Major
Mathematics
Mathematics, Physics, and Computer Studies Department
Evelyn Spratt, Ph.D., Interim Dean, School of Arts, Sciences and Business
Charles Buehrle, Ph.D., Chair
Brian Christy, Ph.D.
Kristyanna Erickson, Ed.D.
Campuses
Main Campus
Summary
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
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.
Degrees and Certificates
-
Mathematics, -
Mathematics, Minor
Courses
MAT-100: Algebra Applications
Credits 4.00Combines 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 Women's College. 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
Credits 3.00Focuses 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 Quantitative Reasoning. [3 credits]
MAT-105: Exploring Math I
Credits 3.00MAT-106: Exploring Math II
Credits 3.00MAT-107: Elementary Functions
Credits 3.00Provides 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 General Education Requirement in Quantitative Reasoning. [4 credits]
MAT-109: A Short Course in Calculus
Credits 3.00Introduction to the tools of calculus: the derivative and the integral. Applications in the life, social and behavioral sciences.
MAT-110: Discrete Mathematics
Credits 3.00Introduces 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-112: Mathematics for Business
Credits 3.00Incorporates activities filled with various business mathematics calculations. Included are payroll, merchandise pricing, calculations of interest on loans or credit sales with various types of discounts, calculations of ways of determining insurance premiums, inventory valuation, depreciation, property taxes, interest-bearing investments and a wide range of other calculations. Fulfills general education requirement in mathematics. [ 3 credits ]
MAT-115: Finite Mathematics
Credits 3.00Covers solving systems of linear equations, matrices, linear programming, Markov chains, basic counting techniques and probability rules. Emphasis is on the application of the techniques studied. Intended for a variety of majors, pre-service elementary educators with a strong interest in mathematics and others interested in these topics. Fulfills the general education requirement in mathematics. [ 3 credits ]
MAT-116: Practical Mathematics
Credits 3.00Examines several fundamental mathematics topics including number sense, proportion, units of measure, growth and decay, compound interest, annuities, elementary probability, and basic statistics, with a focus on their practical applications and developing a quantitative problem solving mindset that is essential to all disciplines. Fulfills the General Education Requirement in Mathematics and Quantitative Reasoning. [ 3 credits ]
MAT-120: Sets, Logic and Numbers
Credits 3.00Covers 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]
MAT-121: Geometry and Graphs
Credits 3.00Covers 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]
MAT-122: Counting, Chance & Statistics
Credits 3.00Explores 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 Quantitative Reasoning. [3 credits]
MAT-125: Elementary Mathematical Models
Credits 3.00Includes 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
Credits 4.00Introduces functions, limits, continuity, differential calculus of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions, as well as basic integration techniques. Applications are considered throughout the course with an emphasis on the natural sciences. Weekly laboratory is an integral part of the ccourse. Graphing calculators are used to explore topics covered. Fulfills the general education requirement in Quantitative Reasoning. Prerequisite: Placement in MAT 211 or successful completion of MAT-107. [ 4 credits ]
MAT-212: Calculus II
Credits 4.00Studies applications of integrals; integration techniques including substitution, integration by parts, and using computer algebra systems; improper integrals; differential equations; infinite sequences and series; basic series convergence tests; and power series and Taylor series. Applications are considered throughout the course with an emphasis on the natural sciences. Weekly laboratory is an integral part of the course. Graphing calculators are used to explore topics covered. Prerequisite: Calculus I or placement into MAT-212. [4 credits]
MAT-213: Calculus III
Credits 4.00Covers 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-213L: Lab: Calculus III
Credits 0.00Lab for MAT-213. 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. Corequisite: MAT-213. [ 0 credits ]
MAT-214: Calculus of Vector Fields
Credits 1.00Analyzes 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
Credits 3.00Introduces 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 MAT-100, MAT-103, or MAT-116 is recommended. [3 credits]
MAT-219: Ethnomathematics
Credits 3.00MAT-243: Linear Algebra
Credits 3.00Studies 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]
MAT-301: Abstract Algebra
Credits 3.00Considers 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
Credits 3.00Introduces 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
Credits 3.00Explores 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 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
Credits 3.00Introduces 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
Credits 3.00Considers 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
Credits 3.00Analyzes 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
Credits 3.00Introduces 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-351: Readings in Mathematics
Credits 3.00Selected readings in mathematics. Discussion of selected topics drawn from current literature.
MAT-403: Introduction to Topology
Credits 3.00Study of the fundamental principles of topology, emphasizing the geometric nature of topology. Topics included are topological spaces, continuity, topological equivalence, connectedness, compactness, separation properties, metrization, subspaces, product spaces and quotient spaces. Prerequisite: MAT 212. 3 credits.
MAT-406: Complex Variables
Credits 3.00Introduces 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-408: Mathematical Foundations of Machine Learning
Credits 3.00Investigates the mathematical foundations for machine learning models including vector and affine spaces, inner products, orthogonal projections, matrix decompositions, higher-order gradients, multivariate Taylor series, discrete and continuous probability distributions, Bayes' Theorem, and optimization of continuous functions. These topics serve as foundation to some basic pillars of machine learning algorithms including regression, dimensionality reduction, density estimation, and formal classification. Prerequisite: MAT-213: Calculus III and MAT-243: Linear Algebra. [ 3 credits ]
MAT-409: Mathematical Methods in Physics
Credits 3.00Studies the use of mathematical tools such as power series, Fourier analysis, vector spaces, ordinary and partial differential equations, complex numbers, contour integrals, and Laplace and Fourier transforms for the study of Physics and Engineering. Emphasis will be placed on applications. Prerequisite: MAT-212, Calculus II.
[ 3 credits ]
MAT-411: Topics in Mathematics
Credits 3.00Explores various topics in Mathematics. Topic will change each offering of the course and will be noted. [ 3 credits ]
MAT-425: Simulation and Modeling
Credits 3.00Considers 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-445: Advanced Linear Algebra
Credits 3.00An introduction to the basics of matrices, linear transformations, and vector spaces along with selected applications. Topics include linear independence, dimension, solutions of linear systems, eigenvalues, and diagonalization. Applications are drawn from areas such as computer graphics, input-output analysis, and least squares. The computer package MATLAB is introduced and used throughout the course. [ 3 credits ]
MAT-455: History of Mathematics
Credits 3.00Focuses 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-456: History of Mathematics
Credits 3.00The study of the great ideas of mathematics and those who proposed them lead to an appreciation of the role mathematics has played in society. The essential relationships between its various branches become evident. Research paper required.
MAT-463: Directed Study in Mathematics
Credits 1.00 3.00Supports guided study of special current topics of interest to the student and approved by the instructor. Prerequisite: MAT-212. [1, 2 or 3 credits]