Admission for M.Phil. in Mathematics (CBSGS) for the Academic Year 2015-16

**Second Merit List, M.Sc.- I admission 2014-15**

Second Categorywise merit list M.Sc.-I admission 2014-15

M.Sc.- I admission 2014-15 General Merit List

M.Sc.-I admission 2014-15 Categorywise merit list

Revised Admission Schedule 2014-15

Revised Admission Schedule for M.Sc.Part-I 2014-15

Revised Admission Schedule 2014-15

Admission Schedule 2014-15

Documents Required for Admission 2014-15

Notice for admission toward M.Phil. Programme in Mathematics

List of Eligible Candidate for Ph.D. admission

Admission to Ph.D. Programme in Mathematics

M.Phil. Programme 2014

PET-2014**Schedule**

Accommodation

List-participant

National conference on Differential Equations and Applications

For Further information visit conference website

Five day training workshop for Women Mathematics Teachers (Indian Women and Mathematics-IWM2013)

Notice for candidates who wish to take admission to Ph.D. Prgoramme in Mathematics**Introduction**The University Department of Mathematics was started in the year 1963 under the Headship of Professor Shrikhande, an eminent mathematician of India. In the subsequent year, the Department was recognised as the Centre of Advanced Study in Mathematics by the University Grants Commission. The Department continued as the Centre of Advanced Study for the complete term of 25 years upto 1999.

The Department has been recognised by the Department of Science and technology as 'DST-FIST sponsored Department' for five years from the year 2002 to receive funds for improving infrastructure. The computer lab has been upgraded and equipped with latest mathematical softwares. Now the Department has about twenty computers spread over two LANs with internet facilities.

The broad areas of specialisation of the faculty are Algebra, Analysis, Combinatorics, Geometry, and Number Theory.

The Department conducts courses for a two year post-graduation M.A./M.Sc. in Mathematics and one year course work for M.Phil. degree, in addition to research programmes leading to M.Sc. by research, Ph.D. degree.

The faculty interacts with various national and international bodies, research centres and Universities in the capacity of organisers, thesis examiners, editors, referees and reviewers for research journals in Mathematics in addition to participating and lecturing in conferences.Every year, the Department conducts Refresher Courses of the Academic Staff College for the college teachers to enhance their graduate level teaching. Also the Department conducts workshops/Instructional conferences at the national level on topics of current research interests.

The computer lab is used by faculty members, M.Phil. and Ph.D. students, and also by the

M. Sc. Part II students for their optional courses.The Department offers a Reading room for M.Sc. students along with borrowing facility for mathematical text books. The reading Room and Library are maintained by the voluntary support of the students and the faculty.

**Contact Address:**Office of the Department of Mathematics,

Room Number 252, Second floor,

Ranade Bhavan, C.S.T Road,

Kalina Campus, Vidyanagari, Santacruz(E),

Mumbai - 400 098.

Phone number (Office): (022) 26528871**Library****Department Library**Room No. 253, II Floor, Ranade bhavan, Kalina Campus, Mumbai 400 098

The Library of the Department of Mathematics has more than eight thousand books on various branches of Pure Mathematics. It currently subscribes to more than twenty international journals on Pure Mathematics. This library is generously funded by the National Board of Higher Mathematics-a unit of the Department of Atomic Energy.

List of journals under subscription by the Department Library - 2012:Annals of Mathematics

American Journal of Mathematics

ARS Combinatoria

Bulletin of the American Mathematical Society

Combinatorica

Communication in Algebra

Differential Geometry & its Applications

Discrete Mathematics

Indian Journal of Pure and Applied Mathematics

International Journal of Number Theory

Journal of Algebra

Journal of Combinatorial Design (Recd. Alongwith Journal of Graph theory)

Journal of Combinatorial Mathematics and Combinatorial Computing

Journal of Combinatorial theory A

Journal of Combinatorial theory B

Journal of Differential Geometry

Journal of Functional Analysis

Journal of Graph Theory

Journal of the American Mathematical society

Mathematical Intelligencer

Mathematical Magazine

Notices of the American Mathematical Society

Pacific Journal of Mathematics

Proceedings of the American Mathematical Society

Transactions of American Mathematical society

The list of mathematical magazines under subscription by the Department Library:

