## 2011-2012 Undergraduate Catalog

WIU Home > Catalog > 2011 - 2012 > Programs

### Mathematics

Chairperson: Dr. Iraj Kalantari

Office: Morgan Hall 476

Telephone: (309) 298-1054 Fax: (309) 298-1857

E-mail: Mathematics@wiu.edu

Website: wiu.edu/math

Faculty: Adeleke, Andreev, Andreeva, G. Baramidze, V. Baramidze, Blackford, Brinker, Campbell, Cherveny, Chisholm, Dimitrov, Ealy, A. Ekanayake, D. Ekanayake, Felt, Hansen, Hartweg, Kalantari, Koissi-Kouassi, Kranjc, Liudahl, Mann, Marikova, Mikos, Mitchell, Mulconrey, Olsen, Orton, B. Petracovici, L. Petracovici, Rosene, Tasdan, Vakil, Weitkamp, Welch, Yang.

Mathematics is a creation of the mind of man. Its diversity sweeps across a continuum from the abstract and theoretical to the applied and practical. Various concepts of mathematics are useful to an increasing number of disciplines in which quantification and logical order are essential.

Occupational fields open to students who have completed one of the department’s programs include mathematical analysis in industry or government, teaching, computerrelated employment, data analysis and other statistical work, and mathematical aspects of business and finance.

The Department of Mathematics provides coursework for a major in Mathematics with options in Mathematics and Teacher Certification (for certification as secondary teachers). Requirements are sufficiently flexible to allow for individual interests and some specialization based upon career goals.

Minors are offered in Mathematics and Statistics.

A concentration in mathematics which will meet the Illinois State Board of Education endorsement in mathematics for upper middle school and junior high teachers is also available for elementary education majors. Service courses are taught for students majoring in business, the physical sciences, and pre-engineering, and courses are available to meet the University General Education requirements.

**GradTrac** is available. See more information about
GradTrac.

**Honors Curriculum**—Academically qualified students in this department are welcome
to complete an honors curriculum in University Honors, Upper Division Honors, or Lower
Division Honors. All Honors students must complete the one-hour honors colloquium (G H
299). Lower Division Honors includes General Honors coursework. Upper Division Honors
includes honors work in the major. University Honors combines Upper and Lower Division
Honors. For more information about honors curricula see the
Centennial Honors College page of the catalog or visit the Centennial Honors College
website at www.wiu.edu/Honors.

#### Advanced Placement

Students scoring 3 or higher on the College Entrance Examination Board Calculus AB Advanced Placement Examination will receive 4 s.h. of credit for MATH 133 and advanced placement into MATH 134. Students scoring 5 or 4 on the Calculus BC Advanced Placement Examination will receive 8 s.h. of credit for MATH 133 and 134 and advanced placement into MATH 231. Students scoring a 3 or 2 on the Calculus BC Advanced Placement Examination will receive 4 s.h. of credit for MATH 133 and advanced placement into MATH 134.

#### Proficiency Examinations

Proficiency examinations are available from the Proficiency Examination Coordinator (Morgan 476) for the material covered in MATH 133, 134, 231, 137, 138, 139, and STAT 276. The Department of Mathematics may approve proficiency examinations in some upper division courses if sufficient justification and evidence of knowledge are presented. Students will receive the appropriate hourly credit for each course for which they pass the proficiency examination.

#### Advisement

The Department of Mathematics provides advising for:

- Mathematics majors and minors
- Statistics minors
- Transfer students
- Area of endorsement in mathematics for elementary education majors

A person seeking advice in one of these areas should contact the Department of Mathematics.

#### Degree Programs

##### Bachelor of Science—Mathematics

All students seeking the Bachelor of Science in Mathematics must complete I, II, and III.A. or III.B. below, and the foreign language/global issues requirement for the major#. The minimum semester hour requirement for the baccalaureate degree is 120 s.h.

*In accordance with the Illinois State Board of Education certification rules, all candidates
seeking teacher certification are required by Western Illinois University to obtain a grade of
“C” or better in all directed general education courses, all core courses, and all courses in the
option. Note C- is below a C.*

- University General Education and College of Arts and Sciences Curriculum
Requirements ): 55 s.h.

