Full-Time Faculty: L. Christine Kinsey, Chair, Metod Alif, Terrence P. Bisson, Richard H. Escobales, Jr., Donald F. Girod, Robert A. Haus, S.J., James G. Huard, Leonid A. Khinkis, Dietrich W. Kuhlmann, Efstratios Prassidis, Karl J. Schroeder, Jr., Michael P. Strzelec, Anthony Weston.

The aim of the Department of Mathematics is, in principle, (1) to transmit an understanding and appreciation of mathematics: its substance, its applicability, its literature, its current directions and problems, its historical development, its human worth and values; and (2) to promote the development of skill in the practice of mathematics.

To meet these objectives in a manner consistent with the interests and needs of its diverse clientele – mathematics, science, and education majors, as well as students in other disciplines – the Department offers a variety of courses and programs. Graduates who major in mathematics can enter careers in research, education, industry, business, and government. Increasingly, they go on to earn advanced degrees in the areas of business, economics, computer science, operations research, statistics, and actuarial science, as well as mathematics. The Mathematics major is available under three options, each of which furnishes a sound foundation for the future.

Option A, the major option, is designed to prepare the student for positions in which mathematical competence is sought, as well as for advanced study in graduate school.

Option B, mathematics with a concentration in another area, allows the student to develop expertise in another area besides mathematics. The option may enable a student to earn a dual major or a minor from another department. Students interested in teaching at the secondary or elementary/early secondary level may take advantage of this option to give themselves a strong background in mathematics while fulfilling the requirements of the Teacher Education Department.

Option C,the statistics option, prepares the student for advanced work and the many careers which utilize statistical thinking. The course work also offers students good preparation for graduate study.

Option B or C, together with appropriate courses in business, can constitute a good preparation for a career in actuarial science.

The Department also offers a Mathematics minor, which is described under Other Programs.

For the nonspecialist in mathematics, the Department offers service courses which provide mathematical techniques necessary in the development of the student’s own field, studies imparting insights into the nature and applications of mathematics generally, and courses treating the historical development or logical foundations of the subject.

Admission

Admission to the major program in mathematics requires departmental approval and satisfactory completion of MAT 111-112, 211, 230, 219, and either 222 or 351. A minimum grade of "C–" is ordinarily expected in all courses in the major.

Mathematics Curriculum:

1.	ENG 101, ENG 102, PHI 101, RST 101	(4 courses)	(12)
2.	Area Studies: Two courses from each of these areas: I or II, III, IV, V, VI, VIII	(12 courses)	(36)
3.	Major course requirements:
	Option A (Mathematics major)	(15 courses)
	Option B (Mathematics with concentration in another area)	(17 courses)
	MAT 111-112	Calculus I and II	(8)
	MAT 211	Calculus III	(4)
	MAT 230	Bridge to Abstract Mathematics	(4)
	MAT 219	Linear Algebra	(4)
	MAT 222	Differential Equations
		OR	(4 or 3)
	MAT 351	Probability and Statistics MAT 311 Abstract Algebra I	(4)
	MAT 321	Real Analysis I	(4)
	MAT 312	Abstract Algebra II
		OR	(3)
	MAT 322	Real Analysis II
	PHY 223-224	General Physics for Physical Science Majors
		OR	(10 or 6)
	Two Economics courses
	Restricted electives:
	Option A: four additional 300 or 400-level
	Mathematics courses		(12)
	Option B: two additional 300 or 400-level
	Mathematics courses, and four courses in another area approved by the Mathematics Department		(18)
	Option C (Statistics)	(15 courses)
	MAT 111-112	Calculus I and II	(8)
	MAT 211	Calculus III	(4)
	MAT 230	Bridge to Abstract Mathematics	(4)
	MAT 219	Linear Algebra	(4)
	MAT 222	Differential Equations
		OR	(4 or 3)
	Mathematics elective: one 300- or 400-level
	Mathematics course
	MAT 351-352	Probability and Statistics	(6)
	MAT 321	Real Analysis I	(4)
	MAT 322	Real Analysis II
		OR	(3 or 4)
	MAT 311	Abstract Algebra I
	PHY 223-224	General Physics for Physical Science Majors
		OR	(10 or 6)
	Two Economics courses	Restricted electives: three additional upper-level Mathematics/Statistics courses
	(MAT 353, 354, 365, 390)................................		(9)
4.	Electives: the Department recommends at least one Computer Science course, such as CSC 111. Students
	planning on graduate work in mathematics should take
	both MAT 312 and MAT 322.
	Option A:	(9 courses)	(27)
	Option B:	(7 courses)	(21)
	Option C:	(9 courses)	(27)
Total		(40 courses)
	Options A and B:		(127-132)
	Option C:		(126-132)

