babasaheb bhimrao ambedkar university, lucknow-226025

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BABASAHEB BHIMRAO AMBEDKAR UNIVERSITY, LUCKNOW-226025 SCHOOL OF PHYSICAL & DECISION SCIENCES

DEPARTMENT OF MATHEMATICS

Course Structure: M.Sc. Mathematics (Two Years)

(As per National Education Policy 2020)

Total Credits: 92 (76 Credits+16 Credits) Total Hours: 92×30=2760 Hours

Core Courses

Compulsory Courses

Discipline Specific Courses 3 Papers × 04 Credits each × 3 Semesters

& 2 Papers × 04 Credits each × 01 Semesters

= 44 Credits

Enhancing Professional Capacities (EPC) / Skill Development

01 paper of 04 Credits in 1^st semester

01 paper of 02 Credits in 2^nd and 3^rd semesters

1 Masters’ Dissertation of 08 Credits in 4^th semester

= 16 Credits

Elective Courses Course from Mathematics Department

01 Paper × 04 Credits each × 4 Semesters

= 16 Credits

CBCS (Open Elective Courses)

Multidisciplinary Courses

Course from any other Department / School other than SPDS / SWAYAM portal

01 Paper × 04 Credits each × 2 Semesters

= 08 Credits

Interdisciplinary Courses

Course from other Departments within SPDS

01 Paper × 04 Credits each × 2 Semesters

= 08 Credits

Foundation Course/Community Services 01 Paper × 0 Credits each × 4 Semester

= 00 Credits

Total Credits =92 Credits

Note-1: A course of 1 Credit shall require a workload of 30 Hours comprising:

1. Teacher – Student Contact hours

a. 10 Hours of Lectures / Organized classroom activity

b. 5 Hours of Laboratory Work / Problem Solving / Field Work / Tutorials / Teacher-led Activities / Mentoring.

2. Student Effort: 15 Hours of other workloads such as independent individual/group work; obligatory/optional work placement; literature survey/library work; data collection/fieldwork; writing of papers/projects/dissertation/thesis;

seminars etc.

Note-2: Maximum up to 20% (20 Credits) of core courses may be opted by the students online from the SWAYAM portal. However, each course so opted must be of at least 4 Credits each.

Note-3: Students cannot earn credit for a course that is similar to a course already completed in previous semesters or running in the current semester.

Page 2 of 6 ACADEMIC SESSIONS: 2022-2023 AND ONWARDS

Program: M.Sc. Mathematics

Course Structure (As per National Education Policy) M.Sc. (Mathematics) First Year

Semester-I

S.

No.

Category Paper Code Paper Title Lecture Practical Tutorial Credits

1 Core Courses-20 Credits

Compulsory Courses

MAM-101 Linear Algebra 3 0 1 4

MAM-102 Real Analysis 3 0 1 4

MAM-103 Ordinary Differential Equations

3 0 1 4

Elective Course MAM-104 Open Elective from the Department of Mathematics

3 0 1 4

Skill

Development Course

MAM-105 Computer

Programming in C

2 2 0 4

2 CBCS (Open Elective Course)

Multidisciplinary Course

Course from any other Department/ School other than SPDS / SWAYAM portal

4 0 0 4

3 Foundation course MPDC-105 Remedial Language- English (or any other course offered by the university)

1

0

^{0 0}

Total credits 24

Semester-II

1 Core Courses-18 Credits

Compulsory Courses

MAM-201 Topology 3 0 1 4

MAM-202 Complex Analysis 3 0 1 4

MAM-203 Abstract Algebra 3 0 1 4

Elective Course MAM-204 Open Elective from the Department of Mathematics

3 0 1 4

Skill

Development Course

MAM-205 MATLAB 0 2 0 2

2 CBCS (Open Elective Courses)

Multidisciplinary Course

Course from any other Department/ School other than SPDS / SWAYAM portal

4 0 0 4

3 Foundation course MPDC-205 Ambedkar Studies (or any other course

1

0

^{0 0}

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offered by the university)

Total credits 22

M.Sc. (Mathematics) Second Year Semester-III

S.

No.

Category Paper Code Paper Title Lecture Practical Tutorial Credits

1 Core Courses- 18 Credits

Compulsory Courses

MAM-301 Measure theory 3 0 1 4

MAM-302 Partial Differential Equations

3 0 1 4

MAM-303 Analytical Dynamics 3 0 1 4

Elective Course MAM-304 Open Elective from the Department of Mathematics

3 0 1 4

Skill

Development Course

MAM-305 Research Methodology

2

0

^{0 2}

2 CBCS

(Open Elective Courses)

Interdisciplinary Course

Course from other Department within SPDS

4 0

^{0 4}

3 Foundation course MPDC-305 Gender Studies (or any other course offered by the university)

1

0

^{0 0}

Total credits 22

Semester-IV

1 Core Courses- 20 Credits

Compulsory Courses

MAM-401 Functional Analysis 3 0 1 4

MAM-402 Numerical Analysis 3 0 1 4

Research Project MAM-403 Masters’

Dissertation

8 0 0 8

Elective Course MAM-404 Open Elective from the Department of Mathematics

3 0 1 4

2 CBCS

(Open Elective Courses)

Interdisciplinary Course

Course from other Department within SPDS

4 0 0 4

3 Foundation course MPDC-405 Community Services (or any other course

1

0

^{0 0}

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offered by the university)

Total credits 24

Elective Courses

Semester-I: Any one of the following courses 1.

