2004-2005 UNIVERSITY CATALOGUE

MATH - Mathematics

010 Developmental Mathematics
3 crs (3-0). F, Sp.
P: For students with minimal high school mathematics or
appropriate score on the mathematics placement test
Not for GE
Not a degree credit course
Audit enrollment not allowed
No credit if taken after any higher-numbered mathematics course. This course is graded on a letter grade basis. The grade received is used in calculating semester, resident, and total GPAs. See Note 1.
Develops basic arithmetic and introductory algebraic skills. These skills are a prerequisite to a further study of algebra.

020 Intermediate Algebra
4 crs (4-0). F, Sp, Su.
P: MATH 010 or one year of college-preparatory algebra
and an appropriate score on the mathematics placement
test
Not for GE
Not a degree credit course
Audit enrollment not allowed
This course is graded on a letter grade basis. The grade received is used in calculating semester, resident, and total GPAs. See Note 1.
The real number system, linear equations and inequalities, operations on polynomials and rational expressions, factoring, solutions of quadratic equations, Cartesian coordinates, functions, and related applications.

101 Mathematical Ideas
3 crs (3-0).
GE-IB
No credit if taken after credit earned in higher numbered
MATH course
Not designed to prepare students for MATH 110 or 112. May not be counted for credit toward a major or minor in mathematics. A grade of a least C (not C-) or a mark of S demonstrates mathematics competency for those programs allowing this course to meet the University mathematics statistics competency requirement.
Fundamental processes in reasoning are applied in an elementary approach to some of the most important ideas in mathematics.

104 Finite Mathematics with Applications
4 crs (4-0). F, Sp.
P: Math 020, or two years of college-preparatory algebra
and a suitable mathematics placement test score
GE-IB
No credit if taken after MATH 114, MATH 212, MATH 314, or
MATH 346
May not be counted toward a major or minor in mathematics with the exception of the middle childhood/early adolescence minor in matematics. A grade of at least C (not C-) or a mark of S demonstrates mathematics competency for the Bachelor of Arts degree in the College of Arts and Sciences.
This course will cover applications from Economics, Social and Biological Sciences. The topics include sets, functions, counting principles, probability, solution of linear systems by graphical and algebraic methods, matrices, linear programming, problem formulation, and solving with graphs and trees.

110 College Algebra
4 crs (4-0). F, Sp, Su.
P: MATH 020, or two years of college-preparatory algebra
and a suitable mathematics placement test score
GE-IB
May not be counted for credit toward a major or minor in mathematics. See Note 1. A grade of at least a C (not C-) or a mark of S demonstrates mathematics competency for the Bachelor of Arts degree in the College of Arts and Sciences.
Algebraic concepts, techniques, and applications including polynomial and rational expressions, linear and quadratic equations, complex numbers, inequalities, absolute value, functions and graphs, exponential and logarithmic functions, systems of equations and inequalities, and zeros of polynomials.

111 A Short Course in Calculus
4 crs (4-0). F, Sp, Su.
P: MATH 110, or three years of above-average work in
college-prep MATH and a suitable mathematics placement
score
GE-IB
No credit if taken after or concurrently with MATH 114
May not be counted for credit toward a major or minor in mathematics. See Note 1. A grade of at least a C (not C-) or a mark of S demonstrates mathematics competency for the Bachelor of Science degree in the College of Arts and Sciences.
Primarily for students in biology, business, economics, psychology, and sociology. Functions, limits, continuity, derivatives, integrals, and applications.

112 Precalculus Mathematics
4 crs (4-0). F, Sp, Su.
P: MATH 110, or three years of above-average work in
college-prep MATH and a suitable mathematics placement
test score
GE-IB
May not be counted for credit toward a major or minor in mathematics. See Note 1. A grade of at least a C (not C-) or a mark of S demonstrates mathematics competency for the Bachelor of Science degree in the College of Arts and Sciences. Does not count for GE-IB if you are seeking a B.S. degree in the College of Arts and Sciences.
Prepares students to enter the Math 114, 215, 216 sequence. Includes absolute value; logarithmic, exponential, and trigonometric functions; inequalities; conic sections; complex numbers; and topics from theory of equations.

