Degree Type:Bachelor of Science
Department:Department of Mathematics
4 years (Standard Entry)
Modes of Study:Regular
Our B.Sc Mathematics with Business programme will prepare you for interesting career opportunities in business and industry. It also qualifies you for advanced studies and professions in fields such as actuary, banking, insurance etc.
9 READING LIST
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Applicants pass Elective Mathematics, Economics and any one (1) of the following elective subjects: Physics, Chemistry Business Management, Principles of Costing and Accounting or Geography.
Mathematics is a challenging and an exciting science of exactness that plays a central role in many aspects of modern life including business. This degree programme combines mathematical concepts, techniques and models with a particular focus on its application to the world of business. It bridges the divide that exists between the two disciplines.
Students will therefore develop a working understanding of business enriched with mathematical perspectives, enhancing their dynamism and perspectives with regards to their professional expertise and intellectual capacities.
MAT 101: Algebra and Trigonometry
This course seeks to prepare students for advanced courses in Mathematics. Students will have a better appreciation of how to perform basic operations on sets, real numbers and matrices and to prove and apply trigonometric identities. The specific topics that will be covered are: commutative, associative and distributive properties of union and intersection of sets. DeMorgan’s laws. Cartesian product of sets. The real number system; natural numbers, integers, rational and irrational numbers. Properties of addition and multiplication on the set of real numbers. Relation of order in the system of real numbers. Linear, quadratic and other polynomial functions, rational algebraic functions, absolute value functions, functions containing radicals and their graphical representation. Inequalities in one and two variables. Application to linear programming. Indices and logarithms, their laws and applications. Binomial theorem for integral and rational indices and their application. Linear and exponential series. Circular functions of angles of any magnitude and their graphs. Trigonometric formula including multiple angles, half angles and identities. Solution to trigonometric equations.
MAT 201: Introduction to Abstract Algebra
This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures. Abstract algebra gives to student a good mathematical maturity and enable learners to build mathematical thinking and skill. The topics to be covered are injective, subjective and objective mappings. Product of mappings, inverse of a mapping. Binary operations on a set. Properties of binary operations (commutative, associative and distributive properties). Identity element of a set and inverse of an element with respect to a binary operation. Relations on a set. Equivalence relations, equivalence classes. Partition of set induced by an equivalence relation on the set. Partial and total order relations on a set. Well-ordered sets. Natural numbers; mathematical induction. Sum of the powers of natural numbers and allied series. Integers; divisors, primes, greatest common divisor, relatively prime integers, the division algorithm, congruencies, the algebra of residue classes. Rational and irrational numbers. Least upper bound and greatest lower bound of a bounded set of real numbers. Algebraic structures with one or two binary operations. Definition, examples and simple properties of groups, rings, integral domains and fields.
MAT 203: Further Calculus
This course is designed to develop advanced topics of differential and integral calculus. Emphasis is placed on the applications of definite integrals, techniques of integration, indeterminate forms, improper integrals and functions of several variables. The topics to be covered are differentiation of inverse, circular, exponential, logarithmic, hyperbolic and inverse hyperbolic functions. Leibnitz’s theorem. Application of differentiation to stationary points, asymptotes, graph sketching, differentials, L’Hospital rule. Integration by substitution, by parts and by use of partial fractions. Reduction formulae. Applications of integration to plane areas, volumes and surfaces of revolution, arc length and moments of inertia. Functions of several variables, partial derivatives.
MAT 202: Vector Algebra and Differential Equations
The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. The topics to be covered are vector algebra with applications to three-dimensional geometry. First order differential equations; applications to integral curves and orthogonal trajectories. Ordinary linear differential equations with constant coefficients and equation reducible to this type. Simultaneous linear differential equations. Introduction to partial differential equations.
MAT 206: Complex Numbers and Matrix Algebra
This course is designed to give an introduction to complex numbers and matrix algebra, which are very important in science and technology, as well as mathematics. The topics to be covered are complex numbers and algebra of complex numbers. Argand diagram, modulus-argument form of a complex number. Trigonometric and exponential forms of a complex number. De Moivre’s theorem, roots of unity, roots of a general complex number, nth roots of a complex number. Complex conjugate roots of a polynomial equation with real coefficients. Geometrical applications, loci in the complex plane. Transformation from the z-plane to the w-plane. Matrices and algebra of matrices and determinants, Operations on matrices up to . inverse of a matrix and its applications in solving systems of equation. Gauss-Jordan method of solving systems of equations. Determinants and their use in solving systems of linear equations. Linear transformations and matrix representation of linear transformations.
MAT 303: Introductory Analysis
This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. The topics to be covered include
limit of a sequence of real numbers, standard theorems on limits, bounded and monotonic sequences of real numbers, infinite series of real numbers, tests for convergence, power series, limit, continuity and differentiability of functions of one variable, Rolle’s theorem, mean value theorems, Taylor’s theorem, definition and simple properties of the Riemann integral.