Except teacher certification students must complete the University General Education Curriculum Requirements—43 s.h. - Core Courses: 20 s.h.

MATH 133, 134, 183, 231, 311, 341, and either 391† or 444† - Options of Study (select A or B)
- Mathematics
- Special Courses

Choose three courses from: MATH 421, 435 or 430, 481; STAT 471: 9 s.h. - Directed Electives: 8 s.h.

Eight hours of upper division electives to include a sequence of two approved 400-level courses in one of the following areas: algebra, analysis, applied mathematics, or statistics.

Statistics minors may not count 471, 472 as a sequence for the major. - Other

CS 211 and 212, or CS 225, or equivalent: 3 s.h. - Any Minor: 16–21 s.h.
- Open Electives: 12–17 s.h.

- Special Courses
- Mathematics-Teacher Certification
- Special Courses: STAT 276; MATH 355, 383, 411, 421: 15 s.h.
- Other
- 8 s.h. science sequence: 8 s.h.
- MATH 211, MATH 303, MATH 304, MATH 389 (1 s.h.), Educ 439: 13 s.h.
- EIS 201, 301, 302, 303 (1 s.h.), 304 (1 s.h.), 401: 13 s.h.
- SPED 310 and SPED 390 or PSY 425 and SPED 390: 4 s.h.
- Student Teaching: 12 s.h.

- Minor: 16 s.h.

- Mathematics

#The foreign language/global issues graduation requirement may be fulfilled by successfully completing one of the following: 1) an intermediate foreign language requirement; 2) a General Education global issues course; 3) any major’s discipline-specific global issues course; or 4) an approved study abroad program.

†MATH 391 or MATH 444 fulfills the Writing Instruction in the Discipline (WID) graduation requirement.

#### Minors

##### Minor in Mathematics: 17 s.h.

- MATH 133, 134: 8 s.h.
- At least 9 hours of approved Mathematics Electives with at least 6 of the hours in courses numbered above 300: 9 s.h.

*Note: Students majoring in physics and minoring in mathematics may count PHYS 468
as one three-hour mathematics elective course numbered above 300.*

##### Minor In Statistics: 18 s.h.

- One semester of calculus or 3 s.h. of approved courses numbered above 183: 3–4 s.h.
- At least 15 s.h. of mathematics and statistics courses numbered above 183 to include STAT 276 and 376 or STAT 471 and 472 (math majors must take 471, 472) and three courses chosen from STAT 474, 476, 478, 490: 15 s.h.

*Note: Students majoring in math and minoring in statistics may count any mathematics/
statistics course (other than STAT 471, 472) in either the major or the minor, but not
both.*

#### Courses Not Counting towards a Mathematics Major or Minor (#)

The following courses do not count towards a mathematics major or minor: MATH 099N, 100, 101, 102, 106, 123, 128, 129, 137, 138, 139, 206, 207, 362, 364, 367, 402, 406, 407, 408; STAT 171, 409. Exception: MATH 137, 138 may count in the minor in statistics.

Note: The symbol # is placed by each of the numbers above in the course descriptions which follow.

#### Course Descriptions

##### MATHEMATICS (MATH)

**#099N Intermediate Algebra. (4)** Number systems,
linear and quadratic equations and inequalities,
exponents, polynomials, rational expressions, and
graphing. Introduction to the concept of function
including exponential and logarithmic functions. Does
not count toward graduation. Graded S/U only.

**#100 Core Competency in Mathematics. (3)
**Introduction to and use of mathematics in problem
solving, modeling, and drawing inferences, through
a study of diverse examples and cases of real-world
problems. Prerequisite: one year of high school geometry
with grade of C or higher and MATH 099N or equivalent
with a grade of S (C grade or higher), or WIU placement.
Graded A, A-, B+, B, B-, C+, C, or U.

**#101 Concepts of Mathematics. (3) (General
Education/Mathematics)** An introduction to sets,
logic, counting and probability, and statistics to provide
students with an insight into mathematical reasoning and
its applications. Prerequisite: MATH 100 or equivalent (C
grade or higher) or WIU placement.
IAI: M1 904.

