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INTEGRATED-M-SC in Mathematics at National Institute of Technology Patna
Patna, Bihar
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About the Specialization
What is Mathematics at National Institute of Technology Patna Patna?
This Integrated B.Sc. - M.Sc. in Mathematics and Computing program at National Institute of Technology Patna focuses on building a strong theoretical foundation in mathematics combined with practical computing skills. It prepares students for diverse roles in data science, scientific computing, finance, and academia, addressing the growing demand for professionals who can leverage mathematical principles to solve complex computational problems in the Indian industry.
Who Should Apply?
This program is ideal for fresh graduates with a strong aptitude for mathematics and an interest in computational applications. It suits individuals aspiring to careers in quantitative finance, data analysis, software development, or research. Professionals seeking to upskill in mathematical modeling and computing, and those transitioning into analytics or scientific computing domains, will also find this curriculum highly beneficial.
Why Choose This Course?
Graduates of this program can expect promising career paths as Data Scientists, Quantitative Analysts, Software Engineers, Research Scientists, or Actuaries in India. Entry-level salaries typically range from INR 6-10 LPA, with experienced professionals earning significantly more. The strong foundation in both fields allows for growth trajectories in cutting-edge areas like AI/ML, FinTech, and R&D within Indian and multinational corporations.
Student Success Practices
Foundation Stage
Strengthen Core Mathematical Concepts- (Semester 1-2)
Dedicate significant time to understanding fundamental calculus, linear algebra, and discrete mathematics. Practice problem-solving rigorously using textbooks and online resources. Engage with professors during office hours to clarify doubts and build a strong theoretical base for advanced courses.
Tools & Resources
NPTEL lectures for Mathematics, MIT OpenCourseware, Khan Academy, NCERT textbooks (for revision)
Career Connection
A solid mathematical foundation is crucial for success in quantitative roles, data science, and advanced research, enabling clearer understanding of algorithms and models.
Master Programming Fundamentals in C/C++- (Semester 1-2)
Actively participate in programming labs and go beyond basic assignments. Solve problems on competitive programming platforms to improve logical thinking and coding efficiency. Understand data structures and algorithms thoroughly, as they are the backbone of computing.
Tools & Resources
HackerRank, CodeChef, GeeksforGeeks, LeetCode, Visual Studio Code
Career Connection
Proficiency in C/C++ and DSA is a non-negotiable skill for software development, algorithmic trading, and high-performance computing roles in top tech companies.
Develop Effective Study Habits & Peer Learning- (Semester 1-2)
Form study groups to discuss complex topics, solve problems collaboratively, and prepare for exams. Learn to manage time effectively between academic commitments and extracurricular activities. Seek feedback on assignments and presentations to continuously improve.
Tools & Resources
Google Docs for collaborative notes, WhatsApp/Telegram groups for discussion, Library resources
Career Connection
Strong academic performance and collaborative skills are highly valued by recruiters, demonstrating a candidate''''s commitment and ability to work in teams.
Intermediate Stage
Undertake Mini-Projects and Internships- (Semester 3-5)
Apply theoretical knowledge to practical problems by working on mini-projects, either self-initiated or under faculty guidance. Seek short-term internships or summer training programs in analytics, software development, or research to gain industry exposure.
Tools & Resources
GitHub for project hosting, Kaggle for datasets, Internshala, LinkedIn for internship searches
Career Connection
Practical project experience and internships enhance your resume, provide networking opportunities, and often lead to pre-placement offers, accelerating career entry.
Specialize in a Niche (e.g., Data Science, OR, Finance)- (Semester 3-5)
Identify areas of interest within Mathematics and Computing (e.g., Data Science, Operations Research, Quantitative Finance) and take relevant professional/open electives. Deep dive into advanced topics and build a portfolio of related projects.
Tools & Resources
Coursera/edX for specialized courses, Python/R for data science, MATLAB for numerical computing, Relevant research papers
Career Connection
Specialization makes you a more attractive candidate for specific roles, demonstrating focused expertise and a clear career trajectory in high-demand fields.
