Mathematics
(Program Homepage)
Faculty: S. Balasubramanian, M. Kannowski, N. Manickam, N. Shifa, R. Smock, L. Smogor, Z. Wu
The study of mathematics encourages the development of skills in analytical thinking and problem solving that have wide applicability. Students who graduate with a major in the department have continued their educations in fields as disparate as mathematics, computer science, physics, operations research, law, business, music, religion, dentistry and medicine; others have accepted employment in a wide variety of occupations. The department has a long tradition of successfully preparing students for the actuarial profession.
A major and minor is offered in Mathematics. The basic sequence of courses for Mathematics majors is MATH 151, 152, 223, 251 and 270. Advanced placement and credit can be granted for satisfactory performance on national or departmental examinations.
Students preparing for secondary teaching: review Section V, Teacher Education, and confer with the chair of the education department about requirements for admission and certification.
Requirements for a major in Mathematics
| Total courses required | Ten |
| Core courses | MATH 151, MATH 152, MATH 223, MATH 251, MATH 270, MATH 495 |
| Other required courses | Students planning graduate work in mathematics should include MATH 361 and MATH 371. Students concentrating in actuarial mathematics should include MATH 331 and MATH 442. |
| # 300 and 400 level courses | Four (not including MATH 495) |
| Senior requirement | MATH 495 |
| Additional information | |
| Recent changes in major |
Requirements for a minor in Mathematics
| Total courses required | Five |
| Core courses | MATH 151, MATH 152, MATH 223, MATH 270 |
| Other courses | |
| # 300 and 400 level courses | One |
| Recent changes in minor |
Courses in Mathematics
| MATH 123. Computational Discrete Mathematics | 1 course | |
| An introduction to the concepts of discrete mathematics with an emphasis on problem solving and computation. Topics are selected from Boolean algebra, combinatorics, functions, graph theory, matrix algebra, number theory, probability, relations and set theory. This course may have a laboratory component. | ||
| MATH 135. Calculus with Review I | 1 course | |
| Extensive review of topics from algebra, trigonometry, analytic geometry, graphing and theory of equations. A study of functions, limits, continuity and differentiability of algebraic and transcendental functions with applications. | ||
| MATH 136. Calculus with Review II | Group 1 | 1 course |
| A continuation of MATH 135. Topics include further study of differentiation, integration of algebraic and transcendental functions with applications, and techniques of integration. Completion of this course is equivalent to completing MATH 151 and is adequate preparation for any course requiring MATH 151. Prerequisite: MATH 135. | ||
| MATH 141. Statistical Reasoning | Group 1 | 1 course |
| This course is designed to develop in the student the ability to reason with quantities through the study of elementary statistics. Whenever possible, the context for the statistics will be from other disciplines. This course may, at the discretion of the instructor, include a laboratory. May not be counted toward a major or minor in mathematics. | ||
| MATH 151. Calculus I | Group 1 | 1 course |
| A study of functions, limits, continuity, differentiation and integration of algebraic and transcendental functions with elementary applications. | ||
| MATH 152. Calculus II | Group 1 | 1 course |
| Techniques of integration, parametric equations, infinite series and an introduction to the calculus of several variables. Prerequisite: MATH 151. | ||
| MATH 197. First-Year Seminar | 1 course | |
| The basic approach in this course will be to present mathematics in a more humanistic manner and thereby provide an environment where students can discover, on their own, the quantitative ideas and mathematical techniques used in decision-making in a diversity of disciplines. Students work with problems obtained from industry and elsewhere. | ||
| MATH 205. Mathematics for Elementary School Teachers I | 1 course | |
| A study of mathematical reasoning and problem solving, the number system through the rationals, the operations of arithmetic and other mathematical topics relevant to elementary education. Includes an introduction to uses of manipulative devices, field experiences and emphasis on how children learn mathematics. For those intending to teach in elementary school. Prerequisite: a major in Elementary Education or permission of instructor. | ||
| MATH 206. Mathematics for Elementary School Teachers II | 1 course | |
| A study of additional topics underlying elementary school mathematics, including informal geometry and probability and statistics. Includes field experiences and emphasis on how children learn mathematics. Prerequisite: a major in Elementary Education or permission of instructor. Prerequisite: MATH 205. | ||
| MATH 223. Theory in Discrete Mathematics | 1 course | |
| An introduction to the concepts of discrete mathematics with an emphasis on theorums and proof. Topics are selected from Boolean algebra, combinatorics, functions, graph theory, matrix algebra, number theory, probability, relations and set theory. This course may have a laboratory component. | ||
