MATHEMATICAL SCIENCES

www.bsu.edu/math

Robert Bell Building 465, 765-285-8640

PROGRAMS

Master of arts (MA) in actuarial science, in mathematics, in mathematics education, and in statistics; master of science (MS) in mathematics

See the Science listing under the College of Sciences and Humanities, page 180, for the doctoral programs in science education and philosophy in environmental science.

MASTER OF ARTS IN ACTUARIAL SCIENCE

The master’s program in actuarial science provides training for careers that involve analyzing and solving financial, business, and social problems related to economic risk. The program includes course work that prepares students for the professional examinations given by the Society of Actuaries and the Casualty Actuary Society.

Admission requirements

Applicants must meet the regular admission requirements of the Graduate School. It is also expected that students will have had three semesters of calculus, a course in linear algebra, at least one semester of probability and one semester of statistics.

Degree requirements

PREFIX NO SHORT TITLE CR HRS

MATHS 551 Math Finance 4

552 Life Cont 1 4

553 Life Cont 2 4

557 Act Model 1 4

559 Mod Fin Econ 3

620 Math Stat 1 4

659 Res Act Sci 3

698 Exit Survey 0

6-8 hours from

FIN 500 Corporation (3)

MATHS 528 Reg Time Ser (3)

554 Math Invest (3)

558 Act Model 2 (3)

621 Math Stat 2 (4)

625 Prob Theor 1 (3)

626 Prob Theor 2 (3)

627 Gen Lin Mod (4)

628 Comput Stat (4)

655 Top Act Sci (1-4)

658 Risk Theory (3)

RMI 570 Risk Mgt Ins (3) 6-8

More hours from this list will be
required if courses are waived due
to undergraduate or actuarial exam
credit.

———

32-34 hrs

MASTER OF ARTS IN MATHEMATICS

The master of arts degree in mathematics provides students with a broad graduate-level mathematical background suitable for community college teaching, for pursuing a PhD degree in the mathematical sciences, or for seeking employment in business, industry, or government.

Admission requirements

Applicants must meet the regular admission requirements of the Graduate School and have an undergraduate major in mathematics or an equivalent background as determined

by the Department of Mathematical Sciences.

Degree requirements

PREFIX NO SHORT TITLE CR HRS

MATHS 511 Abstr Alg 1 3

512 Abstr Alg 2 3

(If the undergraduate equivalent is
not complete. Otherwise course
substitutions in algebra will be
made in conjunction with the
program advisor.)

MATHS 571 Real Anls 1 3

572 Real Anls 2 3

(If the undergraduate equivalent is not
complete. Otherwise course substitutions
in analysis will be made in conjunction
with the program advisor.)

MATHS 645 Topology 1 3

675 Measr Thry 1 3

677 Complx Var 1 3

3-6 hours from

MATHS 516 Thry Numbers (3)

556 Oper Res (3)

562 Numer Anls 1 (3)

563 Numer Anls 2 (3)

573 Bdry Val Pbm (3)

575 P D E (3)

625 Prob Theor 1 (3)

626 Prob Theor 2 (3)

646 Topology 2 (3)

676 Measr Thry 2 (3)

678 Complx Var 2 (3) 3-6

Research component, 3-6 hours from

MATHS 689 Res Mth Stat (3)

694 Res Math Ed (3)

THES 698 Thesis (1-6) 3-6

———

30 hrs

MASTER OF ARTS IN MATHEMATICS EDUCATION

The master of arts in mathematics education provides opportunities for elementary, middle school, and high school teachers to examine various issues related to the teaching and learning of mathematics while continuing to develop their own mathematical content knowledge.

Option 1: Elementary and middle school mathematics

Admission requirements

Applicants must meet the regular admission requirements of the Graduate School; hold a current elementary, middle school, or special education teaching license; and have at least one year of elementary or middle school teaching experience.

