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Academic > Faculty of Sceinces > Mathematics

Programs Offered

  1. BS Mathematics
  2. MSc Mathematics
  3. MPhil Mathematics

Objective (BS Mathematics)

The BS scheme of studies aims to establish the base for lifelong education by creating essential concepts and equipping the student with necessary techniques, needed to start a career of research, development, teaching or financial applications involving mathematics.

Department of mathematics goals for the BS degree are expressed by the following core attributes we seek for BS graduates in our program:

  1. Graduates will be able to approach challenging problems using a variety of mathematical problem solving skills and methods. They will be able to work with learners to encourage and effectively guide the emergence and growth of their own problem solving abilities.
  2. Graduates will competently engage in mathematical reasoning. They will be able to construct and evaluate mathematical arguments, both formal and informal, and they will have an appreciation for mathematical rigor and mathematical inquiry.
  3. Graduates will be skilled in communicating their mathematical thinking to peers, faculty, and others, in a variety of means. They will be able to fully participate in mathematical discourse by listening to, and respecting, the ideas of others as well as by communicating their own questions and understandings. They will seek to encourage and guide the development of mathematical communication, in this same sense, in their own classrooms.
  4. Graduates will recognize through their own experiences of learning mathematics how they, and others, have built and utilized rich connections among mathematical ideas. They will emphasize in their own classrooms, on their own students, the importance of building useful, connected understanding.
  5. Graduates will skillfully use various ways of representing mathematical ideas, including verbal, graphical, numerical, symbolic, to support and deepen mathematical understandings. They will seek to support, and build on the diversity of representations that their students find useful in their own thinking.
  6. Graduates will adopt technology as an essential tool for thoughtfully teaching, learning, doing and understanding important mathematics.
  7. Graduates will have a thorough understanding of the fundamental principles underlying the school mathematics curriculum and how these principles connect to cognition. This includes a rich, fundamentally grounded understanding of numbers and operations, algebra, geometry, calculus, probability, and statistics.
  8. Graduates will be able to recognize (and design) and use mathematically rich tasks as central pieces in building an instructional practice that focuses on developing and using detailed knowledge of learners work and thinking.
  9. Graduates will appreciate that working effectively with students to build mathematical understanding must be grounded in understanding student thinking, as seen through student discourse and use of various representations, as they engage in mathematical practice.
  10. Graduates will have a clear understanding of the many facets of a teacher work in secondary mathematics classrooms, and the skills to work comfortably in that environment. These skills and understandings will be built and supported by rich field experiences in the public schools.
  11. Graduates will have the skills necessary to observe and to reflect, with care, on how important mathematics can be taught and learned. Students will learn this skill as they are brought into the profession through carefully designed mentored research experiences with faculty.

Eligibility

The applicants must have studied Mathematics in Intermediate and secured at least 45% marks in it.

Scheme of Study

BS (Hons) in Mathematics: 4-Year Program

Total Credit Hours 130
Semesters 8

Program Overview

The Bachelor of Science in Mathematics program is designed to provide students extensive knowledge and skills in Applied and pure mathematics and the applications of mathematics. The program enhances analytical and critical thinking skills and prepares students for research and teaching mathematics.

