Humanities & Sciences

 -Who We Are-

The College of Humanities & Sciences is responsible to impart instructions in Humanities, English and  Mathematics  to undergraduate and postgraduate students of programs offered in Applied Sciences & Arts i.e  in Engineering , Computer and Information Sciences, Management Sciences and Media Arts at PAF-KIET.

 -Director’s Profile-

Dr. Muhammad Amin
MSc, Applied Math (PU)
PhD, DIC Imperial College, London (UK)

Dr. Muhammad Amin is a professor of Mathematics and Director of College of Humanities & Sciences at PAF-KIET Karachi. He is a self made professional who started his education career at a village primary school in Sialkot. Through dedication and hard work he ended up as a post graduate student at Imperial College London University (UK). This world famous institution awarded him PhD and DIC in a minimum period of 3 years. Besides, he has the honor to work as a research scholar for one year at Research Establishment, Winfrith (Atomic Energy Authority) UK. There, he made extensive use of packages specially prepared for the Analysis of Nuclear Reactors on IBM computers and produced two research reports. On his return to Pakistan in 1962, he continued the research work and produced research papers published in Journal of Natural Sciences, Govt College Lahore.

During his professional career (1962- to date) he has served as professor of Mathematics and taught students of Engineering at undergraduate and post graduate levels at Institutions of National repute such as: Engineering University Lahore;  PAF College of Aeronautical Engineering (NED) ; Navy Engineering College (NUST);  Usman Institute of Technology (Hamdard) and PAF- KIET Karachi.

Mathematics

The department of Mathematics is assigned the task to conduct mathematics courses which comprise the integral part of syllabi for under graduate and post graduate programs in Electrical Engineering , Computer Science and Management Sciences offered by PAF-KIET. Therefore we run courses in almost all branches of mathematics such as:

1. Mathematics Courses for Management Science Programs

  • Code Course CR-H
    QT102 Business Math 3
    QT203  Statistics & Inferences 3

2. Mathematics Courses for Computer Science Programs

  • Code Course CR-H
    QT101 Algebra and Trigonometry 3
    QT104 Calculus and  Analytical Geometry 3
    QT105 Differential Equations and Multivariable Calculus 3
    QT203 Probability & Statistics 3
    QT 303 Numerical Computing 3

3. Mathematics Courses for Engineering Programs

  • Code Course CR-H
    QT101 Algebra and Trigonometry 3
    QT104 Calculus and  Analytical Geometry 3
    QT105 Differential Equations and Multivariable Calculus 3
    QT203 Probability & Statistics 3
    QT 303 Numerical Computing 3

In due course, we plan to introduce under graduate program in Applied Mathematics, gradually leading to post graduate studies and research dealing with mathematical problems of applied sciences.

Mathematics for Management Science Program

 

QT 102 Business Mathematics

Introduction to real numbers, fractions, powers, roots, exponentials, and logarithms; use of calculator. Simple polynomials, synthetic division and factorization, quadratic equation formula; simple permutations and combinations. Introduction to rectangular coordinates, distance and midpoint formulas; equation of a straight line, graph and application. Introduction to matrices and determinants; cofactors and matrix inversion; solution of system of linear equations by row operations, Cramer’s rule and matrix inversion. Introduction to finance mathematics; interest laws and application to payment computation, annuities and cost-benefits analysis.

 

QT 201 Advanced Business Mathematics

Algebra:

Review: arithmetic operations and use of calculators; evaluation of powers, roots exponential and logs. Simple equations and inequalities in one and two variables; equation of a straight line, slope –intercept form and linear programming ; business applications. Introduction to matrices, determinants and basic mathematical operations; solution of system of linear equations by simple row operations, Cramer’s rule and matrix inversion; application to business problems.

Financial Mathematics:

Introduction, simple and compound interest laws; payment computation and annuity.

Calculus:

Introduction to functions , graphs , limit and continuity; average rate of change, derivative and basic laws of differentiation; instantaneous rate of change , concavity , maxima , minima , point of inflection and business applications. Integral as antidervative , basic formulas and methods of integration. Definite integral as area under the curve, area of simple figures ,mean values and numerical integration; application to business problem.

