academy, Coursera for supplementary learning, Peer study groups, Professor office hours
Career Connection
A robust foundation is critical for excelling in advanced subjects and forms the basis for analytical roles in any industry.
Develop Foundational Programming Skills- (Semester 1-2)
Actively participate in programming labs (C/C++, Python) and practice coding daily. Solve problems on online judges like CodeChef or HackerRank to improve logical thinking and algorithmic skills. Understand data structures and algorithms well, as these are crucial for computational applications of mathematics.
Tools & Resources
CodeChef, HackerRank, LeetCode, GeeksforGeeks, Official programming language documentation, Course textbooks
Career Connection
Essential for roles in data science, software development, and quantitative analysis, enabling practical application of mathematical models.
Engage with Interdisciplinary Subjects- (Semester 1-2)
Pay attention to physics, chemistry, and basic engineering courses. Understand how mathematical principles are applied in these fields. Seek connections between different subjects to build a holistic scientific perspective. This broadens your understanding and opens up diverse career avenues.
Tools & Resources
Interdisciplinary textbooks, Research papers on mathematical applications in science/engineering, Discussions with faculty from other departments
Career Connection
Helps in identifying niche areas for specialization and applying mathematical tools to real-world problems in diverse scientific and engineering domains.
Intermediate Stage
Deep Dive into Advanced Mathematics & Electives- (Semester 3-5)
For semesters 3-5, focus on advanced topics like complex analysis, numerical analysis, probability, and topology. Strategically choose electives (e.g., optimization, computational geometry) that align with your career interests (e.g., finance, data science, pure research). Engage with research papers related to elective topics.
Tools & Resources
Advanced textbooks, NPTEL courses for specific topics, JSTOR, arXiv for research papers, Departmental seminars
Career Connection
Specialized knowledge enhances employability in specific mathematical fields, enabling roles like quantitative researchers or specialized analysts.
Pursue Internships and Projects- (Semester 3-5)
Actively seek summer internships in relevant industries such as finance, IT, or research institutions (e.g., ISI, IISc, CMI). Participate in departmental projects or academic competitions (e.g., Putnam Competition, various hackathons) to apply theoretical knowledge and gain practical exposure. Build a portfolio of small projects.
Tools & Resources
Internship portals (Internshala, LinkedIn), NIT Patna career services, Faculty guidance for research projects, GitHub for project portfolio
Career Connection
Internships provide crucial industry experience, networking opportunities, and often lead to pre-placement offers. Projects demonstrate practical skills to potential employers.
Develop Statistical & Data Handling Skills- (Semester 3-5)
Focus on probability and statistics. Learn statistical software like R or Python libraries (Pandas, NumPy, SciPy) for data analysis. Practice handling real datasets. This builds a strong foundation for modern data-driven roles, an area where mathematical rigor is highly valued.
Tools & Resources
R Studio, Python (Anaconda distribution), Kaggle for datasets and competitions, Online courses on data analysis
Career Connection
Directly applicable to data scientist, business analyst, and machine learning engineer roles, which are high in demand in the Indian job market.
Advanced Stage
Specialized Skill Development & Certification- (Semester 6-8)
In the later stages (Semesters 6-8), deepen your specialization through advanced electives (e.g., Financial Mathematics, Machine Learning, Cryptography). Consider industry-recognized certifications in areas like Python for Data Science, AWS/Azure Data Engineer, or relevant financial modeling tools to bolster your resume.
Tools & Resources
Official certification providers (e.g., Coursera, edX, industry bodies), Online advanced courses, Specialized software (e.g., MATLAB, Mathematica, R, Python)
Career Connection
Demonstrates specific skill sets highly valued by employers, increasing employability and potential salary in specialized technical roles.
Intensive Placement & Research Preparation- (Semester 6-10)
Engage in intensive preparation for placements or higher studies. For placements, focus on aptitude tests, technical interviews, and mock group discussions. For research, identify potential Ph.D. supervisors, refine your research proposal, and prepare for entrance exams like GATE or GRE/TOEFL if aiming abroad. Actively participate in the dissertation/project work in Semesters 9-10.