SEMESTER – I
S. No Course Code Course Title Credit Hours
1 ENG-101 English –I 3
2 IT-101 Introduction to Computer 3
3 MATH-101 Calculus-I 3
4 MATH-103 Discrete Structures 3
5   General-I 3
6   General-II 3
Total Credit Hours:   18
SEMESTER – II
S. No Course Code Course Title Credit Hours
1 ENG-102 English-II 3
2 ISL-100 Islamic Studies 2
3 MATH-102 Calculus -II 3
4 IT-102 Fundamentals of Information System 3
5   General-III 3
6   General-IV 3
Total Credit Hours:   17
SEMESTER – III
S. No Course Code Course Title Credit Hours
1 ENG-201 English –III (Communication Skills for Mathematicians) 3
2 MATH-201 Calculus- III 3
3 MATH-202 Program Languages for Mathematicians 3
4 MATH-208 Program Languages for Mathematicians (Practical) 1
5 MATH-205 Classical Mechanics 3
6   General-V 3
7   General-VI 2
Total Credit Hours:   18
SEMESTER – IV
S. No Course Code Course Title Credit Hours
1 MATH-204 Algebra- I 3
2 MATH-203 Computing Tools for Mathematicians 2
3 MATH-207 Number Theory 3
4 PKS-101 Pakistan Studies 2
5   General-VII 3
6   General-VIII 3
Total Credit Hours:   16
SEMESTER – V
S. No Course Code Course Title Credit Hours
1 MATH-305 Algebra- II  3
2 MATH-306 Vector & Tensor Analysis 3
3 MATH-307 Ordinary Differential Equations 3
4 MATH-301 Real Analysis-I 3
5 MATH-308 Complex Analysis 3
6 MATH-303 Differential Geometry-I 3
Total Credit Hours:   18
SEMESTER – VI
S. No Course Code Course Title Credit Hours
1 MATH-302 Real Analysis-II 3
2 MATH-309 Algebra- III 3
3 MATH-304 Differential Geometry-II 3
4 MATH-311 Topology 3
5 MATH-316 Mathematical Statistics 3
6 MATH-310 Analytical Mechanics 3
Total Credit Hours:   18
SEMESTER – VII
S. No Course Code Course Title Credit Hours
1 MATH-404 Functional Analysis 3
2 MATH-401 Numerical Analysis-I 3
3 MATH-406 Modelling and Simulations 3
4 MATH-403 Partial Diff. Equations 3
5   Elective-I 3
6   Elective-II 3
Total Credit Hours:   18
APPLIED MATHEMATICS (Elective Courses) VII Semester
S. No Course Code Course Title Credit Hours
1 MATH-410 Fluid Mechanics-I 3
2 MATH-441 Special Theory of Relativity 3
3 MATH-419 Optimization Theory 3
4 MATH-405 Research Methodology 3
5 MATH-412 Electromagnetic Theory-I 3
6 MATH-420 Advance Computer Application in Mathematics 3
7 MATH-414 Operational Research-I 3
8 MATH-416 Quantum Mechanics-I 3
 
PURE MATHEMATICS (Elective Courses) VII Semester
S. No Course Code Course Title Credit Hours
1 MATH-434 Theories of Rings & Fields 3
2 MATH-435 Advance Group Theory 3
3 MATH-430 Mathematical Statistic-I 3
4 MATH-436 Lie Algebra 3
PURE MATHEMATICS (Elective Courses) VII Semester
S. No Course Code Course Title Credit Hours
1 MATH-434 Theories of Rings & Fields 3
2 MATH-435 Advance Group Theory 3
3 MATH-430 Mathematical Statistic-I 3
4 MATH-436 Lie Algebra 3
APPLIED MATHEMATICS (Elective Courses) VIII Semester
S. No Course Code Course Title Credit Hours
1 MATH-413 Electromagnetic Theory-II 3
2 MATH-415 Operational Research-II 3
3 MATH-422 Analytical Dynamics 3
4 MATH-417 Quantum Mechanics-II 3
5 MATH-444 General  Theory of  Relativity 3
PURE MATHEMATICS (Elective Courses)  VIII Semester
S. No Course Code Course Title Credit Hours
1 MATH-431 Mathematical Statistics-II 3
2 MATH-438 Theory of Modules 3
3 MATH-437 Decomposition of Modules 3
4 MATH-440 Advance Functional Analysis 3
5 MATH-418 Integral Equations 3

MSc Mathematics: 2-Year Program

Total Credit Hours72
Location G.T Road Campus
Semesters4

Eligibility

Graduation with Mathematics A and B/General Mathematics and Mathematics B with at least 45% marks in both

Program Overview

The M.Sc Mathematics is an innovative program, drawing together traditional and modern mathematical techniques. The program is intended to have broad appeal: to Applied and Pure mathematicians who wish to make themselves more ‘marketable’ by adding some social science aspects to their knowledge and skills based, and to scientists with strong quantitative backgrounds who wish to add to education develop core mathematical skills including abstract thinking, logical analysis and problem solving.

