MINOR
IN MATHEMATICS

MATH 261

The Differential and Integral Calculus/5 credits


MATH 262

The Differential and Integral Calculus/5 credits 

**Electives: 300400 level mathematics/3 credits
200400 level computer science or mathematics/6 credits
TOTAL 19 credits


**Electives may not include :


MATH 267

Applications of Calculus/4 credits


MATH 271

Applied Statistics/3 credits


MATH 309

Numeration Systems/3 credits


MATH 310

Functions, Probability, and Statistics/3 credits


MATH 313

Geometry and Reasoning/3 credits


MATH 451

The Teaching of High School Mathematics/3 credits

ALGEBRA
I ENDORSEMENT
Students who
are preparing to teach and who are majoring in fields other than mathematics
may be endorsed to teach mathematics courses through Algebra I in grades 6 –
12 by taking the courses listed below.

MATH 164

Precalculus/3 credits


MATH 181 
Finite Mathematics/3 credits 

or
MATH 343

Linear Algebra/3 credits


MATH 261

The Differential and Integral Calculus/5 credits


or
MATH 267

Applications
of Calculus/4 credits


MATH 309

Numeration Systems/3 credits


MATH 310

Functions, Probability, and Statistics/3 credits


MATH 313 
Geometry and Reasoning/3 credits 

or
MATH 335

Advanced Euclidean Geometry/3 credits


MATH 451

The Teaching of High School Mathematics/3 credits


CMSC 121

Introduction to Computer Science/3 credits


or
CMSC 204

Introduction to Programming/3 credits


TOTAL 2526 credits 
MATHEMATICS
COURSE DESCRIPTIONS
General
Education Courses *
Writing
Intensive Course **
Mathematics
114.
Mathematics for the Consumer. An
introductory course designed to acquaint the student
with the application of mathematics in the life of the consumer. Special
attention will be given to the algebraic derivation of formulas, the reduction
of real life situations to mathematical models, and the mathematics employed
in banking, budgeting, credit, taxes, insurance, installment buying,
annuities, stocks, bonds, and mortgages. 3 credits.
Mathematics
121.
Functions and Graphs. A study of
polynomial, rational, exponential, logarithmic and trigonometric functions
with emphasis on graphing techniques, algebraic and numerical properties and
applications. Prerequisite: Two years of high school algebra or by placement.
3 credits. *
Mathematics
164.
Precalculus. A study of functions
with an emphasis on exponential, logarithmic, and trigonometric functions in
order to prepare the student for calculus. 3 credits.
Mathematics
171.
Statistical Decision Making. An
elementary statistics course designed to show the student how statistics is
used in problem solving and decision making. Topics include measures of
central tendency and variability; elementary probability concepts; the
binomial, normal and Chisquare distributions, correlation and regression; and
hypothesis testing. Special emphasis is placed upon the proper use of
statistics in real life situations. 3 credits. *
Mathematics
181.
Finite Mathematics. A study of
discrete mathematical structures with applications primarily to business and
economics. Topics will be selected from a review of sets; linear and quadratic
functions; solving systems of linear equations using GaussJordan elimination;
matrix algebra; solutions of inequalities; linear programming, including the
graphical methods and introduction to the simplex method; introductory
probability; introduction to calculus; and mathematics of finance. 3 credits.
Mathematics
261, 262.
The Differential and Integral Calculus.
A unified course dealing with the basic ideas of calculus and analytic
geometry. Prerequisite for MATH 262: successful completion of 261. Students
who do not make a C or better in 261
should have the consent of the chair before enrolling in 262. 5 credits.
Mathematics
267.
Applications of Calculus. A course
designed for students in Business, Economics, and the Social and Life
Sciences. The techniques of calculus are presented in an informal approach.
Emphasis is on applications of the mathematical concepts of calculus, e.g.,
breakeven analysis, optimization, spread of epidemics, population growth
models. Credit will not be given in this course toward the mathematics major.
Prerequisite: MATH 164 or equivalent. 4 credits. *
Mathematics
271.
Applied Statistics. Topics include
measures of central tendency, probability distributions, measures of
dispersion, correlation and linear regression, multiple linear regression,
analysis of variance and covariance. The emphasis will be on linear modeling
techniques to conduct hypothesis tests. Computer applications will be an
integral part of the course. Knowledge of calculus will not be required.
Credit will not be given toward the mathematics majors. 3 credits.
MATHEMATICS
292.
Internship in Mathematics.
A semesterlong, onthejob learning experience designed to apply the
principles of mathematics. 118
credits.
Mathematics
295.
Special Topics. Selected topics in
mathematics. The topics may vary from semester to semester. May be repeated
