# Mathematics Courses

**MTH 0003. Elementary Algebra.** This course is designed for students who desire or need a stronger understanding of the numeration system and how to operate within that system. It is designed to enhance students’ understanding of algebraic expressions and equations. Students will analyze functions using graphical and algebraic techniques. Students with a mathematics ACT score below 17 (or equivalent score from admission exams approved by HSU) are required to complete the course with a grade of C or better before enrolling in MTH 0013, MTH 1033 or MTH 1083. This course cannot be used for degree requirements.

**MTH 0013. Intermediate Algebra.** This course is designed to strengthen basic algebraic manipulation skills. The course develops the characteristics of linear and quadratic functions to solve equations, systems of equations and inequalities. Prerequisite: MTH 0003 (with a grade of C or better), or a mathematics ACT score of at least 17 (or equivalent score from an admission exam approved by HSU). This course cannot be used for degree requirements.

**MTH 1033 (MATH 1003). Quantitative Literacy.** This course consists of units dealing with logic, proportional reasoning, the mathematics of finance, exponential growth and decay, geometry (plane and solid), voting theory, applications of mathematics to music and art, and probability and statistics. Prerequisite: MTH 0003 (with a grade of C or better), or a mathematics ACT score of at least 19 (or equivalent score from an admission exam approved by HSU).

**MTH 1034. Quantitative Literacy - Enhanced.** This course consists of units dealing with logic, proportional reasoning, the mathematics of finance, exponential growth and decay, geometry (plane and solid), voting theory, applications of mathematics to music and art, and probability and statistics. Meets three hours plus an additional two-hour laboratory per week. Prerequisite: MTH 0003 (with a grade of C or better), or a mathematics ACT score of at least 17 (or equivalent score from an admission exam approved by HSU).

**MTH 1053. Number Operations and Number Sense.** Numeration systems from natural numbers through real numbers will be developed including operations and properties with applications using the mathematical practices and supported by varied representational tools, including concrete models as appropriate to the P-8 teacher. Prerequisites: Mathematics ACT score of at least 19 (or equivalent math score from an admission exam approved by HSU) or a grade of C or better in either MTH 1244, MTH 1243, or MTH1273.

**MTH 1083 (MATH 1003). Mathematics through Practical Applications.** The course looks at percentages, calculating and using statistics, unit conversions, mathematical modeling, physics of motion, probability, geometry, estimation, data collection and other applications. The motivation for coverage of the topics will come from various areas chosen by the instructor such as sports, music, art, physics, acoustics, etc. Applications of these topics will be made to everyday life. Prerequisite: MTH 0003 (with a grade of C or better), or a mathematics ACT score of at least 19 (or equivalent score from an admission exam approved by HSU).

**MTH 1213. Algebra for Elementary and Middle Grades.** A course designed to meet the needs of students preparing for elementary and/or middle school licensure. Topics Include: algebraic notation, symbols, expressions, equations, inequalities, and proportional relationships, and their use in describing, interpreting, modeling, generalizing, and justifying relationships and operations; function classes including polynomial, exponential, and sequences; functional representations, characteristics, and notations as a means to describe, reason, interpret, and analyze relationships and to build new functions; and patterns of change in linear, quadratic, polynomial, and exponential functions and in proportional and inversely proportional relationships and types of real-world relationships these functions can model. Concepts will be developed using appropriate manipulatives and technology. Prerequisite: Mathematics ACT score of at least 19 (or equivalent math score from an admission exam approved by HSU).

**MTH 1233. Applied Trigonometry**. Emphasis on applications instead of solving trigonometric equations and proving identities. Topics include angular measurement, trigonometric functions, graphing, Law of Sines, Law of Cosines, Heron’s formula, polar coordinates, parametric equations, and two- and three-dimensional vectors. Students preparing for Calculus should take MTH 1253 instead. Prerequisite or corequisite: MTH 1213, MTH 1243, MTH 1244, MTH 1273, or departmental permission.

