The Faculty of Science offers B. Sc. General Degree programs of threeyear and fouryear duration. Mathematics is available as a subject for both programs.
Industrial Statistics & Mathematical Finance Level 1 Course Modules
Course unit  Title  Credit value  Hours 

FM 1001  Financial Mathematics  2  20L/20P 
FM 1002  Mathematical Methods for Finance I  30L 

FM 1004  Mathematical Economics  2  30L 
FM 1005  Linear Algebra  2  30L 
MS1002  Linear Programming  2  15L 
MS1004  Computing For Finance  1  10L/10P 
PM 1001  Calculus I  2  30L 
Industrial Statistics & Mathematical Finance Level 2 Course Modules
Course unit  Title  Credit value  Hours 

FM 2001  Computational Financial Mathematics I  2  20L/20P 
FM 2002  Actuarial Mathematics I  2  30L 
FM 2004  Mathematical Methods for Finance II  2  30L 
FM 2005  Computational Financial Mathematical II  2  25L/10P 
MS 2002  Quantitative Methods  2  30L 
MS 2003  Qualitative Methods  2  15L 
PM2001  Calculus II  2  30L 
PM2004  Logic and Introduction to Analysis  2  30L 
Industrial Statistics & Mathematical Finance Level 3 Course Modules
Course unit  Title  Credit value  Hours 

FM 3001  Mathematical Programming in Finance  3  30L/30P 
FM 3002  Actuarial Mathematics II  3  45L 
FM 3003  Calculus III  2  30L 
FM 3004  Numerical Methods for Finance  2  25L/10P 
MS 3001  Introduction to Game Theory  3  45L 
MS 3005  Introduction to Management Accounting  2  25L/10P 
The Faculty of Science offers B. Sc. General Degree programs of threeyear and fouryear duration. Mathematics is available as a subject for both programs.
Applied mathematics has been added as a compulsory subject for each combination under physical science stream. Subject combinations that include Pure Mathematics are:
Applied Mathematics,Pure Mathematics, Chemistry, Computer Science
Applied Mathematics,Pure Mathematics, Statistics, Computer Science
Applied Mathematics,Pure Mathematics, Physics, Computer Science
Following Mathematics modules are available under the general degree:
Physical Science Level 1 Course Modules
Course No.  Title  credit value  hours 

PM 1001  Calculus I  2  30L 
PM 1002  Algebra  2  30L 
PM 1004  Sets and Combinatorics  2  30L 
AM 1001  Differential Equations I  2  30L 
AM 1002  Vectors  2  30L 
AM 1003  Metrices  2  30L 
AM 1005  Graph Theory  2  30L 
AM 1006  Geometry with Applications  2  30L 
Physical Science Level 2 Course Modules
Course No.  Title  CREDIT VALUE  hours 

PM2001  Calculus II  2  30L 
PM2002  Linear Algebra  2  30L 
PM2004  Logic and Introduction to Analysis  2  30L 
AM2001  Differential Equations II  2  30L 
AM2002  Numerical Analysis  2  30L 
AM2003  Linear Programming  2  30L 
AM2004  Optimization  2  30L 
AM2005  Differential Equations III  2  30L 
Physical Science Level 3 Course Modules
Course No.  Title  CREDIT VALUE  hours 

PM3001  Real Analysis  3  45L 
PM3002  Complex Analysis  3  45L 
PM3003  Algebra  3  45L 
AM3002  Computer Applications in Discrete Mathematics  3  30L/30P 
AM3004  Mathematical Modeling in Economics and Business  3  45L 
AM3005  Mathematical Methods  3  45L 
AM3006  Financial Mathematics  3  45L 
AM3007  Computer Applications in Discrete Mathematics  3  30L/30P 
General Degree Syllabus
Physical Science Level 1
Dependencies: None
Syllabus:Real Numbers, Positive integers, integers, rationals, irrationals, geometric representation, Inequalities, Archimedian property, Bounded sets; Intervals, Modulus.Real Functions: Definitions, notations, examples (polynomial functions, rational functions, trigonometric functions, exponential function).Continuity: Intuitive idea, formal definition; Simple results; Intermediate value theorem, max, min value theorem (without proofs).Infinite Limits: Limits involving vertical and horizontal asymptotes (graphical illustration only).Inverse Functions: Injections, bijections, Monotonic functions (on intervals), Inverse functions, Definition of the log function and the inverse trigonometric functions.Differentiability: Intuitive idea, formal definition, formal definition of finite limits (including left and right limits), Algebra of limits and the algebra of derivatives, Composition of functions and the chain rule, Sign of the derivative and extreme points, Mean value theorems (without proof), Higher order derivatives and their applications in maxima, minima and concavity, Taylor’s theorem (without proof).
