Introduction
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The Department is the oldest centre of Mathematics in the
northwestern 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 Prepartition 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 19441946), 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.
During the last 70 years, the Department has had the following
Professors as Chairpersons:
Prof S Chawla (1935  47)
Prof S A Hamid (1947  51)
Prof Abdus Salam (1951  52)
Prof Lal Mohammad Chawla (195255,195765,196769)
Prof Sultan Bukhsh (1955  57)
Prof M. A Saeed (196567)
Prof M Yasin (196970)
Prof Capt Abdul Majeed (1970  73)
Prof Dr Mirza M Ahmed (197374)
Prof Dr Munawar Hussain (197482)
Prof Mohammad Amin (198288)
Prof Mohammad Hafeez (1988  95)
Prof Dr Karamat H Dar (1995  2001)
Prof Dr Akhlaq A Siddiqul (20012004)
Prof Dr Muhammad Aslam (20042007)
Prof.
Karamat Hussain Dar (20072011)
Mr. Tahir Saeed
Mir (2011)
Prof Dr Muhammad Aslam (2011)
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 lzazeSabqat, 2002 and
the Rhodes Scholarship, 2003 for DPhil at the University of Oxford.
Facilities
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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.
Academic Programmes
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The Department of Mathematics offers following programmes:

B.Sc (Hons)

M.Sc (Evening Programme)

MPhil

PhD
Research Strengths
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.
Research Groups
Currently following research groups are contributing and
training the graduates in various fields of Mathematics:
Courses
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Courses of B.Sc. (Hons) MATHEMATICS
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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 1102 
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 
ALMATH1201

Pre Calculus (Allied Course)

3 
ALMATH1202

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 
ALMATH2203 
Optimization Theory I (for
students of Economics, Statistics and Business Accounting &
Finance) 
3 
ALMATH2204 
Coordinate Geometry
(for students of Physics and
Electronics) 
3 
ALMATH2205 
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
AnalysisI 
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
CourseI 
3 

Elective
CourseII 
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
CalculusI (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 MathematicsI 
3 
MATH 4111 
Measure
Theory  I 
3 
MATH 4112 
Modern
Algebra  I (Galios Theory & Applications) 
3 
MATH 4113 
NonLinear
Systems  I 
3 
MATH 4114 
Numerical
Solutions
of Partial Differential EquationsI 
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
CalculusII (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 
NonLinear
Systems  II 
3 
MATH 4215 
Numerical
Solutions
of Partial Differential EquationsII 
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 
M.Sc Mathematics
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 
NonLinear 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 Geometery 
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 
NonLinear 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 
M.Phil Mathematics
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 
MATH7499 
Thesis 
12 
Core Subjects 
MATH7101 
Advanced Topology 
3 
MATH7102 
Algebraic Geometry 
3 
MATH7104 
Advance
Functional Analysis 
3 
MATH7105 
Numerical analysis 
3 
Optional Subjects for M. Phil/PhD Programmes 
MATH7106 
Advanced Group Theory 
3 
MATH7107 
Advance Ring Theory 
3 
MATH7108 
Algebraic Topology 
3 
MATH7109 
Algebraic Number Theory 
3 
MATH7110 
Approximation Theory 
3 
MATH7111 
Commutative Algebras 
3 
MATH7112 
Computer Algebra 
3 
MATH7113 
Constructive Approximation 
3 
MATH7114 
C*algebras 
3 
MATH7115 
Differential Topology 
3 
MATH7116 
Di Topology 
3 
MATH7117 
Distribution Theory 
3 
MATH7118 
Fixed Point Theory 
3 
MATH7119 
Fourier Analysis and its Applications in Signal Analysis and
Image Processing 
3 
Math7120 
Galois Theory 
3 
Math7121 
Geo Mathematics 
3 
Math7122 
Generalization of Groups 
3 
Math7123 
Graph Theory and Applications 
3 
Math7124 
Inverse Problem 
3 
Math7125 
Interpolation through Wavelets and Saplines 
3 
Math7126 
Knot Theory 
3 
Math7127 
Spectral Theory in Hilbert Spaces 
3 
Math7128 
Advanced Special
Functions and their applications 
3 
Math7129 
Theory of Splines 
3 
Math7130 
Theory of Wavelets 
3 
Math7131 
Theory of Differential Equations 
3 
Math7132 
Theory of Relativity 
3 
Math7133 
Numerical Approximation Theory 
3 
Math7134 
Numerical Solution of Partial Differential Equations 
3 
Math7135 
Non linear Dynamics and Control theory 
3 
Math7136 
Valuation Theory 
3 
Math7137 
Theory of Semi Rings 
3 
Math7138 
Fluid Dynamics 
3 
Math7139 
Discrete Mathematics 
3 
Math7140 
Number Theory 
3 
Math7141 
Advanced Theory of Semi
Rings 
3 
Math7142 
Advanced Topics in Rings
and Modules 
3 
Math7143 
Nonlinear Systems 
3 
Math7144 
Functional Mathematics 
3 
Math7145 
Homological Algebra 
3 
Math7146 
Graph Labeling 
3 
Math7147 
Numerical methods for
Partial Differential Equations  I 
3 
Math7148 
Numerical methods for
Partial Differential Equations  II 
3 
Note: An optional course will
be offered subject to availability of the instructor.
Faculty
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Name 
Designation 
Area of Interest 
Dr. Muhammad Maroof Gohar,
PhD (Hacettepe) 
Incharge/Assistant Professor 
Compactness in Ditopological
Texture Spaces 
Dr. Muhammad Akram, (on Leave)
M.Phil (BZU), PhD, (Univ. of
Kaiserslautern Germany) 
Associate Professor 
Open Mapping and Fixed Point
Theorems 
Dr. Khurram Shabbir,
PhD (GCUL), Postdoc (IMUNAM
Mexico) 
Associate Professor 
Singularity Theory; Algebraic
Topology; Mathematical Physics 
Dr.
Saif Ullah,
PhD (GCUL) 
Associate Professor 
Control Theory Application in
Nonlinear Dynamics; Fluid Mechanics 
Dr.
Asim Naseem,
MCS, MCP, M.Sc. Mathematics (UET),
Ph.D (ASSMS GCU) 
Assistant Professor 
Valuation Theory, Theory of
fields and polynomials 
Dr. Shahid Ahmed 
Assistant Professor


