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B-TECH-M-TECH-INTEGRATED-DUAL-DEGREE in Mathematics And Computing at Indian Institute of Technology (BHU) Varanasi
Varanasi, Uttar Pradesh
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About the Specialization
What is Mathematics and Computing at Indian Institute of Technology (BHU) Varanasi Varanasi?
This Mathematics and Computing program at IIT BHU focuses on developing a strong foundation in both theoretical mathematics and its computational applications. It uniquely blends advanced mathematical concepts with core computer science principles, catering to the growing demand for professionals adept at solving complex, data-intensive problems in the Indian industry. The curriculum emphasizes analytical thinking, algorithm design, and modern computing paradigms.
Who Should Apply?
This program is ideal for high-achieving fresh graduates with a strong aptitude for mathematics and problem-solving, seeking entry into quantitative finance, data science, or advanced research roles. It also suits individuals passionate about developing sophisticated algorithms and mathematical models for technological advancements across various Indian sectors. Students aiming for higher studies (PhD) in related fields will also find this program highly beneficial.
Why Choose This Course?
Graduates of this program can expect to pursue rewarding careers in India as Data Scientists, Quantitative Analysts, Machine Learning Engineers, Software Developers, or Research Scientists in top-tier companies. Entry-level salaries typically range from INR 10-25 LPA, with experienced professionals earning significantly more. The program prepares students for roles in fintech, AI/ML startups, and R&D divisions of major Indian and multinational corporations.
Student Success Practices
Foundation Stage
Master Core Programming and Math Fundamentals- (Semester 1-2)
Dedicate significant time to thoroughly understand foundational concepts in Calculus, Linear Algebra, Data Structures, and a primary programming language (like C++/Python). Utilize online platforms for practice, such as HackerRank and LeetCode, to solidify coding skills and mathematical problem-solving ability.
Tools & Resources
NPTEL courses for Maths/CS, GeeksforGeeks, HackerRank, Khan Academy for mathematical intuition
Career Connection
A strong foundation is crucial for clearing technical rounds in placements and for advanced coursework in AI/ML, setting the base for lucrative roles in tech and analytics.
Engage in Peer Learning and Study Groups- (Semester 1-2)
Form study groups with peers to discuss challenging concepts, solve problems collaboratively, and prepare for exams. Teaching others reinforces your own understanding and exposes you to diverse problem-solving approaches, enhancing overall academic performance.
Tools & Resources
WhatsApp/Telegram groups, Departmental common rooms for discussions, Online whiteboards for collaborative problem solving
Career Connection
Develops teamwork and communication skills, highly valued in corporate environments for collaborative project execution.
Participate in Coding and Math Competitions- (Semester 1-2)
Regularly participate in competitive programming contests (e.g., CodeChef, Codeforces, ICPC) and math olympiads. This helps in developing quick problem-solving skills, algorithmic thinking, and exposure to a wide range of computational challenges beyond the classroom syllabus.
Tools & Resources
CodeChef, Codeforces, TopCoder, Kaggle for data science contests
Career Connection
Builds a strong competitive profile, which is highly regarded by tech recruiters, and sharpens analytical skills essential for quantitative roles.
Intermediate Stage
Undertake Mini-Projects and Internships- (Semester 3-5)
Actively seek opportunities for short-term projects under faculty guidance or pursue summer internships. Focus on applying learned concepts in Data Structures, Algorithms, Probability, and Machine Learning to real-world problems. Document your work meticulously.
Tools & Resources
LinkedIn for internship searches, Departmental project announcements, GitHub for project showcasing, Jupyter Notebooks for data analysis
Career Connection
Gains practical industry exposure, builds a portfolio of projects, and enhances resume strength for future placements, crucial for roles in software development or data science.
Specialize in a Niche Area of Math and Computing- (Semester 3-5)
Identify an area of interest within Mathematics and Computing, such as Machine Learning, Quantitative Finance, or Cryptography, and take relevant elective courses. Deepen your knowledge through online certifications and specialized workshops.
Tools & Resources
Coursera/edX for specialized courses, DeepLearning.AI, Quantra for financial math, IEEE/ACM student chapters for workshops
Career Connection
Develops expertise in high-demand areas, making you a specialized candidate for targeted roles in AI, fintech, or cybersecurity, leading to higher compensation.
