INTRODUCTION
The Department is the oldest centre of Mathematics in the north-western Subcontinent. It was founded by eminent Mathematician, Prof. W. H. Crank in 1864, after he took over as Officiating Principal of Government College Lahore. The Department maintained high standards ever since its inception. Celebrated Number Expert of the Subcontinent, Dr. S. Chawla was a Pre-partition old Ravain who later became Chairperson of the Department and served from 1935 to 1947. He conducted research in collaboration with leading Mathematicians of his time including C. Bose and Prof. Artin and his contributions were acknowledged by the American Mathematical Society.
The year 1966 marked the advent of a new era for the Department where Master Programme was launched independently at Government College Lahore, on the initiative of a competent teacher and administrator, Prof. L. M. Chawala, who had earlier launched the publication of the journal of “Natural Sciences and Mathematics” in 1961. An esteemed Ravian (session 1944-1946), a great mathematician of the 20th century, and later Chairperson, Department of Mathematics (1951- 1952), Prof. Salam earned international distinction by receiving over 20 prestigious awards, finally winning the Nobel Prize for Theoretical Physics in 1979.
Professors as Chairpersons
| During the last 82 years, the Department has had the following Professors as Chairpersons | |
| Prof. S. Chawla (1935 – 1947) | Prof. S. A. Hamid (1947 – 1951) |
| Prof. Abdus Salam (1951 – 1952) | Prof. Lal Mohammad Chawla (1952-1955,1957-1965,1967-1969) |
| Prof. Sultan Bukhsh (1955 – 1957) | Prof. M. A. Saeed (1965-1967) |
| Prof. M. Yasin (1969-1970) | Prof. Capt. Abdul Majeed (1970-1973) |
| Prof. Dr. Mirza M. Ahmed (1973-1974) | Prof. Dr. Munawar Hussain (1974-1982) |
| Prof. Mohammad Amin (1982-1988) | Prof. Mohammad Hafeez (1988 – 1995) |
| Prof. Dr. Karamat H Dar (1995 – 2001) | Prof. Dr. Akhlaq A. Siddiqul (2001-2004) |
| Prof. Dr. Muhammad Aslam (2004-2007) | Prof. Karamat Hussain Dar (2007–2011) |
| Mr. Tahir Saeed Mir (2011) | Prof. Dr. Muhammad Aslam (2011-2015) |
| Dr. Maroof Gohar(In-charge) (2015-2017) | Prof. Dr. Mujahid Abbas (2017 – ) |
The torch of GCU continues to burn with the flame of the “Courage to Know” here at the Department of Mathematics. One of our recent graduates, Mr. Muhammad Ali Khan, has been awarded the lzaz-e-Sabqat, 2002 and the Rhodes Scholarship, 2003 for DPhil at the University of Oxford.
FACILITIES
Computing Laboratory
The University provides a network of PCs and internet facilities for the needful computing in research. The facility is also available in the Department and has its own computing research lab, which includes latest PCs, projectors, scanners and laser printers etc. The lab is equipped with internet and all the necessary packages for computing and processing. The Math Sci. net facility which is to be set up soon, will be available in addition to the electronic resources.
Career Scope / Opportunities
The programmes are designed in such a way that the graduates can work in banking sector, industries and education department. Research of the graduates and faculty members is recognized worldwide and published in international journals.
Programme Aim
The Department of Mathematics offers following programmes:
- B.Sc (Hons)
- M.Sc (Evening Programme)
- MPhil
- PhD
Presently, the Department is receiving hard copies of more than 50 reputed international research journals and has electronic access to more than 100 research journals. The Department is the main contributor to the “Journal of Natural Sciences and Mathematics” (JNSM), published biannually by the Department of Mathematics in collaboration with the Departments of Physics and Chemistry, under the supervision of the University Research Council. The Department gets a regular subscription of journals like Annals of Mathematics, Bulletin of AMS, Bulletin of London Mathematical Society, Pacific Journal of Mathematics, Mathematical Proceedings of Cambridge Philosophical Society and Michigan Mathematical Journal.