Tools & Resources
Placement cell resources, mock interview platforms, GATE/GRE/TOEFL prep materials, Research papers, academic mentors, Professional networking events
Career Connection
Directly impacts securing desired job offers or admission to prestigious Ph.D. programs, both domestically and internationally.
Networking and Mentorship- (Semester 6-10)
Actively network with alumni, industry professionals, and faculty members. Attend workshops, conferences, and seminars. Seek mentorship from experienced professionals in your target field. Building a strong professional network is invaluable for career guidance, job referrals, and staying updated on industry trends in India.
Tools & Resources
LinkedIn, Alumni network portals, Industry conferences (e.g., Data Science Congress, Financial Analytics Summits), Faculty and guest lecturers
Career Connection
Opens doors to hidden job markets, provides insights into career progression, and builds long-term professional relationships.
Program Structure and Curriculum
Eligibility:
- Admissions through JEE (Main) conducted by National Testing Agency (NTA).
Duration: 10 semesters / 5 years
Credits: 196 Credits
Assessment: Assessment pattern not specified
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA101 | Mathematical Methods-I | Core | 4 | Real Numbers, Functions and Limits, Differential Calculus, Integral Calculus, Sequences and Series |
| MA102 | Discrete Mathematics | Core | 4 | Logic and Proofs, Sets and Functions, Relations, Graph Theory, Trees, Boolean Algebra |
| CH101 | Chemistry | Core | 4 | Atomic Structure, Chemical Bonding, Thermodynamics, Electrochemistry, Reaction Kinetics, Organic Chemistry Basics |
| HS101 | English for Communication | Core | 3 | Communication Skills, Grammar, Reading Comprehension, Writing Skills, Presentation Skills, Technical Writing |
| CS101 | Fundamentals of Computer Programming | Core | 3 | Programming Concepts, Data Types and Operators, Control Structures, Functions and Arrays, Pointers, Strings |
| CS102 | Fundamentals of Computer Programming Lab | Lab | 1 | Programming Practice in C/C++, Problem Solving, Debugging, Basic Algorithms Implementation |
| CH102 | Chemistry Lab | Lab | 1 | Volumetric Analysis, Gravimetric Analysis, pH Measurements, Chemical Reaction Experiments, Spectrophotometry |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA103 | Mathematical Methods-II | Core | 4 | Vector Calculus, Ordinary Differential Equations, Laplace Transforms, Fourier Series, Partial Differential Equations |
| MA104 | Graph Theory | Core | 4 | Graphs and Subgraphs, Paths and Circuits, Trees and Connectivity, Planar Graphs, Coloring and Matching, Digraphs |
| PH101 | Physics | Core | 4 | Optics, Quantum Mechanics, Solid State Physics, Nuclear Physics, Laser Physics, Fiber Optics |
| EE101 | Basic Electrical Engineering | Core | 3 | DC Circuits, AC Circuits, Transformers, Induction Motors, DC Machines, Power Systems |
| EC101 | Basic Electronics Engineering | Core | 3 | PN Junction Diodes, Transistors, Rectifiers and Filters, Amplifiers, Oscillators, Digital Electronics Basics |
| PH102 | Physics Lab | Lab | 1 | Experiments on Optics, Electricity and Magnetism, Semiconductor Devices, Measurement Techniques |
| EE102 | Basic Electrical Engineering Lab | Lab | 1 | Verification of Circuit Laws, Measurement of Electrical Parameters, Transformer Tests, Motor Characteristics, Basic Wiring |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA201 | Real Analysis | Core | 4 | Metric Spaces, Compactness and Connectedness, Sequences and Series of Functions, Riemann-Stieltjes Integral, Lebesgue Theory Basics |
| MA202 | Abstract Algebra | Core | 4 | Group Theory, Rings and Fields, Vector Spaces, Polynomial Rings, Isomorphism Theorems |
