1300: Fundamentals of Mathematics
Cr.
3. (3-0). A survey of pre-college algebra. Topics include signed
numbers, operations with algebraic expressions, first-degree equations
and inequalities in one variable, factoring, the Cartesian coordinate
system, systems of first-degree equations in two variables solved
by graphical and algebraic means, exponents and radicals, an introduction
to quadratic equations, and stated problems. This course may not
be used to satisfy any degree requirements.
1310: College Algebra
Cr. 3. (3-0). Prerequisite: satisfactory score on placement examination. Students
with credit in MATH 1330 or
1431 will not be allowed to
enroll or receive credit in MATH 1310. Quadratic equations, inequalities, logarithmic
and exponential functions, graphs, elements of theory of equations, systems
of equations.
1311: Elementary Mathematical Modeling (formerly
MATH 1315)
Cr. 3. (3-0). Prerequisite: two credits of high school algebra, one credit of
geometry and a satisfactory score on the placement examination. May not be applied
to a major or minor in Mathematics. Students may not receive credit for both
MATH 1310 and MATH 1311. Functions,
graphs, differences and rates of change, mathematical models, mathematics of
finance, optimization, and mathematics of decision-making.
1312: Introduction to Mathematics
(formerly MATH 1308)
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH 1310.
May not apply toward a degree from College of Natural Sciences
and Mathematics.
Ideas in mathematics central to its historical development and its use
in contemporary life; critical thinking and problem solving. Topics
may include logic, algorithms, numbers, geometry, and topics in
the history of mathematics.
1313: Finite Mathematics with Applications
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH
1310. Students with prior credit for MATH 2331 or INDE 2331 will not receive
credit for MATH 1313. May not apply to a major or minor in mathematics. Systems
of linear equations, introduction to linear programming, mathematics of finance,
topics in probability and statistics.
1314: Elements of Calculus
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH
1310. Students with prior credit for MATH
1431 will not be permitted to enroll in or receive credit for MATH 1314.
Curve sketching and graphical analysis, differentiation and integration of elementary
functions, topics in functions of several variables, applications in business
and the natural and social sciences.
1330: Elementary Functions
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH
1310. Students with prior credit in MATH 1432 may
not receive credit for MATH 1330. Functions, graphs, trigonometry, and analytic
geometry.
1397: Topics in Mathematics
Cr. 3. (3-0). Prerequisite:
consent of instructor. Restricted to nonadvanced undergraduates.
May be repeated with approval of chair.
1431: Calculus I
Cr. 4. (4-0). Prerequisite:
MATH 1330. Calculus of
rational functions; limits, derivatives, applications of the derivative,
antiderivatives, the definite integral with applications, mean
value theorem, fundamental theorem of calculus, numerical integration.
1432: Calculus II
Cr. 4. (4-0). Prerequisite: MATH 1431.
Calculus of transcendental functions: additional techniques and
applications of integration, indeterminate forms, improper integrals,
Taylor's formula, infinite series.
1450:1451:
Accelerated Calculus
Cr. 4 per semester. (3-2). Prerequisites: At least one semester of advanced
placement high school calculus and placement out of MATH
1330. Credit may not be received for both MATH 1450 and 1431.
Students with credit in MATH 1451 may not enroll in or receive credit for either
MATH 1432 or 2433.
An accelerated calculus sequence. MATH 1450 will include topics normally covered
in MATH 1431. MATH 1451 will
include topics normally covered in MATH
1432 and 2433.
2303: Elements of Mathematics
Cr. 3. (3-0). Prerequisites:
MATH 1310 and 1313. May not apply toward a major or minor
in mathematics. Principles of logical reasoning, elementary set
theory, number systems, fundamentals of Euclidean geometry, introduction
to number theory.
2311: Introduction to Probability and Statistics
Cr. 3. (3-0). Prerequisite: MATH 1310 or MATH
1311 May not apply toward a degree in mathematics. Students with credit
for MATH 3338 or MATH 3339 may
not enroll in or receive credit for MATH 2311. Probability, correct probabilistic
reasoning, distributions, graphical and descriptive methods, sampling, estimation,
hypotheses, statistical inference.
2431: Linear Algebra
Cr. 4. (3-1). Prerequisite: credit for or concurrent enrollment in MATH
1432 and in a laboratory section. Solutions of systems of linear questions
and of systems of linear differential equations; matrices, linear transformations,
eigen values, and similarity; phase plane portraits.
2433: Calculus III
Cr. 4. (4-0). Prerequisite: MATH 1432.
Calculus of functions of several variables: calculus of vector-valued
functions, partial differentiation, multiple integrals.
3303: Elements of Algebra and Number Theory
Cr. 3. (3-0).