Assessment: End of semester examination.
Dependencies: None
Syllabus:Sets: Notation, containment and equality, intersection, union, empty set, Cartesian product.Complex Numbers: Fundamental operations on the complex numbers, complex conjugate, modulus, Argand diagram, polar representation, de Moivre’s theorem, roots of unity, some simple transformations of the complex plane – translations, rotations and magnifications.Matrices: Matrices over R and over C, Special types of matrices – zero and identity matrices, triangular and diagonal matrices, symmetric and skew symmetric matrices, Hermitian and skew Hermitian matrices, and orthogonal matrices; Matrix operations, Singular and nonsingular matrices, The inverse of a square matrix, evaluation of the inverse of a 2 x 2 matrix.Elementary Number Theory: The division algorithm, Greatest common divisor, The Euclidean algorithm, Prime factorization theorem in N, Congruences, Modulo arithmetic Zn. Generalized notion of a function.Binary Operations: Definition, examples, basic properties.Group Theory: Definition of a group, Examples including the nth roots of unity under multiplication, matrices under addition, nonsingular matrices under multiplication, Abelian and nonabelian groups, Subgroups, Statement of Lagrange’s theorem, Definition of a homomorphism, examples and basic properties.
Assessment: End of semester examination.
PM1004: Sets and Combinatorics
Dependencies: None
Syllabus:Methods of Proofs: If, iff, method of contradiction, counter examplesSets: Definition and Notations, Subsets, Equality, Universal sets, Power set, Set operations and Algebra of sets, Proofs of results using labeled Venn diagrams, Algebraic proofs of results.Combinatorics: Applications of mathematical induction, Basic principles in counting, Permutations and combinatorics, Generalized permutations and combinatorics, Applications of permutations, Combinations and generalized permutations, Pigeonhole principle, Binomial coefficients and combinatorial identities, Generating function and applications of Generating functions, Algorithms for generating permutations and combinations, Applications and combinations in Graph Theory, Counting concepts in graph theory and other areas.
Assessment: End of semester examination.
AM 1001: Differential Equations I (30L, 2C)
Dependencies: None
Syllabus: Ordinary Differential Equations with examples: Particular solution, general solution, singular solution, complete primitive; Remark on existence of solution; First Order First Degree equation; Singular points. Introduction of the Differential.Special types of ODE’s of the first order – Separable ODE’s, Exact equations, Integrating Factor, Bernoulli’s, Riccatitype equations.Orthogonal trajectories; Linear equations of the first order; Linear equations of the second order with constant coefficients; Complementary function, particular integral; Euler’s homogeneous form of the second order.
Assessment: End of semester examination.
Dependencies: None
Syllabus:Introduction: Vectors, scalars; Properties of vectors; Scalar, vector, triple scalar and triple vector products; Geometrical Applications (equation of a line, plane, etc.).Differentiation of vectors: Geometric interpretation of the derivative; Gradient of scalar functions; Geometrical interpretation of grad ; The divergence and curl of the vector and double operators; Physical interpretation of irrotational and solenoidal vector fields;Integration of vectors: Line integrals; Surface and volume integrals; Divergence theorem, Stoke’s theorem, Green’s theorem.
Assessment: End of semester examination.
AM 1003: Matrices (30L, 2C)
Dependencies: None
Syllabus:Introduction, various types of matrices, matrix algebra, inverse, transpose of a matrix and its properties; Matrix expression of a system of linear equations, row operations, augmented matrix, Gaussian method.Determinants, minors, cofactors, properties of a determinant, cofactor and adjoint matrices; Cramer’s rule for matrix solutions.Characteristic polynomial, characteristic values (eigen values) and vectors; Cayley Hamilton theorem.Matrix special function eA. Similar matrices, diagonalization and their applications.System of differential equations, matrix representation of conics.Special determinants and matrices (the Jacobian, the Hessian, the Discriminant).
