# Master of Science (MS) in Mathematics

## Program Overview

Mathematics is one of the oldest academic subjects and is still very much alive and is growing very fast. It is considered to be very important in the learning and understanding of science subjects in particular and other subjects in general. The advent of computers and data acquisition facilities has stretched the limits of what is possible in Mathematics to all branches of human endeavour. New developments are taking place all the time; some as result of fresh ideas or review of old techniques and problems from a fresh standpoint and others prompted by the applications to new and emerging physical, biological and social sciences, economics, computing and so on. This has given rise to new IT based techniques of mathematical study and has created new computational methodologies. Mathematics is one of the most mature and well-developed disciplines of the basic sciences. The study of Mathematics is not only exciting but important Mathematicians have an opportunity to make a lasting contribution to the society by helping to solve problems in such diverse fields as medicine, biology, management, economics, computer sciences, physics, psychology, engineering, and social sciences.

### Program Objectives

The MS in Mathematics degree provides the thorough training related to core mathematical skills required to go aboard for a PhD degree programme in Mathematics or for employment in areas that strongly demand vital mathematical background, such as research needed by industry and development sector.

### A Reflection About Faculty

We are proud to have a group of dynamic researchers and teachers qualified from prestigious institutes of the world. We have **35 PhD faculty members** which are the highest in numbers compared with all institutes across Islamabad providing an excellent platform for distinguished research career.

