|
10-100 | 200
| 300 | 400 | Graduate
Courses
Mathematics
www.math.iastate.edu
Justin Peters, Chair of Department
Distinguished Professors: Athreya, Gunzburger, Levine
Professors: Bergman, Dahiya, Dickson, Evans, Fink, Gautesen, Hentzel,
Hou, E. Johnston, Kliemann, Lieberman, Luecke, Maddux, Murdock,
Peters, Peterson, Rothmayer, Sacks, Smiley, Smith, Tesfatsion, Tondra,
Willson, Wright
Distinguished Professors (Emeritus): Miller, Vinograde
University Professors (Emeritus): Cornette
Professors (Emeritus): Barnes, Cain, Carlson, Colwell, Homer, Mathews,
Peglar, Pigozzi, Rudolph, Sanderson, Seifert, A. Steiner, E. Steiner,
Weiss
Associate Professors: Alexander, Ashlock, Davidson, Gregorac, Hansen,
Hogben, Keinert, Liu, Poon, Sethuraman, Song, Tidriri, Wagner, Wang,
Weerasinghe, Wilson, Wu
Associate Professors (Collaborators): Yan
Associate Professors (Emeritus): Heimes
Assistant Professors: Axenovich, Burstein, D'Alessandro, Emanouvilov
Assistant Professors (Emeritus): Peake
Lecturers: Chan, Doolittle, Hall, Harper,
G. Johnston, Pfantz, Thompson
Undergraduate Study
For the undergraduate curriculum in liberal arts and sciences, major
in mathematics, leading to the degree bachelor of science, see Liberal
Arts and Sciences, Curriculum.
The program in mathematics offers training suitable for students
planning to enter secondary school teaching, to work in mathematics
and computation for industry or government, or to continue their
studies in graduate school. The requirements for an undergraduate
major in mathematics are designed so that the student may have opportunity
for appropriate specialization to meet one or more of the foregoing
objectives and, at the same time, obtain a thorough introduction
to the mathematics underlying all of them.
Graduates understand a broad range of mathematical topics and are
familiar with a broad range of mathematical models. They have skills
for solving problems in diverse situations. They can construct rigorous
arguments to demonstrate mathematical facts. They can communicate
their mathematical methods to others and can justify their assumptions.
The requirements for an undergraduate major include:
(a) The sequence 175, 176 or the sequence 165, 166, 201. Also 265,
301, 317, 414, and either 266 or 267.
(b) 15 additional credits chosen from math courses at the 300 level
or above, 6 of which must be included in (341, 365, 471, 481).
(c) The courses used to satisfy a) and b) above must include one
of the sequences 301, 302; 414, 415; 435, 436.
(d) In addition to the credits in (b), either Math 492 or 2 credits
of C I/LAS 480C. (C I/LAS 480C is available only for students seeking
secondary school certification).
(e) English proficiency requirement: The department requires a grade
of C- or better in each of English 104 and 105 (or 105H) and an
upper-level writing requirement that may be met by writing an acceptable
undergraduate thesis (Math 491) or by taking at least one of Engl
302, 305, 314 or Jl MC 201. A grade of C- or better is required.
The department strongly recommends that each student majoring in
mathematics include in the program substantial supporting work beyond
the minimum general education requirement of the college in one
or more areas of application of mathematics, such as other mathematical
sciences, engineering, natural science, or social science. In particular,
it recommends that each student take Com S 207, 208; Phys 221, 222;
and Stat 341, 342 (or Math 304). It also strongly recommends two
years of French, German, or Russian for students contemplating graduate
study in mathematics. Credits earned in Math 104, 105, 140, 141,
142, 150, 151, 160, 181, 182, 195, 196, 297, cannot be counted toward
graduation by mathematics majors.
The department offers a minor in mathematics which may be earned
by credit in Math 165, 166, 265, 301, 307 or 317, and 266 or 267.
Courses below 165 cannot be used.
Graduate Study
The department offers programs leading to a master of science or
doctor of philosophy degree in mathematics or applied mathematics,
as well as minor work for students whose major is in another department.
The department also offers a program leading to the degree of master
of school mathematics (M.S.M.).
Students desiring to undertake graduate work leading to the M.S.
or Ph.D. degree should have at least 12 semester credits of work
in mathematics beyond calculus. It is desirable that these credits
include advanced calculus and abstract algebra.
The M.S. degree requires at least 30 credit hours and students must
write a creative component or thesis and pass a comprehensive oral
examination over their coursework and their creative component or
thesis. See the department handbook for specific requirements.
The Ph.D. degree requires a student to take 54 hours of coursework
in addition to research hours, pass written qualifying examinations,
pass an oral preliminary exam, and perform an original research
project culminating in a dissertation which is defended by an oral
exam. Ph.D. candidates must have at least one year of supervised
teaching experience. See the department handbook for specific requirements.
(Also see the website: http://www.math.iastate.edu/dept/grad.html
for details.)
The M.S.M. degree is primarily for inservice secondary mathematics
teachers. Students desiring to pursue the M.S.M degree should present
some undergraduate work in mathematics beyond calculus. Candidates
for the M.S.M. degree must write an approved creative component
and pass a comprehensive oral examination over their course work
and their creative component.
Courses open for nonmajor graduate credit: 301, 302, 304, 307, 308,
314, 317, 331, 350, 365, 378, 385, 395, 414, 415, 421, 426, 435,
436, 439, 465, 471, 481, 484, 489.
Courses Primarily for Undergraduate Students
Math 10. High School Algebra.