- The applicant should have obtained at least 60% marks in Intermediate or Diploma of Associate Engineers/BTech. (Pass) in Electrical or Electronics or Instrument Technology/ Telecom / Avionics / IT / Precision Mechanical & Instrument / Radar Technology / Radio Technology / Automation / Instrumentation Process Control.
- The applicant must have passed the entry test for admission to engineering institutions, arranged by the University of Engineering and Technology, Lahore, for the academic session to which the applicant is seeking admission.
- The applicant should not have 3rd division throughout his/her academic career.
Currently following research groups are contributing and training the graduates in various fields of Mathematics:
- Algebraic Topology
- BCK Algebra, Semi Rings
- Control Theory
- Fixed Point Theory
- Geo Mathematics
- Group Theory and Algebraic Modeling
- Industrial Mathematics
- Radical Theory of Rings
COURSES
| Year – 1 | ||
|
Semester – I |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 1101 | Calculus– I (Major Course) |
3 |
| MATH – 1102 | Discrete Structures (Major Course) |
3 |
| ALMATH – 1101 |
Basic Mathematics (Allied Course) |
3 |
| ALMATH – 1102 |
Calculus (for students of Physics and Electronics) (Allied Course) |
3 |
|
Semester – II |
||
| MATH – 1201 | Calculus – II (Major Course) |
3 |
| MATH – 1202 | Number Theory (Major Course) |
3 |
| ALMATH-1201 |
Pre Calculus (Allied Course) |
3 |
| ALMATH-1202 |
Advanced Calculus (for students of Physics and Electronics) (Allied Course) |
3 |
| Year – 2 | ||
|
Semester – III |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 2101 | Calculus – III |
3 |
| MATH – 2102 | Programming Languages for Mathematicians |
3 |
| ALMATH – 2101 |
Differential Equations (for students of Physics and Electronics) (Allied Course) |
3 |
| ALMATH – 2102 |
Calculus (for students of Chemistry, Economics, Statistics and Business Accounting & Finance) (Allied Course) |
3 |
|
Semester – IV |
||
| MATH – 2201 | Algebra – I |
3 |
| MATH – 2202 | Computing Tools for Mathematicians |
3 |
| MATH – 2203 | Probability Theory |
3 |
| ALMATH-2203 |
Optimization Theory I (for students of Economics, Statistics and Business Accounting & Finance) |
3 |
| ALMATH-2204 |
Coordinate Geometry (for students of Physics and Electronics) |
3 |
| ALMATH-2205 |
Calculus of Several Variable (for students of Chemistry) |
3 |
| Year – 3 | ||
|
Semester – V |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 3101 | Algebra – II |
3 |
| MATH – 3102 | Vector & Tensor Analysis |
3 |
| MATH – 3103 | Mathematical Statistics |
3 |
| MATH – 3104 | Numerical Analysis |
3 |
| MATH – 3105 | Ordinary Differential Equations |
3 |
| MATH – 3106 | Real Analysis-I |
3 |
|
Semester – VI |
||
| MATH – 3201 | Algebra – III |
3 |
| MATH – 3202 | Classical Mechanics |
3 |
| MATH – 3203 | Complex Analysis |
3 |
| MATH – 3204 | Mathematical Spaces |
3 |
| MATH – 3205 | Partial Differential Equations |
3 |
| MATH – 3206 | Real Analysis – II |