**#102 Mathematics for General Education. (3)
(General Education/Mathematics)** Three or four
topics chosen from mathematics of social choice and
game theory, management science and graph theory,
linear programming, mathematics of finance, geometry
and symmetry, emphasizing applications. Prerequisite:
WIU placement, or MATH 100 or equivalent (C grade or
better).
IAI: M1 904.

**#106 Mathematics for Elementary School
Teachers. (3) (General Education/Mathematics, 3
credits for the sequence 106/206)** A first course in
mathematics for elementary school teachers examining
the real number system from an algebraic perspective
featuring problem solving, applications, and concrete
representations. Prerequisites: WIU Placement, or
MATH 100 or equivalent (C grade or better). Open only
to elementary education, early childhood education,
bilingual/bicultural education, and special education
majors.

**#123 Modeling with Mathematical Functions. (3)
(General Education/Mathematics)** The application
of numeric, geometric, algebraic, and trigonometric
models to analyze situations and solve problems from
natural, social, and applied sciences, with integrated use
of technology. Not open to students with credit in MATH
128. Prerequisite: MATH 100 (grade of C or higher) or
WIU placement.
IAI: M1 907.

**#128 Precalculus Algebra. (3)** Polynomial, exponential,
logarithmic, and rational functions. Emphasis on
algebraic manipulation. Not open to students with credit
in MATH 131. Prerequisite: WIU Placement, or MATH
100 or equivalent (C grade or better).

**#129 Precalculus Trigonometry. (3)** Trigonometric
and inverse trig functions, graphing, proving identities,
solving equations, and additional trig topics. Some
non-trig material such as polar coordinates and complex
numbers are included. Not open to students with credit in
MATH 131. Prerequisite: MATH 128 (C grade or better)
or equivalent.

**133 Calculus with Analytic Geometry I. (4) (General
Education/Mathematics)** Derivatives and integrals
of elementary functions with applications and analytic
geometry. Prerequisite: MATH 129 or equivalent (C grade
or better).
IAI: M1 900-1; MTH 901.

**134 Calculus with Analytic Geometry II. (4) (General
Education/Mathematics)** Further techniques of
integration with applications, additional topics in analytic
geometry, infinite series. Prerequisite: MATH 133 (C
grade or better).
IAI: M1 900-2; MTH 902.

**#137 Applied Calculus I. (3) (General Education/
Mathematics)** Introduction to differential and integral
calculus with applications to business and social science.
Not open to students who have credit for MATH 133.
Prerequisite: MATH 128 (C grade or better) or equivalent.
IAI: M1 900B.

**#138 Applied Calculus II. (3) (General Education/
Mathematics)** Extension of basic operations to new
functions including functions of several variables with
appropriate applications. Prerequisite: MATH 137 (C
grade or better).
IAI: M1 900B.

**#139 Applied Linear Algebra and Finite
Mathematics. (3) (General Education/Mathematics)** Matrix algebra with applications. Topics from finite
mathematics. Not open to students with credit in MATH
311. Prerequisite: MATH 128 (C grade or better) or
equivalent, or MATH 123 (C grade or better).
IAI: M1 906.

**183 Computer Algebra System Lab. (1)** An
introduction to computer algebra systems in the study
of calculus, focusing on exploring conjectures, solving
problems, and communicating the results. (Except by
special permission, students must co-register in MATH
231 and have some computer programming experience.
Proficiency credit is available for students with experience
using a computer algebra system.) Prerequisite: Coregistration
in MATH 231, or by permission of the
department chair.

**197 Honors Calculus Seminar. (1, repeatable to
2)** A more rigorous development of selected topics
from calculus including limits, continuity, definitions of
derivatives, and definite integrals and notions of proof.
Prerequisites: concurrent enrollment in either MATH 133
or 134 and consent of the Honors Committee.

**#206 Geometry for Elementary School Teachers. (3)
(General Education/Mathematics, 3 credits for the
sequence 106/206)** A second course in mathematics
for elementary school teachers examining geometry and
data analysis featuring problem solving and applications
using concrete and pictorial representations. Prerequisite:
MATH 106 (C grade or better). Open only to elementary
education, early childhood education, bilingual/
bicultural education, and special education majors.
IAI: M1 903.

