Mathematics

Combines algebra preparation and applied algebra, designed to develop students' critical thinking and quantitative reasoning skills needed to understand everyday issues. Provides a thorough study of linear equations and functions as well as an exploration of a variety of nonlinear functions. Data analysis and mathematical modeling focus on real world problems from a variety of fields including science, finance and business. Graphing calculator is used throughout the course. Students meet five times a week in 50-minute classes. Satisfactory completion is a prerequisite for MAT-215, Statistics or MAT-107, Elementary Functions. Available to Women's College students only. Satisfies the General Education Requirement in Mathematics. This course may not be completed for credit after successful completion of MAT-103.  [ 4 credits ]

Focuses on fundamental algebraic concepts and the solution of real world problems through the use of basic mathematical models. Provides a thorough study of linear functions as well as an exploration of a variety of nonlinear functions. Data analysis and mathematical modeling focus on real world problems from a variety of fields including science, finance and business. Graphing calculator is used throughout the course. Intended for students of science, finance and business who have limited algebraic skills. The course may be taken to prepare for MAT-107 Elementary Functions or MAT-215 Basic Statistics. Prerequisite: minimum of one year of high school algebra. Satisfies the General Education Requirement in Mathematics.  This course may not be completed for credit after successful completion of MAT-100. [3 credits]

Provides preparation for study of calculus, and is also designed for pre-service elementary educators with a strong interest in mathematics. Covers polynomial, exponential, logarithmic and trigonometric functions and their applications. Graphing calculator is used throughout the course. Prerequisite: Successful completion of two years of high school algebra. Fulfills the General Education Requirement in Mathematics. [3 credits]

Introduces topics that find their applications in the field of computers and computing. Topics include: logic, proof, graphs, trees and counting techniques. This course is designed for Mathematics Majors, Computer Studies Majors and students with a particular interest in mathematics. [3 credits]

Covers basic set theory and Venn diagram applications, an introduction to formal logic and valid argument forms, elementary number theory, and the arithmetic of integers and the rational numbers. Intended for pre-service elementary educators and others interested these topics. [3 credits]

Covers properties of angles, lines, triangles and quadrilaterals, constructions with a variety of tools, perimeter, area, volume and qualitative graphs. Intended for pre-service elementary educators and others interested in these topics. [3 credits]

Covers fundamental counting rules and basic probability as well as the collection, analysis and interpretation of data. Statistical content includes sampling and experimental design, numerical and graphical presentation of data, regression lines and use of the normal curve. Intended for pre-service elementary educators and others interested in an introduction to statistics (possibly before taking MAT-215, BUS-215 or BUS-225). This course may not be taken after successful completion of MAT-215, BUS-215 or BUS-225. Fulfills the General Education Requirement in Mathematics. [3 credits]

Includes the application of linear, quadratic, exponential and mixed models to real world problems. Models are investigated numerically and graphically as well as algebraically. Graphing calculator is used throughout the course. Intended for pre-service elementary educators and others interested in these topics. Fulfills the General Education Requirement in Mathematics. Prerequisite: minimum of one year of high school algebra. [3 credits]

Introduces functions, limits, continuity, differential calculus of polynomial, rational, exponential and logarithmic functions, as well as basic integration techniques. Applications are considered throughout the course with an emphasis on the life sciences. Weekly laboratory is an integral part of the course. Graphing calculators used to explore topics covered. Fulfills the General Education Requirement in Mathematics Prerequisite: Placement in MAT 211 or successful completion of MAT-107.  [4 credits]

This lab is a corequisite of MAT 211.

Studies trigonometric functions, integration by parts and tables, improper integrals, functions of two variables, partial derivatives, double integrals, differential equations, geometric and power series, basic convergence tests, Taylor polynomials and series, and Fourier polynomials and series. Applications are considered throughout the course with an emphasis on the life sciences. Weekly laboratory is an integral part of the course. Graphing calculator is used to explore topics covered. Prerequisite: Calculus I or placement into MAT-212. [4 credits]

This lab is a corequisite of MAT 212.

Covers visualization of functions of two variables, contour graphs, vector geometry, partial derivatives, gradient vector, directional derivatives, constrained optimization, double integral in rectangular and polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates. Applications are considered throughout the course. Mathematica is used to explore topics covered. Prerequisite: Calculus II or placement into MAT-213. [3 credits]

Analyzes parametric curves and surfaces, vector fields, line integrals and their applications, the Fundamental Theorem of Line Integrals, Green's Theorem, flux integrals, divergence and curl, Stokes' Theorem and the Divergence Theorem. Mathematica is used to explore topics covered. Prerequisite: Calculus III. [1 credit]

Introduces the basic ideas of statistics: descriptive statistics, central tendency variability, probability distributions, sampling, estimation, hypothesis testing, correlation and regression, multinomial experiments, contingency tables and analysis of variance. A statistical software package is used. Designed for students in a variety of fields that rely on regular statistical analysis in decision-making. Fulfills general education requirement in mathematics. Prerequisite: Placement in MAT 215 or successful completion of MAT 100 or MAT 103 is recommended. [3 credits]

