**MATHEMATICS**

Jeter, Donnell, Drici, He, Lee, Rice, Roberts, Shallue

Most students will begin their study of mathematics with one of the two calculus sequences:

(i) Calculus: Math 161, 162, 263, and 264; the traditional sequence.

(ii) Analysis: Math 165, 166, and 267; a calculus sequence which uses a more sophisticated and rigorous approach and integrates multivariate calculus with single variable calculus.

Individuals who do not start their college mathematics with one of the above calculus sequences should take Math 105 or 110, depending on their major interests.

Careful attention should be given to the proper placement in the calculus sequence. Students having a high school calculus background should consider taking the Analysis sequence, Math 165, 166, and 267. The Analysis sequence covers approximately the same material as that contained in the standard Calculus sequence, Math 161, 162, 263 and 264. However, the Analysis sequence builds on one year of successful high school calculus and presents the material with a more rigorous conceptual approach and a significantly different order of presentation. Students who scored at least 4 on the AB or 3 on the BC Advanced Placement exams in high school should take Math 165. It is highly recommended that students begin their college calculus during the fall term of their freshman year.

Placement into Calculus II, III, or IV via AP credit is not allowed.

Credit will not be allowed for both Math 161 and 165. Moreover, credit will not be allowed for any course that is taken after the successful completion of another course for which the first course was a prerequisite.

**Major Sequence in Mathematics:**

A minimum of eleven course units in mathematics to include:

1) One of the calculus sequences (i) or (ii).

2) Math 200 and 215. Both Math 200 and Math 215 should be completed by the end of the second year. Students should consult with a mathematics advisor in order to determine the best time for them to take these courses.

And a minimum of six courses that satisfy the following requirements:

3) Two courses selected from Math 405, 410, 415, 425, 440, or 470. Students must take at least one 400-level course in mathematics in their senior year. Students are allowed to take more than two 400-level courses.

4) Four additional electives selected from Math 300, 307, 310, 324, 325, 330, 340, 351, 405, 410, 415, 425, 440, or approved 370/470.

**Minor Sequence in Mathematics:**

A minimum of six course units in mathematics to include:

1) Math 161 and Math 162, or Math 165 and Math 166.

2) Math 263 or Math 267.

3) Math 200 or Math 215

4) Two additional courses numbered 300 or above, but excluding Math 311, 360, 397, 495, and 499.

Math 105, 106, 110, 135, 235, 397, 495, and 499 will not count towards the Mathematics major or minor.

Mathematics majors and minors who desire secondary certificates and/or middle school and area teaching endorsements should apply to the Teacher Education Program in their sophomore year. Those students should also refer to the Educational Studies curriculum description in this Catalog and the Teacher Education Handbook (http://www.iwu.edu/edstudies/handbooks/) for further information.

The Department of Mathematics maintains two computer labs. A Mathematics Learning Center (MLC) is also maintained throughout the academic year. It is staffed with student assistants under faculty supervision and is open to students enrolled in most first-year courses.

**105 Mathematical Concepts for Elementary Teachers I **The study of number systems (whole, integer, rational, and real), intuitive geometry, and measurement. Open only to elementary education majors. This is not a methods course. Will not count towards the major or minor in mathematics. Prerequisite: two years of high school algebra and one year of high school geometry. *Offered each fall*.

**106 Mathematical Concepts for Elementary Teachers II (FR) **A continuation of Math 105. Topics to be covered include measurement, informal geometry, probability, and statistics. This is not a methods course. Will not count toward the major or minor in mathematics. Prerequisite: 105. *Offered each spring*.

**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. Prerequisite: two years of high school algebra and one year of high school geometry. *Offered each semester*.

**135 Applications of Sets, Logic, and Recursion (FR)** 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 prerequisites. Will not count towards the major or minor in mathematics. Cross-listed with Computer Science 135. *Offered each year*.

**136 Computational Discrete Mathematics** 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. Cross-listed with Computer Science 136. *Offered each fall*.

**161 Calculus I (FR) **Beginning calculus: A rigorous study of limits, continuity and differential calculus of functions of one variable. Prerequisite: four years of high school mathematics including trigonometry. *Offered each semester*.

**162 Calculus II (FR) **Further topics in one variable calculus: introduction to integration, applications of the definite integral, techniques of integration. Prerequisite: 161. *Offered each semester*.

