# Course Descriptions

#### MATH 105 - Mathematical Concepts for Elementary Teachers I

Study of mathematical concepts including counting and cardinality, operations, and algebraic thinking, number and operations (base ten and fractions), with attention to mathematical practices and the historical development of mathematical concepts. Emphasis on mathematical reasoning, including proof. This is not a methods course. Will not count toward the major or minor in mathematics. Prerequisite: ACT score of 22 or SAT score of 1030. Enrollment limited to elementary teacher education majors. Offered each fall.

#### MATH 106 - Mathematical Concepts for Elementary Teachers II (FR)

Study of mathematical concepts including measurement and data, geometry, statistics, probability, with attention to mathematical practices and the historical development of mathematical concepts. Emphasis on mathematical reasoning, including proof. This is not a methods course. Will not count toward the major or minor in mathematics. Prerequisite: MATH 105. Enrollment limited to elementary teaching education majors. Offered each spring.

#### MATH 110 - Finite Mathematics (FR)

Topics to be selected from solving systems of linear equations using Gaussian and Gauss-Jordan Elimination, matrix algebra, linear programming, probability, mathematics of finance, statistics, and Markov chains. Will not count toward the major or minor in mathematics. Prerequisites: Two years of high school algebra and one year of high school geometry. Offered each semester.

#### MATH 120X - Math Immersion I

This course serves as an introduction to the culture of the math program at IWU. Requirements of this course are accruing at least 5 math immersion points throughout the year, creating a math portfolio that will be maintained throughout each student's time at IWU, and meeting once per semester with the math faculty advising group. Credit/No Credit only. To be taken spring of the first year.

#### MATH 135 - Applications of Sets, Logic, and Recursion (FR) (Cross-listed with CS 135)

Introduction to functional programming and discrete mathematics. Sets, functions, and relations. Basic logic including formal derivations in propositional and predicate logic. Recursion and mathematical induction. Programming material: Data types and structures, list processing, functional and recursive programming. No prerequisite. Will not count towards the major or minor in mathematics. Offered each year.

#### MATH 136 - Computational Discrete Mathematics (Cross-listed with CS 136)

Additional concepts in discrete mathematics. Recurrence relations, counting, and combinatorics. Discrete probability. Algorithmic graph theory. Programming with advanced data structures. No prerequisite. Will not count towards the major or minor in mathematics. Offered each fall.

#### MATH 140 - Mathematical Modeling: Finance (FR)

An introduction to the mathematics of finance. Topics will include geometric and arithmetic sequences and series, simple interest, compound interest, bank discounts, treasure bills, time diagrams, ordinary annuities, annuities dues, general annuities, retirement annuities, amortization, sinking funds and other selected topics that could include bonds, life insurance, and stocks. Prerequisite: Two years of high school algebra, or the equivalent. Offered each fall.

#### MATH 141 - Mathematical Modeling: Statistics (FR)

This course introduces some basic statistical methods used in practice: organization and description of data, probability, probability distributions, the normal distribution, sampling distributions, inferences from large and small samples, comparing two treatments. Focus will be placed on the derivation of these methods from first principles and its generalization in decision making. Prerequisites: Two years of high school algebra and one year of high school geometry. Offered in alternate years, spring semester.

#### MATH 143 - Mathematical Modeling:Discrete Structures (FR)

This course explores discrete mathematical structures and their properties. Emphasis is placed on how these structures can be used to model problems encountered in the world. The theory of graphs will be studied, as well as graph algorithms. Topics may include flows in networks, scheduling problems, properties of social networks, matching theory, and others. Prerequisites: Two years of high school algebra and one year of high school geometry. Offered as needed.

#### MATH 145 - Mathematical Modeling: Measurement and Approximation (FR)

An introduction to the mathematic modeling of problems that contain a quantity that cannot be measured directly by performing a simple computation. Approximation methods will be designed to produce a sequence of approximations that approaches the true measurement. One objective of the course is to introduce the sequential definition of limit and to strengthen pre-calculus skills. Prerequisites: Two years of high school algebra and one year of high school geometry. Offered as needed.