Studies systems of linear equations and their respective solution set. Material covered has use in such fields as physical and biological science, business, economics, computing and cryptography. Topics include matrices, vector spaces, linear transformations, determinants, eigenspaces and approximation techniques. Prerequisite: MAT-110 or MAT-211. [3 credits]

Considers groups, rings and fields with emphasis on group theory. Topics include modulo groups, cyclic groups, permutation groups, rings, integral domains and fields, isomorphism and homomorphism, and the Fundamental Theorem of Homomorphism for groups and rings. Prerequisite: MAT-243. [3 credits]

Introduces the theory that underlies the Calculus. Topics include cardinality, the Completeness Axiom and the topology of the real numbers, convergence of sequences, limits and continuity, the derivative and the Mean Value theorem, convergence of infinite series, sequences and series of functions. Prerequisite: MAT-213. [3 credits]

Explores several different geometries. Included are ways of classifying geometries by sets of axioms or by the type of transforms defined. Finite geometries, projective geometry, non-Euclidean geometries, topology and the geometry of inversion are investigated. Designed for Mathematics Majors or educators to be certified to teach Secondary Mathematics. Geometers Sketchpad or Geogebra is used throughout the course. Prerequisite: MAT-212. [3 credits]

Introduces numerical methods. Topics include: numerical linear algebra, interpolation, numerical differentiation and integration, solution of nonlinear equation, numerical treatment of differential equations, and error analysis. Intended for mathematics, physics and engineering majors. Makes use of a mathematical software package such as Mathematica. Prerequisite: MAT-212. [3 credits]

Considers divisibility and unique factorization; congruencies and the Chinese Remainder Theorem; Diophantine Equations; Fermat's, Wilson's and Euler's theorems; perfect numbers; Pythagorean triples; primitive roots; and quadratic congruencies. Designed for Mathematics Majors or educators to be certified to teach Secondary Mathematics. Prerequisite: MAT-212. [3 credits]

Analyzes combinatorial methods; probability and sample spaces; random variables and their distributions (discrete and continuous); moment generating functions; and the relation between probability and statistics. Probability exposes students to the diverse possible applications in such fields as Mathematics, Science, Engineering, Psychology, Social Sciences and Management Science. Prerequisite: MAT-212. [3 credits]

Introduces the solution, applications and theory of ordinary differential equations. Topics include: solutions of differential equations, initial value problems, boundary value problems, Laplace transforms and series solutions. Prerequisite: MAT-212. [3 credits]

Introduces the theory and applications of functions of complex variables. Topics include: powers and roots, analytic functions, contour integrals, Taylor and Laurent series, singularities and residues. Intended for Mathematics, Physics and Engineering Majors. Prerequisite: MAT-213. [3 credits]

Considers mathematical models and their applications. Emphasizes model constructions to promote student creativity and to demonstrate the artistic nature of model building, including the ideas of experimentation and simulation. Prerequisite: MAT-212. [3 credits]

Focuses on the historical development of modern mathematics. Basic research techniques are reviewed. A research paper on an issue of significance in mathematics or a scholar important to the development of the field is required. Students develop oral presentations about their research. Prerequisite: MAT-212. [3 credits]

Supports guided study of special current topics of interest to the student and approved by the instructor. Prerequisite: MAT-212. [1, 2 or 3 credits]

An integration of the study of the rational numbers with reflection on the teaching and learning of arithmetic concepts in the spirit of the NCTM?s Principles and Standards of School Mathematics. Mathematical content includes rational numbers and their fundamental algorithms, the place of the rational numbers in the real number system, scientific notation as a means of expressing very large and very small numbers and number theory topics appropriate for the middle school. [ 3 credits ]

An integration of the study of algebra and its applications to the world around us with reflection on the teaching and learning of algebraic concepts in the spirit of the NCTM's Principles and Standards of School Mathematics. Mathematical content focuses on basic algebraic concepts including signed numbers and their operations, problem solving, quantitative and qualitative graphs, proportional reasoning, linear functions, and functions defined by tables and graphs. Algebra is presented as the study of patterns, as a symbolic language, as a tool for problem solving, and as a way of modeling and understanding the physical world. Graphing calculators are used throughout the course. [ 3 credits ]

An integration of the study of algebraic functions and their applications to the world around us with reflection on the teaching and learning of algebraic concepts in the spirit of the NCTM's Principles and Standards of School Mathematics. Mathematical content focuses on the function concept, function notation, function definition by equation, table and graph, rates of change, linear, quadratic and exponential functions and their applications. Graphing calculators are used throughout the course to explore functions and their properties numerically and graphically. Prerequisite: MAT-503 Fundamentals of Algebra for the Middle School Educator. [ 3 credits ]

An integration of the study of geometric shapes, spatial reasoning, and measurement with reflection on the van Hiele framework and the NCTM's Principles and Standards of School Mathematics. Mathematical content includes two-and three-dimensional shapes and their properties e.g. congruence, similarity and symmetry, spatial reasoning and transformations, the measurement process and techniques. Interactive software will be used in the exploration of these topics. [ 3 credits ]

