Mathematics
Pamela O'Brien, Dean, School of Arts, Sciences and Business
Charles Buehrle, Ph.D., Chair
Brian Christy, 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 their growth as a mathematician and their expanded understanding of the discipline, as well as a presentation of an independent project of their 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.
Traditional Undergraduate Studies
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 traditional undergraduate program. 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 Quantitative Reasoning 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-212, 213 Calculus II, III (7)
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 their final spring semester at the University, each Major writes an essay reflecting on their growth as a mathematician and on their expanded understanding of the discipline of Mathematics. In addition, in consultation with their faculty advisor, each Major develops a poster or presentation on a topic selected from one or more of their 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 with applied algebra and is designed to develop students' critical thinking and qantitative reasoning skills. The course provides a thorough study of linear equations and functions as well as an exploration of a variety of non-linear functions. Data analysis and monumental modeling focus on real world problems from a variety of fields including science, finance and business. Available only in the traditional undergraduate program. Satisfies the General Education Requirement in Quantitative Reasoning. This course may not be taken 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
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, analysis of 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' Theorum and the Divergence Theorem. Applications are considered throughout the course. A computer algebra system is used to explore topics covered. Prerequisite: Calculus II or placement into MAT-213. [4 credits]
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 Quantitative Reasoning. Prerequisite: Placement in MAT-215 or successful completion of MATY-100, MAT-103, or MAT-116 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]