Mathematics and Physics play an important role in understanding the fundamental laws of nature and it directly correlates the other fields of engineering and natural sciences. Understanding the importance and necessity of acquiring knowledge about the most exciting and interesting branch of science and engineering, Department of Mathematics and Physics belongs to the School of Engineering and Physical Sciences.
The Department of Mathematics and Physics is one of the dynamic departments of North South University, which incorporates fundamental, experimental and mathematical study. We are committed to excellence in teaching and research. All our faculty members are highly qualified and they are responsible for teaching the Mathematics, Physics and Statistics courses offered by the University. Twelve of our sixteen fulltime faculty members are Ph.D. s from North America or Western Europe. The breadth of expertise of our faculty members covers almost the entire range of mathematics and physics, pure as well as applied. They are active in all branches of stateofart research which include, but not limited to, the following topics:
Department of Mathematics and Physics (DMP), North South University (NSU), celebrated the pimoment of the century at the campus. Pi is the ratio of the circumference of a circle to its diameter. It is symbolized by the greek letter pi in the lower case (π). This is a fixed quantity, which is usually taken to be 3.14. The number of digits after the decimal is infinite. In the western countries, especially in the US, March 14 (written 3/14 in the American style) is celebrated every year as the piday. March 14 this year is a bit more special. The first ten digits of the value of pi, i.e., 3.141592653 can be arranged as March 14, 15, 9:26:53. We call this special moment as the pimoment. This moment will come again in 2115, one hundred years later.
At this precise moment (according to Bangladeshtime) of this century, students from various departments of NSU participated in a celebration of the moment. They formed a human circle with a diameter. Then dividing the number of people in the circumference by the number of people in the diameter yielded a value close to the actual value of pi. They did the same thing with chairs. At the end a large number of people formed the shape of the symbol π.
Professor Partha Pratim Dey, the chairman of the Department was present at the event along with a few other faculty members, namely, Kazi Abu Sayeed, Hasina Akter, and Muhammad Asaduzzaman. A few part time faculty members were present as well as Golam Dastegir Al Quaderi, a faculty member of the Physics Department at Dhaka University, who participated as a guest. The initiative was taken by Naureen Ahsan, a part time faculty member at NSU and a full time faculty member at Dhaka University.
Pimoment of the century, March 14, 15 9:26:53
Chairman of DMP is seen with faculty members and students.
The human circle yielded a close value to pi A chair circle yielded an even closer value to pi
A human pi symbol
Name of Fculty  Area of Research 
Dr. Partha Pratim Dey  Coding Theory, Mathematical Modeling 
Dr. Miftahur Rahman  Control Systems and CNC Machine 
Dr. Muhammad Nurul Islam  Stochastic Models, Generalized Linear Models, Statistical Genomic 
Dr. Abu M Khan  Theoritical High Energy Physics 
Dr. Mamun Molla  Computational Fluid Dynamics, Parallel Computing 
Dr.Mohammad Sahadet Hossain  Systems and Control Theory, Model Order Reduction, Scientific Computing 
Dr. Subir Chandra Ghosh  Nanometarils and Solar Energy 
Dr. Muhammad AsadUzZaman  Nonlinear Dynamics 
Dr. Hasina Akthar  Dynamical Systems and Ergodic Theory 
Dr. Mohammad Monir Uddin  Systems and Control Theory, Model Order Reduction, Numerical Liner Algebra and Scientific Computing 
Dr Samash Faruki  
Mr. Muhammed Mustak Mia  Computational Fluid Dynamics 
Mr. Zasim U. Mazumder  Pulse Propagation 
Mr. Mahabub Saheen  
Md. Zahangir Hossain  Computational Fluid Dynamics 
Mr. Abu Naser  Numerical Analysis & Scientific Computing 
S M Erfanul Kabir Chowdhury  
Sharmin Sultana 
Projects  Coordinators 
Dr. Partha Pratim Dey  
Dr. Mamun Molla  
Reduced order modeling of periodic control systems with application to circuit problems 
Dr.Mohammad Sahadet Hossain 