- The Mathematical Intelligencer
- Mathematics Magazine
- The Mathematics Gazette

**Courses**

As a rule, admission to M.A./M.Sc. Part I course in Mathematics is confined to only those candidates who have passed B.A./B.Sc. in Mathematics with at least 45% marks.All candidates seeking admission shall submit an application in the prescribed form along with prescribed fee to the Office of Department Mathematics , Room Number 252, Second Floor, Ranade Bhavan, C.S.T. Road, Kalina Campus, Vidyanagari, Santacruz(E), Mumbai 400 098.The details regarding the admission can be obtained from the Office of the Department of Mathematics by first June every year.

All candidates shall submit along with prescribed Application Form, the following:

Certified copies of statement of marks of the first year, second year and third year B.A./B.Sc. examinations along with the original.

An application for a transfer certificate if the candidate is from a constituent college of the University of Mumbai Or a provisional eligibility certificate issued by the Registrar, University of Mumbai if he/she is migrating to this University from another University.

An application for post-graduate registration together with the fee prescribed.

A candidate who fails to fulfill the above formalities will not be admitted.

Application for admission beyond the stipulated time will be rejected.

Application to condole delay in seeking admission will not be entertained.Admitted students will have to pay the following fee in cash at the assigned bank after taking the

**challan form**from the office of the Department of mathematics:Tuition Fees Rs.1000 P.G Registration Fee Rs.850 Library Fee & Library smart card Fee Rs.1000 Students' welfare Fee Rs.50 Sports & Cultural Activities Fee Rs.30 Gymkhana Fee Rs.200 E-Charge Fee Rs.20 E-Suvidha Fee Rs.50 Disaster Fee Rs.10 Other Fees Rs.1975 **Total**Rs. 5245.00

**Note:**- The students of Reserved Category must produce the Caste Certificate, Non Creamy Layer Certificate, copy of Ration Card and copy of third year B.A./B.Sc.marks-sheet at the time of admission for exemption of Admission Fees.
- The Total Fees and Fee structure are subject to change according to the current Rules of the University.

**Renewal of Admission for M.A./M.Sc.(part II):**Students of the Department who have passed M.A./M.Sc.(Part I) can be admitted to M.A./M.Sc.(part II) Course by applying for renewal of admission in the Department and by paying the prescribed fees at the commencement of the academic year.

Those who have passed M.A./M.Sc.(part I) from other universities or those who have passed M.A./M.Sc.(part I) under the external scheme of this university are not eligible for admission to M.A./M.Sc.(part II) in the Department.

**Course Content for M.A./M.Sc. (Part I):**There are five papers and all are compulsory: Paper I- Algebra I, Paper II-Analysis I, Paper III-Topology, Paper IV-Complex Analysis, Paper V- Combinatorics.

The syllabus can be obtained from the Office of the Department of Mathematics.

There will be four lectures of one hour duration for each paper in a week. The classes are conducted in two batches between 9 A.M. to 2 P.M.**Course Content for M.A./M.Sc. (Part II):**There are three compulsory papers and two optional papers for M.A./M.Sc. (Part II). Compulsory papers:Paper I- Algebra II, Paper II- Analysis II, Paper III- Differential Geometry.

The list of optional papers can be found in the syllabus of M.A./M.Sc. (Part II). The classes are conducted between 9 A.M. to 3.30 P.M.During the course of the academic year, there will be two tests of 30 marks each in every paper. The marks of these tests are added up as the internal assessment marks out of the total of 60 marks per paper.

At the end of the academic year, in the month of April, there will be a final examination of 40 marks in each paper.

The result is declared by adding the internal assessment marks and the final examination marks of each paper. Thus marks of each paper is out of a total of 100 marks.

To pass the M.A./M.Sc. (Part I & Part II) examinations, the candidate must secure (i) at least 25 marks in each paper out of 100 marks, (ii) at least 10 marks in each paper out of 40 marks in the final examination and (iii) at least 200 marks out of the grand total of 500 marks of all the five papers.

