# Mathematics

**Women's College**

Overview

Major

Mathematics/Secondary Education Certification

Minor

Four-Year Plan

Course Descriptions

Alexandra L. Chaillou, Ph.D., *Chair*

Darcy Conant, Ph.D.

Margaret Sullivan, Ph.D.

The mathematics/physics/computer science department of the School of Arts and Sciences offers a major or minor in mathematics to students in the Women's College. Students may also prepare for teaching mathematics through the secondary certification program. Recognizing the role our fields plays in other disciplines, we offer courses for department majors and non-majors that serve the students of NDMU in the Catholic Liberal Arts tradition. As an integral part of the liberal arts, we provide the students at NDMU with an understanding of the physical world, quantitative and technologically based knowledge, and enable our students to become leaders in their future professions.

Mathematics majors have completed graduate study at institutions such as University of Maryland Baltimore County, University of Maryland College Park, Boston College, Drexel University, George Washington University and Rochester University. Program graduates have positions with organizations such as CareFirst BlueCross BlueShield of Maryland, Aberdeen Proving Ground, the National Security Agency, Lockheed Martin Information Technologies, Arbitron and the Federal Bureau of Investigation.

Mathematics majors often choose a minor such as computer science, business, accounting or physics. Recent students have successfully completed double majors such as mathematics/physics, mathematics/biology, mathematics/chemistry, and mathematics/art.

The general education requirement in mathematics is normally fulfilled by a variety of 100- or 200-level mathematics courses.

Students must earn a minimum cumulative grade point average of 2.0 in all courses taken to complete the requirements of the math major.

## Programs of Study

### Required Courses for a Major in Mathematics (Credits)

MAT-110 Discrete Mathematics (3)

CST-171 Programming Concepts or CST-295 C++: Object Oriented Programming (3)

MAT-211, 212, 213 Calculus I, II, III (11)

MAT-243 Linear Algebra (3)

MAT-301 Abstract Algebra (3)

MAT-303 Analysis (3)

MAT-311 Theory of Probability (3)

MAT-425 Simulation and Modeling (3)

MAT-455 History of Mathematics (3)

**In addition to required courses, at least three electives from the following:**

MAT-215 Basic Statistics (3)

MAT-305 Geometry (3)

MAT-307 Numerical Analysis (3)

MAT-309 Number Theory (3)

MAT-315 Differential Equations (3)

MAT-406 Complex Variables (3)

**Recommended:**

PHY 101, 102 General Physics I, II (8)

### Mathematics/Secondary Education Certification—Approved Program in Mathematics

Students who wish to prepare for teaching in secondary schools take the courses listed in the program of concentration in mathematics, except that the following three elective courses—MAT-215 Basic Statistics, MAT-305 Geometry and MAT-309 Number Theory—are required, along with the professional education courses offered by the School of education.

### Minor in Mathematics

MAT-211, 212 Calculus I, II (8)

MAT-243 Linear Algebra (3)

Three other courses in mathematics from among MAT-110 and 200-level or higher courses, except MAT-214 Calculus of Vector Fields.

### Mathematics Capstone Experience

The capstone experience for each student majoring in mathematics is twofold. In her final spring semester at the University, each major writes an essay reflecting on her growth as a mathematician and on her expanded understanding of the discipline of mathematics. In addition, in consultation with her faculty advisor, each major develops a poster or presentation on a topic selected from one or more of her courses, or the selected topic may be related to an internship experience. This poster should extend the topic beyond the coverage of the course(s) or internship.

The spring mathematics capstone poster presentation is open to interested faculty, students and guests as a celebration of each student's work and achievements.

## Four-Year Plan

Sample program of study for the mathematics major. Students should select courses with the assistance of a faculty advisor.

Fall | Spring | ||
---|---|---|---|

First year |
|||

MAT-211 Calculus I | 4 | MAT-212 Calculus II | 4 |

** MAT-110 Discrete Mathematics | 3 | CST-171 Programming Concepts+ | 3 |

IDS-100 Perspective in Education | 3 | General Education/Electives | 9 |

General Education/Electives | 6 | [16 credits] | |

[16 credits] | |||

Second year |
|||

CST-295 C++: Object Oriented Programming+ | 3 | MAT-243 Linear Algebra | 3 |

MAT-213 Calculus III | 3 | MAT-215 Basic Statistics | 3 |

PHY-101 General Physics I (recommended) |
4 | PHY-102 General Physics II (recommended) |
4 |

General Education/Electives | 6 | General Education/Electives | 6 |

[16 credits] | [16 credits] | ||

Third or fourth year: odd fall, even spring years |
|||

**MAT-311 Theory of Probability | 3 | **MAT-303 Analysis | 3 |

MAT-307 Numerical Analysis | 3 | *MAT-305 Geometry | 3 |

General Education/Electives | 9 | **MAT-425 Simulation & Modeling | 3 |

[15 credits] | General Education/Electives | 6 | |

[15 credits] | |||

Third or fourth year: even fall, odd spring years |
|||

**MAT-301 Abstract Algebra | 3 | *MAT-309 Number Theory | 3 |

* MAT-406 Complex Variables | 3 | *MAT-315 Differential Equations | 3 |

General Education/Electives | 9 | **MAT-455 History of Mathematics | 3 |

[15 credits] | General Education/Electives | 6 | |

[15 credits] |

*+ One of these two courses is required.
* Cycled elective course.
** Cycled required course.*

## Courses

### MAT-100 Algebra Applications

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. [ 4 credits ]

### MAT-103 Applied Algebra

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 ne year of high school algebra. Satisfies the general education requirement in mathematics. [3 credits]

### MAT-107 Elementary Functions

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: Strong algebraic background (as evidenced by placement test) or completion of MAT 100 or MAT 103. Fulfills the general education requirement in mathematics. [3 credits]

### MAT-110 Discrete Mathematics

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]

### MAT-120 Sets, Logic and Numbers

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. [3 credits]

### MAT-121 Geometry and Graphs

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.[3 credits]

### MAT-122 Counting, Chance & Statistics

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]

### MAT-125 Elementary Mathematical Models

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. Satisfies the general education requirement in mathematics. Prerequisite: minimum of one year of high school algebra. [3 credits]

### MAT-211 Calculus I

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: strong high school algebra background or successful completion of MAT-107. [4 credits]

### MAT-212 Calculus II

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]

### MAT-213 Calculus III

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]

### MAT-214 Calculus of Vector Fields

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]

### MAT-215 Basic Statistics

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: A strong algebraic background (as evidenced by placement test) or successful completion of MAT 100 or MAT 103 is recommended. [3 credits]

### MAT-301 Abstract Algebra

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]

### MAT-303 Analysis

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]

### MAT-305 Geometry

Explores several different geometries. Included are ways of classifying geometries by sets of axioms or by the type of transform defined. Finite geometries, projective geometry, non- Euclidean geometries, topology and the geometry of motion 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]

### MAT-307 Numerical Analysis

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]

### MAT-309 Number Theory

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]

### MAT-311 Theory of Probability

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]

### MAT-315 Differential Equations

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]

### MAT-406 Complex Variables

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]

### MAT-425 Simulation and Modeling

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]

### MAT-455 History of Mathematics

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]

### MAT-463 Directed Study in Mathematics

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]