Program Announcement 2013 - 14 - Institute of Business ...

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Description of Courses172Department of Mathematical SciencesMATHEMATICS COURSESMTS101 Calculus-1 & Plane GeometryThis course develops concepts of Functions and Algebraof Functions, Limits and Continuity of Functions,Derivability and Differentiability. After handling thebasic concepts, deeper indulgence in theoreticalconcepts such as the Mean Value Theorems, Higherderivatives, Generalization of Mean Value theorem,Taylor's and McLaurin's Expansions, Curve Sketchingand other applications of derivatives are taught.Students also explore Integral Calculus by studyingAnti-Derivatives and techniques of Integrations,Riemannian Sum, Fundamental Theorem of IntegralCalculus. Curves in a plane, differential and integralproperties of curves. Successful completion impliesthorough understanding of basic univariate calculus.Pre-requisite: College Algebra or Inter/A-Level Math.MTS102 Introduction to StatisticsThis is intended as an introductory course for dataanalysis, presentation and probability. The aim is toacquaint students with the basic methods of datahandling which are required for different kinds ofanalysis, as well as to provide them with the requisiteknowledge for taking up courses of advances Statisticsand Business Research methods in their academicterm.MTS110 Mathematical MethodsThe methods and investigative techniques ofmathematics as employed in various domains ofapplication, is imparted in this course. This coursecovers Complex Numbers, Circular and HyperbolicFunctions and Complex Exponential and Logarithms.Furthermore, students get exposed to InfiniteSequences and Series, as well as theoretical mattersrelating to Convergence of Sequences and InfiniteSeries. This also includes Piece-wise, continuous andbounded functions, Periodic Functions, and especiallyFourier Series. A little bit of elementary abstract algebrasuch as the concepts of Groups, Rings and Fields, alsoform part of this course. Similarly, some bits ofelementary linear algebra such as Matrix methods andtheir Algebra, Determinants, and elementary VectorSpaces are also included. Successful students maybe expected to use these methods successfully in anyarea of application.MTS202 Statistical Inference (with econometrics lab)This course in intended for sampling, decision analysisand data modeling using sample information. Thiscourse provides basic methods for research andpractice in social and physical sciences and businessadministration. The aim is to acquaint students withthe advanced methods of data.Pre-requisite: MTS101, MTS102MTS203 Linear AlgebraThis is a standard sophomore course of linear algebra,and aims to ground students in linear algebraicconcepts and structures such as Vector spaces; directsums of subspaces of a finite dimensional vector space,as well as linear transformations. Deeper issues suchas Dimension theorem, null spaces, image spaces oflinear transformations, rank and nullity of a lineartransformation, relation between rank, nullity, anddimension of the domain of a linear transformation,etc., are then introduced. Subsequently, students areexposed to advanced concepts such as inner productspaces, Cauchy Schwartz inequality and its application,orthogonal and orthonormal bases, similar matricesand matrix diagonalization. The ultimate aim is toempower students sufficiently so that they may uselinear algebraic techniques in diverse application areas,such as, designing good numerical solution techniquesfor applied problems.MTS211 Discrete MathematicsSymbolism and logic as used in mathematics meritsproper training. This course serves two purposes. Itaims to introduce symbolism and logic as well astreating the subject of discrete mathematics at asophomore standard. Topics at a glance include Logic,Discrete Sets, Functions, Algorithms, and theircomplexity, as well as Mathematical Reasoning, andMethods of Proofs. Graph theory and Boolean Algebraat the sophomore standard are also treated here.MTS232 Calculus-2 & Solid GeometryConcepts from calculus and geometry are integratedin this course. Topics (in brief) include, multivariatedifferential calculus and their applications; Lines,curves and surfaces in 3D;Surface and Solid ofRevolution; Double and triple integrals; Arc length,surface area and volumes; Scalar and Vector Fields;Vector Valued Functions and Elementary VectorCalculus; Gradient Divergence and Curl; Theorems ofGauss and Green. It is expected that students takingthis course, would develop a good understanding ofhow calculus might be employed for solving geometricalproblems.Pre-requisite: MTS101MTS301 Real AnalysisThis is a pure mathematics real analysis course at thejunior standard. Topics include Ordered sets,completeness properties of the real numbers, limitsof numerical sequences, properties of continuousfunctions on closed bounded intervals, Point-wise anduniform convergence. Functions and calculus in severalvariables, properties of continuous functions oncompact sets, and Taylor series in Rnwith applications,the inverse and implicit function theorems. This courseaims to provide a pure grounding in Real Analysis andtherefore facilitates related courses such as Stochasticprocesses.Pre-requisite: MTS232