Degree requirements

PREFIX NO SHORT TITLE CR HRS

Mathematics content, 3-12 hours

MATHS 623 Data Anl Tch 3

And each of the following unless

the undergraduate equivalent is

completed

MATHS 514 Alg Fns Tch 3

517 Nmbr Sys Tch 3

542 Geo Meas Tch 3

Mathematics education, 9 hours

MATHS 690 C I Math Ed 3

694 Res Math Ed 3

696 Act Res Meth 3

Electives in mathematics or

mathematics education, 9-18 hours

(as approved by advisor) from

MATHS 631 Tech Mth Tch (3)

632 Assmt Mth Ed (3)

641 Topics Geom (3)

671 Con Disc Tch (3)

680 Studies Tchg (3)

691 Dev Ins Math (3)

693 Prob & Com (3)

695 Learn Th Mth (3)

697 Lead Math Ed (3) 9-18

———

30 hrs

Option 2: Secondary mathematics

Admission requirements

Applicants must meet the regular admission requirements of the Graduate School; have an undergraduate major in mathematics or an equivalent background as determined by the Department of Mathematical Sciences; hold a current secondary mathematics teaching license; and have at least one year of secondary mathematics teaching experience.

Degree requirements

Mathematics content, 15 hours

MATHS 641 Topics Geom 3

Take each of the following unless
the undergraduate equivalent is
completed.

MATHS 511 Abstr Alg 1 3

571 Real Anls 1 3

Electives in mathematics content, 6-12 hours

(as approved by advisor) from the following

(if undergraduate equivalent is not completed)

MATHS 512 Abstr Alg 2 (3)

516 Thry Numbers (3)

560 Hist of Math (3)

572 Real Anls 2 (3)

620 Math Stat 1 (4)

621 Math Stat 2 (4)

623 Data Anl Tch (3)

645 Topology 1 (3)

675 Measr Thry 1 (3)

677 Complx Var 1 (3) 6-12

Mathematics education, 15 hours

MATHS 690 C I Math Ed 3

694 Res Math Ed 3

696 Act Res Meth 3

Electives in mathematics or
mathematics education, 6 hours (as
approved by advisor) from

MATHS 631 Tech Mth Tch (3)

632 Assmt Mth Ed (3)

693 Prob & Com (3)

695 Learn Th Mth (3)

697 Lead Math Ed (3) 6

———

30 hrs

MASTER OF ARTS IN STATISTICS

The master’s program in statistics provides students with the background suitable for employment as a statistician in business, industry, or government. The degree also provides suitable preparation for pursuing a PhD degree in statistics.

Admission requirements

Applicants must meet the regular admission requirements of the Graduate School. It is also expected that students will have had three semesters of calculus and a course in linear algebra.

Degree requirements

PREFIX NO SHORT TITLE CR HRS

MATHS 522 Sampling 3

528 Reg Time Ser 3

529 Exp Designs 3

620 Math Stat 1 4

621 Math Stat 2 4

625 Prob Theor 1 3

626 Prob Theor 2 3

627 Gen Lin Mod 4

628 Comput Stat 4

689 Res Mth Stat 3

–––––

34 hrs

MASTER OF SCIENCE IN STATISTICS

The master of science in statistics provides students with the background suitable for employment as a statistician in business, industry, or government. The degree also provides suitable preparation for pursuing a PhD degree in statistics. Students pursuing the masters of science degree will be required to complete a 6-hour thesis.

Admission Requirements

Applicants must meet the regular admission requirements of the Graduate School. It is also expected that students will have had three semesters of calculus and a course in linear algebra.

PREFIX NO SHORT TITLE CR HRS

MATH 529 Exp Designs 3

620 Math Stat 1 4

621 Math Stat 2 4

625 Prob Theor 1 3

626 Prob Theor 2 3

627 Gen Lin Mod 4

628 Comput Stat 4

THES 698 Thesis (1-6) 6

3 hours from

MATH 522 Sampling (3)

528 Reg Time Ser (3) 3

–––––

34 hrs

MASTER OF SCIENCE IN MATHEMATICS

The master of science degree in mathematics provides students with a broad graduate-level mathematical background suitable for community college teaching, for pursing a PhD degree in the mathematical sciences, or for seeking employment in business, industry, or government. Students pursuing the master of science degree will be required to write a 6-hour thesis.

Admission requirements

Applicants must meet the regular admission requirements of the Graduate School and have an undergraduate major in mathematics or an equivalent background as determined by the Department of Mathematical Sciences.

