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INTEGRATED-B-SC-M-SC in Mathematics at University of Petroleum and Energy Studies

UPES, Dehradun is a premier UGC-recognized private university established in 2003. Known for its industry-aligned specialized programs across 9 schools, including Engineering, Management, and Law, it features a 44-acre campus. UPES boasts strong placements with a highest CTC of INR 50 LPA and is consistently ranked among India's top universities.

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location

Dehradun, Uttarakhand

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About the Specialization

What is Mathematics at University of Petroleum and Energy Studies Dehradun?

This Applied Mathematics program at UPES, Dehradun, focuses on developing strong foundational and advanced mathematical skills applicable across diverse fields. It integrates theoretical depth with practical problem-solving, aligning with India''''s growing demand for mathematically proficient professionals in data science, finance, and research. The program''''s interdisciplinary nature prepares graduates for complex real-world challenges.

Who Should Apply?

This program is ideal for students with a strong aptitude for mathematics, seeking a rigorous academic journey. Fresh graduates aiming for careers in analytics, scientific computing, or academia will find it beneficial. It also suits individuals looking to transition into quantitative roles or upskill in advanced mathematical techniques, provided they have a strong background in higher secondary mathematics.

Why Choose This Course?

Graduates of this program can expect diverse career paths in India, including Data Scientist, Financial Analyst, Actuary, Research Scientist, or Academician. Entry-level salaries typically range from INR 4-8 LPA, with experienced professionals earning significantly more. The strong mathematical foundation also supports higher studies (PhD) and certifications in quantitative finance or data analytics.

OTHER SPECIALIZATIONS

Student Success Practices

Foundation Stage

Master Core Mathematical Concepts- (Semester 1-2)

Focus intensely on understanding the fundamentals of Calculus, Algebra, and Vector Calculus. Regularly solve problems from textbooks and online platforms. Form study groups to discuss complex topics and clarify doubts, reinforcing foundational knowledge.

Tools & Resources

NPTEL lectures, NCERT textbooks, Khan Academy, BYJU''''S

Career Connection

A strong mathematical base is critical for mastering advanced topics and crucial for quantitative problem-solving roles in technology, finance, and research.

Develop Foundational Programming Skills- (Semester 1-2)

Gain proficiency in C programming and data structures. Actively participate in coding challenges on platforms like HackerRank and CodeChef. Understand how algorithms are implemented and optimized to build a strong computational thinking base.

Tools & Resources

GeeksforGeeks, LeetCode (easy problems), CodeChef, C programming tutorials

Career Connection

Essential for careers in data science, quantitative finance, and software development, enabling practical application of mathematical models and algorithms.

Enhance Communication and Environmental Awareness- (Semester 1-2)

Actively participate in English Communication and Environmental Science classes. Practice academic writing, presentation skills, and engage in discussions about sustainable development. This builds holistic professional skills alongside technical expertise.

Tools & Resources

Toastmasters International (if available), UPES Communication Lab, UN Environment Programme resources

Career Connection

Strong communication is vital for presenting complex mathematical findings, and environmental awareness broadens perspective for diverse roles in today''''s responsible industries.

Intermediate Stage

Apply Numerical and Statistical Methods- (Semester 3-5)

Deepen understanding of Numerical Methods, Probability & Statistics, and Applied Statistical Methods. Work on projects involving data analysis using statistical software or Python. Explore real-world datasets from platforms like Kaggle for hands-on practice.

Tools & Resources

Python (NumPy, SciPy, Pandas, Matplotlib), R, SPSS tutorials, Kaggle datasets

Career Connection

Directly applicable to roles in data analytics, market research, risk management, and scientific research, enhancing employability in data-driven industries.

Engage with Object-Oriented Programming and Machine Learning- (Semester 3-5)

Master OOP concepts in Python and build foundational knowledge in Machine Learning. Implement basic ML algorithms from scratch and use libraries like Scikit-learn. Seek opportunities for mini-projects to apply theoretical knowledge.

Tools & Resources

Python (Scikit-learn, TensorFlow/PyTorch basics), Andrew Ng''''s ML course (Coursera), Google AI Education resources

Career Connection

Opens doors to highly sought-after roles in AI/ML engineering, data science, and advanced analytics in technology firms, addressing modern industry demands.

Explore Specialization Electives and Internships- (Semester 4-5 (especially summer after Sem 4))

Choose electives wisely based on career interests (e.g., Linear Programming, Financial Mathematics). Actively seek summer internships in relevant fields (finance, analytics, research) to gain practical industry exposure and network with professionals.

Tools & Resources

LinkedIn, Internshala, Company career portals, UPES Career Services

Career Connection

Internships provide invaluable experience, build professional networks, and often lead to pre-placement offers, accelerating career entry and professional growth.

