Mathematics-Physics

2005 - 2006 College of the Ozarks Catalog

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Bachelor of Arts, Bachelor of Science

The major in Mathematics will enable students to: 1) obtain a background in mathematics (including Analysis, Algebra and Differential Equations) suffi­cient for graduate work; 2) organize and analyze information, solve problems readily and construct logical arguments; 3) do mathematics, using modern technology when appropriate; 4) appreciate the utility of mathematics.

All prerequisite courses require a grade of C- or better.

COURSES IN MATHEMATICS (MAT)

013 Intermediate Algebra Topics include real and complex numbers, factoring, solving linear and non-linear equations and inequalities in one variable, and applications of equations. Many course topics will be illustrated with calculators and/or computers. Does not satisfy General Education requirements. May not be taken concurrently with or after completion of the equivalent of MAT 133 (or the equivalent of any higher num­bered MAT course) with a C- or better. (F/S)

104 Mathematics for Elementary and Middle School Teachers—Prerequisite: Admission in the Teacher Ed. program or permission. This course prepares prospective teachers of elementary and middle school mathematics. An understanding of the basic operations in mathematics and their grounding in sets is developed. Topics include sets, numeration, measurement, geometry, logic, number theory, algebraic reasoning, statistics, and problem solving. Mathematical learning experiences using manipulatives are the focus of the laboratory portion of the course. Three hours lecture, one two-hour laboratory per week. (F/S)

123 Mathematical Inquiry with Applications—Prerequisite: MAT 013 or Math ACT 19 or greater or MPT 20 or greater. Topics may include logic, sets, probability, statistics, functions, finance, and geometry. (F/S)

133 College Algebra—Prerequisite: MAT 013 or Math ACT 21 or greater or MPT 25 or greater. Topics include graphing functions and relations, conic sections, exponential and logarithmic functions, systems of equations, and matrices. (F/S)

135 Discrete Mathematics and Trigonometry—Prerequisite: MAT 133 or Math ACT 25 or greater or MPT 35 or greater. Topics covered will include sets, functions, elementary propositional and predicate logic, Boolean algebra, elementary graph theory, matrices, proof techniques (including induction and contradiction), combinatorics, probability, theory of random numbers and an introduction to trigonometric functions and their applications. (F/S)

142 Trigonometry—Prerequisite: MAT 013 or Math ACT 21 or greater or MPT 25 or greater. Topics include trigonometric functions, identities, equations, vectors, and inverse functions. (F)

143 Statistics—Prerequisites: MAT 013 or Math ACT 21 or greater or MPT 25 or greater or permission. This course is an algebra-based introduction to descriptive and inferential statistics. Topics include discrete and continuous distributions, measures of central tendency and variability, correlation and regression, and analysis of variance.

175 Calculus I—Prerequisite: MAT 133 and MAT 142 or MAT 135 or permission. Introductory topics to include Analytic Geometry, limits, definition of derivatives, derivatives and differential formulas, applications of derivatives, definition of integrals, the Fundamental Theorem of Calculus, integration formulas and Riemann sums. Four hours lecture, one two-hour laboratory per week. (S)

202 Introduction to the History of Mathematics—Prerequisite: MAT 175 or permission. Designed to give an appreciation of the historical development of mathematics. The course includes a survey of various concepts and their developments from antiquity to present, with emphasis on the people involved in the growth of mathematics. (S–odd)

205 Calculus II—Prerequisite: MAT 175 or permission. Topics include applications of integrals, exponential and logarithmic functions, formal integration of exponential, logarithmic, trigonometric, hyperbolic and inverse functions. Other topics include vectors and analytic geometry. Four hours lecture, one two-hour laboratory per week. (F)

213 Calculus III—Prerequisite: MAT 205 or permission. Infinite series, tests for convergence and divergence, differential calculus of functions of several variables, multiple integration and improper integrals. (S)

Prerequisite for all 300-400 level courses: 45 hours or permission.

303 Number Theory—Prerequisite: MAT 135 or permission. An introduction to the theory of numbers. A variety of topics dealing with the properties of integers will be covered. These include division and factorization properties of integers, prime numbers and perfect numbers, number representations, linear diophantine equations, linear and quadratic congruences, quadratic reciprocity and others.

