Math Sciences

Courses

Mathematics Courses
- Graduate Courses
Statistics Courses
- Graduate Courses
Actuarial Science Courses
- Graduate Courses

Undergraduate Course Offerings Fall 2011 - Summer 2013

Graduate Course Offerings Fall 2012 - Summer 2015

1010 Mathematics for General Studies. Three credits. Prerequisites: Two years of high school algebra and a Math Enhanced ACT of at least 19 or DSPM 0850 or COMPASS placement. Course satisfies the General Education Mathematics requirement and is also part of the mathematics sequence for students preparing to become elementary school teachers. Topics include logic, sets, algebraic reasoning, probability, statistics, and consumer mathematics.

1410 Concepts and Structure of Elementary School Mathematics. Three credits. Prerequisites: Two years of high school algebra and a Math Enhanced ACT of at least 19 or DSPM 0850 or COMPASS placement. Algebra-based study of school mathematics in keeping with the recommendations of the National Council of Teachers of Mathematics. Tools for problem solving, set theory, functions, number theory, and examinations of number systems from counting numbers to irrational numbers.

1420 Informal Geometry. Three credits. Prerequisite: A grade of C or better in MATH 1410. Geometry-based study of school mathematics in keeping with the recommendations of the National Council of Teachers of Mathematics. Studies of plane, solid, coordinate, and motion geometry as well as constructions, congruence, similarity, and concepts of measurement. A variety of instructional technology tools investigated.

1530 Applied Statistics. Three credits. Prerequisites: Two years of high school algebra and a Math Enhanced ACT 19 or greater or equivalent. Descriptive statistics, probability, and statistical inference. The inference unit covers means, proportions, and variances for one and two samples, and topics from one-way ANOVA, regression and correlation analysis, chi-square analysis, and nonparametrics.

1630 College Mathematics for Managerial, Social, and Life Sciences. Three credits. Prerequisites: Two years of high school algebra and a Math Enhanced ACT greater than 25 or MATH 1710. Topics include solving systems of linear equations, Leontief models, linear programming, mathematics of finance, set theory, and probability theory.

1710 College Algebra. Three credits. Prerequisite: DSPM 0850 or two years of high school algebra; a Math Enhanced ACT 19 or greater or COMPASS placement. Course satisfies the General Education Mathematics requirement. Topics include functions—linear, quadratic, exponential, and logarithmic; analysis of graphs; linear systems; inequalities; counting principles; and probability. Graphing calculator required. Course may be taken by correspondence. Not open to those who have had MATH 1730.

1720 Plane Trigonometry. Three credits. Prerequisite: Strong background in algebra recommended. Trigonometric functions of the acute and general angle, circular functions, graphs of trigonometric and inverse functions, identities, solutions of right and general triangles, equations, complex numbers, and vectors. Not open to those who have had MATH 1730. Graphing calculator required.

1730 Pre-Calculus. Four credits. Prerequisite: MATH 1710 or successful completion of high school precalculus course. An integrated and rigorous study of the algebra and trigonometry needed to successfully attempt calculus. Emphasis on functions, their analysis and their applications. Level of algebraic sophistication developed above that found in MATH 1710. Topics included exponentials and logarithms, analysis of graphs, and word problems. Graphing calculator required.

1810 Applied Calculus I. Three credits. Prerequisite: Eligibility to take MATH 1710. First of a four-course sequence. Introduces mathematical modeling applied to real-world problems. Sets, functions, inverse models, limits, continuity, first and second order model building, single variable differentiation, implicit differentiation, inverse problems (exponential and log models). First and second derivatives used to study the behavior of real-world applications.

1820 Applied Calculus II. Three credits. Prerequisite: MATH 1810. Second of a four-course sequence. Riemann Sum, indefinite and definite integrals, modeling using substitution, differential equations with initial conditions, modeling real-world problems using functions of two or more variables, level curves, feasible regions, linear objective functions, system of linear equations, annuities, partial derivatives, least squares, matrix multiplication and addition, inverse matrix, and matrix equations.

1910 Calculus I. Four credits. Prerequisite: MATH 1730 or equivalent. An introduction to calculus with an emphasis on analysis of functions, multidisciplinary applications of calculus, and theoretical understanding of differentiation and integration. Topics include the definition of the derivative, differentiation techniques, and applications of the derivative. Calculus topics related to trigonometric, exponential, and logarithmic functions also included. Course concludes with the fundamental theorem of calculus; the definition of antidifferentiation and the definite integral; basic applications of integrations; and introductory techniques of integration. Graphing calculator required.

1920 Calculus II. Four credits. Prerequisite: MATH 1910. A topics course providing a wide view of different techniques and applications of calculus in the plane. Techniques of integration and applications of integration fully developed. Power series and Taylor series included. Emphasis on multidisciplinary applications includes Taylor series approximation; applications of integration to physics, biology, and business; and geometric and power series applications. Graphing calculator required.

2010 Elements of Linear Algebra. Three credits. Prerequisite: MATH 1910. Vectors and vector spaces, matrices and systems of linear equations, geometry of vector spaces and linear transformations in a vector space.

2050 Probability and Statistics. Three credits. Prerequisite: Calculus I. Data analysis, probability, and statistical inference. The inference material covers means, proportions, and variances for one and two samples, one-way ANOVA, regression and correlation, and chi-square analysis.

