Course Information

1500 - Number Concepts
This is a competency based course. Topics include fractions, percentages, signed numbers, linear equations, word problems, graphing linear equations in two variables, integer exponents, and square roots. Grading is A, B, C, NC. Does not count toward a degree. 4 s.h. (syllabus)

1501 - Elementary Algebraic Models
Arithmetic of integers and of rational numbers; linear equations and inequalities in one variable; polynomials, factoring, algebraic fractions, radicals and quadratic equations; linear systems in two variables; graphs. Grading is A, B, C, NC. Does not count toward a degree. Prereq.: Level 1 on Math Placement Test or MATH 1500. 5 s.h. (syllabus)

1502, 1503 - Beginning Algebra 1, 2
Topics include arithmetic of integers and rational numbers, linear equations and inequalities, quadratic equations, factoring, systems of linear equations, word problems and graphing quadratic functions. Grading is A, B, C, NC. Does not count toward a degree. MATH 1502 and MATH 1503 are equivalent to MATH 1501. 3+3 s.h. (syllabus)

1504 - Intermediate Algebra with Trigonometry
Relations and functions with graphing by algebraic techniques; solving nonlinear equations and inequalities. Right triangle trigonometry. Applications of algebraic and geometric concepts. Prereq.: MATH 1501 or Level 2 on the Mathematics Placement Test, and high school geometry. 5 s.h. (syllabus)

1513 - Algebraic and Transcendental Functions
Function concepts including trigonometric, exponential, and logarithmic functions. Application problems and graphing. Supplemental topics. Prereq.: At least Level 4 on the Mathematics Placement Test and high school geometry, or MATH 1504. 5 s.h. (syllabus)

1548, 1549 - College Business Mathematics 1, 2
Solving and graphing equations and inequalities, algebraic operations and functions, matrices and linear systems, linear programming and simplex method, mathematics of finance. Limits, derivatives and integrals with applications. No credit for students who have completed MATH 1570 or 1571. Prereq.: MATH 1501 or at least Level 3 on the Mathematics Placement Test. MATH 1548 for MATH 1549. 3+4 s.h. (syllabus 1548, 1549)

1564, 2665 - Foundations of Middle School Mathematics 1, 2
Conceptual foundations of topics from number theory, operations, functions, algebra, geometry, measurement, probability, and data analysis. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences with manipulatives and computing technology. Prereq.: At least Level 4 on the Mathematics Placement Test or concurrent registration in MATH 1504 for MATH 1564, MATH 1564 for MATH 2665. 4+4 s.h. (syllabus 1564, 2665)

1570, 2670 - Applied Calculus 1, 2
The elements of differential and integral calculus, with emphasis on applications. Analytical geometry, differentiation and integration techniques and series representations. Introduction to differential equations, transform calculus, and Fourier analysis. This is a basic methods course particularly adapted for those who require applied topics in mathematics. It is not applicable toward the Mathematics major. Credit will not be given for both MATH 1549 and 1570. Prereq.: MATH 1513 or at least Level 5 on the Mathematics Placement Test. MATH 1570 for MATH 2670. 4+5 s.h. (syllabus 1570, 2670)

1571, 1572, 2673 - Calculus 1, 2, 3
A sequence of integrated courses in analytic geometry and calculus. A detailed study of limits, derivatives, and integrals of functions of one and several variables with applications. Prereq.: MATH 1571 requires either four high school units of mathematics (including trigonometry) and at least Level 7 on the Mathematics Placement Test, or MATH 1513. MATH 1571 for MATH 1572, MATH 1572 for MATH 2673. 4+4+4 s.h. (syllabus 1571, 1572, 2673)

1580H, 1581H - Biomathematics 1, 2
Counting techniques, probability, matrices and linear systems. A study of functions, differential and integral calculus. Emphasis on the role of mathematical models in explaining and predicting phenomena in life sciences. Credit will not be given for both MATH 1581H and 1572. Prereq.: Admission to NEOUCOM-YSU program for MATH 1580H. MATH 1580H for 1581H. 2+4 s.h. (syllabus 1580H, 1581H)