| MATH 240. Introduction to Statistics | Group 1 | 1 course |
| This course introduces students to elementary probability and data analysis via visual presentation of data, descriptive statistics and statistical inference. Emphasis will be placed on applications with examples drawn from a wide range of disciplines in both physical and behavioral sciences and humanities. Topics of statistical inference include: confidence intervals, hypothesis testing, regression, correlation, contingency tables, goodness of fit and ANOVA. The course will also develop familiarity with the most commonly encountered tables for probability distributions: binomial, normal, chi-squared, student-t and F. | ||
| MATH 251. Calculus III | Group 1 | 1 course |
| An introduction to the calculus of several variables. Topics include vectors and solid analytic geometry, multidimensional differentiation and integration, and a selection of applications. Prerequisite: MATH 152. | ||
| MATH 270. Linear Algebra | 1 course | |
| Vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors and applications. Prerequisite: MATH 152 or permission of instructor. | ||
| MATH 321. Topics in Geometry | 1 course | |
| Selections from advanced plane, differential, non-Euclidean or projective geometry. Prerequisite: either MATH 270 or MATH 223. | ||
| MATH 331. Mathematics of Compound Interest | 1 course | |
| A mathematical treatment of measurements of interest and discount, present values, equations of value, annuities, amortization and sinking funds and bonds. Also, an introduction to life annuities and the mathematics of life insurance. Prerequisite: MATH 151 or permission of instructor. | ||
| MATH 361. Analysis | 1 course | |
| A study of the theory of limits, continuity, differentiation, integration, sequences and series. Prerequisite: MATH 152 and either MATH 270 or MATH 223. | ||
| MATH 363. Differential Equations | Group 1 | 1 course |
| Equations of the first degree, linear differential equations, systems of equations with matrix methods and applications. Selected topics from power series solutions, numerical methods, boundary-value problems and non-linear equations. Prerequisites: MATH 152 and MATH 270. | ||
| MATH 367. Introduction to Numerical Analysis | 1 course | |
| Analysis of algorithms frequently used in mathematics, engineering and the physical sciences. Topics include sources of errors in digital computers, fixed point iteration, interpolation and polynomial approximation, numerical differentiation and integration, direct and iterative methods for solving linear systems, and iterative methods for nonlinear systems. Numerical experiments will be conducted using FORTRAN, C, or another appropriate high-level language. Prerequisites: MATH 270 and CSC 121 | ||
| MATH 371. Algebraic Structures | 1 course | |
| The structure of groups, group homomorphisms and selected topics from other algebraic structures, such as rings, fields and modules. Prerequisite: MATH 270. | ||
| MATH 382. Number Theory | 1 course | |
| Divisibility and factorization of integers, linear and quadratic congruences. Selected topics from diophantine equations, the distribution of primes, number-theoretic functions, the representation of integers and continued fractions. Prerequisite: MATH 270 or permission of instructor. | ||
| MATH 422. Operations Research | Group 1 | 1 course |
| Topics selected from linear and dynamic programming, network analysis, game theory and queueing theory are applied to problems in production, transportation, resource allocation, scheduling and competition. Prerequisite: MATH 270. | ||
| MATH 423. Advanced Topics in Operations Research | 1 course | |
| Advanced topics in linear programming, integer programming, nonlinear programming, game theory, Markov chains, and dynamic programming. Prerequisite: Math 422 | ||
| MATH 441. Probability and Statistics I | 1 course | |
| Probability, sample spaces and events, discrete and continuous random variables, density and their distributions, including the binomial, Poisson and normal. Prerequisite: MATH 152 and MATH 223. | ||
| MATH 442. Probability and Statistics II | 1 course | |
| Sampling, point and interval estimation, hypothesis testing, correlation, regression and other selected topics. Prerequisite: MATH 441. | ||
| MATH 490. Mathematics Topics | 1/2-1 course | |
| A. Actuarial Mathematics; B. Algebra; C. Analysis; D. Foundations of Mathematics; E. Geometry; F. Probability and Statistics; G. Applied Mathematics; H. Special Topics. Prerequisite: permission of instructor. May be repeated for credit with different topics. | ||
| MATH 495. Seminar: Mathematics | 1 course | |
| Advanced topics considered individually or in small groups. Open only to senior Mathematics majors or by permission of the Department of Mathematics. | ||
| MATH EXP. Statistical Model Analysis | 1 course | |
| The course will focus on fundamental ideas of Statistical models for discovering the relationships among variables; clear, thorough presentation of concepts and applications, and will offer a complete, easily accessible introduction to the fundamentals of Statistical model analysis. Students will be able to fit and check both linear and nonlinear models, using small and large data sests, with calculators or computers. | ||