Dr. Nahid Akhtar,
Ph.D (Germany), M.Phil, M.Sc.
(GCU) 
Assistant Professor 
Approximation Techniques and
Functional Analysis 
Dr. Azhar Iqbal Kashif Butt,
MSc. M.Phil. (QAU) MIT, PMASAAU
Rawalpindi, PhD Mathematics (Industrial), Germany,

Assistant Professor 
Numerical treatment of
Differential Equations, optimization with PDE constrains 
Dr. Nayyer Iqbal 
Assistant Professor


Dr. Hasan Mahmood,
PhD (GCUL) 
Assistant Professor 
Commutative Algebra, Algebraic Combinatorics,
Homological Algebra, Algebraic Systems Theory

Dr. Azhar Ali Zafar,
Ph.D (GCUL) 
Assistant Professor 
Fluid Mechanics, Fixed Point
Theory, Mathematical Statistics 
Tanveer Iqbal,
MPhil (PU) 
Assistant Professor 
General Relativity 
Dr. Muhammad Zulfiqar,
Ph D (QAU), MPhil (GCUL) 
Assistant Professor 
Radicals of Semirings Radical
Theory, Fuzzy Algebras 
Tariq Ismaeel, (on PhD Study Leave to China)
MPhil (PU) 
Lecturer 
General Relativity 
Hafiz Usman Afzal
M.Phil (GCU) 
Lecturer 
Combinatorics, Numerical
Analysis, Graph Theory, SemiRing Theory 
Muhammad Aamir Javed
M.Phil (PU) 
Lecturer 
Group theory, Modular group
action on quadratic fields, Number theory, Fuzzy logic,
Graph theory 
Waheed Ahmad 
Lecturer 

Visiting/Adjunct Faculty 
Prof.
Dr. Muhammad Aslam,
PhD (QAU) 
Syed Rizwan Ahmed,
MSc (PU) 
Iqbal Akhtar

Journals & Publications
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The "Journal of Natural Sciences and Mathematics"
is published under the Departments of Mathematics GC University, Lahore
