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Department of Mathematics Thompson Complex, Central Wing Dr. Peter Hamburger, Head Mathematics courses at the University are designed with the
interests and needs of varying groups of students in mind. Majors and minors
are available to those planning to pursue careers in secondary education as
well as to those whose preparation is being directed toward positions in
business and industry or toward further work in mathematics at the graduate
level. In addition, several courses are offered to meet the demands for the
mathematical training of students whose major educational objectives are not
directly related to mathematics. Mathematics majors are assigned advisors from among the departmental
faculty and are required to consult with these advisors before each
registration period. When planning a program of study in this department, each student
should be aware of the University’s academic requirements and regulations
contained in this catalog in the chapter “Academic Information.” Specific
attention should be given to the sub-sections in the chapter entitled (a)
Academic Programs, (b) General Education Requirements, and (c) Academic
Requirements and Regulations. Students should be aware that some academic programs may require
additional scholastic regulations and standards not specified in the catalog.
To obtain a copy of these regulations, students should contact the department
head.
(A) General Major (728): The student must
complete a minimum of 35 hours of mathematics with a minor or second major
giving a total of at least 54 hours (48 unduplicated) with the following
requirements:
Other acceptable courses for the general major are MATH 275 (up to
3 hours), 305, 315, 323, 329, 331, 398 (up to 3 hours), 405, 406, 415, 417,
423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours), and STAT 301. (B) Extended Major (528): The student must complete a
minimum of 48 hours of mathematics with the following requirements:
Other acceptable courses for the extended major are MATH 275 (up
to 3 hours), 305, 315, 323, 329, 331, 398 (up to 3 hours), 405, 406, 409, 415,
417, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours), and STAT 301. (A) General Certifiable Major (reference number 728): The student must
complete a minimum of 35 hours of mathematics with a minor or second major
giving a total of at least 54 hours (48 unduplicated) with the following
requirements:
Other acceptable courses for the general certifiable major are
MATH 275 (up to 3 hours), 305, 315, 329, 331, 398 (up to 3 hours), 405, 406,
409, 415, 417, 421, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6
hours). (B) Extended Certifiable Major (reference number 528): The student must
complete a minimum of 48 hours of mathematics with the following requirements:
Other acceptable courses for the extended certifiable major are MATH 275 (up to 3 hours), 305, 315, 329, 331, 398 (up to 3 hours), 405, 406, 409, 415, 417, 421, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours). Suggested Program of Study
Suggested
Program of Study
Suggested
Program of Study
Suggested Program of Study
The student who elects a minor in mathematics (either option) must
complete the following courses: the sequence MATH 126, 227 or the sequence MATH
122, 132, 232; and MATH 307. Option 1: Minor for Employment in Industry The student who elects a minor in mathematics but does not plan to
teach is provided a noncertifiable minor that
requires at least eighteen semester hours of mathematics. In addition to the
foundational sequence (MATH 126, 227, 307*) this student is required to select
two courses from MATH 305, 310, 317, 327, 329, 331, or STAT 301**. * Students majoring in engineering may replace MATH 307 with MATH
350. ** Students may not count both MATH 329 and STAT 301 in the minor. Option 2: Minor Certifiable for Teaching Secondary Mathematics The student who elects a minor in mathematics certifiable for
secondary education is required to complete at least twenty-one semester hours
of mathematics. In addition to the foundational sequence (MATH 126, 227, 307)
this student is required to complete the following:
Grades K-5 Certification
For option 1 (two fields) students must complete the following
courses (to total at least 25 hours):
The following sequencing of mathematics courses is recommended for
students seeking middle grades certification in mathematics (two fields):
Note: A student with appropriate high school mathematics
preparation and a math ACT score of 27 or greater may choose to begin with MATH
126 or MATH 119. If a student’s initial course is MATH 119 or 126, MATH 409 or
413 should be selected to complete the hour requirement. Also, if a student
expects to study calculus beyond that required for middle school preparation,
MATH 126 should be selected. For option 2 (one field) students must complete the following
courses (to total at least 30 hours):
The following sequencing of mathematics courses is recommended for
students seeking middle grades certification in mathematics (one field).
