# Mathematics - CPS (MTH)

**MTH 0102. College Mathematics 1. 2.4 Hours.**

Offers the first course in a two-quarter sequence of algebra. Includes a review of polynomials, rational expressions, and rational exponents. Topics include solving equations and inequalities, complex numbers, and linear and quadratic functions. Discusses applications to these topics.

**MTH 0103. College Mathematics 2. 4.8 Hours.**

Offers the second course in a two-quarter sequence of college algebra. Topics include the function concept; linear, quadratic, polynomial, rational, exponential, and logarithmic functions; and systems of equations. Discusses applications to these topics. *Prereq. MTH 0102.*

**MTH 0105. Introduction to Calculus. 1.8 Hour.**

Includes a review of precalculus and conic sections. Topics include limits, continuity, and introduction to differentiation. A graphing calculator is required.

**MTH 0106. Calculus 1. 3.6 Hours.**

Offers a continuation of the study of calculus started in MTH 0105. Topics include differentiation of algebraic, trigonometric, exponential, and logarithmic functions; applications of the derivative; antiderivatives; the definite and indefinite integral; the Fundamental Theorem of Calculus; and integration by substitution. Additional topics include differentiation and integration of hyperbolic and inverse trigonometric functions. A graphing calculator is required. *Prereq. MTH 0105.*

**MTH 0108. Foundations of Mathematics. 4 Hours.**

Designed for college students who have no previous experience in algebra and for those who need a review of basic algebraic concepts. Offers students an opportunity to work with mathematical symbols and operations to develop an understanding of how mathematics can model and solve problems and to obtain the skills necessary to successfully complete MTH 1001. Topics include variables, exponents, the real number system, fractions, basic operations, order of operations, simplifying algebraic expressions, solving linear equations, solving equations containing fractions, solving equations containing decimals, ratios, proportions, and graphing linear equations. Credit for this course cannot be applied to School of Engineering Technology degree programs or to College of Professional Studies degree programs.

**MTH 0115. Prealgebra. 1.5 Hour.**

Covers the simplifying of algebraic expressions; solving and graphing linear equations and inequalities; radicals, exponents, factoring polynomials, rational expressions, systems of equations, and quadratic equations.

**MTH 0120. Prealgebra. 3.6 Hours.**

Covers the simplifying of algebraic expressions; solving and graphing linear equations and inequalities; radicals, exponents, factoring polynomials, rational expressions, systems of equations, and quadratic equations.

**MTH 0901. Algebra, Numbers, and Geometry. 6.8 Hours.**

Develops the principles of beginning and intermediate algebra. Offers students an opportunity to develop a clear understanding of the mathematical concepts involved and to translate personal mathematical accomplishment into effective teaching strategies. Explores elements of arithmetic as a basis for understanding algebra. Uses exciting “tricks” and “puzzles” that can also be used to enliven the classroom experience for students. The tools and techniques of arithmetic then motivate an understanding of the general principles of algebra. Explores visual connections via graphing. Topics include principles of arithmetic (algebraic rules, order of operations, exponents, logarithms), number theory (primes, Euclidean algorithm), elements of combinatorics (counting techniques, divided differences), number systems and bases, polynomial algebra, linear functions, manipulating quadratics, graphing and connections to area, rational functions, complex numbers, and more.

**MTH 0902. Geometry. 6.8 Hours.**

Examines the study and teaching of beginning and intermediate geometry. Offers teachers an opportunity to develop a clear understanding of the mathematical concepts involved and to translate personal mathematical accomplishment into effective teaching strategies. Topics include pi and why it is the same for all circles, the value of pi for a square, what motivated Euclid to develop his controversial parallel postulate, why a straight line is the shortest path between two points, and trigonometry. Other topics include volume, Pythagoras’ theorem, distance and equidistance, parallelism, circles, triangles, polygons, the role of similarity, and conics, all within the framework of innovation, understanding, and an enjoyment of mathematics. .

**MTH 0903. Functions and Trigonometry. 6.8 Hours.**

Serves as a precursor to a course in calculus and as a stand-alone course in methods of advanced algebraic thinking. Introduces the study of functions—their definition, application, methods of manipulating them, generalized notions (so-called multivalued functions and relations), and their algebra. The act of graphing functions provides ties to geometry. This course utilizes innovative geometric insights to provide a sound and comprehensive perspective to the topic. The study of logarithms, the number “e,” complex numbers, trigonometry, growth and decay, and the conic sections find a natural place in this very general setting. Offers students an opportunity to develop a clear understanding of mathematical concepts and a deep global perspective of algebraic thinking as a whole.

**MTH 0904. Mathematics for Social Justice. 6.8 Hours.**

Explores principles of social justice in education as a lens to rethinking school mathematics curriculum and pedagogy. Offers students an opportunity to expand their knowledge and awareness of issues of social justice in the context of mathematics education; to develop a pedagogical model for teaching for social change; to critically examine the content of school mathematics curriculum and instructional practices from the perspective of social justice; and to contemplate the role of the teacher as an agent of change and “transformative intellectual.” Emphasizes the relationship between theory and practice in an attempt to understand some of the complexities and challenges in addressing issues of social justice in mathematics teaching and learning.

