# Mathematics

Majors:

- Bachelor of Arts, Mathematics
- Bachelor of Science, Applied Mathematical Economics
- Bachelor of Science, Mathematics

Minors:

The B.A. program in mathematics provides for a breadth of mathematical study within the context of a liberal arts degree. It may be chosen as a preparation for a professional career in business, education, law or social science. It affords the student a significant distribution of courses in the humanities and social sciences so that he or she can develop a concentration in a field other than mathematics. The student's career goals will generally suggest desirable upper level mathematics electives. For example, prospective secondary mathematics teachers should participate in the licensure program and elect courses such as MTH 370, MTH 395, and MTH 466. Students with an interest in business, law, or social science should complete the probability and statistics sequence MTH 411-MTH 412.

The B.S. program in mathematics provides a foundation for students who wish to pursue graduate studies in any area of the mathematical sciences, to enter the actuarial profession, or to enter careers where mathematics is used in an engineering or science setting. A preparation for graduate programs in a mathematical science should include electives such as MTH 342, MTH 404and MTH 471. Those planning on pursuing an actuarial career should take the actuarial science minor described below. To prepare for using mathematics in an applied context, some useful elective courses are MTH 403, MTH 404, and the MTH 411-MTH 412 sequence. All students pursuing a bachelor of science in mathematics are required to complete a minor in another subject.

The B.S. program in applied mathematical economics provides a foundation in economics, mathematics and statistics needed for graduate study in economics or applied statistics, or for research and technical careers in business or government service. This degree is offered jointly by the Department of Mathematics and the Department of Economics and Finance in the School of Business Administration.

The basic courses are offered every term:

MTH 168 | Analytic Geometry & Calculus I | 4 |

MTH 169 | Analytic Geometry & Calculus II | 4 |

MTH 218 | Analytic Geometry & Calculus III | 4 |

MTH 219 | Applied Differential Equations | 3 |

MTH 308 | Foundations & Discrete Mathematics | 3 |

MTH 310 | Linear Algebra & Matrices | 3 |

Most majors will take MTH 218 and MTH 308 in the same term.

The required core courses are offered at least once a year:

MTH 330 | Intermediate Analysis | 3 |

MTH 361 | Introduction to Abstract Algebra | 3 |

MTH 411 | Probability & Statistics I | 3 |

MTH 430 | Real Analysis | 3 |

However, most of the other upper-level electives for the major are offered only once every two years; thus careful planning for a student's upper-level electives should be done in consultation with the advisor. In addition, the symbolic logic course, PHL 302, is a recommended general education course for all mathematics majors.

A minor in mathematics consists of twelve semester hours (300-400 level).

A minor in actuarial science is offered through the Department of Mathematics. This consists of courses in calculus, statistics, theory of interest, economics, and finance, and is designed to prepare the student to take the actuarial examinations in probability and financial mathematics.

##### Faculty

Joe D. Mashburn, Chairperson

Distinguished Service Professor: Peterson

Professors Emeriti: Back, Friel, Gantner, Kauflin, McCloskey, Mushenheim, Rice, Schleppi, Shaughnessy, R. Steinlage, Strange

Professors: Abueida, Eloe, Higgins, Islam, Mashburn, Raffoul

Associate Professors: Busch, Diestelkamp, Driskell, Gorton, Hovey, Krakowski, Liu, Usman

