First Floor, Zakir Hussain Block, Old Campus
041-9239107 math@gcuf.edu.pk

Scheme of Studies

BS Mathematics

Semester 1

MTH-301

Calculus-I

3(3-0)

MTH-303

Discrete Mathematics

3(3-0)

STA-322

Introduction to Statistical Theory-I

3(3-0)

PHY-325

Physics-I

3(3-0)

ENG-321

Functional English

3(3-0)

ISL-321

Islamic Studies/Ethics

2(2-0)

Semester 2

MTH-302

Calculus-II

3(3-0)

MTH-304

Linear Algebra

3(3-0)

STA-421

Introduction to Statistical Theory-II

3(3-0)

PHY-425

Physics-II

3(3-0)

ENG-322

English Comprehension and Composition

3(3-0)

PST-321

Pakistan Studies

2(2-0)

Semester 3

MTH-401

Calculus-III

3(3-0)

MTH-403

Mechanics –I

3(3-0)

MTH-405

Differential Equations-I

3(3-0)

MTH-407

Number Theory

3(3-0)

CSI-321

Introduction to Computing Applications

3(2-1)

ENG-421

Communication Skills

3(3-0)

Semester 4

MTH-402

Affine and Euclidean Geometry

3(3-0)

MTH-404

Mechanics –II

3(3-0)

MTH-406

Differential Equations-II

3(3-0)

MTH-408

Combinatorics

3(3-0)

MTH-410

C++

3(2-1)

PSY-422

Introduction to Psychology

3(3-0)

Semester 5

MTH-501

Real Analysis-I

3(3-0)

MTH-503

Complex Analysis-I

3(3-0)

MTH-505

Algebra-I

3(3-0)

MTH-507

Vector and Tensor Analysis

3(3-0)

MTH-509

Point Set Topology

3(3-0)

MTH-511

Differential Geometry

3(3-0)

Semester 6

MTH-502

Real Analysis-II

3(3-0)

MTH-504

Complex Analysis-II

3(3-0)

MTH-506

Algebra-II

3(3-0)

MTH-508

Mechanics

3(3-0)

MTH-510

Functional Analysis

3(3-0)

MTH-512

Mathematical Methods

3(3-0)

Semester 7

MTH-601

Numerical Analysis-I

3(3-0)

MTH-603

Partial Differential Equations

3(3-0)

MTH-605

Advanced Set Theory

3(3-0)

Optional Papers (3 out of following group)

Applied Group

MTH-607

Algebraic Number Theory

3(3-0)

MTH-609

Fluid Mechanics-I

3(3-0)

MTH-611

Operations Research

3(3-0)

MTH-613

Special Theory of Relativity

3(3-0)

MTH-615

Quantum Mechanics-I

3(3-0)

MTH-617

Cryptography

3(3-0)

Pure Group

MTH-621

Algebraic Number Theory

3(3-0)

MTH-623

Advanced Group Theory-I

3(3-0)

MTH-625

Advanced Functional Analysis

3(3-0)

MTH-627

Advanced Topology

3(3-0)

MTH-629

Continuous Groups

3(3-0)

MTH-617

Cryptography

3(3-0)

Semester 8

MTH-602

Numerical Analysis-II

3(3-0)

MTH-604

Computing Tools for Mathematics

3(2-1)

MTH-606

Mathematical Statistics

3(3-0)

Optional Papers (3 out of following gorup)

Applied Group

MTH-608

Theory of Optimization

3(3-0)

MTH-610

Fluid Mechanics-II

3(3-0)

MTH-612

Modeling and Simulation

3(3-0)

MTH-614

Special Functions

3(3-0)

MTH-616

Theory of Elasticity

3(3-0)

MTH-618

Quantum Mechanics-II

3(3-0)

Pure Group

MTH-622

Advanced Group Theory-II

3(3-0)

MTH-624

Measure Theory

3(3-0)

MTH-626

Advanced Complex Analysis

3(3-0)

MTH-614

Special Functions

3(3-0)

MTH-628

Rings and Fields

3(3-0)

MTH-630

Operator Theory

3(3-0)

Note: Elective may be offered from the list attached depending on the availability of resources of the department.

MSc Mathematics

Semester 1

MTH-551

Real Analysis-I

3(3-0)

MTH-553

Complex Analysis-I

3(3-0)

MTH-555

Algebra-I

3(3-0)

MTH-557

Vector and Tensor Analysis

3(3-0)

MTH-559

Point Set Topology

3(3-0)

MTH-561

Differential Geometry

3(3-0)

Semester 2

MTH-552

Real Analysis-II

3(3-0)

MTH-554

Complex Analysis-II

3(3-0)

MTH-556

Algebra-II

3(3-0)

MTH-558

Mechanics

3(3-0)

MTH-560

Functional Analysis

3(3-0)

MTH-562

Mathematical Methods

3(3-0)

Semester 3

MTH-651

Numerical Analysis-I

3(3-0)

MTH-653

Partial Differential Equations

3(3-0)

MTH-655

Advanced Set Theory

3(3-0)

Optional Papers (3 out of following group)

Applied Group

MTH-671

Fluid Mechanics-I

3(3-0)

MTH-673

Special Theory of Relativity

3(3-0)

MTH-675

Operational Research

3(3-0)

MTH-677

Quantum Mechanics-I

3(3-0)

MTH-667

Cryptography

3(3-0)

Pure Group

MTH-671

Algebraic Number Theory

3(3-0)

MTH-673

Advanced Group Theory-I

3(3-0)

MTH-675

Advanced Functional Analysis

3(3-0)

MTH-677

Advanced Topology

3(3-0)