**MTH 0905. Classroom Technologies for the Middle and High School. 6.8 Hours.**

Seeks to improve teachers’ skills in bringing together curriculum and technology to support student learning. Technology is an integral part of the modern mathematics classroom, including the almost universal use of the graphing calculator. Two computer programs, Excel and the Geometer’s Sketchpad, have also been extensively used. These technologies are meant to illuminate and enhance concepts and techniques in the math curriculum. The NCTM emphasizes multiple representations of problems and methods, and these programs and calculators are designed for that exact purpose. Because there is little curriculum designed for the classroom use of technology, teachers must acquire and apply their own skills in adapting the technology into their teaching. Participants have the opportunity to practice presenting lessons with particular emphasis on the graphing calculator.

**MTH 0909. Probability and Statistics. 6.8 Hours.**

Introduces probability and statistics. Combines hands-on activities with conceptual exploration. Uses a non-calculus-based introduction to methods of thinking about problems in probability and statistics. Utilizes technology for simulations, evaluation of distribution functions, and experiential learning. In probability, examines continuous situations using either geometrical methods or use of formulas and technology. In statistics, topics covered include sampling methods and various ways of displaying and interpreting data.

**MTH 0910. Precalculus for the Secondary Teacher. 6.8 Hours.**

Explores the behavior and the applications of polynomial, exponential, logarithmic, and trigonometric functions. Examines the wide array of mathematics curves that serve as the foundational examples on which the calculus is then preformed. Considers other curves, such as the circle, ellipse, and hyperbola, as well as disparate topics, such as vectors, sequences, and series. Offers students an opportunity to use technology extensively, mostly the graphing calculator, to facilitate the explorations and to complete the skills necessary for a rigorous calculus course. Uses real-world examples to illuminate each of the elements of the course.

**MTH 0915. Introduction to Quantitative Reasoning for Middle School and High School Mathematics. 6.8 Hours.**

Offers participants an opportunity to understand quantitative reasoning (QR) and to integrate a QR approach and concepts into existing or newly developed middle school and high school curriculum. Focuses on learning and doing mathematical reasoning in a variety of contexts, such as personal finance and demographics. Topics include number sense, real-life probability and statistics, critical thinking and problem solving, interpreting graphs and tables, and modeling. Activities include mathematical problem solving, skill development, using a spreadsheet, reflecting on pedagogical practices, and examining connections to the Common Core Standards. Offers participants an opportunity to design and share problems, lesson plans, and projects to suit the interests and needs of their students and curriculum, working toward preparing students for future success in college, career, and life experiences.

**MTH 0920. Mathematical Thinking in the Middle School. 6.8 Hours.**

Aimed at middle school teachers. Focuses on developing key mathematical thinking in the formative pre-high school years. Explores, at the base level, content in numbers, number sense, and beginning algebra, with connections to geometry, with the goal of transforming procedural practice into clear and effective conceptual understanding. Offers participants an opportunity to reinforce their own personal understanding of mathematics as well as the tools to translate personal mathematical accomplishment into effective teaching strategy. Examines devices to enliven the classroom experience for students. Uses the tools and techniques of arithmetic to motivate and help develop clear understanding of the principles of algebra. Explores visual connections.

**MTH 0937. Differentiating Instruction in the K–8 Mathematics Classroom. 6.8 Hours.**

Presents best practices in differentiating instruction, with a focus on K–8 mathematics. Focuses on how best to reach an understanding about the importance of differentiated instruction, when to differentiate, and what tools are available to assist students achieve greater potential. Teaching and learning the K–8 mathematics curriculum in an inclusive classroom setting with English-language learner (ELL) students, special education students, gifted learners, and regular education students is less of a daunting task when a myriad of learning styles and ways of knowing how to accommodate these styles are seen as pieces of an intricate puzzle. As the range of student learners continues to widen, the challenges educators face to meet their needs simultaneously increases.

**MTH 0949. Conceptual Calculus. 6.8 Hours.**

Covers the techniques and practices of calculus. Offers students an opportunity to develop a deep understanding of the general principles, mechanisms, and issues that make the subject work. Introduces and develops the concepts covered in the standard AB calculus curriculum—limits, continuity, differential calculus, beginning integral calculus, and the fundamental theorem of calculus. Discusses the historical and philosophical context of the mathematics.

**MTH 0963. Geometry and Measurement for Elementary Teachers. 6.8 Hours.**

Focuses on the foundations of informal measurement and geometry in one-, two-, and three-dimensional space. Explores how children develop an understanding of length, area, volume, angles, and geometric relationships, as well as visualization, spatial reasoning, and geometric modeling. Offers students an opportunity to develop the vocabulary of geometry and explore both definitions and attributes of geometric objects. Covers transformational geometry, similarity, congruence, geometric constructions, and how to calculate the perimeter of polygons, areas of two-dimensional shapes, and volumes of three-dimensional shapes.