1585H, 2686H - Calculus 1, 2 Honors
A sequence of honors courses in analytical geometry and calculus which cover essentially the same material as MATH 1571, 1572, 2673, in two semesters instead of three. A detailed study of limits, derivatives, and integrals of functions of one and several variables and their applications. Prereq.: four high school units of mathematics (including trigonometry) and at least Level 9 on the Mathematics Placement Test for MATH 1585H. MATH 1585H for MATH 2686H. This sequence will be offered at most once during each academic year. 5+5 s.h. (syllabus 1585H, 2686H)

1586H, 2687H - Honors Calculus Laboratory 1, 2
Introduction to mathematical modeling of topics covered in calculus. Emphasizes the use of technology such as computer algebra systems, technical document processing, and graphics software for solving problems and reporting solutions. Prereq.: MATH 1571 or concurrent with 1585H for MATH 1586H. MATH 1572 or concurrent with MATH 1586H for MATH 2687H. 1+1 s.h. (syllabus 1586H, 2687H)

2623 - Survey of Mathematics
Mathematics models emphasizing basic ideas in mathematics and statistics, stressing concept formation rather than manipulative skills. Prereq.: MATH 1501 or Level 3 on the Mathematics Placement Test. Credit will not be given for both MATH 2623 and 2625. 3 s.h. (syllabus)

2624 - Probability and Critical Reasoning
Finite probability with supportive material from logic and set language. Connection between critical reasoning in probability and in deterministic settings. Prereq.: MATH 1504 or at least Level 3 on the Mathematics Placement Test. 3 s.h. (syllabus)

2625 - Mathematical Literacy and Critical Reasoning
An introduction to contemporary mathematics and its applications. Topics include basic scientific methods and a variety of practical problems that can be modeled and solved by quantitative means. Prereq.: Math 1501 or at least Level 3 on the Mathematics Placement Test. Credit will not be given for both MATH 2623 and 2625. 4 s.h. (syllabus)

2651, 2652 - Mathematics for Early Childhood Teachers 1, 2
A conceptual development of mathematics topics underlying today’s Pre-K-grade 3 curriculum. Emphasis on multiple approaches, problem solving, and communication of mathematics. Incorporates classroom activities, manipulatives, technology, and activities developmentally appropriate for young children. Prereq.: MATH 1501 or at least Level 3 on the Mathematics Placement Test for 2651, MATH 2651 for MATH 2652. 3+3 s.h. (syllabus 2651, 2652)

Upper-Division Courses

3705 - Differential Equations
Methods and theory of solving differential equations with applications. Existence, uniqueness. First order equations. Higher order linear equations. Introduction to partial differential equations and boundary value problems, including LaPlace’s equation. Prereq.: MATH 2673. 3 s.h. (syllabus)

3715 - Discrete Mathematics
A course in discrete mathematical structures to prepare students for advanced courses. Topics include set theory, functions and relations, logic and quantifiers, truth tables and Boolean expressions, induction and other techniques of proof, and graphs. Credit will not be given for both CSCI 3710 and MATH 3715. Prereq.: MATH 1572. 3 s.h. (syllabus)

3720 - Linear Algebra and Matrix Theory
Matrices; matrix operations; linear transformations; applications. Prereq.: MATH 1572. 3 s.h. (syllabus)

3721 - Abstract Algebra 1
Introduction to abstract algebra investigating fundamental concepts in group and ring theory. Topics include groups, subgroups, cyclic groups, permutation groups, cosets, direct products, homomorphisms, factor groups, rings, integral domains and polynomial rings. Prereq.: MATH 3715 and 3720. 3 s.h. (syllabus)