Prerequisite: QT 102

 

QT 203 Statistics & Inferences

Introduction to statistical data, data collection and sampling techniques; frequency distribution and graphical representation, measures of central tendency, variation, skewness and kurtosis. Introduction to permutations and combinations; sets and probability, basic laws, simple, combined and conditional probabilities. Introduction to random variables and probability distributions; binomial poisson, and normal distributions and applications. Sampling distributions, estimation of parameters, testing of hypothesis and goodness of fit. Simple linear regression and correlation. Use of statistical tables. Prerequisite: QT 201

 

Mathematics for Computer Science Program

QT 101 Algebra and Trigonometry

Algebra

Real numbers, powers, roots, basic laws of exponentials, logs and numerical computation; introduction to complex numbers and simple mathematical operations. Introduction to polynomial functions, graphs and solution of linear equations; second degree polynomials, graphs and factorization; solution of quadratic equations by factorization, basic formula, graph and nature of roots; simultaneous equations. Introduction to matrixes and determinants, simple mathematical operations, minors, cofactors and matrix inversion; system of linear equations and Cramer rule. Sequences and series; AP, GP and HP series, main properties and numerical problems. Simple permutations and combinations , binomial theorem and approximation; Simple partial fractions involving linear, repeated and quadratic factors.

Trigonometry

Introduction to angle in radians; relation and numerical problems. Trigonometric rations, mutual relations and simple identities; variation in four quadrants and graphs; application to height and distance problem. Sum, difference product, double and half angle formulas of T-ratios; area, sine and cosine formulas of a triangle.

QT 104 Calculus & Analytical Geometry

Basic Mathematics: Complex numbers, rectangular, polar and exponential forms, simple mathematical operations, Demoivre’s theorem, powers and roots. Polynomials functions, remainder theorem, synthetic division, factorization and determinations of roots. Simple functions, standard curves, graphs and main properties.

Differential Calculus limit. continuity, derivatives and basic laws of differentiation; simple application to tangent, normal, velocity, acceleration, maxima, minima; Taylor and Maclaurin’s series and. approximation.

Integral Calculus: Integral as anti -derivative, basic formulas; Methods of integration, definite integral as limit of a sum; application to area of plane figures and volume of simple solids of revolution.

Prerequisite QT 101.

QT 105 Differential Equations and Multivariable Calculus

Vectors in two and three dimensions, dot and cross products, equations of line and plane. Multivariable functions, partial derivatives and differentials. Introduction to ordinary differential equations, simple first order differential equations, second order differential equations with constant coefficients and method of undetermined coefficients. Prerequisite QT 104

QT 303 Numerical Computing

Nonlinear equations and solution by Iterative, Newton Raphson, Regula-Falsi and Secant Methods; systems of linear equations, row operation, solution by Gauss, Jordan, Jacobi, Seidel and Crouts methods and matrix inversion; eigen values and vectors. Introduction to finite differences, interpolation by Gregory Newton Lagrange and divided difference formulas; curve fitting by method of least square and application. Numerical differentiation; integration by Trepizidal, Sympson and Gauss rules. Solution of ordinary differential equations by Euler methods.

Prerequisite: QT105

QT 203 Probability & Statistics

Introduction to statistical data, data collection and sampling techniques; frequency distribution and graphical representation, measures of central tendency, variation, skewness and kurtosis. Introduction to permutations and combinations; sets and probability, basic laws, simple, combined and conditional probabilities. Introduction to random variables and probability distributions; binomial poisson, and normal distributions and applications. Sampling distributions, estimation of parameters, testing of hypothesis and goodness of fit. Simple linear regression and correlation. Use of statistical tables.

Mathematics for BE Program

MS 1303 Calculus

Differential Calculus

Introduction to functions, graphs, limits and continuity. Derivatives as a limit , Basic laws of differentiation, chain rule and implicit differentiation. Derivative as a slope and as a rate of change; tangent and normal, critical points, maxima, minima and point of inflection; optimization. Taylor and Maclaurin series and convergence, L’ Hopital rule and mean value theorem.