Prerequisites: MATH 1310 and either MATH 1313 or consent of instructor.
May not apply toward a major or minor in mathematics. May not
satisfy mathematics requirements in the College of Natural Sciences
and Mathematics. Topics in number theory and abstract algebra.
3304: Elements of Mathematical Analysis
Cr. 3. (3-0).
Prerequisites:
MATH 1310 and either
MATH 1313 or consent of instructor. May not
apply toward a major or minor in mathematics. May not satisfy
mathematics requirements in the College of Natural Sciences and
Mathematics. Basic concepts of calculus including limits, derivatives,
and integrals; selected applications.
3305: Formal and Informal Geometry
Cr. 3. (3-0).
Prerequisites:
MATH 1310 and either
MATH 1313 or consent of the instructor.
May not apply toward a major or minor in mathematics. May not satisfy
mathematics requirements in the College of Natural Sciences and
Mathematics. Review of ruler and compass construction, formal axiomatic systems,
finite geometries. Euclid's Elements, non-Euclidean geometry, analytic and
transformational geometry.
3306: Problem Solving in Mathematics
Cr. 3. (3-0).
Prerequisites:
MATH 1310 and either
MATH 1313 or consent of the instructor.
May not apply toward a major or minor in mathematics. May not satisfy
mathematics requirements in the College of Natural Sciences and
Mathematics. Strategies for solving problems in mathematics: reduction to smaller
problems; analogy in mathematics; conjecture and proof; the processes of abstraction,
generalization, and specialization.
3310: History of Mathematics
Cr. 3. (3-0). Prerequisite:
MATH 1431. May not apply toward a major or minor in mathematics.
May not satisfy mathematics requirements in the College of Natural
Sciences and Mathematics. A survey of the history of mathematics
from Euclid to Dedekind focusing on the development of the real
number system and its relation to the Euclidean line.
3321: Engineering Mathematics
Cr. 3. (3-0). Prerequisites: MATH
1432. First order ordinary differential equations and initial value problems;
higher order differential equations; vector spaces, matrices, determinants,
eigenvectors and eigenvalues; applications to systems of first order equations;
Laplace transforms. Students may not receive credit for both MATH 3321 and MATH
3331.
3330: Abstract Algebra
Cr. 3. (3-0).
Prerequisite: MATH 2431.
Introduction to groups, rings, and fields.
3331: Differential Equations
Cr. 3. (3-0). Prerequisites: MATH
2433 and MATH 2431. Systems
of ordinary differential equations; existence, uniqueness and stability of solutions;
initial value problems; bifurcation theory; Jordan form; higher order equations;
Laplace transforms. Computer assignments are required.
3333: Intermediate Analysis
Cr. 3. (3-0). Prerequisite: MATH
2433. Properties of real number system, properties of continuous functions,
and sequences of functions.
3334: Advanced Multivariable Calculus
Cr. 3. (3-0). Prerequisite: MATH
3333. Topology of n-space; continuity, uniform continuity and uniform convergence;
extremal problems; Taylor's theorem for multivariate functions; multiple integrals;
transformations and their derivatives; implicit functions.
3335: Vector Analysis
Cr. 3. (3-0). Prerequisite: MATH 2433
or approval of chair. Algebra and calculus of vectors, vector
differential operators, Green's and Stokes' theorems,
curvilinear coordinates, tensors.
3336: Discrete Mathematics
Cr. 3. (3-0). Prerequisite:
MATH 2431 or equivalent. Topics selected from logic, set theory,
combinatorics, and graph theory.
3338: Probability
Cr. 3. (3-0). Prerequisite: MATH 1432.
Sample spaces, events, and probabilities; random variables and
distributions; expectations, variances, and covariances; basic
discrete and continuous distributions; the central limit theorem.
3339: Statistics
Cr. 3. (3-0). Prerequisite: MATH 3338. Sampling; estimation
and hypothesis testing; regression; analysis of variance; exploratory techniques.
3340: Interest Theory and Applications
Cr. 3. (3-0). Prerequisite: MATH 1432. Definitions of
interest, interest calculations, annuities, amortization and sinking funds,
deterministic cash flow analysis, mortgages and fixed asset analysis.
3341: Applied Probability
Cr. 3. (3-0). Prerequisite:
MATH 2433. Students
with credit for MATH 3341 may not receive credit for MATH 3338. Random variables
and their distributions, expectation, relationships among important distributions,
survival and hazard functions, joint distributions, marginal and conditional
distributions, covariance, moment generating functions, the Central Limit Theorem.
Applications to financial mathematics.
3363: Introduction to Partial Differential Equations
Cr.
3. (3-0). Prerequisites: MATH 2433 and either
MATH 3321 or
MATH 3331. Partial differential
equations and boundary value problems, Fourier series, the heat equation, vibrations of
continuous systems, the potential equation, spectral methods.