Recommended Schedule (Options A and B):

Fall		Spring
Freshman Year
ENG 101	3	ENG 102	3
MAT 111	4	RST 101	3
AS	3	MAT 112	4
AS	3	PHY 223 or Economics	5 or 3
Elective	3	Elective	3
Total	16	Total	18 or 16
Sophomore Year
PHY 224 or Economics	5 or 3	PHI 101	3
MAT 211	4	MAT 219	4
MAT 230	4	MAT 222 or 351	4 or 3
Elective	3	AS	3
AS	3	Elective	3
Total	19 or 17	Total	17 or 16
Junior Year
MAT 311	4	MAT 312 or 322	3
MAT 321	4	Mathematics elective	3
AS	3	AS	3
AS	3	AS	3
Elective	3	Elective	3
Total	17	Total	15
Senior Year
Mathematics elective	3	Mathematics elective	3
Mathematics elective	3	AS	3
AS	3	AS	3
AS	3	Elective	3
Elective	3	Elective	3
Total	15	Total	15
		Total	126-132

Recommended Schedule (Option C):

Fall		Spring
Freshman Year
ENG 101	3	ENG 102	3
MAT 111	4	RST 101	3
AS	3	MAT 112	4
AS	3	PHY 223 or Economics	5 or 3
Elective	3	Elective	3
Total	16	Total	18 or 16
Sophomore Year
PHY 224 or Economics	5 or 3	PHI 101	3
MAT 211	4	MAT 219	4
MAT 230	4	MAT 351	3
AS	3	AS	3
Elective	3	Elective	3
Total	19 or 17	Total	16
Junior Year
MAT 321	4	MAT 322/311 or MAT
MAT 352	4	222/Math elective	3 or 4
AS	3	Statistics elective	3
AS	3	AS	3
Elective	3	AS	3
Total	17	Elective	3
		Total	15 or 16
Senior Year
Math elective/MAT 222 or		Statistics elective	3
MAT 311/322	4 or 3	AS	3
Statistics elective	3	AS	3
AS	3	Elective	3
AS	3	Elective	3
Elective	3	Total	15
Total	16 or 15	Total	128-132

Other Programs

Mathematics Minor:

MAT 111	Calculus I
	OR	(4)
MAT 115	Calculus for Business I
MAT 112	Calculus II	(4)
MAT 211	Calculus III	(4)
MAT 219	Linear Algebra	(4)
MAT 230	Bridge to Abstract Mathematics	(4)
Restricted electives: two courses from any one of the following tracks:
Probability and Statistics: MAT 351, 352, 353, 354, 365, 390
Applied Mathematics: MAT 222, 335, 336, 341
Theoretical Mathematics: MAT 311, 312, 321, 322
Mathematics and Culture: MAT 301, 331		(6-8)
Total	(7 courses)	(26-28)

Double Major or Minor in Another Department

By suitable choice of electives, a student following Option B can also complete the requirements for a minor or a major in another department, most commonly Physics, Chemistry, Computer Science, or Economics.

Additional Information

Students of computer science, physics, chemistry, and engineering, in consultation with their advisers, should consider taking MAT 219 (Linear Algebra), even if this course is not listed as a required course in their major. Increasingly, linear algebra is playing an important role in applications of mathematics. This recommendation is in addition to the required calculus courses so central to the understanding of many physical, biological, chemical, and economic phenomena. Those interested in probability and statistics are encouraged to take MAT 351-352.

COURSES: 2001-2003

MAT 001 Pre-College Mathematics I NC

Intermediate Algebra I: Real numbers, exponents, graphing and solving linear equations and inequalities, systems of linear equations, multiplication, division and factoring of polynomials. Word problems. A good course for overcoming math anxiety through problem solving.

MAT 002 Pre-College Mathematics II NC

Intermediate Algebra II: Simplifying and solving rational equations, conic sections, relations and functions, exponential and logarithmic functions. Word problems.

Prerequisite: MAT 001 or consent of instructor.

