Project No.- 1
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Tittle : Art of
Stereographic projection.Mentor : Dr. Preeti Dharmaraha
Duration : 6 months
Beginning Date : 1st
February 2016
End Date : 31st July
2016.
Outline:
In geometry, the stereographic
projection is a particular mapping (function) that projects a sphere onto a
plane. The stereographic projection is a way of picturing the sphere as the
plane, with some inevitable compromises. Because the sphere and the plane
appear in many areas of mathematics and its applications, so does the
stereographic projection; it finds use in diverse fields including complex
analysis, cartography, geology, and photography.
Student is expected to understand the definition and explore its properties, Wulffnet, applications within and outside mathematics.
Instructions:
Maximum no. of students: 4 (Only for B.Sc(H)
Mathematics 1st and 2nd Year).
Students need to submit their application on A4 paper-sheet with Name, Semester, email, phone number to the respective mentor.
Students will be required to
submit a dissertation at the end and will be examined by an external examiner
on the basis of a viva examination.
On completion, certificate will be awarded to
the students.
Project No.- 2
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Tittle : Scope and Application of Prime Numbers.Mentor : Mr. Brij Mohan
Duration : 6 months
Beginning Date : 1st February 2016
End Date : 31st July 2016.
Outline:
Prime numbers, not only play a significant role in Number Theory but also have an importance in many other fields such as Information Technology, Cryptography, Security Systems, Database Management etc. Many problems such as Goldbach's Conjecture, Twin prime conjecture are remain open, which shows that scope of prime numbers is wide to understand the problems and solve them.
Factorization of large composite numbers into prime numbers, in less time than before is still challenging in current technology world. Different properties of prime numbers are to be used to understand and solve difficult problems.
Student is expected to understand the properties and scope of prime numbers and find out different applications and areas where the prime numbers are to be used.
Instructions:
Maximum no. of students: 4 (Only for B.Sc(H) Mathematics 1st Year).
Students need to submit their application on A4 paper-sheet with Name, Semester, email, phone number to the respective mentor.
Students will be required to submit a dissertation at the end and will be examined by an external examiner on the basis of a viva examination.
On completion, certificate will be awarded to the students.
Mentor : Dr. Mukund Madhav Mishra
Project No.- 3
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Tittle : Change of Variables in Integration and Differential FormsMentor : Dr. Mukund Madhav Mishra
Duration : 6 months
Beginning Date : 1st February 2016
End Date : 31st July 2016.
Outline:
Calculus students in their school are told that when we write dy/dx, we are not writing a ratio of two quantities dy and dx but it is just a notation. At the same time, (dy/dx)=f(x) is rewritten as dy=f(x) dx, something which you would like to do when an actual ratio is given. Is this some kind of paradox Mathematics is surviving it? The answer lies in the study of differential forms.
The project will start with a very simple example of a change of variables formula. Slowly we will see that changing the variables in integration is not that straightforward a job. Certain situation will then suggest how and why to introduce differential forms.
Students will be expected to learn this entire philosophy and come up with concrete examples of applications of the differential forms.
Instructions:
Maximum no. of students: 4 (Only for B.Sc(H) Mathematics 1st and 2nd Year).
Students need to submit their application on A4 paper-sheet with Name, Semester, email, phone number to the respective mentor.
Students will be required to submit a dissertation at the end and will be examined by an external examiner on the basis of a viva examination.
On completion, certificate will be awarded to the students.
Project No.- 4
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Tittle : Study and Analysis of Numerical Methods for Solving Differential Equations.
Mentor : Dr. Arvind
Mentor : Dr. Arvind
Duration : 6 months
Beginning Date : 1st February 2016
End Date : 31st July 2016.
Outline:
In this project, different methods for solving differential equations will be studied and main emphasis is on their comparative analysis.
All methods will be implemented in Matlab or Mathematica.
All methods will be implemented in Matlab or Mathematica.
Instructions:
Maximum no. of students: 4 (Only for B.Sc(H) Mathematics 1st, 2nd and 3rd Year).
Students need to submit their application on A4 paper-sheet with Name, Semester, email, phone number to the respective mentor.
Students will be required to submit a dissertation at the end and will be examined by an external examiner on the basis of a viva examination.
On completion, certificate will be awarded to the students.