The candidates who have failed in M.A./M.Sc. (Part I, Part II) examinations can take the supplementary examination held in the next academic year, in the month of June .

There is a provision for not having the marks of the final examination declared in case the student wishes to improve the marks in th supplementary examination. An application for not having the results declared unless the marks obtained are above the expectation (to be mentioned explicitly) has to be made within seven days of the last day of the examination.

If a student after passing the M.A./M.Sc. ( Part II) examination wishes to improve the results he/she may reappear for the examination in all the ten papers of Part I and Part II under the external scheme (Scheme A).

All the examinations are conducted at the Department. Detailed Rules and Regulations of the examinations can be availed from the office of the Department.

**Ramakant Muzumdar Commemorative Lecture Series**Born in the year 1918 at the close of first world war, Shri Ramakant Muzumdar had an outstanding career winning widely varied distinctions like gold medal for proficiency in Sanskrit and later the much coveted Tripos in the hallowed portals of the Cambridge University in United Kingdom.

He was working on the internal ballistics and thermodynamics of guns in the Royal arsenal at Woolwich before he returned home to join the Indian Ordinance Factories as an Assistant Works Manager. He entered the Organisation when the country had just become independent. Shri Muzumdar had various successful assignments in the Headquarters and the factories and eventually rose to become the Director General in the year 1965. He held this post with distinction until his retirement in 1976.

Shri Muzumdar had deep and profound interest in Mathematics.

Ramakant Muzumdar Commemorative Lecture Series is made possible through a generous donation of grant by Ms. Hema Muzumdar, the widow of late Ramakant Muzumdar. The lecture series is conducted by the Department of Mathematics, University of Mumbai every academic year and carries an honorarium of Rs. 2000/ to the speaker.

Past speakers in this lecture series have been professor K.R. Parthasarathy, Professor Pavman Murthy, professor M.S. Ragunathan, professor M.S. Narasimhan, professor A. Katok, professor R. Parimala, professor B. Weiss, professor S. Ramanan, professor L. Batten, professor M.G. Nadkarni, professor P. Deligne, professor Madhav V. Nori, professor R. Langlands, professor Adimurthy, professor S.G. Dani.

Candidates who have passed the M.Sc. (Mathematics) from University of Mumbai or any other university (recognized as equivalent) with at least 45% marks are eligible to apply for the M.Phil. Course.

The M.Phil. Course begins in the month of November. Regular lectures are conducted on three core subjects of higher mathematics. There will be continuous assessment in the form of seminars and assignments. The papers offered are:

1. Algebra, 2. Analysis, 3. Number Theory, 4. Discrete Mathematics, 5. Topology, 6. Special Topics-I, 7.Special Topics-II.Papers 6 & 7 will be announced in detail only if an expert of a particular specialisation has designed a course with the purpose of teaching a particular batch of M.Phil. Students. It will be applicable only for that academic year.

Detailed Syllabus can be obtained from the office of the Department.The final examination for 100 marks of three hour duration in each paper is conducted in the month of December of the following year. A candidate must secure a minimum of 50% marks in each paper to pass the examination.

A candidate who has passed all the three papers is eligible to submit the Dissertation in the next academic term. On the acceptance of the Dissertation by the external examiner duly appointed, the candidate will be declared to be qualified for the M.Phil. Degree. No class is awarded.

A candidate admitted to the M.Phil. Course is required to pay tuition fees and examination fees as prescribed, from the date of registration till the date of submission of the Dissertation.

The Ph.D.(mathematics) programme is conducted by the University Department of Mathematics, 2nd floor, Ranade Bhavan, Kalina Campus, Santacruz(east), Mumbai 400 098. The Rules for Admission, Registration and Course work for the Ph.D. (Mathematics) programme are guided by the circular No. Exam/Thesis/Univ./VCD/2414 of 2010 issued by the University. Interested candidates may refer to this circular on the website of the University for full details.The existing vacancies against each faculty member along with respective specialisations of the Ph.D. (Mathematics) programme will be put up on the Notice Board of the University Department of Mathematics twice a year (i.e. January/February and July/August).