**MTH 1100. College Algebra. 3 Hours.**

Topics in this course include laws of exponents, factoring, inequalities, polynomials, roots, linear and quadratic equations, complex numbers, rational functions, systems of equations, exponential and logarithmic functions, and inverse functions. Students are required to communicate mathematical ideas using symbolic and written forms and to apply algebraic concepts to real life applications. Seeks to provide students with a solid foundation of concepts and skills necessary to advance to statistics or precalculus. Requires prior knowledge of the manipulation and simplification of basic algebraic expressions.

**MTH 1200. Precalculus. 3 Hours.**

Combines algebraic, geometric, and trigonometric concepts and techniques to model real-world situations (that is, exponential growth and decay, periodic phenomena). Successful completion of this course should strengthen the student’s conceptual understanding of mathematics and critical reasoning. Focuses on linear, polynomial, exponential, logarithmic, trigonometric functions, and conic sections. Emphases understanding, manipulating, and graphing these basic functions, their inverses and compositions, and using them to solve applications drawn from the physical and natural sciences.

**MTH 1990. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions.

**MTH 2100. Calculus 1. 3 Hours.**

Calculus is the branch of mathematics that allows us to use mathematical concepts and ideas to describe how things change. This course focuses primarily on differential calculus. Using mathematical models, students will have an opportunity to make predictions and inferences in variety of applications that relate to the fields of engineering, economics, biology, etc. For example, students can use differential calculus to determine what is the most cost-effective speed to drive a car, using the least amount of fuel. These types of problems, called optimization problems, require an understanding of the derivative as a rate of change. The course focuses on how to apply rules and properties of derivatives to model and solve application problems in science, engineering and technology. As a prelude to MTH 2105, at the end of the semester, the concept of the integral is introduced as a limit of sums and antidifferentiation.

**MTH 2105. Calculus 2. 3 Hours.**

Continues MTH 2100. Calculus is the branch of mathematics that allows us to use mathematical concepts and ideas to describe how things change. Using mathematical models, we are able to make predictions and inferences in variety of applications that relate to the fields of engineering, economics, biology, etc. This course focuses primarily on integral calculus and infinite sequences and series. Topics include definite and indefinite integration, the fundamental theorem of calculus, and the use of integration methods in the calculation of areas and volumes, and other applications. Improper integrals are introduced as well as the study of infinite sequences and series, power series, Taylor series, and techniques for determining convergence or divergence of sequences series. This course provides an in-depth overview of the above concepts and applies them to solve problems in science, engineering, and technology.

**MTH 2110. Calculus 3. 3 Hours.**

Extends concepts and problem-solving techniques of single-variable calculus to multivariate calculus. Employs techniques to evaluate higher-order differentiation and integration, including vector fields and vector calculus in 2D and 3D. Topics include lines and planes; 3D graphing; partial derivatives; the gradient, tangent planes, and local linearization; optimization; multiple integrals; line and surface integrals; the divergence theorem; and theorems of Green and Stokes with applications to science, engineering, and technology.

**MTH 2300. Business Statistics. 3 Hours.**

Offers students an opportunity to obtain the necessary skills to collect, summarize, analyze, and interpret business-related data. Covers descriptive statistics, sampling and sampling distributions, statistical inference, relationships between variables, formulating and testing hypotheses, and regression analysis in the context of business decision making.

**MTH 2310. Statistics for the Behavioral and Social Sciences. 3 Hours.**

Offers students an opportunity to obtain the necessary skills to collect, summarize, analyze, and interpret social and behavioral science data. Covers descriptive statistics, sampling and sampling distributions, statistical inference, relationships between variables, formulating and testing hypotheses, and regression analysis in the context of the social and behavioral sciences.

**MTH 2400. Technology and Applications of Discrete Mathematics. 3 Hours.**

Offers students experience with and exposure to ideas and techniques from discrete mathematics, which is at the foundation of the technological disciplines. Focuses on applications and practical use of discrete mathematics as it is applied to the computing sciences and engineering disciplines. Topics covered include sets; logic; Boolean algebra; machine representations of numbers (decimal, binary, octal, hexadecimal) and arithmetic; counting methods; graphs; and trees. Specific applications include algorithms and complexity, circuits and circuit diagrams, searching and sorting, networks, probability, and finite-state machines. Requires students to select and apply appropriate techniques from discrete math to address common problems found in modern technological systems, especially software and computing hardware design.

**MTH 2990. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions.

**MTH 3200. Differential Equations. 3 Hours.**

Mathematics models are created and used by engineers and scientists to express the laws of nature and other physical phenomena. The use of differential equations is pivotal in constructing such models. This course studies equations involving a single independent variable, also referred to as ordinary differential equations. Reviews techniques to formulate, solve, and interpret ordinary differential and their application in science, engineering, and technology. Topics include numerical methods, Laplace transforms, linear algebra, matrix algebra, systems of algebraic equations, eigenvalues, and eigenvectors.