2090 Mathematics for Health Professions. Two credits. Enables students in the health professions to apply mathematical concepts to interpret and solve drug dosage calculation problems encountered in fields such as nursing. Includes basic math review, solid and liquid doses of medications for adults and children, solutions, and IV administration. Also includes conversions from metric to household and apothecary measurements. Not open to Mathematics majors or minors.

2110 Data Analysis. One credit. Grouping and classifying technical data. Curve fitting by statistical and nonstatistical methods. Graphing of scientific data. Secondary education in mathematics students should take concurrent or subsequent to MATH 2050.

2130 Mathematics of Finance. Three credits. Prerequisites: Two years of high school algebra and a Math Enhanced ACT 19 or greater or DSPM 0850. Investment finance, including general annuities, evaluation of bonds, and life annuities.

2930 Cooperative Education One to three credits. Experiential learning that occurs in real employment situations. Must be taken in sequence or approved by the director of Cooperative Education. Graded on a pass/fail basis.

2940 Cooperative Education One to three credits. Experiential learning that occurs in real employment situations. Must be taken in sequence or approved by the director of Cooperative Education. Graded on a pass/fail basis.

3020 Applied Calculus III. Three credits. Prerequisites: MATH 1810 and MATH 1820. In-depth study of continuity of single variable functions; inverses of functions; differentiation and integration of various functions including trigonometric functions, logarithmic functions, exponential functions, power functions, and piecewise functions; methods of integration; the Riemann Sum, extensive applications of the fundamental theorem of calculus, and arc length of a curve. Emphasis on real-world applications.

3030 Applied Calculus IV. Three credits. (Same as ACSI 3030.) Prerequisite: MATH 3020 . In-depth study of L'Hopital's Rule, improper integrals, sequences, convergence and divergence of series, Taylor and Maclaurin series, approximations for single-variable functions, two- and three-dimensional vector spaces, vector-valued functions, polar coordinates, and partial differentiation and integration of multivariate functions. Emphasis on blending these topics with real-world applications.

3070 College Geometry. Three credits. Prerequisite: MATH 3460. Advanced treatment of standard topics in Euclidean geometry using informal and axiomatic approaches. Includes proofmaking techniques, traditional and transformational geometry, finite geometries, and a brief introduction to other geometries.

3080 Discrete Structures. Three credits. Prerequisites: CSCI 1160 or CSCI 1170 and MATH 1920 or consent of instructor. Topics include formal logic, proof techniques, matrices, graphs, formal grammars, finite state machines, Turing machines, and binary coding schemes.

3110 Calculus III. Four credits. Prerequisite: MATH 1920. Adjusts calculus techniques developed in the plane (Calculus I and II) to make them applicable in three-dimensional space. Introductory study of the nature of three-dimensional space and definition of the algebraic calculations in three-dimensional space. Differential and integral calculus definitions and techniques revised to appropriately transfer into this new space. Topics include multivariate functions, partial differentiation, partial integration, multiple integration, and multidisciplinary applications.

3120 Differential Equations I. Three credits. Prerequisite: MATH 1920. The solution and application of ordinary differential equations with emphasis on first order equations, second order linear equations, Laplace Transform method, systems of differential equations, and numerical methods.

3180 Introduction to Numerical Analysis. Three credits. (Same as CSCI 3180.) Prerequisites: MATH 1920 and CSCI 1160 or CSCI 1170. Topics include series approximation, finite differences, interpolation, summation, numerical differentiation and integration, iteration, curve fitting, systems of equations and matrices, and error analysis.

3190 Deterministic and Probabilistic Models. Three credits. Corequisite: MATH 2050. Linear programming, network analysis, queuing theory, dynamic programming.

3260 Differential Equations II. Three credits. Prerequisite: MATH 3120. A continuation of MATH 3120 with emphasis on series solutions, method of Frobenius, orthogonal functions, equations of Bessel, Legendre, Gauss, Chebyshev; introduction to partial differential equations.

3300 Discrete Mathematics for Middle Grades Teachers. Three credits. Prerequisites: MATH 1410, MATH 1420, and MATH 1710. Supports the development of prospective middle grades teachers' knowledge of discrete mathematics. Topics include set theoretic topics, logic, counting, probability, graph theoretic topics. Focuses on students' learning discrete mathematics topics as well as the teaching of related mathematical topics to middle grades students. Field experience in a nearby middle school incorporated.

3310 Functions: Connecting Algebra and Geometry for Middle Grades Teachers. Three credits. Prerequisites: MATH 1410, MATH 1420, and MATH 1710. Supports the development of prospective middle grades teachers' knowledge of functions and connections between algebra and geometry. Focuses on students connecting mathematics topics as well as the teaching of mathematical topics to middle grades students to support learning about the connected nature of mathematics. Field experience in a nearby middle school incorporated.

3320 Teaching Mathematics in Grades 5-8. Three credits. Prerequisite: Admission to the teacher education program. Required of all Mathematics majors seeking a license to teach mathematics in grades 7-12. Strongly encouraged for elementary education majors with a 5-8 emphasis. Topics from number relationships, mental computation and estimation strategies, patterns and functions, algebra, statistics, probability, geometry, and measurement. Must be taken prior to student teaching.

3330 Teaching Mathematics in Grades 9-12. Three credits. Prerequisites: Admission to teacher education, completion of the mathematics core, and MATH 3320. Required of all Mathematics majors seeking a license to teach mathematics in grades 7-12. In-depth study of mathematics learning and teaching strategies in secondary school mathematics. Selected topics from junior and senior high school curricula provide a foundation for student investigations into the conceptual nature of mathematics and applications in the secondary school curriculum. Must be taken prior to student teaching.