#### MATH 176 - Calculus I (FR)

This is the first course in a three course sequence on differential and integral calculus. Topics covered include limits and continuity, differential calculus of functions of one variable, and introduction to integration. Prerequisites: Two years of high school mathematics including algebra, trigonometry, and pre-calculus. Offered each semester.

#### MATH 177 - Calculus II

Further topics in one variable calculus, applications of the definite integral, techniques of integration, a thorough study of sequences, series, and polar coordinates. Prerequisite: MATH 176 or placement by advisement from the Department of Mathematics. Offered each semester.

#### MATH 178 - Calculus Lab with Mathematica (0.25 units)

Lab explorations of the theory and applications of differential and integral calculus encountered in Calculus I and II, including applications of the derivative and integeral, transcendental functions, and techniques of integration. Offered each semester. Required for math majors. To be completed by the end of the first year. No prerequisite. 0.25 units

#### MATH 200 - Techniques of Mathematical Proof (FR, W)

The course is about thinking precisely and communicating ideas effectively using mathematical notation, terminology, and style. It introduces students to logic and deductive reasoning, and develops their abilities to comprehend and write mathematical proofs, work with definitions, theorems, and conjectures, as well as discover and prove theorems. The mathematical content is selected to cover a broad range of proof techniques and examples are chosen to provide a real-world context for formal reasoning. Offered each semester.

#### MATH 215 - Linear Algebra (FR)

Vector spaces, linear mappings, determinants, matrices, eigenvalues, geometric applications. Offered each semester.

#### MATH 220 (0.25 units) - Math Immersion II

A continuation of Math 120. Requirements include accruing at least 5 math immersion points throughout the year, maintaining the portfolio including completion of a 2-year plan, and meeting with the advising group once per semester. A sophomore project must be approved by the project advisor and completed by the end of the sophomore year. To be taken spring of the sophomore year. Prerequisite: Math 120.

#### MATH 270/370/470 - Topics in Mathematics

Topics in pure and applied mathematics not covered in other offerings. Math 470 will be proof oriented. May be repeated for different topics. Prerequisite: Varies with the topic. Offered as needed.

#### MATH 278 - Calculus III

This is a course in multivariate calculus. Topics include vectors and geometry in 3-D space, the derivative of a function of several variables, partial derivatives, gradients, line integrals and multi-variable integrals, vector-valued functions, and Greens' and Stokes' theorems. Other topics as time permits: vector fields and basic topology of the real number line. Prerequisite: MATH 177 or placement by advisement from the Department of Mathematics. Offered each semester.

#### MATH 310 - Combinatorics and Graph Theory

Topics to include basic counting techniques (counting principles, binomial identities, inclusion/exclusion, recurrences, and generating functions), an introduction to graph theory, and extremal problems. Prerequisites: MATH 200. Offered in alternate years, fall semester.

#### MATH 320 (0.25 units) - Math Immersion III

A continuation of Math 220. Requirements include accuring at least 5 math immersion points throughout the year, maintaining the portfolio, and meeting with the advising group once per semester. A declaration for the capstone experience must be submitted and approved by the project advisor by the end of the junior year. To be taken spring of the junior year. Prerequisite: Math 220.

#### MATH 324 - Probability

An introduction to probability; random variables with discrete and continuous distributions, independence and conditional probabilities, distributions and expectations of random variables, moment generating functions, joint distributions. Prerequisite: MATH 177. Offered each fall.

#### MATH 325 - Mathematical Statistics

Transformation of random variables, order statistics, central limit theorem, estimation and hypothesis testing; point estimation, interval estimation, sufficient statistics, most powerful tests, likelihood ratio tests, chi-square tests. Prerequisite: MATH 324. Offered each spring.

#### MATH 340 - Differential Equations

Topics may include, but are not limited to, first-order equations, linear higher order equations, systems of differential equations, series solutions, Laplace transforms, and other selected topics. Prerequisite: MATH 177. Offered each spring.

#### MATH 360 - Modern Algebra

Groups, rings, ideals, integral domains, and fields. Prerequisites: MATH 177, 200, or 215. Offered in alternate years, spring semester.

#### MATH 362 - Introduction to Complex Analysis

This course provides a rigorous introduction to the theory of functions of a complex variable, which extends Calculus to the complex domain. Topics covered include complex numbers, analytic functions, integrals, power series, elementary complex functions, mappings by elementary functions, elementary conformal mappings, Cauchy's Integral theorem, the Residue theorem, and harmonic functions. Prerequisites: MATH 200 or 215, and 278. Offered in alternate years, spring semester.

