M.Sc (Mathematics) - Pure Mathematics

DETAILS

M.Sc Mathematics with specialization in 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. 

The full term of two years and the syllabus for the Pure mathematics program is divided into four semesters. This Master’s program in Pure mathematics is also an ideal preparation for various PhD programs in basic sciences and engineering.  

 

Duration

Duration of Program

2 years (4 Semesters)

Seats

Seats

5*

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.

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. 

⦁ Lecturer,
⦁ Assistant professor,
⦁ Mathematician,
⦁ Software developer,
⦁ Data analyst, 
⦁ Business analyst,
⦁ Risk and finance management,
⦁ Weather derivative and insurance,
⦁ Mathematical modeller,
⦁ Quantitative developer,
⦁ Statistical officer, 
⦁ Statistician,
⦁ Researcher and accountant and demographer

  • Fill Application Form
  • Screening of Application
  • Short listed student gets an invite for Personal Interview

50% in 10th and 12th (PCM/B) and 50% in graduation in relevant subject

SEMESTER I

 

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

 

  

SEMESTER II

 

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

 

  

SEMESTER III

 

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

 

  

SEMESTER IV

Category Subject Code Subject Credits
Dissertation   Dissertation 10
    Total 10

 

 

Program Electives

 

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

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 

Program Educational Objectives (PEOs)

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. 

Program Specific Outcomes (PSOs)

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. 

Career Prospects

⦁ Lecturer,
⦁ Assistant professor,
⦁ Mathematician,
⦁ Software developer,
⦁ Data analyst, 
⦁ Business analyst,
⦁ Risk and finance management,
⦁ Weather derivative and insurance,
⦁ Mathematical modeller,
⦁ Quantitative developer,
⦁ Statistical officer, 
⦁ Statistician,
⦁ Researcher and accountant and demographer

Admission Criteria
  • Fill Application Form
  • Screening of Application
  • Short listed student gets an invite for Personal Interview
Eligibility

50% in 10th and 12th (PCM/B) and 50% in graduation in relevant subject

Curriculum

SEMESTER I

 

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

 

  

SEMESTER II

 

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

 

  

SEMESTER III

 

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

 

  

SEMESTER IV

Category Subject Code Subject Credits
Dissertation   Dissertation 10
    Total 10

 

 

Program Electives

 

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