(4-0) Cr. 0. F.S.SS. For students who do not have adequate facility
with topics from high school algebra or do not meet the algebra
admission requirement. All students should initially enroll in Math
10. The course is divided into tracks of one- and two-semester lengths.
For most students a diagnostic exam will determine which track must
be taken. Students will receive a grade in Math 25 or 30 respectively
depending on the level of material covered. Satisfactory completion
of Math 30 is recommended for students planning to take Math 140
or 151, while Math 25 is sufficient for Math 104, 105, 150, 195,
Stat 101 or 105. Students must complete Math 30 to remove a deficiency
in the algebra admission requirement. Topics include signed numbers,
polynomials, rational and radical expressions, exponential and logarithmic
expressions, and equations. Offered on a satisfactory-fail grading
basis only.
Math 20. High School Geometry. (4-0)
Cr. 0. S. For students who do not meet the geometry admission requirement.
Elements of Euclidean geometry including congruence, parallel lines,
circles, similar polygons, perimeters, areas, surface areas, and
volumes. Offered on a satisfactory-fail grading basis only.
Math 25. High School Algebra. (4-0)
Cr. 0. F.S.SS. For students who do not have adequate facility with
topics from high school algebra or do not meet the algebra admission
requirement. All students should initially enroll in Math 10. The
course is divided into tracks of one- and two-semester lengths.
For most students a diagnostic exam will determine which track must
be taken. Students will receive a grade in Math 25 or 30 respectively
depending on the level of material covered. Satisfactory completion
of Math 30 is recommended for students planning to take Math 140
or 151, while Math 25 is sufficient for Math 104, 105, 150, 195,
Stat 101 or 105. Students must complete Math 30 to remove a deficiency
in the algebra admission requirement. Topics include signed numbers,
polynomials, rational and radical expressions, exponential and logarithmic
expressions, and equations. Offered on a satisfactory-fail grading
basis only.
Math 30. High School Algebra. (4-0)
Cr. 0. F.S.SS. For students who do not have adequate facility with
topics from high school algebra or do not meet the algebra admission
requirement. All students should initially enroll in Math 10. The
course is divided into tracks of one- and two-semester lengths.
For most students a diagnostic exam will determine which track must
be taken. Students will receive a grade in Math 25 or 30 respectively
depending on the level of material covered. Satisfactory completion
of Math 30 is recommended for students planning to take Math 140
or 151, while Math 25 is sufficient for Math 104, 105, 150, 195,
Stat 101 or 105. Students must complete Math 30 to remove a deficiency
in the algebra admission requirement. Topics include signed numbers,
polynomials, rational and radical expressions, exponential and logarithmic
expressions, and equations. Offered on a satisfactory-fail grading
basis only.
Math 101. Orientation in Mathematics. (1-0)
Cr. R. F. For new majors. Issues to consider in planning a program
of study. Sources of general information and perspectives concerning
mathematics. Discussion of possible areas of study or careers. Offered
on a satisfactory-fail grading basis only.
Math 104. Introduction to Probability and
Matrices. (3-0). Cr. 3. F.S. Prereq: Satisfactory performance
on placement exam, 2 years of high school algebra, 1 year of high
school geometry. Permutations, combinations, probability, binomial
and multinomial theorems, matrices, expected value. Either 104 or
150 may be counted toward graduation, but not both.
Math 105. Introduction to Mathematical Ideas.
(3-0) Cr. 3. F.S. Prereq: Satisfactory performance on placement
exam, 2 years of high school algebra, 1 year of high school geometry.
Topics from mathematics and mathematical applications with emphasis
on their nontechnical content.
Math 140. College Algebra. (3-1) Cr.
3. F.S.SS. Prereq: Satisfactory performance on placement exam,
2 years of high school algebra; 1 year of high school geometry.
Coordinate geometry, complex numbers, quadratic and polynomial equations,
functions, graphing, polynomial and rational functions, exponential
and logarithmic functions, systems of equations. Students in the
College of Liberal Arts and Sciences may not count Math 140, 141,
142, 149, or 195 toward Group III of the General Education Requirements.
Math 141. Trigonometry. (2-0) Cr.
2. F.S.SS. Prereq: Satisfactory performance on placement exam,
2 years of high school algebra; 1 year of high school geometry,
or enrollment in 140. May be taken concurrently with 140. Trigonometric
functions and their inverses, solving triangles, trigonometric identities
and equations, graphing. Students in the College of Liberal Arts
and Sciences may not count Math 140, 141, 142, 149, or 195 toward
Group III of the General Education Requirements. Only one of 141,
142 may count toward graduation.
Math 142. Trigonometry and Analytic Geometry.
(2-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement
exam, 2 years of high school algebra, 1 year of high school geometry,
or enrollment in 140. May be taken concurrently with 140. Trigonometric
functions and their inverses, solving triangles, trigonometric identities
and equations, graphing, polar coordinates, complex numbers, standard
equations of lines and conic sections, parametric equations. Students
in the College of Liberal Arts and Sciences may not count Math 140,
141, 142, 149, or 195 toward Group III of the General Education
Requirements. Only one of 141, 142 may count toward graduation.
Math 149. Precalculus Mathematics.
(5-0) Cr. 4. F. Prereq: Satisfactory performance on placement
exams; 2 years high school algebra; 1 year geometry; 1 semester
of trigonometry. A fast-paced review of topics from algebra,
trigonometry, and analytic geometry required for the Math 165, 166,
265 calculus sequence. Students in the College of Liberal Arts and
Sciences may not count Math 140, 141, 142, 149, or 195 toward Group
III of the General Education Requirements. Only one of 140, 149
may count toward graduation.
Math 150. Discrete Mathematics for Business
and Social Sciences. (2-1) Cr. 3. F.S.SS. Prereq: Satisfactory
performance on placement exam, 2 years of high school algebra, 1
year of high school geometry. Linear equations and inequalities,
linear programming, matrix algebra, discrete probability. Either
104 or 150 may be counted toward graduation, but not both.