Assistant Professors: Keen, Kublik, Qumsiyeh, Ren, Yengulalp

Lecturers: Harrison, Ober, Saintignon, Simon, L. Steinlage

## Bachelor of Arts with a major in Mathematics (mth) Minimum 124 Hours

Common Academic Program (CAP) | ||

*credit hours will vary depending on courses selected | ||

First-Year Humanities Commons ^{1} | 12 | |

The West & the World | ||

Introduction to Religioius & Theological Studies | ||

Introduction to Philosophy | ||

Writing Seminar I ^{2} | ||

Second-Year Writing Seminar ^{3} | 0-3 | |

Writing Seminar II | ||

Oral Communication | 3 | |

Principles of Oral Communication | ||

Mathematics | 3 | |

Social Science | 3 | |

Arts | 3 | |

Natural Sciences | 7 | |

Crossing Boundaries | variable credit | |

Faith Traditions | ||

Practical Ethical Action | ||

Inquiry | ||

Integrative | ||

Advanced Study | variable credit | |

Philosophy and/or Religious Studies | ||

Historical Studies | ||

Diversity and Social Justice | 3 | |

Major Capstone | 0-3 |

^{1} | Completed with ASI 110 and ASI 120. |

^{2} | Or ENG 100A and ENG 100B, or ENG 200H, by placement. |

^{3} | Completed with ENG 200H or ASI 120. |

Liberal Studies Curriculum | ||

Creative and Performing Arts (May include CAP Arts) | 3 | |

L2 Proficiency (Proficiency in a language other than English) | 0-11 | |

Literature (May include CAP Components) | 3 | |

Natural Sciences (Satisfies CAP Natural Science) | 11 | |

Social Sciences (Includes CAP Social Science) | 12 |

Major Requirements | 36 | |

MTH 168 | Anly Geom & Calc I (Satisfies CAP Mathematics) | 4 |

MTH 169 | Anly Geom & Calc II | 4 |

MTH 218 | Anly Geom & Calc III | 4 |

MTH 308 | Fndtn & Discrete Mth | 3 |

MTH 310 | Lin Alg & Matrices | 3 |

MTH 330 | Intermed Analysis | 3 |

MTH 361 | Intro-Abstrct Algbra | 3 |

MTH 411 | Probablty & Stat I | 3 |

MTH 480 | Math Capstone (Satisfies CAP Major Capstone) | 3 |

Select two MTH courses (300/400 level) | 6 |

Breadth | ||

ASI 150 | Intr to the Univ Exp | 1 |

Total Hours to total at least | 124 |

## Bachelor of Science with a major in Applied Mathematical Economics (mte) Minimum 120 Hours

Common Academic Program (CAP) | ||

*credit hours will vary depending on courses selected | ||

First-Year Humanities Commons ^{1} | 12 | |

The West & the World | ||

Introduction to Religioius & Theological Studies | ||

Introduction to Philosophy | ||

Writing Seminar I ^{2} | ||

Second-Year Writing Seminar ^{3} | 0-3 | |

Writing Seminar II | ||

Oral Communication | 3 | |

Principles of Oral Communication | ||

Mathematics | 3 | |

Social Science | 3 | |

Arts | 3 | |

Natural Sciences | 7 | |

Crossing Boundaries | variable credit | |

Faith Traditions | ||

Practical Ethical Action | ||

Inquiry | ||

Integrative | ||

Advanced Study | variable credit | |

Philosophy and/or Religious Studies | ||

Historical Studies | ||

Diversity and Social Justice | 3 | |

Major Capstone | 0-3 |

^{1} | Completed with ASI 110 and ASI 120. |

^{2} | Or ENG 100A and ENG 100B, or ENG 200H, by placement. |

^{3} | Completed with ENG 200H or ASI 120. |

Science Breadth Requirements | ||

Satisfies CAP Natural Science | ||

CPS 150 | Algorthm&Progrm I | 4 |

CPS 151 | Algorthm&Progrm II | 4 |

Select one natural sciences group from: | 8 | |

Concepts of Bio I and Concepts-Bio Lab I and Concepts of Bio II and Concepts-Bio Lab II | ||

General Chemistry and Gen Chemistry Lab and General Chemistry and Gen Chemistry Lab | ||

Physical Geology and Physical Geology Lab and Geolgcl Hst-Earth and Geolgcl Hst-Earth Lb | ||

Gen Physics I Mech and Gen Phy II Ele & Mag and Gen Physics Lab I and Gen Physics Lab II |