3364: Introduction to Complex Analysis
Cr. 3. (3-0). Prerequisite:
MATH 3331. The complex number system, analytic functions, Cauchy
integral theory, series representation, residue theory, and conformal
mapping.
3379: Introduction to Higher Geometry
Cr. 3. (3-0). Prerequisite:
MATH 1432 or approval of chair. Synthetic and algebraic geometry;
harmonic division, cross ratio; groups of projective transformations.
3397: Selected Topics in Mathematics
Cr. 3. (3-0). Prerequisite: consent of instructor. May be repeated with approval
of chair.
3396-4396: Senior Research
Project
Cr. 3. per semester. Prerequisite: approval of chair. Directed research project
culminating in a departmentally approved report.
3399-4399: Senior Honors Thesis
Cr. 3 per semester. Prerequisite: approval of chair.
4198:4298: 4398:4498:
Special Problems
Cr. 1-4 per semester or more by concurrent enrollment. Prerequisite: approval
of chair.
4315: Graph Theory with Applications
Cr. 3. (3-0). Prerequisite:
MATH 3330 or 3336. Introduction to basic concepts, results, methods,
and applications of graph theory.
4331;4332: Introduction to Real
Analysis
Cr. 3 per semester.
(3-0). Prerequisite: MATH 3333 or 3334. Properties of continuous
functions, partial differentiation, line integrals, improper integrals,
infinite series, and Stieltjes integrals.
4333: Advanced Abstract Algebra
Cr. 3. (3-0). Prerequisites:
MATH 3330 and consent of instructor. Direct products, Sylow theory,
ideals, extensions of rings, factorization of ring elements, modules,
and Galois theory.
4335;4336: Partial Differential
Equations
Cr. 3 per semester. (3-0). Prerequisite: MATH
3331. Existence and uniqueness for Cauchy and Dirichlet problems; classification
of equations; potential-theoretic methods; other topics at the discretion of
the instructor.
4337: Point Set Theory
Cr. 3. (3-0). Prerequisite: MATH 3333
or 3334
or consent of instructor.
4340: Nonlinear Dynamics and Chaos
Cr. 3. (3-0). Prerequisite: MATH
3331 or consent of instructor. Dynamical systems associated with one-dimensional
maps of the interval and the circle; elementary bifurcation theory; modeling
of real phenomena.
4350;4351: Differential
Geometry
Cr. 3 per semester. (3-0).
Prerequisites: MATH 2433,
2431 or equivalent. Frenet frames, metric
tensors, Christoffel symbols, Gaussian curvature, differential
forms, moving frames, Euler characteristics, the Gauss-Bonnet
theorem and Euler-Poincare index theorem.
4360: Integral Equations
Cr. 3. (3-0). Prerequisites: MATH
3331 and 3334. Relation
to differential equations; Fredholm, Hilbert-Schmidt, and Volterra type equations;
special devices and approximation methods.
4362: Theory of Ordinary Differential Equations
Cr. 3. (3-0). Prerequisites: MATH
3331 and 3334. Existence,
uniqueness, and continuity of solutions of single equations and systems of equations;
other topics at the discretion of the instructor.
4364;4365: Numerical Analysis
Cr. 3 per semester. (3-0). Prerequisites: MATH 2431,
3331; COSC 1301
or 2101 or equivalent; or consent
of instructor. Topics selected from numerical linear algebra, approximation
of functions, numerical integration and differentiation, interpolation, approximate
solutions of ordinary and partial differential equations, Fourier methods, optimization.
4377;4378: Advanced Linear Algebra
Cr. 3 per semester.
(3-0). Prerequisites: MATH 2431
and a minimum of three semester
hours of 3000-level mathematics. Matrices, eigenvalues, and canonical
forms.
4383: Number Theory
Cr. 3. (3-0). Prerequisite: MATH 3330
or consent of instructor. Perfect numbers, quadratic reciprocity,
quadratic residues, algebraic numbers, and continued fractions.
4385;4386: Mathematical
Statistics
Cr. 3 per semester. (3-0). Prerequisite: MATH
3339 or equivalent. Linear models - estimation, testing and application
to designs of experiments, nonparametric statistical models.
4390: Applied Mathematics Seminar
Cr. 3. (3-0). Prerequisite:
completion of 27 advanced semester hours in the Applied Analysis
Option. A team approach to a case study of a real-world problem;
emphasis on mathematical modeling and analysis and on written
and oral communication; completion of a technical report.
4397: Selected Topics in Mathematics
Cr. 3. (3-0). Prerequisites:
consent of instructor and MATH 3333, 3334, or 3330. May be repeated
with approval of chair.