# 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: A Sequential Approach (FR)

Careful study of the real number system, sequential limits of functions from **R** ^{n} to **R**, definition of the derivative, and derivative rules and applications. Students will learn
the basics of proving limits, as well as their use. Prerequisite: Two years of high
school mathematics including algebra, trigonometry, and pre-calculus. *Offered each semester.*

## MATH 177 Calculus II: A Sequential Approach

A continuation of Math 176 to include: differential calculus of vector-valued functions, vector
fields, differentiation for functions of several variables, and integration for functions
of one variable. Prerequisite: MATH 176. *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. Offered every 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 (W)

Writing mathematical proofs. Topics to include naive set theory, indexing sets (including
arbitrary indexing), relations, equivalence relations, functions, function inverses
and inverse images, composition of functions, induced functions on power sets, finite
and infinite sets, countable sets, mathematical induction. Prerequisite: MATH 176
or consent of instructor. *Offered each semester.*

## MATH 211 Mastering Space and Time in Pre-Modern Mathematics (IT) (Cross-listed with GRS 211 and HIST 211)

Explore humanity's first conceptions of space and time by mastering early mathematical
discoveries! Through analysis of ancient writings, students learn about number systems,
trigonometry, polynomials, absolute value, and other mathematical concepts in their
original contexts, from ancient Mediterranean to Newton's England. Will not count
toward Math major/minor. *Offered occasionally.*

## MATH 215 Linear Algebra (FR)

Vector spaces, linear mappings, determinants, matrices, eigenvalues, geometric applications.
Prerequisite: MATH 176, or consent of the instructor. *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: A Sequential Approach

A continuation of Math 177 to include: infinite series, integration for functions
of several variables and vector fields, Green's and Stokes' Theorems, basic topology
of the real number line. Prerequisite: MATH 177. *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 177 and 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
and 215. *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,
and 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, 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, 215, and 278. *Offered in alternate years, fall semester.*

## MATH 366 Topics in Geometry

Selected topics in geometry emphasizing the pertinent theorems, proofs, definitions,
postulates, and axioms, where applicable. Possible topics include synthetic Euclidean
geometry, convexity, metric geometry, projective geometry, synthetic geometry, etc.
Prerequisites: MATH 177, 200, and 215. *Offered in alternate years, spring semester.*

## MATH 368 Topology

Selected topological topics to include: open sets; closed sets; accumulation points;
the interior, exterior, and boundary of a set; compact sets; connected sets; continuous
functions; and homeomorphisms. Prerequisites: MATH 177, 200, and 215. *Offered in alternate years, fall semester.*

## 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 Regression and Time Series

This course introduces statistical methods used in practice: simple and multiple linear
regressions, hypothesis testing and confidence intervals in the linear regression
models, autoregressive, and ARIMA models, data analysis and forecasting with time
series models. 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 and 215. *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 437 Algorithmic Number Theory

This course introduces the mathematics necessary to understand public key cryptography.
Students will prove results from number theory and analyze algorithms to determine
their running times. Topics include modular arithmetic, units and squares modulo integers,
Fermat's little theorem, determining primality, and factoring composites. Prerequisite:
CS/MATH 135 or MATH 200. *Offered in alternate years.*

## 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 and 215. *Offered in alternate years, spring semester.*

## MATH 495 Independent Study

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.*