MAT 105 Finite Mathematics 3

Introduction to problem solving with linear models, matrices, linear programming, notions underlying probability, interpretation of graphs, and compound interest. (AS VII)

MAT 106 Calculus for the Non-Sciences I 3

Fundamentals of calculus for students in business, or social or behavioral sciences. Credit not allowed if student already has credit for MAT 111 or MAT 115. (AS VII)

MAT 109-110 Calculus with Review I and II 3

For science and mathematics majors. Calculus, with topics from precalculus. Logarithms, exponentials, trigonometric functions, limits, differentiation, related rates, max-min problems, anti-differentiation, definite integral. No credit allowed if student has credit for MAT 111 or MAT 115. (AS VII)

MAT 111 Calculus I2 4

For physical science, pre-engineering, and mathematics majors. Functions of single variable. Functions, limits, differentiation, continuity, graphing, natural logarithm and exponential functions, related rates, max-min problems, mean value theorem, anti-differentiation, definite integral. (AS VII)

MAT 112 Calculus II2 4

Applications of integration. Inverse trigonometric functions, integration techniques, improper integrals, l'H™pital's rule, sequences, series, convergence tests, Taylor's theorem, applications. (AS VII)

Prerequisite: MAT 111 with minimum grade C- for majors in Chemistry, Computer Science, Mathematics, Physics, and Engineering.

MAT 115 Calculus for Business I2 4

First of two semesters of mathematics for business students. Differentiation/integration of functions of one variable. Applications: concepts, examples, and problems in economics and business. (AS VII)

Prerequisite: 31/2 years of high school mathematics.

MAT 116 Calculus for Business II2 4

Continuation of MAT 115. Extends concepts covered in MAT 115 to functions of several variables. Includes matrix algebra, systems of linear equations, linear programming, and game theory. (AS VII)

Prerequisite: MAT 115 or consent of instructor.

MAT 121 The Nature of Mathematics 3

Liberal arts mathematics course. Problem solving techniques, deductive reasoning in mathematics, some modern topics, and quantitative thinking. (AS VII)

Prerequisite: 3 years of high school math or equivalent; Sophomore standing or higher.

MAT 131 Statistics and Computers 3

A first course for majors in social or health sciences. Descriptive statistics, calculators, computer programs, and introduction to inferential statistics. (AS VII)

Prerequisite: High school intermediate algebra.

MAT 141 Inferential Statistics and Computers

for Science 4

Elementary probability theory, descriptive statistics, hypothesis testing, estimation, correlation and regression. The computer will be used with one of the standard statistical packages. (AS VII)

Prerequisite: 31/2 years of high school mathematics.

MAT 150 Excursions in Modern Mathematics 3

Liberal arts course emphasizing applications of math in the social sciences. Covers topics such as voting theory, decisions made by groups, measurement of political power. (AS VII)

Prerequisite: 3 years of high school mathematics or equivalent.

MAT 161 Statistics For Lawyers 3

Liberal arts mathematics course, teaching the basics of probability and statistics with many applications taken from modern court cases. Emphasis is on statistical analysis and decision making. Contains computer component and significant writing component.

Prerequisite: 3 1/2 years of high school mathematics.

MAT 181 Symmetry 3

Liberal arts course exploring the mathematical world of geometry and symmetry. Measurement, billiards, polygons and polyhedra, tilings and wallpaper patterns, spirals and natural growth. (AS VII)

Prerequisite: 3 years of high school mathematics or equivalent.

MAT 191 Introduction to Discrete Mathematics 4

Fundamental topics with computer science applications. Sets and logic, propositional and predicate calculus, elements of combinatorics and counting, elementary discrete probability, functions and relations, graphs.

Prerequisite: 31/2 years of high school mathematics.

MAT 211 Calculus III 4

Continuation of MAT 111-112. Analytic geometry of 3-space and calculus of functions of several variables.

Prerequisite: MAT 112 with minimum grade of C-.

MAT 219 Linear Algebra 4

Vector spaces and inner product spaces. Linear transformations and matrices. Eigenvectors, eigenvalues, and applications. Orthogonal transformations. Quadratic forms and quadric surfaces.

Prerequisite: MAT 112 or consent of the instructor.

MAT 222 Differential Equations 4

Introduction to the theory and applications of ordinary differential equations.

Prerequisite: MAT 211 with minimum grade of C–.

MAT 230 Bridge to Abstract Mathematics 4

Transition from calculus to upper division courses: logic and methods of proof; set theory; relations, orders, and functions; number systems; cardinality.

Prerequisite: MAT 112 with minimum grade of C–, or consent of the instructor.

MAT 301 History of Mathematics 3

Development and interrelations of major areas of mathematics, from ancient to modern times. Emphasis on both historical context and mathematical content. Mathematics as cultural heritage.