Advanced Stage

Undertake Advanced Research Projects- (Semester 6-10)

Dedicate significant effort to Project-I (B.Sc. level), Project-II (M.Sc. level), and the final Dissertation. Choose challenging topics, conduct thorough literature reviews, and aim for high-quality research output demonstrating analytical prowess.

Tools & Resources

Research journals (e.g., IEEE Xplore, arXiv), Academic databases (Scopus, Web of Science), LaTeX for scientific writing

Career Connection

Demonstrates advanced research capabilities, essential for academia, R&D roles, and significantly enhances a strong CV for higher studies or industry positions.

Master Advanced Mathematical and Computational Tools- (Semester 7-9)

Deepen expertise in areas like Functional Analysis, Topology, PDE, and numerical methods. Gain hands-on experience with specialized software like MATLAB/Mathematica for scientific computing, essential for complex problem-solving.

Tools & Resources

Official software documentation, Advanced textbooks, Specialized online courses (e.g., edX, Coursera for advanced math)

Career Connection

Prepares for roles requiring high-level mathematical modeling, simulation, and algorithm development in scientific, engineering, and financial domains, fostering specialized expertise.

Prepare for Placements and Higher Education- (Semester 9-10)

Actively participate in campus recruitment drives. Prepare for technical interviews focusing on core mathematics, programming, and specialized electives. For higher studies, prepare for GRE/GATE and focus on developing strong research proposals.

Tools & Resources

Placement cell resources, Mock interviews, Quantitative aptitude books, Career counseling, University websites for PhD programs

Career Connection

Maximizes chances of securing desirable placements in top companies or gaining admission to prestigious national/international universities for further advanced studies and research.

Program Structure and Curriculum

Eligibility:

  • Minimum 50% marks in Class X and XII with Mathematics as a compulsory subject.

Duration: 5 years (10 semesters)

Credits: 200 Credits

Assessment: Assessment pattern not specified

Semester-wise Curriculum Table

Semester 1

Subject CodeSubject NameSubject TypeCreditsKey Topics
Calculus - ICore Course4Functions, Limits, Continuity, Differentiability, Mean Value Theorems, Applications of Derivatives, Maxima and Minima, Indeterminate Forms
Algebra - ICore Course4Set Theory, Relations, Functions, Principle of Mathematical Induction, Permutations and Combinations, Matrices and Determinants, System of Linear Equations
Programming in CCore Course4C Language Fundamentals, Data Types, Operators, Control Statements (if-else, loops), Functions, Pointers, Arrays, Strings, Structures, Unions, File Handling
English CommunicationAbility Enhancement Compulsory Course3Basic English Grammar and Usage, Paragraph and Essay Writing, Presentation Skills, Public Speaking, Reading Comprehension and Vocabulary, Group Discussions and Interviews
Environmental ScienceSkill Enhancement Course3Natural Resources and Ecosystems, Biodiversity and Conservation, Environmental Pollution and Control, Climate Change and Global Warming, Sustainable Development
Yoga and MeditationAbility Enhancement Compulsory Course2Introduction to Yoga and its Philosophy, Basic Asanas and Pranayama Techniques, Meditation and Relaxation Methods, Stress Management through Yoga, Yogic Lifestyle and Diet

Semester 2

Subject CodeSubject NameSubject TypeCreditsKey Topics
Calculus - IICore Course4Definite and Indefinite Integrals, Applications of Integration (Area, Volume), Sequences and Series, Convergence Tests, Power Series, Taylor and Maclaurin Series, Multivariable Calculus (Partial Derivatives)
Algebra - IICore Course4Vector Spaces, Subspaces, Linear Transformations and their Properties, Eigenvalues, Eigenvectors, Diagonalization, Inner Product Spaces, Orthogonality, Quadratic Forms
Data Structures using CCore Course4Arrays, Linked Lists (Singly, Doubly, Circular), Stacks and Queues, Trees (Binary, BST, AVL), Graphs (Traversal, Shortest Path), Sorting and Searching Algorithms
Vector CalculusCore Course4Vector Algebra and Vector Functions, Vector Differentiation (Gradient, Divergence, Curl), Line Integrals, Surface Integrals, Volume Integrals, Green''''s Theorem, Stokes'''' Theorem, Gauss Divergence Theorem
Academic Writing and Research SkillsSkill Enhancement Course4Research Methodology and Problem Formulation, Literature Review Techniques, Academic Honesty, Plagiarism, Referencing, Report Writing and Dissertation Structure, Effective Presentation of Research