313 Differential Equations—Prerequisite: MAT 205. An introductory course in the methods of solving ordinary differential equations. Emphasis on the techniques for solving linear differential equations with applications to geometric, physical science and engineering problems. (S–odd)

323 Modern Geometry—Prerequisite: MAT 135 or permission. A study of some modern aspects of mathematics, including logical foundations of geometries and an introduction to non-Euclidean geometries. Recommended for prospective secondary teachers of mathematics. (F–odd)

333 Linear Algebra—Prerequisite: MAT 205 or permission. Topics include vector spaces, systems of linear equations, determinants, matrices and linear transformations. (F)

343 Probability and Statistics—Prerequisite: MAT 213. Topics include basic probability theory, introduction to mathematical statistics, random variables, expectations, means, variances, discrete and continuous distributions. (F–even)

353 Numerical Analysis—Prerequisite: MAT 205 and CSC 133 or permission. Topics include finite difference formulas, polynomial approximations and interpolation, numerical differentiation and integration, solutions of differential equations. The emphasis is on numerical techniques used in conjunction with digital computers. Work on the computer will be included. (S–even)

363 Complex Variables—Prerequisite: MAT 135 and MAT 213 or permission. The course will introduce the subject of complex variables. In particular, we will study the properties of complex numbers; analytic and elementary functions; complex integration including definite, contour, and line integrals; series; residues and poles.

401 Mathematics Seminar—Prerequisite: permission. Seminars and discussions of mathematical topics of current interest to the staff and students. Students will generally be expected to present one or more seminars. May be taken as many as three times.

403 Advanced Calculus I—Prerequisite: MAT 135 and MAT 213 or permission. Topics covered include an advanced treatment of the theory of con­tinuous functions in n-dimensional space; line, path, surface integrals and their applications; conditional, absolute, and uniform convergence of series, and the representation of functions by power and trigonometric series. (F)

413 Advanced Calculus II—Prerequisite: MAT 403. A continuation of MAT 403. Topics covered vary but frequently include differentiation, Riemann-Stieltjes Integral, sequences of functions, series of functions, special types of series and functions of several variables.

423 Methods of Teaching Mathematics in the Secondary School Mathematics teaching and learning in grades 7 through 12. Topics include objectives, teaching materials, use of technology in mathematics teaching and learning, curriculum organization and principles of presenting mathematical content to secondary students. Does not count toward a major in mathematics. (S–even)

433 Modern Algebra—Prerequisite: MAT 135 and MAT 213 or permission. Intended for majors and minors. An introduction to abstract algebra. Topics include sets, mappings, equivalence relations, operations and groups. Writing Intensive. (S)

443 General Topology—Prerequisite: MAT 403 or permission. Topics include functions, Metric Spaces, Normed Spaces, Compactness, Completeness, Connectedness and Separation Axioms.

453 Great Ideas in Mathematics—Prerequisite and/or Corequisite: MAT 403 and MAT 433 or permission. This course will attempt to tie together the many concepts already discussed in previous classes as well as to provide a medium in which a student is encouraged to assimilate a variety of complex mathematical ideas into a cohesive and thoughtful presentation. An additional course aspect is the administering of an exam typifyng the subjects common to a degree in mathematics at College of the Ozarks. Writing Intensive. (F)

49V (1-6) Special Problems—Prerequisite: permission. An opportunity to do directed research under the supervision of a program faculty member.

COURSES IN PHYSICS (PHY)

104 Fundamentals of Physical Science An introductory course in the physical sciences designed primarily for non-science majors. This course covers important topics in physics and astronomy. Three hours lecture and one two-hour lab per week. (F/S)

114 Astronomy A course intended for students with little or no scientific background, covering the solar system, distances and motions of stars, the light from stars, stellar evolution, star clusters, galaxies and cosmology. Sky observation with the college’s 8” reflector is included. It is recom­mended that PHY 104 and MAT 013 be taken prior to Astronomy. (F)

124 Introduction to Geology A comprehensive study of physical and historical geology with an emphasis on geological phenomena occurring in North America. Some emphasis is placed on the geology of the Ozark Region. Three hours of lecture and one two-hour lab period per week. (S)

204 Physics for the Life Sciences—Prerequisite: MAT 133 and MAT 142 or MAT 135 or permission. A course intended for Biology majors, Medical Technology and Pre-Nursing students and other interested students. This course will cover the basic concepts of physics (mechanics, heat, light, sound, electricity, atomic and nuclear physics) and their applications to the life sciences. (S–odd)

225 General Physics I—Prerequisite: High school physics or PHY 104 and MAT 175. Covers the principles of mechanics. For engineering and science majors. Three lecture periods and one two-hour experimental laboratory and one two-hour computational laboratory each week. (F)

235 General Physics II—Prerequisite: PHY 225. Covers the principles of mag­netism, electricity, and light. Three lecture periods, one two-hour experimental laboratory one two-hour computational laboratory each week. (S­even)

Prerequisite for all 300-400 level courses: 45 hours or permission.

303 Mechanics I–Statics—Prerequisite: PHY 225. Topics include vectors, force systems, centroids, beams, moment of inertia, principle of virtual work, etc. (F–even)

313 Mechanics II–Dynamics—Prerequisite: PHY 303. Topics include motion of a particle, mass and acceleration, work and energy, impulse and momentum and motion of a rigid body.

49V (1-6) Special Problems—Prerequisite: permission. An opportunity is given to do independent or semi-independent research with the approval and direction of a member of the program.