MATHEMATICS

Virginia M. Buchanan (1987), Chair, Professor of Mathematics
B.S., Delta State University;
M.S., Ph.D., University of Mississippi
Academic Interests: history of mathematics, topology, real analysis

Catherine Erbes (2014), Assistant Professor of Mathematics
B.A., Carleton College;
M.A., Indiana University;
Ph.D., University of Colorado Denver
Academic Interest: graph theory

Dawn-Marie Trehan (2016), Visiting Assistant Professor of Mathematics
B.A., Hiram College;
M.S., The University of Akron;
M.S., Case Western Reserve University
Ph.D., Kent State University
Academic Interest: statistics education, adult learning

Department Web address:

http://www.hiram.edu/mathematics/

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.

Requirements for the Major

Mathematics Pathway

A student majoring in mathematics must complete the following requirements:

Three semesters of calculus or equivalent:

o   MATH 19800 Calculus I
o   MATH 19900 Calculus II
o   MATH 20000 Calculus III

MATH 21700 Discrete Mathematics
MATH 21800 Linear Algebra
MATH 2xxxx Applied Data Analysis or department approved substitute
MATH 37100 Analysis I
MATH 46100 Abstract Algebra I

One of the following two-course upper-level sequences:

o   MATH 30100/30200 Non-Euclidean and Advanced Euclidean Geometries
o   MATH 37100/37200 Analysis I & II
o   MATH 46100/46200) Abstract Algebra I & II

MATH 38500 Junior Seminar
MATH 48000 Senior Seminar
Two additional mathematics courses, one numbered above 20000 and one numbered above 30000
A Correlative Experience chosen by the student in consultation with an advisor in the mathematics department
A Mathematics Portfolio

The Senior Seminar course (MATH 48000) is the mathematics capstone. In this course a student works independently on a substantial mathematics project that involves techniques and concepts beyond the typical content of a single course. The project culminates in a paper and a public oral presentation.

Requirements for the Minor

A student minoring in mathematics must complete the following courses:

MATH 19800
MATH 19900
Two mathematics courses numbered 20000 or above
Three additional mathematics courses numbered 30000 or above

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.

COURSE DESCRIPTIONS

MATH 10100: BASIC MATHEMATICS I 3 hour(s)

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

MATH 10200: BASIC MATHEMATICS II 3 hour(s)

A continuation of 101/10100. Solving equations, problem solving, geometric and graphical properties of functions, systems of equations with applications. (For PGS students only.) Prerequisite: MATH 10100 or placement

MATH 10300: FUNDAMENTALS OF MATHEMATICS I 4 hour(s)

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

MATH 10400: FUNDAMENTALS OF MATHEMATICS II:MM 4 hour(s)

A continuation of 103/10300.Topics include geometry (planar and 3 dimensional figures; transformation, symmetries, and tilings; and congruence and similarity), measurement (length, area, perimeter, volume, surface area), and statistics, probability and data analysis. Students will learn to apply manipulatives, and the technology of both calculators and geometry and statistical software. Students will continue to become familiar with the National Council of Teachers of Mathematics (NCTM) resource Principles and Standards for School Mathematics and the Common Core State Standards. This course satisfies the Modeling Methods core requirement. For early childhood and middle childhood education majors only.

MATH 10800: STATISTICS:MM 4 hour(s)

An introduction to the art and science of obtaining meaning from data. The emphasis is on conceptual understanding and developing statistical thinking, rather than on mere calculation and procedures. Topics include experiments and observational studies, data displays and data summaries, correlation and linear regression, randomization, the normal model, sampling distributions, confidence intervals, and testing hypotheses. Technology is used as an aid in developing concepts and analyzing data. Some sections of this course may be considered service learning (SL).

MATH 11000: COMPUTATIONS FOR NURSING 2 hour(s)

This course provides the students with essential knowledge for the preparation and administration of medications in the clinical setting, including introduction to drug measures, syringe calibrations and dosage calculations as well as intravenous therapy calculations. Also addressed are calculations for pediatrics and older adults. This is a required course for students in the BSN program. For nursing majors only. Prerequisite: NURS (210 or 21000).

MATH 13200: METHODS OF DECISION MAKING:MM 3 hour(s)

An introduction to the field of decision theory. Contemporary mathematical thinking is used to model problems in modern society. Topics may include applications of graph theory, scheduling, voting and apportionment, game theory, and linear programming. This course fulfills the Modeling Methods requirement. Prerequisite: Mathematics Placement Test

MATH 16200: MATHEMATICAL MODELING IN THE LIBERAL ARTS:MM 4 hour(s)

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. This course fulfills the Modeling Methods requirement. Prerequisite: placement

MATH 18000: WORKSHOP 1 hour(s)

This workshop provides the opportunity for students to examine a special topic in mathematics. Through readings, discussions and written assignments there will be opportunities to evaluate the topic at issue. Workshops may be taken Pass/No Credit only. Students may take no more than nine workshops for credit toward graduation. Workshops can be used as elective credit only. Pass/No Credit only. (For PGS students only.)

