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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, Cherveny, Chisholm, Dimitrov, Dofing, Ealy, A. Ekanayake, D. Ekanayake, Felt, Hansen, Hartweg, Kalantari, Kline, Koissi-Kouassi, Liudahl, Mann, Marikova, Mitchell, Mulconrey, Olsen, B. Petracovici, L. Petracovici, Tasdan, Vakil, 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 Education (for licensure 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 curricula see the Centennial Honors College page of the catalog or visit the Centennial Honors College website at wiu.edu/Honors.

Advanced Placement (AP) and College Level Examination Program (CLEP)

Students scoring 3 or higher on the AP calculus AB Examination will receive 4 s.h. of credit for MATH 133 and advanced placement into MATH 134. Students scoring 5 or 4 on the AP Calculus BC 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 AP Calculus BC Examination and with a Calculus AB subscore of 3 will receive 4 s.h. of credit for MATH 133 and advanced placement into MATH 134.

Students scoring 3 or higher on the AP Statistics Examination will receive 3 s.h. of credit for STAT 171.

Students scoring 53 or higher on the CLEP Calculus 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 Hall 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:

  1. Mathematics majors and minors
  2. Statistics minors
  3. Transfer students
  4. 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 licensure rules, all candidates seeking teacher licensure 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.

  1. University General Education and College of Arts and Sciences Curriculum Requirements: 55 s.h.
    Except Teacher Education students must complete the University General Education Curriculum Requirements—43 s.h.
  2. Core Courses: 22 s.h.
    MATH 133, 134, 231, 280, 311, 341, and either 391† or 444†
  3. Options of Study (select A or B)
    1. Mathematics
      1. Special Courses: 12 s.h.
        1. MATH 421 and 435: 6 s.h.
        2. Choose one course from: MATH 333, 383, or 433: 3 s.h.
        3. Choose one course from: MATH 481 or STAT 471: 3 s.h.
      2. Directed Electives: 9 s.h.
        Three upper-division electives (9 s.h.) in addition to the chosen Option Courses. The chosen Option Courses and Directed Electives, together, are to include an approved sequence of two 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.
      3. Any Minor: 16–21 s.h.
      4. Open Electives: 9–14 s.h.
    2. Mathematics—Teacher Education\
      1. Special Courses: STAT 276; MATH 355, 383, 411, 421: 15 s.h.
      2. Upper-Division Mathematics Elective: MATH 433 or 435: 3 s.h.
      3. Other: 51 s.h.
        1. 8 s.h. science sequence: 8 s.h.
        2. MATH 211, 304, 389 (1 s.h.); EDUC 439: 12 s.h.
        3. EIS 202, 301, 303 (2 s.h.), 304 (1 s.h.), 305, 401: 13 s.h.
        4. RDG 387 or ENG 366: 2 s.h.
        5. SPED 210 and 390: 4 s.h.
        6. Student Teaching: 12 s.h.

#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.
  1. MATH 133, 134: 8 s.h.
  2. 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.
  1. One semester of calculus or 3 s.h of approved courses numbered above 183: 3–4 s.h.
  2. At least 15 s.h. of Mathematics and Statistics courses numbered above 183 to include STAT 276 and 376 or STAT 471 and 472
    (Mathematics majors must take 471, 472) and three courses chosen from STAT 474, 476, 478, 490: 15 s.h.

Note: Students majoring in Mathematics and minoring in Statistics may count any Mathematics/Statistics course (other than STAT 471, 172) 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, and may count as General Education/ Mathematics credit for these majors only.

#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 nontrig 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 MATH 129, 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.

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, and may count as General Education/ Mathematics credit for these majors only. 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 MATH 129, or MATH 133, or equivalent.

280 Topics in Computer-Assisted Mathematics. (3) Computer tools in service to mathematical experimentation and investigation in various subjects; tools include a Computer Algebra System, such as Mathematica, and other mathematical software; subjects include calculus, number theory, algebra, geometry, and other areas. Prerequisites: MATH 231 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 Mathematics.

304 Pedagogical Content Knowledge and Reading in Secondary School Mathematics. (4) Study of the secondary Mathematics curriculum for purposes of representing knowledge meaningfully for all students. Focus is on conceptual content knowledge, methods of inquiry, appropriate use of technology in the classroom, creation of learning experiences, and instruction in reading Mathematics. Prerequisites: 2.50 GPA or higher in Mathematics; MATH 341 (C grade or better), and EIS 301; or permission of the department chair. Corequisite: EIS 303 (2 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.

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. Prerequisites: MATH 280 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, 274; 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: Any 400-level course counting toward a major in Mathematics.

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

#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 Problem Solving and the History of Mathematics. (3) Various problems, their solutions, related mathematical concepts, and their historical significance are analyzed through investigation of classic problems and their connection to middle school mathematics. Contributions by Archimedes, Descartes, Eratosthenes, Euler, Gauss, Pascal, Pythagoras, and others are studied. Open only to students majoring in an Elementary Education program. Prerequisite: MATH 123 or 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 311 and 341, or equivalent.

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, sequences, limits, and series. Rigorous introduction to the study of one-variable functions, continuity, differentiability, and integrability based on the epsilon-delta method. Prerequisites: MATH 231 and 341.

439 Teaching and Assessment in Secondary School Mathematics. (4) A study of teaching strategies and current trends in secondary mathematics education. Students will focus on curriculum, lesson-planning, and assessment, and will learn to effectively incorporate technology into the teaching and learning of mathematics. Open to Teacher Education majors 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.

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 Teacher Education curriculum. Credit for Teacher Education 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, 280, and 311; 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, 280, and 311; 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. 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: MATH 133 or 137 or equivalent.

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, nor repeatable) General topics in statistics. Prerequisite: consent of instructor.