114 Calculus I
4 crs (3-2). F, Sp, Su.
P: MATH 112, or four years of above-average work in
college-prep mathematics, including one semester of
trigonometry and a suitable mathematics placement test
score
GE-IB
See Note 1.
Limits, theory, and application of the derivative; introduction to integration.

184 Honors Calculus I
1 cr (1-0).
P: B+ or above in MATH 114
Not for GE
Must be taken with MATH215
If unable to take MATH 215 concurrently, consult instructor.
Enrichment topics associated with Math 114 and 215 selected from functions, analytic geometry, limits, derivatives, integrals, and sequences and series.

203 Mathematics for Elementary/Middle School Teachers I
3 crs (3-0). F, Sp.
P: Two years of college preparatory algebra and a
suitable mathematics placement test score
GE-IB
Limited to elementary or special education majors
May not be counted for credit toward a major or minor in mathematics.
An integrated study of mathematics content, methods, and curricula. Topics include problem solving, reasoning, whole numbers and numeration with an emphasis on cognitively guided instruction, elementary number theory, integers.

204 Mathematics for Elementary/Middle School Teachers II
3 crs (3-0). F, Sp.
P: MATH 203
GE-IB
Limited to elementary or special education majors
Counts only toward the elementary teaching minor in mathematics.
An integrated study of mathematics content, methods, and curricula. Topics include number theory, the rational numbers, ratio and proportion, the real number system and probability. Emphasis on communication and algebraic thinking. Practicum experience included.

212 Calculus and Business Mathematics
3 crs (3-0). Sp.
P: MATH 111 OR 114
GE-IB
May not be counted toward a major in mathematics.
Multivariate calculus, matrix algebra, linear programming, mathematics of finance, and business-oriented applications.

215 Calculus II
4 crs (3-2). F, Sp, Su.
P: MATH 114
GE-IB
Applications and techniques of integration; improper integrals; sequences and series; power series and Taylor's formula.

216 Calculus III
4 crs (4-0). F, Sp.
P: MATH 215
Not for GE
Introduction to functions of several variables, including partial derivatives, multiple integrals, the calculus of vector-valued functions, and Green's Theorem, Stokes' Theorem, and the Divergence Theorem.

245 Introduction to Statistics
3 crs (3-0). F, Sp, Su.
P: One year of high school algebra
GE-IB
No credit if taken after MATH 345, MATH 347, or PSYC 265
Basic statistical analysis, including descriptive statistics, probability, confidence intervals, hypothesis testing, simple linear regression, and correlation.

250 Introduction to Numerical Methods
3 crs (3-0). Sp.
P: MATH 114, C S 170
Not for GE
An introduction to the use of mathematical tools and resources useful in solving computational problems. Potential topics include data analysis, linear algebra, optimization, and differential equations.

255 Statics
3 crs (3-0). F.
P: PHYS 231 or concurrent registration and MATH 215 or
concurrent registration
Not for GE
Calculators may be required.
Designed primarily for pre-engineering students. Includes static equilibrium of rigid bodies, centroids, analysis of structures, friction, and moments of inertia.

256 Dynamics
3 crs (3-0). Sp.
P: MATH 215 and 255
Not for GE
Calculators may be required.
A continuation of Math 255. Dynamics of rigid bodies, moments of inertia, work, energy, impulse, and momentum.

285 Honors Calculus II
1 cr (1-0).
P: B+ or above in MATH 215
Not for GE
Must be taken with MATH216
If unable to take MATH 216 concurrently, consult instructor.
Enrichment topics associated with Math 215 and 216 selected from integrals, sequences and series, vectors and vector- valued functions, and multiple variable calculus.

291 Special Topics
1-3 crs.
Not for GE
Course may be taken 3 time(s)
Topics will vary, depending on interest of students and faculty.

