This Program will provide training to students having Mathematics as honors. Students with little exposure to mathematics are the target audience for this curriculum. This program is organised by P.G. Department of Mathematics, Bhadrak Auto. College, Bhadrak, Odisha.
In this training program, we will cover four core subjects in mathematics i.e. Group theory, Real analysis, Linear algebra, Metric space, and Topology. Each subject will be covered in six classes.
Class schedule: Two classes per day each of one hour and thirty minutes. This includes both theory and problem sessions.
Timing: 8 AM to 9.30 AM and 10 AM to 11.30 AM. ( Sunday is only for problem sessions).
Registration: Google form (Closed)
Selected Participants: List
The last Date for registration is 30.04.2024.
A. A Glimpse Into The Topology via Metric Spaces ( Aakash Gupta):
This short course aims to develop basic analytical skills for undergraduate students to make them well-equipped to understand one of the most beautiful and abstract branches of mathematics called "Topology".
The Tentative Plan:
1) The motivation, Formal Definition of Metric Spaces, and the examples.
2) Some Special kinds of sets associated with Metric Spaces namely Balls, Open and Closed Sets, and a few properties of them.
3)The continuous maps between two metric spaces, An equivalence relation on a collection of all metric spaces.
4) Understanding the nature of sets in Metric Spaces with various properties like Connectedness, Compactness, T-2 axiom, and examples including the standard spaces like GL_n(R) and discrete Metric Spaces.
5) A Layman's Introduction to Topology, Formal Definition of Topology and Examples, Comparison of Topological Spaces and Metric Spaces.
We plan to cover topic 1) to 4) in the first 5 lectures
and topic 5) in the 6th lecture.
Reference Books:
i) Metric Spaces by Mícheál Ó Searcóid.
ii) Metric Spaces by S. Kumaresan.
B. Real analysis (Dr. Alok kumar Sahoo):
Lecture 1- Construction of Real numbers and properties.
Lecture 2 - functions and their properties.
Lectures 3,4- sequence and series, limit, and convergence.
Lecture 5- continuous functions and properties.
Lecture 6- Differentiation and Applications. Root theorem.
Reference books: Real Analysis by S. Kumaresan, Elementary Analysis: the theory of Calculus by kenneth ross.
C. Group theory (Dr. Parbati Sahoo ):
Basic, Group and their subgroups, Homomorphism, Finite groups, Sylow theorems.
D. Linear algebra (Dr. Nirmal Chandra Rout):
Vector Space, LI, and LD, Basis and Dimensions, Matrix representation, Rank and Nullity, Determinants, Solution sets, Eigenvalues, and vectors.
For any changes and updates Contact:
Dr. Alok kumar Sahoo
Dr. Nirmal Chandra Rout.
Organizing committee:
Dr. Ajit Kumar Das (Convener),
Prasanna Kumar Nath,
Dr. Alok Kumar Sahoo (Co-ordinator),
Dr. Debasish Das,
Dr. Nirmal Chandra Rout (Secretary),
Dr. Parbati sahoo.
ATPM - 24 Photos
