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**MATHEMATICAL
SCIENCES**

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)

or

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.