Participate in Coding & Mathematical Competitions- (Semester 3-5)
Regularly participate in coding challenges, hackathons, and mathematical Olympiads. These competitions hone problem-solving skills under pressure, expose you to diverse problems, and provide valuable recognition that stands out on your profile.
Tools & Resources
TopCoder, ACM-ICPC, Google Code Jam, Indian National Mathematical Olympiad (INMO)
Career Connection
Winning or performing well in competitions showcases your analytical prowess and problem-solving abilities, which are highly sought after by top-tier employers.
Advanced Stage
Engage in Research Projects & Dissertation- (Semester 6-8)
Actively work on your Project-I, Project-II, and Dissertation, focusing on original contributions. Collaborate with faculty on research papers and aim for publications in conferences or journals. This deep dive into a specific area builds expertise and critical thinking.
Tools & Resources
ResearchGate, Scopus/Web of Science, LaTeX for thesis writing, Statistical software (SPSS, R, Python libraries)
Career Connection
Strong research experience is invaluable for academic careers, R&D roles, and positions requiring innovative problem-solving in industry.
Prepare for Placements & Higher Studies- (Semester 6-8)
Start preparing for campus placements by refining your resume, practicing technical interviews, and working on aptitude tests. If interested in higher studies (Ph.D. or M.Sc. abroad), prepare for GRE/TOEFL and start applying to universities well in advance.
Tools & Resources
Placement cell workshops, Mock interview platforms, Arun Sharma for CAT/GRE quant, Magoosh/Kaplan for GRE/TOEFL
Career Connection
Proactive preparation ensures you secure desirable placements or admissions into prestigious graduate programs, setting the stage for long-term career success.
Network Professionally & Seek Mentorship- (Semester 6-8)
Attend industry seminars, guest lectures, and alumni meets to build a professional network. Connect with mentors in your chosen field who can provide guidance on career paths, skill development, and industry trends. Utilize platforms like LinkedIn effectively.
Tools & Resources
LinkedIn, Professional conferences (e.g., NCM, ACM India), Alumni network portals
Career Connection
A strong professional network opens doors to job opportunities, collaborations, and valuable insights, which are crucial for navigating and advancing in any career.
Program Structure and Curriculum
Eligibility:
- Candidates must have passed 10+2 with Physics, Chemistry, and Mathematics (PCM) or Physics, Mathematics, and Computer Science (PMCS) from a recognized Board/University with a minimum of 75% marks or be in the top 20 percentile in their respective boards. For SC/ST candidates, a minimum of 65% marks is required. Admission is through JEE (Main) followed by JoSAA/CSAB counseling.
Duration: 5 years (10 semesters)
Credits: 200 Credits
Assessment: Internal: 30%, External: 70%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CY101 | Chemistry | Core | 3 | Quantum Mechanics, Spectroscopy, Chemical Kinetics, Surface Chemistry, Stereochemistry |
| MA101 | Mathematics-I (Calculus) | Core | 4 | Differential Calculus, Integral Calculus, Sequence and Series, Multivariable Calculus, Applications of Calculus |
| ME101 | Engineering Graphics | Core | 3 | Introduction to Engineering Drawing, Orthographic Projections, Sectional Views, Isometric Projections, Computer Aided Drafting |
| EE101 | Basic Electrical Engineering | Core | 3 | DC Circuits, AC Circuits, Transformers, Electrical Machines, Power Systems |
| CS101 | Computer Programming | Core | 3 | C Programming Basics, Control Structures, Arrays and Pointers, Functions, File Handling |
| HS101 | English for Professional Communication | Core | 2 | Grammar and Vocabulary, Reading Comprehension, Writing Skills, Oral Communication, Presentation Skills |
