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Degree of Bachelor of Science
in Mathematics Requirements

(Math Major with Physics or Economics Minor)

The course of study for the degree of Bachelor of Science in Mathematics takes four (4) academic years. The minimum requirements for the degree are 125 semester hours. A candidate must complete his general requirements of forty (40) semester hours as prescribed by the University of Liberia. He must earn forty-three semester hours in his major, eighteen (18) semester hours in his minor and twenty-four (24) semester hours of free and support electives together.

Course Descriptions - Mathematics

003 Mathematics - Fundamentals of Mathematics

Understanding basic concepts underlying algebra, functions, exponents, areas, fractions and percent;. Reasoning skills required for these concepts. Word problems. This is a one semester, non-credit course required of all entering freshmen who do not receive satisfactory scores on the placement examination in mathematics. Satisfactory performance in this course will permit the student to enroll In Mathematics 101.

Credit: no credit

101 Mathematics - Algebra
(Pre-requisite: Passing of placement exam or Mathematics 003)

Properties of real numbers, inequalities, polynomials, factoring, linear and quadratic equations, simultaneous linear equations, functions, graphs, exponents, radicals, logarithms.

Credit: 3 credits/semester

107 Mathematics - Precalculus
(Pre-requisite: Satisfactory performance on
placement exam or Mathematics 101)

A one semester course designed to provide the necessary foundation for the study of calculus. Emphasis on those elementary functions which are of primary interest in calculus. These include polynomial, exponential, logarithmic arid trigonometric functions, and their combinations. Special attention to graphing. The contents include: Real numbers (number line and the plane, absolute value and distance); Functions (terminology, graphs, algebra of functions); Linear equations and inequalities (i ncluding sySterns); Polynomials; Exponentials and logarithms (properties, graphs, tables, applications); Conic sections {circle, parabola, ellipse, hyperbola); Polar coordinates and complex numbers.

Credit: 4 credits/semester

108 Mathematics - Mathematics for Decision Making
(Pre-requisite: Successful completion
of either Mathematics 101 or 107)

A one semester finite mathematics course emphasizing applications in business, the social sciences, and, to some extent, the life sciences. An intuitive, motivated approach with a variety of realistic applications used both to motivate and to illustrate the mathematical concepts. The contents include: Counting techniques (Venn diagrams, tree diagrams, permutations, combinations); Probability (basic concepts, conditional probability. Bayes theorem, independent events, finite stochastic processes, binomial probabilities, expected value); Linear systems (functions, lines, systems of linear equations. linear inequalities); Matrix algabra (vectors, matrices, Gauss-Jordan, Markov chains); Linear programming (geometric solution, simplex method); and Mathematics of finance (simple and compound interest, present and future, value, annuities, sinking

Credit: 4 credits/semester

109 Mathematics - Introduction to Computer Programming
(Pre-requisite; Mathematics 107)

Problem solving methods and algorithm development. An available programming language taught in sufficient detail to enable students to solve non-trivial problems on a computer. How to design, code, debug, and document programs using techniques of good orogramming style.

Credit: 3 credits/semester

201 Mathematics - Calculus I
(Pre-requisite: Mathematics 107)

Differential calculus of algebraic, trigonometric, exponential and logarithmic functions of a single variable. Topics include: functions, limits, continuity, the derivative, differentiation techniques, implicit differentiation, higher derivatives, maxima and minima, concavity, graphing, motion and other applications. Introduction .to integral calculus.

Credit: 4 credits/semester

202 Mathematics - Calculus II
(Pre-requisite: Mathematics 201)

Integral calculus of functions of a single variable. Topics include; limits of sums, definite and indefinite integration, techniques of integration, applications of integration (area, volume, arc length), improper integrals, infinite series (including Taylor's series), introduction to partial derivatives.

Credit: 4 credits/semester

204 Mathematics - Linear Algebra
(Pre-requisite: Mathematics 201)

Matrices, determinants, linear systems, vector spaces, linear transformations, eigenvalues and eigenvectors, applications.

