M.Sc Mathematics
- About Program
- Vision & Mission
- Objectives
- Eligibility
- Program Matrix
- Syllabus
- Careers and Highlights
- Programme Outcomes
Overview
Students undertaking the M.Sc. program in Mathematics at Mount Carmel College are trained to explore and acquire an in-depth understanding of the episteme – Mathematics. By putting in a conscious effort to impart knowledge about the field by reputed professors and lecturers, this program is designed to foster a culture wherein students’ talent is amplified with knowledge, technical training and guidance. Through rigorous evaluation patterns, our students are encouraged to put their skills to use and venture into the field of Mathematics by enhancing their critical thinking abilities and sensibilities. On acquiring knowledge of the qualitative and quantitative techniques as well as gaining an in-depth understanding of the field, Graduates of this degree will be able to demonstrate their skills in Algebra, Numerical Analysis, Computer Graphics, etc. The Curricular and Extracurricular activities are designed in a way to ensure that the students receive a holistic understanding through the curriculum.
Head of Department
Dr. Vijayalakshmi. B
Associate Prof., M.Sc., M.Phil., Ph.D.
Vision
- To provide quality, integral and career oriented education and create a climate for human and educational excellence.
- To assist students in acquiring a conceptual understanding of the nature and structure of mathematics, its processes, and applications.
- To develop and offer dynamic programs in the mathematical sciences that will prepare students to enter various new fields of specializations.
- To ultimately see that the learning of mathematics becomes more alive, vibrant, relevant and meaningful; a program that paves the way to seek and understand the world around them.
Mission
- To create, discover and disseminate mathematics on a broad front.
- To promote the realistic growth of women in all frontiers of life and empower them to be agents of liberative transformation and mathematical proficiency.
- To provide an environment where students can learn and become competent users of mathematics and mathematical application.
- To contribute to the development of students as mathematical thinkers, enabling them to become lifelong learners, to continue to grow in their chosen professions, and to function as productive citizens.
- To extend the frontier of mathematical knowledge by producing quality research with original results and by collaborating with other disciplines.
The objectives of this programme is,
The course is designed to impart knowledge in the subject of Mathematics both theoretical and applied keeping in view of the needs of current teaching, research and industrial applications. The course includes core topics in pure mathematics providing a good foundation for research as well as topics in applied Mathematics to develop a professional career in Mathematics. It incorporates all the essential recommendations of the Curriculum Development Committee set up by the UGC. The course provides opportunity to develop computational and analytical skills using modern computing facilities. The course is structured such that a student can specialize in at least three specific areas of Mathematical applications. The individual project work provides field experience and hands-on training in mathematical modeling.
- To provide students with advanced mathematical and computational skills that prepares them to pursue higher studies and conduct research.
- To train students to deal with the problems faced by software industry through knowledge of mathematics and scientific computational techniques.
- To develop independent learning skills and transferable skills among the students.
- To increase students self-confidence in conducting research independently or within a team.
- To develop an in-depth understanding of the fundamentals of Mathematics and create a foundation of lifelong learning to facilitate progressive careers in industry.
A candidate who has passed B.Sc. Degree Examination with Mathematics as one of the optional subjects from Bangalore University or any other University equivalent thereto with a minimum of 50% marks in the subject of Mathematics and a minimum of 40% in the aggregate is eligible.
