Academic
Academic > Faculty of Sceinces > Mathematics
Programs Offered
- BS Mathematics
- MSc Mathematics
- 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:
- 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.
- 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.
- 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.
- 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.
- 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.
- Graduates will adopt technology as an essential tool for thoughtfully teaching, learning, doing and understanding important mathematics.
- 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.
- 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.
- 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.
- 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.
- 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 Hours | 72 |
| Location | G.T Road Campus |
| Semesters | 4 |
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 |
| Semesters | 4 |
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
- An Introduction to Cosmology
- Inflationary Cosmology
- Quantum Field Theory
- Mathematical Techniques for Boundary Value Problems
- Electrodynamics-I
- Electrodynamics-II
- Astrophysics
- The Classical Theory of Fields
- Numerical Solutions of Partial Differential Equations
- Non-Newtonian Fluid Mechanics
- Numerical Techniques in Astrophysics
- Statistical Mechanics
- Quantum Theory
- Linear Systems Theory
- Theory of Group Graphs
- Lie Algebras
- Several Complex Variables
- Topological Vector Spaces
- Banach Algebras
- Spectral Theory in Hilbert Spaces
- Fixed Point Theory
- Variational Inequalities
- Commutative Algebra-I
- Commutative Algebra-II
- Commutative Semi group Rings
- Theory of Semi rings
- Fuzzy Algebra
- 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, B. Iran.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 |