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165 Analysis I (FR) **Careful study of the real number system, basic topology of the real line, the plane, and three-dimensional space; sequences and their limits; sequential limits of functions from **Rn** to **R**; equivalence of the sequential and delta-epsilon limit definitions for functions of one variable. Prerequisite: One year of high school calculus including trigonometry. Students who scored at least 4 on the AB or 3 on the BC Advanced Placement exams in high school should take this course. *Offered each fall*.

**166 Analysis II **A continuation of Math 165 to include: Differential calculus of vector-valued functions, vector fields, differentiation for functions of several variables, and integration for functions of one variable. Prerequisite: 165. *Offered each spring*.

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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: Consent of the instructor. *Offered each semester*.

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215 Linear Algebra (FR) **Vector spaces, linear mappings, determinants, matrices, eigenvalues, geometric applications. Prerequisite: 161, 165, or consent of the instructor. *Offered each semester*.

**263 Calculus III** Sequences and series, differential calculus of vector-valued functions and functions of several variables. Prerequisite: 162. *Offered each fall*.

**264** **Calculus IV** Integral calculus of functions of several variables and vector fields, including Green's, Gauss,' and Stokes' Theorems. Prerequisite: 263. *Offered each spring*.

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267 Analysis III **A continuation of Math 166 to include: infinite series; integration for functions of several variables and vector fields, Green's, Gauss,' and Stokes' theorems. Prerequisite: 166. *Offered each fall*.

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300 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. Prerequisite: one of the courses 263 or 267, 215, and at least one additional mathematics course at the 200- or 300-level* . *

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303 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: 325 or one of the following: Biology 209, Economics 227, Psychology 227, or Sociology 227. *Offered in spring as needed*.

**307 Numerical Analysis **Numerical processes and error estimates relating to nonlinear equations, linear systems of equations, polynomial interpolation and approximation, spline functions, numerical integration and differentiation, and initial-value problems in ordinary differential equations. Prerequisite: 215, and either 263 or 166. *Offered fall of even-numbered years*.

**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. Prerequisite: 200, and either 267 or 263. *Offered spring semester of even-numbered years*.

**311 Parallel Computing **Theory of parallel computation including parallel architectures, processor communication schemes, algorithm complexities, and scalability. Applications of parallel computation, including cellular automata, neural networks, and numerical linear algebra. Prerequisite: CS 127,Math 263 or 166, Math 215, and consent of instructor. *Offered occasionally*.

**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: 215, and either 263 or 166. *Offered each fall*.

**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: 324. *Offered each spring*.

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330 Linear Programming **Convex sets; primal, dual, and other simplex procedures; duality, linear complementarity, Lemke's complementarity pivoting algorithm, transshipment problems, other applications and topics. Prerequisite: 215, and either 263 or 166. *Offered each spring of even-numbered years*.

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337 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. *Offered in alternate years*.

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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: 263 or 166. *Offered each spring*.

**351 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. Prerequisite: 215, and either 263 or 267. *Offered spring of odd-numbered years*.

**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*.

**397 Internship **This course provides opportunities for junior and senior mathematics majors to apply skills acquired in the classroom to a job-related experience in various professional areas and locations. Will not count towards the major or minor in mathematics. Prerequisite: consent of department head. *Offered as needed*.

**405 Modern Algebra **Groups, rings, ideals, integral domains, fields. Prerequisite: 200, 215, and either 263 or 166.*Offered spring of even-numbered years*.

**410 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: 200, 215, and either 264 or 267. *Offered in spring of even-numbered years*.

**415 Introduction to Real Analysis** A rigorous study of the real number system, functions, limits, continuity, derivatives, integrals, sequences, and series. Prerequisite: 200, 215, and either 263 or 267. *Offered fall of odd-numbered years*.

**425 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. Prerequisite: 200, 215, and either 263 or 166. *Offered spring of odd-numbered years*.

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440 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. Prerequisite: 200, 215, and either 263 or 166. *Offered fall of even-numbered years*.

**495 Directed Study **Individual directed readings on a topic of interest to the student. This course is a preparation for Math 499 (Research/Thesis).The course requires a significant review of the literature that culminates in a committee-reviewed manuscript. Will not count towards the major or minor in mathematics. Prerequisite: two courses in mathematics at the 300-level or higher. Requires permission of department chair and faculty research advisor. Open only to mathematics majors with a cumulative GPA of 3.5 or higher in mathematics. *Offered each semester*.

**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*.