Assessment: End of semester examination.
AM 1005: Graph Theory (30L, 2C)
Dependencies: None
Syllabus:
Introduction to graphs; Subgraphs; Paths; Connectivity of graphs; Cycles; Complete, regular and bipartite graphs.Tree graphs: Binary trees, binary search trees, representing binary trees in memory; Prefix and postfix forms of an expression; Huffman’s algorithm; Implementation of Huffman’s algorithm; Isomorphism of trees; Multigraphs, directed graphs and weighted graphs; Trails; Euler trails; Hamilton cycles and traveling salesperson problem.Network models: Shortestpath algorithm; Minimum spanning tree problem; Planar graphs; Vertex colorings; Edge colorings; Isomorphic and homomorphic graphs; Representing graphs in the computer memory.
Assessment: End of semester examination.
AM 1006: Geometry with Applications (30L, 2C)
Dependencies: None
Syllabus:Analytical Geometry E2(R): Rectangular Cartesian coordinates in E2; Parabola, ellipse, hyperbola, directrix, focus, eccentricity e; General conic and translation of axes; Rotation of axes.Classification of central conics, noncentral conics, Analytical Geometry E3(R): Rectangular Cartesian coordinates in E3; Equation of lines, planes; Direction cosines and change of axes; Translation and rotation; Sphere.Quadratic as a second degree equation S ≡ ax2 + by2 + cz2 + 2fyz + 2gzx + 2hxy + 2ux + 2vy + 2wz + d = 0. Central quadratic S ≡ ax2 + by2 + cz2 + 2fyz + 2gzx + 2hxy + d = 0 and its matrix representation. Noncentral quadratics, classification of quadratics. Introduction to polar, spherical, cylindrical coordinate systems.Applications in Classical Mechanics and EM theory.
Assessment: End of semester examination.
Physical Science Level 2
PM 2001: Calculus II (30L, 2C)
Dependencies: PM 1001
Syllabus:The definite integral of continuous functions: Area under a curve, definition of the integral, basic results; Antiderivative, Fundamental theorem of Calculus; Techniques of integration; Numerical methods.Sequences: Concept of a sequence; Definition of convergence; Boundedness; Supremum and infimum of a subset of real numbers; Monotonic sequences; Basic theorem on monotonic sequences; Cauchy sequences (without proof).Series: Partial sums, definition of convergence; Cauchy condition; Absolute and conditional convergence, tests for absolute convergence (comparison tests, d’Alembert’s ratio test, Cauchy’s root test, Integral test); Alternating series, Leibniz’s test for convergence.Power Series: Radius of convergence; Differentiation and integration of power series (without proof); Taylor’s and Maclaurin’s series.
Assessment: End of semester examination.
PM 2002: Linear Algebra (30L, 2C)
Dependencies: None
Syllabus:Matrices: Rank of a matrix, computation of the rank of matrices using elementary row operations.Vector Spaces: Vector spaces; Subspaces; Intersections and sums of subspaces; Spanning sets and bases; Dimension of a vector space and dimension of a subspace; Dimension of the sum and the intersection of subspaces.Linear Transformations: Algebra of linear transformations; Kernel and range; Linear transformations on finite dimensional spaces – bases and coordinate systems, matrices and linear transformations, kernel and range; Similarity and change of bases – transition matrices and similar matrices.Eigen values and Eigen vectors: Basic ideas; Finite dimensional spaces; Diagonisable linear transformation and direct sum decompositions; Powers of diagonisable matrices.Orthogonal projections: Basic ideas; Gram Schmidt procedure to find an orthonormal basis; Projection matrices.Orthogonal and symmetric matrices: Orthogonal matrices and orthogonal change of basis; Symmetric matrices and diagonalising symmetric matrices; Bilinear forms; Quadratic forms and change of basis.Introduction to inner product spaces. All topics given above should contain less theory but more application and problems.
Assessment: End of semester examination.