3 |
| Year – 4 | ||
|
Semester – VII |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 4101 | Functional Analysis |
3 |
| Elective Course-I |
3 |
|
| Elective Course-II |
3 |
|
| MATH – 4299 | Research Project/Dissertation |
3 |
|
Students can opt one of the following Elective Course |
||
| MATH – 4102 | Abstract Algebra – I |
3 |
| MATH – 4103 | Advanced Calculus-I (Numerical Solutions of PDE) |
3 |
| MATH – 4104 | Advanced Numerical Analysis – I |
3 |
| MATH – 4105 | Astronomy – I |
3 |
| MATH – 4106 | Differential Geometry – I |
3 |
| MATH – 4107 | Electromagnetism – I |
3 |
| MATH – 4108 | Fluid Dynamics – I |
3 |
| MATH – 4109 | Group Theory – I (Fundamentals) |
3 |
| MATH – 4110 | History and Philosophy of Mathematics-I |
3 |
| MATH – 4111 | Measure Theory – I |
3 |
| MATH – 4112 | Modern Algebra – I (Galios Theory & Applications) |
3 |
| MATH – 4113 | Non-Linear Systems – I |
3 |
| MATH – 4114 | Numerical Solutions of Partial Differential Equations-I |
3 |
| MATH – 4115 | Operation Research – I |
3 |
| MATH – 4116 | Projective Geometry – I |
3 |
| MATH – 4117 | Quantum Mechanics – I |
3 |
| MATH – 4118 | Relativity – I |
3 |
| MATH – 4119 | Software Engineering – I (Design and Development) |
3 |
| MATH – 4120 | Theory of Processes – I |
3 |
| MATH – 4121 | Theory of Splines – I |
3 |
| MATH – 4122 | Topology – I (Topological Dimension Theory) |
3 |
|
Semester – VIII |
||
| MATH – 4201 | Modeling & Simulation |
3 |
| MATH – 4202 | Optimization Theory |
3 |
| Elective Course |
3 |
|
| MATH – 4299 | Research Project/Dissertation |
3 |
|
Students can opt one of the following Elective Course |
||
| MATH – 4203 | Abstract Algebra – II |
3 |
| MATH – 4204 | Advanced Calculus-II (Integral Equations) |
3 |
| MATH – 4205 | Advanced Numerical Analysis – II |
3 |
| MATH – 4206 | Astronomy – II |
3 |
| MATH – 4207 | Differential Geometry – II |
3 |
| MATH – 4208 | Electromagnetism – II |
3 |
| MATH – 4209 | Fluid Dynamics – II |
3 |
| MATH – 4210 | Group Theory – II (Study of Symmetries) |
3 |
| MATH – 4211 | History and Philosophy of Mathematics – II |
3 |
| MATH – 4212 | Measure Theory – II |
3 |
| MATH – 4213 | Modern Algebra – II (Commutative Rings and Fields) |
3 |
| MATH – 4214 | Non-Linear Systems – II |
3 |
| MATH – 4215 | Numerical Solutions of Partial Differential Equations-II |
3 |
| MATH – 4216 | Operation Research – II |
3 |
| MATH – 4217 | Projective Geometry – II |
3 |
| MATH – 4218 | Quantum Mechanics – II |
3 |
| MATH – 4219 | Relativity – II |
3 |
| MATH – 4220 | Software Engineering – II (Analysis) |
3 |
| MATH – 4221 | Theory of Processes – II |
3 |
| MATH – 4222 | Theory of Splines – II |
3 |
| MATH – 4223 | Topology – II (Differential Topological) |
3 |
|
Year – I |
||
|
Semester – I |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 301 | Real Analysis – I |
3 |
| MATH – 302 | Abstract Algebra |
3 |
| MATH – 303 | Complex Analysis |
3 |
| MATH – 304 | Ordinary Differential Equations |
3 |