Semester | Course Code | Name of the Course | L:T:P | Credits | CIA Marks | ESE | Total Marks |
---|---|---|---|---|---|---|---|
I | M-CC-01 | Algebra-I | 4:2:0 | 5 | 30+15 | 70+35 | 150 |
M-CC-02 | Real Analysis | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-CC-03 | Topology | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-CC-04 | Numerical Analysis-I with MATLAB Programming | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-AC-01 | Discrete Mathematics | 2:0:0 | 1 | 15 | 35 | 50 | |
M-AC-02 | Computational statistics | 2:0:0 | 1 | 15 | 35 | 50 | |
M-SC- 01 | Soft Course | 2 | 1 | 15 | 35 | 50 | |
CDP Evaluated in II Sem | |||||||
Total | 30 | 23 | 225 | 525 | 750 | ||
II | M-CC-05 | Functional Analysis | 4:2:0 | 5 | 30+15 | 70+35 | 150 |
M-CC-06 | Complex Analysis | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-CC-07 | Ordinary Differential Equations | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-CC-08 | Algebra-II | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-AC-03 | Continuum Mechanics | 2:0:0 | 1 | 15 | 35 | 50 | |
M-AC-04 | Research Methodology | 2:0:0 | 1 | 15 | 35 | 50 | |
M-SC- 02 | Soft Course | 2 | 1 | 15 | 35 | 50 | |
CDP Evaluated in II Sem | 2 | 50 | 50 | ||||
Total | 30 | 25 | 225 | 575 | 800 | ||
III | M-EC-01 | Differential Geometry | 4:2:0 | 5 | 30+15 | 70+35 | 150 |
M-EC-02 | Partial differential equations | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-EC-03 | Fluid Mechanics | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-EC-04 | Graph Theory | 4:0:2 | 5 | 30+15 | 70+35 | 150 | |
M-AC-05 | Numerical analysis-II | 2:0:0 | 1 | 15 | 35 | 50 | |
M-SC-03 | Soft Course | 2 | 1 | 15 | 35 | 50 | |
M-IMC- 01 | Inter/Multidisciplinary Course | 2 | 1 | 15 | 35 | 50 | |
Internship | 2 | 50 | 50 | ||||
Total | 30 | 25 | 225 | 575 | 800 | ||
IV | M-EC-05 | Measure and Integration | 4:0:2 | 5 | 30+15 | 70+35 | 150 |
M-EC-06 | Mathematical methods | 4:2:0 | 5 | 30+15 | 70+35 | 150 | |
M-EC-07 | Elective Paper III | 4:0:0 | 4 | 30 | 70 | 100 | |
M-PR | Project | 8 | 4 | 200 | 200 | ||
Total | 24 | 18 | 120 | 480 | 600 | ||
Grand Total | 91 | 2950 |
Syllabus (CBCS)
Semester I | Semester II |
Algebra | Topology |
Real Analysis with MATHEMATICA | Complex Analysis with MATHEMATICA |
Ordinary Differential Equations | Partial Differential Equations with MATLAB |
Numerical Analysis-I with MATLAB Programming | Linear Algebra with SCILAB |
Discrete Mathematics | Continuum Mechanics |
Computational Statistics | Numerical Analysis-II |
Soft Course | Soft Course |
| CDP |
Semester III | Semester IV |
Measure and Integration | Functional Analysis |
Fluid Mechanics with MATHEMATICA | Mathematical Methods |
Elective Paper-I | Elective Paper-III |
Elective Paper-II | Project-I (on Elective paper-IV) |
Theory of Numbers | Project-II (General Project) |
Soft Course | Soft Course |
Inter/Multidisciplinary Course | Inter/Multidisciplinary Course |
Internship |
|
Semester III | Semester IV |
Web Programming | Computer Based Optimization Techniques |
Computer Graphics | Object Oriented Analysis and Design |
Computer Architecture | Simulation and Modeling |
Data Warehousing and Data Mining | Elective – II |
Elective – I |
|
Electives:
Third semester:
Group A
- Graph Theory
- Fuzzy Set Theory
- Theory of numbers
Group B
- Finite Element Analysis
- Fluid Mechanics
Group C
- Optimization Techniques
- Probability, Reliability And Random Processes
Fourth semester:
Group A
- Algorithmic Graph theory
- Design And Analysis Of Algorithms
Group B
- Magneto Hydrodynamics
- Computational Fluid dynamics
- Fluid Dynamics Of Ocean And Atmosphere
Group C
- Special functions
- Riemann Geometry
Inter/Multidisciplinary Course
Course-1 (III SEM)
- Discrete Mathematics with MATLAB Programming
- Operational research with MATLAB Programming
Summer Internship
M.Sc students are given an opportunity to take up summer internships in association with Companies, industries and institutes such as DELL, Microsoft, City bank, NAL, Bosch, IISC, ISRO,TIFR Pramarta etc.
Placements
Students are well placed in Academic Institutes/ Industry/ Company / Research as in the following DELL, Cognizant, Microsoft, IBM, AXA Life insurance, Earnst and Young, IIT, Bangalore university, International schools .
Colloborations/MOU
- Wolfram
- GT Enterprises
- Pramarta
- Government Science College
- Bangalore University
- IISC
On the successful completion of M.Sc. Mathematics, the students will be able to,
- Formulate complete, concise and correct mathematical proofs.
- Frame problems using multiple mathematical structures and relationships and solve using standard techniques.
- Create quantitative models to solve real world problems in appropriate contexts.
- Recognize and appreciate the connections between theory and applications and effectively use professional level technological tools to support the study of mathematics.
- Clearly Communicate Quantitative and Theoretical Ideas In Mathematics.