# Integrated M. Sc. (Master of Science) Mathematics (Offered at Coimbatore Campus)

### ACADEMICS

The aim of Amrita Vishwa Vidyapeetham is to strive to develop quality research programmes in many of the frontiers of Science and Technology and the programmes in Mathematics are in line with the vision.. The 5-year integrated M.Sc Mathematics offered by the Department of Mathematics will act as a catalyst for initiating many research programmes, theoretical and practical in nature. Employment opportunities for people qualified with M.Sc. in Mathematics are available in the form of teaching positions in various schools and colleges all over India and abroad. They can work as Scientists and Research Associates in highly reputed institutions, like, ISRO, DRDO, CSIR etc. In addition to the above, they also find lucrative jobs and careers in software industries.

Students graduating from our institution will gain good exposure to a lot of applications in various technical fields, which in turn will help them become efficient teachers, scientists, research associates in highly reputed national and international institutions. Curriculum and syllabi for this programme are on par with any reputed educational institution in India and abroad. Syllabus is framed in such a way that the candidates will be competent enough to take up the tests like NET, SLET, GATE etc.

**DURATION**

5-Year Integrated M.Sc Mathematics – 5 years (10 semesters)

**SALIENT FEATURES OF THE INSTITUTION**

- Very comfortable and peaceful ambience for teaching and learning process
- Highly Qualified and Motivated Faculty
- Excellent Infra Structure facilities
- Well equipped library with soft and hard copies of books and articles.
- Guidance to take up NET / SLET / GATE examinations
- Separate Hostels for Boys and Girls
- The hostels and academic blocks are covered by the wireless network system.
- Placement assistance (Separate center for placement and training)
- Guidance to take up international level tests like TOFEL, IELTS, BEC etc.
- Opportunities / facilities for extracurricular and co – curricular activities
- Opportunities for doing interdisciplinary projects.

**SALIENT FEATURES OF THE PROGRAMME**

- State of art computer labs for Applied Mathematics
- Strong Mathematical backgrounds with Engineering Science applications.
- Possibility of placements in software Industries.
- Possibility of getting the posts of a teacher, scientist, research associate etc in highly reputed national and international institutions.
- Provides competency in the preparation of national level scholarship tests such as UGC/CSIR - NET, GATE etc

**Eligibility:** A pass in +2 or equivalent with a separate minimum of 50% marks in Physics, Chemistry and Mathematics and an aggregate of 55% marks.

**CURRICULUM**

**SEMESTER 1**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15ENG101 | Communicative English | 2 0 2 | 3 |

Language I | 2 0 0 | 2 | |

15MAT101 | Differential Calculus | 3 1 0 | 4 |

15CHY102 | Chemistry I | 3 0 0 | 3 |

15CSA100 | Problem Solving and Computer Programming | 3 0 0 | 3 |

15PHY102 | Physics I | 3 0 0 | 3 |

15CSA180 | Problem Solving and Computer Programming Lab | 0 0 2 | 1 |

15CHY181 | Chemistry Lab I | 0 0 2 | 1 |

15CUL101 | Cultural Education I | 2 0 0 | 2 |

Total | 22 |

**SEMESTER 2**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15ENG111 | Professional Communication | 1 0 2 | 2 |

Language II | 1 1 0 | 2 | |

15MAT111 | Integral Calculus | 3 1 0 | 4 |

15CHY112 | Chemistry II | 3 0 0 | 3 |

15CSA116 | Advanced Computer Programming | 3 0 0 | 3 |

15PHY112 | Physics II | 3 0 0 | 3 |

15CSA187 | Advanced Computer Programming Lab | 0 0 2 | 1 |

15PHY181 | Physics Lab I | 0 0 2 | 1 |

15CUL111 | Cultural Education II | 2 0 0 | 2 |

Total | 21 |

**SEMESTER 3**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT201 | Classical Algebra and Trigonometry | 3 1 0 | 4 |

