## Department of Mathematics and Philosophy

### Mathematics Courses

#### 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, 123, 128, 129, 137, 138, 139, 260, 362, 364, 367, 402, 406, 407, 408; STAT 171, 409.

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 Creative Perspectives in Mathematics. (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.**

**#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 900-B as MATH 137/138 sequence.**

**#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 900-B as MATH 137/138 sequence.**

**#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.*

**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.*

**#260 Numeric, Algebraic, and Geometric Reasoning for Teaching and Learning. (4)** A mathematics course for elementary and middle school teachers examining numbers, algebra, geometry, and measurement; featuring problem solving, applications, and concrete and visual representations. *Prerequisite: WIU placement or MATH 128 (C or better) 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 (C grade or better).*

**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 260 or equivalent (C grade or better).*

**#364 Teaching Elementary School Mathematics. (4)** An examination of pedagogical mathematics content in elementary school (Grades 1–6), the development of lesson plans and assessments implementing national and state standards, and integration of technology in the mathematics classroom. *Prerequisites: MATH 260 (C grade or better) or equivalent and permission of the College of Education and Human Services; full acceptance into the Teacher Education Program.*

**#367 Teaching Middle School Mathematics. (3)** An examination of the pedagogical Mathematics content in middle school (Grades 5–8), the development of lesson plans and assessments implementing national and state standards, and integration of technology in the Mathematics classroom. *Prerequisite: MATH 260 (C grade or better) or equivalent and permission of the College of Education and Human Services; full acceptance into the Teacher Education Program.*

**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 with 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. Writing Instruction in the Disciplines (WID) course. *Prerequisites: MATH 231; ENG 280. Corequisite: Any 300- or 400-level MATH or STAT 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. (2)** 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.*

**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.*

**436 Introduction to Real Variables II. (3)** A continuation of Math 435. *Prerequisite: Math 435.*

**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 Disciplines (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.*

**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.*

**483 Biomathematics. (3)** Mathematical modeling of biological systems. Derivation and study of continuous time Markov chain models and corresponding ordinary differential equation models. *Prerequisites: MATH 134 and 311, and either STAT 276 or 471; or equivalent.*

**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.*

**496 Internship. (3–12, repeatable once to a combined maximum of 12)** An internship in an approved area relating to applied mathematics or statistics, conducted at a professional institution or government organization. It is expected that the experience will culminate in a final paper or portfolio. *Only 3 s.h. per semester can be included in the major. A maximum of 6 s.h. may be included in the major. Prerequisites: completion of 12 s.h. of upper-division MATH courses and approval of the department. Graded S/U.*

**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 138 or 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.*

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