Mathematics

Mathematics, Physics, and Computer Studies Department

Alexandra L. Chaillou, Ph.D., Chair
Charles Buehrle, Ph.D.
Kristyanna Erickson, Ed.D.

Degrees offered

Major
Minor

Campuses

Main Campus

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 o 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: 

  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.

Women's College

Overview
Major
Mathematics/Secondary Education Certification
Minor
Four-Year Plan
Course Descriptions 

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.

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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 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.

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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.

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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

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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.

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Courses

CST-171 Programming Concepts

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. Satisfies the technological competency requirement. [3 credits]

CST-295 C++ Object-Oriented Programming

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. Satisfies the technological competency requirement. [3 credits]

IDS-100 Perspectives on Education and Culture

Assists first-year students in making a successful transition to college life. The course has three overlapping themes: becoming an intentional learner, becoming a Notre Dame woman, and acquiring global and intercultural fluency. Each student will examine and reflect upon various aspects of her life, including her relationship to other students, the institution and the community (understanding culture, appreciating diversity). Students will have the opportunity to develop personal, academic, and leadership skills and habits that will enhance their college experiences and promote lifelong learning. Required for first-year traditional age students and transfer students with fewer than 12 credits. [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-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 or successful completion of MAT 100 or MAT 103 is recommended. [3 credits]

MAT-243 Linear Algebra

Studies 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

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 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

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]

NDMU-100 First Year Seminar

First Year Seminar course (formerly Perspectives in Culture and Education - IDS-100)

PHY-101 General Physics I

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]

PHY-102 General Physics II

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]