Build a Strong Professional Network- (Semester 3-5)
Attend industry seminars, conferences, and networking events. Connect with alumni, professors, and industry professionals on platforms like LinkedIn. Participate in departmental events to interact with guest speakers and industry veterans.
Tools & Resources
LinkedIn, Professional conferences (e.g., Data Science Summit, AI Conclave), IIT BHU alumni network platforms
Career Connection
Opens doors to mentorship, internship leads, and future job opportunities, significantly impacting career progression in India''''s competitive job market.
Advanced Stage
Focus on Integrated Dual Degree Project (IDDP)- (Semester 6-8 (B.Tech phase), Semester 9-10 (M.Tech phase))
Invest deeply in your IDDP, ensuring it addresses a significant problem and demonstrates advanced skills in mathematical modeling, algorithm design, and computational implementation. Aim for publishing preliminary findings in workshops or conferences.
Tools & Resources
Research papers (arXiv, IEEE Xplore, ACM Digital Library), LaTeX for thesis writing, Collaboration tools for team projects
Career Connection
A strong IDDP is a powerful resume enhancer, showcasing research capabilities and problem-solving prowess, crucial for R&D roles, academic pursuits, and competitive placements.
Intensive Placement and Interview Preparation- (Semester 7-9)
Start preparing for placements early by practicing interview questions, participating in mock interviews, and refining your resume and cover letter. Focus on both technical aptitude (DSA, ML, Math concepts) and soft skills (communication, logical reasoning).
Tools & Resources
Glassdoor for interview experiences, LeetCode premium, Career services workshops at IIT BHU, Alumni mentorship for interview tips
Career Connection
Maximizes chances of securing top placements in core engineering, data science, or quantitative finance roles at leading Indian and international firms, ensuring a strong start to your career.
Explore Entrepreneurship or Research Opportunities- (Semester 8-10)
For those with an entrepreneurial spirit, explore startup ideas, participate in hackathons, and leverage IIT BHU''''s incubation facilities. For research enthusiasts, collaborate with faculty on advanced research projects, aiming for publications or further academic pursuits like PhDs.
Tools & Resources
IIT BHU Incubation Centre, Startup India initiatives, Research grants and fellowships, Academic journals for publications
Career Connection
Fosters innovation and leadership skills, potentially leading to founding your own venture or a distinguished career in academic or industrial research, contributing to India''''s knowledge economy.
Program Structure and Curriculum
Eligibility:
- Successful completion of 10+2 (or equivalent) with Physics, Chemistry, and Mathematics, followed by qualification in JEE Advanced and subsequent JoSAA counselling for B.Tech admission. IDD specific entry requirements might involve direct admission through JEE Advanced or an internal process for B.Tech students.
Duration: 10 semesters / 5 years
Credits: 208 Credits
Assessment: Internal: 40-50%, External: 50-60%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PHM101 | Physics I | Core | 3 | Classical Mechanics, Special Relativity, Wave Optics, Quantum Mechanics Introduction, Electromagnetism Fundamentals |
| CHM101 | Chemistry I | Core | 3 | Atomic Structure, Chemical Bonding, Thermodynamics, Chemical Kinetics, Electrochemistry |
| MCM101 | Mathematics I (Calculus) | Core | 4 | Differential Calculus, Integral Calculus, Multivariable Calculus, Sequences and Series, Vector Calculus Introduction |
| CSM101 | Introduction to Programming | Core | 4 | Programming Fundamentals (C/Python), Control Structures, Functions and Arrays, Pointers and Structures, File Handling |
| MEM101 | Engineering Graphics and Drawing | Core | 2 | Orthographic Projections, Isometric Views, Sectional Views, Machine Drawing, AutoCAD Basics |
| HSM101 | English Communication Skills | Core | 2 | Grammar and Vocabulary, Reading Comprehension, Writing Skills, Presentation Skills, Group Discussion |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PHM102 | Physics II | Core | 3 | Semiconductor Physics, Lasers and Fiber Optics, Dielectric and Magnetic Materials, Superconductivity, Nano-materials |