Semester 3

Subject CodeSubject NameSubject TypeCreditsKey Topics
Differential EquationsCore Course4First Order Ordinary Differential Equations, Higher Order Linear ODEs, Laplace Transforms and Applications, Series Solutions of ODEs, Introduction to Partial Differential Equations
Numerical MethodsCore Course4Errors in Numerical Calculations, Solutions of Algebraic and Transcendental Equations, Interpolation Techniques, Numerical Differentiation and Integration, Numerical Solutions of ODEs
Object-Oriented Programming using PythonCore Course4Python Fundamentals, Data Types, Control Flow, Introduction to OOP, Classes and Objects, Inheritance, Polymorphism, Encapsulation, File Handling in Python, Exception Handling
Probability and StatisticsCore Course4Probability Theory, Conditional Probability, Random Variables and Probability Distributions, Expectation, Variance, Moments, Sampling Distributions, Central Limit Theorem, Introduction to Hypothesis Testing
Data VisualizationSkill Enhancement Course4Principles of Data Visualization, Types of Charts and Graphs, Data Storytelling and Design Principles, Introduction to Data Visualization Tools (e.g., Matplotlib, Seaborn), Creating Interactive Dashboards

Semester 4

Subject CodeSubject NameSubject TypeCreditsKey Topics
Real AnalysisCore Course4Real Number System, Axioms, Order Properties, Sequences and Series of Real Numbers, Continuity and Uniform Continuity, Differentiability of Functions, Riemann Integral
Discrete MathematicsCore Course4Mathematical Logic, Propositional and Predicate Logic, Set Theory and Relations, Functions, Pigeonhole Principle, Graph Theory (Paths, Cycles, Trees), Combinatorics (Counting, Recurrence Relations)
Theory of ComputationCore Course4Finite Automata (DFA, NFA), Regular Expressions and Regular Languages, Context-Free Grammars and Pushdown Automata, Turing Machines and Computability, Undecidability
Applied Statistical MethodsDiscipline Specific Elective Course4Analysis of Variance (ANOVA), Chi-Square Tests for Association, Correlation and Regression Analysis, Non-parametric Methods, Time Series Analysis Introduction
Introduction to Machine LearningSkill Enhancement Course4Supervised Learning (Regression, Classification), Unsupervised Learning (Clustering), Model Evaluation Metrics, Introduction to Neural Networks, Bias-Variance Tradeoff

Semester 5

Subject CodeSubject NameSubject TypeCreditsKey Topics
Complex AnalysisCore Course4Complex Numbers and Functions, Analytic Functions, Cauchy-Riemann Equations, Complex Integration, Cauchy''''s Integral Theorem, Laurent Series, Singularities, Residue Theorem, Conformal Mappings
Linear ProgrammingDiscipline Specific Elective Course4Linear Programming Problem Formulation, Graphical Method, Simplex Method, Duality in Linear Programming, Transportation Problem, Assignment Problem
Database Management SystemsDiscipline Specific Elective Course4Introduction to DBMS, Data Models, Relational Model, SQL (Queries, Joins), Entity-Relationship (ER) Modeling, Normalization (1NF, 2NF, 3NF, BCNF), Transaction Management, Concurrency Control
Numerical OptimizationDiscipline Specific Elective Course4Introduction to Optimization Techniques, Unconstrained Optimization (Gradient Descent), Constrained Optimization, Lagrange Multipliers, Convex Optimization Basics
Advanced Programming in PythonSkill Enhancement Course4Advanced OOP Concepts and Design Patterns, Web Scraping with Beautiful Soup/Scrapy, Data Manipulation with Pandas, Scientific Computing with NumPy and SciPy, API Integration and Development

Semester 6

Subject CodeSubject NameSubject TypeCreditsKey Topics
Functional AnalysisCore Course4Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Orthonormal Bases, Linear Operators and Functionals, Hahn-Banach Theorem, Spectral Theory Basics
TopologyCore Course4Topological Spaces, Open and Closed Sets, Continuous Functions, Homeomorphisms, Connectedness and Compactness, Product Topology, Quotient Topology, Separation Axioms
Financial MathematicsDiscipline Specific Elective Course4Interest Rates and Present Value Analysis, Annuities, Loans, Bonds, Derivatives (Forwards, Futures, Options), Black-Scholes Model for Option Pricing, Risk Management Concepts
Statistical Software (R/SAS/SPSS)Skill Enhancement Course4Introduction to R/SAS/SPSS Environment, Data Import, Cleaning, and Manipulation, Descriptive Statistics and Exploratory Data Analysis, Hypothesis Testing and Regression Analysis, Creating Statistical Graphics
Project - I (B.Sc. Level)Project/Dissertation4Project Proposal and Planning, Literature Review and Problem Definition, Methodology Design and Data Collection, Preliminary Data Analysis and Interpretation, Report Writing and Presentation

