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Introduction
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The
Department of Mathematics 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,
Government College Lahore. The Department has maintained high standards
ever since. One of the Departments graduates, Mr Ram Parkash Bambah,
obtained 600/600 marks in his MA Mathematics Examination in 1946, which
is still an unbroken record. Celebrated Number Expert of the
Subcontinent, Dr. S. Chawla was a Pre-partition old boy of GC, who went
on to become Chairperson, Department of Mathematics, serving from 1935
to 1947. He conducted research in collaboration with leading
mathematicians of his time including C. Bose and Prof. Artin. Recently,
the American Mathematical Society (AMS) has acknowledged his
contributions to Mathematics.
The
year 1966 marked the advent of a new era for the Department as the
Postgraduate Programme was launched independently here at Government
College Lahore, on the initiative of a competent teacher and
administrator, Prof. L. M. Chawala. Prof. Chawala had earlier launched
the publication of the "Journal of Natural Sciences and Mathematics" in
1961. He was able to put together a team of dedicated teachers to
undertake Postgraduate instructions in the subject of Mathematics. One
of his pupils, later to win fame and fortune, Dr. Abdus Salam
(1924-1997), went on to win laurels for Pakistan. 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 bagging over 20
prestigious awards, finally winning the Nobel Prize for Theoretical
Physics in 1979. The Old Hall of GCU has been renamed Salam Hall in
memory of the great Professor who remains a source of inspiration for
all Ravians for all times to come.
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 (1952-55,1957-65,1967-69)
Prof Sultan Bukhsh (1955 - 57)
Prof M. A Saeed (1965-67)
Prof M Yasin (1969-70)
Prof Capt Abdul Majeed (1970 - 73)
Prof Dr Mirza M Ahmed (1973-74)
Prof Dr Munawar Hussain (1974-82)
Prof Mohammad Amin (1982-88)
Prof Mohammad Hafeez (1988 - 95)
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 )
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
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Computing Laboratory
The
University provides a network of PCs and Internet facility to its
students for conducting research. This facility is also available at the
Department. The Department has its own computing Research Lab, which has
PCs, projectors, scanners and laser-printers. The Lab is equipped with
all the necessary equipment for computing and processing. The Math
Scinet facility on which work will be completed soon will be
available to students in addition to electronic resources.
Research
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 of Mathematics is the
only Department in Pakistan subscribing to the AMS Mathematical Reviews
(containing reviews of almost all international journals). The
Department is the main contributor to an internationally recognised
research journal "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 Journal has earned critical acclaim
in the AMS Mathematical Reviews and Zentra lblatt for Mathematik (also a
reputed mathematical review). It attracts more than 45 research journals
in exchange, including 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 Department has a highly qualified and
enthusiastic research-oriented teaching faculty. Almost all the teachers
at the Department hold Research Degrees including four PhDs.
Research Groups
·
Group Theory and Algebraic Modelling Group
·
BCK Algebra, Semi Rings Group
·
Numerical Analysis Group
·
Algebraic Topology Group
·
Control Theory Group
·
Topology Group
·
Fixed Point Theory Group
·
Radical Theory of Rings Group
·
General Relativity Group
Academic Programmes
The
Department of Mathematics currently offers BSc (Hons). This programme
equips the students with the finest possible tools to excel in the job
market. In addition to providing better job prospectus, this programme
trains the students for research in mathematical science. the quality of
our output is appreciated worldwide.
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 |
3 |
|
MATH 1102 |
Discrete
Mathematics |
3 |
|
Semester II |
|
MATH 1201 |
Calculus
II |
3 |
|
MATH 1202 |
Number
Theory |
3 |
|
Year 2
|
|
Semester III |
|
Course
Code |
Course
Title |
Credit
Hours |
|
MATH 2101 |
Calculus
III |
3 |
|
MATH 2102 |
Programming
Languages for Mathematicians |
3 |
|
Semester IV |
|
MATH 2201 |
Algebra I |
3 |
|
MATH 2202 |
Computing
Tools for Mathematicians |
3 |
|
MATH 2203 |
Probability
Theory |
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 |
4 |
|
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
Courses-I |
3 |
|
MATH 4299 |
Research
Project/Internship |
3 |
|
|
Elective
Courses-II |
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 |
Nonlinear
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 - |
3 |
|
MATH 4122 |
Topology -
I (Topological Dimension Theory) |
3 |
|
Semester VIII |
|
MATH 4201 |
Modeling &
Simulation |
3 |
|
MATH 4202 |
Optimization Theory |
3 |
|
|
Elective
Courses |
