MTH - Mathematics Course Descriptions
Is an introduction to various topics in mathematics designed to teach critical thinking and to impart a general knowledge and appreciation of mathematics. Topics will be selected from logic, geometry, linear and exponential growth, personal finance, discrete mathematics, probability, statistics, and social choice theory.
includes such topics as an introduction to problem solving, set theory, functions, logic, numeration systems, and other number bases, and an overview of the real number system with its subsystems and related properties. Historical development and mathematical connections are stressed. The course is only for majors pursuing early and middle childhood, intervention specialist, and adolescent to young adult licensure, other than mathematics.
Provides application of real and complex numbers, algebraic thinking, Cartesian coordinate system, computing interest, probability and multistage experiments, statistics, and geometry, utilizing graphic calculators, and stressing the historical. This course is only for majors pursuing early and middle childhood or intervention specialist licensure.
includes a comprehensive overview to problem solving strategies, introductory logic, algebraic relationships, mathematical applications, complex numbers, data analysis and probability, plane and coordinate geometry, trigonometry, and functions (linear, exponential, trigonometric, logarithmic, etc.) using various technology, such as Excel, Desmos, and Geogebra. Content is aligned to the National Council of Teachers of Mathematics (NCTM) standards and the competencies examined on the Ohio Middle Childhood and Adolescent to Young Adult (AYA) mathematics licensure exams. The course is limited to candidates seeking licensure in adolescent to young adult in integrated mathematics and middle childhood mathematics.
Is an introduction to mathematical topics and applications required by many college-level major programs. The material covered includes equations, inequalities, systems of linear equations and matrices, linear programming, mathematics of finance and probability.
1 year of high school algebra
A one-semester business calculus course whose topics include functions, limits, differentiation and applications of the derivative, and integration and applications of the integral focusing on business.
2 years of high school algebra
Covers properties of functions, including power, exponential, logarithmic, and trigonometric functions and identities in preparation for calculus.
2 years of high school mathematics including algebra and plane geometry
A differential calculus course, studying the definition, calculations, and applications of the derivative and related topics, including limits and continuity. Also introduces the definite integral and its calculation and properties.
Notes
Additional course fee.
Three years of high school mathematics including two years of algebra or
MTH 160
An integral calculus course, studying a variety of methods of integration and applications, including areas, arc lengths, volumes of revolution, differential equations, parametric equations, polar functions, and Taylor series.
Notes
Additional course fee.
Studies systems of linear equations and develops the theory of matrix algebra motivated by solving systems of equations that arise in a wide range of applications in various areas, including computer science, data science, machine learning, and chemistry.
MTH 161 or permission of instructor
Studies determinants, vectors, linear transformations on Euclidean spaces, eigenvalues and eigenvectors, and applications to selected topics from computer science, data science, machine learning, and chemistry.
is based on the principle that a scientific study requires the measurement and description of phenomena in an objective, systematic manner. This course introduces the student to the fundamental statistical techniques used in the behavioral sciences and other areas of research. These methods include sampling techniques , measures of central tendency, variability, probability, and inferential testing(e.g., t-tests, correlation, confidence intervals).
Notes
for Mathematics majors, this course does not count as one of their needed upper-level electives.
Two years of high school mathematics including high school algebra, or MTH 155
Begins with a close study of portions of Euclid's Elements, including complete coverage of the first book. The historical impact of his axiomatic approach and its ultimate refinement in Hilbert's axioms will be explored. This course will cover some of the history of the attempts to prove the Parallel Postulate, leading up to the discovery of non-Euclidian geometries in the 19th century. The two main models of non-Euclidean geometries (elliptic and hyperbolic) will be described and some of their properties investigated. Finally, the history of geometry since the discovery of non-Euclidean geometries (e.g. Kline's Erlanger Program) will be briefly covered.
One year of high school geometry or MTH 134
Surveys proof techniques, recursion, induction, modeling, and algorithmic thinking. Other topics covered include set theory, discrete number systems, combinatorics, graph theory, Boolean algebra, and a variety of applications. There is an emphasis on oral and written communication of mathematical ideas, cooperative learning, and the proofs of mathematical conjectures.
Considers solid analytic geometry, vectors, partial differentiation, and multiple integration. Discusses the main theorems of vector calculus.
Notes
Additional course fee.
Presents ordinary differential equations and their applications with an emphasis on techniques of solution including numerical methods.