Note: If a student begins his or her college mathematics courses
at a level higher than indicated in item a, the department may grant permission
to substitute higher level mathematics courses.
MATHEMATICS A
student who has earned credit for the listed course with a grade of “C” or
better may not subsequently receive credit for the courses following in
parentheses: MATH 117 (MATH 116); MATH 118 (MATH 116 and 117); MATH 119 (MATH
116 and 118); MATH 122 (MATH 116 and 118); MATH 126 (MATH 116, 117, 118, 119,
and 122); MATH 203 (MATH 116 and 118); MATH 227 (MATH 116, 117, 118, 119, 122,
126, 132, and 232); MATH 310 (MATH 109); MATH 329 (MATH 109 and 203); STAT 301
(MATH 109 and 203). *These
courses fulfill the Mathematics (Category D-II) general education requirement.
math 106 academic
support for math 116E 0
hours Corequisite: MATH 116E Special Requirement: Students who withdraw from MATH 116E must
also withdraw from MATH 106. Provides supervised sessions
in which students work individually or in groups to complete supplementary
assignments or projects; may include assistance with text-specific online
homework and graphing calculators. *math 109 General Mathematics 3 hours GEN
ED D-II Terminal
course for non-science majors suggested for the student who has satisfactorily
completed minimum high school mathematics requirements and needs no further
work in algebra. Topics include sets, introduction to probability and
statistics, geometry, and consumer mathematics. *math 116 (116E) College Algebra
3 hours GEN ED D-II Prerequisites:
High school Algebra I and II and satisfactory score on Math Placement Exam; or
DMA 096C with a grade of C or better. Student must enroll in MATH 116E if
his/her DMA 096C grade was a C, or previous MATH 116 grade was D, F, or W, or
Math ACT and MPE scores indicate need for enhanced version. Corequisite
for MATH 116E: MATH 106, Academic
Support for MATH 116E Special
Requirement: Students who withdraw from
MATH 106 must also withdraw from MATH 116E. Graphing
and problem solving are integrated throughout the study of polynomial, absolute
value, rational, radical, exponential, and logarithmic functions. (Graphing
calculator required.) *math 117 Trigonometry
3 hours gen ed d-ii Prerequisites:
Four years of high school mathematics including Algebra I and II and geometry,
and satisfactory score on Math Placement Exam; or MATH 116 with a grade of C or
better. Unit
circle; trigonometric functions and graphs; trigonometric identities and
equations; right triangle trigonometry; laws of sines
and cosines; DeMoivre’s Theorem; vectors and
applications of trigonometry. (Graphing calculator required.) *math 118 College Algebra and
trigonometry 5 hours
GEN ED D-II Prerequisites:
High school Algebra I and II and geometry, and a satisfactory score on the Math
Placement Exam; or DMA 096C or MATH 096 with a grade of A. (Students who have
completed DMA 096C or MATH 096 are urged to substitute MATH 116-117 for MATH
118.) Real
number system, algebraic manipulations, and solutions of equations and
inequalities, absolute value, exponential and logarithmic functions,
trigonometry, systems of equations, complex numbers. (Graphing calculator
required.) *math 119 Fundamentals of Calculus 4 hours GEN ED D-II
An
introduction to calculus designed for non-science and non-technical majors.
Applications are directed toward the management sciences and related areas. Not
accepted for credit toward a mathematics major or minor. (Graphing calculator
required.) MATH 121 COMPUTATIONAL
problem solving 4
hours Prerequisite: Enrollment in the Gatton
Academy of Mathematics and Science in Kentucky Students will tackle problems
ranging from elementary to advanced, using mathematical methods, algorithmic
techniques, and computational methods.
