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Course
Descriptions
Mathematics
Intensive study of the problem solving process. Algebraic, patterning, modeling and geometric strategies are explored. Consent of the Department is required. This does not fulfill the College General Education requirements in Mathematics.
MATH 101: The Language of Mathematics 3
Logic, sets, properties of the natural numbers, and number systems. Permission of the instructor or department chair is required.
Mathematical modeling through the use of graph theory. Designed primarily for first year college students.
Set theory, probability, linear programming.
Introduction to differential and integral calculus designed primarily for liberal arts students. Limits are treated intuitively. Emphasis on applications.
Matrices, systems of equations, vector spaces, determinants. Emphasis on applications. Prerequisite: MATH 104 or 105.
Finite geometries. Transformational geometry with an introduction to fractals. Euclidean geometry of the polygon and circle, including the golden ratio and tessellation. Introduction to projective geometry and other non-Euclidean geometries. Prerequisite: MATH 104 or 105.
Description and analysis of data distributions for categorical and quantitative variables, including association between variables. Correlation and regression. Introduction to basic sampling and experimental design. Basics of probability, random variables and probability distributions. Sampling distributions. Estimation and hypothesis testing for means and proportions. Use of statistical software. Prerequisite: MATH 104 or 105 or equivalent.
Brief treatment of the real numbers, sets, functions, polynomials and graphs. Differential and integral calculus with special emphasis on the exponential and logarithmic functions and on ordinary differential equations. The last section of the course is equivalent to a three-credit course in statistics including use of statistical software. Motivating examples and exercises will be taken from the biological applications when possible. Not adequate preparation for MATH 231.
Basic properties of the real number system; elementary number theory; numeration systems; problem solving strategies. The course follows the recommendations of the Mathematical Association of America and the National Council of Teachers of Mathematics for the training of elementary teachers. Prerequisite: One college mathematics course.
Functions; limits; continuity; the notion of derivatives; differentiation of algebraic functions; applications of derivatives; related rates; maxima and minima; Rolle's Theorem; Mean Value Theorem; concavity; anti-differentiation; the Riemann sum; properties of definite integrals; logarithmic, exponential and trigonometric functions, their graphs and derivatives; techniques of integration; sequences and series. The course is based on graphical, numerical and symbolic points of view. Graphics calculators are used throughout the course. Prerequisite: At least four years of high school mathematics.
This course is designed for students who have completed a full year of calculus in high school and have mastered the mechanics of differentiation and integration. The basic concepts of calculus, including limits, derivatives, integrals, sequences and series, will be explored in depth. The emphasis of the course is on understanding the theory of calculus and constructing mathematical models.
Mathematics - 200 level courses
Basic number theoretic concepts are studied, with an emphasis on writing proofs. Divisibility; primes; Euclid's algorithm and its consequences; linear diophantine equations; residue classes; linear congruencies; arithmetic functions. Prerequisite: MATH 131 or 118.
Sets, logic, and functions. Introduction to abstract mathematical structures. Writing of mathematical proofs and expository papers.
Power series. Vectors in three dimensions, vector calculus. Functions of several variables: partial derivatives, gradients, multiple integral with applications. Use of software packages for graphing. Prerequisite: MATH 132.
Sampling studies, design of experiments, analysis of variance, regression and correlation, regression modeling, time series. Introduction to operations research: queuing, systems analysis, quality assurance, acceptance sampling. Emphasis on applications to business and economic decision making. Prerequisite: MATH 114. (Also listed as BUAD 341)
An introduction to Operations Research—quantitative models used in management decision-making. The course will focus on the models as tools with computer software used extensively for problem solving and assignments. Case studies are used. Also listed as BUAD 427. Prerequisite: A year of Calculus or MATH 114.
The topics in this course include the mathematical theory of interest, as well as the economic and financial theory of interest. Annuities, amortization schedules and sinking funds are covered. The effect of such factors as inflation, risk, uncertainty and yield curves is studied. The interrelationship between assets and liabilities and the mathematical tools which quantify this relationship are included. Prerequisite: Two semesters of Calculus or its equivalent.