3400 Symbolic Logic. Three credits. (Same as PHIL 3400.) The elements of propositional calculus-propositional connectives and their truth functions, validity, proof, and an introduction to quantification theory. Where appropriate and natural, parallels from elementary set theory are introduced. May count for credit in Philosophy.

3460 Foundation of Higher Mathematics. Three credits. Prerequisite: MATH 1920. The language of mathematics, set theory and proof, relations and functions, number systems, mathematical structures. Focuses on the transition from lower-division study to upper-division study by actively engaging the student in problem solving, mathematical reasoning, and both informal and technical writing.

3970 Cooperative Education. One to three credits. Experiential learning that occurs in real employment situations. Must be taken in sequence or approved by the director of Cooperative Education. Graded on a pass/fail basis.

3980 Cooperative Education. One to three credits. Experiential learning that occurs in real employment situations. Must be taken in sequence or approved by the director of Cooperative Education. Graded on a pass/fail basis.

4010 Selected Topics in Elementary Mathematics. Three credits. Prerequisites: MATH 1410, MATH 1420, and MATH 1010. Required of students who are preparing to teach grades 5-8. Examines in greater depth topics to which the student has prior exposure; emphasizes the relevance and implications of these topics to the middle school classroom.

4200 Introduction to Mathematics of Investment. Three credits. (Same as ACSI 4200.) Prerequisites: MATH 1910 and one semester of probability/statistics; or consent of instructor. Calculus and probability/statistics used to model and analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of a bond as a function of interest rate, developing formulas for duration and convexity to study the sensitivity of price to interest rate, and mathematical modeling of investor preference and attitude toward risk.

4210 Advanced Calculus I. Three credits. Prerequisites: MATH 3110 and 3460. Theory and application of continuity, differentiation, and integration.

4220 Advanced Calculus II. Three credits. Prerequisite: MATH 4210. A continuation of MATH 4210 including theory and application of convergence.

4230 Vector Analysis. Three credits. Prerequisite: MATH 3110. A review of vector algebra and vector differentiation with emphasis on aspects of these topics not covered in previous calculus courses. Stress on line and surface integrals; Divergence Theorem and Stokes' theorem with generalizations and related topics.

4250 Theory of Calculus. Three credits. Prerequisites: MATH 3110 and MATH 3460. Theoretical development of limits, continuity, differentiation, and integration in one dimension.

4270 Introduction to Topology. Three credits. Prerequisites: MATH 3110 and MATH 3460. Fundamental concepts of topology including continuity, compactness, connectedness, separation axioms, and metric spaces.

4280 Undergraduate Research. One to four credits. Prerequisite: Permission of department. Independent investigation of a selected research problem under the guidance of a faculty member resulting in an oral and written report of results. May be repeated for a maximum of four credits.

4310 Numerical Analysis I. Three credits. Prerequisites: CSCI 1170 and MATH 2010 or consent of instructor. Application of computer-oriented numerical algorithms to algebraic equations, differential and integral equations, and linear algebra. Rigorous mathematical treatment of error included.

4320 Numerical Analysis II. Three credits. Prerequisite: MATH 4310. A continuation of MATH 4310.

4420 Number Theory. Three credits. Prerequisite: MATH 3460. Divisibility, congruences, quadratic residues, Diophantine equations, quadratic forms, and continued fractions.

4470 Introduction to Modern Algebra. Three credits. Prerequisite: MATH 3460. A treatment of sets, relations, operations, and the construction of number systems in algebra.

4510 Abstract Algebra I. Three credits. Prerequisite: MATH 3460. An introduction to groups, with a brief introduction to rings, integral domains, and fields.

4530 Abstract Algebra II. Three credits. Prerequisite: MATH 4510/5510. The theory of rings, fields, integral domains, and vector spaces.

4540 Topics in Secondary School Mathematics. Three credits. Prerequisites: Admission to teacher education, completion of the mathematics core, MATH 3070 and MATH 4510. Required of all Mathematics majors seeking a license to teach mathematics in grades 7-12. Examines in greater depth topics to which the student has prior exposure; emphasizes the relevance and applications of these topics to the pre-college level classroom.

4600 Problems in Contemporary Mathematics. One to six credits. Pass/Fail grading in specified sections.

4601 Problems in Contemporary Mathematics Complex Variables. Three credits. Prerequisite: MATH 3460. Fundamental principles and applications of complex variables.

4602 Problems in Mathematics. One to six credits. Prerequisite: Consent of instructor. Problem-oriented course providing opportunities for mathematical study in areas of need.

4620 History and Philosophy of Mathematics. Three credits. Prerequisite: MATH 3460. Background in geometry and number theory helpful. The character of mathematical thought by way of mathematical problems that have occupied the outstanding mathematicians of Babylon, Egypt, Greece, China, the Renaissance, and modern times paralleled with a study of three schools of mathematical philosophy: intuitionism, logicism, and formalism.

4630 Mathematics of Risk Management. Three credits. (Same as ACSI 4630.) Prerequisite: ACSI 4200 or MATH 4200. For students in Actuarial Science, offers preparation for the Society of Actuaries/Casualty Actuarial Society Course 6. Topics include mathematical modeling of volatility; pricing of bonds, stocks, and other derivatives with uncertainty; benchmark portfolios; asset/liability management for property/casualty insurers; liability associated with a financially distressed company. Heath-Jarrow-Morton and Cox-Ingersoll-Ross models.