Examines the mathematics behind two fascinating and inter-related topics, fractals and chaos. Chaos and fractals are components of dynamics, a subject that studies how systems change over time. Through computer experimentation and simulations, students will experience how new mathematics is developed. Topics covered include fractals: feedback and the iterator; classical fractals and self-similarity; length, area, and dimension; fractals with a random component; recursive structures including L-systems; attractors; deterministic chaos; fixed points, stable and unstable; and the period-doubling route to chaos.
Develops the structural concepts that characterize abstract algebra. Topics in this course will be selected from the following: elementary number theory, groups, rings, integral domain, fields, and vector spaces. There is an emphasis on the oral and written communication of mathematical ideas. Students will frequently work in groups on special projects.
Covers both the theory and applications of linear programming, one of the leading methods for large-scale optimization. The simplex method will be studied in detail. Applications include product mix, diet, transportation, and network flow problems. Integer programming will be touched on briefly. Computer tools such as spreadsheet solvers will be introduced and used.
Data science is an interdisciplinary field which blends mathematics, computer science, and various domain-specific fields (such as bioinformatics). The goal is to extract usable information from large sets of data. This course will be an introduction to data science using R, Python or a similar language. Emphasis will be on exploratory data analysis, visualization, model fitting, classification, and prediction.
Computer
Science
Elective
Covers the theory and use of graphs to model relationships between conceptual objects. Topics covered include graph representations, trees, digraphs, and networks, which will delve into the concepts of adjacency matrices, Dijkstra’s algorithm, and spanning trees. Graph coloring and min/max network flow may also be covered.
This courses provides an introduction into the historical and philosophical development of mathematics with particular emphasis on the development of Arithmetic, Algebra, Geometry, and Calculus. Topics and contributions from varied groups and cultures across the world are included. Students will be required to communicate about mathematics and perform non-trivial calculations, using historical techniques appropriate to the level of the prerequisites for this course.
Covers the fundamental algorithms used in both symmetric key and public key cryptography. Algorithms include AES, Diffie-Hellman, RSA, elliptic curve cryptography, as well as cryptographical hash algorithms. Both mathematical foundations and computer implementations will be discussed during the course.
Is a course in finite dimensional vector spaces and linear transformations, including inner product spaces, determinants, eigenvalues, and eigenvectors.
Is designed to teach mathematical science majors the skills necessary to learn mathematics on their own and communicate their knowledge to others in oral and written form. All students will attend presentations made by senior mathematics students. Students will be required to write a short, independently-researched paper and present it to the other students in the junior seminar.
Junior status or permission of instructor
Provides the student with the opportunity to pursue a research project. Students will work on an original mathematics research project by finding and reading background material on a topic and then work to find new results on this topic with the guidance of mathematics faculty.
Notes
This course may be repeated, but only up to 3 credits count towards mathematics major and minor requirements of upper-division electives.
Covers the topics of vector field theory, Fourier series, and partial differential equations.
is a work experience opportunity with the purpose of expanding education by applying accumulated knowledge in mathematical science. The availability of internships is limited to upper-level students, normally seniors with a 2.5 quality point average. Students are approved individually by the academic department. A contract can be obtained from the Career Services Office in Starvaggi Hall. Internships count as general electives.
Mathematical science junior or senior standing and permission of the department chair. Internships must be pre-approved.
Introduces a statistical basis for decision making to the student of applied science in this modern tool of analysis. This will be accomplished by studies in probability theory for both discrete and continuous sample spaces and in an introduction to statistical inference.
Is a continuation of MTH 401, covering additional concepts and techniques of statistics with an emphasis on problem-solving approaches.
Liberates the mathematician from the restrictions imposed by the domain of real numbers when the broader field of complex numbers is made available. Beginning with a study of complex numbers, this course introduces the algebra and the calculus of elementary functions.
Gives a theoretical presentation of the real numbers, sequences, and their limits, including lim sup and lim inf; continuity; sequences of functions and pointwise and uniform convergence; and the (point set) topology of the reals.
Provides students with an intuitive and working understanding of numerical methods of problem solving, an appreciation of the concept of error and the need to control it, and the ability to implement numerical methods using a computer. Topics include: approximation of functions, interpolation, error analysis, numerical integration and differentiation, numerical linear algebra, and numerical solutions to differential equations.
Requires all mathematical science students to write a thesis on an approved mathematical topic. Students must consult closely with a departmental faculty member at each stage in the development of their theses.