Mathematics

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