Structure Preserving Model Reduction of LargeScale Second Order Dynamical Systems Using the PDEG Method and Application to Some Real Problems 
Dr. Mohammad Monir Uddin 
Dr Samash Faruki 
• Lattice Boltzmann Simulation of Airflow and Heat Transfer in a Model Ward of Hospital; M. F. Hasan, T. A. Himika, M. M. Molla ; J. Thermal Science and Engineering Applications, Vol. 9, 0110111, 2017, DOI 10.1115/1.4034817.
• Structure preserving model order reduction using the projection onto the dominant Eigenspace of the Gramian (PDEG) ; M. M. Uddin; in international conference on Electrical, Computer and Communication Engineering (ECCE ), IEEE, 2017, pp. 197202, 2017.
• Efficient techniques to solve the periodic projected Lyapunov equations and model reduction of periodic systems ; M. Sahadat Hossain and M. M. Uddin; Mathematical Problems in Engineering, Vol. 2017, 2017, 11 pages.
• Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems; P. Benner, M. Sahadet Hossain; Numerical Algorithms (Springer), pp. 124, 2017, DOI 10.1007/s110750170288y.
• On Quinary ErrorCorrecting [6,4] Codes; P. Dey, A. K. Ghosh; Journal of DiscreteMathematical Sciences & Cryptography, Vol. 19 (2), pp. 405411, 2016
• LargeEddy Simulation of Pulsatile Flow through a Channel with Double Constrictions; M. M. Molla, M. C. Paul; Fluids, Vol 2017 (2), pp. 119 (2016).
• Prediction of Heat Transfer to FullyDeveloped Pipe Flows with Modified Powerlaw Viscosity Model Fluid ; M. M. Molla, S. G. Moulic, LS Yao; Journal of Mechanics, Vol. 1(1), pp.147, 2016.
• Lattice Boltzmann simulation of airflow and mixed convection in a general word of hospital ; T. A. Himika, M. F. Hasan, M. M. Molla; J. Engineering Computation, Vol. 2016, 15 pages, 2016.
• Natural convection flow of Nanofluid along a vertical wavy surface; F. Habiba, M. M. Molla, M. A. H. Khan; AIP Conf. Proc. 1754, 050018, 2016.
• Natural convection flow in porous enclosure with localized heating from below with heat flux ; M. N. A. Siddiki, M. M. Molla, S. C. Saha; AIP Conf. Proc. 1754, 050016 (2016).
• Natural convection of nonNewtonian fluid along a vertical thin cylinder using modified powerlaw model; S. Thohura, M. M. Molla, M. M. A. Sarker; AIP Conf. Proc. 1754, 040021, 2016.
• Largeeddysimulation of air flow and heat transfer in general ward of hospital using lattice Boltzmann method; F. Hassan, T. Himika, M. M. Molla; AIP Conf. Proc. 1754, 050022 (2016)
• Model Reduction of TimeVarying Descriptor Systems:Numerical Methods, Algorithms, and Applications; Mohammad Sahadet Hossain; Publisher: Scholars' Press, Germany.ISBN: 9783659840012
• ProjectionBased Model Reduction for TimeVarying Descriptor Systems: New results; MohammadSahadet Hossain; Numerical Algebra, Control and Optimization (NACO); PublisherAmerican Institute of Mathematical Sciences(AIMS), vol. 6(1), pp. 7390, 2016.
• Structure preserving mor for large sparse second order index1 systems and application to a mechatronic model ; P. Benner, J. Saak, and M. M. Uddin; Mathematical and Computer Modelling of Dynamical Systems, Vol. 22 (6), pp. 509523, 2016.
• Balancing based model reduction for structured index 2 unstable descriptor systems with application to ow control ; P. Benner, J. Saak, and M. M. Uddin; Numerical Algebra, Control and Optimization (AIMS), Vol. 5(1), pp. 120, 2016.
• Reducedorder modeling of index1 vibrational systems using interpolatory projections ; P. Benner, J. Saak, and M. M. Uddin; in 19th International Conference On Computer and Information Technology (ICCIT), IEEE. pp. 134138, 2016.
• Rational Krylov subspace method (RKSM)for solving the Lyapunov equations of index1 descriptor systems and application to balancing based model reduction ; M. M. Uddin, M. S. Hossain and M. F. Uddin; in 9th International Conference on Electrical and Computer Engineering, IEEE, pp. 451 454, 2016.
• Parametric study on thermal performance of horizontal earth pipe cooling system in summer; S. F. Ahmed, M. T. O. Amanullah, M. M. K. Khan, M. G. Rasul, and N. M. S. Hassan; Energy Conversion and Management, vol. 114, pp. 324337, 2016.
• Lax Pairs and Integrability Conditions of HigherOrder Nonlinear Schr ̈odinger Equations; M. Asaduzzaman, H. Chachou Samet, U. Al Khawaja; Communications in Theoretical Physics, Vol. 66(2), 2016.
Department of Mathematics and Physics (DMP) offers following twenty three (23) courses:
Code  BUS112 
Credit hours  0 
Textbook 