This course is taught jointly by mathematics and computer science
faculty; it is equivalent to CS 121. *math 122 calculus of a single variable
I 3 hours
gen ed D-II Prerequisites:
Four years of high school mathematics, including Algebra II, geometry, and
trigonometry, and satisfactory score on Math Placement Exam; or MATH 117 or MATH
118, with grade of C or better. *math 126 Calculus and Analytic Geometry
i 4.5 hours GEN ED
D-II Prerequisites:
Four years of high school mathematics, including Algebra II, geometry, and
trigonometry, and satisfactory score on Math Placement Exam; or MATH 117 or
MATH 118, with grade of C or better. This
is the first of a sequence of courses which present a unified treatment of
plane and solid analytic geometry and differential and integral calculus.
(Graphing calculator required.) math 132 calculus of a single
variable II
3 hours Prerequisites:
Math 122 with a grade of C or better Integral
calculus. Second course of a three-course sequence presenting a unified
development of analytical geometry, differential and integral calculus, and
series. Math 142 Calculus
with Applications for Life sciences 5
hours Prerequisites: Four years of high school mathematics,
including Algebra I and II, geometry, and a course that includes trigonometry,
and satisfactory Math ACT and math placement scores; or MATH 117 or MATH 118,
with a grade of C or better Exponential and logarithmic
functions, derivatives, integration, first order differential equations, and
systems of linear equations, with major emphasis on applications in life
sciences. math 175 university experience –
mathematics 2 hours Prerequisite:
For beginning college freshmen or transfer students with fewer than 24 semester
hours of credit Transition
to university experience. Topics include study skills, critical thinking
skills, library education, exploration of majors and careers, degree programs,
campus resources and personal development. Specific degree requirements for a
major in mathematics and career opportunities in mathematics are also
discussed. *math 203 Statistics
3 hours GEN ED D-II Prerequisite:
MATH 116 or MATH 118 or permission of instructor Introduction
to elementary probability theory. The analysis of data by means of frequency
distributions and the statistics which describe them. The binomial and normal
probability distributions. Statistical inference. Emphasis is on applied real
world problems. Not accepted for credit toward a mathematics major or minor. math 211
Mathematics for Elementary
Teachers I
3 hours Prerequisite:
Completion of general education math requirement with grade of C or higher.
(For students in the early grades (K-5) teacher certification program or students
pursuing middle grades (5-9) certification with a mathematics emphasis.) Elementary
work with relations, systems of numeration, number systems, and number theory. math 212
Mathematics for Elementary Teachers II 3 hours Prerequisite:
MATH 211 with a grade of C or higher and completion of general education
mathematics requirement. (For students in the early grades (K-5) teacher
certification program or students pursuing middle grades (5-9) certification
with a mathematics emphasis.) Construction
geometry, motion geometry, nonmetric geometry,
measurement including the metric system, and introductions to computers,
probability, and statistics. math 213
Laboratory for Mathematics for elementary teachers I 1 hour Co-requisite:
MATH 211 Hands-on
laboratory, using manipulatives and problem-solving
techniques to strengthen mathematical vocabularies and deepen understanding of
topics from MATH 211. math 214
Laboratory for Mathematics for elemtary teachers II 1 hour Co-requisite:
MATH 212 Hands-on
laboratory, using manipulatives and problem-solving
techniques to strengthen mathematical vocabularies and deepen understanding of
topics from MATH 212. math 227
Calculus and Analytic Geometry II
4.5 hours Prerequisite:
MATH 126 with a grade of “C” or higher The
continuation of MATH 126 math 232
calculus of a single variable iii 3 hours Prerequisite:
MATH 132 with grade of C or better Sequences,
series, parametric equations and polar coordinates, applications using
technology. Third course of a three-course sequence presenting a unified
development of analytical geometry, differential and integral calculus, and
series. math 275
introductory topics in mathematics 1-3
hours Prerequisite:
MATH 126 and permission of instructor Varied
topics selected to give students an early introduction to interesting
mathematical problems or applications not found in the foundation sequence. math 295
