M.Sc. Mathematics - Pure Mathematics

Details

M.Sc. Mathematics is a 2-year postgraduate program. The objective of this program is to cultivate a mathematical aptitude and nurture the interests of students towards problem-solving. Further, it aims at motivating students for research in pure and applied mathematics.

Pure Mathematics includes developing the fundamental tools used by mathematicians such as Algebra and Calculus, describing multi-dimensional space, or a better understanding of the philosophical meaning of Mathematics and numbers themselves. Pure Mathematics is the study of the basic concepts and structures that underlie Mathematics. Its purpose is to search for a deeper understanding and an expanded knowledge of Mathematics itself.

Applied Mathematics focuses on the innovative creation and imaginative use of mathematical concepts to present and solve problems in the various field of Natural Sciences, Engineering Sciences, Medical Sciences, and emerging fields such as Data Sciences and Artificial Intelligence. The program is designed to provide students with an increased knowledge and a comprehensive understanding of Mathematics, particularly in Algorithms, Fluid Mechanics, Differential Equations, Probability and Stochastics, and Optimisation.

Duration

Duration

2 Years (4 semesters)

DESIGN YOUR OWN DEGREE


upes

UPES’ curriculum framework is holistic in its overall structure and yet focuses on the individual need of the student to discover, experience, explore and challenge. Along with the core subject, students have the option to choose from subject-focused specialisations. They are also allowed to choose minor/exploratory subject from other schools at UPES that are: School of Engineering, School of Computer Science, School of Law, School of Business, School of Health Sciences, School of Design, School of Modern Media, and School of Liberal Studies.

Further, based on the multifaceted needs of the global workplace and evolving lifestyles, the curriculum offers Signature and Life-Skills courses through School for Life. To round off this learning experience, students are required to do mandatory internships in the social sector, government/public sector, and industry. The combinations available for students to pick and choose from are endless, ensuring both depth and width of knowledge.

Details
PEO-1: To train students to appreciate theoretical, conceptual, and computational knowledge of mathematics to model and solve multiple challenging problems in a diversified interdisciplinary and multidisciplinary environment.
PEO-2: To provide knowledge of the highest standards in Mathematics so that the students can utilise significant opportunities in various service sectors, and can work as Scientists, Data Analysts, and Faculty in academic and research organisations.
PEO-3: To engage students in independent and lifelong learning and guide them to consistently explore, learn, and adapt new skills that will help them in enhancing their knowledge and professional growth.
PEO-4: To encourage students to be committed towards ethical practices and the development of society.
PSO-1: Understand the advanced mathematical concepts and applications in the field of Algebra, Analysis, Computational Techniques, Optimisation, Differential Equations and Engineering.
PSO-2: Demonstrate advanced understanding of techniques in algebra, analysis, computational techniques, optimisation, differential equations, and engineering to analyse and design algorithms solving a variety of problems related to real-life problems.
PSO-3: Execute new ideas in research and developments in mathematics through seminar and dissertations.
  • Scientific Officer
  • General Management
  • Manual Testing
  • Data Science Modelers
  • Investment Banking
  • Statistical Research
  • Junior Research Fellow

M.Sc. Mathematics Specialisation in Pure Mathematics

Curriculum (2023 – 2025)

 

SEMESTER I

 

Category Course Credits
M Real Analysis 4
M Abstract Algebra 4
M Linear Algebra 4
M Theory of Ordinary Differential Equations 4
M Mathematical Statistics 4
M Integral Equations and Calculus of Variations 4
  Total 24

 

SEMESTER II

 

Category Course Credits
M Complex Analysis 5
M Topology 4
M Theory of Partial Differential Equations 4
M Computational Mathematics 3
M Computational Mathematics Lab 2
M Specialisation Course I (Pure Mathematics/Applied Mathematics) 4
  Total 22

 

SEMESTER III

 

Category Course Credits
M Operations Research 5
M Functional Analysis 5
M Mechanics 4
M Specialisation Course II (Pure Mathematics/Applied Mathematics) 4
M Research Methodology & Ethics 3
M Dissertation I 4
  Total 25

 

SEMESTER IV

 

Category Course Credits
M Specialisation Course III (Pure Mathematics/Applied Mathematics) 4
M Dissertation II 10
  Total 14

 

SPECIALISATION

 

Differential Geometry
Measure and Integration
Multivariate Analysis
Number Theory
Commutative Algebra
Theory of Operators
Representation of Finite Group
Approximation Theory
Algebraic Topology

