Mathematics
Women's College
Overview
Major
Mathematics/Secondary Education Certification
Minor
Four-Year Plan
Course Descriptions
Barbara Mento, M.E.S. , Chair
Alexandra L. Chaillou, Ph.D.
Darcy Conant, Ph.D. candidate
Joseph Di Rienzi, Ph.D.
Margaret Sullivan, Ph.D.
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. The mathematics course of study is designed to help students appreciate the power, beauty and scope of abstract thinking and to discover the fundamental relationship between mathematics and other disciplines. Recognizing the importance of the computer as the basic mode of information communication in today's society, the department has incorporated knowledge of computer science into its program.
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 any 100- or 200-level mathematics course.
Students must earn a minimum cumulative grade point average of 2.0 in all courses taken to complete the requirements of the math 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)
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.
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.
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 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.
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 |
| IDS-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.
Course Descriptions
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.
Prerequisite: minimum of one year of high school algebra. Satisfies the general education requirement in mathematics. [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, graphs, trees and
counting techniques. This course is designed for mathematics majors,
computer science majors and students with a particular interest in
mathematics. Fulfills the general education requirement in
mathematics. [3 credits]
MAT-120 Sets, Logic and Numbers
Covers 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. Fulfills the general education requirement
in mathematics. [3 credits]
MAT-121 Geometry and Graphs
Covers 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. Fulfills the general
education requirement in mathematics. [3 credits]
MAT-122 Counting, Chance and 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 or those who wish to
prepare for MAT-107. 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: 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. Fulfills the general education
requirement in mathematics. 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. Fulfills the general education requirement in
mathematics. 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. [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. Fulfills
general education requirement in mathematics. 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 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]
MAT-463 Directed Study in Mathematics
Supports guided study of special current topics of interest to the
student and approved by the instructor. Prerequisite: MAT-212.
[1, 2 or 3 credits]