Introduction to Research Methodology 1 hour Prerequisite:
Ogden Research Scholar, or 3.2 grade point average at the end of freshman year
or OCSE faculty member recommendation. To
familiarize Ogden Research Scholars and other interested students with the
fundamentals of choosing a research topic, performing a bibliographical search
on a subject, classification of instruments, data taking, data reduction,
professional ethics and related topics. The common points of research
methodology in the different scientific areas will be emphasized, with examples
drawn from various disciplines. Computers will be utilized. (Course does not
count toward any major or minor.) math 305
Introduction to Mathematical Modeling 3 hours Prerequisite:
MATH 227 or MATH 232 Theory
and computer implementation of mathematical models. Deterministic, stochastic,
discrete, continuous, and matrix models. Introduction to advanced topics such
as linear algebra, differential and difference equations, probability,
stochastic processes, and dynamical systems. math 307
Introduction to Linear Algebra
3 hours Prerequisite:
MATH 227 or MATH 232 Systems
of linear equations, matrix algebra, vector spaces, inner product spaces,
linear transformations, eigenvectors, quadratic forms. math 310
Introduction to Discrete Mathematics 3 hours Prerequisite:
MATH 227 or MATH 232 math 315 Theory of Numbers
3 hours Prerequisite:
MATH 307 A
study of the arithmetic of the integers, divisibility, prime numbers, factorization,
diophantine equations, congruences,
quadratic residues. math 317 Introduction to Algebraic
Systems
3 hours Prerequisites:
MATH 307 and MATH 310 Introduction
to groups, rings, polynomial rings, integral domains, and fields. math 323 Geometry I
3 hours Prerequisite:
MATH 307 or permission of instructor Beginning
with a re-examination of elementary Euclidean geometry, the course includes a
study of absolute plane geometry and the parallel postulate, which leads to an
axiomatic treatment of hyperbolic geometry and related topics. math 327 Multivariable Calculus 4
hours Prerequisite:
MATH 227 or MATH 232 Topics
in real-valued functions of several variables including directional
derivatives, implicit functions, gradient, Taylor’s Theorem, maxima, minima, and
Lagrange multipliers. Differential calculus of vector-valued functions
including chain rule and Inverse Function Theorem. Multiple integrals, line
integrals, surface integrals, Stokes’ and Green’s Theorems. math 329 Probability and Statistics
I
3 hours Prerequisites:
MATH 307 and MATH 310 Axioms
and laws of probability; discrete and continuous probability distributions;
multivariate distributions; random variables; expectation; moment generating
functions; Central Limit Theorem. math 331 Differential Equations
3 hours Prerequisite:
MATH 227 or MATH 232 (Recommended corequisite: MATH 307) Methods
of solution of differential equations, existence and nature of solutions,
systems of differential equations, applications, and numerical solutions. math 350
ADVANCED ENGINEERING MATHEMATICS 3 HOURS Prerequisite:
MATH 331 or equivalent Special
topics in Laplace transforms, linear algebra and complex analysis. Designed for
engineering students. math 398 Seminar
1 hour (May
be repeated for up to a total of 3 hours credit.) Prerequisite:
MATH 327 Students
will work on a topic of interest under the direction of a mathematics faculty
member, who will set the requirements for the course. Mathematics majors could have the opportunity
to continue this work in MATH 498. math 403
Geometry For Elementary and middle school teachers 3 hours Prerequisites:
MATH 211 and 212 (For students in the early grades (K-4) teacher certification
program or students pursuing middle grades (5-8) certification with a
mathematics emphasis.) Both
formal and informal methods are used to explain the basic concepts of Euclidean
geometry. Emphasis is given to the investigative approach, organizational
skills, and problem solving. math 405
Numerical Analysis I (CS 405)
3 hours Prerequisites:
MATH 307 or 310 or 327, and CS 230 or CS 240 or permission of instructor Computer
arithmetic, roots of equations, polynomial approximation and interpolation,
numerical differentiation and integration. Computer solutions of problems will
be required. math 406
Numerical Analysis II 3
hours Prerequisites:
MATH 307, 327, 331, and either MATH 405 or CS 405 The
solution of linear systems by direct and iterative methods, matrix inversion,
the calculation of eigenvalues and eigenvectors of
matrices. Initial and boundary value problems in ordinary differential
equations. Computer solution of problems will be required. math 409 History of Mathematics