for credit when topics change. 13 credits.
Mathematics
300.
A Transition to Advanced Mathematics.
An introduction to rigorous mathematical proof with focus on the properties of
the real number system. Topics include elementary symbolic logic, mathematical
induction, algebra of sets, relations, countability, algebraic and
completeness properties of the reals. 3 credits. **
Mathematics
309.
Numeration Systems.
A study of different
numeration systems. The development and characteristics of ancient numeration
systems, base numeration systems and the real number system will be studied.
Problem solving is emphasized. 3 credits.
Mathematics
310.
Functions, Probability and Statistics.
Examines functions, probability and statistics in the context of real life
situations and will include student investigations and hands on activities.
Prerequisite: MATH 309 and
proficiency in computer spreadsheets, or permission of instructor.
3 credits.
MATHEMATICS
311312.
Studies Abroad.
Primarily intended for transfer of credit earned abroad in courses in
mathematics. 118 credits.
Mathematics
313.
Geometry and Reasoning. A basic
study of polygons, polyhedra,
measurement, transformational geometry, coordinate geometry, descriptive
statistics, graphical methods and empirical and theoretical probabilities and
their uses. 3 credits.
Mathematics
330
(SCIENCE 330). Integration
of Mathematics and Science Principles.
An inquiry into basic principles involved in the study of mathematics
and science. Emphasis on measurement, use of manipulatives, inference,
prediction, data analysis, and hypothesizing. For Liberal Studies Majors only.
Students are required to take SCED 330 concurrently with this course. 1.5
credits each.
Mathematics
335.
Advanced Euclidean Geometry. A study
of Euclidean geometry from a more advanced viewpoint. The methods and
techniques of synthetic axiomatic geometry will be stressed through a study of
logic and formal proof, constructions, higher Euclidean geometry, finite
geometries, and nonEuclidean geometries. Prerequisite/corequisite: MATH 261.
3 credits.
Mathematics
336.
Survey of Modern Geometries. A study
designed to widen and enlarge the horizons of the students through an
examination of some of the geometric developments since the time of Euclid.
The characteristics and interrelatedness of various geometriestopological,
projective, affine, similarity, Euclidean, nonEuclidean and inversionwill
be briefly examined through transformations. Prerequisite: MATH 300. 3
credits.
Mathematics
342.
Introduction to Modern Algebra. Sets
and mappings, integers, general algebraic systems, groups, rings, and fields.
Prerequisite: MATH 300. 3 credits.
Mathematics
343.
Linear Algebra. A basic study of
vector spaces, linear transformations, and their relationships to matrix
algebra. Also included are determinants, isomorphism theorems, linear
functionals, and dual spaces. Prerequisite: MATH 262 or consent of department
chair. 3 credits.
Mathematics
345.
Number Theory. An introductory
course in additive and multiplicative number theory. Included are topics such
as: divisibility, prime numbers, congruences, residue systems, linear and
quadratic congruences, Diophantine equations, quadratic residues, and number
theoretic functions. Prerequisite/corequisite: MATH 342 or consent of
instructor. 3 credits.
Mathematics
350 (COMPUTER SCIENCE 350). Ethical
Issues in Mathematics and Computer Science. Consideration of ethical
implications of mathematics and computer science in society. Overview of
ethical theory; case studies of situations illustrating ethical dilemmas. A
knowledge of calculus and algorithms will be assumed. 1 credit. *
Mathematics
351.
Introduction to Topology.
Topological spaces, continuous mappings, homeomorphisms, compactness,
connectedness, metric spaces, and other selected topics in point set topology.
Prerequisite: MATH 361. 3 credits.
Mathematics
361.
Calculus III. Advanced topics in
calculus not considered in MATH 261, 262. Prerequisite: MATH 262. Students who
do not make C or better in 262
should have consent of the chair before enrolling. 3 credits.
Mathematics
371.
Introduction to Probability and
Statistics. Theory of probability; expected values of random variables;
discrete and continuous probability distributions. Prerequisite: MATH 361. 3
credits.
MATHEMATICS
390.
Directed Study in Mathematics.
Individualized study; recommended only when material cannot be studied
through existing course offerings. Must
have permission of department chair. 13
credits. May be repeated as 391, etc.; no more than 6 credits.
MATHEMATICS
392. Internship
in Mathematics. A
semesterlong, onthejob learning experience designed to apply the principles
of mathematics. 118 credits.
Mathematics
405.
Numerical Analysis. An investigation
of numerical techniques of approximation, matrix computations, integration,
and differentiation with emphasis on the solution of nonlinear equations,