Major Requirements | 48 | |

Mathematics | ||

MTH 168 | Anly Geom & Calc I (Satisfies CAP Mathematics) | 4 |

MTH 169 | Anly Geom & Calc II | 4 |

MTH 218 | Anly Geom & Calc III | 4 |

MTH 308 | Fndtn & Discrete Mth | 3 |

MTH 310 | Lin Alg & Matrices | 3 |

MTH 330 | Intermed Analysis | 3 |

MTH 411 | Probablty & Stat I | 3 |

MTH 412 | Probablty & Stat II | 3 |

MTH 480 | Math Capstone (Satisfies CAP Major Capstone) | 3 |

Economics | ||

ECO 203 | Prin of Microecon (Satisfies CAP Crossing Boundaries: Inquiry) | 3 |

ECO 204 | Prin of Macroecon (Satisfies CAP Crossing Boundaries: Inquiry) | 3 |

ECO 346 | Intrmd MicroEco Anly | 3 |

ECO 347 | Intrmd MacroEco Anly | 3 |

ECO 441 | Econometrics | 3 |

Select one ECO course (300/400 level) | 3 |

Breadth | ||

ASI 150 | Intr to the Univ Exp | 1 |

Social and Behavioral Sciences (Includes CAP Social Science) | 6 | |

Total Hours to total at least | 120 |

## Bachelor of Science with a major in Mathematics (mth) Minimum 120 Hours

Common Academic Program (CAP) | ||

*credit hours will vary depending on courses selected | ||

First-Year Humanities Commons ^{1} | 12 | |

The West & the World | ||

Introduction to Religioius & Theological Studies | ||

Introduction to Philosophy | ||

Writing Seminar I ^{2} | ||

Second-Year Writing Seminar ^{3} | 0-3 | |

Writing Seminar II | ||

Oral Communication | 3 | |

Principles of Oral Communication | ||

Mathematics | 3 | |

Social Science | 3 | |

Arts | 3 | |

Natural Sciences | 7 | |

Crossing Boundaries | variable credit | |

Faith Traditions | ||

Practical Ethical Action | ||

Inquiry | ||

Integrative | ||

Advanced Study | variable credit | |

Philosophy and/or Religious Studies | ||

Historical Studies | ||

Diversity and Social Justice | 3 | |

Major Capstone | 0-3 |

^{1} | Completed with ASI 110 and ASI 120. |

^{2} | Or ENG 100A and ENG 100B, or ENG 200H, by placement. |

^{3} | Completed with ENG 200H or ASI 120. |

Science Breadth Requirements | ||

Computer Science (CPS 150 applies to CAP Natural Sciences) | 3-4 | |

Progrmmng-Engr & Sci | ||

or CPS 150 | Algorthm&Progrm I | |

Select one natural sciences group from: (Applies to CAP Natural Science) | 8 | |

Concepts of Bio I and Concepts-Bio Lab I and Concepts of Bio II and Concepts-Bio Lab II | ||

General Chemistry and Gen Chemistry Lab and General Chemistry and Gen Chemistry Lab | ||

Physical Geology and Physical Geology Lab and Geolgcl Hst-Earth and Geolgcl Hst-Earth Lb | ||

Gen Physics I Mech and Gen Phy II Ele & Mag and Gen Physics Lab I and Gen Physics Lab II | ||

Select two courses acceptable for science majors | 6 |

Major Requirements | 45 | |

MTH 168 | Anly Geom & Calc I (Satisfies CAP Mathematics) | 4 |

MTH 169 | Anly Geom & Calc II | 4 |

MTH 218 | Anly Geom & Calc III | 4 |

MTH 219 | Appl Diff Equations | 3 |

MTH 308 | Fndtn & Discrete Mth | 3 |

MTH 310 | Lin Alg & Matrices | 3 |

MTH 330 | Intermed Analysis | 3 |

MTH 361 | Intro-Abstrct Algbra | 3 |

MTH 430 | Real Analysis | 3 |

MTH 480 | Math Capstone (Satisfies CAP Major Capstone) | 3 |

Select four MTH courses (300/400 level) ^{1} | 12 |

Breadth | ||

ASI 150 | Intr to the Univ Exp | 1 |

Social and Behavioral Sciences (Includes CAP Social Science) | 6 | |

Total Hours to total at least | 120 |

^{1} | Departmental approval required. |

## Minor in Actuarial Science (acs)

The Minor in Actuarial Science is designed to prepare students to pass the P and FM actuarial tests. It is also designed to supply students with VEE (Validation by Educational Experience) credit in economics, corporate finance, and applied statistics.

The minor contains eight courses in mathematics for a total of twenty-two semester hours. One of these is a course in the theory of interest and one is a seminar which prepares students to take the P test. Mathematics majors will take all but two of the mathematics requirements for the minor as part of their major requirements.

The minor also contains eight courses in accounting, economics, and finance for a total of twenty-four semester hours. Economics and finance majors will take all of these courses as part of their major requirements. They will be able to substitute two of the mathematics courses for those that they are required to take for their major.