PM 2004: Logic and Introduction to Analysis
Dependencies: PM 1001 and PM 2001
Syllabus: Logic: Pro[ositions, Predicates and propositional variables, Truth tables, Tautologies and contradictions, Arguments involving variables, Basic quantifiers.Relations and functions: Ordered pairs, Cartesian product, Relations, Range and domain, Image of a set under a relation (image of union, intersection and difference of sets), Restriction of a relation on a subset of the domain, Inverse of a relation, Composition of relations, Functions, Injections, sujections and bijections, Inverse functions.Bounded and unbounded sets of real numbers: Maximum and Minimum, Upper and lower bounds, Axiom of completeness of real numbers, Supremum and infimum, Limit points of a set.Sequences: Bounded and unbounded sequence, Convergence of a sequence, Boundedness of a convergent sequence, Algebra of limits, Sandwich theorem.
Assessment: End of semester examination.
AM 2001: Differential Equations II (30L, 2C)
Dependencies: AM 1001
Syllabus:Ordinary differential equations: Linear equations of the second order where the coefficients are functions of the independent variable; Ordinary points; Singular points; Regular singular points;Solution in series: Stability of the solutions; Solution of Laplace’s equation; Revision of Euler’s homogeneous form of the second order ordinary differential equations; Legendre’s equation; Legendre’s polynomials – their linear independence and recurrence relations; Bessel’s function.Introduction to Difference equations: Complementary functions and particular solutions.
Assessment: End of semester examination.
AM 2002: Numerical Analysis I (30L, 2C)
Dependencies: None
Syllabus:Mathematical preliminaries for numerical analysis: Taylor’s theorem and its various forms; Orders of convergence; Big O and small o; Sources of errors; Algorithms and convergence.Solutions to nonlinear equations: Bisection method; Fixed point iteration; NewtonRaphson method; Error analysis for iterative methods.Interpolation and curve fitting: Least square approximation; Polynomial interpolation; Lagrange polynomial; Divided differences; Hermite polynomial; Introduction to spline interpolations.Numerical differentiation and integration: Numerical differentiation; Richardson’s extrapolation; Elements of numerical integration; Composite integration; Romberg integration; Adaptive quadrature methods; Gaussian quadrature.Initial value problems for ordinary differential equations: Elementary theory of initial value problems; Euler’s method; Higher order Taylor methods; RungeKutta methods.
Assessment: End of semester examination.
AM 2003: Linear Programming (30L, 2C)
Dependencies: None
Syllabus:Introduction to mathematical modeling and operational research.Formulation of linear programming models; Assumption of the model; Standard form; General model; Matrix representation.Graphical solution to linear programming problems and sensitivity analysis; Introduction to simplex algorithm; twophase method (2 variables only).Interpolation of final tabular; Applications of linear programming in various fields.
Assessment: End of semester examination.
AM 2004: Optimization (30L, 2C)
Dependencies: AM 2003
Syllabus:Simplex algorithm; Twophase method and Dual simplex methods (for more than two variables); Duality theorem; Sensitivity analysis in detail.Introduction to game theory. Unconstrained and constrained optimization of functions of single and many variables and applications.
Assessment: End of semester examination.
AM 2005: Differential Equations III (30L, 2C)
Dependencies: AM 1001, AM 2001
Syllabus:Ordinary differential equations: Transformation of higher order ordinary differential equations with constant coefficients to a system of first order ODE’s; Fundamental solution; Qualitative theory of ODE’s (stability of linear systems).Partial differential equations: Functions of several variables, partial differentiation; First and second order linear PDE’s with constant coefficients; Classification; Solution by separation of variables; Heat equation, wave equation, Poisson equation, Laplace equation.
Assessment: End of semester examination.
Physical Science Level 3
PM 3001: Real Analysis (45L, 3C)
Dependencies: PM 1001, PM 2001
Syllabus:Preliminaries: Supremum and infimum; Uniform continuity.Riemann Integral: Darboux definition for a bounded function on a closed interval; Necessary and sufficient condition for integrability; Integrability of monotonic functions and continuous functions; Elementary properties of the integral; Differentiation and integration (fundamental theorem of calculus); The integral as the limit of Riemann sums; Mean value theorems; Techniques of integration (integration by parts, integration by substitution).Improper integrals: Tests for convergence of improper integrals (analogues of Cauchy condition, absolute convergence, comparison test, ratio limit test, Dirichlet’s and Abel’s tests); Gamma and Beta functions; Wallis product and Stirling’s formula; Euler’s constant.Functions of several variables: Limits, iterated limits, continuity; Partial derivatives (higher order partial derivatives, composition of functions and the chain rule); Directional derivative; Differentiality; Implicit functions (theorems of existence – without proof); Taylor’s theorem and extremum values.