MATH 19700: PRECALCULUS 4 hour(s)

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. Prerequisite: Mathematics Placement Test

MATH 19800: CALCULUS I:MM 4 hour(s)

The differential calculus. Topics include limits, continuity, differentiation of algebraic and transcendental functions, maxima/minima and other applications of the derivative. This course fulfills the Modeling Methods requirement. Prerequisite: Mathematics (197 or 19700) or Mathematics Placement Test

MATH 19900: CALCULUS II:MM 4 hour(s)

A continuation of 198/19800. The integral calculus.Topics include antidifferentiation, the Riemann integral, the Fundamental Theorem of Calculus, applications of the definite integral, techniques of integration, sequences, and infinite series. This course fulfills the Modeling Methods requirement. Prerequisite: MATH (198 or 19800) or permission.

MATH 20000: CALCULUS III:MM 4 hour(s)

A continuation of 199/19900. Infinite series, multivariable and vector calculus. Topics include parametrizations, polar coordinates, partial derivatives, directional derivatives, multiple integrals. A computer algebra system is used throughout the course. This course fulfills the Modeling Methods requirement. Prerequisite: MATH (199 or 19900).

MATH 21000: PROBLEM SOLVING IN MATHEMATICS 1 hour(s)

Methods, strategies and skills to solve a large variety of mathematical problems will be studied. Topics such as mathematical induction, indirect reasoning, and symmetry will be developed as needed. Pass/No Credit Only.

MATH 21700: DISCRETE MATHEMATICS 3 hour(s)

An introduction to proofs and mathematical reasoning in the context of discrete mathematical structures.Topics include proof techniques, mathematical logic, elementary number theory, set theory, relations, and elementary function theory. Prerequisite: Mathematics Placement Test

MATH 21800: LINEAR ALGEBRA:MM 3 hour(s)

Systems of linear equations, matrix algebra and determinants, vector spaces, eigenvalues, eigenvectors, and linear transformations are studied. This course fulfills the Modeling Methods requirement. Prerequisite: Mathematics Placement Test

MATH 24300: DIFFERENTIAL EQUATIONS:MM 3 hour(s)

A study of the theory, solution, and application of ordinary differential equations. Existence and uniqueness theorems. Solutions of several types of first-order equations. Solution of homogeneous and non-homogeneous higher-order linear equations; Laplace transform methods. Applications for first and second order equations. Prerequisite: MATH (200 or 20000). This course fulfills the Modeling Methods requirement.

MATH 28000: SEMINAR 1 - 4 hour(s)

MATH 28100: INDEPENDENT STUDY 1 - 4 hour(s)

MATH 29800: FIELD EXPERIENCE 1 - 4 hour(s)

MATH 30100: MODERN GEOMETRIES 4 hour(s)

This course surveys selected topics in Euclidean, non-Euclidean, finite, and projective geometries, together with the historical development of these geometries. Prerequisite: MATH (217or 21700).

MATH 30200: ADVANCED EUCLIDEAN GEOMETRY 4 hour(s)

This course presents an advanced study of Euclidean geometry, with a focus on developments since the eighteenth century. Topics include Ceva's Theorem, Menelaus' Theorem, the Euler line, the Nine-Point Circle, Morley’s Theorem, and the Simson line. Dynamic geometry software is used throughout the course. Prerequisite: MATH (217or 21700).

MATH 30800: MATHEMATICAL STATISTICS I 4 hour(s)

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. Prerequisite: MATH (200 or 20000).

MATH 30900: MATHEMATICAL STATISTICS II 3 hour(s)

A continuation of 308/30800 focusing on inferential statistics. Topics include interval and point estimation, tests of statistical hypotheses, and regression analysis. Prerequisite: MATH (308 or 30800).

MATH 33000: HISTORY OF MATHEMATICS:EW 4 hour(s)

This course examines the historical development of major mathematical concepts, focusing on the period through the invention of the calculus in the late seventeenth century. Both European and non-European mathematical developments are explored. This course fulfills the EW requirement. Prerequisite: MATH (199 or 19900) or MATH (217 or 21700).

MATH 37100: ANALYSIS I 4 hour(s)

Real analysis, often called the theory of calculus, is a core course in the mathematics curriculum. Most of the topics will be familiar from the study of elementary calculus; however, theory and deeper understanding will be stressed. Topics include sequences, limits, continuity, and differentiation. Prerequisites: MATH (200 or 20000) and MATH (217 or 21700).

MATH 37200: ANALYSIS II 3 hour(s)

A continuation of MATH 371/37100. Topics include integration, sequences of functions, and series. Prerequisite: MATH (371or 37100).

MATH 38000: Seminar 1 - 4 hour(s)

MATH 38100: TOPICS IN MATHEMATICS 1 - 4 hour(s)

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

MATH 38500: JUNIOR SEMINAR 1 hour(s)

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 capstone project and will have begun research on that topic. (Formerly offered as MATH 38000)

MATH 46100: ABSTRACT ALGEBRA I 4 hour(s)

Abstract algebra is a core course in the mathematics curriculum because of its focus on the basic underlying structures that occur in many mathematical systems. The basic structures of study in this course are groups and rings. Prerequisites: Mathematics (217 or 21700).

MATH 46200: ABSTRACT ALGEBRA II 3 hour(s)

A continuation of 461/46100. The basic structures of study in this course are rings and fields. Prerequisite: MATH (461 or 46100).

MATH 48000: SENIOR SEMINAR 3 hour(s)

The mathematics capstone. In this course a student works independently on a substantial mathematics project that involves techniques and concepts beyond the typical content of a single course. The project culminates in a paper and a public oral presentation. Prerequisite: MATH (385 or 38500).

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