**#207 Basic Concepts of Calculus. (3)** A sequence
approach to limits and the basic ideas of differentiation
and integration. Open only to students majoring in an
elementary education program. Prerequisite: MATH 128
or equivalent.

**211 Euclidean Geometry. (3)** Euclidean geometry
through constructions and proofs. Topics include
angles, triangles, circles, quadrilaterals, congruence and
similarity, area, three-dimensional objects, volume and
surface area, and Euclidean transformations. Prerequisite:
MATH 133 or equivalent, or permission of the department
chair.

**231 Calculus with Analytic Geometry III. (4)
**Vectors, three dimensional analytic geometry, partial
differentiation, and multiple integration. Prerequisite:
MATH 134 (C grade or better).
IAI: M1 900-3; MTH 903.

**255 Discrete Mathematical Structures for Computer
Science. (3) **Topics to be studied include sets, logic,
method of proof, combinatorial methods, graph theory,
and trees. Prerequisite: MATH 128 or equivalent.

**297 Honors Problem Seminar. (2–3)** The study and
analysis of the techniques of problem solving from
different areas of mathematics. Prerequisites: MATH 134
and at least a 3.00 GPA in Math.

**303 Technology and Secondary School Mathematics.
(3)** Using technology such as calculators, computers,
and Internet resources to help teach topics in secondary
mathematics. Included will be a study of classroom
strategies for using technology, research on the use of
technology for mathematics learning, and the evaluation
of software and Internet sites. Prerequisites: 2.50 GPA or
higher in Mathematics; MATH 183, MATH 231, STAT 276
or STAT 471 or co-registration in either STAT 276 or STAT
471; or permission of the department chair.

**304 Pedagogical Content Knowledge of Secondary
School Mathematics. (3)** A study of the secondary
mathematics curriculum for the purpose of developing
ways to represent knowledge meaningfully for all
students. The focus is on conceptual content knowledge,
methods of inquiry, structures of the discipline, and
creation of learning experiences. Prerequisites: 2.50
GPA or higher in Mathematics; MATH 341 (C grade or
better), MATH 303 (C grade or better), and EIS 301; or
permission of the department chair. Co-requisite: EIS 303
(1 s.h.).

**311 Linear Algebra. (3)** Systems of linear equations,
matrix algebra, vector spaces, linear transformations, and
related topics. Prerequisite: MATH 134; or MATH 138;
or MATH 133 and MATH 255 and CS 355; or MATH 137
and MATH 255 and CS 355.
IAI: MTH 911.

**333 Ordinary Differential Equations. (3)** Elementary
theory and applications of ordinary differential equations
including linear equations of first and second order and
linear systems. Prerequisite: MATH 231.
IAI: MTH 912.

**334 Differential Equations Computation Laboratory.
(1) **The computer as an investigative tool to study the
theory and applications of differential equations. Basic
numerical methods such as Euler and Runge-Kutta
are illustrated. Prerequisite: CS 211 and 212 and coenrollment
in MATH 333, or consent of instructor.

**341 Sets and Logic. (3)** Elementary logic, sets and their
properties, relations and functions, Boolean algebras,
and finite and infinite sets. Prerequisite: MATH 134.

**355 Applied Combinatorics. (3)** Applications of
enumerations (counting) and graph theory (networks,
circuits, trees) are covered. Combinatorial problems
including applications in computer science and
operations research are solved through a careful logical
analysis of possibilities. Prerequisite: STAT 276 or MATH
311.

**#362 Teaching Mathematics in the Primary
Grades (K–3). (3) **Methods and content for planning,
implementing, and assessing math curriculum for
children in the primary grades. Prerequisites: ECH 271,
273, 275; MATH 206 or equivalent (C grade or better).

**#364 Teaching School Mathematics I—Elementary
School. (3)** A study of teaching strategies and current
trends in mathematics education as they apply to the
elementary school mathematics curriculum. Prerequisites:
MATH 206 or equivalent and permission of the College of
Education and Human Services; full acceptance into the
Teacher Education Program.

**#367 Teaching School Mathematics II—Elementary
and Middle School. (3)** An examination of the
pedagogical mathematics content in elementary and
middle school, the development of lesson plans
implementing national and state standards, and
integration of technology in the mathematics classroom.
Prerequisite: MATH 364 (C grade or better).

