Duration of Program



UPES provides unique and focused Integrated M.Sc-PhD course aiming to deliver expertise in theoretical and experimental understanding of Mathematics and its allied disciplines. The program is designed such that after completing it, students would be able to excel in academia, industries, and research. The faculty members in the department have diverse research expertise including but not limited to Reliability analysis and optimization, numerical analysis, fluid dynamics, differential geometry, image processing and data analysis, dynamical system and mathematical modelling, etc., which would provide students flexibility in opting for their PhD topic. The curriculum is designed to give exposure not only about the subject but also research ethics, communication and skill augmentation. The completion of the course ensures deep knowledge with wide exposure, intellectual development, and ethical awareness that make students ready for various professional research, industrial and academic opportunities.  

Academic Framework

The foundation of higher learning at UPES since its inception has been to explore and promote areas of learning that are innovative and future focused. This has led to constant evolution in facilitating creative and collaborative learning engagements for students through realignment of curriculum and exploration of virtual tools, and open-source courseware; thereby creating borderless learning and access to limitless information.

The new curriculum framework at UPES, ABLE (Academic Blueprint for Learning Excellence) is holistic in its overall structure and yet focuses on the individual need of the student to discover, experience, explore and challenge. The learning is segmented into core subject studies, core specialism studies, minors/exploratory subjects, and signature and life skills learning. The latter three are offered by the newly-instituted School for Life.

SFL (School for Life) is an intrinsic part of the composite UPES student experience and facilitates learning and education that is a balance between what students want, and what is needed of them as future global citizens and leaders of tomorrow. With courses designed to equip students with lifelong learning skills, a focus on a wide range of contemporary issues, and a mandatory social and professional internship experience that is unique, UPES believes in igniting to inspire the best version within an individual to better the world.

PEO-1: Students will have significant opportunities in various service domains at national and international level, and can work as scientist, analyst, quality controller in academic and research organizations. 

PEO-2: Students will have leadership quality to handle all kind of circumstances in diversities by providing interdisciplinary and multidisciplinary learning environment. 

PEO-3: Students will be continuous learner to learn and adopt new skills and techniques to overcome the problem related with new technologies. 

PEO4: Students will be able to formulate, investigate and analyze scientifically real life problems along with ethical attitude, which works in multidisciplinary team. 

PSO-1:Understand the advanced mathematical concepts and applications in the field of algebra, analysis, computational techniques, optimization, differential equations and engineering. 

PSO-2:Demonstrate advanced understanding of techniques in algebra, analysis, computational techniques, optimization, differential equations, and engineering to analyze and design algorithms solving variety of problems related to real life problems. 

PSO-3:Execute new ideas in research and developments in mathematics through seminar and dissertation. 

  • Faculty members in Universities/Degree Colleges/Research Institutes 
  • Scientist in National Labs like CSIR, DRDO, ISRO and similar labs in Foreign institutions 
  • Quantitative/Financial Analyst in Financial institutions 
  • Post-doctoral researchers 
  • Fill Application Form
  • Screening of Application
  • Short listed student gets an invite for Personal Interview
Semester I

  Category Subject Code Subject Credits
1 Core Course    Real Analysis 4
2 Core Course    Abstract Algebra 4
3 Core Course    Linear Algebra 4
4 Core Course    Theory of Ordinary Differential Equations 4
5 Core Course    Mathematical Statistics 4
6 Core Course    Integral Equations and Calculus of Variations 4
      Total 24


Semester II

  Category Subject Code Subject Credits
1 Core Course    Complex Analysis 4
2 Core Course    Topology 4
3 Core Course    Theory of Partial Differential Equations 4
4 Core Course    Computational Mathematics 3
5 Core Course    Computational Mathematics Lab 1
6 Program Elective    Program Elective I  4
7 Program Elective    Program Elective II 4
      Total 24


Semester III

  Category Subject Code Subject Credits
1 Core Course    Operations Research 4
2 Core Course    Functional Analysis 5
3 Program Elective    Program Elective III 4
4 Program Elective    Program Elective IV 4
5 Program Elective    Program Elective V 4
6 Pre PhD Course    Research and Publication Ethics  2
7 Pre PhD Course    Research Methodology 4
      Total 27


Semester IV

  Category Subject Code Subject Credits
1 Pre PhD Course    Research Specific course-I 3
2 Pre PhD Course    Research Specific course-II 3
3 Pre PhD Course    Research Specific course-III 3
4 Pre PhD Course    Research Specific course-IV 3
5 Pre PhD Course    Literature survey 3
      Total 15


Program Electives

 Pure Mathematics  Applied Mathematics
Differential Geometry Number Theory and Cryptography
Algebraic Topology Stochastic Process
Measure and Integration Formal Languages and Theory of Computation
Commutative Algebra Time Series and Forecasting Methods
Multivariate Analysis Control Theory
Theory of Operators Non-linear Programming
Representation of Finite Group Fluid Mechanics
Approximation Theory Wavelet Theory
Number Theory Financial Mathematics


We at the department believe in experiential teaching and learning and strive to imbibe problem solving skills and critical thinking in the students. The following practices are in place to improve the quality of Teaching-Learning and student experience: 

  • Design and Review of individual Course Plans at the beginning of session 
  • Course Completion Report (CCR) 
  • Academic Planning & Monitoring 
  • Quality Laboratory Experience 
  • Encouraging Advanced Learner 
  • Slow Learners Support 
  • ICT enabled Classroom (sound system, mic and projector) 
  • Guest lectures  
  • Certification Courses  
  • Professional Software Training (PST) and Certification 
  • NPTEL lectures 
  • Use of Virtual labs 
  • Participation in competitive events (In-house/National/International). 
  • Participation in Conferences/Seminars/Workshops (National/International). 
  • Semester Exchange Program. 
  • FDP 


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