#### MATH 364 - Introduction to Real Analysis

A rigorous study of the real number system, functions, limits, continuity, derivatives, integrals, sequences, and series. Prerequisites: MATH 200 or 215, and 278. Offered in alternate years, fall semester.

#### MATH 367 - Geometry and Topology

Geometry and topology are introduced in a unified way, beginning with Euclidean and non-Euclidean geometries, including spherical, hyperbolic, and affine geometries. Elements of group theory are introduced to treat geometric symmetries, leading to the unification of geometry and group theory. Basic topological concepts are introduced and combined with group theory to yield the geometry of transformation groups. Prerequisites: MATH 177 and 215. Offered in alternate years.

#### MATH 397 - Internship

This course provides opportunities for junior and senior mathematics major to apply skills acquired in the classroom to a job-related experience in various professional areas and locations. Requires permission of department chair.

#### MATH 400 - Mathematical Modeling

This course demonstrates the applicability of mathematics in the formulation and analysis of mathematical models used to solve real world problems. Students are expected to write the results of the models obtained in technical reports and to give oral presentations. This course is taught with the aid of a computer lab. Prerequisites: MATH 177 and 215 or 340. Offered in alternate years, fall semester.

#### MATH 403 - Computational Data Analysis

This course introduces regression and time series methods, which are statistical modeling techniques commonly used in practice for the purpose of data analysis. It also includes some selected topics in statistical computations: generation of random numbers, statistical computing, statistical graphics and Monte Carlo simulation techniques. The course introduces and uses the R statistical programming language. Prerequisite: MATH 325 or one of the following: BIO 209, ECON 227, PSYCH 227 or SOC 227. Offered even-numbered years, fall semester.

#### MATH 407 - Numerical Analysis

Numerical processes and error estimates relating to non-linear equations, linear systems of equations, polynomial interpolation and approximation, spline functions, numerical integration and differentiation, and initial-value problems in ordinary differential equations. Prerequisites: MATH 177. Offered in alternate years, fall semester.

#### MATH 412 - Combinatorial Designs

This course will examine many of the standard constructions for Steiner triple systems - the prototypical combinatorial design. Other structures studied include Latin squares, quasi-groups, graph decompositions, Kirkman triple systems, pairwise balanced designs, group divisible designs, and projective and affine planes. Prerequisite: MATH 200. Offered in alternate years, spring semester.

#### MATH 420 (0.25 units) - Math Immersion IV

A continuation of Math 320. Requirements include accruing at least 5 math immersion points throughout the year, finalizing the portfolio including a reflection on the capstone experience, and meeting with the advising group once per semester. To be taken spring of the senior year. Prerequisite: Math 320.

#### MATH 430 - Topics in Linear Algebra

Advanced topics in pure and applied linear algebra, selected by the instructor of the course. Possible topics include, but are not limited to, linear programming, nonlinear programming, linear complementarity theory, canonical representations of matrices for specific applications, finite dimensional vector spaces, and applications in numerical analysis, mathematical modeling and graph theory. Prerequisites: MATH 177, 200, 215 and consent of the department chair. Offered in alternate years, fall semester.

#### MATH 451 - Wavelet Analysis

Topics to be covered include spline functions, inner product spaces, Fourier series, Fourier transform, multiresolution analysis, Haar wavelet analysis, Daubechies wavelets, Frances and multiwavelets. Prerequisites: MATH 177. Offered in alternate years, spring semester.

#### MATH 495 - Independent Study (0.5, 0.75, or 1 unit)

Individual independent study of a topic of interest to the student, requiring a significant review of the literature and culminating in a committee-reviewed manuscript. This course may serve as preparation for Math 499 (Research Thesis). Prerequisites: two courses in mathematics at the 300-level or higher. Requires permission of department chair. Offered each semester.

#### MATH 499 - Research/Thesis

Experimental or theoretical examination of a significant problem in a topic of interest to the student that is not normally part of the curriculum. It includes as a requirement the preparation of a significant paper. Prerequisite: Consent of department chair. Offered each semester.