**383 An Introduction to Mathematical Modeling.
(3)** Modeling using graphs, proportionality, and
the derivative; the modeling process; model fitting;
optimization; dimensional analysis. Prerequisite: MATH
134 or consent of instructor.

**389 Teaching of Algebra Seminar. (1) **A course for
students concurrently assigned to assist in laboratory
sections of MATH 099N. The course will provide
students with a weekly forum to reflect upon and discuss
experiences from the algebra classroom. Prerequisite:
2.50 GPA or higher in Mathematics or permission of the
department chair. Graded S/U only.

**390 Independent Study. (1–3, repeatable to 3)** Prerequisites: sophomore standing and consent of
instructor.

**391 Writing in the Mathematical Sciences. (1)** Issues
of technical writing and the effective presentation of
mathematics in formal and informal formats. Instruction
and practice in writing. Co-registration in an approved
400-level mathematics or statistics course is required.
Writing Instruction in the Discipline (WID) course.
Prerequisites: MATH 231, 311, and 341; ENG 280.
Corequisite: MATH 411, 421, 430, 435, 481 or STAT 471.

**397 Honors Mathematics Seminar. (1–3, repeatable
to 6) **Prerequisites: MATH 134, consent of instructor, and
3.00 GPA in Math.

**#402 Investigations in School Geometry. (3) **A
conceptual development of geometry through the
investigation of geometric relationships and informal
understandings leading to formal deductions. Middle and
junior high school emphasis. Prerequisite: MATH 123 or
MATH 128 or equivalent.

**#406 Mathematical Reasoning in Mathematics. (3)** Problem solving using a variety of reasoning patterns,
proof in mathematics, the concept of a mathematical
group, and related topics. Open only to students majoring
in an elementary education program. Prerequisite: MATH
128 or equivalent.

**#407 Number Theory Concepts in School
Mathematics. (3) **Divisibility, prime numbers, perfect
numbers, modular arithmetic, linear Diophantine
equations, and related topics. Open only to students
majoring in an elementary education program.
Prerequisite: MATH 123 or MATH 128 or equivalent.

**#408 Mathematical Topics and Technology for
Middle School. (3)** The study of programming,
algorithms, and technology resources to investigate
concepts and connections in the content areas of middle
school mathematics. Prerequisite: MATH 123 or MATH
128 or equivalent.

**411 Geometry. (3)** A rigorous study of Euclidean and
non-Euclidean geometries. The necessary axioms are
introduced and several models including the hyperbolic
geometry are examined. Prerequisite: MATH 341.

**421 Abstract Algebra. (3)** An introduction to the basic
properties of groups, rings, and fields. Prerequisite:
MATH 341.

**424 Advanced Linear Algebra. (3)** Matrix algebra,
vector spaces, linear independence, bases, linear
transformations, canonical forms, inner product spaces.
Prerequisite: MATH 421 or consent of instructor.

**430 Multivariable Calculus. (3)** The algebra of
functions, continuity, differentiation, and integration
of n–place functions, and related topics. Prerequisites:
MATH 231 and 311.

**431 Partial Differential Equations. (3)** Fourier series,
partial differential equations, Bessel and Legendre
functions, and transform methods. Numerical techniques
illustrated using the computer. Prerequisite: MATH 333 or
consent of instructor.

**433 Complex Variables and Applications. (3)** Functions of a complex variable including differentiation,
integration, series, residues, and conformal mappings.
Applications to evaluation of real integrals and boundary
value problems. Prerequisite: MATH 231.

**435 Introduction to Real Variables I. (3)** Topology
of the real line, limits, derivatives, integrals, improper
integrals, sequences, series; introduction to calculus and
functions of several variables. Prerequisites: MATH 231
and 341.

**439 The Teaching of Secondary School Mathematics.
(3)** A study of teaching strategies and current trends in
mathematics education as they apply to the secondary
school mathematics curriculum. Credit for teacher
certification major only. Prerequisite: 2.50 GPA or
higher in mathematics; MATH 304, MATH 341, and coregistration
in EIS 304; or permission of the department
chair.

