# Mathematics Courses (MTH)

## MTH 0096 - 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.*

## MTH 1100 - 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.*

## MTH 1105 - 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.*

## MTH 1110 - 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.*

## MTH 1112 - 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.*

## MTH 1114 - 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.*

## MTH 1125 - 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.*

## MTH 1126 - 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.*

## MTH 2201 - 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.*

## MTH 2215 - 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.*

## MTH 2220 - 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.*

## MTH 2227 - 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.*

## MTH 2230 - 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*

## MTH 2251 - 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.*

## MTH 2252 - 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.*

## MTH 3300 - 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.

## MTH 3311 - 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.*

## MTH 3318 - Introduction to Advanced Mathematics (3)

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

## MTH 3325 - 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.*

## MTH 3331 - Linear Algebra (3)

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

## MTH 3364 - Vector Calculus (3)

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

## MTH 4412 - 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.*

## MTH 4415 - Introduction to Partial Differential Equations (3)

Partial differential equations and boundary value problems, Fourier series, the heat
equations, vibrations of continuous systems, the potential equation, spectral methods.* Prerequisites: MTH 3311 and MTH 3331*

## MTH 4420 - 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.*

## MTH 4422 - 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.*

## MTH 4424 - Real Analysis I (3)

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

## MTH 4425 - 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.*

## MTH 4426 - 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.*

## MTH 4436 - Number Theory (3)

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

## MTH 4437 - Matrix Analysis and Applications (3)

Fundamentals of operators in finite dimensional Hilbert spaces, mapping and algebras,
functional calculus, matrix monotone and matrix convex functions, quantum entropy,
matrix means, majorization and singular values. *Prerequisites: MTH 4424 and MTH 3331*

## MTH 4441 - 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.*

## MTH 4442 - 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.*

## MTH 4460 - Topology (3)

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

## MTH 4474 - 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.*

## MTH 4480 - 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.*

## MTH 4481 - 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.*

## MTH 4490 - 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.*

## MTH 4491-92 - Guided Independent Research (1 to 3 credit hours)

Additional information is indexed under Independent Study and Research.

## MTH 4493-94 - Guided Independent Study (1 to 3 credit hours)

Additional information is indexed under Independent Study and Research.

## MTH 4498 - Math Education Capstone (3)

This course is designed to culminate the student’s experience in the Math Education
program. Students will complete a comprehensive exam and a capstone project that integrates
educational research , curriculum design, math content application, and assessment.
Based on a literature evaluation of a specific concept or problem in math teaching,
the student will develop a new curricular unit, or redesign an existing one, to be
implemented in a college, high school, or middle school math course. This unit must
apply math content from their degree program courses and the student must assess the
impact of the new/revised unit on student learning. *Prerequisite: Junior Status*

## MTH 4499 - 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.*