Degree requirements

PREFIX NO SHORT TITLE CR HRS

MATHS 511 Abstr Alg 1 3

512 Abstr Alg 2 3

(If the undergraduate equivalent is
not complete. Otherwise course
substitutions in algebra will be

made in conjunction with the

program advisor.)

MATHS 571 Real Anls 1 3

572 Real Anls 2 3

(If the undergraduate equivalent is

not complete. Otherwise course
substitutions in analysis will be

made in conjunction with the

program advisor.)

MATHS 645 Topology 1 3

675 Measr Thry 1 3

677 Complx Var 1 3

3 hours from

MATHS 516 Thry Numbers (3)

556 Oper Res (3)

562 Numer Anls 1 (3)

563 Numer Anls 2 (3)

573 Bdry Val Pbm (3)

575 P D E (3)

625 Prob Theor 1 (3)

626 Prob Theor 2 (3)

646 Topology 2 (3)

676 Measr Thry 2 (3)

678 Complx Var 2 (3) 3

THES 698 Thesis (1-6) 6

–––––

30 hrs

GRADUATE CERTIFICATE IN ELEMENTARY MATHEMATICS TEACHER LEADERSHIP

PREFIX NO SHORT TITLE CR HRS

MATHS 514 Alg Fns Tch 3

690 C I Math Ed 3

697 Lead Math Ed 3

3 hours from

MATHS 517 Nmbr Sys Tch (3)

542 Geo Meas Tch (3)

623 Data Anl Tch (3) 3

3 hours from

MATHS 631 Tech Mth Tch (3)

632 Assmt Mth Ed (3)

691 Dev Ins Math (3)

693 Prob & Com (3)

694 Res Math Ed (3)

695 Learn Th Mth (3) 3

———

15 hrs

MIDDLE SCHOOL/JUNIOR HIGH MATHEMATICS LICENSE (GRADUATE LEVEL)

Admission requirements

Open only to candidates who currently hold an elementary, middle school, or special education license. Middle school/junior high licensure in mathematics will be granted when the following criteria are met:

· completion of the following mathematics content courses with a 3.0 minimum GPA, with grade of C- or better in 100- and 200-level mathematics content courses and grade of C or better in 500- and 600-level mathematics content courses;

· completion of the following professional education courses with a 3.0 minimum GPA, with grade of C or better in all professional education courses;

· passing score on Praxis II for Middle School Mathematics; and

· Decision Point Requirements.

PREFIX NO SHORT TITLE CR HRS

Mathematics content

MATHS 201 Num Alg Prob 4

202 Dat Geo Meas 3

MATHS 161 Appl Calc 1 (3)

165 Calculus 1 (4) 3-4

514 Alg Fns Tch 3

517 Nmbr Sys Tch 3

542 Geo Meas Tch 3

623 Data Anl Tch 3

631 Tech Mth Tch 3

Professional education

EDJHM 512 Instrl Strat 3

690 Practicum (1-9) 6

MATHS 690 C I Math Ed 3

–––––

37-38 hrs

MATHEMATICAL SCIENCES (MATHS)

511 Abstract Algebra 1. (3) The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange’s Theorem, quotient structures, homomorphism, automorphisms, group actions, Sylow’s Theorems, structure of finite abelian groups, generators, and relations.

Prerequisite: MATHS 311 or permission of the department chairperson.

Not open to students who have credit in MATHS 411.

512 Abstract Algebra 2. (3) An introduction to the theory of rings, including integral domains, division rings, and fields. Quotient fields of integral domains. Homomorphisms, ideals, and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions. Aspects of Galois theory.

Prerequisite: MATHS 411 or 511 or permission of the department chairperson.

Not open to students who have credit in MATHS 412.

514 Algebra and Functions for Elementary and Middle School Teachers. (3) Algebra as the study of patterns, as a symbolic language, as a tool for problem solving, as the study of functions, as generalized arithmetic, and as a way of modeling physical situations.

Prerequisite: at least one year of elementary or middle school teaching experience or permission of the department chairperson.

516 Theory of Numbers. (3) Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibility criteria; the sigma, divisor, and phi functions; Diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity.

Prerequisite: MATHS 215 or permission of the department chairperson.

Not open to students who have credit in MATHS 416.