| CHM102 | Chemistry II (Environmental Chemistry) | Core | 3 | Air and Water Pollution, Green Chemistry Principles, Waste Management, Renewable Energy Sources, Catalysis |
| MCM102 | Mathematics II (Linear Algebra and Differential Equations) | Core | 4 | Vector Spaces, Matrices and Determinants, Eigenvalues and Eigenvectors, First Order Differential Equations, Higher Order Differential Equations |
| ECM101 | Basic Electrical Engineering | Core | 3 | DC and AC Circuits, Network Theorems, Transformers, Electrical Machines, Power Systems Introduction |
| EIM101 | Basic Electronics Engineering | Core | 3 | Semiconductor Devices, Diodes and Rectifiers, Transistors, Operational Amplifiers, Digital Logic Basics |
| CSM102 | Data Structures Lab | Lab | 2 | Array Operations, Linked Lists, Stack and Queue Implementations, Tree Traversals, Graph Algorithms |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM201 | Discrete Mathematics | Core | 4 | Set Theory, Logic and Proof Techniques, Combinatorics, Graph Theory, Recurrence Relations |
| CSM201 | Data Structures and Algorithms | Core | 4 | Arrays, Linked Lists, Stacks, Queues, Trees and Heaps, Graph Algorithms, Sorting and Searching, Hashing Techniques |
| MCM203 | Probability and Statistics | Core | 4 | Probability Theory, Random Variables and Distributions, Sampling Distributions, Hypothesis Testing, Regression Analysis |
| CSM203 | Object Oriented Programming | Core | 4 | Classes and Objects, Inheritance and Polymorphism, Encapsulation and Abstraction, Templates and Exceptions, STL in C++ |
| HSM201 | Economics for Engineers | Core | 3 | Microeconomics Basics, Macroeconomics Overview, Market Structures, Financial Analysis, Project Evaluation |
| CSM205 | Data Structures and Algorithms Lab | Lab | 2 | Implementation of data structures, Algorithm design practice, Performance analysis, Debugging techniques, Problem solving |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM202 | Numerical Methods | Core | 4 | Root Finding Methods, Interpolation and Approximation, Numerical Integration and Differentiation, Solving ODEs and PDEs numerically, Matrix Computations |
| CSM202 | Operating Systems | Core | 4 | Process Management, CPU Scheduling, Memory Management, File Systems, Concurrency and Deadlocks |
| MCM204 | Optimization Techniques | Core | 4 | Linear Programming, Simplex Method, Duality Theory, Network Optimization, Non-linear Programming Introduction |
| CSM204 | Database Management Systems | Core | 4 | Relational Model, SQL Queries, Normalization, Transaction Management, Indexing and Hashing |
| HSM202 | Environmental Science and Engineering | Core | 3 | Ecosystems, Biodiversity Conservation, Pollution Control, Sustainable Development, Environmental Policies |
| CSM206 | Operating Systems Lab | Lab | 2 | Shell Scripting, Process Synchronization, Memory Management simulation, File system calls, Multithreading |
Semester 5
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM301 | Stochastic Processes | Core | 4 | Markov Chains, Poisson Processes, Queuing Theory, Random Walks, Martingales Introduction |
| CSM301 | Computer Networks | Core | 4 | OSI and TCP/IP Models, Network Layer Protocols (IP, Routing), Transport Layer Protocols (TCP, UDP), Application Layer Protocols (HTTP, DNS), Network Security Basics |
| MCM303 | Mathematical Modeling | Core | 4 | Introduction to Modeling, Dynamical Systems, Differential Equation Models, Optimization Models, Statistical Modeling |
| CSM303 | Theory of Computation | Core | 4 | Finite Automata, Regular Languages, Context-Free Grammars, Turing Machines, Undecidability |
| HSM301 | Professional Ethics and Human Values | Core | 3 | Ethics in Engineering, Human Values, Moral Dilemmas, Environmental Ethics, Corporate Social Responsibility |
| CSM305 | Database Management Systems Lab | Lab | 2 | SQL DDL and DML, ER Modeling, Stored Procedures, Database connectivity (JDBC/ODBC), Query Optimization |
Semester 6
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM302 | Abstract Algebra | Core | 4 | Groups, Rings, Fields, Vector Spaces, Polynomial Rings |
| CSM302 | Design and Analysis of Algorithms | Core | 4 | Algorithm Complexity, Divide and Conquer, Dynamic Programming, Greedy Algorithms, Graph Algorithms Advanced |
