MATHEMATICS DEPARTMENT

CONCORDIA COLLEGE

MOORHEAD, MINNESOTA

e-mail address: mathcs@cord.edu

 

COURSE OFFERINGS:

 

 97:E1               High School Algebra.  No course credit.

            Topics from high school algebra for students who did not complete Algebra II in high school or need a review of those topics.

 

102:E                Fundamental Concepts of Modern Mathematics.  Full course.

            Numeration, number systems, geometry and other topics addressed in the elementary school curriculum.  Required for students majoring in elementary education.

 

105:E                Exploring Mathematics.  Full course. 

This course uses real-world problems and situations to improve students’ problem solving skills, to improve their ability to apply mathematics, and to enhance their appreciation of the importance of mathematics in our modern world.  Topics will be chosen from voting theory, fair division, apportionment, scheduling, networking, probability, statistics, consumer mathematics, population growth, logic, game theory and symmetry.  This course can be used to fulfill the math exploration requirement.

 

110:E                Precalculus.  Full course.

            A study of the function concept and properties of the polynomial, exponential, logarithmic and trigonometric functions.  Prerequisites: High school geometry and higher algebra.

 

121:E                Calculus I.  Full course.

            An introduction to the concepts of limit and continuity, the derivative and its applications, and an introduction to the definite integral.  Some review of trigonometry and analytic geometry is included.  Prerequisite: Mathematics 110 or equivalent.

 

122:E                Calculus II.  Full course.

            Applications of the definite integral, techniques of integration, parametric equations, introduction to differential equations, sequences, series and Taylor and Maclaurin Series.  Prerequisite: Mathematics 121.

 

203:E                Mathematics for the Behavioral Sciences.  Full course.

            The course examines combinatorics, probability, matrices, systems of linear equations, linear inequalities and mathematics of finance.  Examples and applications drawn from the various behavioral sciences.  Prerequisite: High school higher algebra.

 

205:E1              Introduction to Statistics.  Full course.

This is an introductory course in statistical methods for science and mathematics students.  The object of this course is to provide students with a conceptual introduction to the field of statistics, including the determination of the appropriate procedures for data analysis and the proper interpretation of results.  The theory will be illustrated by examples from biology, engineering, industry and medicine.  In addition, a statistical software program will be used to facilitate the understanding of statistical concepts and analysis of data sets.

 

207:E                Discrete Mathematics.  Full course.

Logic, sets, functions, sequences and series, matrices, algorithms, methods of proof, combinatorics, recurrence relations, linear programming, graphs and trees.  Prerequisite: High school higher algebra.

 

210:E                Linear Algebra.  Full course.

            Vectors, matrix algebra, systems of linear equations, determinants, vector spaces, span and basis, eigenvalues and eigenvectors.  Also includes an introduction to proof.  Prerequisite: Mathematics 122 or consent of the instructor.

 

215:E2              Introduction to Probability and Statistics.  Half course.

            Basic concepts of data analysis, randomness and uncertainty required for elementary mathematics specialization.  Topics include:  data collection, exploratory data analysis, measures of central tendency and spread, theoretical probabilities in simple and compound events, basics of experimental design, and evaluating predictions and arguments from data.  Prerequisite: High school higher algebra or Mathematics 102 or 105.

 

220:E2              Introduction to Geometry Concepts.  Half course.

            Basic geometry content for students seeking elementary mathematics specialization.  Topics will include:  deriving and describing shapes, characteristics of geometric objects, spatial reasoning with geometric models, elementary geometric transformations, analysis and presentation of geometric arguments, and measurement and estimation.  Prerequisite: Mathematics 102.

 

223:E                Calculus III.  Full course.

            Multivariable calculus and applications, line integrals, surface integrals, Green’s Theorem, Stoke’s Theorem and the Divergence Theorem.  Prerequisite: Mathematics 122.

 

250:A2              Pre-May Seminar.  Full course.  (2008-09)

            An introduction to the art and science of mathematics, the axiomatic system that forms its foundation; the historical factors that have influenced its development; its close ties to astronomy, the sciences, art and religion; and its role in the development of Western culture.

 

300:MS             May Seminar.  Full course.  (2008-09)

            Four weeks of travel and study in Europe and Egypt providing firsthand experiences with many cultural implications of mathematics.  Both the practical importance and the aesthetic value of mathematics are considered in visits to ancient monuments and ruins, Renaissance cathedrals, museums, and universities.  Prerequisite:  Mathematics 250.

 

311:E1              Differential Equations.  Full course.

            Differential equations and models, analytic solutions and approximations, second-order equations, harmonic ascillators, Laplace transforms, initial value problems.  Prerequisite: Mathematics 122.

 

312:B3              Applied Mathematics.  Half course.

            An introduction to Fourier and other methods for solving partial differential equations, including the heat, wave, and potential equations, and related boundary value problems.  Prerequisites: Mathematics 210, 223, 311.

 

315:E2              Probability and Mathematical Statistics.  Full course.

            Introduction to the basic concepts in probability theory, including discrete and continuous probability functions, independence, random variables, order statistics, expected value, variance and moment generating functions.  Specific attention given to normal, Poisson and geometric distributions, as well as estimation and estimators.  Prerequisite: Mathematics 223.

 

320:E2              Geometry.  Full course.

            Euclidean, non-Euclidean, projective and other geometries as time permits.  Prerequisite: Mathematics 210.

 

325:E1              Modern Algebra I.  Full course.

            Introduction to basic algebraic systems: groups, rings, integral domains and fields.  Special attention is given to the ring of integers.  Prerequisite: Mathematics 210.

 

328:A2              Complex Analysis.  Full course. (2008-09)

            The algebra and geometry of complex numbers, elementary analytic functions, complex functions defined by power series, differentiation and integration of complex functions with selected applications.  Prerequisite: Mathematics 223.

 

330:A1              Real Analysis I.  Full course.  (2007-08)

            Sets, real numbers, sequences and convergence, limits of functions, continuity and differentiability, the Riemann integral infinite series, and sequences and series of functions.  Prerequisites: Mathematics 210, 223.

 

335:D                Operations Management/Research.  Full course.  (Cross listed with C SC 335, BUS 460)

An introduction to quantitative modeling, with applications to computer simulation and business resource management.  Topics include linear and nonlinear programming, network analysis, game theory, deterministic and probabilistic models and queuing theory.  Consent of the instructor.

 

380:D                Special Topics.  Half to full course.

            Topics not ordinarily explored in other mathematics courses are addressed.

 

390:E                Cooperative Education.  Half to two full courses.

 

402:E2              Senior Seminar.  Half course.

            Required of all senior mathematics majors.  With the guidance of faculty members, each student researches a topic and delivers an oral presentation, and prepares a paper on that topic.  Prerequisite: Senior standing in mathematics or permission.

 

425:A2              Modern Algebra II.  Half course. (2007-08)

            Further study of the basic algebraic systems introduced in Mathematics 325.  Prerequisite: Mathematics 325.

 

430:A2              Real Analysis II.  Half course. (2007-08)

            Further study of topics listed under Mathematics 330.  Prerequisite: Mathematics 330.

 

480:E                Independent Study.  Quarter to half course.

            Study or research under the guidance of a staff member.  A seminar on non-routine problems sometimes is conducted.  Prerequisite: Consent of staff.