SYLLABUS for POST GRADUATE STUDIES in MATHEMATICS

University of North Bengal

(To be introduced from the Academic session beginning from August 2011)

Main Features of the Revised Syllabus:

This is a revised syllabus of the Post Graduate Syllabus for post graduate studies in mathematics Mathematics in the University of North Bengal to be introduced from the academic session 2011-2012 and was approved in the Faculty Council Meeting of 19th July, 2011. The revision is мейд keeping Syllabus for post graduate studies in mathematics in view of the current trends and expectations in the curricula of Post Graduate Mathematics in the major Indian Universities.

This syllabus prescribes a general outline of the intended courses. The respective teacher Syllabus for post graduate studies in mathematics shall have the freedom to improvise the actual course material depending on his/her requirements keeping in view of the level of awareness of the students in a particular year/semester.

The Syllabus for post graduate studies in mathematics Optional papers shall be decided on the availability of teaching staffs and will be notified before the beginning of the Semester.

SYLLABUS for POST GRADUATE STUDIES in MATHEMATICS

University of North Syllabus for post graduate studies in mathematics Bengal

(To be introduced from the Academic session beginning from August 2011)

SEMESTER 1

Paper: Full marks:

Paper I: Abstract Algebra I 60

Paper II: Real Analysis 60

Paper III: Topology I 60

Paper IV: Complex Analysis Syllabus for post graduate studies in mathematics 60

Paper V: Ordinary Differential Equations 60

Class Test: 5 x 10 = 50

Seminar and viva-voce: 25 + 25 =50

SEMESTER 2

Paper: Full marks

Paper VI: Abstract Algebra II 60

Paper VII: Calculus on Rn 60

Paper VIII: Topology II 60

Paper IX: Partial Differential Equations Syllabus for post graduate studies in mathematics &

Integral Equations 60

Paper X: Differential Geometry 60

Class Test: 5 x 10 = 50

Seminar and viva-voce: 25 + 25 =50

SEMESTER 3

Paper: Full marks

Paper XI: Integration Theory 60

Paper XII: Functional Analysis 60

Paper XIII: Computer Aided Numerical

Analysis 60

OPTIONAL PAPERS: Papers Syllabus for post graduate studies in mathematics XIV and XV 60 + 60

(Two sets of papers to be taken out of the following. The students will have to inform their choices before the beginning of 3rd semester. However combinations will be Syllabus for post graduate studies in mathematics decided by the Departmental Committee on the basis of the availability of teaching staffs and/or other requirements. The corresponding papers are to be continued in the next semester also)

| 3rd Semester | | 4th Syllabus for post graduate studies in mathematics Semester |

A | Advanced Real Analysis I | A | Advanced Real Analysis II |

B | Advanced Complex Analysis I | B | Advanced Complex Analysis II |

C | Advanced Topology I | C | Advanced Topology II |

D | Advanced differential Geometry I | D | Advanced differential Geometry II |

E | Advanced Discrete Mathematics I | E | Advanced Discrete Mathematics Syllabus for post graduate studies in mathematics II |

F | Advanced Functional Analysis I | F | Advanced Functional Analysis II |

G | Nonlinear Diff. Equations | G | Dynamical Systems |

H | Fluid & Plasma Dynamics I | H | Fluid & Plasma Dynamics II |

I | Theory of General Relativity and Astrophysics | I | Cosmology |

Class Test 5 X 10 = 50

Seminar and Viva-voce: 25 + 25 =50

SEMESTER 4

Paper: Full marks

Paper XVI: Graph Theory Syllabus for post graduate studies in mathematics/ Operation Research/

Fuzzy Sets and Applications 60

Paper XVII: Analytical Dynamics,

Chaos & Fractals 60

Paper XVIII: Computer Aided Numerical Analysis 60

- Practical

OPTIONAL PAPERS: Papers XIX and XX 60 + 60

(Students have to continue with the Syllabus for post graduate studies in mathematics optional papers offered to them in the 3rd semester. Every student of Semester 4 shall make a seminar presentation on a topic outside the prescribed syllabus).

| 3rd Semester | | 4th Semester |

A | Advanced Real Analysis I | A | Advanced Real Analysis Syllabus for post graduate studies in mathematics II |

B | Advanced Complex Analysis I | B | Advanced Complex Analysis II |

C | Advanced Topology I | C | Advanced Topology II |

D | Advanced differential Geometry I | D | Advanced differential Geometry II |

E | Advanced Discrete Mathematics I | E | Advanced Discrete Mathematics II |

F | Advanced Functional Analysis I | F | Advanced Functional Analysis II |

G | Nonlinear Diff. Equations | G | Dynamical Systems |

H | Fluid Syllabus for post graduate studies in mathematics & Plasma Dynamics I | H | Fluid & Plasma Dynamics II |

I | General Relativity and Astrophysics | I | Cosmology |

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