Math 151. Calculus for Business and Social
Sciences. (2-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance
on placement exam, 2 years of high school algebra, 1 year of high
school geometry. Differential calculus, integral calculus, introduction
to max-min theory for functions of two variables. Will not serve
as prerequisite for 265 or 266. Only one of 151, 160, the sequence
165-166, the sequence 175-176, or the sequence 181-182 may be counted
towards graduation.
Math 160. Survey of Calculus. (4-0)
Cr. 4. F.S. Prereq: Satisfactory performance on placement exam,
2 years of high school algebra, 1 year of geometry. Analytic
geometry, differentiation and integration of elementary functions.
Will not serve as a prerequisite for 265 or 266. Only one of 151,
160, the sequence 165-166, the sequence 175-176, or the sequence
181-182 may be counted towards graduation.
Math 165. Calculus I. (4-0) Cr. 4.
F.S.SS. Prereq: Satisfactory performance on placement exam, 2
years of high school algebra, 1 year of geometry, 1 semester of
trigonometry or enrollment in 141 or 142. Functions, limits,
continuity, differentiation, derivatives of vector-valued functions,
applications of derivatives. Only one of 151 or 160 or the sequence
165-166, the sequence 175-176, or the sequence 181-182 may be counted
towards graduation.
Math 165H. Honors Calculus I. (4-0)
Cr. 4. F. Prereq: Satisfactory performance on placement exam,
2 years of high school algebra, 1 year of geometry, 1 semester of
trigonometry. High math placement scores recommended but not
required. Functions, limits, continuity, differentiation, derivatives
of vector-valued functions, applications of derivatives. Additional
material of a theoretical, conceptual, computational, or modeling
nature. Some of the work may require more ingenuity than is required
in Math 165. Preference will be given to students in the University
Honors Program. Only one of 151 or 160 or the sequence 165-166 or
the sequence 175-176, or the sequence 181-182 may be counted towards
graduation.
Math 166. Calculus II. (4-0) Cr. 4.
F.S.SS. Prereq: Grade of C- or better in 165, 165H, or 175 or
high math placement scores. Integration, applications of the
integral, matrices, differentiation of functions of several variables.
Only one of 151, 160, the sequence 165-166, the sequence 175-176,
or the sequence 181-182 may be counted towards graduation.
Math 166H. Honors Calculus II. (4-0)
Cr. 4. F.S. Prereq: Permission of instructor and 165, 165H, or
175, or high math placement scores. Integration, applications
of the integral, matrices, differentiation of functions of several
variables. Additional material of a theoretical, conceptual, computational,
or modeling nature. Some of the work may require more ingenuity
than is required for Math 166. Preference will be given to students
in the University Honors Program. Only one of 151, or 160, the sequence
165-166, the sequence 175-176, or the sequence 181-182 may be counted
towards graduation.
Math 181. Calculus and Differential Equations
for the Life Sciences. (3-2) Cr. 4. F.S. Prereq: Satisfactory
performance on placement exam, 2 years of high school algebra, 1
year of high school geometry, 1 semester of trigonometry or enrollment
in 141 or 142. Exponential and logarithm functions, derivative,
first order linear difference equations and differential equations.
Examples taken from laboratory experiments. Only one of 151, 160,
the sequence 165-166, the sequence 175-176, or the sequence 181-182
may be counted towards graduation.
Math 182. Calculus and Differential Equations
for the Life Sciences. (3-2) Cr. 4. F.S. Prereq: 181.
Integral, nonlinear and second order difference equations, and differential
equations. Examples taken from laboratory experiments. Only one
of 151, 160, the sequence 165-166, the sequence 175-176, or the
sequence 181-182 may be counted towards graduation.
Math 195. Mathematics for Elementary Education
I. (2-2) Cr. 3. F.S. Prereq: Satisfactory performance
on placement exam, 2 years high school algebra, 1 year of high school
geometry, enrollment in elementary education. Language of sets,
systems of whole numbers, numeration and algorithms for computation,
topics from number theory, geometric shapes and measurement, congruence,
similarity and transformations, probability and statistics.
Math 196. Mathematics for Elementary Education
II. (2-2) Cr. 3. F.S. Prereq: Grade of C- or better in
195. Language of sets, systems of whole numbers, numeration
and algorithms for computation, topics from number theory, geometric
shapes and measurement, congruence, similarity and transformations,
probability and statistics.
Math 201. Introduction
to Proofs. (2-0) Cr. 2. F.S. Prereq: 166 or 166H.
Reading and writing simple proofs. Proofs involving sequences and
the definitions of limit, derivative, and the definite integral.
Proofs by mathematical induction. Only one of the sequence 175-176
or 201 may be counted towards graduation.
Math 205. Computer Programming in FORTRAN.
(Same as Com S 205.) See Computer Science.
Math 265. Calculus III. (4-0) Cr.
4. F.S.SS. Prereq: Grade of C- or better in 166, 166H, or 176.
Multiple integrals, vector fields and vector integrals, sequences
and series.
Math 265H. Honors Calculus III. (4-0)
Cr. 4. F.S. Prereq: Permission of the instructor; and 166, 166H,
or 176. Multiple integrals, vector fields and vector integrals,
sequences and series. Additional material of a theoretical, conceptual,
computational, or modeling nature. Some of the work may require
more ingenuity than is required in Math 265. Preference will be
given to students in the University Honors Program.
Math 266. Elementary Differential Equations.
(3-0) Cr. 3. F.S.SS. Prereq: Grade of C- or better in 166, 166H,
or 176. Solution methods for ordinary differential equations.