| MCM304 | Real Analysis | Core | 4 | Sequences and Series of Functions, Riemann Integration, Metric Spaces, Measure Theory Introduction, Functional Analysis Basics |
| CSM304 | Artificial Intelligence | Core | 4 | Problem Solving Agents, Search Algorithms (Heuristic, Adversarial), Knowledge Representation, Machine Learning Introduction, Natural Language Processing Basics |
| XXXOE1 | Open Elective I | Elective | 3 | Interdisciplinary topics, Management principles, Entrepreneurship, Foreign language, Art and Culture |
| CSM306 | Computer Networks Lab | Lab | 2 | Socket Programming, Network simulation tools, Packet analysis, Client-server applications, Network configuration |
Semester 7
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM401 | Computational Linear Algebra | Core | 4 | Matrix Decompositions, Iterative Methods for Linear Systems, Eigenvalue Problems, Sparse Matrix Techniques, Applications in Data Science |
| CSM401 | Machine Learning | Core | 4 | Supervised Learning, Unsupervised Learning, Regression and Classification, Deep Learning Introduction, Model Evaluation |
| MCM403 | Partial Differential Equations | Core | 4 | First Order PDEs, Second Order PDEs (Wave, Heat, Laplace), Separation of Variables, Fourier Series, Green''''s Functions |
| XXXDE1 | Departmental Elective I | Elective | 3 | Data Mining, Cryptography, Image Processing, Financial Mathematics, Game Theory |
| XXXOE2 | Open Elective II | Elective | 3 | Social Sciences, Humanities, Advanced Engineering Topics, Innovation and Entrepreneurship, Ethics and Law |
| CSP401 | Project I | Project | 2 | Problem Identification, Literature Review, Methodology Design, Implementation Basics, Report Writing |
Semester 8
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM402 | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Linear Operators, Spectral Theory Introduction |
| CSM402 | Big Data Analytics | Core | 4 | Hadoop Ecosystem, Spark Programming, NoSQL Databases, Data Warehousing, Stream Processing |
| XXXDE2 | Departmental Elective II | Elective | 3 | Advanced Cryptography, Computational Finance, Deep Learning, IoT and Edge Computing, Quantum Computing |
| XXXDE3 | Departmental Elective III | Elective | 3 | High Performance Computing, Reinforcement Learning, Statistical Inference, Number Theory and Cryptography, Bioinformatics |
| MCM404 | Mathematical Aspects of Computer Vision | Core | 4 | Image Representation, Image Filtering, Feature Detection, Object Recognition, Geometric Computer Vision |
| CSP402 | Project II | Project | 2 | Advanced Implementation, Experimental Design, Data Analysis, Technical Report Writing, Presentation Skills |
Semester 9
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM501 | Advanced Numerical Optimization | Core | 4 | Convex Optimization, Lagrange Multipliers, KKT Conditions, Interior Point Methods, Stochastic Optimization |
| CSM501 | Advanced Machine Learning | Core | 4 | Generative Models, Transformers and Attention, Causal Inference, Federated Learning, Ethical AI |
| XXXDE4 | Departmental Elective IV | Elective | 3 | Natural Language Processing, Quantum Information Theory, Actuarial Science, Advanced Cryptography, Bio-inspired Computing |
| XXXDE5 | Departmental Elective V | Elective | 3 | Financial Econometrics, Distributed Systems, Computer Graphics, Advanced Database Systems, Human-Computer Interaction |
| IDDP1 | Integrated Dual Degree Project (Phase I) | Project | 6 | Project Proposal, Detailed Design, Pilot Implementation, Initial Results Analysis, Mid-term Review |
Semester 10
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MCM502 | Advanced Topics in Pure Mathematics | Core | 4 | Algebraic Topology, Differential Geometry, Complex Analysis, Number Theory, Set Theory Axioms |
| CSM502 | Advanced Topics in Theoretical Computer Science | Core | 4 | Advanced Complexity Theory, Logic in Computer Science, Formal Methods, Randomized Algorithms, Approximation Algorithms |
| IDDP2 | Integrated Dual Degree Project (Phase II) | Project | 10 | Comprehensive Implementation, Extensive Experimentation, Rigorous Data Analysis, Final Thesis Writing, Viva-voce Examination |
| XXXDE6 | Departmental Elective VI | Elective | 3 | Financial Engineering, Applied Cryptography, Bioinformatics Algorithms, Operations Research, Computational Geometry |
