20102011 Catalog [ARCHIVED CATALOG]
Mathematics


Introduction
The Department of Mathematics offers majors and minors in mathematics, applied mathematics and mathematics education. Combined majors are offered in mathematics and computer science, biology and mathematics, chemistry and mathematics, economics and mathematics, and physics and mathematics. The department also offers a Master of Science degree in which there is an emphasis on applied mathematics.
By taking a significant number of graduate math courses as an undergraduate, it is possible to earn both a Bachelor of Science and a Master of Science degree in mathematics within five years of study. Detailed requirements for this option are available from the Department of Mathematics.
The majors mentioned above will serve as components of a liberal education, but each one also prepares the recipient for a career in business, industry, government or education. Further information about career opportunities is available in the department office. Persons planning a career in almost any field will find their opportunities for interesting and challenging positions enhanced by the study of mathematics. A person who develops the ability to formulate and solve quantitative problems will be able to attack many of the complex problems of society.
Mathematics
Mathematics has developed from attempts to find simple general laws governing the behavior of the phenomena we observe around us, phenomena as diverse as the motion of the planets, the evolution of biological systems and the movement of traffic.
These attempts have been remarkably successful, although many problems remain to be solved. The concepts involved are profound and exciting; their development and use require imagination and careful deductive reasoning.
Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics is a diverse discipline that deals with data, measurements, and observations from science, with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.
As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and change. As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs observation, simulation, and even experimentation as means of discovering truth.
The special role of mathematics in education is a consequence of its universal applicability. The results of mathematics — theorems and theories — are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty.
In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power — a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives.
Mathematics empowers us to understand better the informationladen world in which we live.
— Excerpts from Everyone Counts: A Report to the Nation on the Future of Mathematics Education
© 1989, National Academy of Sciences
The purpose of the mathematics and applied mathematics majors is to acquaint the student with mathematical concepts; to provide the student with the tools needed to apply the concepts in other fields; and to continue to learn and develop new ideas.
A student primarily interested in the application of mathematical ideas in another field should elect the major in applied mathematics or mathematics and computer science. A student who is interested in some branch of mathematics itself, or who is considering graduate study in mathematics, should choose the mathematics major. A student considering a career as an actuary should consult the department for specific course suggestions. A student who is unsure about future plans should probably choose the mathematics major because of the greater flexibility it offers.
Faculty
TJALLING J. YPMA (1987) Chair and Professor. BSc, University of Cape Town; MSc, DPhil, Oxford University.
EDOH Y. AMIRAN (1989) Associate Professor. BA, University of Chicago; PhD, Massachusetts Institute of Technology.
AMY ANDERSON (2007) Assistant Professor. BS, Central Washington University; MA, University of Oregon; PhD, University of Washington.
ARPAD BENYI (2005) Associate Professor. BS, MS, West University of Timisoara, Romania; MA, PhD, University of KansasLawrence.
DONALD R. CHALICE (1967) Associate Professor. BA, University of Wisconsin; MA, PhD, Northwestern University.
VICTOR CHAN (2001) Associate Professor. BA, Whitman College; MS, State University of New YorkStony Brook; MS, PhD, Iowa State University.
JESSICA S. COHEN (2010) Assistant Professor. BS, Western Oregon University; MS, PhD, Oregon State University
BRANKO CURGUS (1988) Professor. BS, MS, PhD, University of Sarajevo.
RICHARD J. GARDNER (1991) Professor. BSc, PhD, University College, London; DSc, University of London.
TILMANN E.C. GLIMM (2005) Associate Professor. First Degree, Technische Universitat, Berlin; MS, PhD, Emory University.
DAVID A. HARTENSTINE (2004) Associate Professor. BA, University of Pennsylvania; PhD, Temple University, Philadelphia.
NORA HARTSFIELD (1984) Professor. BA, Humboldt State University; MA, PhD, University of CaliforniaSanta Cruz.
ROBERT I. JEWETT (1970) Professor. BS, California Institute of Technology; MS, PhD, University of Oregon.
JERRY L. JOHNSON (1984) Professor. BA, Augsburg College; MS, California Institute of Technology; MA, University of CaliforniaLos Angeles; PhD, University of Washington.
MILLIE J. JOHNSON (1991) Associate Professor. BS, University of Minnesota; MEd, University of Washington.
