Mathematics

Major/Minor

The Mathematics program develops critical thinking skills to create analytical thinkers and problems solvers. The curriculum covers how to use mathematical software and technologies, problem solve, communicate mathematically through proofs, and analyze data, in addition to how to relate mathematics to a variety of other disciplines.

Program Locations

Available Majors

  • Mathematics

Available Minors

  • Mathematics

Additional Study Options

Course Topics

  • Discrete Mathematics
  • Programming Concepts
  • Object Oriented Programming
  • Calculus
  • Linear Algebra
  • Abstract Algebra
  • Analysis
  • Theory of Probability
  • Simulation and Modeling
  • History of Mathematics

Faculty

Courses

  • Programming Concepts: CST-171 (3 credits)

    Introduces computer programming using a common small business language such as Microsoft Visual Basic. Emphasizes programming structures such as decisions, repetitions, sub procedures, functions, and arrays using structured program design with object-oriented concepts. Students learn to write a variety of program types to meet various business needs. [3 credits]
  • C++ Object-Oriented Programming: CST-295 (3 credits)

    Introduces object-oriented programming including objects, classes, inheritance and polymorphism. Includes high-level structures such as pointers and arrays as well as data structures with stacks and queues. Prerequisite: CST-171 or MAT-211. [3 credits]
  • Discrete Mathematics: MAT-110 (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]

  • Calculus I: MAT-211 (4 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: strong high school algebra background or successful completion of MAT-107. [4 credits]

  • Calculus II: MAT-212 (4 credits)

    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]

  • Calculus III: MAT-213 (3 credits)

    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]

  • Calculus of Vector Fields: MAT-214 (1 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]

  • Basic Statistics: MAT-215 (3 credits)

    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]

  • Abstract Algebra: MAT-301 (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]

  • Analysis: MAT-303 (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]

  • Geometry: MAT-305 (3 credits)

    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]

  • Numerical Analysis: MAT-307 (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]

  • Number Theory: MAT-309 (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]

  • Theory of Probability: MAT-311 (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]

  • Differential Equations: MAT-315 (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]

  • Complex Variables: MAT-406 (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]

  • Simulation and Modeling: MAT-425 (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]

  • History of Mathematics: MAT-455 (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]

  • First Year Seminar: NDMU-100 (3 credits)

    First Year Seminar course (formerly Perspectives in Culture and Education - IDS-100)
  • General Physics I: PHY-101 (4 credits)

    Studies the fundamental physical laws of nature and their use in understanding natural phenomena. Course provides a knowledge base for study in all areas of science and mathematics. Topics include kinematics, dynamics of motion, Newton's laws, rotational mechanics and conservation of energy and momentum. Development of the concepts of vector algebra and calculus are provided as needed. Three lectures, one three-hour laboratory weekly. Fulfills general education requirement in natural science. [4 credits]

  • General Physics II: PHY-102 (4 credits)

    Continues studies of the fundamental physical laws of nature and their use in understanding natural phenomena. Topics include classical wave motion, acoustics, optics, electricity and magnetism. Development of the concepts of vector algebra and calculus are provided as needed. Three lectures, one three-hour laboratory weekly. [4 credits]

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 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.

MAT-215 Basic Statistics is offered every semester and can be taken at any time.

What to Expect Studying at Notre Dame of Maryland University

Small class sizes and personal attention enhance the student expertise. Internships and practica allow you to apply learning beyond the classroom to real world experiences.

Program Goals

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

  1. Develop mathematical thinking and communication skills;
  2. Develop skills with a variety of technologies; and
  3. Develop a broad view of the mathematical sciences.
Student
Danielle Neumeister
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Future Engineer

Student, NDMU Class of 2015 Mathematics, Physics

Notre Dame’s campus has seen lots of construction activity—and one of our students has helped bring some of those projects to fruition. Danielle spent the summer of 2014 as a project engineer intern with the Whiting-Turner Contracting Company, one of the country's largest general contracting and construction management companies.

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Research & Internship Opportunities

Examples of internship and employment opportunities include:

Mathematics Capstone Experience

In your final spring semester, you will complete a two-step capstone:

  1. Write an essay reflecting on your growth as a mathematician and on your expanded understanding of the discipline of mathematics.
  2. Consult with your advisor and develop a presentation on a topic selected from one or more of your courses, an internship, or a research experience.

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

Mathematics Careers

  • Finance
  • Computing
  • Science
  • Education
  • Defense Industry

The mathematics program also provides a foundation for the pursuit of further study not only in mathematics, but in:

  • Analytics
  • Law
  • Medicine
  • Engineering