**MTH 3300. Applied Probability and Statistics. 3 Hours.**

Covers randomness, finite probability space, probability measure, events; conditional probability, independence, Bayes’ theorem; discrete random variables; binomial and Poisson distributions; concepts of mean and variance; continuous random variables; exponential and normal distribution, probability density functions, calculation of mean and variance; central limit theorem and implications for normal distribution; purpose and the nature of sampling; nature of estimates, point estimates, interval estimates; maximum likelihood, least-squares approach; confidence intervals; estimates for one or two samples; development of models and associated hypotheses; nature of hypothesis formulation, null and alternate hypotheses, testing hypotheses; test statistics: t-test, chi-squared test; correlation and regression; Markov processes, discrete time systems, and continuous time systems; queuing theory, including system simulation and modeling, queuing methods.

**MTH 3990. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions.

**MTH 4896. Experiential Education Directed Study. 1-4 Hours.**

Draws upon the student’s approved experiential activity and integrates it with study in the academic major.

**MTH 4950. Seminar. 1-4 Hours.**

Offers an in-depth study of selected topics.

**MTH 4955. Project. 1-4 Hours.**

Focuses on in-depth project in which a student conducts research or produces a product related to the student’s major field.

**MTH 4983. Topics. 1-4 Hours.**

Covers special topics in mathematics.

**MTH 4990. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions.

**MTH 4991. Research. 1-4 Hours.**

Offers students an opportunity to conduct research under faculty supervision.

**MTH 4992. Directed Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic.

**MTH 4993. Independent Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic.

**MTH 4994. Internship. 1-4 Hours.**

Provides students with an opportunity for internship work.

**MTH 4995. Practicum. 1-4 Hours.**

Provides eligible students with an opportunity for practical experience.

**MTH 5976. Directed Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic.

**MTH 5978. Independent Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic.

**MTH 5984. Research. 1-4 Hours.**

Offers students an opportunity to conduct research under faculty supervision.

**MTH 6016. Calculus-Based Probability and Statistics. 4 Hours.**

Focuses on probability theory. Topics include conditional probability and independence; discrete and continuous probability distributions for one and for several random variables; expectation variance; special distributions, including binomial, Poisson, and normal distributions; the law of large numbers and central limit theorem. Introduces basic statistical theory, including estimation of parameters, confidence intervals, and hypothesis testing. *Prereq. One semester of multivariable calculus.*

**MTH 6108. Precalculus. 4 Hours.**

Serves as a precursor to a rigorous course in calculus giving a swift review of the necessary techniques and practices of algebra and trigonometry. Topics covered include a review of polynomial and rational functions (their algebraic manipulation and their graphing), exponential functions and population models, logarithmic functions, derivation of Euler’s number “e,” trigonometry, conic sections, complex numbers theory, limits and continuity, and the study of systems of equations (beginning linear algebra and linear programming). Successful students of this course are prepared to take MTH 6208. .

**MTH 6201. Algebra, Numbers, and Geometry. 4 Hours.**

Develops the principles of algebra. Offers students an opportunity to develop a clear understanding of the mathematical concepts involved and to translate personal mathematical accomplishment into effective teaching strategies. Explores arithmetic as a basis for understanding algebra. Uses exciting “tricks” and “puzzles” that can be used in the classroom. The tools and techniques of arithmetic then motivate an understanding of the general principles of algebra. Explores visual connections via graphing. Covers principles of arithmetic (algebraic rules, order of operations, exponents, logarithms), number theory (primes, Euclidean algorithm), elements of combinatorics (counting techniques, divided differences), number systems and bases, polynomial algebra, linear functions, manipulating quadratics, graphing and connections to area, rational functions, and complex numbers. Emphasizes algebra and numbers, though integral elements of geometry appear throughout discussions.

**MTH 6202. Geometry. 4 Hours.**

Examines the study and teaching of beginning and intermediate geometry. Offers teachers an opportunity to develop for themselves a clear understanding of the mathematical concepts involved, and to translate personal mathematical accomplishment into effective teaching strategies. Topics covered include area and volume, Pythagoras’ theorem and its consequences, distance and equidistance, parallelism, circles, triangles, polygons, the role of similarity, trigonometry, and conics, all within the framework of innovation, understanding, and an enjoyment of mathematics.

**MTH 6203. Functions and Trigonometry. 4 Hours.**

Serves as a precursor to a course in calculus and as a stand-alone course in methods of advanced algebraic thinking. Introduces the study of functions—their definition, application, methods of manipulating them, generalized notions (so-called multivalued functions and relations), and their algebra. The act of graphing functions provides ties to geometry. Utilizes innovative geometric insights to provide a sound and comprehensive perspective to the topic. The study of logarithms, the number “e,” complex numbers, trigonometry, growth and decay, and the conic sections find a natural place in this very general setting. Offers students an opportunity to develop a clear understanding of mathematical concepts and a deep global perspective of algebraic thinking as a whole.

**MTH 6207. Problem Solving. 4 Hours.**

Offers K–3 teachers an opportunity to expand and refine problem-solving skills while improving content knowledge of generalized arithmetic, algebra, and the role it plays in doing math in the primary classroom. Utilizes hands-on experiences to provide participants opportunities to solve problems in more than one way, to reason and think, to communicate in a variety of ways, and to represent concepts with symbols. Making connections and supporting the Mathematics Curriculum Framework strands of number sense and operations, patterns, relations, and algebra, data analysis, statistics, and probability are embedded in each task.