301 Mathematics - Calculus III
(Pre-requisite; Mathematics 202)

Calculus of functions of several variables- Topics include: vectors in space, vector functions of several variables, limits, continuity, partial derivatives, the total differential, tangent planes and normal tines, chain rule, gradient, directional derivatives, maxima and minima, Lagrange multipliers, iterated and multiple integrals, change of coordinates in integration, line integrals, Green's theorem, Gauss' theorem. Stoke's theorem.

Credit: 4 credits/semester

302 Mathematics - Real Analysis
(Pre-requisite: Mathematics 301)

Topology of the real line, limits, continuity, differentiability, integration.

Credit: 3 credits/semester

304 Mathematics- Differential Equations
(Pre-requisite: Mathematics 202)

Ordinary differential equations of first and higher orders. Applications. Introduction to Laplace transforms, systems of equations, and power series solutions.

Credit: 3 credits/semester

305 Mathematics - Probability and Statistics I
(Pre-requisite: Mathematics 301)

Sample spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probability Bayes' theorem. Random variables, probability distributions, expectation, mean, variance, moment-generating functions. Standard distributions (binomial, Poisson, normal, gamma, t and F), multivariate distributions, transformations of random variables, conditional and marginal distributions. Chebychev's Inequality, limit theorems (Law of Large numbers, Central Limit Theorem). Examples of stochastic processes such as random walks and Markov chains.

Credit: 3 credits/semester

308 Mathematics - Numerical Analysis
(Pre-requisite: Mathematics 109 and 202)

Introduction to wide selection of numerical procedures with continuous discussion of error analysis to stress the effectiveness and efficiency of the methods. Topics include: Computer arithmetic; Solution of a single algebraic equation (convergence, Newton's method, interpolation); Solution systems of equations (Gaussian methods, iterative methods, matrix inversion); Interpolating polynomials (Lagrange interpolation, least squares, truncation errors); Numerical integration; Numerical solution of ordinary differential equations.

Credit: 3 credits/semester

310 Mathematics - Advanced Differential Equations
(Pre-requisite: Mathematics 304)

Series solutions of second order linear differential equations, special functions (gamma, beta, hypergeometric, Bessel's equation, Legen-dres equation), Fourier series, difference equations, Laplace transforms, Introduction to partial differential equations.

Credit: 3 credits/semester

401 Mathematics - Modern Algebra
(Pre-requisite: Junior standing in
mathematics or science)

Group theory (definition and elementary properties, isomorphism, subgroup, cyclic group, coset decomposition and Lagrange's theorem, homomorphism, normal subgroup, factor group, fundamental theorem of homomorphism, permutation groups and Cayley's theorem, finitely generated abelian groups, Sylow theorems); Ring theory (definition and elementary properties, quotient rings, polynomial rings); Vector fields.

402 Mathematics - Complex Variables
(Pre-requisite: Mathematics 302)

Complex numbers, analytic functions, conformal mapping, elementary functions and power series, complex integration, calculus of residues.

Credit: 3 credits/semester

404 Mathematics - Probability and Statistics II
(Pre-requisite: Mathematics 305)

Estimation (consistency, unbiasedness, maximum likelihood, confidence intervals). Testing hypothesis (power functions, Type I and II errors, Ney man-Pears on lemma, likelihood ratio tests, tests for means and variances. Regression and correlation. Chi-square tests. Additional selected topics in statistics as time permits.

Credit: 3 credits/semester

405 Mathematics-Special Topic
(Pre-requisite: Consent of instructor)

Choice of topics: Number Theory, Mathematical Logic, Introduction to Topology, Algebraic Topology, Modern Geometry.

Credit: 3 credits/semester

406 Mathematics - History of Mathematics
(Pre-requisite: Junior standing in mathematics
or science)

Selected topics in the development of mathematics.

Credit: 3 credits/semester

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