**441 Mathematical Logic. (3) **Introduction to some
of the principal topics of mathematical logic. Topics
include propositional calculus, quantification theory,
the Completeness Theorem, formal theories, models of
theories, and recursion theory. Prerequisite: MATH 341.

**444 Undergraduate Research Project. (1–2)** Dedicated, individual pursuit of a mathematical topic/
application from an area of research that is represented
within the department culminating in a final paper or
presentation to peers and faculty. Writing Instruction in
the Discipline (WID) course. Prerequisites: MATH 341,
ENG 280, junior standing, and consent of instructor.

**461 Introductory Topology. (3)** Basic properties of
topological spaces. Open and closed sets, compactness,
the intermediate value theorem, metric spaces,
completeness, and uniform continuity. Prerequisite:
MATH 341 or consent of instructor.

**480 Student Teaching. (12)** See STCH 480 in
Educational Leadership curriculum. Credit for teacher
certification major only.

**481 Numerical Analysis I. (3)** A survey of current
methods in numerical analysis. Error analysis, solution
of nonlinear equations and systems of linear equations,
polynomial interpolation and approximations, and
related topics. Prerequisites: MATH 231 and 311; CS
211 and 212, or CS 225 or equivalent; or consent of
instructor.

**482 Numerical Analysis II. (3)** A continuation of MATH
481. Numerical differentiation and integration, numerical
solution of ordinary and partial differential equations,
function approximations in various norms. Prerequisite:
MATH 481 or consent of instructor.

**488 Models in Applied Mathematics. (3) **Theory
and computer exploration of mathematical models
using difference equations, differential equations, and
dynamical systems. Applications from the sciences.
Prerequisites: MATH 231 and 311; CS 211 and 212, or CS
225 or equivalent, or CS 240; or consent of instructor.

**497 Honors Mathematics Seminar. (1–3, repeatable
to 6)** Prerequisites: 3.00 GPA in Mathematics and either
MATH 341 or consent of instructor.

##### STATISTICS (STAT)

**#171 General Elementary Statistics. (3) (General
Education/Mathematics)** Principles and applications
of sampling, estimation, and hypothesis testing. Not open
to students who have completed or are currently enrolled
in DS 203. Prerequisite: WIU Placement, or MATH 100 or
equivalent (C grade or better).
IAI: M1 902.

**276 Introduction to Probability & Statistics.
(3)** Probability laws, random variables, probability
distribution functions, population parameters, counting
rules, statistics and sampling, estimating, testing
hypotheses, regression, and correlation. Not open to
students with credit in STAT 471. Prerequisite: one
semester of calculus.

**376 Methods of Statistics. (3) **Analysis and estimation
of experimental results using analysis of variance,
correlation and regression, contingency tables, analysis
of covariance, and some nonparametric methods.
Prerequisite: STAT 276 or equivalent.

**#409 Probability and Statistics for Middle School
Teachers. (3)** Probability laws, random variables,
probability distributions, estimation and inference,
sampling and data analysis, emphasis on concepts and
connections of probability and statistical content to
the challenges of teaching statistics for middle school
teachers. Prerequisite: MATH 123 or 128, or equivalent.

**471 Introduction to Mathematical Statistics I. (3)** The
mathematical foundations of probability and statistics,
principles of probability, sampling, distributions,
moments, and hypothesis testing. Prerequisite: MATH
231 or equivalent.

**472 Introduction to Mathematical Statistics II. (3)** Continuation of STAT 471 including further topics in
estimation and hypothesis testing. Prerequisite: STAT
471.

**474 Regression and Correlation Analysis. (3) **Least
squares theory; correlation theory; simple, multiple,
and stepwise regression; computer assisted model
building; and applied problems. Prerequisite: STAT 276
or equivalent.

**476 Surveys and Sampling Methods. (3) **The design
of surveys and the study of sampling methods including
simple random, stratified random, systematic, and cluster
sampling. Prerequisite: STAT 171 or equivalent.

**478 Analysis of Variance. (3)** A study of analysis of
variance and covariance with applications. Includes
experimental design. Prerequisite: STAT 276 or
equivalent.

**490 Topics in Statistics. (1–6, not repeatable)** General
topics in statistics. Prerequisite: consent of instructor.

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