305 Mathematics for Elementary/Middle School Teachers III
3 crs (3-0). F, Sp.
P: MATH 204 or consent of the mathematics department.
Exceptions to the Math 204 prerequisite may be made
for students who are certifying only in special educ.
GE-IB
Limited to elementary or special education majors
Minimum junior standing
Counts only toward the elementary teaching minor in mathematics.
An integrated study of mathematics content, methods, and curricula. Topics include statistics, measurement, geometries, patterns, and functions. Emphasis on communication and algebraic thinking. Practicum experience included.

311 /511 Differential Equations
3 crs (3-0). F, Sp.
P: MATH 216
Not for GE
Ordinary differential equations of first and second order, linear differential equations, Laplace transforms, series solutions, and systems of linear differential equations.

313 /513 Fourier Methods
3 crs (3-0). Sp, odd-numbered years.
P: MATH 311
Not for GE
An introduction to the principal techniques and applications of Fourier series, Fourier integrals, and Legendre series. Applications to problems in vibrations, heat conduction, electrostatics, and optics.

314 /514 Discrete Mathematics
3 crs (3-0). F, Sp.
P: MATH 114 or 212
GE-IB
No credit if taken after CS 240
Introductory course in discrete mathematics. Topics include elementary combinatorics, graph theory, trees, and Boolean algebra. The course emphasizes an algorithmic approach to problem solving.

315 /515 Advanced Calculus I
3 crs (3-0). F, Sp.
P: MATH 216 and 324
Not for GE
Differential and integral calculus of several variables; vector calculus; line, surface, and space integrals including Green's theorem, Divergence theorem, and Stokes' theorem.

316 /516 Introduction to Real Analysis
3 crs (3-0). F, Sp.
P: MATH 216 and 324
Not for GE
Real numbers, introductory topological topics, limits, sequences of numbers, continuity, sequences of functions, and series.

318 /518 Introduction to Complex Variables
3 crs (3-0). Sp.
P: MATH 316/516
Not for GE
Elementary functions of a complex variable, complex integrals, and residue theory.

322 Abstract Algebra for Elementary Teachers
3 crs (3-0). Sp.
P: 11 cr MATH to include MATH 111 or 114; MATH 204
Not for GE
Limited to elementary education majors
Includes sets, functions, and abstract algebraic structures such as groups, rings, and fields.

324 /524 Linear Algebra and Matrix Theory
3 crs (3-0). F, Sp.
P: MATH 215
Not for GE
An introductory course in linear algebra including matrix algebra, systems of linear equations, vector spaces, linear transformations, and eigenvalues.

330 /530 Modern Geometry
3 crs (2.5-0.5). F, Sp.
P: MATH 114 & basic knowledge of Euclidean Geometry
Not for GE
Contemporary and classical Euclidean geometry, with emphasis on constructions, transformations, and proof. The Mira and geometry software will be used to illustrate these topics. Some non-Euclidean geometry included.

333 Geometry for Elementary Teachers
3 crs (3-0).
P: 12 credits of MATH including MATH 305
Not for GE
Limited to elementary or special education majors
No credit if taken after or concurrently with MATH 330
Constructions, congruence, similarity, measures, transformations, coordinate geometry, related proofs, and non-Euclidean geometry.

335 /535 Introduction to Point-Set Topology
3 crs (3-0). F, even-numbered years.
P: MATH 216
Not for GE
Theory of sets, continuity of functions, neighborhoods of points, topological and metric spaces, connectedness and compactness.

338 Introduction to Differential Geometry
3 crs (2.5-0.5). Sp, odd-numbered years.
P: MATH 216
Not for GE
An introduction to the study of curves and surfaces. Topics on curves include curvature, torsion, and the Frenet frames. Topics on surfaces include curvature, minimal surfaces, and Gauss' Remarkable Theorem.

341 Classical Number Theory
3 crs (3-0). Sp, odd-numbered years.
P: MATH 114
Not for GE
Classical number theory including divisibility, primes and their properties, theory of congruences, Diophantine equations, number theoretic functions, primitive roots, and selected optional topics.

342 Mathematical Logic and Proof
3 crs (3-0). Sp.
P: MATH 215
Not for GE
Introductory logic statements, inference, quantification, and methods of proof with applications in sets, number theory, relations, and algebra.