A total of forty-six semester hours are required for the minor.

Actuarial Science | ||

ACC 207 | Intro-Financial Acc | 3 |

ECO 203 | Prin of Microecon ^{1} | 3 |

ECO 204 | Prin of Macroecon ^{1} | 3 |

ECO 410 | Bus&Eco Forecasting ^{2} | 3 |

FIN 301 | Intro to Financial Mgt ^{3} | 3 |

FIN 360 | Investments | 3 |

FIN 470 | Fixed Inc Sec | 3 |

FIN 480 | Optns&Futures Mkts | 3 |

MTH 168 | Anly Geom & Calc I | 4 |

MTH 169 | Anly Geom & Calc II | 4 |

MTH 218 | Anly Geom & Calc III | 4 |

MTH 229 | Theory of Interest | 3 |

MTH 328 | Actuarial Prob Sem | 1 |

MTH 411 | Probablty & Stat I | 3 |

MTH 412 | Probablty & Stat II | 3 |

Total Hours | 46 |

^{1} | ECO 203 and ECO 204 together qualify for VEE Economics credit in Economics. |

^{2} | VEE credit in Applied Statistics. |

^{3} | This course counts as VEE credit in Corporate Finance. |

## Minor in Mathematics (mth)

Mathematics | ||

Select four MTH courses (300/400 level) | 12 | |

Total Hours | 12 |

### Courses

**MTH 102. Fundamentals of Math. 3 Hours**

Sets, functions and graphs, exponents, polynomials and algebraic equations, systems of equations.
Prerequisite(s): One year of high school algebra.

**MTH 114. Contemporary Math. 3 Hours**

Study of contemporary mathematical topics and their applications. Topics may include management science, statistics, social choice, size and shape, and computer mathematics.
Prerequisite(s): Two years of high school algebra.

**MTH 116. Precalculus Math. 4 Hours**

Review of topics from algebra and trigonometry including polynomials, functions and graphs, exponential and logarithmic functions, trigonometric functions and identities.
Prerequisite(s): Two years of high school algebra.

**MTH 128. Finite Mathematics. 3 Hours**

Topics from mathematics used in business including systems of equations, inequalities, matrix algebra, linear programming and logarithms; applications to compound interest, annuities and other finance problems.
Prerequisite(s): MTH 102 or sufficient college preparatory mathematics.

**MTH 129. Calculus for Business. 3 Hours**

Topics from differential and integral calculus used in business; applications to optimizing financial functions, marginal functions in economics, and consumer or producer surplus.
Prerequisite(s): MTH 128 or sufficient college preparatory mathematics.

**MTH 137. Calculus I with Review. 4 Hours**

Introduction to the differential and integral calculus with an extensive review of algebra and trigonometry; differentiation and integration of algebraic and transcendental functions with applications.
Prerequisite(s): Two years of high school algebra.

**MTH 138. Calculus I with Review. 4 Hours**

Introduction to the differential and integral calculus with an extensive review of algebra and trigonometry; differentiation and integration of algebraic and transcendental functions with applications.
Prerequisite(s): MTH 137.

**MTH 148. Introductory Calculus I. 3 Hours**

Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to the life and social sciences.
Prerequisite(s): MTH 116 or equivalent.

**MTH 149. Introductory Calculus II. 3 Hours**

Continuation of MTH 148. Multivariable calculus, matrices, difference equations, probability, discrete and continuous random variables, and differential equations with applications to the life and social sciences.
Prerequisite(s): MTH 138 or MTH 148.

**MTH 168. Analytic Geometry & Calculus I. 4 Hours**

Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to science and engineering.
Prerequisite(s): MTH 116 or equivalent.

**MTH 169. Analytic Geometry & Calculus II. 4 Hours**

Continuation of MTH 168. Conic sections, techniques of integration with applications to science and engineering, infinite series, indeterminate forms, Taylor's theorem.
Prerequisite(s): MTH 138 or MTH 168.

**MTH 204. Mathematical Concepts I. 3 Hours**

First course of a two-semester sequence designed for pre-service teachers. Concepts necessary for an understanding of the structure of arithmetic and its algorithms, number patterns, sets, problem solving, percent, relation and proportion, use of calculators.
Prerequisite(s): One year of high school algebra; one year of high school geometry.