| MA203 | Object-Oriented Programming | Core | 4 | C++ Basics, Classes and Objects, Inheritance and Polymorphism, Exception Handling, File I/O, Templates |
| CE101 | Environmental Science & Engineering | Core | 3 | Ecosystems and Biodiversity, Air Pollution, Water Pollution, Solid Waste Management, Environmental Ethics, Sustainable Development |
| ME101 | Engineering Mechanics | Core | 3 | Statics of Particles and Rigid Bodies, Dynamics of Particles, Kinematics and Kinetics, Work and Energy, Friction, Centroid and Moment of Inertia |
| CE102 | Environmental Science & Engineering Lab | Lab | 1 | Water Quality Analysis, Air Pollution Monitoring, Soil Testing, Solid Waste Characterization, Environmental Impact Assessment |
| ME102 | Engineering Drawing Lab | Lab | 1 | Orthographic Projections, Isometric Views, Sectional Views, Dimensioning and Tolerancing, CAD Basics, Assembly Drawing |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA204 | Complex Analysis | Core | 4 | Complex Numbers and Functions, Analytic Functions, Conformal Mappings, Cauchy''''s Integral Formula, Residue Theorem, Series Expansions |
| MA205 | Numerical Analysis | Core | 4 | Error Analysis, Solutions of Non-linear Equations, Interpolation, Numerical Differentiation and Integration, Numerical Solution of ODEs, Systems of Linear Equations |
| MA206 | Data Structures and Algorithms | Core | 4 | Arrays and Linked Lists, Stacks and Queues, Trees and Heaps, Graphs, Sorting Algorithms, Searching Algorithms |
| BT101 | Biology for Engineers | Core | 3 | Cell Biology, Genetics, Biochemistry, Microbiology, Biotechnology Applications, Bioethics |
| IT101 | Operating Systems | Core | 3 | Process Management, CPU Scheduling, Deadlocks, Memory Management, File Systems, I/O Systems |
| BT102 | Biology for Engineers Lab | Lab | 1 | Basic Microbiology Techniques, DNA Extraction, PCR and Gel Electrophoresis, Enzyme Kinetics, Microscopic Techniques |
| IT102 | Operating Systems Lab | Lab | 1 | Linux Commands and Utilities, Shell Scripting, Process Creation and Synchronization, Memory Allocation, File System Operations |
Semester 5
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA301 | General Topology | Core | 4 | Topological Spaces, Continuous Functions, Connectedness, Compactness, Separation Axioms, Product Spaces |
| MA302 | Linear Algebra | Core | 4 | Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors, Inner Product Spaces, Quadratic Forms, Diagonalization |
| MA303 | Probability and Statistics | Core | 4 | Probability Axioms, Random Variables and Distributions, Joint Distributions, Hypothesis Testing, Regression and Correlation, ANOVA |
| MA304 | Computer Networks | Core | 3 | Network Topologies, OSI and TCP/IP Models, Data Link Layer, Network Layer, Transport Layer, Application Layer |
| MA305 | Computer Networks Lab | Lab | 1 | Network Configuration, Socket Programming, Protocol Analysis, Network Security Tools, Packet Tracing |
| MA511 | Applied Abstract Algebra | Elective-I (Theory) | 3 | Groups and Codes, Boolean Algebras, Finite Fields, Applications in Cryptography, Symmetry Groups, Coding Theory |
| MA512 | Commutative Algebra | Elective-I (Theory) | 3 | Rings and Ideals, Noetherian Rings, Artinian Rings, Localization, Primary Decomposition, Algebraic Geometry Connection |
| MA513 | Logic & Set Theory | Elective-I (Theory) | 3 | Propositional Logic, First-Order Logic, Axiomatic Set Theory, Ordinal and Cardinal Numbers, Axiom of Choice, Consistency and Completeness |
| MA514 | Number Theory | Elective-I (Theory) | 3 | Divisibility and Congruences, Prime Numbers, Diophantine Equations, Quadratic Residues, Arithmetic Functions, Applications in Cryptography |