Assessment: End of semester examination.
PM 3002: Complex Analysis (45L, 3C)
Dependencies: None
Syllabus:Sets of complex numbers: Open sets; Closed sets; Boundary of a set; Domains and regions.Complex functions: Conformal mappings (isometries, bilinear transformations); Limits and continuity; Polynomial and rational functions; Roots of a polynomial; Differentiability and analytical functions; CauchyRiemann equations.Power Series: Sequences; Series (absolute convergence, ratio and root tests); Power series; Radius of convergence; Analyticity of a power series.Elementary functions: Exponential, logarithmic and complex powers (branch cut, principal value and branches), and trigonometric functions.Integration: Curves in the complex plane; Integration on contours; The Cauchy integral theorem (without proof); Cauchy’s integral formula; Taylor’s series; Laurent series; Zeros and poles.
Assessment: End of semester examination.
Syllabus:Group Theory: Definition of a group, examples, basic properties; Subgroups; Order of an element, properties; Cyclic groups and cyclic subgroups; Cosets; Lagrange’s Theorem; Product of subgroups; Normal subgroups; Quotient groups; Homomorphisms; Isomorphism theorems; Permutation groups and Cayley’s Theorem; Action of a group on a set.Ring Theory: Definition of a ring, examples, basic properties; Subrings; Ideals; Homomorphisms; Isomorphism theorems; Field of Quotients of an Integral Domain; Prime and Maximal Ideals; Unique Factorization Domains and Euclidean Domains; Polynomial rings.
Assessment: End of semester examination.
AM 3002: Computer applications in discrete mathematics (30L/30P, 3C)
Dependencies: A certain number of students will be selected by the total mark of the 1st and 2nd year Applied Mathematics core courses. In addition to this, any student doing Mathematics Special or the joint special ‘Mathematics, Statistics with Computer Science’ could also follow the course.
Syllabus:Most of the following languages and packages will be used in applying discrete mathematics – JAVA (only introductory material), 3D modeling packages, Linux and Window packages; Connecting to databases using relevant packages. Any language or package can be replaced by another equivalent language or package.Advanced Topics: Complexity of algorithm; Introduction to graph theory; Huffmann Codes; Encoding matrices; Decoding tables; Breadth first search and depth first search for spanning trees; Prim’s algorithm and Kruskal’s algorithm for minimum spanning trees; Shortest path algorithm; Euclidean algorithm; Sorting algorithms and sorting trees; Search algorithms; Complexity of algorithms; Analysis of algorithms; Infix, prefix and postfix forms; Binary strings; Traveling salesman problem; Algorithms with applications in Java, C++. Automata, grammars and languages; Finitestate machines; Finite state automata; Languages and grammars; Contestfree grammars and contextsensitive grammars; String fractals.
Assessment: End of semester examination.
AM 3004: Mathematical modeling in Economics and Business (45L, 3C)
Dependencies: None
Syllabus:Introduction: Introduction to economics and business; Role of mathematics in economics and business; General study of demand, supply and market equilibrium.Economic models: Static and comparativestatic analysis of market models, inventory models, inputoutput models and selected macro economic models; Effect of taxation on static market models; Dynamic analysis (in continuous and discrete time) of market models, inventory models, inputoutput models, financial models and some macro economic models; Effect of taxation on dynamic market models.Elasticity and other economic concepts: Elasticity of demand and supply; Point and cross elasticities; Analysis of single product and joint products cost, revenue, average cost, price, profit functions etc.; Marginal analysis, consumer’s surplus and producer’s surplus; Optimisation of revenue, cost and profit functions of single product and joint products.Consumer demand theory: Derivation of utility functions; Maximizing utility functions with and without budget constraints; Derivation of demand functions; Indifference curves; Marginal rate of substitution and contract curves (Edgeworth box).Introduction to game theory: Zerosum matrix games; Single and mixed strategy games; Optimal strategies; Dominance; Simple applications.