| CS102 | Computer Programming Lab | Lab | 2 | C Programming Exercises, Debugging Techniques, Algorithm Implementation, Problem Solving, Data Structure Basics |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PH101 | Physics | Core | 3 | Quantum Physics, Solid State Physics, Electromagnetism, Optics, Semiconductor Devices |
| MA102 | Mathematics-II (Linear Algebra & Differential Equations) | Core | 4 | Matrices and Determinants, Vector Spaces, Linear Transformations, First Order Differential Equations, Higher Order Differential Equations |
| CE101 | Basic Civil Engineering | Core | 3 | Building Materials, Surveying, Structural Mechanics, Hydraulics, Environmental Engineering |
| EC101 | Basic Electronics Engineering | Core | 3 | Semiconductor Diodes, Transistors, Operational Amplifiers, Digital Electronics, Communication Systems |
| ME102 | Manufacturing Processes | Core | 3 | Casting, Forming, Machining, Welding, Additive Manufacturing |
| CY102 | Chemistry Lab | Lab | 2 | Volumetric Analysis, Chemical Synthesis, Instrumental Methods, Physical Chemistry Experiments, Organic Chemistry Practical |
| PH102 | Physics Lab | Lab | 2 | Optics Experiments, Electronics Experiments, Mechanics Experiments, Thermal Physics Experiments, Modern Physics Practical |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA201 | Complex Analysis | Core | 4 | Complex Numbers, Analytic Functions, Complex Integration, Series Expansions, Conformal Mappings |
| MA202 | Data Structures and Algorithms | Core | 4 | Arrays and Linked Lists, Stacks and Queues, Trees and Graphs, Sorting Algorithms, Searching Algorithms |
| CS201 | Discrete Mathematics | Core | 4 | Logic and Proofs, Set Theory, Relations and Functions, Graph Theory, Combinatorics |
| MA203 | Real Analysis | Core | 4 | Metric Spaces, Continuity and Differentiation, Riemann Integration, Sequence and Series of Functions, Lebesgue Measure |
| HS201 | Soft Skills and Professional Ethics | Core | 2 | Communication Skills, Teamwork and Leadership, Time Management, Ethical Dilemmas, Professionalism |
| MA204 | Data Structures and Algorithms Lab | Lab | 2 | Implementation of Data Structures, Algorithm Analysis, Problem Solving with DSA, Graph Algorithms, Sorting and Searching Practice |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA205 | Modern Algebra | Core | 4 | Groups, Rings, Fields, Vector Spaces, Galois Theory |
| MA206 | Numerical Methods | Core | 4 | Root Finding Methods, Interpolation, Numerical Differentiation, Numerical Integration, Numerical Solution of ODEs |
| CS202 | Operating Systems | Core | 4 | Process Management, Memory Management, File Systems, I/O Systems, Concurrency and Deadlocks |
| MA207 | Probability and Statistics | Core | 4 | Probability Theory, Random Variables, Probability Distributions, Hypothesis Testing, Regression Analysis |
| MA208 | Numerical Methods Lab | Lab | 2 | Implementation of Numerical Algorithms, Error Analysis, Scientific Computing, Data Visualization, Software Tools for Numerical Methods |
| HS202 | Human Values and Ethics | Core | 2 | Values and Self-Exploration, Harmony in the Family, Harmony in Society, Harmony in Nature, Professional Ethics |
Semester 5
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA301 | Partial Differential Equations | Core | 4 | First Order PDEs, Second Order PDEs, Wave Equation, Heat Equation, Laplace Equation |
| MA302 | Graph Theory | Core | 4 | Basic Graph Concepts, Trees, Connectivity, Euler and Hamiltonian Paths, Graph Coloring |
| CS301 | Database Management Systems | Core | 4 | Relational Model, SQL, Database Design, Transaction Management, Concurrency Control |
| MA303 | Optimization Techniques | Core | 4 | Linear Programming, Simplex Method, Duality Theory, Transportation Problem, Non-Linear Programming |
| OE-I | Open Elective-I | Elective | 3 | Selected topics from other disciplines as per student interest |
| CS302 | Database Management Systems Lab | Lab | 2 | SQL Queries, Database Creation, PL/SQL Programming, Normalization, Mini Project |
| HS301 | Constitution of India | Core | 1 | Preamble and Fundamental Rights, Directive Principles, Union and State Government, Judiciary, Emergency Provisions |
