# Mathematics

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

Charles Buehrle, Ph.D.

Kristyanna Erickson, Ed.D.

## Degrees offered

Minor

## Campuses

Mathematics students develop critical thinking skills, becoming analytical thinkers and problems solvers. They learn to use mathematical software and technologies, to problem solve, to communicate mathematically through proofs, data analysis, and programming, and to relate mathematics to a variety of other disciplines. Each student completes a capstone project that includes an essay reflecting on her growth as a mathematician and her expanded understanding of the discipline, as well as a presentation of an independent project of her choosing.

Built on the recommendations of the Mathematical Association of America's Committee on Undergraduate Programs in Mathematics, the goals of the mathematics program are:

- develop mathematical thinking and communication skills;
- develop skills with a variety of technologies; and
- develop a broad view of the mathematical sciences.

**Women's College**

Overview

Major

Mathematics/Secondary Education Certification

Minor

Four-Year Plan

Course Descriptions

The Mathematics/Physics/Computer Studies Department of the School of Arts, Sciences and Business offers a Major or Minor in Mathematics to students in the Women's College. Students may also prepare for teaching mathematics through the Secondary Education 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 Mathematics 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)

MAT-214 Calculus of Vector Fields (1)

### 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 presentation should extend the topic beyond the coverage of the course(s).

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

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

Students who wish to prepare for teaching in secondary schools complete the courses required for the Mathematics Program of Study, 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

## 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 |

NDMU-100 First Year Seminar | 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. This course may not be completed for credit after successful completion of MAT-103. [ 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 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]

### 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: Successful completion of two years of high school algebra. 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

### MAT-121 Geometry and Graphs

### 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 and others interested in these topics. Fulfills 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: Placement in MAT 211 or successful completion of MAT-107. [4 credits]

### MAT-211L Lab: Calculus I

This lab is a corequisite of MAT 211.

### MAT-212 Calculus II

### MAT-212L Lab: Calculus II

This lab is a corequisite of MAT 212.

### MAT-213 Calculus III

### MAT-214 Calculus of Vector Fields

### 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: Placement in MAT 215 or successful completion of MAT 100 or MAT 103 is recommended. [3 credits]

### MAT-243 Linear Algebra

### MAT-301 Abstract Algebra

### MAT-303 Analysis

### MAT-305 Geometry

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]

### MAT-307 Numerical Analysis

### 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

### 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

### 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]