Semester 7

Subject CodeSubject NameSubject TypeCreditsKey Topics
Advanced Abstract AlgebraCore Course4Group Theory (Sylow Theorems, Solvable Groups), Ring Theory (Ideals, Factor Rings, Polynomial Rings), Field Extensions, Galois Theory, Modules and Vector Spaces over Fields, Advanced topics in Group Homomorphisms
Measure Theory and IntegrationCore Course4Lebesgue Measure on Real Line, Measurable Functions, Lebesgue Integral and its Properties, Convergence Theorems (MCT, DCT), Lp Spaces
Partial Differential EquationsCore Course4First Order Linear and Non-linear PDEs, Classification of Second Order PDEs, Wave Equation, Heat Equation, Laplace Equation, Method of Separation of Variables
Operation ResearchDiscipline Specific Elective Course4Queuing Theory Models, Inventory Control Models, Dynamic Programming, Game Theory (Two-person zero-sum games), Simulation Techniques
Mathematical ModellingDiscipline Specific Elective Course4Introduction to Mathematical Models, Deterministic Models (Growth, Decay), Stochastic Models (Random Walks), Modelling with Differential Equations, Applications in Science and Engineering

Semester 8

Subject CodeSubject NameSubject TypeCreditsKey Topics
Advanced Real AnalysisCore Course4Riemann-Stieltjes Integral, Functions of Several Variables, Implicit Function Theorem, Inverse Function Theorem, Lebesgue Measure and Integration (Review), Fourier Series and Transforms
Fluid DynamicsDiscipline Specific Elective Course4Kinematics of Fluid Flow, Euler''''s and Navier-Stokes Equations, Inviscid Flow, Potential Flow, Viscous Flow, Boundary Layer Theory, Dimensional Analysis and Similarity
Tensor AnalysisDiscipline Specific Elective Course4Cartesian Tensors, General Tensors, Tensor Algebra (Addition, Multiplication, Contraction), Covariant and Contravariant Tensors, Riemannian Geometry Basics, Applications in Mechanics and Relativity
Bio-StatisticsDiscipline Specific Elective Course4Experimental Design in Biology, Clinical Trials and Meta-Analysis, Survival Analysis, Epidemiological Studies, Statistical Genetics and Bioinformatics
Image Processing and Computer VisionSkill Enhancement Course4Image Filtering and Enhancement, Edge Detection and Segmentation, Feature Extraction (SIFT, HOG), Object Recognition and Tracking, Introduction to Deep Learning for Vision

Semester 9

Subject CodeSubject NameSubject TypeCreditsKey Topics
Advanced Numerical AnalysisCore Course4Numerical Solutions of Partial Differential Equations, Finite Difference Methods, Finite Element Methods, Spectral Methods, Error Analysis for Numerical Schemes
CryptologyDiscipline Specific Elective Course4Classical Ciphers, Number Theory in Cryptography, Symmetric Key Cryptography (AES, DES), Asymmetric Key Cryptography (RSA, ECC), Hashing Functions and Digital Signatures, Key Exchange and Management
Fuzzy MathematicsDiscipline Specific Elective Course4Fuzzy Sets and Membership Functions, Fuzzy Logic and Fuzzy Relations, Fuzzy Arithmetic, Fuzzy Numbers, Fuzzy Control Systems, Applications of Fuzzy Sets in Decision Making
Scientific Computing with MATLAB/MathematicaSkill Enhancement Course4MATLAB/Mathematica Environment and Programming, Numerical Solvers for Differential Equations, Symbolic Computing and Algebra, Data Visualization and Plotting, Algorithm Implementation and Optimization
Project - II (M.Sc. Level)Project/Dissertation4Advanced Research Methodology, In-depth Literature Review and Problem Refinement, Development of Novel Solutions or Models, Extensive Data Analysis and Validation, Scientific Report Writing and Oral Presentation

Semester 10

Subject CodeSubject NameSubject TypeCreditsKey Topics
Mathematical BiologyDiscipline Specific Elective Course4Population Dynamics (Logistic, Predator-Prey Models), Epidemiology Models (SIR, SIS), Mathematical Ecology and Biomechanics, Neuroscience Models, Applications in Genomics and Proteomics
Stochastic ProcessesDiscipline Specific Elective Course4Markov Chains and Markov Processes, Poisson Processes, Random Walks, Brownian Motion, Stochastic Differential Equations, Ito Calculus, Applications in Finance and Queuing Theory
Computational Fluid DynamicsDiscipline Specific Elective Course4Discretization Methods (Finite Difference, Finite Volume), Grid Generation Techniques, Numerical Schemes for Fluid Flow Equations, Turbulence Modeling, Software for CFD (e.g., ANSYS Fluent basics)
Research Methodology and IPRAbility Enhancement Compulsory Course4Research Design and Ethics, Data Collection and Analysis Techniques, Scientific Communication and Publication, Intellectual Property Rights (Patents, Copyrights), Research Proposal Writing
Dissertation / ThesisProject/Dissertation4Independent Advanced Research, Comprehensive Literature Review, Methodology Development and Execution, Data Interpretation and Critical Analysis, Thesis Writing and Oral Defense
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