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:

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.