Academic Course Descriptions
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References to the timing of course offerings which follow
apply only to day courses. Evening and summer school course offerings
are scheduled according to need. Christian Brothers University reserves
the right to cancel classes at any time due to insufficient enrollment.
MATHEMATICS COURSES
Note: Most Mathematics courses require the use of a graphing
calculator.
MATH 101. FUNDAMENTALS OF ALGEBRA
The course is designed to give the student fundamental quantitative
and algebraic skills needed in other mathematics and science courses.
Topics include: equations and inequalities, linear systems, exponents,
factoring, rational expressions, rational exponents, quadratic equations,
and functions. The course does not supply any portion of the mathematics
credits required in any CBU degree program. You may not receive credit
for MATH 101 after completing any mathematics course numbered above
101. Prerequisite: One year of high school algebra. One semester; three
credits
MATH 105. FINITE MATH (Formerly MATH
112)
This course contains introductory topics in mathematics for students
in arts and business. Topics include lines, linear systems, matrices,
linear programming, introduction to probability and statistics, financial
math. Prerequisites: MATH 101 or Passing a placement exam. Offered in
the Fall and Spring. One semester; three credits
MATH 106. APPLIED MATH WITH AN INTRODUCTION TO
CALCULUS
(Formerly MATH 111) This course contains introductory topics in mathematics
for students in arts and business. Topics include: functions; graphs;
linear, polynomial, rational, exponential, and logarithmic models; introduction
to differential and integral calculus. A student can receive credit
for only one of MATH 106 or MATH 131. A student can receive credit for
only one of MATH 106 or MATH 108. Prerequisite: MATH 105 or MATH 117.
Offered in the Fall and Spring. One semester; three credits
MATH 108. MATH MODELING FOR THE LIBERAL ARTS
The course uses models appropriate to arts majors to motivate the study
of algebra. Topics include: algebraic expressions; symbol manipulation;
linear and quadratic equations; functions; graphs; linear, polynomial,
rational, exponential, and logarithmic models. The course stresses interpretation
of the mathematical model and its diverse applications. A student may
receive credit for only one of MATH 108 or MATH 117. A student may receive
credit for only one of MATH 106 or MATH 108. Prerequisite: MATH 105.
Offered in the Fall and Spring. One semester; three credits
MATH 117. PRECALCULUS
The goals of the course are to teach the student the basic concepts
of college algebra, linear equations, quadratic equations, word problems,
functions, graphs, exponential and logarithmic functions, right triangle
trigonometry, trigonometric functions. The course stresses problem solving
by the student with the use of a graphing calculator. Prerequisite:
MATH 101 or equivalent. Offered in the Fall and Spring. One semester;
three credits
MATH 131. CALCULUS I
The goals of the course are to teach the student important concepts
of calculus and its applications. Topics include functions, the derivative
and its interpretations, the definite integral and its interpretations,
the Fundamental Theorem of Calculus, rules of differentiation, applications
of the derivative and antiderivatives. Three lectures and one laboratory
period per week. Prerequisite: MATH 117. This prerequisite is waived
for a student who passes a departmental placement test. Offered in the
Fall and Spring. One semester; three credits
MATH 132. CALCULUS II
The goals of the course are to teach the student additional important
concepts of calculus begun in MATH 131. Topics include integration including
parts, partial fractions and use of tables, applications of integration,
differential equations and modeling, approximations using Taylor and
Fourier polynomials and series. Prerequisite: MATH 131. Offered in the
Fall and Spring. One semester; three credits
MATH 141. INTRODUCTION TO DISCRETE MATHEMATICS
This course considers a variety of discrete mathematical themes and
subjects. These themes include problem solving, abstraction, representation,
mathematical reasoning and proof, recursion, induction, modeling and
synthesis. Topics include logic, graphs, sets, algorithms and combinatorics.
Prerequisite: MATH 106 or 117. Offered in the Spring semester. One semester;
three credits
MATH 201. APPLIED STATISTICS
The course concerns the use of statistical methodology in planning,
presentation, analysis and interpretation of scientific experiments
and field observations. Topics are chosen from elements of probability
and statistical inference, including estimates of parameters, confidence
intervals, tests of hypotheses for quantitative and qualitative observations,
correlation, nonparametric methods. Its goal is to allow science majors
to analyze real data in a correct statistical manner. Offered in the
Fall semester. Prerequisite: MATH 131. One semester; three credits
MATH 231. DIFFERENTIAL EQUATIONS
This course is an introduction to the concepts and methods of ordinary
differential equations. Topics include: first-order equations, elementary
numerical methods, qualitative analysis, second-order homogeneous linear
equations, the methods of undetermined coefficients and variation of
parameters for nonhomogeneous equations, Laplace transforms, and models
in science and engineering. Prerequisite: MATH 132. Offered in the Fall
and Spring semesters. One semester; three credits.