First order equations, linear equations, constant coefficient equations.
Elgenvalue methods for systems of first order linear equations.
Introduction to stability and phase plane analysis.
Math 267. Elementary Differential Equations
and Laplace Transforms. (4-0) Cr. 4. F.S.SS. Prereq: Grade
of C- or better in 166, 166H, or 176. Same as 266 but also including
Laplace transforms and series solutions to ordinary differential
equations.
Math 268. Laplace Transforms. (1-0)
Cr. 1. F. Prereq: 266. Laplace transforms and series solutions
to ordinary differential equations. Together, 266 and 268 are the
same as 267.
Math 273. Introduction to Scientific Computation.
(3-0) Cr. 3. F.S.SS. Prereq: Math 265 or enrollment in Math 265;
Math 266 or Math 267; knowledge of Fortran or C. Vector, matrix
and graphics programming for scientific applications. Algorithms
for interpolation, systems of linear equations, least squares, nonlinear
equations and optimization in one and several variables, and ordinary
differential equations. Emphasis on high quality mathematical software,
its strengths and limitations.
Math 290. Special Problems. Cr. 1
to 3 each time taken.
H. Honors
Math 297. Intermediate Topics in Elementary
Mathematics. (2-2) Cr. 3. F.S. Prereq: Grade of C- or
better in 196. Additional topics in geometry including coordinates,
congruence similarity, and transformations. Pre-algebraic reasoning.
Topics in mathematics of current importance to prospective elementary
teachers.
Math 298. Cooperative Education. Cr.
R. F.S.SS. Prereq: Permission of the department cooperative education
coordinator; sophomore classification. Required of all cooperative
education students. Students must register for this course prior
to commencing each work period.
Math 301. Introduction
to Abstract Algebra. (3-0) Cr. 3. F.S. Prereq: 166 or
166H or 176 and 307 or 317. Introduction to the theory of groups
and rings. Emphasis on writing proofs. Nonmajor graduate credit.
Math 302. Introduction to Abstract Algebra. (3-0) Cr. 3.
S. Prereq: 301. Theory of fields, abstract vector spaces,
and linear algebra. Emphasis on writing proofs. Nonmajor graduate
credit.
Math 304. Introductory Combinatorics.
(3-0) Cr. 3. F. Prereq: 166, 166H or 176. Permutations, combinations,
binomial coefficients, inclusion-exclusion principle, discrete probability,
classical probability. Additional topics selected from recurrence
relations, generating functions, random walks, and Markov chains.
Nonmajor graduate credit.
Math 307. Theory of Matrices. (3-0)
Cr. 3. F.S.SS. Prereq: 2 semesters of calculus. Systems of
linear equation, determinants, vector spaces, inner products, linear
transformations, eigenvalues and eigenvectors. Emphasis on methods
and techniques. Only one of 307, 317 may be counted toward graduation.
Nonmajor graduate credit.
Math 308. Application of Linear Algebra to
Discrete Optimization. (3-0) Cr. 3. S. Prereq: 307 or
317. Linear programming and topics chosen from game theory,
transportation and assignment problems, discrete dynamic processes,
and multiple objective linear programming. Nonmajor graduate credit.
Math 314. Graphs and Networks. (3-0)
Cr. 3. S. Prereq: 166, 166H or 176. Graphs, directed graphs,
and trees. Connectedness. Graph colorings. Eulerian and Hamiltonian
chains. Matching and covering. Optimization for networks. Applications.
Nonmajor graduate credit.
Math 317. Theory of Linear Algebra.
(4-0) Cr. 4. F.S. Prereq: 166. Systems of linear equations,
determinants, vector spaces, inner product spaces, linear transformations,
eigenvalues and eigenvectors. Emphasis on writing proofs and results.
Nonmajor graduate credit. Only one of 307, 317 may be counted toward
graduation.
Math 331. Topology. (3-0) Cr. 3. Alt.
S., offered 2005. Prereq: 307 or 317. Topological properties
of metric spaces, including Rn, sequences, continuous functions,
completeness, compactness. Nonmajor graduate credit.
Math 341. Introduction to Theory of Probability
and Statistics. (Same as Stat 341.) See Statistics.
Math 342. Introduction to Theory of Probability
and Statistics. (Same as Stat 342.) See Statistics.
Math 350. Number Theory. (3-0) Cr.
3. Alt. S., offered 2005. Prereq: 307 or 317. Properties
of the integers. Diophantine equations, prime number distribution
and representation problems. Applications to cryptography. Nonmajor
graduate credit.
Math 365. Complex Variables with Applications.
(3-0) Cr. 3. F.S. Prereq: 265. Functions of a complex variable,
including differentiation, integration and series expansions, residues,
evaluation of integrals, conformal mapping. Only two of 365, 385,
395 may be counted toward graduation. Nonmajor graduate credit.
Math 378. Optimization and Modeling with
Artificial Life. (3-0) Cr. 3. S. Prereq: One of 301, 304,
Com S 330 or other discrete math. Familiarity with programming.
Introduction to the modeling and optimization techniques that together
are called artificial life or alife. Biological paradigms from evolution
and ecology are used to solve problems in biology, engineering and
areas such as combinatorial or functional optimization. Evolutionary
programming, genetic algorithms, genetic programming, evolutionary
neural nets, and their uses in optimization and modeling. Nonmajor
graduate credit.
Math 385. Introduction to Partial Differential
Equations. (3-0) Cr. 3. F.S. Prereq: 265 and one of 266,
267. Separation of variables methods for elliptic, parabolic,
and hyperbolic partial differential equations. Fourier series, Sturm-Liouville
theory, Bessel functions, and spherical harmonics. Only two of 365,
385, 395 may be counted toward graduation. Nonmajor graduate credit.