4640 Mathematics of Options, Futures, and Other Derivatives. Three credits. Prerequisites: ACSI 4630 or MATH 4630 or ACSI 4200 or MATH 4200. For students in Actuarial Science, offers preparation for the Society of Actuaries/Casualty Actuarial Society Course 6. Topics include risk management using options, interest rate swaps, interest rate caps, Black-Scholes analysis, Taylor series expansion to obtain hedge parameters, portfolio insurance, numerical procedures, interest rate derivatives, and use of Black's model.

4700 Combinatorics and Graph Theory. Three credits. Prerequisites: MATH 2010 and MATH 3460. Selected topics in combinatorics and graph theory emphasizing combinatorial problem solving and algorithmic proof.

4800 Seminar in Mathematics with Technology. Three credits. Prerequisite: 18 semester hours in mathematics including calculus or consent of instructor. Examine and utilize the technological tools available for doing mathematics. Emphasis on non-numerical tools such as theorem provers and algebraic manipulation systems.

4990 Seminar in Mathematics. Three credits. Open only to Mathematics majors; normally taken during last regular semester of coursework. Required of all Mathematics majors. Offers graduating Mathematics majors a broad perspective of mathematics, mathematical activity, and problem solving in various areas of application; offers preparation for professional examinations; acquaints students with job possibilities and aids in career decisions; acquaints students with the nature of graduate study in mathematics. Pass/Fail.

GRADUATE COURSES:

5010 Concepts of Mathematics. Three credits. Recommended for students preparing to become elementary school teachers. Topics include complex numbers, finite mathematical systems, linear equations and inequalities, functions and their graphs, introductory matrix algebra, interest and consumer credit, and microcomputer applications in the mathematics classroom.

5200 Introduction to Mathematics of Investment. Three credits. (Same as ACSI 5200.)

5270 Introduction to Topology. Three credits. Prerequisites: MATH 3110 and a previous course in which the student has been required to write proofs. Fundamental concepts of topology including continuity, compactness, connectedness, separation axioms, and metric spaces.

5310/ 5320Numerical Analysis I and II. Three credits each. Prerequisite: CSCI 3180 or equivalent. Application of computer­oriented numerical algorithms to algebraic equations, differential and integral equations, and linear algebra. Rigorous mathematical treatment of error included.

5420 Number Theory. Three credits. Divisibility congruences, quadratic residues, Diophantine equations, quadratic forms, and continued fractions.

5470 Introduction to Modern Algebra. Three credits. A treatment of sets, relations, operations, and the construction of number systems in algebra.

5510 Abstract Algebra I. Three credits. Groups with a brief introduction to rings, integral domains, and fields.

5530 Abstract Algebra II. Three credits. Prerequisite: MATH 4510/5510. Theory of rings, fields, integral domains, matrices, and vector spaces.

5600 Problems in Contemporary Mathematics. One to six credits. Pass/Fail grading in specified sections.

5620 History and Philosophy of Mathematics. Three credits. Prerequisites: Background in geometry, number theory, and/or symbolic logic helpful. The character of mathematical thought by way of mathematical problems which have occupied successively the outstanding mathematicians of Babylon, Egypt, Greece, China, the Renaissance, and modern times paralleled with a study of three schools of mathematical philosophy: intuitionism, logicism, and formalism. Open only to senior and graduate mathematics majors.

5700 Combinatorics and Graph Theory. Three credits. Prerequisite: MATH 2010 or 3080. Selected topics in combinatorics and graph theory emphasizing combinatorial problem solving and algorithmic proof.

6100 Mathematics for Teachers. Three credits. Mathematics as problem solving, communication, and reasoning. Connecting different fields of mathematics. Topics include number and number relationships, number systems and number theory, computation and estimation, patterns and functions, statistics and probability, algebra, geometry, measurement.

6120 Advanced Linear Algebra. Three credits. Prerequisite: MATH 2010. Continuation of linear algebra topics in MATH 2010 including advanced topics in inner product spaces and structure of linear operators.

6140 Selected Topics of Modern Mathematics: Algebra. Three credits. Prerequisite: MATH 5530 or consent of instructor. Extension of previous work in algebra with emphasis on topics not treated in other courses.

6141 Selected Topics of Modern Mathematics: Analysis. Three credits. Prerequisite: MATH 6200 or consent of instructor. Extension of previous work in analysis with emphasis on topics not treated in other courses.

6142 Selected Topics of Modern Mathematics: Topology. Three credits. Prerequisite: MATH 4270/5270 or consent of instructor. Extension of previous work in topology with emphasis on topics not treated in other courses.

6170 Sets and Logic. Three credits. Includes topics in three categories: 1) Propositions, predicates, quantifiers, truth tables, tautologies, and methods of mathematical proof including mathematical induction. 2) Sets, relations, functions, graphs, cardinality, and the Axiom of Choice. 3) Applications of these foundations to selected results in algebra and analysis as time permits. It is recommended that this course be taken early in the graduate program.

6190 Analysis I. Three credits. Prerequisite: MATH 4250 or equivalent. Rigorous treatment of limits, continuity, differentiation, and integration in n-dimensional Euclidean space; infinite series; introduction to metric spaces.

6200 Analysis II. Three credits. Prerequisite: MATH 6190 or equivalent. A continuation of MATH 6190. Lebesgue measure, Lebesgue integral, functions of bounded variation.

6210 Complex Variables. Three credits. Prerequisite: MATH 6190. Theory of functions of complex variables and their application in mathematics and physics.

