Bridge Course
Analysis, Algebra & Linear Algebra
July 28 - August 1, 2025
Department of Mathematical Sciences
Kannur University, Mangattuparamba Campus
About the Program
The Department of Mathematical Sciences is organizing a Bridge Course in Analysis, Algebra, and Linear Algebra under the PM-USHA Scheme. This course is designed for incoming first-year M.Sc. Mathematics students, aiming to bridge the academic gap between undergraduate and postgraduate studies.
The program focuses on strengthening students' understanding of key concepts and enhancing analytical and problem-solving skills. It is particularly beneficial for students from socially and economically disadvantaged groups (SEDG). Sessions will be interactive, combining lectures and problem-solving activities led by experienced and reputed teachers.
- Focus on core foundations in Analysis, Algebra, and Linear Algebra
- Emphasis on conceptual clarity and problem-solving
- Aims to bridge the gap between undergraduate and postgraduate coursework
- Combined sessions of lectures and problem solving
Resource Persons
Prof. A. J. Jayanthan
Kerala School of Mathematics (KSoM)
Prof. Jayanthan is a well-known mathematics educator currently at KSoM, previously Head of the Department of Mathematics at Goa University. He is a long-time contributor to the MTTS program and is known for his engaging teaching in Algebra.
Dr. Pranav Haridas
Kerala School of Mathematics (KSoM)
Dr. Pranav Haridas received his Ph.D. from IISc Bangalore and has held postdoctoral positions at IIT Madras and CMI. His area is Complex Analysis. He is a widely respected teacher and organizer of several research workshops.
Dr. Renjith T
Indian Statistical Institute (ISI), Bangalore
Dr. Renjith received his Ph.D. from IISc Bangalore. His area is Partial Differential Equations. He is a popular teacher at instructional and research workshops.
Syllabus
Real Analysis
- Completeness Property of R: bounds, supremum, infimum
- Properties: Archimedean, density, uncountability
- Sequences and Series: convergence, MCT, BWT, Cauchy sequences
- Series Tests: convergence tests, special series
- Limits and Continuity: types, differentiability
Abstract Algebra
- Finite set
- Groups, subgroups, cosets, cyclic and abelian groups
- Group examples: $S_{n}$, $A_{n}$, $D_{n}$, $Q_{8}$
- Homomorphism, Isomorphism
- Group Actions
Linear Algebra
- Matrices and systems, diagonalization
- Vector spaces, fields, subspaces
- Span, linear independence, basis, dimension
Program Schedule
Dates: July 28 - August 1, 2025
Venue: DMS Seminar Hall, Kannur University, Mangattuparamba Campus
Time Table
| Date | 9:30-11:00 | 11:30-1:00 | 2:00-3:30 | 3:40-5:00 (Tutorial) |
|---|---|---|---|---|
| 28 July | PH | PH | RT | Tutorial |
| 29 July | AJ | PH | AJ | Tutorial |
| 30 July | AJ | RT | AJ | Tutorial |
| 31 July | AJ | RT | RT | Tutorial |
| 1 August | PH | PH | RT | Tutorial |
Speaker Abbreviations:
- PH - Dr. Pranav Haridas (Algebra)
- RT - Dr. Renjith T (Analysis)
- AJ - Prof. A. J. Jayanthan (Linear Algebra)
Tutorial Tutors:
- Praveena P.
- Shahana K.
- Sreedevi P.
Contact Information
For further information, please contact:
Organizers: Anoop V. P., Sruthymurali
Department of Mathematical Sciences, Kannur University