The candidates who have passed NET/SET examination or completed M.Phil. degree as per UGC guidelines shall submit their application at Office of the University Department of Mathematics with a fee of Rs. 100/ (cash) for admission to the Ph.D. programme during the specified period of the year. These candidates are referred to as 'PET exempt candidates'.

The candidates who do not have the above qualifications are required to take the Ph.D. Entrance Test (Mathematics) (PET) conducted twice a year by the Controller of Examinations. The applications for PET are submitted at the Thesis section of the University at Fort Campus along with a demand draft of Rs. 1000/ (Rs. 500/ for candidates belonging to the reserve category) payable to 'Finance & Accounts Officer of the University of Mumbai'. These application forms can downloaded from the website of the University. The 'PET exempt candidates' can also use the same application from for convenience.

The candidates who have passed the PET with a minimum of 50% marks shall submit their application with a fee of Rs. 100/ (cash) at Office of the University Department of Mathematics for admission to the Ph.D. programme during the specified period within 3 years of declaration of PET result. They will be called for the interview along with the PET exempt candidates. The list of successful candidates will be put up on the Notice Board of the University Department of Mathematics.

The candidates who have qualified in the interview can enroll for the Ph.D. course work. The candidates with M.Phil. degree who have qualified in the interview are exempted from the course work. After completion of the course work, the candidates shall submit the 'Topic Approval Form' forwarded through the research guide for consideration of RRC. The Topic Approval Form contains the reserch proposal of the candidate amongst other details. After receiving the approval of the RRC, the candidate shall submit the Ph.D. Registration Form at the University Department of Mathematics. The Ph.D. thesis can be submitted to the thesis section for evaluation after a period of two years from the date of Ph.D. registration.

**Term Fees:**Tuition Fees Rs.4000 P.G Registration Fee Rs.1000 Library Fee Rs.1000 Students' Welfare Fee Rs.50 Gymkhana Fee Rs.200 E-Charge Fee Rs.20 E-Suvidha Rs.50 Sports & Cultural Activities Fee Rs.30 Disaster Relief Fund Fee Rs.10 Group Insurance Rs.40 VC Fund Fee Rs.20 Other Fee Rs.1875 **Total**Rs. 8295.00 **Faculty****Name of the Faculty Member Specialization****Name of the Faculty Member****Specialization**Dr. Rajendra. P. Deore, Professor and Head, Algebra Dr. Mangala V. Manohar, Professor, Algebraic Geometry Dr. Ravindranath Aithal, Professor, Differential Geometry Dr. Jayendra R. Junghare, Associate Professor Atmospheric Turbulence Dr. Rajendra M. Pawale, Associate Professor, Design Theory Dr. Bhausaheb S. Desale, Associate Professor, Differential Equations Dr. Vinayak. S. Kulkarni Associate Professor, Differential Equations Mr. Deepak Sarve, Assistant Professor Mr. Kamalakar Surwade, Assistant Professor Dr. Anuradha Garge, Assistant Professor, Algebraic Number Theory Dr. Shantilal D. Shendge, Assistant Professor Dr. Madumita Gangopadhyay, Assistant Professor, Differential Equations, Fluid Dynamics Dr. Mahendra G. Nadkarni, Professor Emeritus, Ergodic Theory Dr. R. C. Cowsik, Visiting Professor, Commutative Algebra Dr. Ashok Pandit, Visiting Faculty, Differential Equations **Administrative Staff**- Mrs. Surekha Mayekar (Superintendent)
- Mrs. Nanda More (Senior Typist Clerk)
- Ms. Shweta Kadam (Jr. Clerk (Temporary))
- Mrs. Sheetal Bandekar (Jr. Clerk (Temporary))
- Mr. V.P. Mhatre (Peon)
- Mr. Umakant G. Gurav (Peon)
- Mr. Sanjay Gaware (Hamal (Temporary))
- Librarian of the Student's Library & Department Library: Mrs. Ketki Joshi