**MTH 6208. Calculus. 4 Hours.**

Covers the techniques and practices of calculus and offers students an opportunity to develop a deep understanding of the principles, mechanisms, and issues that make the subject work, allowing one to begin to apply theory to a wide range of contexts. Personal accomplishment and a sense of perspective enable one to be an effective educator. Explores the computation of the area of curved figures (as discussed since antiquity) and the problem of grinding parabolic lenses with flat grinding planes (as arose with the invention of the telescope in the early 1600s). The impact of Newton’s and Leibniz’ discovery that these two problems are intimately connected and that the solution of one, in fact, solves the other provides the historical and mathematical context of the course.

**MTH 6209. Probability and Statistics. 4 Hours.**

Develops the practices and principles of probability theory, descriptive statistics, and beginning inferential statistics, vast, historically rich, and philosophically perturbing subjects. Identifies the key concepts and principles behind these works and demystifies the approaches that seem counter to intuition. Uses give-and-take conversation, guided by both conceptual and practical exploration, to build up knowledge. As such, classes are interactive. Topics covered include naïve probability theory, models of probability theory, philosophical consequences, sampling, descriptive techniques (plot diagrams and numeric descriptives—mean, median, mode, variance, deviation), correlation and regression, distributions, inferential methods, reliability, techniques, and practices.

**MTH 6218. History of Mathematics. 4 Hours.**

Begins with arithmetic, protoalgebra, and geometry of the people of the fertile crescent (the Mesopotamians), the people of the valley of the Nile River (the Egyptians), and the early civilization on Crete (the Minoans), who were the forerunners of the Mycenaean Greeks and the classical ancient Greeks. Studies the people of the middle and lower Yellow River (the Chinese) and the people of the area near the Indus River valley (the Indians). The roots of the above cultures seem to have begun about 4,000 years ago. Building upon the discoveries and creations of these five ancient cultures, the inheritors of Alexander the Great’s conquests, the Hellenistic Greeks and the Islamic societies, made great strides in advancing mathematics. Renaissance Italy built upon this mathematical edifice.

**MTH 6219. Introduction to Analysis. 4 Hours.**

Provides the theoretical underpinnings of calculus and the advanced study of functions needed for teaching AB or BC advanced placement calculus. Emphasizes precise definitions and rigorous proofs. Offers students an opportunity to understand a rigorous proof of the Fundamental Theorem of Calculus and to learn how to write careful, logical, and understandable mathematical proofs. Topics include the construction of real numbers from rational numbers, completeness, continuity, uniform continuity, and differentiability of functions in the inverse function theorem and the Riemann integral.

**MTH 6220. Linear Algebra. 4 Hours.**

Surveys linear algebra, including the study of systems of linear equations, linear mappings. and their applications. Topics include matrices and solving systems of equations by the Gauss-Jordan elimination algorithm, geometric, and algebraic properties of vectors; properties of vector spaces (e.g., basis, dimension); the matrix of representing a linear transformation; and inverses, determinants, and the definitions and basic properties of groups, rings, and fields.

**MTH 6222. Number Theory. 4 Hours.**

Introduces elementary number theory. Includes linear Diophantine equations, congruencies, modular arithmetic, design of magic squares, Fermat’s little theorem, Euler’s phi function, the RSA encryption system, and the law of quadratic reciprocity. Discusses additional topics, such as Diophantine approximation, Pell’s equation, elliptic curves, and Fermat’s last theorem, if time permits.

**MTH 6228. Calculus 2. 4 Hours.**

Follows the standard BC calculus curriculum. Reviews differentiation and integration and the Fundamental Theorem of Calculus, followed by a study of further integration techniques, differential equations, numerical methods and error analysis, sequences and series, Taylor series, polar coordinates, and parametric equations. Familiarity with algebra and trigonometry is assumed.

**MTH 6232. Multivariable Calculus. 4 Hours.**

Surveys multivariable calculus, which serves as the gateway to advanced mathematics courses and is a basic prerequisite for applied mathematics programs. Offers students an opportunity to learn to visualize mathematical shapes and ideas in two and three dimensions and to understand the derivative of a function of two and three variables and the integral to multivariable functions.

**MTH 6237. Differentiating Instruction in the K–8 Mathematics Classroom. 4 Hours.**

Presents best practices in differentiating instruction, with a focus on K–8 mathematics. Focuses on how best to reach an understanding about the importance of differentiated instruction, when to differentiate, and what tools are available to assist students achieve greater potential. Teaching and learning the K–8 mathematics curriculum in an inclusive classroom setting with English-language learner (ELL) students, special education students, gifted learners, and regular education students is less of a daunting task when a myriad of learning styles and ways of knowing how to accommodate these styles are seen as pieces of an intricate puzzle. As the range of student learners continues to widen, the challenges educators face to meet their needs simultaneously increases.