3 |
|
MATH 4299 |
Research
Project/Internship |
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 |
Nonlinear
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 |
Allied Mathematics for Major in Business Accounting &
Finance, Economics, Statistics
|
Year 1 |
|
Semester I |
|
ALMATH 1101 |
Basic
Mathematics |
3 |
|
Semester II |
|
ALMATH 1201 |
Pre
Calculus |
3 |
|
Year 2 |
|
Semester III |
|
ALMATH
2101 |
Calculus |
3 |
|
Semester IV |
|
ALMATH 2203 |
Optimization Theory |
3 |
Allied Mathematics for Major in Chemistry
|
Year 1 |
|
Semester I |
|
ALMATH 1101 |
Basic
Mathematics |
3 |
|
Semester II |
|
ALMATH 1201 |
Pre
Calculus |
3 |
|
Year 2 |
|
Semester III |
|
ALMATH
2101 |
Calculus |
3 |
|
Semester IV |
|
ALMATH 2202 |
Calculus of
Several Variables |
3 |
Allied Mathematics for Major in Electronics and
Physics
|
Year 1 |
|
Semester I |
|
ALMATH 1102 |
Calculus |
3 |
|
Semester II |
|
ALMATH 1202 |
Advance
Calculus |
3 |
|
Year 2 |
|
Semester III |
|
ALMATH 2102 |
Differential Equations |
3 |
|
Semester IV |
|
ALMATH 2201 |
Coordinate
Geometry |
3 |
Elementary Mathematics for Languages,
Biological Sciences, Arts and Social Sciences
|
Semester IV |
|
EMATH 2201 |
Elementary
Mathematics-I (for languages and Biological Sciences
Disciplines) |
3 |
|
EMATH 2202 |
Elementary
Mathematics-II (for non-languages Disciplines) |
3 |
Semester Breakup for M.Phil
|
Semester I |
|
Semester |
Course
Title |
Credit
Hours |
|
I |
Two Core
courses from the following list of core courses will be
offered |
3+3=6 |
|
|
Two optional courses will be
offered from the following list of courses |
3+3=6 |
|
II |
Four optional courses will be
offered from the following list of optional courses |
4x3=12 |
|
III & IV |
Thesis |
12 |
M.Phil Mathematics
|
Core Subjects |
|
MATH-7101 |
Advanced Topology |
3 |
|
MATH-7102 |
Algebraic Geometry |
3 |
|
MATH-7103 |
Foundation of Mathematics |
3 |
|
MATH-7104 |
Functional Analysis in Applied Mathematics and Engineering |
3 |
|
MATH-7105 |
Numerical analysis |
3 |
|
Optional Subjects |
|
MATH-7106 |
Advanced Group Theory |
3 |
|
MATH-7107 |
Advance Ring 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-7114 |
C*-algebras |
3 |
|
MATH-7115 |
Differential Topology |
3 |
|
MATH-7116 |
Di Topology |
3 |
|
MATH-7117 |
Distribution Theory |
3 |
|
MATH-7118 |
Fixed Point 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-7122 |
Generalization of Groups |
3 |
|
Math-7123 |
Graph Theory and Applications |
3 |
|
Math-7124 |
Inverse Problem |
3 |
|
Math-7125 |
Interpolation through Wavelets and Saplines |
3 |
|
Math-7126 |
Knot Theory |
3 |
|
Math-7127 |
Spectral Theory in Hilbert Spaces |
3 |
|
Math-7128 |
Special Functions and their applications |
3 |
|
Math-7129 |
Theory of Splines |
3 |
|
Math-7130 |
Theory of Wavelets |
3 |
|
Math-7131 |
Theory of Differential Equations |
3 |
|
Math-7132 |
Theory of Relativity |
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-7299 |
Thesis |
12 |
Note: An optional course will
be offered subject to availability of resource person.
Faculty
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|
Name |
Designation |
Area
of Interest |
|
Dr. Karamat Hussain Dar,
PhD (Birmingham) |
Chairperson |
Group Theory, BCK
Algebras |
|
Prof. Muhammad Aslam,
PhD
(QAU) |
Professor
|
Theory of Ring,
BCK Algebra and their Generalisations, Theory of Semi-rings |
|
Mr. Tahir Saeed
Mir,
MPhil (QAU) |
Associate
Professor |
Bifurcation Theory
|
|
Dr.
Muhammad Akram, M.Phil (BZU), PhD, (Univ. of Kaiserslautern
Germany) |
Assistant
Professor |
Open Mapping and
Fixed Point Theorems |
|
Dr. Muhhamad Maroof Gohar,
PhD
(Hacettepe) |
Assistant
Professor |
Compactness in
Ditopological Texture Spaces |
|
Dr. Khurram Shabbir,
PhD (GCUL) |
Assistant
Professor |
Singularity
Theory; Algebraic Topology; Mathematical Physics
|
|
Dr. Saifullah,
PhD (GCUL) |
Assistant
Professor |
Control Theory
Application in Non-linear 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 |
|
Tanveer Iqbal, MPhil (PU) |
Lecturer
|
General Relativity |
|
Ms. Nahid Akhtar,
MPhil
(GCUL) |
Lecturer |
Graph Algebra |
|
Ms. Qaisra
Fazal,
MPhil
(PU) |
Lecturer |
Spline Theory |
|
Azhar Ali Zafar,
MPhil (GCUL) (on study leave) |
Lecturer
|
Fixed Point
Theory,
Mathematical
Statistics
|
|
Mr. Muhammad Zulfiqar,
MPhil (GCUL) (on PhD Study Leave) |
Lecturer
|
Radicals of
Semi-rings Radical Theory |
|
Hasan Mahmood, MSc (GCUL) |
Lecturer |
Algebraic
Topology |
|
Muhammad Noman Aslam,
MSc (GCUL) |
Lecturer
|
Numerical
Solutions of Poisson Equation |
|
Muhammad Munir Butt,
MSc
(GCUL) |
Lecturer
|
Numerical Analysis
with Computer Application |
|
Shahbaz
Ahmad,
MPhil (GCUL) |
Lecturer
|
Operations
Research |
|
Tariq
Ismaeel,
MPhil (PU) |
Lecturer
|
General Relativity |
|
Tanveer Sohail,
MSc (GCUL) |
Lecturer
|
|
|
Visiting Faculty |
|
Syed Rizwan
Ahmed,
MSc (PU) |
|
Arif Javed, MSc (PU) |
|
Khalid Salim MPhil (QAU) |
Journals & Publications
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The "Journal of Natural Sciences and Mathematics"
is published under the Departments of Mathematics GC University, Lahore
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