| MATH – 305 | Vector and Pencil Analysis |
3 |
| MATH – 306 | Discrete Structures & Computer Tools |
3 |
|
Semester – II |
||
| MATH – 351 | Real Analysis – II | 3 |
| MATH – 352 | Typology | 3 |
| MATH – 353 | Numerical Analysis – I | 3 |
| MATH – 354 | Classical Mechanics | 3 |
| MATH – 355 | Linear Algebra | 3 |
| MATH – 356 | Partial Differential Equations | 3 |
|
Year – 2 |
||
|
Semester – III |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 401 | Measure Theory |
3 |
| MATH – 402 | Functional Analysis |
3 |
| MATH – 403 | Numerical Analysis – II |
3 |
| MATH – 404 | Mathematical Statistics – I |
3 |
| Optional Course |
3 |
|
| Optional Course |
3 |
|
|
Optional Course |
||
| MATH – 405 | Advanced Abstract Algebra – I | 3 |
| MATH – 406 | Advanced Calculus – I (Numerical Solution of PDE) | 3 |
| MATH – 407 | Advanced Numerical Analysis | 3 |
| MATH – 408 | Astronomy – I | 3 |
| MATH – 409 | Advanced Differential Geometry – I | 3 |
| MATH – 410 | Electromagnetism – I | 3 |
| MATH – 411 | Fluid Dynamics – I | 3 |
| MATH – 412 | Modern Algebra – I (Galios Theory & Applications) | 3 |
| MATH – 413 | Non-Linear System – I | 3 |
| MATH – 414 | Numerical Solutions of Partial Differential Equations – I | 3 |
| MATH – 415 | Operation Research – I | 3 |
| MATH – 416 | Projective Geometry – I | 3 |
| MATH – 417 | Relativity – I | 3 |
| MATH – 418 | Software Engineering – I (Design & Development) | 3 |
| MATH – 419 | Rings and Modules | 3 |
|
Semester – IV |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH – 451 | Mathematical Statistics |
3 |
| MATH – 452 | Differential Geometry |
3 |
| MATH – 453 | Graph Theory |
3 |
| MATH – 454 | Mathematical Statistics – II |
3 |
| Optional Course |
3 |
|
| Optional Course |
3 |
|
|
Optional Course |
||
| MATH – 455 | Advanced Abstract Algebra – II | 3 |
| MATH – 456 | Advanced Calculus – II (Integral Equations) | 3 |
| MATH – 457 | Advanced Numerical Analysis – II | 3 |
| MATH – 458 | Astronomy – II | 3 |
| MATH – 459 | Advanced Differential Geometry – II | 3 |
| MATH – 460 | Electromagnetism – II | 3 |
| MATH – 461 | Fluid Dynamics – II | 3 |
| MATH – 462 | Modern Algebra – II | 3 |
| MATH – 463 | Non-Linear System – II | 3 |
| MATH – 464 | Numerical Solutions of Partial Differential Equations – II | 3 |
| MATH – 465 | Operation Research – II | 3 |
| MATH – 466 | Projective Geometry – II | 3 |
| MATH – 467 | Relativity – II | 3 |
| MATH – 468 | Software Engineering – II (Design & Development) | 3 |
|
Year – I |
||
|
Semester – I |
||
|
Course Code |
Course Title |
Credit Hours |
|
Students will study Two Core Courses |
3+3 |
|
|
Students will study Two Optional Courses |
3+3 |
|
|
Semester – II |
||
|
Students will study Four Optional Courses |
3+3+3+3 |
|
|
Year – II |
||
|
Semester – III & IV |
||
|
Course Code |
Course Title |
Credit Hours |
| MATH-7299 | Thesis |
12 |
| Core Subjects | ||
|
MATH-7101 |
Advanced Topology |
3 |
|
MATH-7103 |
Advanced Algebra |
3 |
|
MATH-7102 |
Algebraic Geometry |
3 |
|
MATH-7104 |
