Mathematics

Virginia M. Buchanan (1987), Professor of Mathematics
B.S., Delta State University;
M.S., Ph.D., University of Mississippi

Academic Interest: history of mathematics, topology, real analysis, abstract algebra

Carrie Dugan (2007), Adjunct Assistant Professor of Mathematics

B.S., Marshall University;

M.S., Kent State University;

Ph.D., Kent State University

Academic Interest: character theory

Bradley S. Gubser (1990), Chair, Professor of Mathematics
B.A., Blackburn College;
M.S., Miami University;
Ph.D., Louisiana State University

Academic Interest: statistics, teacher preparation

Michael A. Grajek (1973), Professor of Mathematics and Dean, Emeritus, Director of Institutional Research and Planning
B.S., M.S., Clarkson University;
M.A., Ph.D., University of Iowa

Academic Interest: decision mathematics, mathematics education 

Edward J. Smerek (1969), Emeritus Professor of Mathematics

B.S., M.S., Ph.D., University of Pittsburgh

Academic Interest: chaotic dynamical systems, real analysis

 

Department web address:   http://home.hiram.edu/www/math/mathhome.html

Introduction

The Department of Mathematics offers both a major and a minor in mathematics. The mathematics program is designed to prepare students for positions in business and industry, for graduate work in mathematics, statistics, and operations research, for professional programs,  and for teaching mathematics. The department extensively uses current mathematics software and graphing calculators.

Requirements for the Major

A student majoring in mathematics must complete the following requirements:

MATH 198

MATH 199

MATH 200

MATH 217

MATH 218

MATH 308

MATH 371

MATH 461

One of MATH 309, 372, 462

MATH 380

MATH 480 (the mathematics capstone)

Two additional mathematics courses numbered above 200

A Correlative Experience chosen by the student in consultation with an advisor in the mathematics department

A Mathematics Portfolio

The Senior Seminar course (MATH 480) is the mathematics capstone.  In this course the student will undertake a project that will involve significant independent learning in an area not included in the standard undergraduate mathematics curriculum.  The project will culminate in a paper and a public oral presentation.

 

Requirements for the Minor

A student minoring in mathematics must complete the following courses:

MATH 198

MATH 199

Three additional mathematics courses numbered above 300

Two additional mathematics courses numbered above 199

Departmental Honors

Mathematics departmental honors will be determined by a vote of the mathematics department faculty.  Only students who meet the college’s minimum requirements for honors will be considered.

101 Basic Mathematics I                                                                      3 hours

Development of basic mathematical skills necessary for other mathematics courses. The number system and its operations, use of percent, problem solving. (Not for students with prior credit for college-level mathematics. For Weekend College students only.)

102 Basic Mathematics II                                                                    3 hours

A continuation of Mathematics 101. Solving equations, problem solving, geometric and graphical properties of functions, systems of equations with applications. (Not for students with prior credit for college-level mathematics. For Weekend College students only.) Prerequisite: Mathematics 101 or the equivalent.

103 Fundamentals of Mathematics I                                                   4 hours

A study of elementary school mathematics topics to promote a deep understanding in the areas of problem solving; number (whole number, integers, rational and irrational numbers) and operations (addition, subtraction, multiplication, division); algebra and functions; and statistics, probability and data analysis. Students will learn to apply the technology of both calculators and statistics software. Students will become familiar with the National Council of Teachers of Mathematics (NCTM) resource Principles and Standards for School Mathematics.  For education majors only.

 

104 Fundamentals of Mathematics II                                                 3 hours

A continuation of 103. Topics include geometry (planar and 3-dimensional figures; transformation, symmetries, and tilings; and congruence and similarity) and measurement (length, area, perimeter, volume, surface area). Students will learn to apply the technology of both calculators and geometry software.  For education majors only.  Prerequisite: Mathematics 103

108 Statistics MM                                                                                 4 hours

An introduction to the science of collecting, tabulating, summarizing, and interpreting data. Both descriptive and inferential statistics are studied. Descriptive topics include levels of measurement, measurement of central tendency and dispersion, the normal and binomial distributions, and correlation. Inferential topics include hypothesis testing, interval estimation, regression analysis, and the use of nonparametric methods. This course is especially useful for students in the social or natural sciences. Either high school algebra and placement or Math 162 is required.

132 Methods of Decision Making MM                                                   3 hours

An introduction to the field of decision theory. Contemporary mathematical thinking is used to seek connections between mathematics and modern society. Topics include applications of graph theory, scheduling, voting and apportionment, game theory and linear programming.  Either high school algebra and placement or Math 162 is required.