Assessment: End of semester examination.
AM 3005: Mathematical Methods (45L, 3C)
Dependencies: None
Syllabus:Systems of ordinary differential equations, phase diagrams, stability of solutions, Fourier series, Fourier transforms, Laplace transforms and their applications,Partial differential equations: Laplace equation, Heat equation, wave equation, Finite difference approximation of partial differential equations, Variational principle and its applications.
Assessment: End of semester examination.
AM 3006 Financial Mathematics (3C, 45L)
Dependencies: None
Syllabus:Introduction: Accumulation functions, present values, simple interest, compound interest,discounts,forces of interest and discout,interest rates in discrete and continues timeAnnuities: Elementary annuities – immediate and due, perpetuities, more general annuities, annuities payable less or more frequently than interest conversion, continuous annuities, payments varying in arithmetic/geometric/other patterns,continuosly varying annuitiesAmortization schedules and sinking funds: Outstanding principle, amortization schedules, sinking funds, schedules when payment periods and interest conversion periods coincide and when these periods are different, varying series of payments, yield rates, reinvestment rates.Bonds and other securities: Types of securities and bonds, price of a bond, premium and discount , valuation between interest payment dates, callable/serial bonds, valuation of securities.Basic option theory: Introduction, Call option, Put option, Asian option.
Assessment: End of semester examination
AM 3007: Computer Applications in Combinatorics (30L,30P, 3C)
Dependencies: None
Syllabus:Problems related to counting, Problems related to cyclic order, Pigeonhole principle, Ordered and unordered selections, Counting problems related to partition functions, Algorithms in generating combinations and permutations, Generalized permutations and combinations, Introduction to VC++, Working with Timers, Menus, Toolbars, Status bars and Dialog boxes. Using Visual C++ (swing), creating a user interface to solve counting problems. Examples of permutations and Combinations in applied probability, Applications of permutations and combinations using Visual C++ and other programming languages, Generalized multiplications, Binormial expansion, Binormial coefficients, Binormial expansion and its relation with combinations, Multinomial coefficients and Multinomial expansions, Combinatorial identities (for some special cases), Counting problems. Proofs to combinatorial identities using permutations and combinations, Problems related to combinatorial identities. VC++ may be replaced by another Object Oriented Language.
Note: Any special students having to take AM 3002 as a compulsary course may opt to take AM 3007 instead. A student is not allowed to take this course if he or she is taking AM 3002
Assessment: End of semester examination.
Industrial Statistics & Mathematical Finance Level 1
FM 1001: Financial Mathematics (20L, 20P, 2C)
Dependencies: None
Syllabus:Accumulation function, simple and compound interest, present values, discounting; interest rates in discrete and continuous time.
Basic annuities: introduction, annuity – immediate/due, perpetuities.More general annuities: annuities payable less/more frequently than interest is convertible, continuous/basic varying annuities, general/continuous varying annuities.Yield rates: discounted cash flow analysis, yield rate, reinvestment rate, capital budgeting, borrowing/lending models.
Assessment: End of semester examination
FM 1002: Mathematical Methods for Finance I (30L, 2C)
Dependencies: None
Syllabus:Expected learning outcomes: Fundamentals of Mathematical methods in the sense of financial applicationsIntroduction, Ordinary Differential Equations with examples in financial applications (first order ordinary differential equations: Differentials, Classical solution methods, second order constant coefficient ordinary differential equations).Introduction to first and second order constant coefficient difference equations, classical solution methods, application in finance.Eigenvalues / Eigenvectors, Diagonalization, Solving systems of linear difference equations,
Assessment: End of semester examination
FM 1004: Mathematical Economics (30L, 2C)
Dependencies: None
Syllabus:Introduction to Economics, Role of mathematics in economics, General study of demand, supply and equilibrium.Static analysis of market models and selected macro economic models. Effect of taxation on static market models.Dynamic analysis in continuous and discrete time of market models and selected macro economic models. Effect of taxation on dynamic market models.Elasticity and other economic concepts: elasticity of demand and supply – point and cross elasticities. Analysis of single product functions and joint products functions { cost, revenue, profit, etc}. Consumer’s and Producer’s surpluses. Optimisation of single product functions and joint products functions { cost, revenue and profit functions}.Utility functions: introduction, derivation, maximizing with and without budget constraints ; derivation of demand functions, marginal rate of substitution, indifference curves and contract curves (Edgeworth box).