3750 - History of Mathematics
A survey of the historical development of mathematics. Prereq.: MATH 2673 or 3715. 3 s.h. (syllabus)

3751 - Real Analysis 1
Introduction to the properties of the real number system and metrics and metric properties, with critical analysis of limits, continuity, differentiability, integration, and other fundamental concepts underlying the calculus. Prereq.: MATH 2673 and 3715. 3 s.h. (syllabus)

3760 - Numerical Analysis 1
The theory and techniques of numerical computation. The solution of a single equation, interpolation methods, numerical differentiation and integration, direct methods for solving linear systems. Prereq.: MATH 3720 and CSIS 2610. 3 s.h. (syllabus)

3767, 3768 - Algebra/Geometry for Middle School Teachers
An integrated, conceptual, and functioncentered approach to the foundations of algebra, geometry, and trigonometry for preservice middle childhood mathematics specialists. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences. Not applicable to the mathematics major. Prereq.: MATH 2665 for MATH 3767 and MATH 3767 for MATH 3768. 4+4 s.h. (syllabus 3767, 3768)

3785 - Numerical Methods
Matrices, matrix operations, and the application of numerical methods. Not applicable to the Mathematics major. Prereq.: MATH 2670 and STECH 1505, or equivalent. 3 s.h. (syllabus)

3795 - Topics in Mathematics
The study of a mathematical topic or the development of a special area of mathematics. May be repeated once. Prereq.: MATH 1549 or 1570 or 1571 or 2623 or 2651. 2-3 s.h. (syllabus)

4830 - Foundations of Geometry
The development of Euclidean and non-Euclidean geometries from postulate systems. Prereq.: MATH 3715. 3 s.h. (syllabus)

4869 - Functions, Calculus, and Applications for Middle School Teachers
Polynomial and exponential functions, limits, derivatives, integrals, and applications. Interpretation of slope and area in graphs of functions from applied settings. Applications of limits to the derivations of geometric formulas. Relations between tables, graphs, and the symbolic representation of functions. Prereq.: MATH 3768 or consent of instructor. 3 s.h. (syllabus)

4870 - Mathematics Seminar for Middle School Teachers
Approaches to and practice with problem solving from a broad spectrum of mathematics. Equal emphasis on problems suitable for contests in the seventh or eighth grade (such as the American Mathematics Competition 8 and MathCounts) and at the level of the Praxis II examination for Middle School Mathematics. May be repeated 2 times. Prereq.: MATH 2624 or STAT 2601 and either MATH 4869 or concurrent with MATH 4869.2 s.h. (syllabus)

4893 - Mathematics Internship
A program of work and study in the public or private sector centered upon the development of a significant mathematics project, under the direction of University faculty member(s) and designated member(s) of the participating agency. This course can be substituted for MATH 4896 to fulfill the major requirements with approval from the department chairperson. See department for more details. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751 and consent of the department chairperson. May be repeated twice. 2 s.h. (syllabus)

4896 - Senior Undergraduate Research Project
Individualized study of a topic in mathematics culminating in a written report and an oral presentation at a national or regional meeting or a local seminar. May be repeated once. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751 and permission of the department chairperson. 2 s.h. (syllabus)

4897H - Thesis
Individualized study of a topic in mathematics culminating in a written report and an oral presentation at a national or regional meeting or a local seminar. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including both MATH 3721 and 3751 and permission of the department chairperson. 2 s.h. (syllabus)

5821 - Topics in Abstract Algebra
A course in abstract algebra aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3721 and 5821. Prereq.: MATH 3715 and 3720. 3 s.h. (syllabus)

5822 - Abstract Algebra 2
A continuation of MATH 3721 with special emphasis of fields. Additional topics in pure or applied algebra. Prereq.: MATH 3721 or equivalent. 3 s.h. (syllabus)

5825 - Advanced Linear Algebra
A study of abstract vector spaces, linear transformations, duality, canonical forms, the spectral theorem, and inner product spaces. Prereq.: MATH 3721. 3 s.h. (syllabus)

