## 2010-2011 Undergraduate Catalog

WIU Home > Catalog > 2010 - 2011 > 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, Hansen,
Hartweg, Kalantari, Koissi-Kouassi, Kranjc, Liudahl, Mann, Marikova, Mikos,
Mitchell, Moniri, 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, computer-related 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 to Mathematics majors. 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 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. 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 - 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

†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, B, 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: Co-registration 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 co-enrollment 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
co-registration 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.*

**456 Theory of Numbers. (3)** Divisibility, congruences, periodic
decimals, Fermat's Theorem, Wilson's Theorem, Diophantine equations, primitive
roots, and other topics. *Prerequisite: MATH 341.*

**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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