^Core

Courses

Elective Courses

MAM-104 Calculus of Variations &

Integral Equations

3 0 1 4

2.

^MAM-104 Advanced Mathematical

Modeling

3 0 1 4

3.

^MAM-104 Discrete Mathematics 3 0 1 4

4.

^MAM-104 Special Functions 3 0 1 4

5.

^MAM-104 Algebraic Coding Theory 3 0 1 4

Semester-II: Any one of the following courses 1.

^Core

Courses

Elective Courses

MAM-204 Probability and Probability Distributions

3 0 1 4

2.

^MAM-204 Number Theory 3 0 1 4

3.

^MAM-204 Commutative Algebra 3 0 1 4

4.

^MAM-204 Numerical Solutions of

Partial Differential Equations

3 0 1 4

5.

^MAM-204 Matrix Analysis 3 0 1 4

6.

^MAM-204 Fuzzy system & Analysis 3 0 1 4

7.

^MAM-204 Biomathematics 3 0 1 4

Semester-III: Any one of the following courses 1.

^Core

Courses

Elective Courses

MAM-304 Operations Research 3 0 1 4

2.

^MAM-304 Finite Elements Methods 3 0 1 4

3.

^MAM-304 Field Extension Theory 3 0 1 4

4.

^MAM-304 Algebraic Topology 3 0 1 4

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5.

^MAM-304 Cryptography 3 0 1 4

6.

^MAM-304 Financial Mathematics 3 0 1 4

7.

^MAM-304 Differential Geometry 3 0 1 4

Semester-IV: Any one of the following courses 1.

^Core

Courses

Elective Courses

MAM-404 Fluid Dynamics

3

^{0 1 4}

2.

^MAM-404 Wavelet Analysis

3

^{0 1 4}

3.

^MAM-404 Theory of Distributions

3

^{0 1 4}

4.

^MAM-404 Operator Theory

3

^{0 1 4}

5.

^MAM-404 Algebraic Number Theory

3

^{0 1 4}

6.

^MAM-404 Dynamical Systems

3

^{0 1 4}

7.

^MAM-404 Advanced Complex

Analysis

3

^{0 1 4}

8.

^MAM-404 Differentiable Manifolds

3

^{0 1 4}

9.

^MAM-404 Computational Fluid

Dynamics

3

^{0 1 4}

10.

^MAM-404 Lie Groups and Lie

Algebras

3

^{0 1 4}

Courses offered by the Department of Mathematics to the students of other Departments/Schools other than SPDS

Semester-I

S.

No .

Category Paper Code Paper Title Lecture Practical Tutoria

l

Credits

1 CBCS

(Open Elective Course)

Multidisciplinary Course

MAM-106 Linear Programming and Optimization

3 0 1 4

Semester-II

2 CBCS

(Open Elective Course)

Multidisciplinary Course

MAM-206 Mathematical Modeling 3 0 1 4

Courses offered by the Department of Mathematics to the Students of other Departments within SPDS

Semester-III

3. CBCS (Open

Interdisciplinary Course

MAM-306 Mathematical Methods 3 0 1 4

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Elective Course)

Semester-IV

4. CBCS (Open Elective Course)

Interdisciplinary Course

MAM-405 Numerical Methods 3 0 1 4

Multiple Entry and Multiple Exit

The Department of Mathematics is initiating the provision for multiple entries from the session 2022-23. According to the nature of the academic programme and its structural necessity at the PG level, the provision has been created and put in place to be implemented flexibly to suit the individual needs of the student as well as different stakeholders of education at higher education level.

There will be entries at three points during the programme, first entry point in second semester, second entry point in third semester and third entry in the fourth semester subject to the availability of seats and credit equivalence. If a student leaves after the completion of first semester, he/she will be awarded with Certificate in Mathematics (C.M.). Second exit point will be at the end of the second semester where the student will be awarded with Post Graduate Diploma in Mathematics (P.G.D.M.). The third and the last exit point of the course will be after the completion of the third semester where the student will be awarded with Advance Post Graduate Diploma in Mathematics (A.P.G.D.M.).

Academic Bank of Credit

This will allow the students to Exit and Enter the course within a stipulated time. For Academic

Bank of Credits (ABC), the departmental level examination cell shall maintain the academic record

of the students which shall subsequently be forwarded to the controller of Examinations (COE) of

the university for maintaining and executing ABC at the university level.