MATHEMATICS (MATH)
MATH 100 - DEVELOPMENTAL MATHEMATICS
Prerequisite: None
Developmental Mathematics is designed to prepare students for courses which have basic algebra and geometry prerequisites. The course reviews arithmetic, basic algebraic operations, and basic geometry and provides the mathematical experience necessary for success in courses such as Math 110, Math 108 and Math 217. The course does not satisfy any mathematics or science requirement for graduation and is not open to students who have received a grade of C or higher in any other mathematics course at Ashland University. The course is graded S/U and, if a student earns a U, they must repeat the course.
Credit: 3
MATH 108 - INTRODUCTORY STATISTICS
Prerequisite: Math ACT score of 18 or math SAT score of 480 or MATH 100
An introductory course designed to meet the needs of students in biology, business, economics, education, nursing, psychology, and sociology. Sample and theoretical frequency distributions, data dispersion and central tendency, estimation, hypothesis testing, correlation, and analysis of variance are topics studied. Meets Core credit for math/logic.
Credit: 3
MATH 110 - FINITE MATHEMATICS
Prerequisite: Two years of high school algebra or MATH 100
Covers some topics of modern mathematics including principles of counting, probability, matrices, linear programming, and mathematics of finance with applications to biology, business, economics, and other social sciences. Meets Core credit for math/logic.
Credit: 3
MATH 111 - PRECALCULUS
Prerequisite: Two years of high school algebra
A study of functions, functional notation, trigonometric functions, logarithmic and exponential functions. Preparation for calculus.
Credit: 3
MATH 201 - APPLIED CALCULUS I
Prerequisite: Two years of high school algebra; one year of high school geometry;
This is the first course in the Calculus with Applications sequence for non-mathematics majors. Functions, limits, derivatives and techniques of differentiation with applications to natural, social and management sciences are studied. Meets Core credit for math/logic.
Credit: 3
MATH 202 - APPLIED CALCULUS II
Prerequisite: MATH 201
A continuation of Math 201. Techniques of integration and multivariate calculus with applications to natural, social and management sciences are studied.
Credit: 3
MATH 205 - CALCULUS I
Prerequisite: MATH 111 or equivalent
This is the first course in the Calculus sequence for science and math majors. The focus is on theory and techniques for limits, derivatives, antiderivatives and definite integrals, and their applications. Meets Core credit for math/logic.
Credit: 5
MATH 206 - CALCULUS II
Prerequisite: MATH 205
This is the second course in the Calculus sequence for science and math majors. The focus is on transcendental functions and their applications, techniques of integration, indeterminate forms and improper integrals, and an introduction to infinite sequences and series.
Credit: 5
MATH 217 - THEORY OF ARITHMETIC AND GEOMETRY
Prerequisite: Math ACT score of 18, Math SAT score of 480, or MATH 100
A study of the mathematical theories and concepts underlying intermediate arithmetic and geometry. Topics include number theory, number systems, elementary probability, geometry, estimation, mathematical reasoning, problem solving, and communication. The course will emphasize the use of group work and manipulatives. Meets Core credit for math/logic.
Credit: 3
MATH 218 - GEOMETRY FOR MIDDLE GRADES TEACHERS
Prerequisite: MATH 217
A study of mathematical concepts and procedures for teaching in the middle schools. Topics include knowledge of the NCTM Standards, 3- dimensional geometry, axiomatic systems, experimental probability, algebra, algorithmic techniques, and technology. Emphasis on group work and manipulatives.
Credit: 3
MATH 223 - DISCRETE MATHEMATICS I
Prerequisite: Three years high school college prep math
An introduction to set theory, logic, relations, functions, sequences, algorithms, number theory, and combinatorics. Meets Core credit for math/logic.
Credit: 3
MATH 224 - DISCRETE MATHEMATICS II
Prerequisite: MATH 223
A continuation of Math 223. A further exploration of foundational discrete structures and their applications to computer science. Topics include recurrence relations, graph theory, tree structures, and network models.
Credit: 3
MATH 230 - MATHEMATICAL MODELING
Prerequisite: MATH 206, MATH 223
This course is an introduction to the elements of mathematical modeling. It presents application-driven mathematical methods motivated by problems from within and outside of mathematics, exemplifies the usefulness of mathematics in problem solving, and demonstrates the connections among different mathematical topics.
Credit: 3
MATH 250 - MATHEMATICAL PROOF
Prerequisite: MATH 223
An introduction to the elements of mathematical proofs. Various forms and techniques of writing mathematical proofs are covered.
Credit: 1
MATH 305 - CALCULUS III
Prerequisite: MATH 206
A study of infinite series, power series, solid analytical geometry, and multivariate calculus.
Credit: 4
MATH 307 - LINEAR ALGEBRA
Prerequisite: MATH 202, MATH 206 or MATH 224
A study of vector spaces, linear transformations, determinants, and matrices.
Credit: 3
MATH 308 - OPERATIONS RESEARCH
Prerequisite: MATH 224 or MATH 230
An introduction to the theory and computer assisted solution of problems in operations research, such as Markov chains, replacement models, inventory models, queuing theory, linear programming, and transportation models.
Credit: 3
MATH 309 - HISTORY OF MATHEMATICS
Prerequisite: MATH 206 OR 202, and MATH 223
A survey of the historical development of mathematics through the calculus, together with problems appropriate to the topics and period being studied.