Math 395. Intermediate Engineering Mathematics.
(4-0) Cr. 4. F.S. Prereq: 265 and 267. Complex variables
and analytic functions, complex integration techniques, complex
series, Fourier series, separation of variables in partial differential
equations. Only two of 365, 385, 395 may be counted toward graduation.
Nonmajor graduate credit.
Math 398. Cooperative Education. Cr.
R. F.S.SS. Prereq: Permission of the department cooperative education
coordinator; junior classification. Required of all cooperative
education students. Students must register for this course prior
to commencing each work period.
Math 414. Advanced Calculus.
(3-0) Cr. 3. F.S.SS. Prereq: 201 or 176; 265; and 307 or 317.
A careful development of calculus of functions of a real variable:
limits, continuity, differentiation, integration, series. Nonmajor
graduate credit.
Math 415. Advanced Calculus. (3-0)
Cr. 3. S. Prereq: 414. Sequences and series of functions
of a real variable, uniform convergence, power series and Taylor
series, Stone-Weierstrass Theorem, elementary functions, Fourier
series, introduction to measure theory and Lebesgue integration.
Other topics at the discretion of the instructor. Nonmajor graduate
credit.
Math 421. Logic for Mathematics and Computer
Science. (Same as Com S 421.) (3-0) Cr. 3. S. Prereq:
301 or 307 or 317 or Com S 330. Propositional and predicate
logic, Horn logic, equational logic, resolution and unification,
foundations of logic programming, reasoning about programs, program
specification and verification. Nonmajor graduate credit.
Math 426. Mathematical Methods for the Physical
Sciences. (3-0) Cr. 3. F. Prereq: 266 or 267. A fast-paced
course primarily for first-year graduate students in physics and
chemistry. Emphasis on techniques needed for quantum mechanics and
electrodynamics. Functions of a complex variable and contour integration,
integral transforms and applications, series methods for ordinary
differential equations, Green's functions, Sturm-Liouville problems
and orthogonal functions, boundary-value problems for partial differential
equations. Credit will not be given for both 395 and 426. Nonmajor
graduate credit.
Math 435. Geometry. (3-0) Cr. 3. F.
Prereq: 307 or 317. Euclidean geometry through properties
invariant under similarity transformations. Use of both synthetic
and analytic methods. Nonmajor graduate credit.
Math 436. Geometry. (3-0) Cr. 3. S.
Prereq: 435. Non-Euclidean geometry through properties invarient
under isometric transformations. Analytic methods applied to at
least two of elliptic, projective, and hyperbolic geometries. Nonmajor
graduate credit.
Math 439. Mathematics of Fractals.
(3-0) Cr. 3. Alt. S., offered 2004. Prereq: 265; some knowledge
of programming. Topology of metric spaces; iterated function
systems; algorithms for generation of fractals; fractal dimension;
Julia sets and the Mandelbrot set; applications to chaotic systems.
Nonmajor graduate credit.
Math 465. Advanced Calculus for Applied
Mathematics. (4-0) Cr. 4. F.SS. Prereq:
265. Frequently applied concepts from multivariable calculus,
presented with enough theory to promote understanding of applications.
Topics may include derivative matrices, Taylor polynomials, curvilinear
coordinates, Green's theorem, divergence theorem, Stokes's theorem,
uniform convergence, operations on series and integrals, improper
integrals. Nonmajor graduate credit.
Math 471. Computational Linear Algebra
and Fixed Point Iteration. (Same as Com
S 471.) (3-0) Cr. 3. F.S. Prereq: 265 and either 266, or 267;
knowledge of FORTRAN or C. Computational error, solutions of
linear systems, least square methods, similarity methods for eigenvalues,
non-linear equations, fixed point iteration in one and several variables,
Newton's method in several variables. Nonmajor graduate credit.
Math 481. Numerical Solution of Differential
Equations and Interpolation. (Same as
Com S 481.) (3-0) Cr. 3. S.SS. Prereq: 265 and either 266 or
267; knowledge of FORTRAN or C. Orthogonal polynomials, least
square and spline methods, numerical differentiation and integration,
Euler, Taylor, Runge-Kutta, and predictor-corrector methods for
solution of systems of ordinary differential equations. Nonmajor
graduate credit.
Math 484. Computational Mathematics
for Biologists. (Same as BCB 484.) (3-0)
Cr. 3. F. A survey of graph theory, linear algebra, discrete math,
and algorithms used in computational biology with examples taken
from genomics, phylogenetics, and structure problems. This course
provides mathematics background for BCB/Gen/Com S/Math 594. Nonmajor
graduate credit.
Math 489. History of Mathematics.
(3-0) Cr. 3. S. Prereq: 6 credits in mathematics at the 300 level
or above. History of mathematical ideas found in the undergraduate
curriculum. It includes a discussion of the historical and cultural
settings in which these ideas arose, and the influence of the culture
on the type of mathematical ideas that developed. Some of the particular
cultures and their mathematics that are studied include: Babylonian
and Ancient Egyptian. Ancient Greek, Arabic, Indian, Western European
and Chinese. Nonmajor graduate credit.
Math 490. Independent Study.
Cr. 1 to 3 each time taken. Prereq: 301 or 317; 6 credits in
mathematics. No more than 9 credits of Math 490 may be counted
toward graduation.
H.Honors
Math 491. Undergraduate Thesis.
Cr. 2 or 3. Writing a formal mathematics paper. Upon approval by
the department, the paper will satisfy the departmental advanced
English requirement.
Math 492. Undergraduate Seminar.
Cr. 2. S. Prereq: Consent of instructor. Introduction to
mathematics research. Mathematical presentation, mathematical literature
search, participating in seminar on advanced topics in mathematics.