| MA515 | Operator Theory | Elective-I (Theory) | 3 | Bounded Linear Operators, Spectral Theory, Compact Operators, Self-Adjoint Operators, Banach and Hilbert Spaces, Applications |
| MA516 | Fuzzy Sets & Applications | Elective-I (Theory) | 3 | Fuzzy Set Theory, Fuzzy Relations, Fuzzy Logic, Fuzzy Numbers, Fuzzy Control Systems, Applications in AI |
| MA517 | Wavelets & Applications | Elective-I (Theory) | 3 | Fourier Analysis Review, Wavelet Transforms, Multiresolution Analysis, Orthogonal Wavelets, Wavelet Packets, Applications in Signal/Image Processing |
| MA518 | Computational Geometry | Elective-I (Theory) | 3 | Convex Hulls, Voronoi Diagrams, Delaunay Triangulations, Geometric Searching, Robot Motion Planning, Algorithms for Geometric Problems |
| MA519 | Design & Analysis of Algorithms | Elective-I (Theory) | 3 | Algorithm Complexity, Divide and Conquer, Dynamic Programming, Greedy Algorithms, Graph Algorithms, NP-Completeness |
| MA520 | Scientific Computing with Python | Elective-I (Theory) | 3 | Python Fundamentals, NumPy for Numerical Computing, SciPy for Scientific Computing, Matplotlib for Plotting, Symbolic Computing (SymPy), Data Analysis with Pandas |
| MA521 | Linear Programming & Game Theory | Elective-I (Theory) | 3 | Linear Programming Formulation, Simplex Method, Duality Theory, Transportation and Assignment Problems, Two-Person Zero-Sum Games, Nash Equilibrium |
| MA522 | Digital Image Processing | Elective-I (Theory) | 3 | Image Fundamentals, Image Enhancement, Image Restoration, Image Compression, Image Segmentation, Feature Extraction |
| Elective-I Lab | Elective-I Lab (Practical component for chosen Elective-I Theory course) | Lab Elective | 1 | Practical Application of Chosen Elective-I Theory, Software Implementation, Data Analysis, Problem Solving Exercises |
Semester 6
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA306 | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Bounded Linear Operators, Dual Spaces, Compact Operators |
| MA307 | Differential Geometry | Core | 4 | Curves in Space, Surfaces, First and Second Fundamental Forms, Geodesics, Curvature of Surfaces, Differential Forms |
| MA308 | Optimization Techniques | Core | 4 | Linear Programming, Simplex Method, Duality Theory, Transportation and Assignment Problems, Non-Linear Programming Basics, Lagrangian Multipliers |
| MA309 | Database Management Systems | Core | 3 | ER Model, Relational Model, SQL Queries, Normalization, Transaction Management, Concurrency Control |
| MA310 | Database Management Systems Lab | Lab | 1 | SQL Commands and Queries, Database Design, ER Diagrams Implementation, PL/SQL Programming, NoSQL Database Basics |
| MA523 | Advanced Graph Theory | Elective-II (Theory) | 3 | Connectivity, Matchings, Colorings, Flows in Networks, Algebraic Graph Theory, Random Graphs |
| MA524 | Coding Theory | Elective-II (Theory) | 3 | Error-Detecting Codes, Linear Codes, Cyclic Codes, BCH Codes, Convolutional Codes, Decoding Algorithms |
| MA525 | Theory of Computation | Elective-II (Theory) | 3 | Finite Automata, Context-Free Grammars, Turing Machines, Decidability, Complexity Classes (P, NP), Undecidability |
| MA526 | Fuzzy Logic & Neural Networks | Elective-II (Theory) | 3 | Fuzzy Sets and Relations, Fuzzy Logic Systems, Artificial Neural Networks, Perceptrons, Backpropagation, Fuzzy-Neural Systems |
| MA527 | Integral Transforms & Applications | Elective-II (Theory) | 3 | Laplace Transforms, Fourier Transforms, Z-Transforms, Hankel Transforms, Mellin Transforms, Applications to ODEs and PDEs |
| MA528 | Mathematical Modeling | Elective-II (Theory) | 3 | Modeling Process, Dimensional Analysis, Discrete Models, Continuous Models, Optimization Models, Case Studies |