6230 Teaching of Introductory College Mathematics. Three credits. Foundations and pertinent topics in college algebra, trigonometry, analytic geometry, and calculus with emphasis on techniques of presentation.

6250 Real Analysis. Three credits. Prerequisite: MATH 6200. A continuation of MATH 6200. Advanced topics in real analysis. Abstract measure and integration theory. Introduction to functional analysis.

6260 Advanced Differential Equations I. Three credits. Prerequisites: MATH 3120 and 4250. Qualitative and quantitative analysis of systems of differential equations. Gradient systems, Sturm-Liouville problems. Elementary techniques for boundary value problems of partial differential equations.

6270 Advanced Differential Equations II. Three credits. Prerequisite: MATH 6260. Solution techniques for boundary value problems. Problems involve heat, wave, and potential equations. Topics include the method of characteristics, series solutions, integral transforms, and Green's functions.

6300 Optimization. Three credits. Prerequisite: MATH 5320 or consent of instructor. Constrained and unconstrained optimization problems, including the generalized least squares problem and Eigenvalue problems. Methods include orthogonalization, conjugate gradient, and quasi-Newton algorithms.

6310 Control Theory. Three credits. Prerequisite: MATH 6260 or consent of instructor. Vector space applications to system analysis; observability, controllability, and stabilization of systems; feedback systems; Lyapunov methods; optimal control, and the calculus variations.

6320 Mathematical Problem Solving. Three credits. Prerequisite: Permission of instructor. A basis for reflection on teaching and learning mathematics. Problem-solving strategies and heuristics. Focuses on all branches of mathematics, providing an opportunity to synthesize mathematical knowledge.

6330 Algebra for Teachers. Three credits. Prerequisite: Permission of instructor. Review and extension of algebraic skills and concepts as they relate to the teaching and learning of algebra. Focus on algebraic thinking and problem solving, algebraic systems, functions, graphing, and linear algebra.

6340 Geometry for Teachers. Three credits. Prerequisite: Permission of instructor. Investigations into the foundations of plane, solid, and coordinate geometry, motion geometry, similarities and congruencies, measurement and the application of geometry. Instruction will model the suggested pedagogy appropriate for school mathematics.

6350 Probability and Statistics for Teachers. Three credits. Prerequisite: Permission of instructor. Relation to school mathematics. Development of central tendency and variation, concepts of chance including sample space, randomness, conditional probability, and independence.

6360 Technology Tools for School Mathematics. Three credits. Integrates technology into the teaching and learning process for teachers of middle and secondary school mathematics. Investigates a variety of mathematical subject matter appropriate for middle and secondary school students via technology. Lessons designed for use with a variety of technologies, including graphing calculators, dynamic geometry software, spreadsheets, authoring software, presentation software, and the World Wide Web. Highly individualized due to varying backgrounds and interests of students.

6380 Current Trends in Mathematics Education. Three credits. Prerequisite: Permission of instructor. Innovative topics or critical issues related to the teaching and learning of mathematics. Includes history of mathematics education, pedagogical content knowledge, assessment and evaluation, and technologies.

6400 Advanced Geometry. Three credits. Prerequisite: MATH 3070 or consent of instructor. Detailed study of one or more of the various branches of geometry including non-Euclidean geometry, projective geometry, algebraic geometry, and differential geometry.

6410 Computer-Aided Geometric Design. Three credits. Prerequisites: MATH 5320 and 6400 or consent of instructor. Parametric curves and surfaces; Bezier and B-spline interpolation and approximation techniques; visual smoothness and parameterization for curves; Coons, Bezier, and triangular patches; scattered data methods.

6510 Advanced Algebra. Three credits. Prerequisite: MATH 5530. Polynomial rings, theory of fields, vector spaces and intermediate group theory necessary for Galois theory, and Galois theory.

6601- Problems in Mathematics. One to nine credits (in 6601-6608).

6608 Prerequisite: Mathematical maturity, preparation in the area, and normally nine semester hours of graduate study. Problems course dealing with theory methods and applications.

6601 Advanced Calculus
6602 Number Theory
6603 Mathematics of Finance
6604 Mathematics of Life Contingencies
6605 Numerical Analysis
6606 Topology
6607 Abstract Algebra
6608 Combinatorics and Graph Theory

6610 Introduction to Graduate Study. Two credits.

6640 Thesis Research. One to six credits. Selection of a research problem, review of pertinent literature, collection and analysis of data, and composition of thesis. Once enrolled, student should register for at least one credit hour of master's research each semester until completion. S/U grading.

6700 Advanced Combinatorics and Graph Theory. Three credits. Prerequisite: MATH 4700/5700. Selected topics in combinatorics and graph theory extending topics studied in MATH 4700/5700.

6900Research in Mathematics Education. Three credits. Prerequisite: Permission of instructor. An examination of factors influencing research and critical analyses of selected research in mathematics education. Studies representing different methodologies critiqued.

6999 Comprehensive Examination and Preparation. One credit. Open only to students who are not enrolled in any other graduate course and who will take the master's comprehensive examination during the term. The student must contact the graduate advisor during the first two weeks of the term for specifics regarding the details of this comprehensive examination preparatory course. Credit may not be applied to degree requirements.

7060 Independent Study. One to nine credits.

7640 Dissertation Research. One to six credits. Selection of a research problem, review of pertinent literature, collection and analysis of data, and composition of dissertation. Once enrolled student should register for at least one credit hour of doctoral research each semester until completion. S/U grading.