517 Number Systems and Number Theory for Elementary and Middle School Teachers. (3) Number development, number systems, properties and characteristics of classes of numbers, number sense, number theory, operations and their relationships, and algorithms.

Prerequisite: at least one year of elementary or middle school teaching experience or permission of the department chairperson.

522 Theory of Sampling and Surveys. (3) Survey designs; simple random, stratified, cluster, and systematic sampling; ratio estimates; regression estimates; cost and variance functions.

Prerequisite: MATHS 321 or the equivalent.

528 Regression and Time Series Models. (3) Addresses regression topics that include simple and multiple linear regression, polynomial regression, regression diagnostics, and forecasting. Also introduces time series topics that include exponential smoothing, auto-regressive, integrated, moving average (ARIMA) models, and forecasting.

Prerequisite: MATHS 321 or the equivalent.

Not open to students who have credit in MATHS 428.

529 Analysis of Variance in Experimental Design Models. (3) Multivariate normal distribution; quadratic forms; linear models; simple random, randomized block, Latin squares, factorial, split-plot, balanced incomplete block designs; analysis of covariance; confounding; and multiple comparison tests.

Prerequisite: MATHS 321 or equivalent.

Not open to students who have credit in MATHS 429.

542 Geometry and Measurement for Elementary and Middle School Teachers. (3) Students will develop visualization skills; identify two- and three-dimensional shapes and know their properties; connect geometry to other mathematical topics; research historical topics relevant to elementary and middle school geometry.

Prerequisite: at least one year of elementary or middle school teaching experience or permission of the department chairperson.

551 Mathematics of Finance. (4) Mathematical theory of compound interest, force of interest, annuities, equations of value, yield rates, amortization, sinking funds, bonds, market derivatives, depreciation, and current topics in finance.

Prerequisite: MATHS 166.

Not open to students who have credit in MATHS 351.

552 Mathematics of Life Contingencies 1. (4) Survival distributions, life tables; the mathematics of life insurance, life annuities, net premiums, and net premium reserves.

Prerequisite: MATHS 321.

Parallel: MATHS 551.

Not open to students who have credit in MATHS 452.

553 Mathematics of Life Contingencies 2. (4) Mathematics of expense loaded premiums and reserves, asset shares, multiple life functions, multiple decrement models, discrete time Markov Chain models, and simulation.

Prerequisite: MATHS 552.

Not open to students who have credit in MATHS 453.

554 Mathematics of Investments. (3) Mathematical analysis and actuarial principles of investments and asset management.

Prerequisite: MATHS 320 (or 620), 351 (or 551); or permission of the

department chairperson.

Not open to students who have credit in MATHS 454.

555 Topics in Actuarial Science. (2) Selected topics in actuarial science with emphasis on individualized study for the actuarial exams given by the Society of Actuaries and the Casualty Actuarial Society.

Prerequisite: permission of the department chairperson.

556 Introduction to Operations Research. (3) Optimization techniques of linear programming, dynamic programming, and integer programming. Optimal solutions of PERT-CPM networks. Optimal decision strategies.

Prerequisite: MATHS 162 or 166, 217 or permission of the department chairperson.

Not open to students who have credit in MATHS 456.

557 Actuarial Models 1. (4) Loss and frequency distributions, limited expected value, effects of inflation, parametric and non-parametric models, identification procedures for insurance company data, bootstrapping, Bayesian analysis, compound frequency, methods for censored and truncated data, classical and Bayesian credibility models, experience rating.

Prerequisite: MATHS 321 or 620.

Not open to students who have credit in MATHS 457.

558 Actuarial Models 2. (3) Basic functions related to actuarial models, common parametric models, maximum likelihood estimation for censored or truncated data, nonparametric estimation, hypothesis testing, models with co-variables, simulation, and other topics as time permits.

Prerequisite: MATHS 321, 557; one year of mathematical probability and statistics.

Not open to students who have credit in MATHS 458.

559 Models in Financial Economics. (3) Mathematical and economic analysis of financial instruments and the management of financial and investment risk.

Prerequisite: MATHS 320 (or 620), MATHS 351 (or 551), or permission of the department chairperson.

560 History of Mathematics. (3) The development of mathematics from pre-history to the seventeenth century. Topics may include number concepts and numeration, algebra, geometry, trigonometry, analytic geometry, and calculus.

