DEPARTMENT
OF MATHEMATICS
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
funds).
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