**MTH 205. Mathematical Concepts II. 3 Hours**

Continuation of MTH 204. Topics include probability, representing and interpreting data, the metric system, elementary geometry, geometric patterns, coordinate geometry, algebra and geometry, transformations, computer literacy. Prerequisite(s): MTH 204.

**MTH 207. Introduction to Statistics. 3 Hours**

Introduction to the concepts of statistical thinking for students whose majors do not require calculus. Methods of presenting data, including graphical methods. Using data to make decisions and draw conclusions. Basic ideas of drawing a sample and interpreting the information that it contains.
Prerequisite(s): Two years of high school algebra.

**MTH 214. Mathematical Concepts for Middle School Teachers. 3 Hours**

Concepts necessary for an understanding of the arithmetic taught in both elementary and middle grades. Includes a study of the structure of arithmetic and its algorithms; problem solving; reasoning and proof; proportional reasoning; use of computers and calculators to solve problems.
Prerequisite(s): Two years of high school algebra.

**MTH 215. Algebra, Functions & Graphs. 3 Hours**

Development of the algebra of various families of functions including polynomial, exponential, logarithmic, and trigonometric functions; factoring and roots; interpretation of graphs; use of calculators and data collection devices to solve problems.
Prerequisite(s): MTH 214.

**MTH 216. Calculus Concepts & Applications. 3 Hours**

Develop conceptual understanding of basic calculus concepts; introduction to the notion of limit; rates of change; slopes and area computations; use of calculators and data collection devices to make predictions, estimations, and solve problems. Prerequisite(s): MTH 215.

**MTH 218. Analytic Geometry & Calculus III. 4 Hours**

Continuation of MTH 169. Solid analytic geometry, vectors and vector functions, multivariable calculus, partial derivatives, multiple integrals.
Prerequisite(s): MTH 169.

**MTH 219. Applied Differential Equations. 3 Hours**

First order equations, linear equations with constant coefficients, systems of equations, the Laplace transform, numerical methods, applications.
Prerequisite(s): MTH 218.

**MTH 229. Theory of Interest. 3 Hours**

Rigorous, calculus-based treatment of the Theory of Interest. Topics covered include interest, compounding, discounting, annuities, sinking funds, amortization, bonds, yield rates, and applications of these ideas and processes to problems in finance.
Prerequisite(s): MTH 169.

**MTH 250. Advanced Technical Mathematics. 3 Hours**

Appropriate analytical techniques for students of engineering technology; topics include integration by parts, multivariable calculus, complex numbers, matrices and system of linear equations, and first and second order differential equations. Applications are appropriate for the engineering technology programs (circuits, vibrations, and heat transfer).
Prerequisite(s): MTH 138 or MTH 168.

**MTH 266. Discrete & Finite Mathematics for Middle School Teachers. 3 Hours**

Topics in finite and discrete mathematics; linear programming; applications in finance; graph theory; mathematics of social choice; logic; use of computers and calculators to model and solve problems.
Prerequisite(s): MTH 214.

**MTH 270. Geometry Concepts & Applications. 3 Hours**

Introduction to the geometry of two- and three-dimensional space; patterns in geometry; measurement systems; transformations and similarity; coordinate geometry; the algebra of geometry; trigonometry; use of dynamic computer software to explore geometric concepts.
Prerequisite(s): MTH 214.

**MTH 290. Topics in Mathematics. 1-3 Hours**

Exploration of varying topics appropriate for the needs of the pre-service training of teachers of mathematics. May be repeated as topics change.
Prerequisite(s): One mathematics course beyond MTH 102; permission of department chairperson and/or instructor.

**MTH 295. Historical Roots of Elementary Mathematics. 3 Hours**

Fundamental historical development of modern arithmetic, algebra, geometry, and number systems from early Egyptian, Babylonian, and Greek sources. Students may not receive credit for both this course and MTH 395.
Prerequisite(s): MTH 214.

**MTH 308. Foundations & Discrete Mathematics. 3 Hours**

An introduction to proof using topics in foundational and discrete mathematics; propositional logic; number theory; sequences and recursion; set theory; relations; combinatorics; linear programming.
Prerequisite(s): MTH 169.

**MTH 310. Linear Algebra & Matrices. 3 Hours**

Fundamental concepts of vector spaces, determinants, linear transformations, matrices, inner product spaces, and eigen-vectors. Offered each term.
Prerequisite(s): MTH 218, MTH 308. (May be taken as corequisites).