**MTH 6254. Conceptual Calculus. 4 Hours.**

Covers the techniques and practices of calculus. Offers students an opportunity to develop a deep understanding of the general principles, mechanisms, and issues that make the subject work. Introduces and develops the concepts covered in the standard AB calculus curriculum—limits, continuity, differential calculus, beginning integral calculus, and the fundamental theorem of calculus. Discusses the historical and philosophical context of the mathematics.

**MTH 6302. Geometry 2: Geometry since 1800. 4 Hours.**

Introduces more recent Euclidean geometry, such as Feuerbach’s nine-point circle, the Euler line, and Morley’s theorem. Looks at geometry on the surface of the spherical earth and the passage to elliptic geometry and some features of hyperbolic geometries. Uses the Geometer’s Sketchpad to study transformations of friezes and to visualize the geometry in the above paragraph, including pictures of the geometry of the hyperbolic plane. Introduces the six regular polytopes in four-dimensional space. Abbott’s *Flatland* and Dewdney’s *The Planiverse* are among the readings and are suitable for secondary classrooms.

**MTH 6505. Classroom Technologies for the Middle and High School. 4 Hours.**

Seeks to improve teachers’ skills in bringing together curriculum and technology to support student learning. Technology is an integral part of the modern mathematics classroom, including the almost universal use of the graphing calculator. Two computer programs, Excel and the Geometer’s Sketchpad, have also been extensively used. These technologies are meant to illuminate and enhance concepts and techniques in the math curriculum. The NCTM emphasizes multiple representations of problems and methods, and these programs and calculators are designed for that exact purpose. Because there is little curriculum designed for the classroom use of technology, teachers must acquire and apply their own skills in adapting the technology into their teaching. Participants have the opportunity to practice presenting lessons with particular emphasis on the graphing calculator.

**MTH 6506. Interactive Mathematics Program Year 1. 4 Hours.**

Offers teachers an opportunity to learn how to use the problem-solving units in geometry, algebra, and numbers. These units could in turn be used to develop middle grade students’ understanding of mathematical concepts. Models and discusses alternative pedagogy for helping students make sense of mathematics.

**MTH 6510. Mathematics Content Development. 4 Hours.**

Offers students an opportunity to explore mathematical tasks in order to experience the conceptual and pedagogical power of mathematical skills and concepts. Examines the topics and concepts developed under the strands of mathematics in a standard K–6 program. Explores numeration, operations, algebra, geometry, measurement, and data and probability, as well as strategies to adjust mathematical tasks for students of varying abilities through a differentiated approach to instruction.

**MTH 6515. Introduction to Quantitative Reasoning for Middle School and High School Mathematics. 4 Hours.**

Offers participants an opportunity to understand quantitative reasoning (QR) and to integrate a QR approach and concepts into existing or newly developed middle school and high school curriculum. Focuses on learning and doing mathematical reasoning in a variety of contexts, such as personal finance and demographics. Topics include number sense, real-life probability and statistics, critical thinking and problem solving, interpreting graphs and tables, and modeling. Activities include mathematical problem solving, skill development, using a spreadsheet, reflecting on pedagogical practices, and examining connections to the Common Core Standards. Offers participants an opportunity to design and share problems, lesson plans, and projects to suit the interests and needs of their students and curriculum, working toward preparing students for future success in college, career, and life experiences.

**MTH 6520. Mathematical Thinking in the Middle School. 4 Hours.**

Aimed at middle school teachers. Focuses on developing key mathematical thinking in the formative pre-high school years. Explores, at the base level, content in numbers, number sense, and beginning algebra, with connections to geometry, with the goal of transforming procedural practice into clear and effective conceptual understanding. Offers participants an opportunity to reinforce their own personal understanding of mathematics as well as the tools to translate personal mathematical accomplishment into effective teaching strategy. Examines devices to enliven the classroom experience for students. Uses the tools and techniques of arithmetic to motivate and help develop clear understanding of the principles of algebra. Explores visual connections.

**MTH 6527. Mathematics for Middle School Science Teachers. 4 Hours.**

Explores mathematical concepts using examples from science. Offers participants an opportunity to enhance the mathematical skills needed to teach middle school science more effectively. Topics include ratios and proportions, algebraic equations (linear and quadratic), systems of linear equations, functions (linear and quadratic), graphical representation, fundamentals of statistical analysis, plane geometry, trigonometry, and vector analysis. .

**MTH 6531. Developing Mathematical Ideas: Building a System of 10s. 4 Hours.**

Designed to help experienced K–6 teachers explore the structure of our base-10 number system and examine how children develop an understanding of it. Uses sets of classroom episodes (cases) to illustrate student thinking. In addition, the curriculum offers opportunities to view and discuss videos of mathematics classrooms; explore mathematics in instructor-led lessons; share student work; plan, conduct, and analyze student interviews; analyze innovative elementary mathematics curricula; and read and reflect on related research.

