MA: Courses in Mathematics
Department of Mathematics, Engineering, and
Computer Science
MA 105 Introduction to Contemporary Mathematical Applications 3 credit
A course for students with varied mathematical interests and backgrounds.
Stresses applications of contemporary mathematics in modern
society. Topics include management science, statistics, social choice,
patterns, population sizes, and computers. Emphasizes conceptual understanding
and appreciation. This course satisfies the Carroll College
Core Curriculum for mathematics, but not as a statistics requirement.
Prerequisite: Intermediate Algebra. Spring semester.
MA 112 Precalculus: Functions and Graphs 3 credit
A comprehensive study of elementary functions to prepare students
for a college course in calculus. Topics include a review of intermediate
algebra including the solution of equations and inequalities, and an
in-depth look at functions, inverse functions, their graphs, symmetries,
asymptotes, intercepts, and transformations. Linear, polynomial, rational,
radical, exponential, logarithmic, and trigonometric functions
are studied, and graphing calculators are used extensively. Prerequisite:
Mathematics preparation at least through Intermediate Algebra. Spring
semester.
MA 117 Difference Equations and Linear Algebra 3 credit
Introductory college mathematics course in finite difference equations
and linear algebra. Topics include sequences, differences, linear
and nonlinear difference equations, systems of difference equations,
numerical solutions of linear and nonlinear equations, and analytical
techniques for solving linear systems using linear algebra. Applications
from many fields are studied and the role of mathematical modeling
is a central focus. Formal computer labs are a part of the course each
week, with spreadsheets being the primary software employed. This
course satisfies a Carroll College Core Curriculum for all students
and the mathematics requirement for business majors. Prerequisite:
three years of high school mathematics through Intermediate Algebra.
Each semester.
MA 121 Differential Calculus 3 credit
This is the first of a two-semester, six-credit calculus sequence. We
begin the first semester by reviewing functions from several perspectives
(symbolic, numeric, and graphic). For most of the course we
study differential calculus, emphasizing how we can use calculus to
understand real-world problems such as police radar detection, laying
an oil pipeline around a swamp, and understanding motion. We use
computers and calculators extensively, and we also focus on learning
how to explain mathematics verbally and in writing. The sequence MA
121-MA 122 is considered to be equivalent to MA 131.Prerequisite:
Four years of high school mathematics including precalculus.
MA 122 Integral Calculus 3 credit
This is the second of a two-semester, six-credit calculus sequence.
In this course we study topics in integral calculus, emphasizing how
we can use calculus to understand real-world problems such as fluid
pumping and lifting, how rain catchers are used in city drain systems,
and how a compound bow fires an arrow. We use computers and
calculators extensively, and we also focus on learning how to explain
mathematics verbally and in writing. The sequence MA 121-MA 122
is considered to be equivalent to MA 131. Prerequisite: A grade of C
or better in MA 121.
MA 131 Calculus of Single Variable Functions 4 credit
This course covers all aspects of single-variable calculus including derivatives,
antiderivatives, definite integrals, and the fundamental theorem
of calculus. We highlight how we can use calculus to understand
real-world problems such as laying an oil pipeline around a swamp,
fluid pumping and lifting, and how rain catchers are used in city drain
systems. We use computers and calculators extensively, meeting in the
computer lab once each week. We also focus on learning how to explain
mathematics verbally and in writing. This is the same material that is
covered in MA 121-122, except this is an accelerated course that does
not review precalculus material. Prerequisite: Previous calculus experience
or strong precalculus background. Fall semester.
MA 201 Mathematics for Elementary Education I 3 credit
A course primarily for prospective elementary teachers, designed to give
a background in logic, set theory, the set of integers and their properties,
the system of rational numbers, and real numbers as an extension of the
rationals. Prerequisite: Intermediate Algebra. Fall semester.
MA 202 Mathematics for Elementary Education II 3 credit
An extension of MA 201 into geometry and measurement, functions
and their graphs, and a brief introduction to probability and statistics.