**MTH 328. Actuarial Probability Seminar. 1 Hour**

Problem solving seminar to develop and improve skills in applied probability. This seminar will focus on actuarial applications of probability theory.
Prerequisite(s): MTH 411.

**MTH 329. Actuarial Finance Seminar. 1 Hour**

Problem solving seminar to develop and improve skills in applied mathematical finance. This seminar will focus on integrating the mathematical presentation of the Theory of Interest to the field of finance.
Prerequisite(s): FIN 470; MTH 229.

**MTH 330. Intermediate Analysis. 3 Hours**

Theoretical development of the calculus of a real-valued function of a real variable. Topics include the algebraic and topological properties of the real line, limits of sequences and functions, continuity, differentiability, and integration. Prerequisite(s): MTH 310.

**MTH 342. Set Theory. 3 Hours**

Elementary set theory including relations, functions, indexed families, denumerable and nondenumerable sets, cardinal and ordinal arithmetic, Zorn's Lemma, the well-ordering principle and transfinite induction.
Prerequisite(s): MTH 218, MTH 308.

**MTH 343. Mathematics for Electrical & Computer Engineers. 3 Hours**

Linear algebra and matrices, complex variables, mathematical transforms and their inter-relations. Focus on mathematical theories as well as applications and an extensive use of MATLAB.
Prerequisite(s): MTH 219.

**MTH 361. Introduction to Abstract Algebra. 3 Hours**

Fundamental concepts of groups, rings, integral domains and fields.
Prerequisite(s): MTH 218, MTH 308.

**MTH 367. Statistical Methods I. 3 Hours**

Probability distributions including binomial, hypergeometric, Poisson, and normal. Estimation of population mean and standard deviation: Confidence intervals and tests of hypotheses using t-, Chi-square, and F-statistics. Mathematics majors enroll in MTH 411 instead of MTH 367.
Prerequisite(s): MTH 149 or MTH 169.

**MTH 368. Statistical Methods II. 3 Hours**

Distribution-free methods including rank tests, sign tests, and Kolmogorov-Smirnov test. Method of least squares, correlation, linear regression, analysis of variance. Design of experiments and computer applications. Mathematics majors enroll in MTH 412 instead of 368.
Prerequisite(s): MTH 367.

**MTH 370. Introduction to Higher Geometry. 3 Hours**

Projective, affine, and hyperbolic geometries using synthetic and/or analytic techniques.
Prerequisite(s): MTH 218, MTH 308.

**MTH 376. Number Theory. 3 Hours**

Topics include Diophantine equations, Chinese Remainder theorem, Mobius inversion formula, quadratic residues and the Law of Quadratic Reciprocity, Gaussian integers, and integral quaternions.
Prerequisite(s): MTH 218, MTH 308.

**MTH 395. Development of Mathematical Ideas. 3 Hours**

The evolution of mathematical ideas and techniques from ancient times to the present with emphasis on the Greek era. Famous people and famous problems. Chronological outline of mathematics in each of its branches along with applications.
Prerequisite(s): MTH 218, MTH 308.

**MTH 403. Boundary Value Problems. 3 Hours**

Introduction to the Sturm-Liouville problem. Fourier trigonometric series, Fourier integrals, Bessel functions, and Legendre polynomials. The heat equation, wave equation, and Laplace's equation with applications. Solutions by the product method.
Prerequisite(s): MTH 219, MTH 310.

**MTH 404. Complex Variables. 3 Hours**

Functions of a complex variable, conformal mapping, integration in the complex plane. Laurent series and residue theory.
Prerequisite(s): MTH 219.

**MTH 411. Probability & Statistics I. 3 Hours**

Mathematical probability, random variables, Bayes' Theorem, Chebyshev's Inequality, Binomial, Poisson, and Normal probability laws, moment generating functions, limit theorems, descriptive statistics, large sample statistical inference. MTH 308 is recommended as preparation for this course.
Prerequisite(s): MTH 218.

**MTH 412. Probability & Statistics II. 3 Hours**

Multivariate distributions, transformations of random variables, sampling distribution theory, estimation of parameters including maximum likelihood, confidence intervals, the Neyman-Pearson lemma, tests of hypotheses, likelihood ratio tests.
Prerequisite(s): MTH 411.