Further information about individual faculty please Click Here

### Curriculum

**List of Graduate Courses**

S # | Course Code | Course Title | Credit Hours | Prerequisite(s) |

1. | MTH601 | Hilbert Space Methods | 3(3, 0) | |

2. | MTH602 | Optimization Theory | 3(3, 0) | |

3; | MTH603 | Perturbation Methods I | 3(3, 0) | |

4. | MTH604 | Fixed Point Theory and Applications | 3(3, 0) | |

5. | MTH605 | Numerical Solution of ODEs | 3(3, 0) | |

6. | MTH606 | Advanced Numerical Analysis | 3(3, 0) | |

7. | MTH607 | Numerical Linear Algebra | 3(3, 0) | |

8. | MTH608 | Approximation Theory and Applications | 3(3, 0) | |

9. | MTH609 | Advanced Partial Differential Equations | 3(3, 0) | |

10. | MTH610 | Variational Inequalities & Applications | 3(3, 0) | |

11. | MTH611 | Integral Inequalities | 3(3, 0) | |

12. | MTH612 | Numerical Solutions of PDEs-I | 3(3, 0) | |

13. | MTH 615 | Advanced Mathematical Statistics | 3(3, 0) | |

14. | MTH 616 | Time Series analysis and Forecasting | 3(3, 0) | |

15. | MTH 617 | Linear Statistics Models | 3(3, 0) | |

16. | MTH 618 | Advanced Topics in Graph Theory | 3(3, 0) | |

17. | MTH 619 | Commutative Algebra | 3(3, 0) | |

18. | MTH 620 | Advanced Topology-I | 3(3, 0) | |

19. | MTH 621 | Algebraic Topology | 3(3, 0) | |

20. | MTH 622 | Mathematical Analysis | 3(3,0) | |

21. | MTH 623 | General Relativity | 3(3,0) | |

22. | MTH 624 | Probability Models and Application | 3(3,0) | |

23. | MTH 625 | Numerical Optimization | 3(3,0) | |

24. | MTH 626 | Introductory Cryptography | 3(3,0) | |

25. | MTH 627 | Complexity Theory | 3(3,0) | |

26. | MTH 628 | Finite Fields | 3(3,0) | |

27. | MTH 629 | Fuzzy Logic and Applications | 3(3,0) | |

28. | MTH 630 | Fuzzy Probability and Statistics | 3(3,0) | |

29. | MTH631 | Topology | 3(3, 0) | |

30. | MTH632 | Geometric Function Theory | 3(3, 0) | |

31. | MTH633 | Advanced Convex Analysis | 3(3, 0) | |

32. | MTH634 | Advanced Modern Algebra with Applications | 3(3, 0) | |

33. | MTH635 | Theory of Groups | 3(3, 0) | |

34. | MTH636 | Representation Theory of Finite Groups | 3(3, 0) | |

35. | MTH637 | Field Extensions and Galois Theory | 3(3, 0) | |

36. | MTH638 | Advanced Topology II | 3(3, 0) | |

37. | MTH640 | Differential Subordinations and Applications | 3(3, 0) | |

38. | MTH641 | Convolutions in Geometric Function Theory | 3(3, 0) | |

39. | MTH 642 | Semigroup Theory | 3(3, 0) | |

40. | MTH 643 | Further Algebraic Geometry | 3(3,0) | |

41. | MTH 644 | Lattice Boltzmann Transport Method | 3(3,0) | |

42. | MTH 646 | Homological Algebra | 3(3,0) | |

43. | MTH 647 | Relativistic Theory of Black Holes | 3(3,0) | |

44. | MTH 648 | Classical Theory of Fields | 3(3,0) | |

45. | MTH 650 | Theory of Abel Grassmann’s Gropoids | 3(3, 0) | |

46. | MTH651 | Symmetry Methods in Differential Equations | 3(3, 0) | |

47. | MTH 652 | General Linear Model | 3(3, 0) | |

48. | MTH 653 | Multivariate Analysis in Mathematics | 3(3, 0) | |

49. | MTH 654 | Continuum Mechanics | 3(3, 0) | |

50. | MTH 655 | Introduction to Algebraic Geometry | 3(3,0) | |

51. | MTH 658 | Direct and Inverse Problems in Wave Propagation | 3(3,0) | |

52. | MTH 659 | Commutative Algebra and Algebraic Geometry | 3(3,0) | |

53. | MTH 660 | Rough Set Theory and its Applications | 3(3,0) | |

54. | MTH661 | Viscous Fluids I | 3(3, 0) | |

55. | MTH662 | Viscous Fluids II | 3(3, 0) | |

56. | MTH663 | Perturbation Methods II | 3(3, 0) | |

57. | MTH664 | Numerical Solutions of PDEs II | 3(3, 0) | |

58. | MTH665 | Heat Transfer | 3(3, 0) | |

59. | MTH666 | Elastodynamics | 3(3, 0) | |

60. | MTH667 | Fluid and Thermodynamics | 3(3, 0) | |

61. | MTH668 | Magneto Hydrodynamics | 3(3, 0) | |

62. | MTH669 | Group Theoretic Methods | 3(3, 0) | |

63. | MTH670 | Advanced Analytical Dynamics | 3(3, 0) | |

64. | MTH 671 | Momentum and Thermal Boundary-Layer Theory | 3(3, 0) | |

65. | MTH672 | MHD and Porous Media | 3(3, 0) | |

66. | MTH 673 | Physical Turbulent Flows | 3(3,0) | |

67. | MTH 681 | Mathematical Methods in Machine Learning | 3(2,1) | |

68. | MTH 682 | Data Analytic Techniques | 3(2,1) | |

69. | MTH710 | Numerical Methods for Variational Inequalities | 3(3, 0) | |

70. | MTH761 | Non-Newton Fluid Mechanics | 3(3, 0) | |

71. | MTH762 | Spectrum Methods in Fluid Dynamics | 3(3, 0) | |

72. | MTH763 | Topics in Applied Mathematics | 3(3, 0) | |

73. | MTH764 | Topics in Pure Mathematics | 3(3, 0) | |

74. | MTH765 | Topics in Numerical Mathematics | 3(3, 0) | |

75. | MTH 766 | Simple Linear Regression Model | 3(3, 0) | |

76. | MTH 767 | Multiple Linear Regression Model | 3(3, 0) | |

77. | MTH 768 | Topics in Mathematics Statistics | 3(3, 0) | |

78. | MTH 769 | Topics in Applied Commutative Algebra | 3(3, 0) | |

79. | MTH 770 | Advanced Topics in Graph Valuation Theory | 3 (3,0) | |

80. | MTH 771 | Numerical Methods for Incompressible Flows | 3(3, 0) | |

81. | MTH 772 | Topics in Graph Valuations | 3(3,0) | |

82. | MTH 800 | MS Thesis | 6(6,0) | |

83. | MTH 899 | PhD Thesis | 9(9,0) |

### Research Opportunities:

Few fields of specialization are provided here.

**Field of Specialization:**

- Mathematical Modelling and Optimization
- Mathematical Data Science
- Mathematical Methods in Machine Learning
- Dynamical Models
- Computational Fluid Dynamics
- Mathematical Biology
- Fractional Differential Equations
- Soliton Theory
- Fluid Mechanics
- Heat Transfer
- Algebraic geometry/ Algebraic Topology
- Graph Theory
- Abstract Algebra
- Commutative Algebra
- Real And Complex Analysis
- Topology
- Functional Analysis
- Convex Analysis
- Stochastic Process
- Survival Analysis
- Operation Research
- Distribution Theory
- Quality Control
- Quality and Reliability Engineering

### Career Opportunities:

752 graduates have successfully completed their MS degree from our department and engaged in teaching, serving and leading in various institutes across the nation. Moreover, we also provide jobs to our MS and PhD students by hiring them as research associates from funding agencies like HEC, PSF, etc. Furthermore, by studying new courses related to mathematics of machine learning methods, our students may work in multi-nationals as data analysts, data scientist, business analyst, database administrators, and analytics managers along with many other available opportunities.

### Admission Requirements:

- A I6-year degree, in the relevant field, from an accredited educational institution.
- Minimum CGPA of 2.5/4.0 (semester system) or First Division (annual system) with no third division (annual system) or 'D' grade (semester system) throughout the academic career.
- NTS GAT(General)with a minimum of 50%marks (must be valid on the date of admission) or 60% score in any other entry test adopted by the university.

### Scholarships available:

Few scholarships are available from different research projects such as, HEC, PSF and TWAS etc.