Dual Credit Mathematics Instruction Certificate

Program Overview

Dual Credit Mathematics Instruction Certificate

Elevate your impact.

The Dual Credit Mathematics Instruction Certificate offers an opportunity for secondary education instructors to strengthen their mathematical background and build skills to be effective dual-credit mathematics instructors.

Format

This is an online certificate consisting of 5 full-semester courses. The Department of Mathematical Sciences offers at least one course each fall, spring and summer (full summer). The typical course rotation is as follows:

• Math 510 - Summers (even numbered years)
• Math 520 - Summers (odd numbered years)
• Math 530 - Fall semester (odd numbered years)
• Math 540 - Spring semester
• Math 550 - Fall semester (even numbered years)
• Math 580 - On demand

Program Requirements & Course Descriptions

This 18-hour certificate includes 5 courses. Students are expected to have experience with single variable and multivariable calculus (including limits, derivatives, and integration techniques), linear algebra, an introductory level proof-writing course, as well as an introductory statistics course.

Required courses

Math 510 – Applied Statistical Analysis (3 credit hours)

This course covers design of experiments, analyzing data, and developing statistical hypotheses to answer research questions in the student’s discipline. Topics include estimation and hypothesis testing, analysis of variance and covariance, simple and multiple regression techniques, logistic regression, count data analysis, and nonparametric methods. Students develop experimental designs to collect appropriate data, and a modeling protocol so research questions can be answered. This course is meant to provide a broad overview of various statistical designs to enable students to analyze data using statistical methods developed in the course. The course emphasizes the link between statistical graphics and formal statistical tests and involves the use of Excel and or R: a statistical programming language. Homework and labs focus on interesting topics that can be adapted for a high school AP statistics course.

Math 520 – Number Theory (3 credit hours)

Number theory is the study of properties and relationships of numbers, especially the positive integers. Topics in elementary number theory include divisibility properties of integers, properties of primes, congruences, quadratic reciprocity, and integer solutions to basic equations (e.g. Diophantine equations). Even though number theory is one of the oldest disciplines in mathematics, it has been a contributor to solving many modern practical problems in areas such as coding theory, cryptography, and information technology. In this course students will demonstrate an understanding of the fundamental results in elementary number theory and extend their understanding beyond typical undergraduate number theory by exploring modern applications and other interesting problems in number theory.

Math 530 – Abstract Algebra (4 credit hours)

This course is an in-depth study of topics from group, ring, and field theory, including properties of polynomials. This provides the foundation for exploration of advanced topics such as Sylow Theory, field extensions, Galois Theory, and geometric constructions. Connections will be made to topics covered in high school math classrooms.

Math 540 – Modern Geometries (4 credit hours)

A review of the basic techniques of straight edge and compass construction, including constructions requiring propositions from Book III of Euclid's (ca. 300 BC), gives students an intuitive foundation necessary for the approaches that follow. First is an overview of the nature of postulates and propositions in Euclid, which are radically different from their modern counterparts. From there, the bulk of the course is devoted to geometry based in Hilbert's axioms (1899), where the theory of plane geometry is built with an eye toward understanding the dilemma of Euclid's parallel postulate. The historical development leading from Euclid to hyperbolic and elliptic geometry is then situated in this mathematical context.

Math 550 – Mathematical Analysis (4 credit hours)

This course focuses on the theoretical foundations of the calculus sequence and consists essentially of an advanced treatment of the concepts of limits, differentiation and integration, both in the univariate and in the multivariate settings. Topics include higher order partial derivatives, generalizations of the mean value theorem and the fundamental theorem of calculus, evaluation of multiple integrals using the change of variables method, line integrals, implicit functions and the implicit function theorem. Additional topics include theory of infinite series, uniform convergence, and power series.

Math 580 – Special Topics (0.5-4 credit hours)

Advanced or special topics not covered in other graduate mathematics courses, such as advanced number theory, topics in advanced abstract algebra or real analysis or topology, differential geometry, mathematical logic, set theory, complex analysis, graph theory, probability and stochastic processes, advanced statistics, directed student research, or operations research. Students may enroll in this course more than once, but only once for a given topic. Consent of the department required.