MAT 305: Linear Algebra I
This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications. The topics to be covered are axioms for vector spaces over the field of real and complex numbers. Subspaces, linear independence, bases and dimension. Row space, Column space, Null space, Rank and Nullity. Inner Products Spaces. Inner products, Angle and Orthogonality in Inner Product Spaces, Orthogonal Bases, Gram-Schmidt orthogonalization process. Best Approximation. Eigenvalues and Eigenvectors. Diagonalization. Linear transformation, Kernel and range of a linear transformation. Matrices of Linear Transformations.
MAT301: Advanced Calculus I
Limit and continuity of functions of several variables; partial derivatives, differentials, composite, homogenous and implicit functions; Jacobians, orthogonal curvilinear coordinates; multiple integral, transformation of multiple integrals; Mean value and Taylor’s Theorems for several variables; maxima and minima with applications.
MAT302: Advanced Calculus II
This course covers vector valued functions. It introduces students to the concept of change and motion and the manner in which quantities approach other quantities. Topics include limits, continuity, derivatives of vector functions, gradient, divergence, curl, formulae involving gradient, divergence, laplacian, orthogonal curvilinear coordinates, line integrals, Green’s theorem in the plane, surface integrals. Other topics are the divergence theorem, improper integrals, Gamma functions, Beta functions, the Riemann Stieltjes Integral, pointwise and uniform convergence of sequence and series, integration and differentiation term by term.
Limits, continuity and derivatives of vector functions; gradient, divergence and curl; formulae involving gradient, divergence, curl and laplacian and orthogonal curvilinear coordinates; line integrals; Green’s theorem in the plane; surface integrals; the divergence theorem; improper integrals; Gamma and Beta functions; The Riemann Stieltjes integral; pointwise and uniform convergence of sequence and series; integration and differentiation term by term.
MAT 306: Linear Algebra II
This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving direct sum of subspaces, complement of subspace in a vector space and dimension of the sum of two subspaces. Other topics to be covered are one-to one, onto and bijective linear transformations, isomorphism of vector spaces, matrix of a linear transformation relative to a basis, orthogonal transformations, rotations and reflections, real quadratic forms, and positive definite forms.
MAT 310: Abstract Algebra I
This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics to be covered are: axioms for groups with examples, subgroups, simple properties of groups, cyclic groups, homomorphism and isomorphism, axioms for rings, and fields, with examples, simple properties of rings, cosets and index of a subgroup, Lagrange’s theorem, normal subgroups and quotient groups, the residual class ring, homomorphism and isomorphism of rings, subrings.
MAT 405: Ordinary Differential Equations
The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. Topics covered include linear differential equation of order n with coefficients continuous on some interval J, existence-uniqueness theorem for linear equations of order n, determination of a particular solution of non-homogeneous equations by the method of variation of parameters, Wronskian matrix of n independent solutions of a homogeneous linear equation, ordinary and singular points for linear equations of the second order, solution near a singular point, method of Frobenius, singularities at infinity, simple examples of Boundary value problems for ordinary linear equation of the second order, Green’s functions, eigenvalues, eigenfunctions, Sturm-Liouville systems, properties of the gamma and beta functions, definition of the gamma function for negative values of the argument; Legendre, Bessel, Chebyshev, Hypergeometic functions and orthogonality properties.
MAT 405: Ordinary Differential Equations
MAT 406: Partial Differential Equations
This course introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include first and second order partial differential equations, classification of second order linear partial differential equations, derivation of standard equation, methods of solution of initial and boundary value problems, separation of variables, Fourier series and their applications to boundary value problems in partial differential equation of engineering and physics, internal transform methods; Fourier and Laplace transforms and their application to boundary value problems.
MAT 415: Financial Mathematics
STA 403: Statistical Method II
MAT 404: Complex Analysis
This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. The topics to be covered in the course are: complex numbers, sequences and series of complex numbers, limits and continuity of functions of complex variables, elementary functions of a complex variable, Cauchy-Riemann criterion for differentiability, analytic functions, complex integrals, Taylor’s and Laurent’s series, calculus of residues, contour integration and conformal mapping.
MAT 407: Numerical Analysis I
This course is designed to equip students with the basic techniques for the efficient numerical solution of problems in science and engineering. Topics covered include round off errors and floating-point arithmetic, solution of non-linear equations, bracketing, fixed point methods, secant method, Newton's method, zeros of polynomials, Polynomial interpolation, orthogonal polynomial, least squares approximations, approximation by rational function, numerical differentiation, numerical integration, and adaptive quadrature.
MAT 408: Introductory Functional Analysis
This course is intended to introduce the student to the basic concepts and theorems of functional analysis and its applications. Topics covered include linear spaces, topological spaces, normed linear spaces & Banach Spaces, inner product spaces, Hilbert spaces, linear functional and the Hahn-Banach theorem.
MAT 416: Dynamical Systems
The course offers an introduction to Dynamical Systems from an applied and practical point of view. It will offer students the opportunity to learn how to compute the behaviour of differential equations as parameters varies. Topics include: linear dynamical systems and their stability, Routh-Hurwitz conditions, autonomous Systems, non-linear dynamical systems, equilibrium points and their stability, almost linear systems, phase plane analysis: direction fields and phase portraits, Lyapunov stability (simple and damped pendulum), periodic solutions, limit cycles, bifurcation theory, chaos and attractions.
MAT 499: Project Work (Optional)