Semester 6
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA304 | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Bounded Linear Operators, Spectral Theory |
| MA305 | Differential Geometry | Core | 4 | Curves in Space, Surfaces, First and Second Fundamental Forms, Geodesics, Curvature |
| CS303 | Object Oriented Programming | Core | 4 | OOP Concepts, Classes and Objects, Inheritance, Polymorphism, Templates and Exceptions |
| PE-I | Professional Elective-I | Elective | 3 | Advanced topics in Mathematics or Computing |
| OE-II | Open Elective-II | Elective | 3 | Selected topics from other disciplines as per student interest |
| CS304 | Object Oriented Programming Lab | Lab | 2 | C++ Programming Practice, Object-Oriented Design, GUI Programming, Data Structures with OOP, Mini Project |
| MA306 | Seminar | Project | 2 | Technical Presentation Skills, Literature Survey, Report Writing, Subject Specific Research, Public Speaking |
Semester 7
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA401 | Topology | Core | 4 | Topological Spaces, Continuous Functions, Compactness, Connectedness, Separation Axioms |
| MA402 | Mathematical Modelling | Core | 4 | Introduction to Modelling, Differential Equation Models, Discrete Models, Optimization Models, Simulation |
| CS401 | Introduction to Data Science | Core | 4 | Data Preprocessing, Exploratory Data Analysis, Machine Learning Basics, Statistical Inference, Data Visualization |
| PE-II | Professional Elective-II | Elective | 3 | Specialized topics in Mathematics or Computing |
| OE-III | Open Elective-III | Elective | 3 | Selected topics from other disciplines as per student interest |
| MA403 | Project-I | Project | 3 | Problem Identification, Literature Review, Methodology Development, Implementation, Project Report Writing |
Semester 8
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA404 | Measure Theory and Integration | Core | 4 | Measure Spaces, Lebesgue Measure, Measurable Functions, Lebesgue Integration, Convergence Theorems |
| MA405 | Advanced Numerical Analysis | Core | 4 | Numerical Solution of PDEs, Finite Difference Methods, Finite Element Methods, Spectral Methods, Error Control |
| CS402 | Machine Learning | Core | 4 | Supervised Learning, Unsupervised Learning, Deep Learning Basics, Model Evaluation, Ensemble Methods |
| PE-III | Professional Elective-III | Elective | 3 | Specialized topics in Mathematics or Computing |
| OE-IV | Open Elective-IV | Elective | 3 | Selected topics from other disciplines as per student interest |
| MA406 | Industrial Internship | Core | 2 | Real-world Project Experience, Industry Best Practices, Professional Networking, Report Writing, Presentation Skills |
Semester 9
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA501 | Operations Research | Core | 4 | Network Flows, Queueing Theory, Inventory Control, Dynamic Programming, Game Theory |
| MA502 | Advanced Functional Analysis | Core | 4 | Fixed Point Theory, Compact Operators, Unbounded Operators, Banach Algebras, Distribution Theory |
| PE-IV | Professional Elective-IV | Elective | 3 | Advanced specialized topics in Mathematics or Computing |
| PE-V | Professional Elective-V | Elective | 3 | Advanced specialized topics in Mathematics or Computing |
| MA503 | Project-II | Project | 4 | Advanced Research, Methodology Refinement, Extensive Implementation, Thesis Writing, Defense Preparation |
Semester 10
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MA504 | Stochastic Processes | Core | 4 | Markov Chains, Poisson Processes, Random Walks, Brownian Motion, Applications in Finance |
| PE-VI | Professional Elective-VI | Elective | 3 | Highly specialized topics in Mathematics or Computing |
| PE-VII | Professional Elective-VII | Elective | 3 | Highly specialized topics in Mathematics or Computing |
| MA505 | Dissertation | Project | 7 | Independent Research, Advanced Problem Solving, Comprehensive Literature Review, Original Contribution, Thesis Defense |
