# Math Courses (MTH)

###### Pre-Algebra (3)

Developmental / remedial instruction including operations with whole numbers, decimals, and fractions. Ratio, percent and equation solving will be emphasized. Note: This course is for institutional credit only and will not be used in meeting degree requirements. This course will not substitute for any general studies requirement.

###### Fundamentals of Algebra (3)

Developmental / remedial instruction including integer and rational arithmetic, linear equations, inequalities, integer exponents, polynomials and factoring, rational expression. Prerequisite: Placement or a grade of C or better in MTH 0096. Note: This course is for institutional credit only and will not be used in meeting degree requirements. This course will not substitute for any general studies requirement.

###### Intermediate Algebra (3)

Developmental / remedial instruction including real and complex numbers; polynomials and factoring; rational exponents; roots and radicals; linear equations and inequalities; quadratic equations; and graphing. Prerequisite: placement or a grade of C or better in MTH 1100. Note: This course is for institutional credit only and will not be used in meeting degree requirements. This course will not substitute for any general studies requirement.

###### Finite Mathematics (3)

Topics include a survey of logic, sets, counting, permutations, combinations, basic probability, an introduction to statistics, and matrices and their applications to graph theory. Prerequisite: appropriate score on mathematics placement test, advanced placement, or a grade of C or better in MTH 1105. Note: Credit will not count toward a major or minor in mathematics.

###### Pre-Calculus Algebra (3)

Topics include the algebra of functions, including polynomial, rational, exponential, and logarithmic functions. The course also contains systems of equations and inequalities, linear and quadratic equations and inequalities, graphs of polynomials, and the binomial theorem. Prerequisite: appropriate score on mathematics placement test, advanced placement, or a grade of C or better in MTH 1105. Note: Credit will not count toward a major or minor in mathematics.

###### Pre-Calculus Trigonometry (3)

This course covers trigonometric functions including definitions, identities, and trigonometric equations, applications as well as properties and graphs of trigonometric functions and their inverses. Also included are the law of sines, the law of cosines, polar coordinates, vectors, and conic sections. Prerequisite: MTH 1112 with a grade of C or better or advanced placement. Note: Credit will not count toward a major or minor in mathematics.

###### Calculus I (4)

Topics include limits of functions, derivatives of algebraic, trigonometric, exponential and logarithmic functions and their inverses and the definite integral and its application to area problems. Applications of the derivative including maximum and minimum problems, and curve sketching using calculus. Prerequisite: A grade of C or better in MTH 1114 or advanced placement.

###### Calculus II (4)

Applications of integration (such as volume, arc length, work, and average value), techniques of integration, indeterminate forms, infinite series, polar coordinates, and parametric equations. Prerequisite: MTH 1125.

###### Calculus and its Applications (3)

An introduction to the basic ideas and techniques of differential and integral calculus, especially as they relate to problems involving maximum and minimum values of functions and marginal analysis. Prerequisite: MTH 1112 or 1114 with a grade of C or better, or advanced placement. Note: Credit will not count toward a major or minor in mathematics.

###### Introductory Statistics (3)

A beginning course in statistics intended for students in a wide variety of fields of study. Course topics include descriptive statistics, normal distribution, correlation and regression, basic concepts of probability, binomial distribution, sampling distribution, confidence intervals and hypothesis testing for mean(s) and proportion(s). Students also have the opportunity to analyze data sets using Statistics software. Prerequisite: A grade of C or better in MTH 1112. Note: Credit will not count toward Area III requirements nor will it count toward any major or minor in mathematics.

###### Applied Discrete Mathematics (3)

Discrete mathematics with a computer science orientation is presented. Topics include sets, relations, logic, algorithms, and recursion. Prerequisite: A grade of C or better in MTH 1112. Note: Credit will not count toward Area III requirements nor will it count toward any major or minor in mathematics.

###### Computer Programming for Mathematics (3)

Structured programming of a mathematical nature, arithmetic computations, algorithm design and control structures, functions and subroutines intrinsic functions, array processing. Prerequisite: MTH 1125.

###### Calculus III (4)

Topics include vector functions, multi-variable functions, partial derivatives and their applications, quadric surfaces, multiple integrals, and vector calculus, including Green’s theorem, curl, divergence, surface integrals, and Stoke’s theorem. Prerequisite: MTH 1126.

###### Applied Linear Algebra (3)

This course covers some topics in Linear Algebra with an orientation towards applications in fields that use least squares regression. Topics include the algebra and geometry of vectors, matrices and their operations, determinants, systems of linear equations, linear independence, transformations, linearization and least square problems. Prerequisite: MTH 1125

###### Mathematical Concepts for K-6 Teachers I (3)

An examination of some of the major topics encountered in the teaching of elementary mathematics with emphasis on number theory order of operations, definitions of and operations with rational and irrational numbers, estimation, definitions and algorithms of the four operations, numeration systems, bases other than 10, and problem solving. Prerequisite: MTH 1110 or 1112. Note: Credit will not count toward Area III requirements nor will it count toward any major or minor in mathematics.

###### Mathematical Concepts for K-6 Teachers II (3)

An examination of some of the major topics encountered in the teaching of elementary school geometry with emphasis on measurement, area, volume, congruence, polygons, circles, constructions, motion geometry, polyhedra, and similarity. Prerequisite: MTH 1110 or 1112. Note: Credit will not count toward Area III requirements nor will it count toward any major or minor in mathematics.

###### Selected Topics (3)

Examination of a designated topic of special and/or current interest and importance, which is generally not covered in regularly offered courses in the mathematics curriculum.