5828 - Number Theory
A study of congruences, Diophantine equations, quadratic residues, special number theory functions, and selected applications. Prereq.: MATH 3721. 3 s.h. (syllabus)

5832 - Euclidian Transformations
General properties of functions and transformations; isometries and transformations of the Euclidian plane; the complex plane, its geometry and subfields; transformational, analytical, and vector approaches to Euclidian geometry; connections to other branches of mathematics and applications. Prereq.: MATH 3720 and 4830. 3 s.h. (syllabus)

5835 - Introduction to Combinatorics and Graph Theory
The pigeonhole principle; permutations, combinations, the binomial theorem; the inclusionexclusion principle; recurrence relations; graphs and digraphs, paths and cycles, trees, bipartite graphs and matchings. Prereq.: MATH 3715 and 3720. 3 s.h. (syllabus)

5843 - Theory of Probability
The mathematical foundation of probability theory including the study of discrete and continuous distributions. Other topics selected from limit theorems, generating functions, applications. Credit will not be given for MATH 5843 and STAT 5843. Prereq.: STAT 3743 and MATH 2673. 3 s.h. (syllabus)

5844 - Theory of Statistics
The mathematical theory of statistical inferences including likelihood principle, sufficient statistics, theory of statistical estimation, hypothesis testing and related topics. Credit will not be given for MATH 5844 and STAT 5844. Prereq.: MATH 5843. 3 s.h. (syllabus)

5845 - Operations Research
An introduction to operations research with emphasis on mathematical methods. Topics may include: linear programming, sensitivity analysis, duality theory, transportation problems, assignment problems, transhipment problems, and network problems. Prereq.: MATH 3715 and 3720. 3 s.h. (syllabus)

5851 - Topics in Analysis
A course in analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3751 and 5851. Prereq.: MATH 2673, 3720, and 3715. 3 s.h. (syllabus)

5852 - Real Analysis 2
Uniform convergence of sequences of functions and some consequences; functions on n-space: derivatives in vector spaces, mean value theorem, Taylor’s formula, inverse mapping theorem, implicit mapping theorem. Prereq.: MATH 3720 and 3751 or equivalent. 3 s.h. (syllabus)

5855 - Ordinary Differential Equations
A second course in differential equations with emphasis on nonlinear problems and qualitative methods or on boundary value problems. Topics are chose from: proofs of fundamental theorems, phase plane analysis, limit cycles and the Poincare-Bendixon theorem, biological models, stability via Liapunov functions, asymptotic methods, and boundary value problems. Prereq.: MATH 3705 and 3721. 3 s.h. (syllabus)

5860 - Topics in Numerical Analysis
A course in numerical analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3760 and 4860. Prereq.: MATH 3720 and CSIS 2610. 3 s.h. (syllabus)

5861 - Numerical Analysis 2
Numerical methods of initial-value problems, eigenvalue problems, iterative methods for linear and nonlinear systems of equations, and methods involving least squares, orthogonal polynomials, and fast Fourier transforms. Prereq.; MATH 2673 and 3760 or equivalent. 3 s.h. (syllabus)

5875 - Complex Variables
Complex numbers and their geometric representation, analytic functions of a complex variable, contour integration, Taylor and Laurent series, residues and poles, conformal mapping. Prereq.: MATH 3751 or equivalent. 3 s.h. (syllabus)

5880 - Introduction to Topology
An introduction to the basic concepts of general topology: compactness, connectedness, and continuity in topological spaces. Prereq.: MATH 3721 and 3751. 3 s.h. 5884. Mathematical Logic. An introduction to the study of theories in formalized languages and to the theory of models. Prereq.: MATH 3721 or PHIL 3719. 3 s.h. (syllabus)

5895 - Selected Topics in Mathematics
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751. 2-3 s.h.