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MATHEMATICS AT EUREKA
Mathematics,
more than any other human endeavor, relies on deductive reasoning to produce new
knowledge from the investigation of natural events, whether they occur in our
immediate environment or in the immensity of space. It serves as a universal language
which represents, interprets, and integrates all such knowledge. The subject of
mathematics is divided into algebra, geometry, analysis, and probability. Some
of the concepts of each of these subdivisions are particularly useful in helping
to discuss or solve problems in other fields. These concepts are frequently called
Applied Mathematics.
REQUIREMENTS FOR A MATHEMATICS MAJOR
38 hours including
the following:
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MAT 130 |
Calculus with Analytical
Geometry I |
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MAT
140 |
Calculus with Analytical Geometry II |
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MAT 250 |
Linear Algebra |
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MAT 255 |
Calculus with Analytical
Geometry III |
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MAT 275 |
Differential Equations |
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MAT 280 |
Discrete Mathematics |
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MAT 310W |
Probability and
Statistics |
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MAT
320 |
Abstract Algebra |
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MAT340W |
Foundations of Geometry |
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MAT370 |
Real Analysis |
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S&M
200W |
Methods of Science and Critical Thinking |
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Plus one of the following courses: |
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CSC
135 |
Computer Programming - Pascal |
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CSC
165 |
Introduction to Programming |
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Total |
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REQUIREMENTS FOR A MATHEMATICS MAJOR WITH
TEACHER CERTIFICATION
(1) The Mathematics major outlined above plus PHS
111 Introduction to Earth Science.
(2) Plus Professional Education Courses
Requirements. (For a list of these courses please refer to the Education section
concerning requirements for certification in Secondary Education.)
(3) To
qualify for Student Teaching, a student must have an overall 2.50 GPA and a 2.75
GPA in the Mathematics major outlined above.
REQUIREMENTS FOR A MAJOR IN
ELEMENTARY EDUCATION WITH A MATHEMATICS SPECIALIZATION
17 semester hours
of coursework. Please refer to the Education section for a listing of required
courses.
REQUIREMENTS FOR A MATHEMATICS MINOR
20 hours of course work
in Mathematics numbered 130 or above with at least 6 hours at the 300 level.
MATHEMATICS
COURSES
098R Elementary Algebra -- 3 hours
The first in a two-semester developmental mathematics sequence. Topics of study
include arithmetic, real numbers, order of operations, ratio and proportion, percent,
scientific notation, variables, the language of algebra, solving linear equations
and inequalities, graphing linear equations, and solving application problems.
Mathematical study skills will be studied and applied throughout the course. This
course will meet five days a week. (Does not count toward major, minor, general
education, or graduation requirement.) Graded Pass/Fail.
099R
Intermediate Algebra -- 3 hours
Prerequisite: MAT 098, an ACT Math
score of at least 19, or placement by divisionally designated nationally normed
placement test. (e.g. COMPASS)
The second course in a two-semester developmental
mathematics sequence, this course builds upon a student's early exposure to algebra
in an effort to develop those skills needed in the further study of mathematics,
science, or related fields. Topics will include a review of basic algebra, graphs,
factoring, polynomials, linear and quadratic equations and inequalities, systems
of equations, exponent, roots and radicals, rational expressions, and problem
solving.(Students who have received academic credit for MAT 121, MAT 130, or MAT
260 may not enroll in MAT 099. Does not count toward major, minor, general education,
or graduation requirements.) Graded Pass/Fail.
121
Precalculus -- 4 hours
Prerequisite: MAT 099R or an ACT Math score
of at least 23 or placement by divisionally designated, nationally normed placement
test. (E.g. COMPASS)
Study of functions, graphing (with technology), and
geometry of Cartesian and polar coordinate plane. Emphasis on function concept
as modeling, including polynomial, rational, algebraic, exponential, logarithmic
and trigonometric functions. Geometric representations and manipulations as showing
richness of marriage of geometric to algebraic. Students who have received academic
credit for MAT 130 cannot enroll in MAT 121 for academic credit. (Does not count
toward major or minor requirements.)
130 Calculus
with Analytical Geometry I -- 4 hours
Prerequisite: MAT 121 or
by placement.
Study of the limits extended to differentiation and integration
of polynomial and trigonometric functions with coordinate geometry interpretations.
An introduction to the definite integral. The calculus will be presented in multiple
representations: verbal, numerical and symbolic.
140
Calculus with Analytical Geometry II -- 4 hours
Prerequisite: MAT
130; MAT 122 highly recommended.
Extension of differentiation and integration
to exponential and logarithmic functions with emphasis on general techniques of
integration. The introduction to infinite series and Taylor series. Calculators
and computers will be used.
161 Finite Math and Statistics
for Business -- 4 hours
Prerequisite: MAT 099R, an ACT Math score
of at least 23, or placement by divisionally designated, nationally normed placement
test (e.g. COMPASS).