Prerequisite: MATHS 161 or 165.

Not open to students who have credit in MATHS 460.

562 Numerical Analysis 1. (3) Topics include error analysis, locating roots of equations, interpolation, numerical differentiation and integration, spline functions, smoothing of data. Includes programming of numerical algorithms.

Prerequisite: MATHS 162 or 166; MATHS 259 or CS 120; or permission of the department chairperson.

Not open to students who have credit in MATHS 362.

563 Numerical Analysis 2. (3) Topics include direct and iterative methods for solving systems of linear equations, eigenvalue problems; minimization of functions and linear programming. Includes programming of numerical algorithms.

Prerequisite: MATHS 217; MATHS 362 or 562.

Not open to students who have credit in MATHS 363.

568 Unpaid Professional Experience in Mathematical Sciences. (1-8) Supervised unpaid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation.

Prerequisite: permission of the department chairperson.

A total of 8 hours of credit may be earned.

A total of 8 hours of credit may be earned in MATHS 568 and 569 combined. No more than 3 hours can be counted as electives toward a departmental major or minor.

569 Paid Professional Experience in Mathematical Sciences. (1-8) Supervised paid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation.

Prerequisite: permission of the department chairperson.

A total of 8 hours of credit may be earned.

A total of 8 hours of credit may be earned in MATHS 568 and 569 combined. No more than 3 hours can be counted as electives toward a departmental major or minor.

571 Real Analysis 1. (3) Properties of the real numbers. Cardinality. Topological properties of metric spaces: compactness, completeness, connectedness. Sequences and series. Continuous functions. Differential calculus of real- and vector-valued functions of one real variable.

Prerequisite: MATHS 215, 267; or permission of the department chairperson.

Not open to students who have credit in MATHS 471.

572 Real Analysis 2. (3) The Reimann-Stieltjes integral and Fundamental Theorem of Calculus. Sequences and series of functions. Differential calculus of functions of several variables. Inverse and implicit function theorems. Extremum problems. Lebesgue integration and comparison with the Riemann integral.

Prerequisite: MATHS 471 or 571.

Not open to students who have credit in MATHS 472.

573 Boundary Value Problems. (3) Fourier Series and integrals, heat and wave equations in one dimension, Laplace equation in two dimensions, problems in higher dimensions, and numerical methods of solving boundary value problems.

Prerequisite: MATHS 374.

Not open to students who have credit in MATHS 473.

575 Topics in Partial Differential Equations. (3) Classical solution techniques for linear PDEs. Topics include first- and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green’s functions, and fundamental solutions. A computer algebra system is utilized.

Prerequisite: MATHS 267, 374, or permission of the department chairperson.

Not open to students who have credit in MATHS 475.

599 Special Studies in Mathematics. (1- 8) Individual work under the direction of a staff member of the department will involve assigned reading and reports and may involve class attendance in related courses.

Prerequisite: permission of the department chairperson.

A total of 8 hours of credit may be earned.

601 Workshop in Mathematics Education. (1-12) A one- or two-week workshop addressing specific topics in mathematics education.

A total of 12 hours of credit may be earned.

619 Special Studies in Geometry, Algebra, or Topology. (1-8) Individual work under the direction of a faculty member of the department; will involve assigned reading and reports and may involve class attendance in related courses.

Prerequisite: permission of the department chairperson.

A total of 8 hours of credit may be earned. MATHS 619, 669, and 679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

620 Mathematical Theory of Statistics 1. (4) Probability set functions, random variables, density and distribution functions, mathematical expectations, marginal and conditional distributions, sampling distributions, and limiting distributions. The mathematical rigor requires a strong background in calculus.

Prerequisite: MATHS 166, 215.

621 Mathematical Theory of Statistics 2. (4) Estimation theory and statistical tests of hypothesis. Topics include: classical and Bayesian estimation, sufficiency, completeness, uniqueness, likelihood function, exponential families, Rao-Blackwell Theorem, Rao-Cramer inequality, hypothesis testing, Neyman-Pearson Lemma, likelihood ratio tests, goodness-of-fit, contingency tables, nonparametric tests, distribution of quadratic forms, and correlation and regression, bootstrapping.

Prerequisite: MATHS 620.