Description of CoursesMTS302 Complex AnalysisThis course, in its own spite, is the complement of theReal Analysis course MTS 301. It includes the algebraand the geometry of complex numbers, Cauchy-Riemann equations, and harmonic functions. The studyof complex calculus is amply treated here in juniorstandard detail, and includes, Contour integrals, theCauchy-Goursat Theorem, Cauchy integral formulas,the Morera Theorem, maximum modulus principle,the Liouville theorem, and the fundamental theoremof algebra. Advanced topics covered expose studentsto Laurent series, uniqueness of representation, zerosof analytic functions. Residues and poles, integralsaround a branch point., the argument principle, andthe Roche theorem.Pre-requisite: MTS301MTS303 Advanced Differential EquationsThis course mainly deals with partial differentialequations (PDEs). PDEs form the mathematical modelof many problems of interest, typically, the ones thatadmit a mathematically analyzing approach. A thoroughgrounding in the analytic methods and techniques offorming models and solving PDEs therefore meritsinclusion in this program. This course exposes studentsto first order PDEs, the classification of second-orderPDEs, and their canonical forms. Then the standarddiffusion, heat, and the wave, equations in Cartesian,cylindrical and spherical-polar coordinates are treated.The solution of PDEs by different methods is introducednext, closely followed by the Fourier, the Laplace andthe Hankel transforms. Students finishing this courseare expected to have the skills required for modelingand solving important problems in a diverse applicationarea.Pre-requisite: MTS241MTS304 Stochastic ProcessesStochastic processes form the basis of mathematicalmodels of many phenomena which have amathematical side to them. They include credit-crisis,stock movements in stock markets, dynamics offinancial derivative prices, as well as the dynamics ofelementary particles. This subject here is only treatedupto the junior standard. Briefly, it includes basicstochastic processes, probability spaces, randomvariables and moments. Then moves on to developrandom walks, Gambler's ruin, Markov chains,decomposition of state space etc. After that stochasticcalculus is introduced and the concepts of continuity,differentiability, Ito's lemma, Ito's integral, spectralrepresentation, and Martingales, is brought in. Finallysome advanced topics such as white noise, andKolmogorov forward/backward equations are handled.The goal is this course is to impart the understandingand the appreciation of non-deterministic phenomena,and their mathematical treatment.Pre-requisite: MTS202, & MTS301MTS305 Abstract Algebra-IThis is a pure mathematics abstract algebra course,and aims to develop the skills of recognizingmathematical abstractions. Purely abstract conceptssuch as groups, subgroups, generators, cyclic groups,cosets and quotient sets are introduced first.Permutations, symmetric, and alternating groups,rings, finite and infinite fields are treated next. Finallyadvanced concepts, such as Normalizers andCentralizers of a subset of a group, congruency classesof a group, quotient groups, homomorphism andisomorphism between groups, as well as ,automorphisms, finite p-groups, orbits, and the 1st,the 2nd and the 3rd Sylow theorems are given.Pre-requisite: MTS110MTS306 Numerical AnalysisPhenomenally, mathematical models of differentproblems happen to be much more sophisticated thanthe available analytic solution methods. Fortunately,this issue can be addressed in most cases by resortingto numerical and computational techniques that aimto approximate the real solution upto a prescribedaccuracy. This course imparts the skills of numericalanalysis and techniques for different problems.Computer arithmetic is introduced, and differentiterative methods for the solution of nonlinear equationsand their error analysis is treated. Interpolation andnumerical calculus follows, incorporating importanttechniques and algorithms. Finally, direct numericalsolution of systems of linear equations is treated.Pre-requisite: MTS232MTS241 Introduction to Differential EquationsThis course introduces the concepts of equationsinvolving derivatives. The Introduction, formation,solution and applications of first-order-differentialequations is first dealt, paving the way for theintroduction and solution of higher order lineardifferential equations. The approach to this subject inthis course is analytic (as opposed to numerical/computational). Advanced concepts that merit aninclusion at the sophomore standard such asdifferential equations with variable coefficients; Sturm-Liouville (S-L) system and boundary-value problemsare brought in next. The course culminates on conceptssuch as series solutions and Bessels Function.Pre-requisite: MTS232MTS411 Functional Analysis-1This senior level Functional Analysis course deals withthe following topics.Completeness, convergence, andcompletion of metric spaces. Normed spaces, Banachspaces, Bounded and continuous linear operators andfunctionals, Dual spaces, Finite dimensional spaces,F. Riesz Lemma, The Hahn-Banach Theorems, Theopen mapping theorem, The closed graph theorem,Uniform boundedness principle and its applications.Applications in Differential and Integral equations. Alsoincluded are the Inner-product space, Hilbert space,orthogonal complements, the Gram-Schmidtorthogonalization process, besides other topics.The course facilitates Functional Analysis-2.Pre-requisite: MTS302173
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OUR VISION“To become a world-clas
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Full Time FacultyDepartment of Comp
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Full Time FacultyDepartment of Econ
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Programs of Study34Overview of the
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Academic Calendar 2013 - 201436Acad
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JULYSun Mon Tue Wed Thu Fri Sat2013
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Enhancing our OutreachCenter for Ex
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Admission Policy42Admission PolicyI
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Admission Policy44*All equivalency
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Rules & Regulations46Rules & Regula
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Rules & Regulations48Transcript of
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Grading & Evaluationorder to be eli
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MS (Computer Science)110MS (Compute
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