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Courses in Statistics [STAT]

3150 Mathematical Statistics I. Three credits. Prerequisite: Two semesters of calculus. Probability theory including basic probability laws, properties of distributions, mathematical expectation, special discrete and continuous distributions, functions of random variables, and selected applications.

4190 Mathematical Statistics II. Three credits. Prerequisite: STAT 3150 or equivalent. Theory of statistical inference. Topics include sampling distributions, decision theory, estimation, test of hypothesis, regression analysis, analysis of variance, and selected applications.

4200 Statistical Methods for Forecasting. Three credits. Prerequisite: STAT 4190. Topics include application of regression models in forecasting and exponential smoothing methods to forecast nonseasonal time-series, seasonal series, and globally constant seasonal models; stochastic time series models; and forecast evaluation.

4280 Undergraduate Research. One to Four credits. Prerequisite: Permission of department. Independent investigation of a selected research problem under the guidance of a faculty member resulting in an oral and written report of results. May be repeated for a maximum of four credits.

4320 Probability and Stochastic Processes. Three credits. Prerequisites: Two semesters of calculus and STAT 3150 (or MATH 2050) or consent of instructor. Theoretical basis for stochastic processes and their use as models of real-world phenomena. Topics include Markov chains, Poisson processes, Brownian motion and stationary processes. Applications include Gambler's Ruin, birth and death models, hitting times, stock option pricing, and the Black-Scholes model.

4360 Regression Analysis. Three credits. Prerequisite: MATH 2050 or QM 3620. Theory and application of regression models. Approaches to model building and data analysis. Computation and interpretation of results facilitated through the use of statistical software packages.

4370 Nonparametric Statistics. Three credits. Prerequisite: MATH 2050 or equivalent. Statistical tests that require no assertions about parameters or about the form of the population from which the samples are drawn. A wide range of practical problems studied.

4380 Experimental Design. Three credits. Prerequisite: MATH 2050 or QM 3620. Topics include one-way analysis of variances, multiple comparison, multifactor analysis of variance, and various practical issues in experimental design. Computation and interpretation of results facilitated through the use of statistical software packages.

4600 Problems in Statistics. One to six credits. Prerequisites: Senior standing and consent of instructor. Students wishing to enroll must submit a written course/topic proposal to the department prior to the semester in which STAT 4600 is taken. Proposal must be approved prior to taking the course. At the conclusion, each enrollee must submit a written report to the department.

GRADUATE COURSES:

5130 Applied Statistics. Three credits. Prerequisite: 2 years of high school algebra or equivalent. Topics include descriptive statistics, probability, and statistical inference. The inference unit covers means proportions and variances for one and two samples, one-way ANOVA, regression and correlation analysis, chi-square analysis, and topics in nonparametrics.

5140 Probabilistic and Statistical Reasoning. Three credits. Prerequisite: STAT 5130 or equivalent or enrollment in the Master's of Science in Professional Science program. Focuses on probability and statistics concepts. Topics include binomial and normal probabilistic modeling; important statistical concepts such as confounding, randomization, sampling variability and significance; statistical testing of significant differences and associations; and design experiments to test research hypotheses.

5190 Mathematical Statistics II. Three credits. Prerequisite: STAT 3150 or equivalent. Theory of statistical inference. Topics include sampling distributions, decision theory, estimation, test of hypothesis, regression analysis, analysis of variance, and selected applications.

5200 Statistical Methods for Forecasting. Three credits. Prerequisite: STAT 4190. Application of the regression model in forecasting regression and exponential smoothing methods to forecast nonseasonal time-series, seasonal series and globally constant seasonal models, stochastic time series models; and forecast evaluation. (Prepares actuarial science students for the Society of Actuaries Exam #120 and Exam Part 3A administered by the Casualty Actuarial Society.)

5320 Probability and Stochastic Processes. Three credits. Prerequisite: Two semesters of calculus and STAT 3150 (or MATH 2050) or consent of instructor. Theoretical basis for stochastic processes and use as models of real-world phenomena. Topics include Markov chains, Poisson processes, and Brownian motion and stationary processes. Applications include Gambler's Ruin, birth and death models, hitting times, stock option pricing, and the Black-Scholes model.

5360 Regression Analysis. Three credits. Prerequisite: STAT 3150 or equivalent. Theory and application of regression models. Approaches to model building and data analysis treated. Computation and interpretation of results facilitated through use of statistical software packages.

5370 Nonparametric Statistics. Three credits. Prerequisite: STAT 3150 or equivalent. Statistical tests that require no assertions about parameters or about the form of the population from which the samples are drawn. A wide range of practical problems.

5380 Experimental Design. Three credits. Prerequisite: STAT 3150 or equivalent. Topics include one-way analysis of variance, multiple comparison, multifactor analysis of variance, and various practical issues in experimental design. Computation and interpretation of results are facilitated through the use of statistical software packages.

5600 Problems in Statistics. One to six credits. Prerequisites: Senior standing and consent of instructor. Students wishing to enroll must submit a written course/topic proposal to the department prior to the semester in which STAT 5600 is taken. Proposal must be approved prior to student taking the course. At the conclusion of the course, each enrollee must submit a written report to the department.

6020 Introduction to Biostatistics. Three credits. Prerequisite: Introductory probability/statistics course or permission of instructor. Contemporary and medical research methodology for biostatistics. Descriptive and inferential statistics including parametric and nonparametric hypothesis testing methods, sample size, statistical significance and power, survival curve analysis, relative risk, odds ratios, chi square modeling, and analysis of variance. Data will be analyzed using statistical software.