Credit: 3
MATH 311 - MODERN GEOMETRY
Prerequisite: MATH 206, MATH 223, MATH 250
A study of fundamental geometric properties such as straightness, symmetry, congruency, and parallelism as they exist in planes and other surfaces.
Credit: 3
MATH 313 - DIFFERENTIAL EQUATIONS
Prerequisite: MATH 305
An introductory course in elementary differential equations with applications to geometry, chemistry, physics, and the life and social sciences. Some topics include exactness, Bernoulli's equations, differential operators, and Laplace transform.
Credit: 3
MATH 317 - PROBABILITY
Prerequisite: MATH 223, MATH 250; MATH 202 or MATH 206
A study of the fundamental concepts of probability theory, discrete and continuous probability functions, independence, conditional probability, Bayes' theorem, joint densities, and mathematical expectations.
Credit: 3
MATH 318 - MATHEMATICAL STATISTICS
Prerequisite: MATH 250, MATH 305, and MATH 317
Introduction to the theory and applications of mathematical statistics, moment generating functions, central limit theorem, estimation, and hypothesis testing.
Credit: 3
MATH 319 - NUMBER THEORY
Prerequisite: MATH 206, MATH 223, and MATH 250; CS 121 recommended
An introductory course in the fundamentals of number theory. Emphasis on proof techniques, Euclidean algorithm, primes, congruencies, continued fractions, and Euler Phi function, with applications to computer science, cryptography, and mathematics education.
Credit: 3
MATH 320 - FINANCIAL MATHEMATICS
Prerequisite: MATH 223, MATH 305
Introduction to the fundamental concepts of financial mathematics, and how these concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. The course content is based on the syllabus for the Society of Actuaries (SOA) professional Exam FM - Financial Mathematics.
Credit: 3
MATH 341 - APPLIED REGRESSION ANALYSIS
Prerequisite: MATH 108 or MATH 318
The student will learn to execute three major steps in the data analysis process: to identify the appropriate statistical technique for a given research problem; to conduct analyses (one-sample, dependent-samples, and independent-samples t tests, one-way ANOVA, two-way ANOVA, simple regression and correlation, multiple regression, chi-square tests, discriminant analysis, factor analysis, and multivariate analyses) using statistical software (such as SPSS or R); and to interpret the statistical values generated by these various analytical tools.
Credit: 3
MATH 415 - ABSTRACT ALGEBRA
Prerequisite: MATH 223, MATH 250, and MATH 307
An introduction to abstract algebraic systems through the study of groups, rings, and fields.
Credit: 3
MATH 417 - REAL ANALYSIS
Prerequisite: MATH 250 and MATH 305
The real number system, indeterminate forms, partial differentiation, infinite series, and multiple and improper integrals are treated more rigorously than in the elementary calculus course.
Credit: 3
MATH 450 - SEMINAR
Prerequisite: Junior or Senior math/integrated math/actuarial science minors and majors
Various topics in mathematics will be investigated. Content will vary depending upon the interests and needs of the students. Students, invited speakers, and faculty will present topics. May be repeated for a total of 4 hours.
Credit: 1
MATH 470 - SPECIAL TOPICS IN MATHEMATICS
Prerequisite: MATH 305 or MATH 307
A course devoted to various topics of mathematical interest. May be repeated for credit as topics change.
Credit: 1-3
The following graduate-level mathematics courses are intended for high school teachers seeking the credentials necessary in order to teach introductory college-level mathematics courses at their schools as part of their College Credit Plus program.
MATH 610 - COMPLEX ANALYSIS
Prerequisite: An undergraduate course in Real Analysis
Complex variables; elementary functions, differentiation and analytic functions; integration and Cauchy’s theorem; power series and Laurent series; residue theorem; applications such as conformal mappings, inversion of integral transform.
Credit: 3
MATH 620 - ABSTRACT ALGEBRA
Prerequisite: An undergraduate course in Modern/Abstract Algebra
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory.
Credit: 3
MATH 630 - NUMBER THEORY
Prerequisite: None
Euclidean algorithm, unique factorization theorem, congruencies, primitive roots, indices, quadratic residues, number-theoretic functions, Gaussian integers and continued fractions.
Credit: 3
MATH 640 - SPECIAL TOPICS
Prerequisite: None
The faculty member proposing the course must complete all the data for this course syllabus. Successful courses will be reviewed by the Graduate Education Department for permanent status.
Credit: 1-3
MATH 650 - COMBINATORICS
Prerequisite: None
An introduction to the basics of enumerative combinatorics: counting methods such as generating functions, recurrence relations, and the inclusion-exclusion formula.
Credit: 3
MATH 660 - NUMERICAL ANALYSIS
Prerequisite: None
Numerical methods for solving systems of linear equations and nonlinear equations. Polynomial and spline interpolation techniques, and numerical approximation of derivatives and integrals. Approximate solutions of ordinary differential equations.
Credit: 3
MATH 670 - STATISTICAL METHODS
Prerequisite: An undergraduate course in Introductory Statistics
Steps in the data analysis process: how to identify the appropriate statistical technique for a given research problem; how to conduct analysis using software; and how to interpret the statistical values generated by various analytical tools.
Credit: 3