Prerequisites  High School Mathematics. 
Course Content  Fundamentals of Algebra: Real Numbers, Fundamentals of Algebra: Exponents, Polynomials, Fundamentals of Algebra: Factoring, Rational expressions, Radicals, Linear equations, Formulas and Applications, Quadratic equations, Other types of Equations, Inequalities, Cartesian Coordinate systems, Graphing Relations, Functions, Linear Functions, Equations of a line, Symmetry, Algebra of Functions, Inverse Functions, Quadratic Functions, Synthetic Division, Exponential Functions, Logarithmic Functions, Equations on Exponential and Logarithmic functions, Systems of Equations, Systems of Inequalities; Linear Programming, Matrix Solution of Linear Systems, Properties of Matrices, Determinants, Cramer's rule, Matrix Inverse. 
Code  MAT116 
Credit hours  0 
Textbook 

Prerequisites  High School Mathematics. 
Course Content  Behavior of functions in some depth including properties, graphs, inverses, transformations, and compositions. This course pays particular attention to linear, quadratic, polynomial, rational, exponential, and logarithmic functions. It covers trigonometric functions and inverse trigonometric functions as well. 
Code  MAT120 
Credit hours  3 
Textbook 

Prerequisites  MAT116. 
Course Content  Tangent lines; limits and continuity; differentiation: definition, basic rules, chain rule, rules for trigonometric, inverse trigonometric, exponential and logarithmic functions; implicit differentiation; rates of change, related rates problems, linear approximation and differentials; L'Hospital's rule; concepts of local and absolute maximum and minimum including first and second derivative tests; integration: definition, antidifferentiation, area; integration by simple substitution; Fundamental Theorem of Calculus. 
Code  MAT125 
Credit hours  3 
Textbook 

Prerequisites  MAT116 or an adequate test score. 
Course Content  Homogeneous and Nonhomogeneous System of Linear Equations, Echelon form, Gaussian Elimination Method (unique, infinite numbers and no solutions)Properties of Determinants, Determinant by Cofactor Expansion, Evaluating Higher Order Determinants by Row Reduction, Cramer’s Rule .Matrices and Matrix Operations, Transpose, Properties of Transpose, Triangular, Symmetric and Skew Symmetric Matrices, Inverse, Properties of Invertible Matrices,Method of Finding the Inverse of a Matrix, Further Results on System of Linear Equations using Inverse Matrix Technique, Rank .Introduction to Vectors, Vector addition and Scalar multiplication, Norm of a vector, Dot Product, Projections, Euclidean nSpace, Real Vector Space, Subspace, Linear Combinations, Linear Dependence and Independence, Spanning Set, Basis, Dimensions, Solution Space, Null Space, Rank and Nullity. General Linear Transformation, Kernel and Image of Linear Mapping, Rank and Nullity of Linear Mapping. Eigenvalues and eigenvectors, Cayley Hamilton Theorem, Diagonalization.Geometric Linear Programming, Applications in Business and Economics. 
Code  MAT130 
Credit hours  3 
Textbook 

