Introduction to the
OF MATHEMATICS &
Fact and Fiction; The Real Truth about Mathematics
1. The computer revolution has lessened the need of mathematics in modern
FALSE: On the contrary, increased computational ability allows for higher -
level mathematics to be brought to bear on important problems in
traditional areas and also in areas which previously relied almost
entirely on experimentation.
2. Mathematics provides great flexibility and individuality in a career choice.
TRUE: Mathematics is used in many forms to describe diverse problems,
ranging from economics to finance to biology to engineering. Also,
the discipline and skills gained in studying mathematics are highly
prized, and often lead to careers in many areas not traditionally
associated with mathematics.
3. Math majors usually go into teaching.
FALSE: Slightly less than half of JMU's math graduates go into teaching.
The others go on to jobs in government or industry or enter
4. Salaries for mathematicians are not compe titive with those of science,
engineering, and other high-profile majors.
FALSE: Salaries of the mathematicians entering government and business
are very competitive with those of other majors. Moreover, with
increasing demand for middle-school and high-school teachers of
mathematics, teaching salaries have risen significantly in recent
years. The flexibility and versatility of math majors often contribute
to increasing financial rewards over time. For example, a recent
survey from the Bureau of Labor Statistics showed that, for men
aged 35-44 who had been out of college for at least five years,
those with an undergraduate degree in mathematics ranked second
in salary only to those with engineering degrees.
5. You have to be a “brain” to be a ma thematics major and a “genius” to do
anything really meaningful as an undergraduate.
FALSE: While an adequate high school mathematical background is
necessary, the main requirements for success as a math major –
as with all majors – is desire and interest. The Department of
Mathematics and Statistics offers a variety of opportunities for its
majors, including internships and research projects.
6. The Mathematics Department at JMU provides an excellent small-school
TRUE: Mathematics faculty members interact with math students in many
positive ways. Faculty sponsor and participate in several student
organizations, hold local competitions, train students for national
and international competitions, are generous in their giving of help
outside of class, and give students the option of independent study
or research. Also, students participate in the life of the department
in many ways such as recruiting new faculty and students. With
this attention to individuals, for which smaller schools are famous,
the JMU Mathematics Department has some favorable large-school
attributes as well. The faculty is large enough to have a wide
variety of interests which they enjoy teaching, and there is a
sufficient number of students, both from within the department and
from other areas, to allow diverse course offerings.
7. Most successful math majors are men. Women are a minority in mathematics
FALSE: At JMU men and women are equally successful in mathematics.
Women actually form a majority in most JMU mathematics
8. Many scientific jobs involve only very elementary mathematics.
FALSE: Almost any applied problem can be approached by some form of
mathematical analysis. Just because some claim to use no
sophisticated mathematics in their work, it does not mean that they
could not use it to great advantage if they had known it.
9. Mathematicians always work alone, have their heads in the clouds, and do
not care if their work has practical application.
FALSE: Mathematicians work on diverse problems, in a variety of different
ways. Some work alone and some in teams, analyzing and solving
a range of difficult problems. Many select these problems from
mathematical descriptions of real phenomena.
10. Many Math majors have a minor or a second major. They also often do
graduate work in these major or minor areas.
TRUE: Many students appreciate their mathematics even more when they
see how it can be applied to diverse areas. Mathematical training,
in general, strengthens a person's abilities to perform in many
11. You can learn more about courses and careers in mathematics and statistics
at James Madison University.
TRUE: For more information, please see the complete Handbook for
Students of the Department of Mathematics and Statistics. These
handbooks are available from the Department of Mathematics and
Statistics (MSC 7803), James Madison University, Harrisonburg,
VA 22807. For further information or to arrange a campus
interview, please call or write Professor J. R. Hanson (540)568-
6286. More information is also available at the department's web
A Word From The Faculty and Staff
Welcome to JMU and to the Department of Mathematics and Statistics. As
members of the faculty and staff we are dedicated to helping you make your
undergraduate major years a challenging and rewarding experience. We want to
answer your questions about programs of study and be of assistance as you
work toward the completion of your degree. WE ARE HERE FOR YOU.
This handbook has been developed to be helpful to you as you decide on a
major and choose among many available options. It contains information about
the department and its academic programs, resources, policies and procedures.
We hope you will read it all and keep it for future reference. Some of the
information may change while you are a student at JMU, so you should stay in
touch with your department advisor. The handbook is a supplement to, not a
replacement for, the Undergraduate Catalog which is your best single source of
academic information for undergraduates at JMU.
Why study Mathematics or Statistics?
You want to keep your career options open after graduation. As a major in
the department you will develop skills that are relevant to a wide range of
careers and occupations. Also your deeper understanding of logic and
critical thinking will be useful long after graduation.
You have studied mathematics or statistics at a fairly high level, you enjoy
the subject, and would like to find out more about it.
You want qualifications which place you in a strong and flexible position for a
You want to study a subject that will stretch you, keep your interest and allow
you to develop your own ideas. As a math major you will have opportunities
to solve interesting problems and be involved in scientific inquiry and
research. You will get to choose from a large variety of electives and areas
of concentration as you further your own skills. The small student-teacher
ratio in your major classes will provide you with much individual attention as
you gain a thorough grounding in major areas of mathematics and statistics
and learn how to apply technology effectively. You will be challenged and
supported as you strive to meet your goals.