Special emphasis will be given to the development of skills in problemsolving
and to applications. Prerequisite: MA 201. Spring semester.
MA 207 Elementary Statistics 3 credit
The basic concepts used in statistics such as measures of central tendency,
variation, probability distributions, and statistical inference are
stressed. Applications are made in the social, communication, health,
biological, and physical sciences. This course does not count toward a
major or minor in mathematics. Prerequisites: Intermediate Algebra.
Each semester.
MA 232 Differential Equations & Linear Algebra I 4 credit
This course is an introduction to difference equations, differential
equations, and linear algebra. Specific topics include analytical and
numerical solutions to difference equations and first-order linear
differential equations, phase line analysis, stability of equilibrium,
matrix equations and eigenvalues. We emphasize how this mathematics
can be used on many real-world problems such as how to predict
the spread of a disease, how a home mortgage works, and how to
understand the growth of animal populations. We use computers and
calculators extensively, meeting in the computer lab once each week.
We also focus on learning how to explain mathematics verbally and
in writing. Prerequisite: A grade of C or better in MA 131 or in MA
122. Spring semester.
MA 233 Multivariable Calculus 4 credit
In this course we study multivariable and vector calculus including
vectors, parametric equations, surfaces, partial differentiation, multiple
integrals, and vector calculus. The big spotlight in this course is using
these ideas to understand things like force fields, the flow of water, and
magnetic fields. Once a week we meet in the computer lab to use the
power of computers to focus on the visual aspects of these concepts to
gain insight into more complex situations. We also focus on learning
how to explain mathematics verbally and in writing. Prerequisite: A
grade of C or better in MA 131 or in MA 122. Fall semester.
MA 301 Foundations of Mathematics 3 credit
An examination of logic, sets, functions, and methods of proof as a
foundation for the study of mathematics. Other topics covered include
mathematical induction, recursive definitions, relations (equivalence
relations), elementary number theory, transformational geometry, and
some history of mathematics. Prerequisite: Grade of “C” or better in
MA 233. Spring semester.
MA 328 Modern Applications of Discrete Mathematics 3 credit
A look at some actual applications of discrete mathematics that emphasize
such unifying themes as mathematical reasoning, alagorithmic
thinking, modeling, combinatorial analysis, the kinds of structures
used in discrete mathematics, and the use of technology. Possible topics
include cryptography, primes and factoring, computer passwords,
networking problems, shortest paths, scheduling problems, building
circuits, modeling computation, and correctness of algorithms. Three
one-hour class periods with a substantial computing component illustrating
the technology and the ideas studied. Prerequisite: Grades
of “C” of better in MA 131 or MA 121-122. Fall semester.
MA 334 Differential Equations & Linear Algebra II 4 credit
In this course, we focus on both systems of differential equations, with
special attention given to modeling, linearization, and equilibrium
analysis; as well as the mathematical language of systems – linear
algebra, especially transformations and vector spaces. We will motivate
the material through applications such as population models,
structural, and electrical systems, and linear algebra applications such
as 3-D imaging, Markov processes, and Leslie matrices. Technology
will again play a major role in this course, as we will have frequent
computer demonstrations in class and weekly computer labs to explore
the quantitative aspects of these topics. You will have the opportunity
to explore topics beyond the textbook on a series of group projects
throughout the semester. Prerequisite: A grade of C or better in MA
232. Spring semester.
MA 336 Probability and Statistics I 2 credit
This course is a calculus-based introduction to basic concepts in
probability and statistics. Topics in probability include: probability of
simple and compound events; an introduction to discrete and continuous
random variables including the uniform, binomial, and normal
distributions, and random event simulation. Topics in statistics include
statistical measures and graphs and simple linear regression. We begin
to learn how to perform statistical analysis on data sets and draw appropriate
conclusions based on their analysis. Prerequisite: A grade of
C or better in MA 131 or in MA 122. Spring semester.