linear systems and differential equations. The course will require use of the
computer. Attention will be given to the problems of rounding error,
conditioning, and stability. Prerequisite: MATH 343, 361 and CMSC 204 or
equivalent. 3 credits.
Mathematics
435 (COMPUTER SCIENCE 435). Queuing
Theory and Simulation. A course covering the basic mathematics of queuing
systems and the principles of the computer simulation of queuing systems.
Topics include M/M1, M/G/1, and G/M/1 queues, Laplace and ztransforms,
priority queuing, and basic computer simulation techniques. Prerequisite: CMSC
204 or equivalent, MATH 371. 3
credits.
Mathematics
451.
The Teaching of High School Mathematics.
A study of current practices in high school mathematics teaching with emphasis
on principles, techniques, and materials. Required for those planning to teach
high school mathematics. 3 credits.
Mathematics
460.
Differential Equations. Primarily a
study of ordinary differential equations of the first and second order with
application to elementary work in mechanics and physics. Prerequisite: MATH
361. 3 credits.
Mathematics
461. Senior
Seminar. A capstone course for the
mathematics major focusing on a historical perspective.
Emphasis will be on problem solving, connections between various
branches of mathematics, and the historical development of mathematical
structures. In addition, students
will be expected to research and present mathematical topics not covered in
other courses. Prerequisite: Mathematics Major and Senior Status. 3 credits.
**
Mathematics
462.
Advanced Calculus. A theoretical
approach to the study of limits, continuity, differentials, derivatives, and
integrals. Development of the real number system, elementary point set theory,
functions of several variables, infinite series, and power series.
Prerequisite: MATH 300, 361. 3 credits.
Mathematics
472.
Introduction to Mathematical Statistics.
Distribution of functions of random variables; moments and moment generating
functions; T, F and Chisquare distributions; limiting distributions; interval
estimation; tests of hypotheses; the Central Limit Theorem; regression
analysis; ANOVA. Prerequisite: MATH 361 and 371. 3 credits.
Mathematics
481.
Complex Analysis. An introduction to
the fundamental concepts of complex analysis, including the complex plane,
holomorphic functions, the exponential function, Cauchy integral formula,
Taylor series, Laurent series, conformal maps, the notion of residues and some
applications in physics. Prerequisite: MATH 361. 3 credits.
Mathematics
490.
Directed Study in Mathematics.
Individualized study; recommended only when material cannot be studied through
existing course offerings. Must have permission of department chair. 13
credits. May be repeated for no more than 6 credits.
mathematics
492. Internship
in Mathematics.
A semesterlong, onthejob learning experience designed to apply the
principles of mathematics. 118
credits.
Mathematics
495.
Special Topics in Mathematics.
Selected topics in mathematics. The topics may vary from semester to semester.
May be repeated for credit when topics change. 13 credits.
MATHEMATICS
498.
Honors Research in Mathematics.
Students conduct research in mathematics under the direction of a
faculty member and the Senior Honors Research Committee.
May be repeated as 499. 3
credits.
For
Graduates and
Advanced
Undergraduates
Mathematics
513.
The Teaching of Probability and
Statistics. This course is designed especially for teachers and will use
an experiential, informal, activitybased approach. There will be handson
activities and experiments relating empirical and theoretical probabilities.
Quick descriptive statistics and new graphical methods will be presented.
These techniques are useful in describing, comparing, exploring and
interpreting sets of data. There will also be intuitive ideas from inferential
statistics. 3 credits.
Mathematics
595.
Special Topics in Mathematics. 13
credits. Selected topics in mathematics. The topics may vary from semester to
semester. May be repeated for credit when topics change. 13 credits.
COMPUTER
SCIENCE PROGRAM
Faculty
John E. Arehart, Ed.D., Associate
Professor of Computer Science and Mathematics
Jeffery H. Peden, Ph.D., Associate
Professor of Computer Science
Robert P. Webber, Ph.D., Professor
of Mathematics and Computer Science
While every
attempt is made to state the requirements and concentrations available in the
department as succinctly as possible, it is recommended that every student
majoring or minoring in the department continue in close communication with
the academic advisor assigned by the department in order to plan the program
best suited to individual needs
and goals.
Students desiring a minor in computer science must successfully
complete the appropriate program described below, and must see the Chair of
the Department of Mathematics and Computer Science to officially declare a
minor in this field.
COMPUTER
SCIENCE MAJOR, B.A., B.S. DEGREE

