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M.Sc Mathematics


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.


  • 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.


  • 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



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



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
Numerical Analysis-II

Project-II (General Project)

Soft Course

Soft Course

Inter/Multidisciplinary Course

Inter/Multidisciplinary Course



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
Cyber Law
Network Security

Elective – I
Multimedia Technology



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.


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 .


  • 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.

Placement Policy & Guidelines for Students

The Placement Policy is applicable to all students registered with the Placement Cell of Mount Carmel College, Autonomous, and is to be followed during their entire tenure at the college.

  1. The Placement Officer & the Placement Coordinator are the facilitators and counsellors for placement related activities and will be responsible for all concerned activities & functioning of the Placement Cell.
  2. The Student Placement Committee will be assisting the Placement Officer & the Placement Coordinator in all activities related to placements.
  3. Neither the College nor the Placement Cell guarantees a job. The Placement Cell will facilitate and coordinate the placement activities on campus including bringing in companies, coordinating the recruitment drives, organizing recruitment training and other related activities leading to the successful placements of the deserving students.
  4. Applying for a company, getting recruited, joining a company is entirely the responsibility/decision of the student concerned.
  5. Opting to register for placements is completely the choice of the students. As some would want to pursue higher studies or other opportunities, such students can refrain from registering with the Placement Cell.
  6. Students are required to check the ELIGIBILITY CRITERIA for registering with the Placement Cell before registering.
  7. All final year students with an aggregate score of 60% and above and with NO ACTIVE BACKLOGS are eligible to register for placements.
  8. All registered students are required to MANDATORILY attend the recruitment training conducted by the Placement Cell and meet the necessary threshold of 75% attendance and 80% completion of the practice tests & assessments to qualify for applying to the cos. Failing to qualify may result in re-training of the student at an additional cost which is to be borne at actuals by the concerned student.
  9. The Placement Cell will notify all the registered students about the upcoming recruitment drives through mails and Whatsapp group notifications and not individually. The students are to be alert and keep a track of the notifications and apply as per their interest and eligibility.
  10. Once a student registers/enrolls for a particular company, she is expected to complete the entire recruitment process as relevant and required. Failing to do so, will result in the student being debarred from sitting for further recruitment drives. Exceptions will be made at the sole discretion of the Placement Cell only in genuine cases. Such cases/reasons to be formally communicated to the Placement Office over mail at least one day prior to the drive.
  11. The student has a choice not to participate in the recruitment process of a company after attending the Pre-Placement Talk. If she decides to continue, then she will be bound by the College Placement Policy to attend the rest of the recruitment process of the company as stated above.
  12. Students will not be allowed to participate in the selection process of a company for which she has missed the PPT.
  13. While the Placement Cell will do its due diligence and bring in the right companies, it is the responsibility of every student to check the company profile, eligibility, Job Profile and the Job Role before applying. The same will also be mailed and/or updated on the Notice Boards or social media groups.
    a. Ex 1- If a company requires the applicant to have an average of 70%, be well assured that you meet the criteria before applying to that company.
    b. Ex 2- If the company requires you to have NO standing arrears/backlogs at the time of attending the placement process, kindly DO NOT APPLY to the company if you do not meet this criterion.
  14. If, after being selected by a company, for some reason the student is not satisfied either with the pay, the timings, work allotted, etc during onboarding, she will need to take it up with the concerned within the company. The Placement Cell will not be able to intervene in internal matters. However, it is important that the students reach out to us in case there are major deviations from the terms mentioned by the company at the time of recruitment.
  15. A student can apply to as many companies as she wants and appear for interviews until the first job is secured. A student will be considered to have secured a job if her name appears in the final select list of a company.
  16. The Placement Office of MCC follows a strict “ONE OFFER PER STUDENT” Policy. However, if a student has been offered a job with a CTC less than or equal to INR 2 lakhs PA, she can opt to apply for ONE more company, subject to prior formal approval by the Placement Office.
  17. Once a student’s name appears in the final selects of a company, it is obligatory for the student to accept the offer. Rejecting offers is strictly not allowed. Defaulters will be required to submit a letter to the Principal along with a penalty fee which could be equivalent to one month’s salary being offered by the said company.
  18. Recruitment Process: All companies generally follow the following procedure (however they could be exceptions) –
    a. Presentation about the company & Job Profile (Pre-Placement Talk)
    b. Written Exam (Aptitude / Technical Test)
    c. Group Discussion and/or Task (Assignments)
    d. Interview (Technical/HR/Others)
    e. Verification of Documents
    f. Offer Letter
  19. Students are to strictly ensure the following for all recruitment drives:
    a. Must report on time as mentioned in the schedules
    b. Wear Business Formals for every recruitment process. Students wearing casuals during recruitment process will be sent back
    c. Always carry one folder containing resumes (2-3 copies), passport size photos, copies of mark sheets, certificates & stationery
    d. Compulsorily carry College & Govt. ID Cards
  20. Most companies require applicants to have Govt. ID – Aadhar & PAN. Hence it is advised for all students to apply for these before registering for placements.
    Students are not allowed to contact the Company / HR team directly for any reason through the recruitment process. In case of any issues or concerns, they are advised to contact their Placement Office and discuss their problems.
  21. Strict action will be taken against students found to be engaged in maligning the College or the Placement Office with the companies. Any grievances you may have, are to be brought to the notice of the of the Placement Officer for resolution.
  22. If a student makes any false claims in the Resume/Student Registration Form, her registration will be cancelled immediately and job offer if any, will be revoked.
  23. All companies conduct a thorough background check/verification. If the company finds that you have manipulated your marks / documents in any manner/or mis-represented any information, your job offer will be terminated, and your name will be blacklisted.
  24. Strict discipline needs to be followed by every student during the recruitment process. Any sort of indecent behavior/misbehavior which affects the decorum of the Placement Cell or the reputation of the College or the Company, will attract severe penalty and disqualification.
  25. Unless explicitly permitted by the companies, use of mobile phones is strictly prohibited during the recruitment process.
  26. Malpractice in all forms or marking proxies during the selection process and beyond, is strictly prohibited and those caught indulging in such activities would be debarred from the placement process. Also, note that no concessions in any form shall be made in such cases.
  27. It may happen that the campus recruitment process can stretch till late evenings. Students are required and prepared to be available accordingly. In case of off-line drives, students are to inform their parents and should arrange their own transportation.
  28. In case of virtual (online) recruitment drives, it is the responsibility of the students to ensure they have the necessary equipment (laptop/PC with functional webcam and mic) and sufficient internet bandwidth for seamless conduction of the process.
  29. Students are required to provide correct email IDs and contact numbers at the time of registration. These will be used for all communication from the Placement Cell and the recruiting companies. The onus is on the students to ensure the contact details provided are correct and up to date.
  30. Students are advised to check their mails regularly as all communication related to placements will be sent through mails.
  31. It is mandatory that once you receive an Intent Letter/Offer Letter from the Company, a copy must be submitted to the Placement Office. Failing which, the end semester examination Hall Ticket/results will be withheld.
  32. All students registered for placements will be bounded by the Attendance Policy of the College. Any exception to the above is permitted only through formal approval of the Placement Office and the respective Department Heads.


For all matters not covered in the above policy, the Placement Office will use its discretion to take appropriate decisions as and when required.

The above guidelines are to ensure a smooth process in the best interest of our students and the participating companies.