SEMESTER – I
S. No Course Code Course Title Credit Hours
1 MATH-305 Algebra- II  3
2 MATH-306 Vector & Tensor Analysis 3
3 MATH-307 Ordinary Differential Equations 3
4 MATH-301 Real Analysis-I 3
5 MATH-308 Complex Analysis 3
6 MATH-303 Differential Geometry-I 3
Total Credit Hours:   18
SEMESTER – II
S. No Course Code Course Title Credit Hours
1 MATH-302 Real Analysis-II 3
2 MATH-309 Algebra- III 3
3 MATH-304 Differential Geometry-II 3
4 MATH-311 Topology 3
5 MATH-316 Mathematical Statistics 3
6 MATH-310 Analytical Mechanics 3
Total Credit Hours:   18
SEMESTER – III
S. No Course Code Course Title Credit Hours
1 MATH-404 Functional Analysis 3
2 MATH-401 Numerical Analysis-I 3
3 MATH-406 Modelling and Simulations 3
4 MATH-403 Partial Diff. Equations 3
5   Elective-I 3
6   Elective-II 3
Total Credit Hours:   18
APPLIED MATHEMATICS (Elective Courses) III Semester
S. No Course Code Course Title Credit Hours
1 MATH-410 Fluid Mechanics-I 3
2 MATH-441 Special Theory of Relativity 3
3 MATH-419 Optimization Theory 3
4 MATH-405 Research Methodology 3
5 MATH-412 Electromagnetic Theory-I 3
6 MATH-420 Advance Computer Application in Mathematics 3
7 MATH-414 Operational Research-I 3
8 MATH-416 Quantum Mechanics-I 3
PURE MATHEMATICS (Elective Courses) III Semester
S. No Course Code Course Title Credit Hours
1 MATH-434 Theories of Rings & Fields 3
2 MATH-435 Advance Group Theory 3
3 MATH-430 Mathematical Statistic-I 3
4 MATH-436 Lie Algebra 3
SEMESTER – IV
S. No Course Code Course Title Credit Hours
1 MATH-407 Measure Theory and Lebseque Integration 3
2 MATH-402 Numerical Analysis-II 3
3 MATH-442 Methods of Mathematical Physics 3
4 ----------- Elective-III 3
5 MATH-445 Thesis 6
Total Credit Hours:   18
APPLIED MATHEMATICS (Elective Courses) IV Semester
S. No Course Code Course Title Credit Hours
1 MATH-413 Electromagnetic Theory-II 3
2 MATH-415 Operational Research-II 3
3 MATH-422 Analytical Dynamics 3
4 MATH-417 Quantum Mechanics-II 3
5 MATH-444 General  Theory of  Relativity 3
PURE MATHEMATICS (Elective Courses) IV Semester
S. No Course Code Course Title Credit Hours
1 MATH-431 Mathematical Statistics-II 3
2 MATH-438 Theory of Modules 3
3 MATH-437 Decomposition of Modules 3
4 MATH-440 Advance Functional Analysis 3
5 MATH-418 Integral Equations 3

MS/MPhil Mathematics: at least 2-Year Program

Total Credit Hours 72
Semesters4

Eligibility

As per UOG Policy.

Program Overview

In MS/MPhil program of Mathematics you will study advanced courses in Applied or Pure Mathematics chosen from a broad range and complete a dissertation exploring an area in greater depth. You can broaden your mathematical education develop core mathematical skills including abstract thinking, logical analysis and problem solving.

Scheme of Study

  1. An Introduction to Cosmology
  2. Inflationary Cosmology
  3. Quantum Field Theory
  4. Mathematical Techniques for Boundary Value Problems
  5. Electrodynamics-I
  6. Electrodynamics-II
  7. Astrophysics
  8. The Classical Theory of Fields
  9. Numerical Solutions of Partial Differential Equations
  10. Non-Newtonian Fluid Mechanics
  11. Numerical Techniques in Astrophysics
  12. Statistical Mechanics
  13. Quantum Theory
  14. Linear Systems Theory
  15. Theory of Group Graphs
  16. Lie Algebras
  17. Several Complex Variables
  18. Topological Vector Spaces
  19. Banach Algebras
  20. Spectral Theory in Hilbert Spaces
  21. Fixed Point Theory
  22. Variational Inequalities
  23. Commutative Algebra-I
  24. Commutative Algebra-II
  25. Commutative Semi group Rings
  26. Theory of Semi rings
  27. Fuzzy Algebra
  28. Algebraic Coding Theory