Prerequisites  MAT120. 
Course Content  Area between two curves, Length of plane curves, Area of surface of revolution, Volumes by slicing disks and washers, Volumes by cylindrical shells, Hyperbolic functions and hanging cables & Integrations. Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integrating rational functions by partial fractions, Improper integrals.Polar coordinates, Area in polar coordinates, Tangent lines and arc length for parametric and polar curves, Conic sections in calculus. 
Code  MAT240 
Credit hours  3 
Textbook 

Prerequisites  MAT130. 
Course Content  Sequences, Monotone Sequences, Infinite Series, Convergence Test, The Comparison, Ratio, and Root Tests, Alternating Series; Conditional Convergence, Maclaurin and Taylor Polynomials, Maclaurin and Taylor Series; Power Series.Rectangular Coordinates in 3Space; Spheres; Cylindrical Surfaces , Vectors, Dot Product; Projections, Cross Product, Parametric equations of lines, Planes in 3space, Quadric Surfaces, Cylindrical and Spherical Coordinates.Introduction to Vector Valued Functions, Calculus of Vector Valued Functions, Change of Parameter; Arc length, Unit Tangent, Normal, and Binormal Vectors, Curvature. 
Code  MAT250 
Credit hours  3 
Textbook 

Prerequisites  MAT240 
Course Content  Infinite Series, Vector Valued Functions, Functions of two variables, Limit and Continuity, Partial Derivatives. Differentiability and Chain Rule, Directional Derivatives and Gradients.Tangent Planes and Normal Vectors, Maxima and Minima of Functions of two variables, Double Integrals over rectangular regions, Double Integrals over nonrectangular regions. Double Integrals in Polar Coordinates, Triple Integrals, Centroid, Center of Gravity, Change of variables in Multiple Integrals; Jacobean. Triple Integrals,Vector fields and vector valued function, Line integrals, Green’s Theorem, Surface Integrals, The Divergence, Theorem, and Stokes Theorem. 
Code  MAT350 
Credit hours  3 
Textbook 

Prerequisites  MAT250 
Course Content  Complex analysis, Fourier series and transforms, Laplace transforms and the solution of ordinary differential equations, in particular Bessel function and Legendre polynomials. 
Code  MAT361 
Credit hours  3 
Textbook 

Prerequisites  MAT250 
Course Content  Basics of elementary probability theory; discrete and continuous random variables along with their probability distributions(cumulative distribution function; expected values and variance); special random variables: Bernoulli, binomial, geometric, negative binomial, Poisson, hypergeometric, uniform, exponential and normal distributions);multivariate distributions(joint distributions; marginal and conditional distributions; covariance and correlation); descriptive statistics and sampling distribution of statistics;parameter estimation by moment and maximum likelihood method; comparing the performance of estimators using properties of unbiasedness, efficiency and minimum variance; confidence interval estimation for the mean and difference of two means; hypothesis testing on mean and difference of two means. 
Code  MAT370 
Credit hours  3 
Textbook 

Prerequisites  MAT250 
Course Content  The Real Numbers, Sequences, Limits, Continuity and Uniform Continuity of Real Variable Functions, Differentiation, The Sequences of Functions and their Convergence, The Riemann Integral, Fundamental Theorem of Real Calculus and its Proof, Complex Variable Functions, Limits and Continuity of Complex Functions, Derivative, Analyticity, CauchyRiemann Equations, Fundamental Theorem of Complex Calculus and its Proof. 
Code  MAT480 
Credit hours  3 
Textbook 

Prerequisites  MAT250 
Course Content  Introduction to Differential Equations, Firstorder Differential Equations, Applications of first order Differential Equations, Linear Differential Equations of higherorder, Applications of secondorder Differential Equations with variable coefficient, Systems of Linear Differential Equations. 
Code  MAT490 
Credit hours  3 
Textbook 