345 /545 Introduction to Probability and Mathematical Statistics
4 crs (4-0). Sp.
P: MATH 215 or concurrent registration
Not for GE
Credit cannot be earned in both MATH 345/545 & MATH 346/546
MATH 245 may not be taken for credit after or concurrently with MATH 345/545.
Counting techniques, discrete and continuous random variables, probability distributions, sampling distributions, estimation, hypothesis testing, linear regression, correlation, nonparametric statistics. Students who desire more extensive probability and statistics should take Math 346/546, 347/547.

346 /546 Introduction to Probability
3 crs (3-0). F.
P: MATH 215
Not for GE
Credit cannot be earned in both MATH 345/545 & MATH 346/546
Probability in discrete and continuous sample spaces, conditional probability, counting techniques, probability functions, moment generating functions, and the binomial, Poisson, and normal distributions.

347 /547 Mathematical Statistics
4 crs (3-2). Sp.
P: MATH 215; MATH 346/546
Not for GE
MATH 245 may not be taken for credit after or concurrently with MATH 347/547.
Transformations of variables; normal, chi-square, t, and F distributions; estimation; hypothesis testing; regression; correlation; nonparametric statistics; and analysis of variance.

350 Theory of Interest
3 crs (3-0). Sp.
P: MATH 215 or consent of instructor
Not for GE
Mathematical theory of simple and compound interest and discount, annuities, yield rates, amortization and sinking funds, and valuation of securities. This course is meant, in part, to prepare students for the second actuarial exam.

351 /551 Numerical Analysis I
3 crs (3-0). F.
P: MATH 215 and 324 and one of the following: C S 163,
170, 255, or a working knowledge of a high-level
procedural programming language
Not for GE
Nonlinear equations, interpolation and approximation, least squares, systems of linear equations, and error analysis.

352 /552 Numerical Analysis II
3 crs (3-0). Sp.
P: MATH 351/551
Not for GE
Numerical solution of differential equations, numerical differentiation and integration, and the eigenvalue problem.

354 /554 Introduction to Mathematical Modeling
3 crs (3-0). F.
P: MATH 215
Not for GE
Topics include discrete dynamical systems, discrete and continuous stochastic models including elements of queuing theory, applications of Markov chains, empirical modeling using regression theory and interpolation techniques, and modeling with differential equations.

355 /555 Linear Programming
3 crs (3-0). F, odd-numbered years.
P: MATH 212 or MATH 324
Not for GE
Introductory topics in linear programming including computational development of the simplex method, duality theory of linear programming, dual simplex method, transportation problem, and the use of the linear programming package on the microcomputer.

358 /558 Introduction to Optimization
3 crs (3-0). Sp, odd-numbered years.
P: MATH 216 and 324
Not for GE
An introduction to the theory and application of optimization techniques. Analytic and numerical methods for linear and nonlinear problems of both constrained and unconstrained type will be considered.

365 Patterns of Problem Solving
3 crs (3-0). Sp.
P: MATH 110 or equivalent coursework
GE-IB
May not be counted for credit toward a major or minor in mathematics except in elementary education.
Provides tools and concepts needed in problem solving in a variety of disciplines. Common difficulties, symbolic logic and language, proper attitude toward information gathering, use of models and their limitations, decision-making, optimization models, and selected applications.

395 Directed Studies
1-3 crs. F, Sp, Su.
P: 2.00 GPA in mathematics
Not for GE
May be repeated - additional restrictions may apply
Get form from department office
For the student who wishes to pursue independent study of a topic in mathematics under the supervision of a member of the mathematics department.

399 Independent Study - Juniors
1-3 crs. F, Sp.
Not for GE
Minimum junior standing
May be repeated - additional restrictions may apply
Get form from department office

425 /625 Abstract Algebra I
3 crs (3-0). F, Sp.
P: MATH 324/524
Not for GE
No credit if taken after or concurrently with MATH 322
An introduction to the abstract concepts of algebra such as groups, rings, and fields. Topics such as direct products, group homomorphisms, factor groups, integral domains, and polynomial rings will be included.