The life, times and work of the notable women from Hypatia to Noether. Recent history of American women in mathematics. The societal and cultural influences which cause women to leave mathematics at all levels. Students in turn assume leadership of discussion. Prerequisite: three college mathematics courses.
Mathematics - 300 level courses
Review of basic properties of the complex number system. Foundations of Euclidean geometry with additional study of transformational geometry. Use of handheld calculators. Elementary probability and statistics. The course meets for an additional required one-hour laboratory weekly. Recommendations of CUPM and NCTM are continued. Prerequisites: Two MATH courses including MATH 118.
The study of linear transformations on vector spaces. Topics include systems of linear equations, linear independence of vectors, matrices, dimension, determinants, eigenvalues, inner products and canonical form. Prerequisites: MATH 225 and 231.
Computer arithmetic and algorithm convergence. Solutions of equations, polynomial interpolation, numerical differentiation and integration. Ordinary differential equations, numerical approximations of solutions to initial value problems. Error analysis. Prerequisite: MATH 231.
Introduction to graph theoretic and combinatoric models: planar graphs; circuits; spanning trees; network flows; counting; generating functions; recurrence relations. Prerequisites: MATH 225, CPSC 207.
Construction of reals; topology of En; limits, continuity and differentiability of multivariate functions; Implicit Function Theorem; Riemann integrations; infinite series, series of functions and series expansion. Prerequisites: MATH 225, 231.
A calculus-based approach to probability theory. Topics include probability spaces, random variables, distributions, transformations of random variables, random sampling, the law of large numbers, the central limit theorem and moment generating functions. Prerequisite: MATH 231 or its equivalent.
Topics include estimation, tests of hypotheses, sampling distributions, analysis of variance, regression and correlation analysis, experimental design, modeling and decision criteria. The application of statistical analysis to decision problems is stressed. Prerequisite: MATH 345 or its equivalent.
Basic algebraic systems: groups, rings, and fields. Applications, including symmetry groups and algebraic coding theory. Prerequisites: MATH 225, 326.
Historical and formal development of Euclidean and non-Euclidean geometries; role of axiom systems; congruence, parallelism, measurement. Prerequisite: MATH 225.
Basic concepts of point set topology, including separation axioms, connectedness, compactness and continuous mapping. Prerequisite: MATH 231.
Stochastic models of contingent payment, survival, frequency, severity and ruin. Compound distribution models. Forecasting and time series. Emphasis on application to actuarial models. Prerequisite: MATH 345.
The examination, analysis and preparation of a variety of mathematical models of real-world phenomena from economics, science and industry. Models of discrete, continuous, and statistical situations are included. May be repeated for credit. Only one hour may be used for the mathematics major. Prerequisites: MATH 345 and invitation by the department.
Mathematics - 400 level courses
Topics include model building; classical optimization; linear programming; integer programming; non-linear programming. Use of the computer is encouraged. Prerequisite: senior status. (Formerly MATH 338)
Topics in Mathematics not covered in the regular department offerings. May be repeated for credit with a different topic.
Student presentation of selected topics. Prerequisite: Consent of the department chair.
Provides properly qualified students with an opportunity for independent study and careful consideration from an advanced standpoint of selected topics in undergraduate mathematics. Consent of the department chair.
Mathematics - 500 level courses
Workshop in topics of undergraduate mathematics and related pedagogy. Designed for faculty currently teaching or preparing to teach the specified topics. May be repeated for credit. Prerequisite: Appropriate mathematical preparation.
A survey of the content of the AP Mathematics syllabus. The selection of topics and their applications will be guided by the preparation of the students. Appropriate technology will be used. Instructional technique and design of an AP course will be discussed. Problem-solving sessions are an integral part of the course. May be repeated for up to a maximum of four hours of credit.
The life, times and work of notable women in mathematics and science from history. A study of recent research on gender differences in preferred learning styles and cultural influences which affect progress in school. Readings and class discussion will culminate in planning school projects in which to celebrate the great women. Prerequisite: a baccalaureate degree and position as teacher of mathematics or science.