| MA529 | Scientific Visualization | Elective-II (Theory) | 3 | Visualization Principles, 2D and 3D Data Visualization, Volume Rendering, Flow Visualization, Information Visualization, Tools and Libraries |
| MA530 | Advanced Numerical Methods for PDEs | Elective-II (Theory) | 3 | Finite Difference Methods, Finite Element Methods, Spectral Methods, Stability Analysis, Numerical Schemes for Convection-Diffusion, High-Performance Computing |
| MA531 | Cryptography & Network Security | Elective-II (Theory) | 3 | Classical Cryptography, Symmetric Key Cryptography, Asymmetric Key Cryptography, Hash Functions, Digital Signatures, Network Security Protocols |
| MA532 | Cloud Computing | Elective-II (Theory) | 3 | Cloud Computing Concepts, Service Models (IaaS, PaaS, SaaS), Deployment Models, Virtualization, Cloud Security, Cloud Platforms |
| MA533 | Data Warehousing & Data Mining | Elective-II (Theory) | 3 | Data Warehousing Concepts, OLAP, Data Mining Techniques, Association Rule Mining, Classification, Clustering |
| Elective-II Lab | Elective-II Lab (Practical component for chosen Elective-II Theory course) | Lab Elective | 1 | Practical Application of Chosen Elective-II Theory, Software Implementation, Case Studies, Algorithm Development |
Semester 7
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA401 | Measure and Integration | Core | 4 | Lebesgue Measure, Measurable Functions, Lebesgue Integral, Convergence Theorems, Product Measures, Radon-Nikodym Theorem |
| MA402 | Partial Differential Equations | Core | 4 | First Order PDEs, Classification of Second Order PDEs, Wave Equation, Heat Equation, Laplace Equation, Green''''s Functions |
| MA403 | Mechanics | Core | 4 | Lagrangian Mechanics, Hamiltonian Mechanics, Central Forces, Rigid Body Dynamics, Small Oscillations, Canonical Transformations |
| MA404 | Data Science Fundamentals | Core | 3 | Data Collection and Cleaning, Exploratory Data Analysis, Data Visualization, Statistical Learning, Linear Regression, Logistic Regression |
| MA405 | Data Science Fundamentals Lab | Lab | 1 | Python for Data Science, Pandas and NumPy, Matplotlib and Seaborn, Basic Machine Learning Models, Data Preprocessing, Feature Engineering |
| MA534 | Fluid Dynamics | Elective-III (Theory) | 3 | Inviscid Flow, Viscous Flow, Boundary Layers, Turbulence, Compressible Flow, Applications |
| MA535 | Theory of Relativity | Elective-III (Theory) | 3 | Special Relativity, Lorentz Transformations, General Relativity, Curved Spacetime, Black Holes, Cosmology |
| MA536 | Mathematical Biology | Elective-III (Theory) | 3 | Population Dynamics, Epidemiology Models, Biochemical Kinetics, Spatial Models, Ecological Models, Bioinformatics |
| MA537 | Operations Research | Elective-III (Theory) | 3 | Network Models, Inventory Management, Queueing Theory, Dynamic Programming, Simulation, Decision Analysis |
| MA538 | Information Theory | Elective-III (Theory) | 3 | Entropy, Mutual Information, Channel Capacity, Source Coding, Channel Coding, Information Compression |
| MA539 | Advanced Statistical Methods | Elective-III (Theory) | 3 | Multivariate Analysis, Non-parametric Methods, Time Series Analysis, Bayesian Statistics, Survival Analysis, Generalized Linear Models |
| MA540 | Stochastic Modeling | Elective-III (Theory) | 3 | Random Walks, Markov Chains, Poisson Processes, Queueing Models, Stochastic Differential Equations, Monte Carlo Simulation |
| MA541 | Mathematical Finance | Elective-III (Theory) | 3 | Financial Markets, Derivatives, Options Pricing, Black-Scholes Model, Stochastic Calculus for Finance, Risk Management |