CMSC 204

Introduction to Programming/3 credits


CMSC 206 
Data Structures in Advanced Programming/3 credits


CMSC 300 
Discrete Mathematics for Computer Science/3 credits 

CMSC 301 
Computer Organization and Assembler Language Programming/3 credits


CMSC 306

Computer Organization/3 credits


CMSC 308 
Organization of Programming Languages/3 credits


CMSC 310 
Introduction to Operating Systems and Computer Architecture/3 credits


CMSC 316 
ObjectOriented Programming/3 credits


CMSC 360 
Computer Network Theory/3 credits


CMSC 362 
Theory of Databases/3 credits 

CMSC 461

Seminar in Computer Science/3 credits


ENGL 214 
Technical Writing/3 credits


MATH 261 
The Differential and Integral Calculus/5 credits


MATH
262 
The Differential and Integral Calculus/5 credits


MATH 271 
Applied Statistics/3 credits


Options. (Choose one)
Option One 12 credits
Four
courses, one of which must be any mathematics or computer science course at
the 200 level or above, and the remaining three of which must be any computer
science courses at the 300 level or above.


Option Two 34 credits
Secondary Teaching Endorsement, grades 612
See professional education requirements:
Secondary Education Program
AddOn Endorsements
Additional endorsement requirement:
MATH 451 , The Teaching of High School Mathematics, 3 credits.


MATH 300 may be substituted for CMSC 300. Both may be taken for credit.

D.

General Electives NonTeaching Majors:
B.A./B.S. degree with Option One  16/17

E.

Total Credits Required for B.A. or B.S. degree 
120
Total Credits Required for B.A. or B.S. degree with
Secondary Teaching Endorsement 
125/126