Integral Calculus

Integral as anti-derivative, basic formulas and tables, indefinite and definite integrals. Methods of integration: substitution, by parts and partial fractions. Definite integral as limit of a sum, application to area, mean values and volume of solids of revolution. Polar coordinates, simple curves, graphs and area of plane figures ; parametric curves, arc length and surface of a solid of revolution.

Introduction to multivariable functions, partial derivatives and differentials.

Pre-Requisite: Pre-Engg Maths

MS 1302 Linear Algebra

Introduction to complex numbers, geometrical representation and simple mathematical operations; polar and exponential forms, DeMoivre’s theorem, powers and roots.

Introduction to matrices and determinants , simple mathematical operations and special matrices. Simple row operations; Gauss elimination , echelon form , rank, linear independence and system of linear equation ; Gauss-Jordan elimination , matrix inversion and Cramer rule. Vector spaces, basis and dimensions; inner products, Gram- Schmidt process and orthogonalization; eigen values and vectors .

Vectors in space, dot and cross products; physical and geometrical application; equations of lines and planes; curves in space and length of arc; simple surfaces.

Pre-Requisite: MS 1303 Calculus

MS 2304 Differential Equations and Transforms

Introduction to ordinary linear differential equations: formulation, order, degree and linearity of differential equation. First order differential equations; second order homogenous and non homogenous differential equations with constant coefficients, complimentary, particular solutions and method of undetermined coefficients; variation of parameters and Cauchy-Euler differential equation; initial- and boundary-value problems; solution in series. Introduction to Laplace transformation; Laplace transform of simple functions and tables; Laplace inversion by partial fractions and convolution , application to initial value problems. Introduction to unit step and delta functions, Laplace transform of discontinuous, periodic and discrete phenomena.

Introduction; periodic functions and Fourier series; half range Fourier series, Fourier integrals and transforms of simple functions. Introduction to partial differential equations and method of separation of variables.

Pre-Requisite: MS-1303 Calculus

MS 2305 Complex Variable and Multivariable Calculus

Complex variable

Complex variable and functions; analytic functions , Cauchy-Riemann equations, derivatives, orthogonal and harmonic properties of conjugate functions. Introduction to Complex integration: Cauchy integral theorem, Cauchy integral formula, poles , residues and residue theorem; contour integration; improper integrals.

Multivariable Calculus

Introduction to Multivariable integration; evaluation of area and volume of simple geometrical figures. Scalar and vector fields; Del operator, gradient, divergence, curl and laplacian; vector differential calculus. Line, surface and volume integrals; Green, Stokes and Gauss theorems. Simple applications.

Pre-Requisite: MS 1302 Linear Algebra

MS 2304 Differential Equations and Transforms

MS 3306 Probability Methods in Engineering

Introduction to statistical data, frequency distribution and graphical representation. Measures of central tendency and variation. Basic concepts of probability, simple combined and conditional probabilities, independent events, Baye’s theorem and application. Introduction to random variables; discrete and continuous probability distributions (binomial, poisson, normal, uniform and exponential); probability density function, expected values, mean, variance and standard deviation. Sampling distributions, estimation of parameters, testing of hypothesis and goodness of fit. Scatter diagram, linear regression , coefficients of correlation and determination; inferences. Use of SPSS.

Pre-Requisite: MS-1303 Calculus

MS 4307 Numerical Methods (3 + 0)

Introduction to numerical methods and estimation of errors. Non linear algebric equations; Newton-Raphson , secant and Regula falsi methods; system of linear equations and LU method; Eigen values and Eigen vectors by power method. Calculus of finite differences and interpolation (equal and unequal intervals); curve fitting by least squares. Numerical differentiation; numerical integration by trapezoidal, Simpson and Gauss rules. Solution of first order ordinary differential equations by Euler and Runge – Kutta methods; system of linear differential equations. Introduction to numerical solution of partial differential equations. Use of MATLAB.