| MA542 | Internet of Things (IoT) | Elective-III (Theory) | 3 | IoT Architecture, Sensors and Actuators, Communication Protocols, IoT Platforms, Data Analytics in IoT, IoT Security |
| MA543 | Big Data Analytics | Elective-III (Theory) | 3 | Big Data Concepts, Hadoop Ecosystem, Spark, NoSQL Databases, Streaming Data Analytics, Big Data Tools and Techniques |
| MA544 | Software Engineering | Elective-III (Theory) | 3 | Software Development Life Cycle, Requirements Engineering, Software Design, Software Testing, Project Management, Software Quality |
| Elective-III Lab | Elective-III Lab (Practical component for chosen Elective-III Theory course) | Lab Elective | 1 | Practical Application of Chosen Elective-III Theory, Simulation Tools, Programming Exercises, Data Analysis and Modeling |
Semester 8
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA406 | Stochastic Processes | Core | 4 | Markov Chains, Poisson Processes, Birth-Death Processes, Brownian Motion, Martingales, Applications in Finance |
| MA407 | Advanced Abstract Algebra | Core | 4 | Field Extensions, Galois Theory, Modules over Principal Ideal Domains, Tensor Products, Representation Theory Basics, Advanced Ring Theory |
| MA408 | Financial Mathematics | Core | 4 | Interest Rate Models, Derivative Pricing, Black-Scholes Model, Stochastic Calculus for Finance, Risk Management, Bond Pricing |
| MA409 | Machine Learning | Core | 3 | Supervised Learning, Unsupervised Learning, Reinforcement Learning, Neural Networks, Deep Learning Basics, Model Evaluation |
| MA410 | Machine Learning Lab | Lab | 1 | Scikit-learn, TensorFlow/PyTorch, Model Training and Testing, Hyperparameter Tuning, Data Preprocessing for ML, Evaluation Metrics |
| MA545 | Dynamical Systems | Elective-IV (Theory) | 3 | Phase Space, Fixed Points, Limit Cycles, Chaos Theory, Bifurcations, Applications in Biology/Physics |
| MA546 | Algebraic Topology | Elective-IV (Theory) | 3 | Homotopy, Fundamental Group, Covering Spaces, Homology Theory, Cohomology Theory, Applications |
| MA547 | Ergodic Theory | Elective-IV (Theory) | 3 | Measure Preserving Transformations, Poincaré Recurrence Theorem, Ergodic Theorem, Mixing, Entropy of Dynamical Systems, Applications |
| MA548 | Approximation Theory | Elective-IV (Theory) | 3 | Weierstrass Approximation Theorem, Polynomial Approximation, Spline Approximation, Fourier Approximation, Least Squares Approximation, Best Approximation |
| MA549 | Queueing Theory | Elective-IV (Theory) | 3 | Queueing Models, Birth-Death Processes, Markovian Queues, Non-Markovian Queues, Network of Queues, Applications in Telecommunications |
| MA550 | Image & Video Processing | Elective-IV (Theory) | 3 | Image Filtering, Edge Detection, Image Segmentation, Video Representation, Motion Estimation, Video Compression |
| MA551 | Bioinformatics | Elective-IV (Theory) | 3 | Sequence Alignment, Phylogenetic Trees, Protein Structure Prediction, Gene Expression Analysis, Biological Databases, Algorithms in Bioinformatics |
| MA552 | Deep Learning | Elective-IV (Theory) | 3 | Neural Network Architectures, Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Transformers, Generative Models, Deep Learning Frameworks |
| MA553 | Artificial Intelligence | Elective-IV (Theory) | 3 | Intelligent Agents, Search Algorithms, Knowledge Representation, Reasoning, Machine Learning Principles, Natural Language Processing |
| MA554 | Block Chain Technology | Elective-IV (Theory) | 3 | Blockchain Fundamentals, Cryptocurrency, Distributed Ledger Technology, Smart Contracts, Consensus Mechanisms, Blockchain Applications |
| Elective-IV Lab | Elective-IV Lab (Practical component for chosen Elective-IV Theory course) | Lab Elective | 1 | Practical Application of Chosen Elective-IV Theory, Computational Experiments, Algorithm Implementation, Software Development |