**MTH 6532. Developing Mathematical Ideas: Making Meaning of Operations. 4 Hours.**

Designed to help experienced K–8 teachers examine the actions and situations modeled by the four basic mathematical operations. Issues covered include young children’s counting strategies and an examination of children’s developing ideas of the four basic operations in the context of rational numbers. Uses case studies to illustrate student thinking as described by their teachers. Offers participants an opportunity to view and discuss videos of mathematics classrooms; explore mathematics in lessons led by the instructor; share and discuss student work; plan, conduct, and analyze mathematics interviews of students; analyze innovative lessons; and read and reflect on related research.

**MTH 6533. Assessing Student Understanding in Today’s Mathematics Classroom. 4 Hours.**

Seeks to provide students with an in-depth focus on authentic assessment in the elementary mathematics classroom and how to use the results of assessment to chart more effective pathways for instruction. Topics include the different types of assessment strategies, the distinction between evaluation and assessment, the nature of authentic assessment, and the design and use of rubrics and checklists. Seeks to review research that shows how assessment can enrich and focus learning, to examine national and state assessment items, to develop model assessments to be shared on a database, and to experience ways to evaluate student work to probe student understanding.

**MTH 6534. Reasoning About Algebraic Operations. 4 Hours.**

Focuses on how children’s study of operations leads into articulation of generalizations in the number system and justification of such generalizations. Offers students an opportunity to explore related mathematical ideas for themselves, thus preparing them to support similar thinking in their own classrooms. Designed to enhance students’ understanding about how this mathematical work in the elementary grades is related to the algebra that is more conventionally studied in later grades. This course is part of the Developing Mathematical Ideas (DMI) series, a professional development curriculum designed to help teachers think through the major ideas of K–7 mathematics and examine how children develop those ideas.

**MTH 6535. Patterns, Functions, and Change. 4 Hours.**

Seeks to help K–8 teachers examine the connections between repeating patterns and mathematical functions and how two quantities change in relationship to one another. Offers teachers an opportunity to explore the conceptual issues people face as they work to represent relationships between two quantities using tables, graphs, arithmetic rules, and symbolic notation. Studies a variety of functions (linear, quadratic, and exponential), the graphs for these functions, and how these two quantities change in relation to one another. Offers opportunities for discussion by using case studies, visuals, exploring mathematics in instructor-led lessons, sharing of work, analyzing lessons taken from innovative elementary mathematics curricula, and for reading and reflecting on overviews of related research.

**MTH 6536. Assessing Student Work in Mathematics and Its Impact on Instruction. 4 Hours.**

Focuses on how to use assessment results to inform instruction in mathematics. Offers participants an opportunity to examine student work critically in order to evaluate what students have learned regarding key concepts in mathematics. Explores how to edit and perfect teacher-developed assessments to probe for deeper understanding and design learning opportunities for students that deepen their mastery of content and standards.

**MTH 6560. Creating the Ideal Learning Environment for Elementary Mathematics . 4 Hours.**

Seeks to assist students to become confident and effective inquiry-based mathematics teachers. Explores the learning environment that is most conducive for teaching and learning elementary mathematics in today’s classrooms and how children develop foundational mathematical understanding at a very early age. Provides an introductory, hands-on, exploratory experience in number sense, arithmetical operations, geometry, measurement, and algebra. The work is approached from the perspective of the student learner. Offers students an opportunity to delve into the mathematical concepts behind the experiences to gain an understanding of how these early skills are scaffolded at the upper-grade levels. Emphasizes making sense of student thinking, investigating alternative solution strategies, refining lesson planning, sharing instructional strategies, and creating a community of learners.

**MTH 6561. Number and Place Value. 4 Hours.**

Offers students an opportunity to develop a comprehensive understanding of number systems and how their structure is related to computation and problem solving. Begins with a look at a historical perspective of numbers and number systems and continues with the study of place value and the base-10 structure of the number system. Emphasizes understanding the concept of place value, since it forms the foundation for understanding other major mathematical concepts such as decimal fractions, scientific notation, standard algorithms, mental math, estimation, and rounding. Explores decimals, fractions, percentages, and mixed numbers and the connections among them. Uses the number line as a tool for depicting positive and negative numbers and fractions.

**MTH 6562. Arithmetic Operations. 4 Hours.**

Offers an in-depth look at the four arithmetic operations—addition, subtraction, multiplication, and division of whole numbers—and then revisits the operations in the context of rational numbers. Emphasizes the connections among the operations. Uses the number line for simple arithmetic operations. Offers students an opportunity to explore the standard and nonstandard algorithms for the four operations and why they work. Explores the properties of arithmetic and develops estimation skills and the skills known collectively as number sense and mental math.

**MTH 6563. Geometry and Measurement. 4 Hours.**

Focuses on the foundations of informal measurement and geometry in one-, two-, and three-dimensional space. Explores how children develop an understanding of length, area, volume, angles, and geometric relationships, as well as visualization, spatial reasoning, and geometric modeling. Offers students an opportunity to develop the vocabulary of geometry and explore both definitions and attributes of geometric objects. Covers transformational geometry, similarity, congruence, and geometric constructions. Covers how to calculate the perimeter of polygons, areas of two-dimensional shapes, and volumes of three-dimensional shapes.