An integration of the study of data analysis and statistics with reflection on the teaching and learning of data analysis in the spirit of the NCTM's Principles and Standards of School Mathematics. Mathematical content includes experimental design and data collection, displaying data, exploring and interpreting data, measures of center and spread, ways to investigate the association between two variables and misuses of statistics. Graphing calculators and spreadsheet software are used throughout the course. [ 3 credits ]

An integration of the study of discrete mathematics (sets, logic, counting) and probability with reflection on the teaching and learning of these concepts in the spirit of the NCTM's Principles and Standards of School Mathematics. Mathematical content includes sets and their operations, logical connectives and quantified statements, types of mathematical arguments and proofs, counting techniques, the probability of simple and compound events, sample spaces, probability distributions, and the use of simulations to generate data for determining probabilities and to test conjectures. Graphing calculators are used throughout the course. [ 3 credits ]

An integration of the study of calculus and its connections to the middle school curriculum with reflection on the teaching and learning of these concepts in the spirit of the NCTM's Principles and Standards of School Mathematics. Mathematics content includes sequences and series, functions, differentiation, integration and applications. Graphing calculators are used throughout the course. [ 3 credits ]

An integration of the study of the whole numbers and the integers with the approach to mathematics teaching and learning found in the National Council of Teachers of Mathematics' Principles and Standards of School Mathematics and the Maryland State Standards. Mathematical content includes place value, estimation, conceptual underpinnings of the conventional computational algorithms for whole numbers and extending these ideas to the integers. Early number concepts, how students develop number sense, how to judge when student-developed procedures are mathematically sound, common misconceptions and how to address these misconceptions are integral to this course. [ 3 credits ]

A continuation of Number and Operations for Elementary School Educators extending the ideas developed for whole numbers and integers to the rational numbers (represented as fractions and decimals) and the behavior of units under the four basic operations. Mathematical content also includes ratio and proportion as well as basic concepts of number theory. The mathematical content is integrated with the approach to mathematics teaching and learning found in the National Council of Teachers of Mathematics' Principles and Standards of School Mathematics and the Maryland State Standards. Common misconceptions related to this material and how to address these misconceptions are integral to the course. [ 3 credits ]

Mathematical content focuses on the development of visualization skills, familiarity with basic shapes, their properties, and the relationships between them (e.g., transformations, similarity and congruence), the communication of geometric ideas, the process of measurement, and working with length, area and volume. The mathematical content is integrated with the approach to the teaching and learning of these concepts found in the National Council of Teachers of Mathematics' Principles and Standards of School Mathematics and the Maryland State Standards. Reflection on the van Heile model for the development of geometric understanding is integral to the course as is the consideration of relevant common misconceptions and how to address them. [ 3 credits ]

An integration of the study of probability and statistics with the approach to the teaching and learning of these concepts found in the National Council of Teachers of Mathematics' Principles and Standards of School Mathematics and the Maryland State Standards. Mathematical content includes designing data investigations, describing data in graphical and numerical formats, drawing conclusions, theoretical and empirical probability for simple events and two or more independent events, randomness and the difference between predicting individual events and predicting patterns of events. How students learn these concepts, associated misconceptions and how to address them are also considered in the course. [ 3 credits ]

Mathematical content includes the study of patterns, representing and justifying the resultant generalizations using algebraic notation and other representations, expressing functional relationships in symbolic and graphical format, proportional reasoning, solving linear equations and inequalities through the application of basic properties of the real numbers. The mathematical content is integrated with the approach to mathematics teaching and learning found in the National Council of Teachers of Mathematics' Principles and Standards of School Mathematics and the Maryland State Standards. Common misconceptions related to this material and how to address these misconceptions are integral to the course. [ 3 credits ]

A continuation of Patterns and A lgebraic Thinking for Elementary School Educators, extending the ideas considered there to functions defined by tables and graphs and to functions defined in either closed or recursive forms. Mathematical content also includes quantitative and qualitative graphs, proportional reasoning, linear and quadratic functions, the field properties of the real numbers, rates of change, and applications of algebraic concepts in problem solving. The mathematical content is integrated with the approach to mathematics teaching and learning found in the National Council of Teachers of Mathematics' Principles and Standards of School Mathematics and the Maryland State Standards. Common misconceptions related to this material and how to address these misconceptions are integral to the course. [ 3 credits ]

Covers concepts of testing for use in professional sciences, including simple linear regression, correlation, multiple regression, fixed and random effects, analysis of variance, analysis of covariance, experimental design, multivariate methods and various statistical packages, including R. Prerequisite: MAT-576. [ 3 credits ]

Provides an application-oriented introduction to the modeling techniques used to structure the way we think about managerial decision situations. Methodologies considered include decision analysis, simulation, optimization and sensitivity analysis. Stochastic models are developed with applications to finance, operations management, logistics and resource allocation. [ 3 credits ]