3 hours Prerequisite:
Six hours of approved mathematics courses at the 300 and/or 400 level or
permission of instructor. History
of mathematics from ancient times through the development of calculus, with
emphasis on famous problems. Provides knowledge and appreciation useful in the
classroom. This course cannot be accepted as part of the 35-hour requirement
for the non-certifiable mathematics major. Term papers will be required. math 411
Problem Solving for Elementary and middle school teacherS 3 hours Prerequisites:
MATH 403 or 323 or permission of instructor Integrates
concepts developed in algebra, geometry, logic, statistics, probability, and
elementary number theory. Students are encouraged to use problem-solving
strategies, models, and technologies, and to create problems of their own. math 413
Algebra and technology for middle grades teachers 3 hours Prerequisite:
MATH 212 or equivalent The
use of graphing calculators and computer software to explore algebraic ideas
including patterns, functions, equations, inequalities, linear programming,
curve fitting, and practical applications of algebra and technology. math 415
Algebra and Number Theory
3 hours Prerequisite:
MATH 315 or 317 An
integrated survey of modern algebra and number theory. Topics include number
systems, divisibility, congruences, groups and their
application to number theory. math 417
Algebraic Systems
3
hours Prerequisite:
MATH 317 Theory
of groups. math 421
Problem Solving for Secondary Teachers 3 hours Prerequisites:
MATH 307 and 310; MATH 329 and 323, or permission of instructor Utilizes
various techniques and technology to solve mathematical problems. Integrates
concepts from algebra, geometry, trigonometry, probability, statistics, number
theory, discrete mathematics, linear algebra, and calculus. math 423
Geometry II
3 hours Prerequisite:
MATH 323 An
axiomatic development of hyperbolic geometry based on the hyperbolic parallel
postulate and the absolute geometry developed in MATH 323, including an
emphasis on contrasts with Euclidean geometry. math 429
Probability and Statistics II
3 hours Prerequisites:
MATH 327 and MATH 329 Multivariate
probability distributions; sampling distributions, statistical inference; point
and interval estimation, properties of estimators; hypothesis testing;
regression and correlation; analysis of variance; non-parametric methods. math 431
Intermediate Analysis I
3 hours Prerequisite:
MATH 317 Topics
chosen from cardinality, limits, continuity, elementary topological concepts,
sequences and series, differentiation and integration, elementary functional
analysis. math 432
Intermediate Analysis II
3 hours Prerequisite:
MATH 431 Continuation
of MATH 431 math 435
Partial Differential Equations
3 hours Prerequisites:
MATH 307, 327 and 331 Equations
of first and second order; elliptic, hyperbolic and parabolic equations; Sturm-Liouville theory; applications to equations of mathematical
physics using separation of variables and Fourier series. math 439 Topology
3 hours Prerequisite:
MATH 317 or permission of instructor Topological
spaces, mappings, separation axioms, compactness, connectedness, arcwise connectedness, metric spaces. math 450 Complex Variables
3 hours Prerequisite:
MATH 327 Complex
number plane, analytic functions of a complex variable, integration, power
series, calculus of residues, conformal representation, applications of
analytic function theory. math 470 Introduction to Operations
Research 3 hours Prerequisite:
MATH 307 and 327 or permission of instructor Principles
and techniques of operations research including linear programming, integer
programming, quality theory, sensitivity analysis, and dynamic programming. math 475 Selected Topics in
Mathematics
1-3 hours Prerequisite:
Permission of instructor A
consideration of special topics to acquaint the advanced undergraduate student
with significant problems and developments of current interest in mathematics.
Topics may vary each semester offered. MATH 498
senior seminar
1 hour Prerequisites:
MATH 317 and MATH 327 and senior standing, or permission of instructor Students
will study articles in current mathematical journals or undertake independent
investigations in mathematics. Written and oral presentations are required. STATISTICS Prerequisite:
MATH 126 or MATH 132 A
calculus-based introduction to applied statistics, with emphasis on analysis of
real data. Curve fitting, probability
models, estimation and testing for means and proportions, quality control; use
of computers for data analysis and simulation. |
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