162 Mathematical Modeling in the Liberal Arts MM                             4 hours

Motivated by naturally occurring phenomena in areas such as medicine, economics, business, and ecology, students will use data together with linear, quadratic, polynomial, exponential, and logarithmic functions to model relationships within these and other disciplines.  Numerical, graphical, verbal, and symbolic modeling methods will all be examined. 

197 Precalculus                                                                                   4 hours

Exponential and logarithmic functions, the trigonometric functions, analytic trigonometry, and topics in analytic geometry. For students who plan to study calculus but need to supplement their prior mathematics courses.  Placement is required.

198 Calculus I MM                                                                                4 hours

The differential calculus. Topics include limits, continuity, differentiation of algebraic and transcendental functions, maxima/minima and other applications of the derivative.  Mathematics 197 or equivalent is required.

199 Calculus II MM                                                                               4 hours

A continuation of 198. The integral calculus. Topics include antidifferentiation, the Riemann integral, the Fundamental Theorem of Calculus, applications of the definite integral, techniques of integration, and infinite series. Prerequisite: Mathematics 198.

200 Calculus III MM                                                                             4 hours

A continuation of 199. Multivariable and vector calculus. Topics include parametrizations, polar coordinates, partial derivatives, directional derivatives, multiple integrals. Prerequisite: Mathematics 199.

217 Discrete Mathematics                                                                   3 hours

An introduction to proofs and mathematical reasoning in the context of discrete mathematical structures. Topics include proof techniques, mathematical logic, set theory, relations, elementary function theory, and the Division Algorithm.  Placement is required.

218 Linear Algebra                                                                              3 hours

Systems of linear equations, matrix algebra and determinants, vector spaces, eigenvalues, eigenvectors, and linear transformations are studied. Placement is required.

243 Differential Equations                                                                   3 hours

A study of the theory, solution, and application of differential equations. Existence and uniqueness theorems. Solutions of several types for first-order equations. Solution of homogeneous and non-homogeneous higher-order linear equations; Laplace transform methods. Applications for first and second order equations. Prerequisites: Mathematics 200 and 218.

280 Seminar                                                                                   1 - 4 hours

281 Independent Study                                                                  1 - 4 hours

298 Internship Program: Field Experience                                   1 - 4 hours

                                                    

301 Modern Geometries                                                                      4 hours

Selected topics in Euclidean, non-Euclidean, finite, and projective geometries together with the historical development of these geometries. Prerequisite: Mathematics 217

308 Mathematical Statistics I                                                              4 hours

A calculus-based, mathematical approach to the study of probability. Includes basic discrete and continuous probability models, moment-generating functions, multivariate distributions, distributions of random variables and functions of random variables, limiting distributions, the Central Limit Theorem, and approximations for discrete distributions. Statistical software will be used to analyze real data. Prerequisite: Mathematics 200.

309 Mathematical Statistics II                                                            3 hours

A continuation of Mathematics 308 focusing on inferential statistics. Includes interval and point estimation, tests of statistical hypotheses, regression analysis, and nonparametric methods. Prerequisite: Mathematics 308.

330 History of Mathematics                                                                 4 hours

This course examines the historical development of major mathematical concepts, with special emphasis on the period through the invention of the calculus in the late seventeenth century. Both European and non-European mathematical developments are explored, with emphasis on the many common ideas present in widely separated cultures. Prerequisite: Mathematics 199 or 217.

371 Analysis I                                                                                      4 hours

A first course in real analysis. Topics include sequences, limits, continuity, and differentiation. Prerequisites: Mathematics 200 and 217.

372 Analysis II                                                                                    3 hours

A continuation of 371. Topics include compactness, Riemann-Stieltjes integration, sequences of functions, and series. Prerequisite: Mathematics 371.

380 Junior Seminar                                                                               1 hour

Pass/No credit only. The student will read and evaluate mathematics literature on topics not included in the standard undergraduate curriculum.  By the end of the course, the student will have selected a topic for the senior seminar project.

381 Topics in Mathematics                                                             3 - 4 hours

Various advanced topics, such as topology, complex variables, combinatorics, number theory, coding theory, and modeling are offered when need and sufficient interest are demonstrated. Credit hours and prerequisites are established for each offering. May be taken more than once for credit.

461 Abstract Algebra I                                                                        4 hours

A study of basic algebraic structures: Group theory and ring theory. Prerequisites: Mathematics 217 and 218.

462 Abstract Algebra II                                                                       3 hours

A continuation of 461. Ring theory and field theory. Prerequisite: Mathematics 461.

480 Senior Seminar                                                                             3 hours

The mathematics capstone.  In this course the student will undertake a project that will involve significant independent learning in an area not included in the standard undergraduate mathematics curriculum.  The project will culminate in a paper and a public oral presentation.  

481 Independent Research                                                            1 - 4 hours

498 Internship                                                                                1 - 4 hours

 

Additional Information