MINOR
IN COMPUTER SCIENCE
A minor in computer science shall
consist of 18 credit hours of computer science courses, at least 12 hours of
which must be at the 300 or 400 level.
COMPUTER
SCIENCE COURSE DESCRIPTIONS
General Education *
Writing Intensive Course **
Computer
Science 121.
Introduction to Computer Science. An
introduction to computer science for nonspecialists. Basic computer
architecture and design, storage formats, principles of computer operation,
and algorithms. Application software that emphasizes the computer as a tool. 3
credits. *
Computer
Science 201. Beginning
COBOL. An introduction to
programming in a businessoriented language (COBOL) with emphasis on
commercial applications and elementary concepts of file processing.
3 credits.
Computer
Science 204.
Introduction to Programming. An
introductory course in computer science emphasizing programming and algorithm
development. Topics will include basic language structures, assignment,
iteration, control flow, language and programmer defined variable types, and
basic data manipulation models. 3 credits.
Computer
Science 206.
Data Structures in Advanced Programming.
A onesemester course in advanced programming utilizing data structures and
models. The course emphasizes advanced programming techniques in the
manipulation of data structures. Prerequisite: CMSC 204. 3 credits.
Computer
Science 215.
Introduction to Fortran. An overview
of the FORTRAN programming language, with emphasis on applications to
mathematics and science. Prerequisites: knowledge of another computer
language. 3 credits.
Computer
Science 290.
Self Study in Programming.
Independent study of a specific programming language, its syntax and
applications, based on prior study of programming languages in general. May
not duplicate other language courses. Must be arranged with an instructor and
approved by department chair before registering. May be repeated for credit
with different languages. Prerequisite: CMSC 206. 1 credit.
COMPUTER
SCIENCE 292.
Internship in Computer Science.
A semesterlong, onthejob learning experience designed to apply the
principles of computer science. 118
credits.
Computer
Science 295.
Special Topics. Selected topics in
computer science. The topics may vary from semester to semester. May be
repeated for credit when topics change. 13 credits.
Computer
Science 300.
Discrete Mathematics for Computer
Science. Topics in discrete mathematics used in computer science,
including methods of proof, graphs, computability, and formal grammars.
Prerequisites: CMSC 204 or 206. 3 credits.
Computer
Science 301.
Computer Organization and Assembler
Language Programming. Assembler language programming; addressing
techniques; internal storage structure; machinelevel representation of
instructions and data; subroutines. Prerequisites: Computer Science 206 or
consent of instructor. Fall only; 3 credits.
Computer
Science 302.
Data Abstraction Programming. A
onesemester course in advanced programming utilizing the data abstraction
programming paradigm. The course emphasizes advanced programming techniques
used in the design, definition, and manipulation of abstract data types.
Prerequisites: CMSC 206 (or equivalent) using a language of instruction other
than C++ and CMSC 315 (or equivalent). Note: This course may not be taken for
credit if credit has been received for CMSC 206 (or equivalent) using C++ as
the language of instruction. 3 credits.
Computer
Science 306. Computer
Organization. The organization and structuring of the major hardware
components of computers; the mechanics of information transfer and control
within a computer system; standard computer architectures; the fundamentals of
logic design. Prerequisite: CMSC 301. 3 credits.
Computer
Science 308.
Organization of Programming Languages.
Topics include language and definition structure, data types and structures,
control structures and data flow, runtime characteristics and lexical
analysis and parsing. Programming assignments will involve the use of several
different languages. Prerequisite: CMSC 206 or permission of instructor. 3
credits. **
Computer
Science 310.
Introduction to Operating Systems and
Computer Architecture. Emphasis will be placed on concepts rather than
case studies and on the interdependence of operating systems and architecture.
Topics include instruction sets, I/O and interrupt structure, addressing
schemes, microprogramming, memory management and recovery procedures.
Prerequisite: CMSC 301. 3 credits.
COMPUTER
SCIENCE 311,312.
Studies Abroad.
Primarily intended for transfer of credit earned abroad in courses in
computer science. 118 credits.
Computer
Science 316.
ObjectOriented Programming. A
course in the techniques of objectoriented programming in an objectoriented
programming language. Topics covered include inheritance, function and