Prerequisites  MAT250 
Course Content  Laplace Transform, Existence of Laplace Transform, Inverse Laplace Transform, Laplace Transform of Derivatives and Integrals, Shifting on the saxis, Shifting on the taxis, Differentiation and Integration of Laplace Transform, Convolution, Inverse Laplace Transform of partial Fractions, Inverse Laplace Transform of periodic Functions, Fourier Series FS for Functions of Period 2p or arbitrary period, Fourier Series for Even and odd Functions, HalfRange Fourier Expansion, Determination of Fourier Coefficients without Integration, Fourier Approximations and minimum square error, The Fast Fourier Transform, Complex Variable Functions, Limits and Continuity, Derivatives, Analyticity and CauchyRiemann Equations, Conformal Mapping, Relation between Analyticity and Coformality, Mobius and other Transformations, Complex Integrals, Cauchy Integral Formulae, Taylor’s Series, Singular Points, Laurent’s Series, Residues and Residue Theorem, Evaluation of Real Definite Integrals using Complex Integrals. 
Code  MAT495 
Credit hours  3 
Textbook 

Prerequisites  MAT250 
Course Content  Sets and Equivalence Relations, Semigroups&Monoids, Free Semigroup& Free Monoid, Congruence Relations and Quotient Structures, Fundamental Theorem of Semigroup Homomorphism, Groups, Sn, Zn, Subgroups, Normal Subgroups, Generating Sets, Generators, Fundamental Theorem, Lagrange’s Theorem, Quotient Group, Cyclic Subgroups, Generating Sets, Generators, Fundamental Theorem of group Homomorphism, Rings and Ideals, Fundamental Theorem of Ring Homomorphism, Integral Domain, Principal Ideal Domain, Divisibility in Integral Domain, Unique Factorization Domain, Field, K [T] the polynomials over a field K, K [t] as a Principal Ideal Domain and Unique Factorization Domain, Fundamental Theorem of Algebra, Ordered Sets and Lattices, Principle of Duality, Bounded Lattices, Distributive Lattices, Complemented Lattice. 
Code  PHY105 
Credit hours  3 
Textbook 

Prerequisites  None 
Course Content  Vectors, equations of motions, Newton’s laws, conservation laws of energy, linear momentum, WorkEnergy theorem, extension of linear into rotational motion including the conservation laws, gravitation, simple harmonic motion, travelling waves, calorimetry, thermal equilibrium, 1st and 2nd laws of thermodynamics. 
Code  PHY105L 
Credit hours  1 
Textbook 

Prerequisites  PHY105 
Course Content  Introduction to Measurements and Statistical Error, Force table, Atwood machine, Hook’s law, Massspring oscillation, Simple pendulum, Compound pendulum and Static equilibrium. 
Code  PHY107 
Credit hours  3 
Textbook 

Prerequisites  MAT120 and Physics in HSC/A Level 
Course Content  Vectors, equations of motions, Newton’s laws, conservation laws of energy, linear momentum, WorkEnergy theorem, extension of linear into rotational motion including the conservation laws, gravitation, simple harmonic motion, travelling waves, calorimetry, thermal equilibrium, 1st and 2nd laws of thermodynamics. 
Code  PHY107L 
Credit hours  1 
Textbook 

Prerequisites  PHY107 
Course Content  Introduction to Measurements and Statistical Error, Force table, Atwood machine, Hook’s law, Massspring oscillation, Simple pendulum, Compound pendulum and Static equilibrium. 
Code  PHY108 
Credit hours  3 
Textbook 

Prerequisites  MAT130 and PHY107 
Course Content  Electricity and Magnetism: Coulomb’s Law,Electric field and Gauss’s Law, Potential, Capacitance field, Magnetic forces,Induced Electromotive force,AC circuit.Electric Field and Potential: Conceptually, Electric Field and Potential: Discrete System , Electric Field and Potential: Continuous System, Electric Field and Potential: Gauss’s Law, Capacitors and Capacitance, Dielectric, Ohm’s Law, Circuit Theory, Magnetic Force I, Magnetic Force II, BiotSevert Law, Ampere’s Law, Inductance I, Inductance II, Alternating Fields and Current I, Alternating Fields and Current II, Maxwell’s Equation, Magnetic Properties of Matter. 
Code  PHY108L 
Credit hours  1 
Textbook 

Prerequisites  PHY108 
Course Content  Introduction to electric equipment, Verification of Ohm’s law, Charging and Discharging of capacitor, Time constant of a Circuit with resistor and capacitor in series and Magnetic induction. 
Code  BSC201 
Credit hours  3 
Textbook 