We, at the department, believe in experiential teaching and learning and strive to imbibe problem-solving skills and critical thinking in 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 and monitoring
  • Real-world/Project-based assignments
  • Quality laboratory experience
  • Encouraging advanced learner
  • Slow learners support
  • ICT-enabled classroom (sound system, mic and projector)
  • Guest lectures from industry experts
  • Industry-led courses
  • Certification courses
  • Professional Software Training (PST) and Certification
  • NPTEL lectures
  • Prototype development
  • Use of virtual labs
  • Participation in competitive events (in-house/national/international)

Participation in conferences/seminars/workshops (national/international)

Minimum 50% in Class X and XII (PCM/B) and 50% in graduation in relevant subject

Personal Interview

Details

PROGRAM EDUCATIONAL OBJECTIVES (PEOs)
PEO-1: To train students to appreciate theoretical, conceptual, and computational knowledge of mathematics to model and solve multiple challenging problems in a diversified interdisciplinary and multidisciplinary environment.
PEO-2: To provide knowledge of the highest standards in Mathematics so that the students can utilise significant opportunities in various service sectors, and can work as Scientists, Data Analysts, and Faculty in academic and research organisations.
PEO-3: To engage students in independent and lifelong learning and guide them to consistently explore, learn, and adapt new skills that will help them in enhancing their knowledge and professional growth.
PEO-4: To encourage students to be committed towards ethical practices and the development of society.
PROGRAM-SPECIFIC OUTCOMES (PSOs)
PSO-1: Understand the advanced mathematical concepts and applications in the field of Algebra, Analysis, Computational Techniques, Optimisation, Differential Equations and Engineering.
PSO-2: Demonstrate advanced understanding of techniques in algebra, analysis, computational techniques, optimisation, differential equations, and engineering to analyse and design algorithms solving a variety of problems related to real-life problems.
PSO-3: Execute new ideas in research and developments in mathematics through seminar and dissertations.
CAREER PROSPECTS
  • Scientific Officer
  • General Management
  • Manual Testing
  • Data Science Modelers
  • Investment Banking
  • Statistical Research
  • Junior Research Fellow
CURRICULUM

M.Sc. Mathematics Specialisation in Pure Mathematics

Curriculum (2023 – 2025)

 

SEMESTER I

 

Category Course Credits
M Real Analysis 4
M Abstract Algebra 4
M Linear Algebra 4
M Theory of Ordinary Differential Equations 4
M Mathematical Statistics 4
M Integral Equations and Calculus of Variations 4
  Total 24

 

SEMESTER II

 

Category Course Credits
M Complex Analysis 5
M Topology 4
M Theory of Partial Differential Equations 4
M Computational Mathematics 3
M Computational Mathematics Lab 2
M Specialisation Course I (Pure Mathematics/Applied Mathematics) 4
  Total 22

 

SEMESTER III

 

Category Course Credits
M Operations Research 5
M Functional Analysis 5
M Mechanics 4
M Specialisation Course II (Pure Mathematics/Applied Mathematics) 4
M Research Methodology & Ethics 3
M Dissertation I 4
  Total 25

 

SEMESTER IV

 

Category Course Credits
M Specialisation Course III (Pure Mathematics/Applied Mathematics) 4
M Dissertation II 10
  Total 14

 

SPECIALISATION

 

Differential Geometry
Measure and Integration
Multivariate Analysis
Number Theory
Commutative Algebra
Theory of Operators
Representation of Finite Group
Approximation Theory
Algebraic Topology
INNOVATIVE TEACHING AND LEARNING

We, at the department, believe in experiential teaching and learning and strive to imbibe problem-solving skills and critical thinking in 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 and monitoring
  • Real-world/Project-based assignments
  • Quality laboratory experience
  • Encouraging advanced learner
  • Slow learners support
  • ICT-enabled classroom (sound system, mic and projector)
  • Guest lectures from industry experts
  • Industry-led courses
  • Certification courses
  • Professional Software Training (PST) and Certification
  • NPTEL lectures
  • Prototype development
  • Use of virtual labs
  • Participation in competitive events (in-house/national/international)

Participation in conferences/seminars/workshops (national/international)

Eligibility

Minimum 50% in Class X and XII (PCM/B) and 50% in graduation in relevant subject

Selection Criteria

Personal Interview

Enquiry Form