Assessment: End of semester examination
FM 1005: Linear Algebra (30L, 2C)
Dependencies: None
Syllabus:Sets and relations ; set operations, equivalence relation, partial order, order.Vectors and Matrices; Rank, Range, Nullspace, Linear equations. Vector spaces – subspaces, basis and dimension. Linear transformation, change of basis.Inner products ; Orthogonality, Orthogonalization process.
Assessment: End of semester examination
MS 1002: Linear Programming (20L, 20P, 2C)
Dependencies: None
Syllabus:Formulation of linear programming problems, Solving 2 variable LP problems using the graphical method.The Simplex algorithm. The Simplex method in matrix notation. The degeneracy and convergence of the Simplex algorithm. Sensitivity and parametric analyses.The Dual Simplex method, Big M method and the Two phase Simplex method.
Assessment: End of semester examination
MS 1004: Computing For Finance (10L, 10P, 1C)
Dependencies: None
Syllabus:Use of computer software packages like TORA, LINGO or MatLab to maximize/ minimize functions subject to certain constraints.Use of or Java to analyze and solve specific problems that come up in areas like Management, Finance, Economics and Applied Mathematics in general.Computer applications of Optimization techniques in solving and analyzing problems.
Assessment: End of semester examination
Industrial Statistics & Mathematical Finance Level 2
FM 2001: Computational Financial Mathematics I (20L, 20P, 2C)
Dependencies: None
Syllabus:Elementary Numerical methods and applications : Introduction to numerical methods, Taylor’s Theorem and its various forms.Different forms of numerical errors, orders of approximations, solution of nonlinear equations and their applications in finance, interpolation techniques; polynomial interpolations, introduction to splines.Amortization schedules and Sinking funds : outstanding principal, amortization schedules, sinking funds, differing payment/interest conversion periods, varying series of payments.Bonds and other securities : types of securities, price of a bond, premium/discount, coupon payments, callable bonds, serial bonds, valuation of securities.
Assessment: End of semester examination
FM 2002: Actuarial Mathematics I (30L, 2C)
Dependencies: None
Syllabus:Survival distribution of life tables, Life insurance, Life annuities, Net premiums, Net premium reserves, Multiple life functions, Multiple decrement models, Valuation theory for pension plans.
Assessment: End of semester examination
FM 2004: Mathematical Methods for Finance II (30L, 2C)
Dependencies: FM1005
Syllabus:Idea of well possness of a problem, initial/boundary value problem(ODE), existence, uniqueness theorems(without proof) and related results, Matrices, Eigen values and related results, Fundamental matrices and their elementary properties, application in solving system of ordinary differential equations, Fourier series/transforms and their applications, calculus of variations, systems of linear equation and analytical method of solving them.Introduction to stochastic differential equations.
Assessment: End of semester examination
Expected learning outcomes: Understanding of advanced topics in Mathematical Methods.
FM 2005: Computational Financial Mathematical II (25L, 10P, 2C)
Dependencies: FM1003
Syllabus:Numerical approximation of a derivative. Numerical solutions of Ordinary differential equations. One step methods, introduction to multistep methods, definition of consistency, stability and convergence.Insurance mathematics: utility theory, utility and insurance, optimal insurance and insurance policies.Index numbers : introduction to price, volume and value relatives, linked and chain relatives, tests for index numbers, price/simple/simple aggregate index numbers and their properties. Applications.
Assessment: End of semester examination
MS 2002: Quantitative Methods (30L, 2C)
Dependencies: None
Syllabus:Arguments with Sets and Venn diagrams.Decision theory and Group Decisions : Under uncertainity – various views and the study of risk, Under competition – competitive games.Input output models – Leontief open and closed, static and dynamic models.Stochastic matrices and determination of long run market shares of products.Inventory management and deterministic inventory models (static and dynamic models).Equipment selection and replacement methods (static and dynamic models).