426 /626 Abstract Algebra II
3 crs (3-0). F, Sp.
P: MATH 425/625
Not for GE
No credit if taken after MATH 322
A continuation of Math 425 including more advanced topics from groups, rings, and fields, such as the Sylow theorems, prime and maximal ideals, unique factorization domains, and finite fields.

440 Fourier Optics
3 crs (2.5-0.5). F, odd-numbered years.
P: MATH 311 and PHYS 340
Not for GE
Cross-listed with PHYS 440
Credit may not be earned in both MATH 440 and PHYS 440
Applications of Fourier Analysis to optics. Topics include: coherency of light, diffraction, wave optical theory of lenses and imaging, and image processing.

441 Linear Regression Analysis
3 crs (3-0). F, even-numbered years.
P: MATH 345 or 347 or MATH 245 with consent of instructor
and MATH 212 or 324.
Not for GE
Simple and multiple regression, transformation of variables, model checking, analysis of residuals, regression diagnostics, stepwise regression, index variables, confidence intervals, and computer software.

443 Experimental Design and Analysis
3 crs (3-0). F, odd-numbered years.
P: MATH 345 or 347; or MATH 245 with consent of
instructor
Not for GE
Basic concepts of statistical design of experiments; linear models; randomized block, Latin square, factorial, fractional factorial, rotatable, and incomplete block designs and applications.

445 Survey Sampling
2 crs (2-0). Sp, odd-numbered years.
P: MATH 345 or 347; or MATH 245 with consent of
instructor
Not for GE
Survey sampling including random sampling, stratified sampling, cluster sampling, and design of surveys.

447 Nonparametric Statistics
2 crs (2-0). Sp, even-numbered years.
P: MATH 345 or 347; or MATH 245 with consent of
instructor
Not for GE
Hypothesis testing and confidence intervals based on the binomial distribution, contingency tables, Wilcoxon Test, Mann-Whitney Test, rank correlation, and Kruskal-Wallis and Friedman analysis of variance. Comparisons with normal theory methods.

450 /650 Foundations of Actuarial Science
3 crs (3-0). F.
P: MATH 215 and 346 or consent of instructor
Not for GE
Actuarial theory of financial mathematical models for contingent events as applied to life insurance, annuities, pensions, and reserving. This course is meant, in part, to prepare students for the third actuarial exam.

451 /651 Teaching 6-12 Mathematics with Technology
3 crs (3-0). Sp.
P: C I 357 or concurrent enrollment or consent of
instructor
Not for GE
May not be counted for credit toward a major or minor in mathematics except in the Mathematics Teaching major or Mathematics Teaching minor.
In this course students will investigate teaching mathematics effectively with technology. Technology used includes graphing calculators, spreadsheets, interactive software, and calculator based laboratories. Topics include functions, statistics, probability, geometry, and mathematical modeling.

453 /653 Integrated Mathematics and Science Using Technology for Grades 5-9 Teachers
3 crs (2-2). F.
P: MATH 114
Limited to Education majors and certification students
Not for GE
Middle Childhood/Early Adolescent minors may also enroll
Minimum junior standing
May not be counted for credit toward a major or minor in mathematics except in elementary education Minor: Mathematics, Middle Childhood/Early Adolescence. No credit if taken after MATH 491 with the same topic.
An integration of mathematics and physical science content where students will be exploring and investigating realistic, integrated, hands-on activities that utilize calculator technologies to collect raw data for analysis and also emphasize appropriate pedagogy for the teaching of grades 5-9.

456 /656 Operations Research
2-3 crs. Sp, even-numbered years.
P: MATH 215, 324; MATH 345 or 346
Not for GE
Students who have earned credit in an upper division linear programming course may earn only two credits in this course. This two-credit option is available only to those who have taken such a course. For students earning two credits due to this restriction, attendance will be optional during the linear programming unit.
An introduction to the theory and application of operations research techniques. Several important topics including linear programming, inventory models, waiting time models, and replacement models will be discussed.