Finite mathematics with business applications. Finite
math portion introduces Euler circuits, Hamiltonian circuits, digraphs, linear
programming and other mathematical techniques used in solution of optimization
problems. Mathematics of finance, including computation of interest rates, amortization
of loans, annuities, etc. are also covered. Study of statistical techniques needed
in business settings, interpretation of information in graphical formats, and
statistical information in graphic form.
162 Applied
Functions and Calculus for Business -- 4 hours
Prerequisite: MAT
099R, an ACT Math score of at least 23, or placement by divisionally designated,
nationally normed placement test (e.g. COMPASS).
Deals with functions,
modeling, and algebra topics with introduction to deferential calculus. Topics
geared to business applications and problem solving, functions and how they are
represented graphically , in tabular forms, in mathematical formulas, and in words.
Focus on linear, exponential, and polynomial functions, in expressing and solving
business problems, as well as construction of models representing real world business
applications. Derivative is introduced and applied in marginal revenue, profit
and cost problems, and optimization.
250 Linear Algebra
-- 3 hours
Prerequisite: MAT 140 with programming language recommended.
Introductory course in linear and matrix algebra with primary concern for finite
real vector spaces. Computer software will be used for various applications.
255 Calculus with Analytic Geometry III -- 4 hours
Prerequisite: MAT 250.
Discussion of partial differentiation, multiple
integrals, line integrals, Green's Theorem, and parametric equations.
260 Statistics -- 3 hours
Prerequisite: Math
Competency Exam (MCE).
Discussion of fundamental methods of descriptive
statistics, statistical inference, and an introduction to non-parametric statistics
and to basic probability. (Does not count in any mathematics major.)
262 Mathematics for Life and Art -- 3 hours
Prerequisite:
Math Competency Exam (MCE).
Exploration of a variety of mathematical topics
that mix the concrete and applicable with the aesthetic in order to broaden an
deepen the mathematical experience and understanding of the student of the liberal
arts and sciences. Topics may include: interest and present value, mathematics
of voting, finite probability, statistical significance, game theory, exponential
growth models, mathematics of music, fractals, the traveling salesman problem,
etc.
264 Nature of Mathematics -- 3 hours
Prerequisite: Math Competency Exam (MCE).
Topics may include: do
numbers exist? are the laws of mathematics arbitrary? is statistical significance
significant? how is research possible in mathematics? how big is infinite? what
is a proof? is illogical knowledge possible? do androids truly understand their
own speech?
275 Differential Equations -- 3 hours (Offered in alternate years.)
Prerequisite: MAT 255.
Discussion
of first and second order ordinary differential equations, LaPlace Transforms,
eigenvalues of linear systems.
280 Discrete Mathematics
-- 3 hours
Prerequisite: MAT 130, with CSC 135 or CSC 165 recommended.
Concepts in discrete mathematics as applied to computer science. Sets, logic,
mathematical induction, relations, functions and graphs are discussed. Emphasis
will be placed on algorithmic processes.
310W Probability
and Statistics -- 3 hours (Offered in alternate years.)
Prerequisite:
MAT 140.
Study of concepts of probability leading to discussion of the
binomial, poisson, and normal distributions, as a foundation for statistical inference.
320 Abstract Algebra -- 3 hours (Offered in
alternate years.)
Prerequisite: MAT 255.
Introduction of the concept
of algebraic structures with particular reference to the properties of groups
and rings.
340W Foundations of Geometry -- 3 hours (Offered in alternate years.)
Prerequisite: MAT 255.
Systematic
treatment of the foundation of Euclidean Geometry with an introduction to several
finite and non-Euclidean geometries.
370 Real Analysis
-- 3 hours (Offered in alternate years.)
Prerequisite: MAT 255.
Study of limit processes applied to continuous or differentiable real-valued functions.
Careful definitions and rigorous methods of proof are emphasized. Topology is
introduced as the proper framework for continuous functions. Advanced calculus
techniques are reviewed.
Additional science & mathematics requirements
The courses
in this area can be required for a particular major or minor in the Science and
Mathematics Division.
200W Science & Mathematics
Seminar -- 1 hour
Prerequisite: sophomore standing and 8 credits
of science or mathematics.
Drawn from the fields of physics, mathematics,
biology, chemistry, and geology, this course focuses upon the great paradigms
of these areas - relativity, evolution, cell theory, atomic theory, and plate
tectonics. Questions to be addressed include: In science, what is a hypothesis?
a theory? a law? How are scientific theories constructed? What is falsification?
What are the criteria for adequacy in a scientific theory? How does one think
logically and critically in science? Scientific theories and disciplines will
be contrasted with a variety of pseudosciences.
390
Experimental Studies -- 1-4 hours
Prerequisite: Satisfactory completion
of two courses at the 300 level in the area of research.
Individual experimental
research by the student in a topic or problem arranged in cooperation with a faculty
member in the area and concurrence of the Division chairperson. Arrangements for
research must be completed before the beginning of the term of study. A maximum
of four hours may be counted toward a major. Departmental designations are assigned
to each individual subject.
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