Pre-Requisite: MS 1302 Linear Algebra

MS 2304 Differential Equations and Transforms

Author

Title of Paper

Name of Journal

Ms Sahar Altaf

An efficient haar wavelet technique for solution of fractional partial differential equation.

 Science International ,Lahore

Ms Sahar Altaf

Analyzing Human Communities using Fuzzy Graphs.

Pakistan Journal of Engineering, Technology & Science

Ms. Kahkashan Iqbal

When is the center of a near ring It’s sub near ring?

39th Annual Iranian Mathematics Conference (published in proceedings)

Ms.Kahkashan Iqbal

Assessment Using MATLAB- A Project Overview

Published in electronic proceedings of ATCM’08 Bangkok

Mr.Wajdan Raza

A Rating Scale to Assess English Speaking Proficiency of University Students in Pakistan

International Conference on Language Teaching and Learning in October-2008 at Panang (Malaysia)

Ms.Kahkashan Iqbal

On Units in Near Rings

Published in Technology Force of PAF-KIET/ LUMS 2nd International Conference on Mathematics (LICM’08)

Mr.Shahbaz Khan &

Ms.Kahkashan Iqbal

Students; absents during semester: A simulation based study

Presented in 2nd Mathematics Colloquium 2008 at Institute of Business Management

Ms.Kahkashan Iqbal

Study of Commutativity in Matrix Near Rings

Ohio University Conference of Alg & its Application

Ms.Kahkashan Iqbal

Quantitative Analysis on Data of Sales of Honda Atlas Cars Pakistan Ltd.

Presented in 1st Mathematics Colloquium 2007 at Institute of Business Management

Ms.Kahkashan Iqbal

How learning and teaching of Mathematics can be made interesting: a case study

Presented in the Twelfth Asian Technology Conference in Mathematics / Published in electronic proceeding of ATCM’07.

Mr.Wasi Zaidi

The Roaring Nineties (Book Review)

Published in Market Forces of PAF-KIET

Mr.Irfan Sheikh

‘Identity and Violence: The Illusion of Density’ (Book Review)

Published in Market Forces of PAF-KIET

Ms.Kahkashan Iqbal

Some Remarks on Matrix Rings (An Article)

Published in Technology Force of PAF-KIET

Ms.Kahkashan Iqbal

On Near – Integral Domain

Published in Technology Force of PAF-KIET/LUMS Summer Conf.2007

Welcome to Humanities & Sciences Faculty

The faculty is keen to prepare students for positions of greater responsibility in their chosen field of profession and aims to inspire students to develop specialized skills. The faculty aims not just to pass on human capital but also social capital in the form of social norms and rules to participate more effectively in the formal and informal events in the society.

The Faculty of Social Sciences encourages students to combine their theoretical knowledge of the contemporary world with an understanding of the cultural and political processes to participate more effectively in the formal and informal events, which it does through the students’ Societies at the Institute.

 

Permanent Faculty Profiles

Dr.-Amin

Prof. Dr.Muhammad Amin
MSc, Applied Math (PU)
PhD, DIC Imperial College, London (UK)

Professional Profile:
Director College of Humanities & Sciences, PAF-KIET, 2002 – Present.
Professor at Usman Institute of Technology, Hamdard University, 1995 to 2002
Professor of Mathematics, Navy Engg. College, 1987 to 1994
Professor & Head (HS) at PAF-CAE, NED from 1966 to 1987
Associate Professor at University of Engineering and Technology, Lahore, 1953 to 1966

Research Interest:
Application of Mathematics in Science and Engineering.

shabaz

Mr. Muhammad Shahbaz Khan
MS (Statistics and Soft Computing), IoBM
MSc Statistics University of Karachi    

Profile:
Assistant Professor, PAF-KIET since 2001
Lecturer, Department of Statistics, UoK
Statistician, MAB/ Paradigms 2004-2005
17 years experience of teaching in Statistics and Mathematical courses at various Institutions.(PAF-KIET, SZABIST, and IoBM)