###### Differential Equations (3)

An introduction to ordinary differential equations. Topics include first order methods, linear equations, the Laplace transforms, systems of equations, and applications. Prerequisite: MTH 2227.

###### Introduction to Advanced Mathematics (3)

Topics include set theory, equivalence relations and partitions, logic, number systems, functions, and proof writing techniques. Prerequisite: MTH 1126.

###### College Geometry (3)

Axiomatic systems; incidence and separation properties of planes and space; metric and synthetic approaches; geometric inequalities; parallel postulate; area-theory; circles in a plane; models for hyperbolic and elliptic geometries; and constructions with a straightedge and compass. Prerequisite: MTH 3318.

###### Linear Algebra (3)

Matrices, systems of equations, determinants, eigenvalues and eigenvectors. Prerequisite: MTH 1126.

###### Statistical Methods and Computations (3)

This course is designed to provide students with a foundation in statistical methods, including data exploring and strategies in sample surveys, estimation and testing hypotheses of means and variances, analysis of variance, regression analysis, contingency tables. These concepts are taught with heavy emphasis on statistical computing software and real world datasets. Students will learn basic skills of SAS, a statistical software package that is widely used in business, industry, government, and research. Prerequisite: MTH 2210.

###### Survey Sampling (3)

Topics include sampling frames, questionnaire design, simple random, systematic, stratified, and cluster sampling, comparing domain means, contingency table analysis. Prerequisite: MTH 2210.

###### Vector Calculus (3)

Differentiation in several variables. Line and surface integrals. Potential theory and differential Prerequisite: MTH 2227.

###### Discrete Mathematics (3)

Topics can include counting techniques such as Pigeonhole Principle, permutations, combinations, binomial coefficients, inclusion-exclusion, and relations and graphs. Prerequisites: MTH 2227 and 3318.

###### Graph Theory (3)

The elements of graph theory including: trees; bipartite, chordal and planar graphs; graph coloring; graph traversals; and flows. Prerequisites: MTH 2227 and 3318 or permission of instructor.

###### Numerical Analysis (3)

Topics include finite differences, interpolation, numerical integration and differentiation, solutions of equations of one variable, linear systems, and numerical solutions of ordinary differentia equations. Prerequisites: MTH 2220, 2227 and 3331, or permission of instructor.

###### Real Analysis I (3)

The real number system, completeness, limits, continuity, sequences, differentiation, and the Riemann integral. Prerequisites: MTH 2227 and 3318.

###### Real Analysis II (3)

Sequences and series of functions, series, and a continuation of the integral to include the Fundamental Theorem of Calculus. Prerequisite: MTH 4424.

###### Complex Analysis (3)

Complex numbers, elementary functions and their mappings, complex limits and power Cauchy integral formula. Prerequisites: MTH 2227 and 3318 or permission of instructor.

###### Number Theory (3)

Divisibility, congruencies, prime numbers, Fermat’s theorem, Diophantine equations, number theoretic functions. Prerequisites: MTH 2227, 3318.

###### Abstract Algebra I (3)

Properties of the integers, modular arithmetic. Elementary theory of groups, finite groups, subgroups, cyclic groups, permutation groups. Group isomorphisms and homomorphisms. Prerequisites: MTH 2227, 3318, and 3331.

###### Abstract Algebra II (3)

Elementary theory of rings, polynomial rings, divisibility, unique factorization domains. Integral domains, ideals, factor rings, divisibility in integral domains. Elementary theory of fields. Extension fields. Prerequisite: MTH 4441.

###### Mathematics of Finance (3)

The fundamental concepts of financial mathematics and how these concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in the following: reserving, valuation, pricing, asset/ liability management, investment income, capital budgeting, and valuing contingent flows. Prerequisite: MTH 4451.

###### Topology (3)

An introduction to metric and topological spaces and associated topics, separation axioms, compactness, and connectedness. Prerequisites: MTH 2227, 3318.

###### Internship in Mathematics Education (9)

The Professional Internship Program is the culminating clinical field-based experience for students seeking certification in a teaching field. The Professional Internship Program provides the student with the opportunity to conduct classes and assume the role of a teacher while receiving supervision from a classroom teacher and a university supervisor for a period of one full semester. The student will demonstrate skills of the informed, reflective decision maker throughout the internship experience. Prerequisite: admission to TEP. Co-requisite: SED 4454.

###### Study Abroad in Mathematics (1-3)

Provides the opportunity for students to experience mathematics in the global community through cultural immersion in a study abroad program. Prerequisites: 6 credit hours at the 4000-level, permission of instructor, and successful completion of TROY Study Abroad Program requirements and fees.

###### Methods and Materials for the Secondary Teacher (3)

A survey of teaching methods and materials appropriate for teaching in the content areas for grades 6-12. Topics addressed will include teacher evaluation in the public schools, collaboration with special education teachers, and lesson planning formats. In addition, teaching methods, selections organization and use of mathematics materials for grades 6-12 will be covered in detail. A professional laboratory experience is included in this course. Prerequisite: admission to TEP.

###### Senior Seminar (1 to 3 credit hours)

Individualized study of a topic in mathematics culminating in a written and oral presentation. Prerequisites: MTH 3318 and senior status.

###### Guided Independent Research (1 to 3 credit hours)

Additional information is indexed under Independent Study and Research.

###### Guided Independent Study (1 to 3 credit hours)

Additional information is indexed under Independent Study and Research.

###### Internship in Mathematics/Statistics (1-3)

A supervised experience in planning, staging, and evaluating a formal practicum in a related field. Prerequisites: 6 credit hours at the 4000-level or MTH 4451, or permission of the department chair.