6160 Advanced Mathematical Statistics I. Three credits. Prerequisite:Two semesters of calculus or permission of instructor. Introductiont o theoretical probability used in statistics with an emphasis on the mathematical theory. A rigorous treatment of random variables, their probability distributions, and mathematical exceptions in aunivariate and multivariate setting. Includes conditional probabili­ties, stochastic independence, sampling theory, and limit laws.

6180 Advanced Mathematical Statistics I. Three credits. Prerequisite: STAT 6160 or permission of instructor. Theory of estimation and hypothesis tests. Topics include minimum variance unbiased estimation, methods of estimation, most powerful tests, likelihood ratio tests, decision theory, and sequential test procedures.

6510 Biostatistical Methods. Three credits. Prerequisites: STAT 6020 and 6160 or permission of instructor. Biostatistical methods focusing on the design and analysis of clinical trials and sample surveys. Topics include clinical trial designs and phases, bias, random error, sample size, power, estimating clinical effects, design-based methods of data analysis from sample surveys, sampling techniques, nonresponse, and sampling frame issues.

6520 Advanced Biostatistical Methods. Three credits. Prerequisites: STAT 6020 and 6160 or permission of instructor. Mathematically rigorous presentation of categorical data analysis methods for univariate and correlated multivariate responses including contingency table analysis, logistic regression, and loglinear models; survival analysis for analyzing time-to-event data including survivor functions, Kaplan-Meier curves, and Cox proportional hazards model; and other health applications of multivariate analysis methods.

6600- Problems in Statistics. One to nine credits (in 6601-6604).

6604 Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.

6601 Mathematical Statistics
6602 Regression Analysis
6603 Nonparametric Statistics
6604 Experimental Design

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Courses in Actuarial Science [ACSI]

4140 Mathematical Foundations of Actuarial Science. Three credits. Prerequisites: MATH 3020 (or MATH 3110) and STAT 3150; or consent of instructor. Integrates calculus, probability, and risk management topics into fundamental tools for assessing risk in an actuarial environment. Calculus and probability topics include derivatives, integrals, partials, random variables, distributions, and conditional probability. Risk topics include frequency and severity. Insurance concepts such as retention, deductible, coinsurance, and risk premiums. For students in Actuarial Science, a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 1.

4200 Introduction to Mathematics of Investment. Three credits. (Same as MATH 4200.) Prerequisites: MATH 1910 and one semester of probability/statistics; or consent of instructor. Calculus and probability/statistics used to model and analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of a bond as a function of interest rate, developing formulas for duration and convexity to study the sensitivity of price to interest rate, and mathematical modeling of investor preference and attitude toward risk.

4220 Mathematics of Pricing Theory. Three credits. Prerequisites: ACSI 4200/MATH 4200 and ECON 2410, ECON 2420; or consent of instructor. Applies calculus and theory of interest tools to intermediate topics in microeconomics. Topics include mathematics of supply, demand, and equilibrium; prices, costs, and the gains from trade; consumer behavior; elasticities; competition; monopoly; market power, collusion, and oligopoly; the mathematics of risk and uncertainty; and surplus economics. For students in Actuarial Science, a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 2.

4230 Mathematics of Compound Interest. Three credits. Prerequisite: ACSI 4200 or consent of instructor. For students in Actuarial Science, offers preparation for the Society of Actuaries/Casualty Actuarial Society Exam 2. Topics include measurement of interest (including accumulated and present value factors), annuities certain, yield rates, amortization schedules, sinking funds, and bonds and related securities.

4240 Mathematics of Interest Theory, Economics and Finance. Three credits. Prerequisite: ACSI 4230 or consent of instructor. Applies calculus and theory of interest tools to intermediate topics in microeconomics and macroeconomics and topics in finance. Topics include pricing activities, the simplified Keynesian model, interest and discount rates, valuation of payment streams, yield rates, amortization, cash flows and internal rate of return, stock and bond valuation, portfolio risks, the Capital Asset Pricing Model (CAPM), efficient markets, capital structure, leverage, financial performance measurement, and basic option pricing and the Black-Scholes model. For students in Actuarial Science, a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 2.

4280 Undergraduate Research. One to four credits. Prerequisite: Permission of department. Independent investigation of a selected research problem under the guidance of a faculty member resulting in an oral and written report of results. May be repeated for a maximum of four credits.

4330 Actuarial Mathematics I. Three credits. Prerequisites: ACSI 4230 and STAT 4190; or consent of instructor. First of a two-semester sequence; offers preparation for the Society of Actuaries/Casualty Actuarial Society Course/Exam 3. Topics include survival distributions and life tables, life insurance, life annuities, and net premiums.

4340 Actuarial Mathematics II. Three credits. Prerequisite: ACSI 4330. Second of a two-semester sequence; offers preparation for the Society of Actuaries/Casualty Actuarial Society Course/Exam 3. Topics chosen from net premium reserves, multiple life functions, multiple decrement models, valuation theory and pension plans, and insurance models (including expenses and nonforfeiture benefits and dividends).

4600 Problems in Actuarial Science. One to six credits. Prerequisites: Senior standing and consent of instructor. Students wishing to enroll must submit a written course/topic proposal to the department prior to the semester in which ACSI 4600 is taken. Proposal must be approved prior to taking the course. At the conclusion, each enrollee must submit a written report to the department.