Semester 9
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA501 | Advanced Numerical Methods | Core | 4 | Finite Difference Methods, Finite Element Methods, Spectral Methods, Numerical Solution of PDEs, Convergence and Stability, Error Bounds |
| MA502 | Cryptography | Core | 4 | Classical Ciphers, Symmetric Key Cryptography, Asymmetric Key Cryptography, Hash Functions, Digital Signatures, Key Management |
| MA503 | Research Methodology | Core | 4 | Research Design, Literature Review, Data Collection Methods, Statistical Analysis, Report Writing, Ethics in Research |
| MA504 | Scientific Computing | Core | 3 | MATLAB/Python for Scientific Computing, Numerical Algorithms, Data Visualization, High-Performance Computing Concepts, Parallel Computing Basics, Optimization Libraries |
| MA505 | Scientific Computing Lab | Lab | 1 | Implementation of Numerical Algorithms, Data Processing and Analysis, Scientific Visualization, Problem Solving with Computational Tools |
| MA555 | Finite Element Methods | Elective-V (Theory) | 3 | Variational Formulation, Shape Functions, Element Assembly, Boundary Conditions, Applications to PDEs, Computational Implementation |
| MA556 | Control Theory | Elective-V (Theory) | 3 | Linear Control Systems, State-Space Analysis, Stability Analysis, Controllability and Observability, Optimal Control, Nonlinear Control |
| MA557 | Actuarial Mathematics | Elective-V (Theory) | 3 | Interest Theory, Life Contingencies, Life Insurance, Pensions, Risk Theory, Ratemaking |
| MA558 | Time Series Analysis | Elective-V (Theory) | 3 | Time Series Components, Autoregressive Models (AR), Moving Average Models (MA), ARIMA Models, Forecasting Techniques, Spectral Analysis |
| MA559 | Bio-Statistics | Elective-V (Theory) | 3 | Clinical Trials, Epidemiological Studies, Hypothesis Testing in Biology, Survival Analysis, Genomic Data Analysis, Statistical Software for Bio-stats |
| MA560 | Optimization for Data Science | Elective-V (Theory) | 3 | Convex Optimization, Gradient Descent, Stochastic Gradient Descent, Regularization Techniques, Optimization in Machine Learning, Distributed Optimization |
| MA561 | Game Theory | Elective-V (Theory) | 3 | Strategic Form Games, Extensive Form Games, Nash Equilibrium, Subgame Perfect Equilibrium, Cooperative Games, Applications in Economics |
| MA562 | Pattern Recognition | Elective-V (Theory) | 3 | Feature Extraction, Classification Techniques, Clustering Algorithms, Dimensionality Reduction, Pattern Recognition Systems, Applications in Image/Speech |
| MA563 | Natural Language Processing | Elective-V (Theory) | 3 | Text Preprocessing, Tokenization and Stemming, Part-of-Speech Tagging, Syntactic and Semantic Analysis, Language Models, Machine Translation |
| MA564 | Reinforcement Learning | Elective-V (Theory) | 3 | Markov Decision Processes, Dynamic Programming, Monte Carlo Methods, Temporal Difference Learning, Policy Gradient Methods, Deep Reinforcement Learning |
| Elective-V Lab | Elective-V Lab (Practical component for chosen Elective-V Theory course) | Lab Elective | 1 | Practical Application of Chosen Elective-V Theory, Software Simulation, Advanced Programming Projects, Research Implementation |
Semester 10
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA506 | Dissertation | Project/Dissertation | 8 | Independent Research Project, Literature Review, Methodology Development, Data Analysis and Interpretation, Thesis Writing, Oral Defense |
| MA507 | Project | Project/Dissertation | 8 | Applied Project Work, Problem Definition, Solution Design, Implementation and Testing, Report Writing, Project Presentation |