operator overloading, object construction, visibility, information hiding, and
multiple inheritance. Prerequisite: CMSC 206. 3 credits.
Computer
Science 350. (MATHEMATICS 350). Ethical
Issues in Mathematics and Computer Science. Consideration of ethical
implications of mathematics and computer science in society. Overview of
ethical theory; case studies of situations illustrating ethical dilemmas. A
knowledge of calculus and algorithms will be assumed. 1 credit. *
Computer
Science 360.
Computer Network Theory. A course
covering the theory and design of modern computer networks. Topics include
local and wide area networks, the OSI network model, basic network performance
analysis, and real time networks. Prerequisite: CMSC 206. 3 credits.
Computer
Science 362.
Theory of Databases. A course
covering the theory and practice of modern databases design and
implementation. Topics include relational and hierarchical database design,
database query languages, update consistency, and distributed databases.
Prerequisite: CMSC 206. 3 credits. **
Computer
Science 389.
Artificial Intelligence. An advanced
theory and programming course covering the theory and techniques of artificial
intelligence. Topics covered include computer vision, game playing, minmax
algorithms, and an introduction to the LISP programming language.
Prerequisite: CMSC 206. 3 credits.
COMPUTER
SCIENCE 390.
Directed Study in Computer
Science. Individualized
study; recommended only when material cannot be studied through existing
course offerings. Must have
permission of department chair. 13
credits. May be repeated as CMSC
391, etc.; no more than 6 credits.
COMPUTER
SCIENCE 392.
Internship in Computer Science.
A semesterlong, onthejob learning experience designed to apply
the principles of computer science. 118
credits.
Computer
Science 408.
Ada and Software Engineering. Syntax
and semantics of the Ada programming language. Principles of Software
Engineering. Prerequisites: CMSC 204 or 206. 3 credits.
Computer
Science 415.
Theory of Computation. The basic
theories underlying computer science, such as language and automata theory,
and the computability of functions. Emphasis is placed on the development of
theoretical machine and language descriptions. Prerequisite: CMSC 300. 3
credits.
Computer
Science 435 (MathEMATICS 435) Queuing
Theory and Simulation.
A course covering the basic mathematics of queuing systems and the principles
of the computer simulation of queuing systems. Topics include M/M1, M/G/1, and
G/M/1 queues, Laplace and ztransforms, priority queuing, and basic computer
simulation techniques. Prerequisite: CMSC 204 or equivalent, MATH 371. 3
credits.
Computer
Science 445.
Compiler Design.
A course covering the basic theory and techniques of compiler and code
translation systems. Topics include lexical analysis, parsing, and code
generation, and the various techniques used when handling differing source
language classes. A programming intensive course. Also covered are the
techniques of topdown and bottomup parsing. Prerequisite: CMSC 300. 3
credits.
Computer
Science 452.
Computers in Education. A survey of
programming languages, software, and hardware commonly found in an educational
setting. Prerequisite: CMSC 121 or consent of instructor. 3 credits.
Computer
Science 461.
Seminar in Computer Science.
Students will work individually and in teams on the development,
implementation, and maintenance of a large software project. This course is
the capstone experience in the computer science major. A segment on assessment
will be included. Corequisite: Satisfaction of all other requirements for the
computer science major or consent of instructor. 3 credits.
Computer
Science 490.
Directed Study in Computer Science.
Individualized study; recommended only when material cannot be studied through
existing course offerings. Must have permission of department chair. 13
credits. May be repeated for no more than 6 credits.
COMPUTER
SCIENCE 492.
Internship in Computer Science.
A semesterlong onthejob learning experience designed to apply the
principles of computer science. 118
credits.
Computer
Science 495.
Special Topics. Selected topics in computer science. The topics may vary from
semester to semester. May be repeated for credit when topics change. 13
credits.
COMPUTER
SCIENCE 498.
Honors Research in Computer
Science. Students conduct
research in computer science under the direction of a faculty member and the
Senior Honors Research Committee. May
be repeated as 499. 3 credits.
For
Graduates and
Advanced
Undergraduates
Computer Science 505. Computers
in Mathematics Education. Techniques
and existing programs in computerassisted instruction, computermanaged
instruction, simulation and modeling. Offered on demand.
3 credits.
Longwood College
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