Prerequisite: MAT 111-112. 2000-2001 only

MAT 311 Abstract Algebra I 4

Introduction to the basic structures of abstract algebra: groups, rings, fields.

Prerequisite: MAT 230 and MAT 219 with minimum grades of C–.

MAT 312 Abstract Algebra II 3

Continuation of MAT 311. Selected topics from rings, integral domains, field extensions, and Galois theory.

Prerequisite: MAT 311. 2000-2001 only

MAT 313 Number Theory 3

Divisibility, prime numbers, numerical functions, congruencies, quadratic reciprocity, Diophantine equations.

Prerequisite: MAT 230. 1999-2000 only

MAT 321 Real Analysis I 4

Advanced study of differentiation and integration of functions.

Prerequisite: MAT 211, 230, 219 with minimum grades of C–; or MAT 211, 230 and consent of instructor.

MAT 322 Real Analysis II 3

Continuation of MAT 321. Selected topics from functions of one or several variables.

Prerequisite: MAT 321 with minimum grade of C-. 1999-2000 only

MAT 331 Introduction to Modern Geometry 3

Axioms for geometry and their consequences: independence of the parallel postulate. Rudiments of hyperbolic geometry. Geometric transformations.

Prerequisite: MAT 230. 1999-2000 only

MAT 335-336 Mathematical Analysis for Physicists 4-4

Theory and applications of infinite series. Fourier series, Green's functions. Fourier integrals, vector calculus, linear algebra, partial differential equations, and complex variables.

Prerequisite: MAT 222 or consent of instructor.

MAT 341 (CSC 341) Numerical Analysis 3

The methods used to obtain numerical solutions of functional, integral, and differential equations.

Prerequisite: An elementary knowledge of computer programming and MAT 219. 2000-2001 only

MAT 351-352 Probability and Statistics 3-3

Introduction to the mathematical aspects of modern probability theory and the theory of statistics.

Prerequisite: MAT 211.

MAT 353 Regression Analysis 3

Linear regression and correlation. Covariance, residual sum of squares, residual variance, correlation coefficient, tests of significance for correlation coefficient and for regression coefficients. Non-linear regression.

Prerequisite: MAT 351-352 or consent of instructor. 1999-2000 only

MAT 354 Experimental Design and Statistical Computing 3

Analyzing data; one-way/two-way blocking; chi-square, goodness of fit. Statistical computing package; Monte-Carlo simulation- subset selection, central limit theorem; residual plots.

Prerequisite: MAT 351-352 or permission of instructor. 1999-2000 only

MAT 365 Logistic Regression 3

Statistical analysis of dichotomous data. Univariate and multivariate cases are covered. Applied problems solved on the computer.

Prerequisite: MAT 352 or ECO 256. 2000-2001 only

MAT 370 Independent Study 3

Topics in statistics.

Prerequisite: Consent of instructor and chair.

MAT 400 (PHY 400) Math/Physics Reading Group 1

Study of a book on recent developments in math and science. Book subject varies. May be taken more than once.

Prerequisite: By permission.

MAT 411 Topology 3

An introduction to topology, stressing concrete examples including surfaces. Point-set, geometric, and algebraic topology with interconnections and applications.

Prerequisite: MAT 230 or permission of instructor. 2000-2001 only

MAT 416 Differential Geometry 3

Curves in the plane and 3 space: Frenet formulas, isoperimetric inequalities. Basic elements of surface theory. Curvature and mean curvature. Gauss's Theorema Egregium. Rigidity questions.

Prerequisite: MAT 321. 1999-2000 only

MAT 421 Complex Analysis 3

Complex numbers, analytic functions and mappings. Cauchy-Riemann equations, harmonic functions, Cauchy's theorem, integral formula and inequalities. Power series, residues, singularities and zeros, RouchŽ's Theorem.

Prerequisite: MAT 321 or permission of the instructor. 2000-2001 only

MAT 498 Internship in Mathematics 1-3

Internship involving non-routine tasks linking academic concepts to practical experience. May be used for free elective credit only.

Prerequisite: Consent of chair.

MAT 499 Independent Study 3

Prerequisite: Consent of instructor and chair.

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1 Area II is automatically fulfilled because this program is in the Mathematics area. Either Area I or Area II is fulfilled, depending on whether the student takes PHY 223-224 or two economics electives. In Options B and C there may be an additional exclusion based on the student’s other concentration or major.

2 Credit is not allowed for both MAT 111 and MAT 115 or for MAT 112 and MAT 116.