623 Data Analysis and Probability for Teachers. (3) Students will select and use appropriate statistical methods to analyze data, develop, and evaluate inferences and predictions that are based on data, and understand and apply the basic concepts of probability.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

625 Probability Theory and Applications. (3) Basic probability theory, random variables, conditional probability and conditional expectation, Poisson process, interarrival time, and waiting time distributions.

Prerequisite: MATHS 166 or equivalent.

626 Probability and Stochastic Processes. (3) Discrete and continuous time Markov chains, queuing theory, renewal theory.

Prerequisite: MATHS 625 or the equivalent.

627 Generalized Linear Models with Applications. (4) Methods needed to analyze non-normal data. Topics include exponential family of distributions, an overview of generalized linear models. Models for: continuous data with constant variance, binary data, polytomous data, count data, time to events or survival data.

Prerequisite: MATHS 621 or permission of the department chairperson.

628 Computational Methods in Statistics. (4) Theory and application of simulation techniques used in statistics. The use of statistical software such as SAS and R in statistical analysis.

Prerequisite: MATHS 620 or the equivalent.

631 Technology for Mathematics Teachers. (3) Modeling, computational, and communication tools used in teaching mathematics.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

632 Assessment in Mathematics Education. (3) Issues related to assessment in mathematics education and the relationship of assessment to curriculum and instruction. Examination of various types of assessments administered in mathematics classrooms, as well as large-scale local, national, and international assessments.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

641 Topics in Geometry. (3) A survey of topics in contemporary geometry from various perspectives, including conjecture and exploration, formal analysis, and application beyond geometry.

Prerequisite: MATHS 345 or the equivalent.

645 Topology 1. (3) Introduction to point-set topology. Topics include set-theoretic preliminaries, topological spaces, continuous functions, metric spaces, product and quotient spaces, connectedness,

compactness, countability and separation axioms, Urysohn’s Metrization Theorem, Tietze’s Extension Theorem, and Tychonoff’s Theorem.

Prerequisite: MATHS 471 or 571.

646 Topology 2. (3) A second semester course in point-set topology. Stone-Cech compactification, paracompactness, metrization theorems, Ascoli’s

Theorem, Baire’s Category Theorem, introduction to homotopy theory, Jordan Curve Theorem, Invariance of Domain, Brouwer Fixed-Point Theorem.

Prerequisite: MATHS 645.

655 Topics in Actuarial Science. (1-4) Focuses on advanced studies in actuarial science. Actuarial science uses knowledge from many areas including mathematics, statistics, and finance. It also continually expands its scope to include latest developments from multiple areas. The instructor will have flexibility to determine course content.

Prerequisite: permission of the department chairperson.

A total of 4 hours of credit may be earned.

658 Risk Theory. (3) Individual and collective risk theory. Probability of ruin. Probability distributions of random numbers of random variables.

Prerequisite: MATHS 552.

659 Research Seminar in Actuarial Science. (3) Research study in actuarial subjects of current interest in life, property/casualty, health, pension, and/or financial risk management. Literature searches on selected topics. Articles from research journals may be read and discussed. Will use actuarial skills from several courses. A paper will be required. Case studies and special projects will be completed and results presented on a team basis.

Prerequisite: MATHS 557.

Parallel: MATHS 553.

660 Topics in the History of Mathematics. (3) In-depth study of selected topics in the history of mathematics.

Prerequisite: MATHS 162 or 165, 460 or 560.

669 Special Studies in Applied Mathematics. (1-8) Individual work under the direction of a faculty member of the department; will involve assigned reading and reports and may involve class attendance in related courses.

Prerequisite: permission of the department chairperson.

A total of 8 hours of credit may be earned. MATHS 619, 669, and 679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

671 Continuous and Discrete Mathematics for Elementary and Middle School Teachers. (3) Fundamental concepts and applications of calculus and discrete mathematics.

Prerequisite: MATHS 514 or permission of the department chairperson.

675 Measure Theory and Integration 1. (3) The concept of measurability, simple functions, properties of measures, integration of positive as well as complex functions, sets of measure zero, Riesz representation theorem, Borel and Lebesgue measures, LP-spaces, approximation by continuous functions, elementary Hilbert space theory.