Prerequisites  None 
Course Content  Representation of functions numerically, graphically and algebraically, linear, quadratic, polynomial, rational, root/power, piecewisedefined, exponential, logarithmic, trigonometric and inverse trigonometric functions. The algebraic structure and graph of a function, intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes. Concept of heat, temperature, laws of thermodynamics, and different types of thermal processes. The kinetic theory of gases, specific heat of ideal gases, Maxwell’s laws of equipartition of energy and related problems. 
Code  MAT140 
Credit hours  3 
Textbook 

Prerequisites  MAT230 
Course Content  Probability and the laws of probability. Conditional probability. Independence. Expectation. Discrete and continuous distributions. Point and interval estimation. Regression and Correlation. Illustrations from Engineering. 
Code  MAT230 
Credit hours  3 
Textbook 

Prerequisites  MAT130 
Course Content  Linear Algebra: Definition of matrix. Algebra of matrices. Multiplication of matrices. Transpose of a matrix and inverse of matrix. Rank and elementary transformation of matrices. Solution of linear equation. Linear dependence and independence of vectors. Matrix polynomials. Determination of characteristic roots and vectors. Null space and nullity of matrix. Quadratic forms.Vector Analysis: Vectors: Scalar and vector products and associated geometrical interpretation. Vector field, gradient field, divergence and curl of a vector field, Line integral, Green’s theorem, Surface integral, Divergence theorem, Stokes’ theorem. 
Code  MAT260 
Credit hours  3 
Textbook 

Prerequisites  MAT130 
Course Content  efinition of ordinary differential equation, Solution of first order ordinary differential Equations by various methods, Solution of second order ordinary differential equations with constant coefficients, Series solutions of ordinary differential equations by power series and Frobenius series, Solution of Bessel’s equation and Legendre’s equation. Definition of partial differential equations, Derivation of classical partial differential equations and their solutions. 
The Department of Mathematics and Physics is located on the 10^{th} floor of the SAC building. It does not offer an undergraduate degree like a Bachelor of Science degree in Mathematics or Physics yet. It is because the department came into existence only six months ago. However, the department serves a significant number of students through a wide range of service courses. It primarily imparts the mathematics and physics training for the undergraduate students of the university. The department also runs a thirty–credit minor program in mathematics.
Currently we have fulltime and parttime faculty members in our department. Ten of our thirteen fulltime faculty members are Ph.D. s from North America or Western Europe. The parttime faculty members are from among the best faculty members of the reputed universities in Dhaka like Dhaka University, Bangladesh University of Engineering and Technology etc. The breadth of expertise of our faculty members covers almost the entire range of mathematics and physics, pure as well as applied.
We have a plan to transform our department from present service position to a fullfledged Department of Mathematical Sciences, which among other things will offer a major in mathematics as well as a major in Physics. I believe, given our faculty strength, this transformation should be a piece of cake.
Partha Pratim Dey
Professor & Chair
Department of Mathematics and Physics (DMP)
Title: Efficient Reduced Order Modeling of Periodic Control Systems with Application to Circuit Problems.
Abstract:
In this seminar, we have presented a method for the model order reduction of continuous linear timevarying (LTV) periodic descriptor systems where the system's matrices are singular. This model order reduction strategy is based on the linear timeinvariant (LTI) reformulation of the LTV model through suitable discretization scheme. The resulting linear timeinvariant (LTI) system is then reduced using balanced truncation model reduction method. We use the LowRank Cholesky Factorized Alternating Directions Implicit (LRCFADI) iteration to approximate the solutions of the corresponding timeinvariant Lyapunov equations. Due to the singularity of the system's matrices, we have used the Pseudoinverses to find the optimal shift parameters that are used in LRCFADI approximation. The step responses, bode plots and eigenstructures of both the original and reduced system are compared to show the accuracy of the proposed model reduction approach.
Postal Address:
Department of Mathematics and Physics
North South University
Plot 15, Block B
Bashundhara,
Dhaka 1229
Bangladesh
PABX: +880 2 55668200 (Ex 1561)
Fax: +880 2 55668202
Email: info_dmp@northsouth.edu
Website: http://www.northsouth.edu/academic/seps/dmp.html