**MTH 1243 (MATH 1103). College Algebra.** A course designed to meet the general education needs of students in business, sciences, and other programs outside of mathematics. Topics include linear, non-linear, inverse, polynomial, rational, exponential and logarithmic functions; systems of linear equations, linear and quadratic inequalities. Problem-solving techniques with be discussed with and without the use of technology. Prerequisite: MTH 0013 (with a grade of C or better), or a mathematics ACT score of at least 20 (or equivalent math score from an admission exam approved by HSU). An ACT math score of 22 or above is recommended.

**MTH 1244. College Algebra-Enhanced. **A course designed to meet the general education needs of students in business, sciences, and other programs outside of mathematics. Topics include linear, non-linear, inverse, polynomial, rational, exponential and logarithmic functions; systems of linear equations, linear and quadratic inequalities. Problem-solving techniques will be discussed with and without the use of technology. Meets three hours plus an additional two-hour laboratory per week. MTH 0003 with a grade of C or better, or MTH ACT of 17 or better.

**MTH 1253 (MATH 1203). Plane Trigonometry.** Topics to include angular measurement, trigonometric functions, identities, graphing, Law of Sines, Law of Cosines, Heron’s formula, polar coordinates, complex numbers, vectors, and parametric equations. Prerequisite or corequisite: MTH 1243, MTH 1244, or MTH 1273, or departmental permission.

**MTH 1273. Precalculus Mathematics.** This course is designed to prepare students for MTH 1294. The course includes a study of linear and non-linear equations, systems of equations, and inequalities, an introduction to matrices, sequences, and series, as well as conic sections. Prerequisite: Two units of high school algebra. A mathematics ACT of 20+ or MTH1243 or MTH1244 is required. An ACT mathematics score of 25 or above is recommended.

**MTH 1294 (MATH 2405). Calculus I.** Topics include limits, derivatives, and integrals of algebraic and transcendental functions. Theory, computation, and applications are emphasized. Prerequisites: (MTH 1253 and MTH 1273) or consent of the department.

**MTH 2044 (MATH 2505). Calculus II. **This course is a continuation of MTH 1294-Calculus I. Additional topics will include integration techniques, improper integrals, infinite series, parametric equations and polar coordinates. Theory, computation, and applications are emphasized. Prerequisite: MTH 1294 or consent of the department.

**MTH 2283. Discrete Mathematics.** A study of mathematical structures that are fundamentally discrete rather than continuous in nature. The course includes a study of logic, mathematical writing and proofs, an introduction to sets, relations, and counting methods. Prerequisites: MTH 1243 or MTH 1273; MTH 1294 Recommended.

**MTH 2483. Geometry I for the Elementary and Middle Grades.** Geometrical understanding and mathematical practices will be developed, supported by appropriate technology and varied representational tools, including concrete models. Topics include Euclidean geometry in two and three dimensions, geometric constructions, analytic and coordinate geometry, transformations, congruence, and similarity; the identification, classification, representation, as well as measurement formula rationale and derivation of two- and three-dimensional objects, with attention to units. Prerequisites: A grade of C or better in MTH 1053 and in one of the following: MTH 1244, MTH 1243, or MTH1273.

**MTH 2543. Data Analysis, Statistics, and Probability for the Elementary and ****Middle Grades.** Concepts of data analysis, statistics, and probability appropriate for P-8 grade levels will be developed using the mathematical practices and supported by appropriate technology and varied representational tools, including concrete models. Topics include univariate and bivariate graphical techniques, measures of center and dispersion, normal distribution,

**MTH 2611, 2612, 2613, 2614, 2615, 2616. Internship in Mathematics.** See MTH 4621.

**MTH 3023. (WI) Systems of Geometry I. **The course introduces the concept of an axiomatic mathematical system through the development of neutral and Euclidean geometries with an emphasis on valid arguments. Non-Euclidean geometry will also be investigated. Prerequisites: MTH 1294 and MTH 2283.

**MTH 3063. Advanced Algebra for the Elementary and Middle Grades.** Reviews the basic concepts of algebra, use of manipulatives, and the use of technology. Prerequisite: MTH 2483.

**MTH 3073. Geometry II for the Middle Grades (4-8).** An informal study of the concepts of position, shape, size, construction with straightedge and compass, the structure of geometry, and measurement. Prerequisite: MTH 2483.