Advance Functional Analysis |
3 |
|
MATH-7105 |
Numerical analysis |
3 |
| Optional Subjects for M. Phil/PhD Programmes | ||
|
MATH-7106 |
Advanced Group Theory |
3 |
|
MATH-7108 |
Algebraic Topology |
3 |
|
MATH-7109 |
Algebraic Number Theory |
3 |
|
MATH-7110 |
Approximation Theory |
3 |
|
MATH-7111 |
Commutative Algebras |
3 |
|
MATH-7112 |
Computer Algebra |
3 |
|
MATH-7113 |
Constructive Approximation |
3 |
|
MATH-7115 |
Differential Topology |
3 |
|
MATH-7116 |
Di Topology |
3 |
|
MATH-7117 |
Distribution Theory |
3 |
|
MATH-7119 |
Fourier Analysis and its Applications in Signal Analysis and Image Processing |
3 |
|
Math-7120 |
Galois Theory |
3 |
|
Math-7121 |
Geo Mathematics |
3 |
|
Math-7123 |
Graph Theory and Applications |
3 |
|
Math-7124 |
Inverse Problem |
3 |
|
Math-7126 |
Knot Theory |
3 |
|
Math-7128 |
Advanced Special Functions and their applications |
3 |
|
Math-7133 |
Numerical Approximation Theory |
3 |
|
Math-7134 |
Numerical Solution of Partial Differential Equations |
3 |
|
Math-7135 |
Non linear Dynamics and Control theory |
3 |
|
Math-7136 |
Valuation Theory |
3 |
|
Math-7137 |
Theory of Semi Rings |
3 |
|
Math-7138 |
Fluid Dynamics |
3 |
|
Math-7139 |
Discrete Mathematics |
3 |
|
Math-7140 |
Number Theory |
3 |
|
Math-7141 |
Theory of Semi Rings |
3 |
|
Math-7142 |
Advanced Topics in Rings and Modules |
3 |
|
Math-7143 |
Nonlinear Systems |
3 |
|
Math-7144 |
Functional Mathematics |
3 |
|
Math-7145 |
Homological Algebra |
3 |
|
Math-7146 |
Graph Labeling |
3 |
|
Math-7147 |
Numerical methods for Partial Differential Equations – I |
3 |
|
Math-7148 |
Numerical methods for Partial Differential Equations – II |
3 |
FACULTY
Prof. Dr. Mujahid Abbas
Ph.D (Universitat Politecnica De Valencia, Spain),
Ph.D Applied Mathematics (NCBAE, Lahore)
Post-Doc (University of Birmingham),
Post-Doc (Indiana University Bloomington),
Designation:
Chairperson / Professor
Dr. Khurram Shabbir,
PhD (GCUL), Postdoc (IM-UNAM Mexico)
Designation:
Associate Professor
Dr. Saifullah Khalid,
PhD (GCUL)
Designation:
Associate Professor
Dr. Asim Naseem,
MCS, MCP, M.Sc. Mathematics (UET), Ph.D (ASSMS GCU)
Designation:
Assistant Professor
Dr. Muhammad Zulfiqar,
Ph D (QAU), MPhil (GCUL)
Designation:
Assistant Professor
Engr. Prof. Dr Noor Muhammad Sheikh
PhD Electrical Engineering (UET, Lahore)
Designation:
Professor
Dr. Azhar Iqbal Kashif Butt, (on Leave)
MSc. M.Phil. (QAU) MIT, PMAS-AAU Rawalpindi, PhD Mathematics (Industrial), Germany,
Designation:
Assistant Professor
Dr. Nahid Akhtar,
Ph.D (Germany), M.Phil, M.Sc. (GCU)
Designation:
Assistant Professor
Dr. Muhammad Zulfiqar,
Ph D (QAU), MPhil (GCUL)
Designation:
Assistant Professor
Dr. Tariq Ismaeel,
PhD (Xi’an P.R China), M.Phil.(PU)
Designation:
Assistant Professor
Dr. Waqas Nazeer,
Designation:
Assistant Professor
Mr. Hafiz Usman Afzal
M.Phil (GCU)
Designation:
Lecturer
Mr. Waheed Ahmad
M. Phil (GCUL), M. Sc (GCUF)
Designation:
Lecturer
Mr. Muhammad Aamir Javed
M.Phil (PU)
Designation:
Lecturer