Full-Time Faculty: Leonid A. Khinkis, Chair; Metod Alif, Terrence P. Bisson, Richard H. Escobales, Jr., James G. Huard, L. Christine Kinsey, Dietrich W. Kuhlmann, Efstratios Prassidis, Karl J. Schroeder, Jr., Michael P. Strzelec, Anthony Weston.
The Department of Mathematics has two principle aims: (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 non-specialist 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 MAT 351 Probability and Statistics MAT 311 Abstract Algebra I |
(4 or 3) | ||
| MAT 321 Real Analysis I | (4) | ||
| MAT 311 Abstract Algebra I | (3) | ||
| MAT 322 Real Analysis II | (3) | ||
| MAT 312, 313, 322, 411, 416, 421 | (3) | ||
| 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 Two Economics courses |
(10 or 6) | ||
| Restricted electives: three additional upper-level Mathematics/Statistics courses from (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 | One of these: MAT 312, 313 ,322,421 |
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 222/Math elective |
3 or 4 | |||
| MAT 352 | 4 | Statistics elective | 3 | |||
| AS | 3 | AS | 3 | |||
| AS | 3 | AS | 3 | |||
| Elective | 3 | Elective | 3 | |||
| Total | 17 | 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 | 16 or 15 | Total | 15 | |||
| Total | 128-132 |
Other Programs
Mathematics Minor:
| MAT 111 Calculus I | (4) | |
| OR MAT 115 Calculus for Business I | ||
| OR MAT 117 Calculus I Integrated with Physics 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 advisors, 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: 2005 - 2007
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, 115, or 117. (AS VII)
MAT 107 Calculus for the Non-Sciences II 3
Continuation of MAT 106. Integral calculus and calculus of several variables with applications. (AS VII).
MAT 109-110 Calculus with Review I and II 4-4
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, 115, or 117. (AS VII)
MAT 111 Calculus I 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 II 4
Applications of integration. Inverse trigonometric functions, integration techniques, improper integrals, l’Hospital’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 I 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: 3 1/2 years of high school mathematics.
MAT 117 (PHY223A) Calculus I Integrated with General Physics I 6
For physical science, pre-engineering and mathematics majors. Coordinate systems, vector and matrix algebra, quadratic curves, scalar and vector functions of one variable, limits, continuity, differentiation, the definite integral, system of physical units, motions in space, Newton’s laws, linear momentum. 5 hours lecture and 1 1/2 hrs lab per week. (AS I and VII)
MAT 118 (PHY223B) Calculus II Integrated with General Physics I 7
Integrated continuation of MAT 117/PHY 223A. Fundamental theorem of calculus, relative and absolute extrema, curve sketching, parametric and polar equations, arc length, volume of solids, techniques of integration, power series, angular momentum, torque, work, energy. 8 hours lecture and 1 1/2 lab per week. (AS I and VII) Prerequisite: MAT 117/PHY 223A with minimum grade C -.
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: 3-1/2 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: 3-1/2 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.
MAT 311 Abstract Algebra I 4
Introduction to the basic structures of abstract algebra; groups, rings, fields. Prerequisites: 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.
MAT 313 Number Theory 3
Divisibility, prime numbers, numerical functions, congruencies, quadratic reciprocity, Diophantine equations. Prerequisite: MAT 311 or permission of instructor.
MAT 321 Real Analysis I 4
Advanced study of differentiation and integration of functions. Prerequisites: 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 -.
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.
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. Prerequisites: An elementary knowledge of computer programming and MAT 219.
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. Prerequisites: MAT 351-352 or consent of instructor.
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. Prerequisites: MAT 351-352 or permission of instructor.
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.
MAT 370 Topics in Statistics 3
Prerequisite: MAT 352 or permission of instructor.
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.
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.
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, Rouch’s Theorem. Prerequisite: MAT 321
or permission of the instructor.
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.