**MTH 3104. Calculus III.** A study of 2-D and 3-D vectors and geometry, vector functions, partial differentiation, multiple

**MTH 3113. Linear Algebra. **Topics include vector spaces, linear transformations and matrices, sets of linear transformations and matrices, eigenvalues and eigenvectors of linear transformations, and similar matrices. Only one of MATH 3113 and MATH 3663 may be applied to a mathematics, computer science, or statistics degree, track, minor, or certificate. Prerequisites: MTH 1294 and MTH 2283. MTH 3573 is recommended.

**MTH 3124. Differential Equations.** Analytic, approximate, and graphical solutions to ordinary differential equations, the theory of the existence and uniqueness of solutions, and applications of these ideas to the physical sciences. Prerequisite: MTH 2044.

**MTH 3163. Probability and Statistics I.** The mathematical theory of probability and application of this theory to statistical inference. Topics include descriptive statistics, independence, conditional probability, expectation, variance, discrete and continuous distributions, moment generating functions, and the central limit theorem. Prerequisites: MTH 2283 and MTH 2044.

**MTH 3383. Mathematics for Secondary Teachers.** This course develops problem-solving strategies and proofs in a variety of mathematical contexts, emphasizing the connections between algebra and geometry. The historical development of mathematics and how it affects mathematics today will be explored. Prerequisites: (MTH 1243 or MTH 1273) and MTH 1253 and MTH 2283.

**MTH 3553. Mathematics of Calculus and Technology for the Middle Grades**. An intuitive understanding of limits, derivatives with applications, and integration with applications will be developed using the mathematical practices and supported by appropriate technology and varied representational tools, including concrete models as appropriate for middle-level mathematics teachers. Prerequisite: grade of C or better in MTH 2483 and in one of the following: MTH 1213, MTH 1243, MTH1244, MTH 1273.

**MTH 3573. Transition to Advanced Mathematics. **A rigorous study of fundamental concepts of higher order mathematics, including set theory, logic, equivalence relations, and functions. Written and oral communication of mathematics with precision and rigor will be emphasized, particularly writing proofs. Prerequisites: MTH1294 and MTH2283.

**MTH 3633. Advanced Mathematics for Middle Grades.** A course designed to meet the needs of students preparing for middle school licensure. At the completion of this course, students should be able to demonstrate their understanding of the basic concepts of advanced mathematics by representing, describing, interpreting, modeling, and generalizing mathematical phenomena. Technology and tools will be used strategically. Prerequisites: grade of C or better in MTH 2483 and in one of the following: MTH 1213, MTH 1243, MTH1244, MTH1273.

**MTH 3663. Applied Linear Algebra.** Topics may include systems of linear equations, vector spaces, linear transformations, matrix decompositions, orthogonality, determinants, eigenvalue problems, and diagonalization. Emphasis will be on concepts, calculations, applications, and appropriate software. Only one of MATH 3113 and MATH 3663 may be applied to a mathematics, computer science, or statistics degree, track, minor, or certificate. Prerequisite: MTH 1294.

**MTH 4093, 5093. **Systems of Geometry II. Continuation of MTH 3023. Prerequisite: MTH 3023.

**MTH 4133, 5133. (WI) Algebraic Structures I.** An introduction to the fundamental algebraic structures: groups, rings, and fields. Emphasis is placed on developing mathematical sophistication and rigor of proof. Prerequisite: MTH 1294 and MTH 2283.

**MTH 4143, 5143. Algebraic Structures II.** Continuation of MTH 4133; advanced group theory and Galois theory. Prerequisite: MTH 4133.

**MTH 4153, 5153. History of Mathematics.** This course is an overview of the development of elementary mathematics from primitive counting to modern accomplishments in algebra, geometry, and calculus. Prerequisite: MTH 2044.

**MTH 4223, 5223. Introduction to Topology.** An introduction to topological spaces, homeomorphism, compactness, separations, and connectedness. Prerequisite: MTH 4133.

**MTH 4233, 5233. Advanced Calculus I.** A rigorous development of calculus of one and of several variables. Topics include sequences, series, continuous and differentiable functions, integration theory, and series of functions. Prerequisites: MTH 2044 and MTH 4133.