Assessment: End of semester examination
MS 2003: Qualitative Methods (15L, 1C)
Dependencies: None
Syllabus:Discussion on Hard OR (Classical OR / Quantitative methods) and Soft OR (Qualitative methods). Introduction to Soft OR.Qualitative Problem Structuring Methods and Modeling Interactive Decision Making processes : Strategic options development and analysis ( SODA), Soft system methodology (SSM), Strategic Choice (SC), simple and hyper games, etc..
Assessment: End of semester examination
Industrial Statistics & Mathematical Finance Level 3
FM 3001: Mathematical Programming in Finance (30L, 30P, 3C)
Dependencies: None
Syllabus:Formulating integer programming problems related to finance.Using Lingo and Access databases to solve integer programming problems related to capital budgeting problem.Short term financial planning problem, Fixed charge problem, Risk insurance problem, Cutting stock problem, Problems related to cost curves, Traveling salesperson problem, Port folio optimization problem.The branch and bound method. The implicit enumeration method using dual simplex algorithm. The cutting plane algorithm.Formulating and solving Dynamic programming problems related to finance. The Wagner – Whitin algorithm. Forward recursion. Using spreadsheet to solve Dynamic programming problems in finance.
Assessment: End of semester examination
FM 3002: Actuarial Mathematics II (45L, 3C)
Dependencies: None
Syllabus:The economics of insurance, Individual risk models for a short term, Collective risk models for a single period, Collective risk models over an extended period,Application of risk theory, Insurance models including expenses, Nonforfeiturebenefits and dividends, Special annuities and insurance, Advance multiple theory.
Assessment: End of semester examination
FM 3003: Calculus III (30L, 2C)
Dependencies: None
Syllabus:Plain curves : Conics, parametric equations, polar coordinates and graphs.Vectors : Vectors in plane and space, Dot and Cross products, Lines, planes and surfaces in space, Cylindrical and Spherical coordinates.Vector valued functions : Differentiation and integration, Tangent and normal vectors, Arc length and curvature.Functions of several variables : Graphs of surfaces, Limits and continuity, Partial derivatives and differentiability, Linear approximation and error bounds, Chain rule, Directional derivatives and gradients, Tangent planes and normal lines, Extrema of functions of two variables and applications, Lagrange multipliers.Multiple integration : Iterated integrals, Double integrals and volumes, Change of variables and polar coordinates, Surface area, Triple integrals, Change of variables.Vector analysis : Vector fields, Line integrals, Conservative vector fields, Green’s theorem, Surface integrals, Divergence theorem, Stoke’s theorem.
Assessment: End of semester examination
FM 3004: Numerical Methods for Finance (25L, 10P, 2C)
Dependencies: None
Syllabus:Expected learning outcomes: Understanding of advance topics in Numerical Methods.Linear multistep method of solving ordinary differential equations, consistency, stability and convergence, Numerical methods of solving a linear system of equations, sparse systems, direct and iterative methods, convergence, Interpolation techniques of higher order accuracy.
Assessment: End of semester examination
MS 3001: Introduction to Game Theory (45L, 3C)
Dependencies: None
Syllabus:Introduction to: Static and Dynamic games with complete information, Static games with incomplete information, Payoff matrix, applications.Static games with complete information : Standard games, zerosum games, Prisoner’s dilemma, battle of sexes, coordinate games, Chicken or Hark versus Dove.Basic Theory and Applications : Normal form games, Nash equilibrium, Iterated elimination of strictly dominated strategies. Cournot Model of Duopoly, Bertrand Model of Duopoly.Mixed strategies: Game theory applications in industry, politics, etc..
Assessment: End of semester examination
MS 3005: Introduction to Management Accounting (25L, 10P, 2C)
Dependencies: None
Syllabus:Accounting Theory and Financial Statements : Basic principles, Ledger accounting and Control accounts, Bank reconciliation, Intangibles, Suspense accounts, Trading, Profit and Loss accounts, Balance sheet, Trial balance, Income and Expenditure accounts, Incomplete records, Using Financial accounting packages.Cost Accounting Cost classification, Materials and Stocks control, Labour cost allocation and Overheads classification and analysis, Absorption and Marginal costing, Manufacturing and Departmental accounts, Budgets and budgetary control, Standard costing and variances, Integrated accounting systems and using Cost accounting packages.