Research Interest: 
Fuzzy time series
Design of experiments

sahar

Ms. Sahar Altaf
PhD Mathematics, IoBM (in progress)
MS, Applied Mathematics, IoBM
MSc, Mathematics, University of Karachi

Profile:
Assistant Professor, PAF-KIET since 2013
Visiting Faculty member, PAF-KIET, 2012
Visiting Faculty member, IoBM since 2013
Permanent Lecturer, University College 2011
7 years experience of teaching Mathematics at various Institutions

Research Interest: 
Applied Mathematics and Computation
(Partial Differential Equation Numerical Analysis Non- Linear waves & dynamics)

faraz

  Mr. Ahmed Faraz Ayubi
MS, Applied Mathematics, NED-UET
MSc, Mathematics, University of Karachi

Profile:
Assistant Professor, PAF-KIET since 2014
12 years experience of teaching Mathematics at various Institutions

Research Interest: 
Differential Equation

amara

Ms. Ammarah Nazakat
MS, Applied Mathematics, NED-UET
MSc, Mathematics, University of Karachi  

Profile:
Permanent Faculty member, PAF-KIET since 2016
Visiting Faculty member, PAF-KIET, 2015
Visiting Faculty member, Dadabhoy Institute of Higher Education.
Co-operative Lecturer, NED University
6 years experience of teaching Mathematics at various Institutions

Research Interest: 
Numerical Analysis
Differential Equation

Mr.-Jamil-Ahmed-122x146

Mr. Jamil Ahmad
MSc, Mathematics, Almeda College University (U.S.A)

Profile:
Permanent Faculty Member, PAF-KIET since January, 2017.
Visiting Faculty member, PAF-KIET since 2011 to 2015.
31 years experience of teaching Mathematics at various Institutions.


Mr. Muhammad Imran
MS, Mathematics, Bacha Khan University, Khyber Pakhtunkhwa
MSc, Mathematics, Gomal University D-I-Khan    

Profile:
Permanent Faculty Member, PAF-KIET since January, 2018.
Lecturer at DHA Suffa University since 2015 to 2017
Lecturer at Gandahara Institute of Engineering and Technology Peshawar,2015
Lecturer at Kardan University, Kabul, Afghanistan Since 2010 to 2014.
Lecturer in Government Degree College Landikotal Khyber Agency Since 2008 to 2009.
Section Officer / Internee in Civil Secretariat Peshawar Education Department Sine 2007 to 2008.
10 years experience of teaching Mathematics at various Institutions.


Adjunct Faculty Profiles

saeed

Mr. Muhammad Saeed    
MSc, Applied Maths University of Karachi

Profile:
Visiting Faculty member, PAF-KIET since 2010
12  years experience of  teaching Mathematics at various Institutions


Pervez-Akhtar-122x150

Mr. Pervaiz Akhter Abbasi
MA Applied Mathematics University of Karachi

Profile: 
Visiting Faculty member, PAF-KIET since 2010.
Visiting Faculty member IoBM since 2014
Visiting Faculty member KASBIT since 2015
26 years experience of teaching Mathematics at various Institutions


ismail

Mr. Ismail Khan
MS, Statistics and Soft Computing (In process), IoBM
MSc, Applied Mathematics University of Karachi

Profile:
Visiting Faculty member, PAF-KIET since 2012
Visiting Faculty member, FAST-National University
6 years experience of teaching Mathematics at various Institutions.


amanullah

Mr. Syed Khawaja Amanullah
Mphil leading to Phd, Mathematics (KU)
MCS; Applied Mathematics (KU)

Profile:
Visiting Faculty member, PAF-KIET Since 2008.
Permanent faculty member, CS department PAF-KIET, 2001-2008.
Visiting Faculty member, DHA Suffa University.
Visiting Faculty member, Bharia University.
Lecturer, Operational Research & Statistical Inference, UoK
External evaluator for computer sciences courses, ICMAP
Visiting Faculty member, IoBM, 2000-2004.
Assistant Professor, Government Degree Science and Commerce College.
16 years experience of teaching Mathematics at various Institutions.