**MTH 4303, 5303. Advanced Calculus II.** Continuation of MTH 4233. Prerequisite: MTH 4233.

**MTH 4331-3, 5331-3. Independent Study.** Independent study in an area of 161 mathematics selected by the student and faculty advisor. Credit will vary from one (1) to three (3) hours. May be repeated. Prerequisite: consent of faculty advisor.

**MTH 4373, 5373. Numerical Analysis.** An introduction to numerical methods of problem-solving to include error analysis, approximate solutions to equations of one variable, interpolation and polynomial approximation, numerical differentiation and integration, numerical solutions of differential equations, linear systems, and approximation of functions. Prerequisites: MTH 2044 and CSC 1104.

**MTH 4433, 5433. Probability and Statistics II.** The mathematical theory of probability and application of this theory to statistical inference. Topics include multivariable distributions, confidence intervals, tests of statistical hypotheses, linear models, 1-way analysis of variance, and quality control through statistical methods. Prerequisite: MTH 3163.

**MTH 4473, 5473. Simulation Theory.** See CSC 4213.

**MTH 4491-3, 5491-3. Special Topics in Mathematics Education.** A broad range of topics in mathematics content that will include, but not be limited to, algebra, geometry, probability, statistics, and data representation, and the use of technology. Topics will be addressed to middle school and/or high school teachers. Students will be able to repeat the course for credit when different topics are being presented than when the student previously took the class. A designation of the topics covered will be recorded on the transcript. Prerequisites: Secondary - MTH 1243 or MTH 1294 or consent of the instructor. Middle School - MTH 1053 or MTH 2483 or departmental consent.

**MTH 4563. Math Modeling and Applications for the Middle Grades**. This course will serve as the capstone course for students pursuing licensure in Middle School Mathematics and Science. Connections between other mathematics courses in the program will be broadened and explored using appropriate materials through laboratory experiences. The use of technology, including the Internet as an instructional source, as is appropriate for the middle grades will be incorporated to enhance problem-solving, communication and reasoning skills. Prerequisite: MTH 3553 or departmental consent.

**MTH 4621, 4612, 4613, 4614, 4615, 4616. Internship in Mathematics.** The professional internship is intended to provide a learning opportunity for students to 1) apply knowledge and skills acquired in the classroom in a professional context; 2) understand which skills are transferable to new contexts; 3) identify and understand the practices and protocols of the industry in which they are working; and 4) refine and reassess their own career goals as a result of the experience. Current employment may not be used for credit in this course. This is a credit/no credit course and may be repeated for a maximum of 6 credit hours. Prerequisite: Consent of Department.

**MTH 4673, MTH 5673. Complex Analysis.** This course will introduce functions of a complex variable. Topics will include complex numbers, polar form and topology of complex numbers, complex functions and mappings, limits and continuity, analytic and harmonic functions, elementary functions, complex integration, the Cauchy-Goursat Theorem, the Cauchy Integral Formula and its consequences, sequences and series of complex numbers, Taylor and Laurent series, classification of isolated singularities, residue theory and its applications, and conformal mappings and their applications. Course Prerequisites: MTH 3104 or consent of the department

**MTH 4893. (WI) Special Methods/Math.** This course emphasizes the strategies of teaching mathematics, the planning for teaching mathematics, and mathematical assessment programs. Topics include developing objectives, creating lessons, building units, designing an assessment plan, and appropriate use of manipulatives and technology. Prerequisite: MTH 3383 or departmental consent.

**MTH 4901. (WI) Senior Project - Mathematics.** Completion of a research paper on a topic consistent with student’s degree track. Each student will work with a primary faculty mentor as well as a second reader; the paper will follow established departmental guidelines. This project will be completed during one of the last two semesters prior to graduation. Students will be required to present their papers in a departmental colloquium. Students will take the Major Field Test (Mathematics) as part of the grade for this course. Prerequisites: Senior Standing and departmental approval.

**MTH 4961-3, 5961-3. Special Topics in Mathematics.** Topics selected from the areas of analysis, algebra, geometry, topology, logic, statistics, or other areas according to student needs and the instructor’s specialization. The student’s transcript will indicate the specific topic covered. Because course content will vary, students may repeat the course for a maximum of six hours credit. Prerequisite: Departmental consent.