15MAT202 | Differential Equations | 3 1 0 | 4 |

15MAT203 | Discrete Mathematics | 2 1 0 | 3 |

15MAT204 | Probability and Statistics | 3 1 0 | 4 |

15MAT205 | Vector Analysis | 2 1 0 | 3 |

15ENV200 | Environmental Studies | 3 1 0 | 4 |

15SSK201 | Life Skills I | 1 0 2 | 2 |

15AVP201 | Amrita Value Programme I | 1 0 0 | 1 |

Total | 25 |

**SEMESTER 4**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT211 | Applied Statistics | 3 1 0 | 4 |

15MAT212 | Foundations of Modern Algebra | 3 1 0 | 4 |

15MAT213 | Fourier Series and Integral Transforms | 3 1 0 | 4 |

15MAT214 | Numerical Methods | 3 1 0 | 4 |

15MAT215 | Statics | 2 1 0 | 3 |

Free/Open Elective I | 3 0 0 | 3 | |

15MAT280 | Mathematical SoftwareMatLab | 0 0 2 | 1 |

15SSK211 | Life Skills II | 1 0 2 | 2 |

15AVP211 | Amrita Value Programme II | 1 0 0 | 1 |

Total | 26 |

**SEMESTER 5**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT301 | Dynamics | 2 1 0 | 3 |

15MAT302 | Linear Algebra | 3 1 0 | 4 |

15MAT303 | Number Theory | 2 1 0 | 3 |

15MAT304 | Operations Research | 3 1 0 | 4 |

15MAT305 | Real Analysis | 3 1 0 | 4 |

Free/Open Elective II / Live-in-Lab | 3 0 0 | 3 | |

15SSK301 | Life Skills III | 1 0 2 | 2 |

Total | 23 |

**SEMESTER 6**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT311 | Basics of Complex Analysis | 3 1 0 | 4 |

15MAT312 | Calculus of Variations and Integral Equations | 3 1 0 | 4 |

15MAT313 | Formal Languages and Automata Theory | 3 1 0 | 4 |

15MAT314 | Optimization Techniques | 3 1 0 | 4 |

15MAT315 | Special Functions | 3 1 0 | 4 |

Total | 20 | ||

15MAT399 | Project (for Exit-option students) | 6 | |

Total | 26 |

**Total Credit (for Exit-option students): **143

**SEMESTER 7**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT501 | Advanced Algebra | 4 0 0 | 4 |

15MAT502 | Advanced Real Analysis | 4 0 0 | 4 |

15MAT503 | Topology | 4 0 0 | 4 |

15MAT504 | Ordinary Differential Equations | 4 0 0 | 4 |

15CUL101 | Elective I | 3 0 0 | 3 |

Total | 19 |

**SEMESTER 8**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT511 | Advanced Complex Analysis | 4 0 0 | 4 |

15MAT512 | Functional Analysis | 4 0 0 | 4 |

15MAT513 | Graph Theory | 4 0 0 | 4 |

15MAT514 | Partial Differential Equations | 4 0 0 | 4 |

15CSA116 | Elective II | 3 0 0 | 3 |

Total | 19 |

#### Electives( any one stream)

**Algebra Stream**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT631 | Algebraic Geometry | 3 0 0 | 3 |

15MAT632 | Algebraic Topology | 3 0 0 | 3 |

15MAT633 | Coding Theory | 3 0 0 | 3 |

15MAT634 | Commutative Algebra | 3 0 0 | 3 |

15MAT635 | Lie Algebra | 3 0 0 | 3 |

15MAT636 | Theory of Manifolds | 3 0 0 | 3 |

**Analysis Stream**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT641 | Fixed Point Theory | 3 0 0 | 3 |

15MAT642 | Fractals | 3 0 0 | 3 |

15MAT643 | Harmonic Analysis | 3 0 0 | 3 |

15MAT644 | Nonlinear Partial Differential Equations | 3 0 0 | 3 |

15MAT645 | Wavelet Analysis | 3 0 0 | 3 |

**Statistics Stream**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT651 | Queuing Theory and Inventory Control Theory | 3 0 0 | 3 |

15MAT652 | Random Process | 3 0 0 | 3 |

15MAT653 | Statistical Pattern Classifications | 3 0 0 | 3 |

15MAT654 | Statistical Quality Control and Six Sigma Quality Analysis | 3 0 0 | 3 |

15MAT655 | Theory of Sampling and Design of Experiments | 3 0 0 | 3 |

15MAT656 | Time Series Analysis | 3 0 0 | 3 |

**Fluid Mechanics Stream**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT661 | Advance Boundary Layer Theory | 3 0 0 | 3 |

15MAT662 | Computational Fluid Dynamics | 3 0 0 | 3 |

15MAT663 | Finite Element Methods | 3 0 0 | 3 |

15MAT664 | Magneto-Hydro Dynamics | 3 0 0 | 3 |

15MAT665 | Mathematical Foundations of Incompressible Fluid Flow | 3 0 0 | 3 |

**Computer Stream**

Code No | Course Title | L T P | Cr |
---|---|---|---|

15MAT671 | Advanced Data Structures and Algorithms | 3 0 0 | 3 |

15MAT672 | Advanced Graph Theory | 3 0 0 | 3 |

15MAT673 | Computer Aided Design of VLSICircuits | 3 0 0 | 3 |

15MAT674 | Cryptography | 3 0 0 | 3 |

15MAT675 | Fuzzy Sets and its Applications | 3 0 0 | 3 |

15MAT676 | Introduction to Soft Computing | 3 0 0 | 3 |

15MAT677 | Object-Oriented Programming and Python |

#### Language

Code No | Course Title | L T P | Cr |
---|---|---|---|

15HIN101 | Hindi I | 2 0 0 | 2 |

15KAN101 | Kannada I | 2 0 0 | 2 |

15MAL101 | Malayalam I | 2 0 0 | 2 |

15SAN101 | Sanskrit I | 2 0 0 | 2 |

15TAM101 | Tamil I | 2 0 0 | 2 |

Code No | Course Title | L T P | Cr |
---|---|---|---|

15HIN111 | Hindi II | 1 1 0 | 2 |

15KAN111 | Kannada II | 1 1 0 | 2 |

15MAL111 | Malayalam II | 1 1 0 | 2 |

15SAN111 | Sanskrit II | 1 1 0 | 2 |

15TAM111 | Tamil II | 1 1 0 | 2 |

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## Contact us

Amrita Vishwa Vidyapeetham

Amritanagar, Coimbatore - 641 112

Tamilnadu, India