MA 341 Probability and Statistics II 3 credit
A calculus-based course in applied probability and statistics. Many
types of univariate and multivariate probability distributions are
derived and applications are studied. Exposes the student to various
decision-making techniques when working with statistical information.
Students also gain experience with statistical computing software.
Prerequisite: A grade of “C” or better in MA 336. Fall semester. Fulfills
writing intensive requirement.
MA/CS 342 Numerical Computing and Visualization 3 credit
In this course we study the basic numerical methods used by computers
to solve a wide variety of problems, emphasizing how we can use graphics
to understand how things work. We focus not just on how these
methods work, but when they are appropriate, where they fail, and
how to interpret their results. This course is designed around a series
of open-ended projects based on real-world problems, such as how to
predict the price of heating oil, testing rocket orbital trajectories, and
studying the flow of heat throughout a building. The topics we study
include least squares regression methods, interpolation, curve fitting,
and the numerical solution of a wide range of differential equations
(both ODEs and PDEs). Prerequisite: A grade of “C” or better in MA
334, or taken concurrently with MA 334. Spring semester. Fulfills
Writing Intensive requirement.
MA 366 Junior Seminar 1 credit
This is a one-credit, pass/fail, seminar-style course. There will be three
main segments: select a faculty director for either an honors thesis or a
senior project and write a research proposal, write a resume and research
job opportunities, and write a graduate school essay and research graduate
school opportunities. The overall goal of this course is to prepare
students for their senior year and beyond. This course should be taken
in the spring of the year before intended graduation (typically in the
spring of the junior year). Spring semester annually.
MA 401 Modern Algebra and Applied Geometry 3 credit
This course covers the traditional topics from abstract algebra, including
groups, rings, integral domains, fields, and homomorphic and
isomorphic relationships, as well as standard topics from geometry,
including axiomatic systems in both Euclidean and Non-Euclidean
geometrics and transformational geometry with vectors and matrices.
The focus for the class is the contemporary applications of the concepts
presented, together with the weaving together of geometric and
algebraic themes. Linear algebra is the integrating theme. Prerequisites:
Grade of “C” or better in MA 301.
MA/CS 403 Introduction to Modern Cryptography 4 credit
This course is intended to be an introduction to the essential core
areas of modern cryptography. We begin with a look at historical
cryptography and then move into more modern concepts. Mathematical
background is provided as needed and informal descriptions
of the cryptosystems along with more precise psuedo-code descriptions
are given. Algorithms and systems will be illustrated with many
examples, and their mathematical underpinnings carefully explained.
Because of the heavy use of mathematics made in this course (number
theory, discrete mathematics, probability, linear algebra and probably
some calculus), this course is cross-listed and may be taken either for
mathematics or computer science credit. The course is lab-based
with each lab illustrating cryptosystems and concepts studied in class.
Prerequisites: Grades of “C” or better in MA 131 or MA 122 and MA
328. Fall semester.
MA 421 Mathematical Optimization, Applications, and Analysis 3 credit
This course is a project-based exploration of topics in optimization
and mathematical programming, such as linear, integer, nonlinear, and
stochastic programming. We explore the modeling, algorithmic and
heuristic solution approaches to, and sensitivity analysis of problems
such as the Knapsack problem, Traveling Salesman problem, and the
Ising spin glass problem. Computers and technology will again play
an important role as we investigate both the implementation and
the theoretical basis of solution techniques. This course will bring
together topics from single and multivariable calculus, linear algebra,
and probability. Prerequisite: Grades of C or better in MA 334 and in
MA 336. Fall semester.
MA 471 History Seminar in Mathematics 1 credit
This course in the history of mathematics is intended to give students
an insight into some of the great masterpieces of mathematics, as seen in
their historical contexts. Developing an understanding of the individuals
who were the creators of mathematics helps one better appreciate
their creations. Required course for mathematics secondary-education
majors. Offered when demand is sufficient.