Prerequisite: MATHS 472 or 572.

676 Measure Theory and Integration 2. (3) Banach spaces, Baire’s theorem, Hahn-Banach theorem, complex measures, total variation, absolute continuity, Radon-Nikodym theorem, bounded linear functionals on LP, the Riesz representation theorem, differentiation of measures, the fundamental theorem of calculus, integration on product spaces, the Fubini theorem, completion of product measures, convolutions, distribution functions.

Prerequisite: MATHS 675.

677 Complex Variables 1. (3) Complex number systems, differentiation and integration, functions (analytic, entire, meromorphic) of one complex variable, singularities, complex integration, Cauchy’s theorem, Cauchy’s integral formula, power series, Laurent series, calculus of residues.

Prerequisite: MATHS 471 or 571.

678 Complex Variables 2. (3) Analytic continuation, Riemann surfaces, theorems of Weierstrass and Mittag-Leffler, solution of two-dimensional potential problem, conformal mapping, Schwartz-Christoffel transformations and their applications.

Prerequisite: MATHS 677.

679 Special Studies in Analysis. (1-8) Individual work under the direction of a faculty member of the department; will involve assigned reading and reports and may involve class attendance in related courses.

Prerequisite: permission of the department chairperson.

A total of 8 hours of credit may be earned. MATHS 619, 669, and 679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

680 Special Studies in the Teaching of Mathematics. (1-6) The student will work under the direction of a staff member in the Department of Mathematical Sciences. Assigned reading and reports; possible class attendance in related courses.

Prerequisite: permission of the department chairperson.

A total of 6 hours of credit may be earned.

689 Research Methods in Mathematics and Statistics. (3) The scientific method in mathematical research. Location of relevant journal articles, reference books, and reviews. Development of research and problem-solving techniques. Each student will write a mathematical paper. The instructor will assist students whose work is of exceptional quality in submitting their results for publication.

690 Curriculum and Instruction in Mathematics Education. (3) Focuses on the mathematics curriculum, with emphasis on current issues and trends, on teaching strategies, and standards-based teaching. Looking at mathematics curriculum from a K-12 perspective, we will work on understanding these recommendations in light of previous mathematics curriculum experiences.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

691 Developmental Instruction in Mathematics. (3) Materials and methods used in developing conceptual understanding of mathematics for all students in elementary school, middle school, high school, and community college. Includes assessment and remediation techniques.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

693 Problem Solving and Communication in Mathematics. (3) Knowledge and skills for teaching and learning mathematics through problem solving. Knowledge and skills for orchestrating oral and written communication to promote mathematical reasoning in student-centered mathematics classrooms.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

694 Research Methods in Mathematics Education. (3) Research analysis and methodology in mathematics education.

Prerequisite: at least one year of teaching experience, and 18 hours of graduate credit in mathematics or mathematics education, including 690 and either 632 or 695, or permission of the department chairperson.

695 Learning Theories in Mathematics Education. (3) In-depth study of learning theories; discussion of the psychology of mathematics learning (i.e., what we know about the ways in which students learn mathematics). These issues will be discussed from a “teacher’s perspective,” looking for classroom implications of our knowledge about K-12 students’ mathematical thinking.

Prerequisite: at least one year of teaching experience or permission of the department chairperson.

696 Action Research in Mathematics Education. (3) Teachers conduct an action research project in a mathematics classroom and present their findings in a written report.

Prerequisite: MATHS 694 or permission of the department chairperson.

697 Teacher Leadership in Mathematics Education. (3) Development of strategies and skills for teacher leadership in mathematics education, with a focus on models for professional development of mathematics teachers.

Prerequisite: MATHS 690, 694.

698 Actuarial Science Exit Survey. (0) This 0-credit course consists of an exit survey that should be completed by all students who attain an MA in Actuarial Science from Ball State University. The survey will ask students about professional actuarial exams completed prior to graduation, actuarial internships held during their time in the program, and their employment or education plans after graduation.

Prerequisite: students will either have completed all course requirements for an MA in Actuarial Science or will complete all requirements by the end of the current semester.

699 Seminar in Mathematics. (1-6) For students who wish to pursue some particular problem or group of problems in mathematics. Assigned readings and conferences.

A total of 6 hours of credit may be earned.