4630 Mathematics of Risk Management. Three credits. (Same as MATH 4630.) Prerequisite: ACSI 4200/MATH 4200. For students in Actuarial Science, offers preparation for the Society of Actuaries/Casualty Actuarial Society Course 6. Topics include mathematical modeling of volatility; pricing of bonds, stocks, and other derivatives with uncertainty; benchmark portfolios; asset/liability management for property/casualty insurers; liability associated with a financially distressed company. Heath-Jarrow-Morton and Cox-Ingersoll-Ross models.

4640 Mathematics of Options, Futures, and Other Derivatives. Three credits. (Same as MATH 4640.) Prerequisites: ACSI 4630 or MATH 4640 and ACSI 4200 or MATH 4200. For students in Actuarial Science, offers preparation for the Society of Actuaries/Casualty Actuarial Society Course 6. Topics include risk management using options, interest rate swaps, interest rate caps, Black-Scholes analysis, Taylor series expansion to obtain hedge parameters, portfolio insurance, numerical procedures, interest rate derivatives, and use of Black's model.

GRADUATE COURSES:

5140 Mathematical Foundations of Actuarial Science. Three credits. Prerequisites: ACSI/MATH 3020 (or MATH 3110) and STAT 3150 or consent of instructor. A preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 1. Integrates calculus, probability, and risk management topics into fundamental tools for assessing risk in an actuarial environment. Calculus and probability topics include derivatives, integrals, partials, random variables, distributions, and conditional probability. Risk topics include frequency and severity. Insurance concepts such as retention, deductible, coinsurance, and risk premium.

5200 Introduction to Mathematics of Investment. Three credits. (Same as MATH 5200.) Prerequisites: MATH 1910 and one semester of probability/statistics, or consent of instructor. Calculus and probability/statistics used to model and analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of a bond as a function of interest rate, developing formulas for duration and convexity to study the sensitivity of price to interest rate, and mathematical modeling of investor preference and attitude toward risk.

5220 Mathematics of Pricing Theory. Three credits. Prerequisites: ACSI/MATH 4200/5200 and ECON 2410, 2420, or consent of instructor. A preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 2. Applies calculus and theory of interest tools to intermediate topics in microeconomics. Topics include the mathematics of supply, demand, and equilibrium; prices, costs, and the gains from trade; consumer behavior; elasticities; competition; monopoly; market power, collusion, and oligopoly; the mathematics of risk and uncertainty; and surplus economics.

5230 Mathematics of Compound Interest. Three credits. Prerequisite: ACSI/MATH 4200/5200 or consent of instructor. A preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 2. Topics include measurement of interest (including accumulating and present value factors), annuities certain, yield rates, amortization schedules, sinking funds, and bonds and related securities.

5240 Mathematics of Interest Theory, Economics and Finance. Three credits. Prerequisites: ACSI 4230/5230 or consent of instructor. A preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 2. Applies calculus and theory of interest tools to intermediate topics in microeconomics and macroeconomics and topics in finance. Topics include pricing activities, the simplified Keynesian model, interest and discount rates, valuation of payment streams, yield rates, amortization, cash flows and internal rate of return, stock and bond valuation, portfolio risks, the Capital Asset Pricing Model (CAPM), efficient markets, capital structure, leverage, financial performance measurement, and basic option pricing and the Black-Scholes model.

5330 Actuarial Mathematics I. Three credits. Prerequisites: ACSI 4230/5230 and STAT 4190 or consent of instructor. First of a two-semester sequence; a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 3. Topics include survival distributions and life tables, life insurance, life annuities, and net premiums.

5340 Actuarial Mathematics II. Three credits. Prerequisite: ACSI 4230/5230 and STAT 4190 or consent of instructor. Second of a two-semester sequence; a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 3. Topics chosen from net premium reserves, multiple life functions, multiple decrement models, valuation theory and pension plans, and insurance models (including expenses and nonforfeiture benefits and dividends).

5600 Problems in Actuarial Science. One to six credits. Prerequisites: Consent of instructor. Students wishing to enroll must submit a written course/topic proposal to the department prior to the semester in which ACSI 5600 is taken. The proposal must be approved prior to student taking the course. At the conclusion of this course, each enrollee must submit a written report to the department.

5630 Mathematics of Risk Management. Three credits. Prerequisite: ACSI/MATH 4200/5200. A preparatory course for the Society of Actuaries Course 6. Topics include mathematical modeling of volatility; pricing of bonds, stocks, and other derivatives with uncertainty; benchmark portfolios; asset/liability management for property/casualty insurers; liability associated with a financially distressed company. Heath-Jarrow-Morton and Cox-Ingersoll-Ross models studied.

5640 Mathematics of Options, Futures, and Other Derivatives. Three credits. Prerequisites: ACSI/MATH 4630/5630 and 4200/5200. A preparatory course for the Society of Actuaries Course 6. Topics include risk management using options, interest rate swaps, interest rate caps, Black-Scholes analysis, Taylor series expansion to obtain hedge parameters, portfolio insurance, numerical procedures, interest rate derivatives, and use of Black&'s model.

6010 Credibility Theory and Loss Distributions. Three credits. Prerequisite: STAT 5190 or consent of instructor. A preparatory course for Exam Part 4B of the Casualty Actuarial Society. Topics include Bayes Theorem and its relationship to credibility theory and analysis of statistical distributions for modeling insurance claims by size.

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MTSU Department of Mathematical Sciences
MTSU BOX 34
Murfreesboro, Tennessee 37132
Phone: (615) 898-2669
Fax: (615) 898-5422