STEPHEN R. MCDOWALL (2001) Associate Professor. BS, MS, University of Canterbury, New Zealand; PhD, University of Washington.
KIMBERLY A. MARKWORTH (2010) Assistant Professor. BA, Dartmouth; M.Ed. Harvard; PhD, University of North Carolina, Chapel Hill.
MICHAEL NAYLOR (1999) Associate Professor. BS, Michigan State University; MS, PhD, Florida State University.
ADAM NYMAN (2008) Assistant Professor. BS, Massachusetts Institute of Technology; PhD, University of Washington.
THOMAS T. READ (1967) Professor. BA, Oberlin College; MA, PhD, Yale University.
AMITES SARKAR (2007) Assistant Professor. BA, PhD, Cambridge University.
YUNQIU SHEN (1988) Professor. BS, University of Science and Technology of China; MS, PhD, Michigan State University.
STEPHANIE A. TRENEER (2008) Assistant Professor. BA, Whitman College; PhD, University of Illinois at UrbanaChampaign.
JIANYING ZHANG (2006) Assistant Professor. BS, MS, Tsinghua University, China; PhD, University of CaliforniaSanta Barbara.
Declaration Process
Students who intend to complete a major in the department are urged to declare the major formally at an early point in their Western career so that a program of study can be planned in collaboration with a departmental advisor. This does not in any way decrease the opportunity to change plans, but does ensure an efficient program which is not subject to future catalog revisions.
Departmental Honors
The mathematics department offers two means of recognition for outstanding students. One, Graduation with Merit in Mathematics, is an award which recognizes outstanding scholastic achievement in courses required for the major. The second, Graduation with Distinction in Mathematics, is a program which rewards exceptional achievement in mathematics as evidenced by meeting all the requirements for Graduation with Merit and completing certain additional requirements detailed below. While Graduation with Merit is automatically conferred on all students who qualify, students must apply to the Chair of the Department of Mathematics to participate in the program for Graduation with Distinction in Mathematics.
Students interested in these programs should also inquire into the possibility of earning both a Bachelor of Science and a Master of Science degree in mathematics within five years of study. Detailed requirements for this option are available from the Department of Mathematics.
Graduation with Merit
To graduate with merit in mathematics, a student must complete one of the majors or combined majors offered by mathematics alone or by mathematics in cooperation with another department.
The student’s program must include at least 32 quarter hours of mathematics or mathcomputer science courses taken at Western, including MATH 225, 304 and 312 and at least 23 approved credits at the 400 level or above. The cumulative GPA for mathematics and mathcomputer science classes taken at Western must be at least 3.6.
Graduation with Distinction
To graduate with distinction in mathematics, a student must meet all the requirements for graduation with merit in mathematics.
Furthermore, the student must successfully complete:
 A comprehensive examination covering MATH 124, 125, 224, 225, 226, 204, 331
 An approved senior project
The comprehensive examination should be taken no later than the junior year. This examination may be retaken if necessary, but must be passed no later than fall of the senior year and before beginning the senior project.
The senior project is subject to approval of the Undergraduate Committee and is undertaken under the direction of a faculty member. It includes some independent work, the preparation of a report and a colloquium presentation. The senior project constitutes a course at the 400 level and is letter graded with 4 credits applicable towards the major.
Students interested in graduating with distinction in mathematics should declare their interest to the chair of the Department of Mathematics at an early point in their career at Western in order to receive appropriate advice and guidance.
Other Departmental Information
Mathematics Education
The Bachelor of Arts in Education major may be completed with either of two concentrations; one prepares the graduate for teaching mathematics on the secondary level, the other concentrates on the elementary level. Those who intend to pursue one of these concentrations must complete certain courses in calculus, linear algebra, discrete mathematics, statistics, number theory, geometry, history of mathematics, and computer science. Successful completion of these courses provides a good part of the training necessary for technical expertise in the classroom.
The elementary concentration emphasizes breadth in mathematics. Breadth of experience is important so that the teacher may expose elementary students to a wide variety of mathematical topics. The specialist in mathematics on the elementary level must be particularly skilled at transforming the material mastered in college to a form suitable for the level in question.
Secondary majors learn the methods of teaching mathematics in MATH 483; elementary majors learn such methods in MATH 381, 382, 383 and 491.