Seminar content varies.
Math 497. Teaching Secondary School
Mathematics. (Same as C I 497.) See Curriculum
and Instruction.
Math 498. Cooperative Education.
Cr. R. F.S.SS. Prereq: Permission of the department cooperative
education coordinator; senior classification. Required of all
cooperative education students. Students must register for this
course prior to commencing each work period.
Courses Primarily for
Graduate Students, Open to Qualified Undergraduate Students
Math 501. Introduction to Real Analysis.
(3-0) Cr. 3. F. Prereq: 265 and 307 or 317. A careful development
of the real numbers. Study of metric spaces, completeness, continuity,
and sequences, with particular attention to Rn and real valued functions
of one and several variables. Differentiation and integration of
real valued functions, sequences of functions, limits and convergence,
equicontinuity.
Math 502. Numerical Analysis I.
(3-0) Cr. 3. F. Prereq: 414. Numerical linear algebra including
eigenvalue problems; numerical solution of nonlinear equations and
optimization problems.
Math 503. Numerical Analysis II. (3-0)
Cr. 3. S. Prereq: 414. Approximation theory, including polynomial
interpolation and best approximation; numerical integration; numerical
methods for ordinary differential equations.
Math 504. Abstract Algebra.
(3-0) Cr. 3. F. Prereq: 302. First semester of full-year
course. Algebraic systems and their morphisms, including groups,
rings, modules, and fields.
Math 505. Abstract Algebra.
(3-0) Cr. 3. S. Prereq: 504. Continuation of 504.
Math 507. Numerical Solution of Ordinary
Differential Equations. (Same as Com S
507.) (3-0) Cr. 3. SS. Prereq: 481 or 465 or 415; knowledge of
FORTRAN or C. One step methods for initial value problems, one-step
methods for systems, multistep methods, boundary-value problems.
Examples using university computers.
Math 510. Linear Algebra.
(3-0) Cr. 3. S. or SS. Prereq: 302 or 307 or 317. Advanced
topics in linear algebra including canonical forms, inner product
spaces, bilinear forms, tensor products, and applications to other
branches of mathematics.
Math 511. Functions of a Single Complex
Variable. (3-0) Cr. 3. S. or SS. Prereq:
465 or 414. Theory of analytic functions, integration, topology
of the extended complex plane, singularities and residue theory.
Math 514. Measure Theory.
(3-0) Cr. 3. F. Prereq: 414. Measure and integration, construction
of measures (Lebesgue and Lebesgue-Stieltjes measures), Lp spaces,
Hilbert spaces, differentiation, Radon-Nikodym theory, product measures,
finite measure spaces. Primarily for non-majors, particularly statistics.
Math 515. Real Analysis I.
(3-0) Cr. 3. F. Prereq: 414 or 501. Measure and integration,
differentiation, topology of metric spaces, Lp spaces, Hilbert spaces.
Math 516. Real Analysis II. (3-0)
Cr. 3. S. Prereq: 515. Elementary theory of Banach spaces.
Product integration, Fubini's theorem. Decomposition of measures;
differentiation theory. Fourier analysis.
Math 517. Finite Difference Methods.
(3-0) Cr. 3. F. Prereq: 414. Finite difference methods for
parabolic equations; finite difference methods for linear hyperbolic
equations and hyperbolic conservation laws; elliptic equations and
iterative methods.
Math 518. Finite Element Methods.
(3-0) Cr. 3. S. Prereq: 414. Elements of functional analysis;
Sobolev spaces; variational principles and weak formulations; approximation
theory in finite element spaces; analysis of finite element methods;
implementation issues; applications.
Math 519. Methods of Applied Mathematics
I. (3-0) Cr. 3. F. Prereq: 365 or 385
or 426 or 465. Techniques of classical and functional analysis
with applications to partial differential equations, integral equations,
and boundary value problems for ordinary differential equations.
Math 520. Methods of Applied Mathematics
II. (3-0) Cr. 3. S. Prereq: 519. Continuation
of Math 519.
Math 525. Numerical Analysis of High
Performance Computing. (Same as Com S
525, Cpr E 525.) (3-0) Cr. 3. S. Prereq: Cpr E 308, or one of
Math 471, 481; experience in scientific programming; knowledge of
FORTRAN or C. Development, analysis, and testing of efficient
numerical methods for use on current state-of-the-art high performance
computers. Applications of the methods to the students' areas of
research.
Math 527. Mathematics of Complex Physical
Systems. (3-0) Cr. 3. S. Prereq: 365
or 426; 385. Classical "molecular" dynamics, stochastic
modeling and Monte-Carlo techniques, random walks and diffusion
processes, nonlinear dynamics and pattern formation.
Math 531. Introduction to Functional
Analysis. (3-0) Cr. 3. Alt. F, offered
2003. Prereq: Permission of instructor. First semester of
full-year course. Fundamental theory of normed linear spaces and
algebras emphasizing aspects that provide a framework for the study
of boundary-value problems, eigenvalue problems, harmonic analysis,
analytic function theory, and modern operator theory.
Math 532. Introduction to Functional
Analysis. (3-0) Cr. 3. Alt. S., offered
2004. Prereq: 531. Continuation of 531.
Math 533. Cryptography.
(Same as Cpr E 533, InfAs 533.) (3-0) Cr. 3. S. Prereq: Math
301 or Cpr E 310 or Com S 330. Basic concepts of secure communication,
DES and IDEA, public-key cryptosystems, elliptic curves, hash algorithms,
digital signatures, applications. Relevant material on number theory
and finite fields.
Math 534. Topology.
(3-0) Cr. 3. F. Prereq: Permission of instructor. Introduction
to general topology. Emphasizes topics useful in analysis.