**MTH 430. Real Analysis. 3 Hours**

Continuation of MTH 330. Topics include the theory of convergence of sequences and series of functions in the context of metric spaces, uniform continuity, uniform convergence, and integration.
Prerequisite(s): MTH 330.

**MTH 435. Advanced Multivariate Calculus. 3 Hours**

Topics include directional derivatives, chain rule, Lagrange multipliers, Taylor's formula, the mean value theorem, inverse mapping theorem, implicit function theorem, integration, Fubini's theorem, change of variables, line integrals, Green's theorem and Stoke's theorem. Prerequisite(s): MTH 310.

**MTH 440. Introduction to Mathematical Modeling. 3 Hours**

Introduction to the use of mathematical techniques and results in constructing and modifying models designed to solve problems encountered in everyday life. Computer simulation and limitations thereof, dimensional analysis, scaling and approximations at various levels are discussed.
Prerequisite(s): MTH 219, MTH 310.

**MTH 441. Mathematics Clinic. 1 Hour**

Student teams will be responsible for the development and/or modification and testing of a mathematical model designed for a particular purpose. Faculty guidance.
Prerequisite(s): MTH 440; permission of department chairperson.

**MTH 445. Special Topics in Mathematics. 1-3 Hours**

Lectures in specialized areas such as abstract algebra, applied mathematics, complex variables, differential forms, functional analysis, Galois theory, game theory, general topology, normed linear spaces, probability theory, real variables, topological groups. May be taken more than once.
Prerequisite(s): Permission of department chairperson.

**MTH 458. Mathematical Models in Finance. 3 Hours**

Mathematical models in finance which include discrete and continuous models for stock price, interest rate model, bond pricing model, and option pricing model. Quantitative methods are introduced and employed. The methods include Black-Scholes formula, Monte-Carlo simulation, and binomial tree. Markowitz's optimal portfolio selection method is introduced and employed.
Prerequisite(s): MTH 310.

**MTH 465. Linear Algebra. 3 Hours**

Vector spaces, linear transformations and matrices, determinants, inner product spaces, invariant direct-sum decomposition and the Jordan canonical form. Prerequisite(s): MTH 310.

**MTH 466. Graph Theory & Combinatiorics. 3 Hours**

Graphs as algebraic structures; Eulerian, Hamiltonian, complete, connected and planar graphs. Applications include scheduling and routing problems. Discussion of algorithms for optimal or near-optimal solutions. Combinatorial topics could include generating functions, recurrence relations, Polya's theorem and Ramsey Theory. Prerequisite(s): MTH 308 or MTH 310.

**MTH 467. Combinatorial Design Theory. 3 Hours**

Topic include discussion of Latin squares, mutually orthogonal Latin squares, orthogonal and perpendicular arrays, Steiner triple systems, block designs, difference sets, and finite geometries.
Prerequisite(s): MTH 308.

**MTH 471. Topology. 3 Hours**

Introduction to topological spaces and continuous functions including a study of separation and countability axioms and elementary properties of metric spaces, connected spaces, and compact spaces.
Prerequisite(s): MTH 308.

**MTH 477. Honors Thesis Project. 3 Hours**

First of two courses leading to the selection, design, investigation, and completion of an independent, original Honors Thesis project under the guidance of a faculty research advisor. Restricted to students in the University Honors Program with permission of the program director and department chairperson. Students pursuing an interdisciplinary thesis topic may register for three semester hours each in two separate disciplines in consultation with the department chairpersons. Prerequisite(s): Approval of University Honors Program.

**MTH 478. Honors Thesis Project. 3 Hours**

Second of two courses leading to the selection, design, investigation, and completion of an independent, original Honors Thesis project under the guidance of a faculty research advisor. Restricted to students in the University Honors Program with permission of the program director and department chairperson. Students pursuing an interdisciplinary thesis topic may register for three semester hours each in two separate disciplines in consultation with the department chairpersons. Prerequisite(s): Approved 477; approval of University Honors Program.

**MTH 480. Math Capstone. 3 Hours**

No description available.

**MTH 490. Readings in Mathematics. 1-3 Hours**

Individual study in specialized areas carried out under the supervision of a staff member. May be taken more than once.
Prerequisite(s): Permission of department chairperson.