Students who wish to teach mathematics on the secondary level also can gain certification in mathematics by completing any one of the Bachelor of Science majors in mathematics, applied mathematics or mathematicscomputer science. In addition to the requirements for the major, they are expected to complete these courses: MATH 302, MATH 360, MATH 419 and MATH 483.
Recommendation for teaching endorsement requires the completion of the major with a minimum grade point average of 2.50 in the courses required for the major. The state of Washington requires a minimum grade of C (2.0) or better for all courses used to meet major certification or endorsement requirements. To gain the Initial Teaching Certificate, students must also complete a program of studies in professional education, including student teaching. Early in their careers at Western, students should seek formal advisement on the appropriate program in education. It is essential that the interested reader consult the Elementary Education and Secondary Education sections of this catalog for further information.
Academic Placement
Initial placement in most mathematics courses at Western is on the basis of the results of an appropriate placement test, except for students who have successfully completed at least one quarter of calculus in college. Mathematics placement tests are administered throughout the state of Washington each year, and both freshmen and transfer students who are residents in Washington are advised to take the appropriate examination prior to arrival on campus. Full information on which test to take and how to take it is available from the admissions office or the mathematics department.
Students who have completed at least one year of high school calculus or at least one quarter of college calculus should consult a departmental advisor before registering.
Except by permission of the chair of the Department of Mathematics, a student may not receive credit for any of MATH 101, 106, 107, 112, 114, 115, 118, 156 or 157 if that course is completed after completion of any higher numbered course in this list or after completion of a course in calculus for which college credit has been received.
Advice to Entering Students
The Bachelor of Science degrees in mathematics, applied mathematics and mathematicscomputer science are based on the following core:
The Bachelor of ArtsSecondary Education degree has the same core except for
These courses, except for Math 312, represent the minimum that a student planning one of these majors should complete during the first two years. In addition, most students pursuing a Bachelor of Science degree in the department should complete Math 225, the second quarter of multivariable calculus. A wellprepared student will be able to build a stronger program, possibly including some graduatelevel courses in the senior year, by completing some 300level work chosen under advisement in addition to the list above. In particular, Math 331 (differential equations) will be suitable for many students.
Transfer students, especially those intending to enter Western with an Associate of Arts degree, should normally complete as much as possible of the core program above, certainly including the entire calculus sequence and linear algebra. Students should be aware that 200level differential equations courses may not transfer as equivalent to MATH 331, and that certain third quarter calculus courses also may not transfer as equivalent to either MATH 224 or 226.
The Bachelor of Arts major in mathematics provides exposure to a wide range of courses but, relative to the Bachelor of Science major, has fewer requirements for courses in analysis and other upperdivision courses. A Bachelor of Science major in mathematics is generally more appropriate than a Bachelor of Arts major in mathematics for students intending to pursue graduate studies in any mathematically intensive discipline.
Instructors in many courses require that students use a graphing calculator. Students should contact the department for recommendations before purchasing a calculator.
Accelerated BSMS Program
By taking a significant number of graduate math courses as an undergraduate, it is possible to earn both a Bachelor of Science and a Master of Science degree in mathematics within five years of study. Detailed requirements for this option are available from the Department of Mathematics.
Enrollment Preference for Majors
The department will give enrollment preference for certain highdemand courses to its majors.
Information
Those interested in the study of mathematics are welcome to write, phone or visit the Chair of the Department of Mathematics, Western Washington University, Bellingham WA 98225, phone 3606503785.
Graduate Study
For a concentration leading to the Master of Science degree, see the Graduate School section of this catalog.
By taking a significant number of graduate math courses as an undergraduate, it is possible to earn both a Bachelor of Science and a Master of Science degree in mathematics within five years of study. Detailed requirements for this option are available from the Department of Mathematics.
Undergraduate Degrees and Programs
Economics/Mathematics, BA
Mathematics, BA
Chemistry/Mathematics  Secondary, BAE
Mathematics — Elementary, BAE
Physics/Mathematics — Secondary, BAE
Mathematics — Secondary, BAE
Applied Mathematics, BS
Biology/Mathematics, BS
Mathematics, BS
Mathematics/Computer Science, BS
Mathematics Minor
Mathematics — Secondary Minor
Graduate Degrees and Programs
Mathematics, NonThesis, MS
Mathematics, Thesis, MS
Mathematics Courses