**MTH 6564. Standard and Metric Measurements. 4 Hours.**

Focuses on the operation and function of measurement in everyday life. Investigates the fundamentals of measurement. Covers both the American system of measurement and the metric system. Introduces an assortment of tools to measure length, distances, capacity, volume, weight, mass, time, and temperature. Asks students to convert from one unit of measurement to another within the same measurement system and to use measurement to design and construct objects and draw scaled drawings with attention to accuracy and precision of measurements.

**MTH 6565. Functions and Algebra. 4 Hours.**

Demonstrates how to scaffold prealgebra and algebra skills in the elementary grades. Algebra, once considered too advanced for the elementary classroom, is now recognized as a gatekeeper subject. Offers students an opportunity to attain depth and understanding of mathematical expressions, formulas, equations, and functions (linear, exponential, polynomial). Explores the relationship among ratio, proportion, constant rates, and linear functions, as well as how graphs, equations, tables, and words can be used to describe relationships. Covers the power of variables and how they are used to describe patterns. The use of the graphing calculator plays an important role in these explorations.

**MTH 6566. Data Analysis and Probability. 4 Hours.**

Offers students an opportunity to develop a deeper understanding of data analysis, descriptive statistics, and probability. Students formulate questions, design investigations, gather data, and then organize and analyze that data. The descriptive statistic topics covered include measures of central tendency (mean, median, mode), dispersion (range, standard deviation), distributions, and regression. Includes basic principles and calculation methods of probability. .

**MTH 6575. Assessment in the Elementary Mathematics Classroom. 4 Hours.**

Explores a range of assessments that can be implemented in the elementary classroom. Offers participants an opportunity to create a comprehensive picture of student achievement through data collection as well as to delineate clearly student learning needs. Examines formal assessments (standardized tests) and informal assessments (student observation) in mathematics and provides an opportunity to weigh the benefits and limitations of each. Covers questioning strategies and a protocol for looking at student work.

**MTH 6576. Creating a Student-Centered Mathematics Classroom: Meeting the Needs of All Students. 4 Hours.**

Explores specific instructional strategies that support differentiation in the mathematics classroom. Examines the teacher’s current role in the classroom, discusses ways to facilitate student learning through inquiry-based activities, and promotes student independence. Explores ensuring equitable access to all members of a diverse learning population, as well as how to identify students in need of services in mathematics, how to explore particular mathematical learning disabilities such as dyscalculia, and how to support ELL students.

**MTH 6577. Integrating Technology into the Mathematics Classroom. 4 Hours.**

Offers students an opportunity to obtain knowledge about, and strengthen their ability to select, computer software and Web sites that can be integrated into the mathematics classroom. Reviews research supporting the use of software and Web sites in mathematics classrooms at all levels. Students select, review, analyze, and evaluate various software and Web sites and then design technology-based lesson plans.

**MTH 6610. Precalculus for the Secondary Teacher. 4 Hours.**

Explores the behavior and the applications of polynomial, exponential, logarithmic, and trigonometric functions. Examines the wide array of mathematics curves that serve as the foundational examples on which the calculus is then preformed. Considers other curves, such as the circle, ellipse, and hyperbola, as well as disparate topics, such as vectors, sequences, and series. Offers students an opportunity to use technology extensively, mostly the graphing calculator, to facilitate the explorations and to complete the skills necessary for a rigorous calculus course. Uses real-world examples to illuminate each of the elements of the course.

**MTH 6961. Internship. 1-4 Hours.**

Provides students with an opportunity for internship work.

**MTH 6962. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions.

**MTH 6964. Co-op. 0 Hours.**

Provides eligible students with an opportunity for work experience.

**MTH 6966. Practicum. 1-4 Hours.**

Provides eligible students with an opportunity for practical experience.

**MTH 6970. Seminar. 1-4 Hours.**

Offers an in-depth study of selected topics.

**MTH 6980. Capstone. 1-4 Hours.**

Offers students an opportunity to integrate their course work, knowledge, and experiences into a capstone project.

**MTH 6983. Topics. 1-4 Hours.**

Covers special topics in mathematics.

**MTH 6995. Project. 1-4 Hours.**

Focuses on in-depth project in which a student conducts research or produces a product related to the student’s major field.

**MTH 7961. Internship. 1-4 Hours.**

Provides students with an opportunity for internship work.

**MTH 7962. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions.

**MTH 7976. Directed Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic.

**MTH 7978. Independent Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic.

**MTH 7980. Capstone. 1-4 Hours.**

Offers students an opportunity to integrate their course work, knowledge, and experiences into a capstone project.

**MTH 7983. Topics. 1-4 Hours.**

Covers special topics in mathematics.

**MTH 7990. Thesis. 1-4 Hours.**

Offers thesis supervision by members of the department.

**MTH 7994. Thesis Continuation—PT. 0 Hours.**

Offers continuing thesis supervision by members of the department.

**MTH 7995. Project. 1-4 Hours.**

Focuses on in-depth project in which a student conducts research or produces a product related to the student’s major field.

**MTH 7996. Thesis Continuation. 0 Hours.**

Offers continuing thesis supervision by members of the department.