Math 537. Algebraic Topology.
(3-0) Cr. 3. Alt. S., offered 2005. Prereq: 331 or 534; 301.
Foundations of algebraic topology. Simplicial complexes. Simplicial
and singular homology groups.
Math 540. Seminar in Mathematics Education.
(3-0) Cr. 3. Offered on a 3-year cycle,
offered SS. 2005. Prereq: Enrollment in the master of school
mathematics program or professional studies in education. Research
studies in mathematics learning and teaching, exemplary practices
in mathematics education, and current state and national trends
in the mathematics curriculum in grades K-12.
Math 542. Investigating the Teaching
and Learning of Secondary Mathematics.
(1-0) Cr. 1. Alt. F., offered 2004. Prereq: Enrollment in master
of school mathematics program, professional studies in education
or by permission for secondary mathematics education majors.
Research, discussion and evaluation of efforts to improve instruction
in the mathematics classroom. Math 542 may be taken for credit multiple
times.
Math 543. Seminar in Mathematics Education.
(1-0) Cr. 1. F. Prereq: Teaching a mathematics course. Selected
topics in collegiate mathematics education including cooperative
learning, instructional use of technology, writing in mathematics,
and cognitive learning theories. Research studies, exemplar practices,
and trends in mathematics education.
Math 545. Intermediate Calculus.
(4-0) Cr. 4. Offered on a 3-year cycle, offered SS. 2004. Prereq:
3 semesters of calculus and enrollment in the master of school mathematics
program. Further development of the fundamental concepts of
calculus and their applications with an emphasis on a constructivist
approach to learning, cooperative groups, problem solving, the use
of technology.
Math 546. Algorithms in Analysis and
Their Computer Implementation. (2-2) Cr.
3. Offered on a 3-year cycle, offered SS. 2004. Prereq: 3 semesters
in calculus or concurrent enrollment in 545 and enrollment in the
master of school mathematics program. The use of technology
in secondary mathematics with an emphasis on the exploration and
implementation of algorithms.
Math 547. Discrete Mathematics and
Applications. (4-0) Cr. 4. Offered on
a 3-year cycle, offered SS. 2006. Prereq: Enrollment in the master
of school mathematics program. Applications of graph theory,
game theory, linear programming, recursion, combinatorics and algebraic
structures. Issues in integrating discrete topics into the secondary
curriculum. Use of the computer to explore discrete mathematics.
Math 549. Intermediate Geometry.
(3-0) Cr. 3. Offered on a 3-year cycle, offered SS. 2006. Prereq:
435 or equivalent and enrollment in the master of school mathematics
program. A study of geometry with emphasis on metrics, the group
of isometries, the group of similarities, and the affine group.
Specific spaces studied normally include the Euclidean plane, the
2-sphere, and projective 2-space. Emphasis on analytical methods.
Math 551. Design Theory and Association
Schemes. (3-0) Cr. 3. F. Prereq: 301
or 304 or 307 or 317. Combinatorial designs and Latin squares.
Construction methods including finite fields. Error-correcting codes.
Adjacency matrices and algebraic combinatorics.
Math 552. Enumerative Combinatorics
and Ordered Sets. (3-0) Cr. 3. S. Prereq:
301 or 304 or 307 or 317. Ordered sets and lattices. Generating
functions. Möbius inversion and other enumeration methods.
Math 554. Introduction to Stochastic
Processes. (Same as Stat 554.) (3-0) Cr.
3. S. Prereq: Stat 542. Markov chains on discrete spaces
in discrete and continuous time (random walks, Poisson processes,
birth and death processes) and their long-term behavior. Optional
topics may include branching processes, renewal theory, introduction
to Brownian motion.
Math 555. Theory of Stochastic Processes.
(Same as Stat 555.) (3-0) Cr. 3. F. Prereq: 514 or 515 , Stat
542. Martingales. Markov processes on continuous spaces and
their qualitative behavior. Wiener processes. Optional topics may
include elementary theory of Ito calculus and diffusions, linear
stochastic systems, advanced topics in branching process.
Math 557. Ordinary Differential Equations.
(3-0) Cr. 3. F. Prereq: 266 or 267; 307 or 317; 415 or 465.
First semester of full-year course. The initial-value problem, existence
and uniqueness theorems, continuous dependence on parameters, linear
systems, stability and asymptotic behavior of solutions, topics
from dynamical systems and two-point boundary-value problems.
Math 558. Ordinary Differential Equations.
(3-0) Cr. 3. Alt. S., offered 2005. Prereq: 557. Continuation
of 557.
Math 561. Dynamical Systems.
(3-0) Cr. 3. Alt. S., offered 2005. Prereq: 414. Smooth mappings
and flows on manifolds. Fixed points, stable, unstable and center
manifolds, normal forms. Structural stability, bifurcations. Horseshoe
maps, introduction to chaotic behavior.
Math 562. Manifolds, Tensors and Differential
Geometry. (3-0) Cr. 3. Alt. S., offered
2004. Prereq: 414. Geometry of curves and surfaces. Manifolds,
coordinate systems. Tensors, differential forms, Riemannian metrics.
Connections, covariant differentiation, curvature tensors.
Math 567. Boolean Algebras.
(3-0) Cr. 3. Alt. S., offered 2005. Prereq: 302 or 421. Structure
of Boolean algebras and their representations. Stone spaces and
duality. Atomicity, completeness, distributivity, operators, extensions
of homomorphisms. Examples and applications from mathematical logic
and topology.
Math 571. Mathematical Logic.
(3-0) Cr. 3. Alt. F., offered 2004. Prereq: 421. First semester
of full-year course. Algebraic structures in logical systems, recursive
functions, consistency, undecidability and incompleteness of axiomatic
theories, results of Gentzen and Gödel, theory of models, ultraproducts
and ultralimits, nonstandard analysis.
Math 572. Mathematical Logic.
(3-0) Cr. 3. Alt. S., offered 2005. Prereq: 571. Continuation
of 571.
Math 573. Random Signal Analysis and
Kalman Filtering. (Same as Aer E 573,
E E 573, M E 573.) (3-0) Cr. 3. F. Prereq: E E 321 or Aer E 331
or M E 370 or M E 411 or Math 341 or 395. Elementary notions
of probability. Random processes. Autocorrelation and spectral functions.
Estimation of spectrum from finite data. Response of linear systems
to random inputs. Discrete and continuous Kalman filter theory and
applications. Smoothing and prediction. Linearization of nonlinear
dynamics.
Math 574. Optimal Control.
(Same as Aer E 574, E E 574, M E 574.) (3-0) Cr. 3. S. Prereq:
577. The optimal control problem. Variational approach. Pontryagin's
principle. Hamilton-Jacobi equation. Dynamic programming. Time-optimal,
minimum fuel, minimum energy control systems. The regulator problem.
Structures and properties of optimal controls.
Math 575. Introduction to Robust Control.
(Same as E E 575.) See Electrical Engineering.
Math 576. Digital Feedback Control
Systems. (Same as Aer E 576, E E 576,
M E 576.) (3-0) Cr. 3. F. Prereq: 415 or Aer E 432 or E E 475
or M E 411 or M E 414; and Math 267. Sampled-data, discrete
data, and the z-transform. Design of digital control systems using
transform methods: root locus, frequency response and direct design
methods. Design using state-space methods. Controllability, observability,
pole placement, state estimators. Digital filters in control systems.
Microcomputer implementation of digital filters. Finite wordlength
effects. Linear quadratic optimal control in digital control systems.
Simulation of digital control systems.
Math 577. Modern Control Systems I.
(Same as Aer E 577, E E 577, M E 577.) (3-0) Cr. 3. F. Prereq:
415 or Aer E 331 or M E 414; and Math 307 or 317. State variable
and input-output descriptions of linear continuous-time and discrete-time
systems. Solution of linear dynamical equations. Controllability
and observability of linear dynamical systems. Canonical descriptions
of linear equations. Irreducible realizations of rational transfer
function matrices. Canonical form dynamical equations. State feedback.
State estimators. Decoupling by state feedback. Design of feedback
systems. Stability of linear dynamical systems.
Math 578. Modern Control Systems II.
(Same as Aer E 578, E E 578, M E 578.) (3-0) Cr. 3. S. Prereq:
577. Well-posedness of nonlinear control systems. Approximate
analysis methods. Poincaré perturbation method and describing
function method. Lyapunov stability theory. Absolute stability of
feedback systems. Input-output stability. Large-scale systems.
Math 579. Adaptive Control.
(Same as E E 579.) See Electrical Engineering.
Math 584. Category Theory.
(3-0) Cr. 3. Alt. F., offered 2004. Prereq: 302. Categories
and functors and their applications.
Math 585. Partial Differential Equations.
(3-0) Cr. 3. Alt. F., offered 2003. Prereq: 515 or 519. First
semester of full-year course. First order equations and systems.
General theory of linear partial differential equations including
wave, heat and potential equations in several variables; maximum
principles, theory of distributions and fundamental solutions. Variational
and Hilbert space methods; evolutionary equations and applications
of semigroup theory; introduction to the theory of nonlinear equations
and systems. One or more of ill posed problems, singularity formation,
regularity theory, equations of mixed type, bifurcation theory.
Math 586. Partial Differential Equations.
(3-0) Cr. 3. Alt. S., offered 2004. Prereq: 585. Continuation
of 585.
Math 588. General Theory of Algebraic
Structures. (3-0) Cr. 3. Alt. F., offered
2003. Prereq: 504. First semester of full-year course. Subalgebras,
homomorphisms, congruence relations, and direct products. Lattices
and closure operators. Varieties and quasivarieties of algebras,
free algebras, Birkhoff's theorems, clones, Mal'cev conditions.
Advanced topics.
Math 589. General Theory of Algebraic
Structures. (3-0) Cr. 3. Alt. S., offered
2004. Prereq: 588. Continuation of 588.
Math 590. Special Topics.
Cr. var.
Math 594. Computational Molecular
Biology. (Same as Gen 594.) See Zoology
and Genetics.
Math 597. Introductory Computational
Structural Biology. (Same as BCB 597.)
(3-0) Cr. 3. S. Prereq: Math 265 and some knowledge of programming.
Mathematical and computational approaches to protein structure prediction
and determination. Topics include molecular distance geometry, potential
energy minimization, and molecular dynamics simulation.
Math 599. Creative Component. Cr.
var.
Courses for Graduate Students
Math 610. Seminar.
Cr. var.
Math 642. Advanced Probability Theory.
(Same as Stat 642.) See Statistics.
Math 690. Advanced Topics.
Cr. var. Prereq: Permission of instructor.
A. Algebra
B. Functional Analysis
C. Measure Theory
D. Approximation Theory
E. Linear Algebra
F. Calculus of Variations
H. Harmonic Analysis
I. Combinatorics
K. Mathematics Education
L. Logic and Foundations
M. Complex Analysis
N. Numerical Analysis
O. Ordinary Differential Equations
P. Partial Differential Equations
Q. Group Theory
R. Mathematical Physics
S. Set Theory
T. Topology
U. Automata Theory
V. Optimization Theory
W. Probability and Stochastic Processes
Y. Special Functions
Z. Ring Theory
Math 699. Research.
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