MATH 232. CALCULUS III
Algebra of vectors in a plane and in space; the calculus of vectors;
vector functions; basic concepts of multivariable calculus; partial
derivatives; multiple integrals. Prerequisite: MATH 231. Offered in
the Fall and Spring. One semester; three credits
MATH 301. GEOMETRY AND HISTORY OF MATHEMATICS
The course contains topics in geometry and the history of mathematics.
Topics include Euclidean and non-Euclidean geometry, mathematical structures
and the historical development of mathematical concepts. Prerequisite:
MATH 132. Offered every other year. One semester; three credits
MATH 308. STATISTICS
The course considers statistical methods with applications in engineering
and science. Topics are selected from an introduction to probability,
descriptive statistics, sampling methods, design of statistical experiments,
concepts of hypothesis testing and confidence intervals, correlation,
linear regression and analysis of variance. Offered in the Spring semester.
Prerequisite: MATH 232. One semester; three credits
MATH 309. PROBABILITY
The course considers fundamental topics in probability with applications
in engineering and science. Topics are selected from: basic concepts
in probability, random variables, expectation, variance, covariance,
moment generating functions, common distributions such as binomial,
hypergeometric, Poisson, geometric, uniform, normal, exponential, chi-square,
T and F distribution, probability models, central limit theorem and
functions of a random variable, bivariate, marginal, and conditional
distributions. Offered in the Fall semester. Prerequisite: MATH 232.
One semester; three credits
MATH 329. APPLIED NUMERICAL ANALYSIS
The course teaches the student the basic techniques of modeling and
numerical computation with emphasis on applications and the use of numerical
software. Topics will be chosen from the following: modeling of physical
systems with algebraic, differential and integral techniques; algorithms
for approximation; fitting functions to data; algorithms for the solution
of linear systems and for finding eigenvalues and eigenvectors; algorithms
for the solution of differential and integral equations; Fourier transforms.
Offered in the Fall semester. Prerequisite: MATH 232 and a computer
language. One semester; three credits
MATH 401. LINEAR ALGEBRA
This course contains an introduction to the basic concepts of linear
algebra; namely Gaussian elimination, the theory of simultaneous linear
equations, determinants, vector spaces, eigenvalues, eigenvectors and
linear transformations. The course includes applications of linear algebra
to selected topics from engineering, biology, and business. Prerequisite:
MATH 232. Offered every other year. One semester; three credits
MATH 402. ABSTRACT ALGEBRA
The course contains an introduction to some basic concepts of abstract
algebra, namely groups, rings, and fields and includes applications.
Prerequisite: MATH 232. Offered in the Spring semester of even numbered
years. One semester; three credits
MATH 405. DISCRETE MATHEMATICS
This course is an introduction to graph theory and combinatorics. The
topics will be chosen from the following: the basic properties of graphs
and digraphs, graphs as models, Eulerian and Hamiltonian circuits, graph
coloring, trees, network algorithms, generating functions, and recurrence
relations. Prerequisite: MATH 231. Offered every other year. One semester;
three credits
MATH 413. COMPLEX ANALYSIS (Formerly
MATH 403)
This course concerns itself with the rudiments and techniques of complex
analysis. Topics that are covered include: complex sequences, the derivative
of a complex function, the Cauchy-Riemann equations, integration in
the complex plane and the Cauchy-Goursat theorem, Cauchy’s integral
formula, Morera’s theorem, Taylor and Laurent series, residue
theory, and the evaluation of definite integrals. Prerequisite: MATH
232. Offered in the Fall semester of even numbered years. One semester;
three credits
MATH 414. REAL ANALYSIS (Formerly MATH
302)
The course develops the theory of calculus. It stresses the proofs of
the theorems for functions of one variable. Topics include sequences,
series, functions, limits, continuity, differentiation and integration.
Prerequisite: MATH 232. Offered in the Spring semester of odd numbered
years. One semester; three credits
MATH 461-462. SENIOR SEMINAR I AND II
The student conducts an independent investigation in some field of mathematics.
The course requires both written and oral reports. In addition, the
student must pass a comprehensive assessment test in mathematics. Prerequisites:
Junior or Senior standing and approval of the department head. Offered
in sequence in the Fall and Spring. Pass/Fail Grading for Math 461.
One semester each; zero and two credits respectively.
MATH 470-479. TOPICS IN MATHEMATICS
This course is designed to meet the current needs of the students and
to express the particular interests of the instructor. Prerequisites:
Junior standing, MATH 232 and Permission of instructor. One semester;
one to three credits
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