Projects/Research

Name Title
Safyan Ahmad, Muhammad Naeem Classes of Simplicial Complexes which admit non-trivial Cohen-Macaulay modifications, “Studia Scientiorum Mathematician Hungrica, 2(4), 2015 423-433. (IF:0.205)
ZaffarIqbal, BarbuBerceanu Universal upper bound for the growth of Artinmonoids, Communications in Algebra, 43:5(2015), 1967-1982.                                                 (I.F:  0.388)
ZaffarIqbal, A. R.Nizami, Usman Ali, Sadia Noureen Growth rate of braid monoid MBn+1, n ≤ 6”, Sci.Int.(Lahore), 27(3), 1723-1730, 2015.                    (ISI)
M. Munir, A. R. Nizami, M. Athar, Moazzam Ali and ZaffarIqbal Some polynomial invariants of a family of graphs”, Sci.Int.(Lahore), 27(3), 1783-1790, 2015.                     (ISI)
ZaffarIqbal, Iftikhar Ahmad, ShamsaAslam Spherical growth series of the free product of groups Zm Zn”, Sci.Int.(Lahore), 27(4), 3241-3244, 2015.       (ISI)
  Hilbert series of the finite dimensional generalized Hecke algebras, Turk J      Math (2015) 39: 698-705.   (I.F:  0.333)
Usman Ali, BarbuBerceanu and ZaffarIqbal Relative Garside elements of Artinmonoids, Rev. Roumaine Math. Pures Appl. (60) 2015, 3, 267-279.
Iftikhar Ahmad, AreejMukhtar The numerical treatment for the solution of  multi- pantograph differential equation arises in Cell-Growth model
Raja M. A. Z., Iftikhar Ahmed., Khan I., Syam M. I., Wazwaz A.M, Neuro-Heuristic Computational Intelligence for solving nonlinear Pantograph Systems
Iftikhar Ahmad and M. Shahbaz Mimentic Computing  Approach  for Solving higher Order Differential Equations
A.Ali  Z. Raza and A.A.Bhatti Some vertex-degree-based topological indices of polyomino chains, J. Comput.Theor.Nanosci.12(9), (2015) 2101-2107.(IF: 1.343)
A.Ali  Z. Raza and A.A.Bhatti Vertex-degree-based topological indices of some dendrimernanostars, Optoelectron. Adv. Mater.-Rapid Comm. 9(2), (2015) 256-259. (IF: 0.394)  
A. Ali A.A.Bhatti and Z. Raza The augmented Zagreb index, vertex connectivity and matching number of graphs, BIran.Math. Soc. 42(2), (2016) 417-425.(IF: 0.262)  
A.Ali Z. Raza and A.A.Bhatti More on comparison between first geometric-arithmetic index and atom-bond connectivity index, Miskolc Math. Notes 17(1), (2016) In Press, http://mat76.mat.unimiskolc.hu/mnotes/forthcoming?volume=0&number=0.(IF: 0.229)
A. Ali Z. Raza and A.A.Bhatti Bond incident degree (BID) indices for some nanostructures, Optoelectron. Adv. Mater.-Rapid Comm. 10(2), (2016) 108-112. (IF: 0.394)
Z.Raza A.A.Bhatti and Z. Raza On the augmented Zagreb index, Kuwait J. Sci. 43(2), (2016) 48-63.(IF: 0.091)
A. Ali A.A.Bhatti and Z. Raza A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles, Kuwait J. Sci., In Press. (IF: 0.091)
A. Ali A.A.Bhatti A note on the minimum reduced reciprocal Randic index of n-vertex unicyclic graphs, Kuwait J. Sci., In Press.(IF: 0.091)
A. Ali A.A.Bhatti Bond Incident Degree Indices of Polyomino Chains: A   Unified Approach, Appl. Math. Comp., In Press. (IF: 1.55)
A. Ali A.A.Bhatti and Z. Raza Topological Study of Tree-Like Polyphenylene Systems, Spiro Hexagonal Systems and PolyphenyleneDendrimerNanostars, Quantum Matter 5(4), (2016) doi:10.1166/qm.2016.1345.
A. Ali A.A.Bhatti and Z. Raza Further Inequalities between Vertex-Degree-Based Topological Indices, International Journal of Applied and Computational Mathematics, (2016) In Press.
Jamshad Ahmad*, and Syed TauseefMohyud-Din On some nonlinear fractional PDEs in physics
Jamshad Ahmad* and GhulamMohiuddin Application of Homotopy Perturbation Method to Nonlinear System of PDEs
Jamshad Ahmad*, Sana Bajwa and IffatSiddique Solving The Klein-Gordon Equations Via Differential Transform Method  
Jamshad Ahmad, Syed TauseefMohyud-Din, H. M. Srivastava, and Xiao-Jun Yang Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators