

In this Department




Catalog






Other
Links







Mathematics
As
mathematics is both a cultural and a technical field of
study, the curriculum is planned with the following objectives:
(1) to offer students an introduction to mathematics as
an important area of human thought; (2) to prepare students
for graduate study in pure or applied mathematics, and in
such related fields as statistics and operations research;
(3) to serve the needs of students in fields that rely substantially
on mathematics, such as the physical, biological, social
and information sciences, engineering, and business administration;
and (4) to provide liberal arts students with an introduction
to the kinds of mathematical and quantitative thinking important
in the contemporary world.
Individual
guidance in the selection of courses and the design of course
sequences to serve particular needs and interests is offered
by all members of the Department to all students, but the
following information will provide a preliminary basis for
making plans and choices.
Advanced
Placement. Students who have taken one of the two College
Board Advanced Placement Program examinations in calculus,
or the examination in statistics, will receive credit as
follows. Students scoring 4 or 5 on the BC examination in
calculus receive eight hours credit, equivalent to Mathematics
133 and 134. Students scoring 3 on the BC examination in
calculus with an AB subscore of 4 or 5 receive four hours
credit, equivalent to Mathematics 133. Students scoring
4 or 5 on the AB examination in calculus receive four hours
credit, equivalent to Mathematics 133. Students scoring
4 or 5 on the examination in statistics receive four hours
credit, equivalent to Mathematics 113.
Students
given credit for one or more courses in this way do not
need to take a Mathematics Placement Exam. They are encouraged
to place themselves at the appropriate level in the mathematics
curriculum according to the guidelines given below (see
Initial Placement and Course Sequence Suggestions) in consultation
with a member of the Mathematics Department.
Mathematics
Placement Exams. Students wishing to enroll in an entrylevel
calculus course (Mathematics 131, 132, or 133) must take
the Calculus Readiness Exam. Likewise, students wishing
to enroll in an entrylevel statistics course (Mathematics
113 or 114) must take the Statistics Readiness Exam. The
placement exams are given twice during orientation. At other
times they may be taken by arrangement with the Mathematics
Department secretary. Please note that all students, regardless
of their examination scores, are encouraged to consult with
a member of the Mathematics Department concerning their
placement in the mathematics curriculum.
Initial
Placement and Course Sequence Suggestions. Students
who wish to continue their study of mathematics can choose
among the following courses:
Courses
Without Prerequisites. Students who wish to satisfy
the quantitative proficiency requirement, or who, simply
out of curiosity, want to take a course in mathematics are
encouraged to consider the courses numbered 100 and below.
Entrylevel
Statistics Courses. Students whose primary interest
is in the social or behavioral
sciences and who have no need for calculus are encouraged
to consider enrolling in Mathematics 113  Statistical Methods
for the Social and Behavioral Sciences or Mathematics 114
 Statistical Methods for the Biological Sciences. These
courses presuppose good algebra skills and require an appropriate
score on the Statistics Readiness Exam. Students with less
background are encouraged to consider enrolling in Mathematics
100  Elementary Statistics.
Entrylevel
Calculus Courses. Students whose interests are in mathematics,
or in a field requiring calculus, will normally enroll in
Mathematics 131  Calculus Ia: Limits, Continuity, and Differentiation,
or in Mathematics 133  Calculus I: Limits, Continuity,
Differentiation, Integration, and Applications. The particular
course, Mathematics 131 or Mathematics 133, depends on the
student's score on the Calculus Readiness Exam. Note that
students who wish to continue with calculus after completing
Mathematics 131 should take its sequel, Mathematics 132
 Calculus Ib: Integration and Applications. The twosemester
sequence Mathematics 131, 132 is equivalent to the more
intensive single semester course, Mathematics 133.
Courses
Following Entrylevel Calculus. Students whose secondaryschool
preparation includes satisfactory work in calculus obtained
in the College Board Advanced Placement Program or in another
comparable course of study, as well as students who have
completed either Mathematics 132 or 133, can continue their
study of calculus with Mathematics 134  Calculus II: Special
Functions, Integration Techniques, and Power Series. This
course completes the standard introduction to the calculus
of functions of one variable.
Courses
Following Calculus. Students who have completed Mathematics
134 or have been granted credit for this course through
the College Board Advanced Placement Program or another
comparable course of study can register for Mathematics
220  Discrete Mathematics, or Mathematics 231  Multivariable
Calculus, or Mathematics 232  Linear Algebra. Students
planning to major in mathematics are strongly encouraged
to enroll first in Mathematics 220, and thereafter in Mathematics
231 and Mathematics 232. Students planning a concentration
in Applied Mathematics will also need to take Mathematics
113  Statistical Methods for the Social and Behavioral
Sciences or Mathematics 114  Statistical Methods for the
Biological Sciences. Firstyear students should not register
for a 300level mathematics course without consulting with
a member of the Mathematics Department.
Major.
A major in mathematics consists of thirtyfour hours, including
Mathematics 220, 231 and 232. In addition, students select
one of the following two concentrations:
Concentration
in applied mathematics. Students selecting this concentration
must take either Mathematics 113 or Mathematics 114, and
at least 12 hours of advanced mathematics courses numbered
300 and above, including either Mathematics 301 or 327,
and three courses from among 331, 335, 336, 337, 338, and
340.
Concentration
in pure mathematics. Students selecting this concentration
must take at least 12 hours of advanced mathematics courses
numbered 300 and above, including both Mathematics 301 and
327, and at least one of the following twocourse sequences:
Mathematics 301/302, 301/356, 301/358, 327/328 or 327/329.
Important
note: Students planning to pursue graduate work in mathematics,
or a closely related field, need to complete more than the
minimum requirements for the mathematics major. Such students
should plan their major carefully with the advice of a member
of the Mathematics Department.
It
is strongly urged that students specializing in mathematics
also obtain substantial background in some field that uses
mathematics. In particular, students majoring in mathematics
are encouraged to gain some experience with computing. To
that end, credit for one computer science course (that would
also count toward a Computer Science major) may also be
counted toward the thirtyfour hour requirement for the
major in mathematics. Private readings are also available,
with the consent of an instructor, in any area of mathematics
appropriate for a student's major. Finally, interdisciplinary
majors involving a coherent program of work in mathematics
and a related field can be arranged through the College
Individual Majors Committee to suit special student interests
and needs.
Minor.
A minor in mathematics consists of at least fifteen hours
of course work, including any three of Mathematics 220,
231, 232, 234, and at least six hours of courses numbered
300 and above.
Honors.
At the end of their junior year, students with outstanding
records are invited to participate in the Mathematics honors
program. Seniors in the program normally elect three hours
of independent study each semester. This special study is
supervised by a faculty advisor who works closely with the
student. Honors students take a comprehensive examination,
written and oral, at the end of the senior year. This honors
examination is conducted by an outside examiner and is designed
to test both the candidate's knowledge of undergraduate
mathematics and mastery of the subjects emphasized in his
or her independent honors study.
Winter
Term. Most members of the Mathematics Department will
be participating in Winter Term 2002, and will be available
to sponsor projects.
Mathematical
interests in the department include abstract algebra, algebraic
geometry, combinatorics, dynamical systems, mathematics
and computation, differential equations, differential geometry,
history of mathematics, mathematics education, nonEuclidean
geometry, number theory, operations research, probability,
real and complex analysis, topology, and statistics.
Avocational
interests of Department members which could form the basis
for a sponsored Winter Term project include electronic composition
and synthesis of music, games of strategy, and juggling.
For further information regarding these possibilities, inquire
in the Mathematics Department office.
Distinguished
Visiting Scholar. Thanks to the generosity of alumni,
the Mathematics Department is able to sponsor an annual
visit by an eminent mathematical scientist who will conduct
classes and deliver a public lecture.
John
D. Baum Memorial Prize in Mathematics. Established by
the Mathematics Department, this $100 prize is awarded annually
to the Oberlin College student who has achieved the highest
score on the William Lowell Putnam Mathematical Competition.
Rebecca
Cary Orr Memorial Prize in Mathematics. Established
by the family and friends of Rebecca Cary Orr, this $2000
prize is awarded annually by the Mathematics Department
on the basis of scholastic achievement and promise for future
professional accomplishment.

back
to top

Introductory
Courses
030. Topics
in Contemporary Mathematics 3 hours
3NS, QPf
The interaction of mathematics with the social sciences
is the central theme. Topics are drawn from: graph theory,
game theory, linear programming, coding theory, exploratory
data analysis, and combinatorics. Applications are given
to social choice, decisionmaking, management and ecological
modeling. Prerequisites: A working knowledge of elementary
algebra and geometry. Notes: This course does not
count toward a major in Mathematics. It is intended for
students who have not satisfied the quantitative proficiency
requirement. Enrollment Limit: 30.
Sem 1 MATH03001 MWF
3:304:20 Mr. Henle
Sem 2 MATH03001 MWF
9:009:50 Mr. Balasuriya
050. Dots,
Lines, and Coin Flips 3 hours
3NS, QPf
Next offered 20022003.
080. Lies,
Damned Lies, and Decisions 3 hours
3NS, QPf
An introduction to the use of data in everyday life, particularly
decisionmaking. Topics include descriptive statistics and
graphics, data collection methods, probability trees, utility
theory, and decision trees. Notes: This course is
not equivalent to elementary statistics (MATH 100, MATH
113, or MATH 114) and does not count toward a major in mathematics.
It is intended for students who have not satisfied the quantitative
proficiency requirement. Students may not receive credit
for both MATH 080 and any of MATH 100, MATH 113, or MATH
114. Enrollment Limit: 30.
Sem 1 MATH08001 MWF 1:302:20 Mr. Witmer
090. Environmental
Mathematics 3 hours
3NS, QPh
This course focuses on the application of mathematics to
problems concerning the environment. Topics include simulation
(models of population growth, predatorprey relationships,
and epidemics); optimization (applications to groundwater
hydrology, herbivore foraging, and transportation of hazardous
wastes); and decision analysis (applications to management
of endangered species and resolution of environmental disputes).
Notes: This course does not count toward a major
in mathematics. It is intended for students who have not
satisfied the quantitative proficiency requirement. Not
open to any student who has received credit for a course
in mathematics numbered 133 or higher. Enrollment Limit:
20.
Sem 2 MATH 09001 MWF
2:303:20 Mr. Bosch
100. Elementary
Statistics 4 hours
4NS, QPf
An introduction to the statistical analysis of data. Topics
include exploratory data analysis, probability, sampling,
estimation, and hypothesis testing. Statistical software
is introduced, but no prior computer experience is assumed.
This course focuses on statistical ideas and downplays mathematical
formulas. It is intended for students in the social sciences
and humanities with minimal mathematical experience who
have not satisfied the quantitative proficiency requirement.
Notes: MATH 100 does not count toward a mathematics
major and is not open to students who have completed a semester
of calculus. Students may not receive credit for more than
one of MATH 100, MATH 113, and MATH 114. Enrollment Limit:
36.
Sem 1 MATH10001 MTuThF
1:302:20 Mr. Bosch
Sem 2 MATH10001 MTuThF
1:302:20 Mr. Andrews, Mr. Bosch
113. Statistical
Methods for the Social and Behavioral Sciences 4 hours
4NS, QPf
A standard introduction to statistics for students with
a good background in mathematics. Topics covered include
exploratory data analysis, descriptive statistics, probability,
sampling, estimation, and statistical inference. A broad
spectrum of examples is employed. Statistical software is
introduced, but no prior computer experience is assumed.
Prerequisite: An appropriate score on the Statistics
Readiness Exam. Notes: The statistical content of this course
is largely the same as MATH 114; the applications are different.
Students may not receive credit for more than one of MATH
100, MATH 113, and MATH 114. Consent of instructor required.
Sem 1 MATH11301 MWF
10:0010:50 Mr. Andrews Limit: 36
Laboratories

MATH11302 
Tu
9:009:50 
Mr.
Andrews 
Limit:
18 

MATH11303 
Th
10:0010:50 
Mr.
Andrews 
Limit:
18 
Sem
2 
MATH11301 
MWF
10:0010:50 
Mr.
Witmer 
Limit:
36 
Laboratories
MATH11302 Tu 9:009:50 Mr.
Witmer Limit: 18
MATH11303 Th 10:0010:50 Mr.
Witmer Limit: 18
114. Statistical
Methods for the Biological Sciences 4 hours
4NS, QPf
A standard introduction to statistics for students with
a good background in mathematics. Topics covered include
exploratory data analysis, descriptive statistics, probability,
sampling, estimation, and statistical inference. Biological
and medical examples are emphasized. Statistical software
is introduced, but no prior computer experience is assumed.
Prerequisites: An appropriate score on the Statistics
Readiness Exam. Notes: The statistical content of
this course is largely the same as MATH 113; the applications
are different. Students may not receive credit for more
than one of MATH 100, MATH 113, and MATH 114. Consent
of instructor required.
Sem 1 MATH11401 MWF
9:009:50 Mr. Andrews Limit: 36
Laboratories

MATH11402 
Tu
10:0010:50 
Mr.
Andrews 
Limit:
18 

MATH11403 
Th
9:009:50 
Mr.
Andrews 
Limit:
18 
Sem
2 
MATH11401 
MWF
9:009:50 
Mr.
Andrews 
Limit:
36 
Laboratories
MATH11402 Tu 10:0010:50 Mr.
Andrews Limit: 18
MATH11403 Th 9:009:50 Mr.
Andrews Limit: 18
131. Calculus
Ia: Limits, Continuity and Differentiation 4 hours
4NS, QPh
A first course in the calculus of functions of one variable
including supporting material from algebra and trigonometry.
Topics include limits, continuous functions, solution of
equations and inequalities, differentiation of realvalued
functions of one variable, and the graphical analysis of
functions. The twocourse sequence MATH 131, MATH 132 is
equivalent to the more intensive MATH 133. Prerequisite:
An appropriate score on the Calculus Readiness Exam. Consent
of instructor required. Enrollment Limit: 32
Sem 1 MATH13101 MTuThF
10:0010:50 Ms. Knight
MATH13102 MTuThF 1:302:20 Mr.
Henle
132. Calculus Ib: Integration and Applications 4
hours
4NS, QPf
Continuation of MATH 131. Topics include integration of
realvalued functions of one variable, basic properties
of the trigonometric and exponential functions, the fundamental
theorems of the calculus, and applications. Prerequisite:
MATH 131 or an appropriate score on the Calculus Readiness
Exam. Consent of instructor required. Enrollment Limit:
32.
Sem 2 MATH13201 MTuThF
9:009:50 Ms. Knight
MATH13202 MF 10:0010:50,
W 9:0010:50 Mr. Schirokauer
133. Calculus I: Limits, Continuity, Differentiation, 4
hours
Integration, and Applications
4NS, QPf
A standard first course in the calculus of functions of
one variable. Topics include limits, continuous functions,
differentiation and integration of realvalued functions
of one variable, the fundamental theorems of calculus, and
applications. This course is equivalent to the twocourse
sequence MATH 131, MATH 132. Prerequisite: An appropriate
score on the Calculus Readiness Exam. Consent of instructor
required. Enrollment Limit: 32.
Sem
1 

MATH13301 
MTuThF
8:008:50 
Ms.
Colley 


MATH13302 
MTuThF
9:009:50 
Ms.
Colley 


MATH13303 
MTuThF
1:302:20 
Mr.
Balasuriya 
Sem
2 

MATH13301 
MTuThF
10:0010:50 
Mr.
Balasuriya 


134.
Calculus II: Special Functions, Integration Techniques,
and Power Series 4 hours
4NS, QPf
Continuation of the study of the calculus of functions of
one variable. Topics include logarithmic, exponential and
the inverse trigonometric functions, techniques of integration,
polar coordinates, parametric equations, infinite series,
and applications. The course sequences MATH 133, 134 and
MATH 131, 132, 134 both provide a standard introduction
to singlevariable calculus. Prerequisites: MATH
132 or MATH 133. Enrollment Limit: 32.
Sem
1 
MATH13401 
MTuThF
10:0010:50 
Mr.
Balasuriya 

MATH13402 
MTuThF
1:302:20 
Ms.
Colley 
Sem
2 
MATH13401 
MTuThF
9:009:50 
Mr.
Walsh 

MATH13402 
MTuThF
1:302:20 
Mr.
Young 

back
to top

Intermediate
Courses
210. Chaos
and Fractals: An Introduction 3 hours
3NS, QPf
Next offered 20022003.
220. Discrete
Mathematics 3 hours
3NS, QPf
An introduction to a wide variety of mathematical ideas
and techniques that do not involve calculus. Topics such
as graph theory, combinatorics, difference equations, elementary
number theory, recursion, mathematical induction, and logic.
Prerequisite: MATH 133. Enrollment Limit:
32.
Sem
1 

MATH22001 
TuTh
11:0012:20 
Mr.
Schirokauer 


MATH22002 
TuTh
1:302:50 
Mr.
Schirokauer 
Sem
2 

MATH22001 
MWF
11:0011:50 
Mr.
Henle 


MATH22002 
MWF
1:302:20 
Mr.
Henle 
231.
Multivariable Calculus 3 hours
3NS, QPf
An introduction to the calculus of several variables. Topics
considered include vectors and solid analytic geometry,
multidimensional differentiation and integration, and a
selection of applications. Prerequisite: MATH 134.
Enrollment Limit: 32.
Sem
1 

MATH23101 
MWF
11:0011:50 
Mr.
Young 
Sem
2 

MATH23101 
MWF
11:0011:50 
Mr.
Young 


MATH23102 
MWF
3:304:20 
Mr.
Young 
232.
Linear Algebra 3 hours
3NS, QPf
An introduction to linear algebra. Topics considered include
the algebra and geometry of Euclidean nspace, matrices,
determinants, abstract vector spaces, linear transformations,
and diagonalization. Prerequisites: MATH 134 or MATH
220. Enrollment Limit: 32.
Sem
1 

MATH23201 
TuTh
8:359:55 
Mr.
Walsh 
Sem
2 

MATH23201 
MWF
9:009:50 
Ms.
Colley 


MATH23202 
MWF
2:303:20 
Mr.
Walsh 
234.
Differential Equations 3 hours
3NS, QPf
An introduction to analytic, qualitative and numerical methods
for solving ordinary differential equations. Topics include
general first order equations, linear first and second order
equations, numerical methods (Euler, RungeKutta), systems
of first order equations, phase plane analysis, and Laplace
Transforms. There is emphasis throughout the course on geometric
and qualitative interpretations of differential equations,
as well as applications to the natural sciences. Prerequisite:
MATH 231. Enrollment Limit: 32.
Sem 1 MATH23401 TuTh
11:0012:20 Mr. Walsh
240. Applied
Mathematics 3 hours
3NS, QPf
This course will cover several areas of applied mathematical
modeling including linear programming and optimization,
multiple regression, and dynamical systems. Knowledge of
these topics will permit students to construct models that
accurately represent data in a wide range of fields from
image compression to economic theory to population dynamics.
Students will use a variety of software packages to analyze
real world data. Prerequisites: MATH 133 and either
MATH 113 or MATH 114. Enrollment Limit: 20.
Sem 2 MATH24001 MWF
11:0011:50 Mr. Andrews, Mr. Bosch

back
to top

Advanced
Courses
301. Advanced
Calculus 3 hours
3NS, QPf
A rigorous examination of the basic elements of analysis.
The structure of the real number system, continuity, differentiability,
uniform continuity, integrability of functions of a single
variable, sequences, series, and uniform convergence are typical
topics to be explored. Prerequisite: MATH 231. MATH
220 is also highly recommended.
Sem 1 MATH30101 MWF
1:302:20 Mr. Young
302. Topics
in Advanced Calculus: Chaos, Fractals and Dynamics 3
hours
3NS, QPf
This course applies the techniques of Advanced Calculus to
the study of chaotic dynamical systems. One and two dimensional
dynamics, attractors, iterated function systems, and fractal
dimension are typical topics to be explored. Application to
the physical sciences, computer graphics and other branches
of mathematics will be given. Prerequisite: MATH 301
or consent of instructor. Note: Given in alternate
years only.
Sem 2 MATH30201 MWF
11:0011:50 Mr. Walsh
305. Partial
Differential Equations 3 hours
3NS, QPf
A course on analytical solution techniques for partial differential
equations (PDEs) and boundary value problems. Topics include
separation of variables, Fourier series, solutions to classical
PDEs in standard geometries, SturmLiouville theory, and Fourier
transforms. Based on student interest, additional topics may
be chosen from among: numerical solutions techniques to PDEs,
Green's functions, method of characteristics, discrete Fourier
transforms, and specific applications. Note: Given
in alternate years only. Prerequisite: MATH 234.
Sem 1 MATH30501 MWF
3:304:20 Mr. Balasuriya
317. Number
Theory 3 hours
3NS, QPf
This course is an introduction to number theory. Topics include
primality, divisibility, modular arithmetic, finite fields,
cryptography, and elliptic curves. Emphasis will be placed
both on theoretical questions and on algorithms for computation.
Prerequisite: MATH 301 or consent of the instructor.
Note: Given in alternate years only.
Sem 2 MATH31701 MWF
2:303:20 Mr. Schirokauer
327. Group
Theory 3 hours
3NS, QPf
A first course in the modern algebraic structures and techniques
fundamental to mathematics and useful in many areas of science
and engineering. Topics include: groups, subgroups, quotient
groups, isomorphism theorems, permutation groups, finite groups,
and applications to combinatorics, geometry, symmetry, and
crystallography. Prerequisite: MATH 232. MATH 220 is
also highly recommended.
Sem 2 MATH32701 MWF
1:302:20 Ms. Colley
328. Computational
Algebra and Algebraic Geometry 3 hours
3NS, QPf
Next offered 20022003.
329.
Abstract Algebra: Rings and Fields 3 hours
3NS, QPf
This is one of two courses introducing algebraic structures
and techniques fundamental to mathematics and useful in many
areas of science and engineering. Topics include: rings, subrings,
ideals, fields, integral domains, polynomial rings, extension
fields, finite fields, famous impossible constructions. Galois
theory, and algebraic coding theory. Prerequisite:
MATH 232. In addition, MATH 220 is highly recommended. Note:
Given in alternate years only.
Sem 1 MATH32901 MWF
9:009:50 Mr. Schirokauer
331. Optimization 3
hours
3NS, QPf
An introduction to linear, integer, and nonlinear programming.
Emphasis is placed on the theory of mathematical programming
and the analysis of optimization algorithms. These are applied
to significant problems in the fields of medicine, finance,
public policy, transportation, and telecommunications. Prerequisites:
MATH 231 and MATH 232.
Sem 1 MATH33101 MWF
3:304:20 Mr. Bosch
335. Probability 3
hours
3NS, QPf
An introduction to the mathematical theory of probability
and its applications. Topics include discrete and continuous
sample spaces, combinatorial problems, random variables, probability
densities, probability distributions, limit theorems, and
stochastic processes. Prerequisite: MATH 231. MATH
220 is also strongly recommended.
Sem 1 MATH33501 MWF
2:303:20 Mr. Andrews
336. Mathematical
Statistics 3 hours
3NS, QPf
Next offered 20022003.
337. Data
Analysis 3 hours
3NS, QPf
In this course students will be given an introduction
to the theory and use of regression graphics. Special regression
and graphics software will be used to study relationships
among several variables. Topics will include regression smoothing,
residual plots, scatterplot matrices, threedimensional plots,
transformations of predictors and of response variables, and
addedvariable plots. Note: Given in alternate years
only. Prerequisites: MATH 113 or 114 and MATH 232 or
consent of the instructor.
Sem 2 MATH33701 MWF
3:304:20 Mr. Witmer
338. Probability
Models and Random Processes 3 hours
3NS, QPf
An introduction to operations research models which incorporate
methods of probability theory. Topics will be chosen from
inventory theory, queueing theory, decision analysis, game
theory, simulation, Markov chains, and project management.
Computer software for selected topics will also be discussed
and utilized. Note: Given in alternate years only.
Prerequisite: MATH 335.
Sem 2 MATH33801 TuTh
3:004:20 Mr. Bosch
340. Practicum
in Applied Mathematics 3 hours
3NS, QPf
Next offered 20022003.
343. Combinatorics 3
hours
3NS, QPf
Next offered 20022003.
350. Geometry 3
hours
3NS, QPf
This course explores some of the mathematics used to describe
space and distance. Topics will include some or all of the
following: comparison of Euclidean and nonEuclidean geometries,
models of hyperbolic spaces, constructibility problems, and
the differential geometry of curves and surfaces in threespace.
Notes: Given in alternate years only. Prerequisite:
MATH 220.
MATH 231 and MATH 232 are also strongly recommended.
Sem 1 MATH35001 MWF
10:0010:50 Mr. Henle
353. Topology 3
hours
3NS, QPf
Next offered 20022003.
356. Complex
Analysis 3 hours
3NS, QPf
Next offered 20022003.
401. Honors 24
hours
24NS
Consent of instructor required.
995. Private
Reading 13 hours
13NS
Consent of instructor required.

back
to top