Najumddin-122x150

Mr. Muhammad Najam Uddin
PhD (Pursuing), Statistics, University of Karachi
Phil, Statistics, University of Karachi
MSc, Statistics (Gold medalist), University of Karachi

Profile:
Visiting Faculty Member, PAF-KIET since 2012.
Visiting Faculty Member, IBA
Visiting Faculty Member, Bahria University
Lecturer, (Statistics) Federal Urdu University since 2009
More than 10years’ experience of teaching Statistics &Mathematics at various Institutions.


Dr. Muhammad Tahir
PhD, (Economics) University of Karachi
MSc, (Economics & Econometrics), University of Essex, UK
M.Phil, (Economics), IoBM
M.A.S, (Applied Economics) from AERC, UoK MBA, (IBA) 

Profile:
Visiting Faculty, PAF-KIET
Visiting Faculty member, IoBM
Visiting Faculty member,(Economics & Statistic Department) UoK
Visiting Faculty member, Bharia University
Visiting Faculty member, ZABIST
Deputy Director (M&E) Economist,
Head of Examination and paper setter, Board of Intermediate Education
Head of Examination and paper setter, Graduation Level, UoK
17 years experience ofteaching Statistic & Economics at various


Mr. Zia Uddin
Phil Computer Science, University of Sindh
M.C.S University of Karachi
MSc Economics, University of Karachi

Profile:
Visiting Faculty, PAF-KIET Since 2005
Visiting Faculty, IoBM Since 2005
Permanent Faculty member & Asst. Controller Examination, BIZTEK since 2004
Co-operative Lecturer and Network Administrator, Govt, College for Women since 2001.
Database Administrator, IMIT since 2002.
Visiting Faculty member, Preston University.
16 years experience of teaching Mathematics at various Institutions.


Mr. Imran Shaheen
MS/PhD Mathematics, (IBA) in progress
MSc. Mathematics, University of Karachi

Profile:
Visiting Faculty, PAF-KIET Since 2016
Teaching assistant of Mathematics at IBA
Lecturer of Mathematics and Statistics at SAIMS
Lecturer of Mathematics and Statistics at KIMS
Lecturer of Mathematics and Statistics at IBAAS
Lecturer of Mathematics and Statistics at PALPA
Lecturer of Mathematics Department of Mathematics, University of Karachi


Ms. Atifa Mehmood
MSc. Mathematics, University of Karachi

Profile:                        
Visiting Faculty, PAF-KIET Since 2017
Permanent Faculty Member,  at PAF-KIET 2011-2013
Lecturer of Mathematics and Statistics at Pakistan Institute of Professional Sciences 2009-2011.
Lecturer of Mathematics and Statistics at College of Management and Sciences 2009-2011.
Lecturer of Mathematics and Statistics at MIDASIA Institute 2009.
Lecturer of Mathematics and Statistics at Indus Public College 2008-2011.


Mr. Fazal Tariq
MS, Applied Mathematics, NED-UET
MSc, Mathematics, Federal Urdu University  Karachi  

Profile:                                             
Visiting Faculty, PAF-KIET Since 2018
Lecturer, Quaid-e-Azam Rangers School.
Lecturer, College North Nazimabad Campus


Mr. Rizwan Ur Rashid
PhD Mathematics, University of Karachi (in progress)
MS, Computer Science, NED-UET
MIBM, Master in Industrial & Business Mathematics, University of Karachi

Profile:                                             
Visiting Faculty, PAF-KIET Since 2016
Director R&D and HR in BDMC 2015
Associate Professor at MAJU 2005-2015
Permanent Faculty Member, at PAF-KIET 2000-2005
Visiting Faculty, Bharia University 2014.
Visiting Faculty, SZABIST 2004 – 2013.
Visiting Faculty, IoBM 2001 – 2003.
Visiting Faculty, Commecs Institute in 1997.