MTH-679

Continuous Groups

3(3-0)

MTH-667

Cryptography

3(3-0)

Semester 4

MTH-652

Numerical Analysis-II

3(3-0)

MTH-654

Computing Tools for Mathematics

3(2-1)

MTH-656

Mathematical Statistics

3(3-0)

Optional Papers (3 out of following Group)

Applied Mathematics

MTH-658

Theory of Optimization

3(3-0)

MTH-660

Fluid Mechanics-II

3(3-0)

MTH-662

Modeling and Simulation

3(3-0)

MTH-664

Special Functions

3(3-0)

MTH-666

Theory of Elasticity

3(3-0)

MTH-668

Quantum Mechanics-II

3(3-0)

Pure Mathematics

MTH-672

Advanced Group Theory-II

3(3-0)

MTH-674

Measure Theory

3(3-0)

MTH-676

Advanced Complex Analysis

3(3-0)

MTH-664

Special Functions

3(3-0)

MTH-678

Rings and Fields

3(3-0)

MTH-680

Operator Theory

3(3-0)

MPhil/PhD Mathematics

*MTH-701

Algebra

*MTH-702

Functional Analysis

*MTH-703

Numerical Analysis

MTH-704

Theoretical Physics (Plasma Physics)

MTH-705

Heat Transfer-I

MTH-706

Heat Transfer-II

MTH-707

Non-Newtonian Fluid Mechanics

MTH-708

Lie Algebra

MTH-709

Representation Theory of Symmetric Groups

MTH-710

Numerical Solutions of Ordinary Differential Equations

MTH-711

Algebraic Topology

MTH-712

Graph Theory and its Applications

MTH-713

Numerical Solutions of Partial Differential Equations

MTH-714

Approximation Theory

MTH-715

Sobolev Spaces

MTH-716

Theory of Semi Groups

MTH-717

Advanced Fluid Dynamics

MTH-718

Viscous Fluid Flow

MTH-719

Commutative Algebra

MTH-720

Acoustics

MTH-721

Geometric Function Theory

MTH-722

Integral Transforms

MTH-723

Convex Analysis

MTH-724

Differential Subordinations and its Applications

MTH-725

Inequalities Involving Convex Functions

MTH-726

Perturbation Methods-I

MTH-727

Perturbation Methods-II

MTH-731

Advanced Partial Differential Equations

MTH-732

Theory of Interpolation Spaces

MTH-733

Magneto- Hydrodynamics

MTH-734

Monomial Algebra

MTH-735

Variational Inequalities and its Applications

MTH-736

Integral Equations

MTH-737

Theory of Majorization

MTH-738

Distribution Theory and Transform Analysis

MTH-739

Group Theoretic Methods

MTH-740

Homological Algebra

MTH-741

Fixed Point Theory

MTH-742

Multiplicative Ideal Theory

MTH-743

Fuzzy Logic and Its Applications

MTH-744

Algebraic Graph Theory

MTH-745

Topics in Mathematical Inequalities

MTH-746

Algebraic Geometry

MTH-747

Optimization

MTH-748

Advanced Combinatorics

MTH-749

Theory of Group Actions

MTH-750

Theory of Group Graphs

MTH-751

Algebraic Cryptography

MTH-752

Topics in advanced advanced analysis

Other Mandatory Requirements for MPhil

MTH-728

General Seminar

MTH-729

Research Seminar

MTH-730

Thesis (3rd & 4th Semesters)

Other Mandatory Requirements for PhD

MTH-758

General Seminar

MTH-759

Research Seminar

MTH-760

Thesis

*Core courses for M Phil program; the students will have to take three core courses as and when offered by the department.

N.B: Overall 24 teaching credit hours for M Phil program are mandatory and overall 18 teaching credit hours for PhD program are mandatory. However, the research supervisor of students may recommend additional courses. The department will offer the courses keeping in view the availability of teachers and nature of research to be conducted.

Vision

Mathematics develops computational skills, critical thinking, and problem solving skills. The theory, discipline, and techniques taught in mathematics courses are especially important in today’s society. The faculty of the Department of Mathematics recognizes this and strives to ensure that the student learner obtains this knowledge. At the same time, the faculty contributes to the discipline by fundamental research in pure and applied mathematics, statistics, and mathematics education.

Mission

The Department of Mathematics will offer courses and programs of study that will ensure that the student learner will be able to contribute to today’s society. The students will obtain abilities to critically assess numerical and graphical information; learn to formulate strategies for solving problems; and acknowledge the importance of being intellectually curious throughout their adult lives. The Department, through its faculty, will continue to contribute to the body of knowledge of the discipline, whether in traditional research, applied research, or research in the teaching of Mathematics.

Introduction

Established in 1963 the Department of Mathematics is one of the oldest departments of this institution. It has rich history of excellence and performance and produced renowned mathematicians who are serving in various organizations with distinction and credit.
At the University level this department is now running BS, MSc, M. Phil and PhD programms in the subject of Mathematics.
The Department has produced outstanding students who are serving in academic institutions, Pakistan Atomic Energy Commission, Banks and Industries, and in particular, the Aerospace, Oil and Electronic Industry etc.. The mission of the Department is to enhance the research skills of the creative minds through active involvement in the research-oriented activities.
The Department has qualified and experienced teachers who are devotedly inculcating in the students the zeal, spirit and determination necessary to compete with the new scientific challenges in every walk of life. The Department is also providing teaching assistance in the subject of Mathematics to other Departments of the University, namely Physics, Chemistry, Environmental Science, Geography, Economics, Banking & Finance, Statistics, Bioinformatics, Pharmacy etc.