You want to become part of a department that is characterized by high-quality
students and a caring faculty that stress quality teaching. You will be
encouraged to become involved in the many departmental activities for
students such as the Math Club and Pi Mu Epsilon. You may elect to do a
research or honors project or participate in the Calculus Contest, the Putnam
Competition or the Math Modeling Competition. The study lounge for majors
in Burruss 117 (where punch and cookie time is held weekly) and the
department's outstanding computing facilities may become a second home for
you. You will work hard, make friends and grow intellectually.
In a single major it is difficult to meet all these expectations, but by choosing a
major in mathematics, or a major with a substantial mathematical or statistical
content, you have every chance of fulfilling them.
What Can You Expect to Find if You Major in Mathematics?
You will strengthen and extend your knowledge of the kinds of mathematics and
statistics you may already be familiar with, such as differential and integral
calculus, and descriptive statistics. However, you will also meet whole areas that
you have probably not seen before, such as number theory, topology, abstract
algebra and numerical analysis. Techniques explored in a course like number
theory have many unexpected and powerful applications, both in other branches
of mathematics and areas such as cryptography, and exemplify a branch of
mathematics known as pure mathematics. All majors in mathematics study some
material of this type. The core curriculum also provides all mathematics majors
with experience in applied mathematics and the utilization of computer
technology to solve scientific problems of practical interest. You will also learn to
use statistical reasoning to analyze data and answer questions about hypothesis
testing, experimental design and quality control. The electives you choose will
allow you to concentrate your skills on areas you find particularly interesting. So
your major will have a core that introduces you to the fundamental areas of the
discipline as well as provide you with the flexibility for more individualized study.
The courses offered in the Department of Mathematics and Statistics at James
Madison University will allow you to study an exciting mixture of classical and
contemporary mathematics and statistics.
The Other Education
Your participation in the informal activities of the department will enhance your
growth in mathematics and statistics. You will get to know other students having
similar interests as well as with departmental staff and faculty, and you will have
opportunities to participate in mathematics and statistics activities outside the
The department recognizes the importance of students being able to mingle
informally with other students, faculty and staff. As a result, a large, comfortably
furnished room has been set aside as a student common room. About once a
week the room also is used for "cookie time," a time at which the faculty, staff,
and students wander in and out and talk with one another while eating cookies
and having soft drinks. Sometimes a student or professor will make a short
presentation about a topic of interest during this time.
The department has both a mathematics club and an honorary organization, Pi
Mu Epsilon( ). The Mathematics Club is open to all students interested in
mathematics or statistics. Pi Mu Epsilon, being an honorary association, of
course has membership criteria. Both organizations sponsor speakers and
events generally open to anyone interested. Talks are given by professors,
students and former students on topics ranging from mathematics or statistics to
job-hunting and life in the "real world." Meetings often include pizza or ice
cream. The organizations also sponsor informal gatherings such as picnics,
bowling, hiking, biking, and canoeing. All these activities include students,
faculty, and staff.
Center for Computational Mathematics and Modeling (CCMM)
The Center maintains up-to-date computing equipment, including a recently
installed parallel processing system. The Center is used for research and study
by faculty and students from all the sciences and mathematics, and other
disciplines across campus. You will have ample opportunity to either work with
faculty on their projects or to work on projects of your own under the supervision
of a professor. Many students have presented papers or talks at local, regional
and national meetings on research accomplished at the Center.
Office of Statistical Services (OSS)
The Office of Statistical Services offers statistical consulting to campus persons
and groups as well as businesses. You will be able to work with faculty and the
"customers" to design the proper gathering of data and to interpret the resulting
information. Often these projects have led to talks and papers by the students
As a first-year student you can participate in a test on elementary calculus with
prizes awarded to the top finishers. All students have the opportunity to
participate in the Putnam Competition, a prestigious mathematical competition
(started in 1939) among students from colleges and universities in the United
States and Canada. The department also fields teams that participate in the
COMAP Mathematical Modeling contest. Students interested in either of the
latter two competitions meet regularly with their peers and faculty mentors to
practice. The department also sponsors a „Problem of the Week‟ competition,
awarding each winner a $5 gift certificate to a popular local restaurant.
Research and Projects
The faculty in the department have research interests ranging from
computational mathematics and statistics to theoretical considerations. Many of
these projects encourage significant student participation. You might work with
faculty through the previously-mentioned Center for Computational Mathematics
and Modeling or the Office for Statistical Services or with individual faculty and
students outside these centers. The projects can be "just-for-the-fun-of-it" or as
part of a more formal setting. Students may work on projects leading to the
awarding of honors at graduation. Stude nts also participate in summer research
programs such as the REU (Research Experiences for Undergraduates), here at
JMU and at other universities. Others find summer jobs that are essentially
research projects. Activities like these can lead to your maki ng presentations
locally, or at regional or national conferences.
As a student in this department you will be eligible for two small scholarships
awarded annually, a few complimentary one -year memberships in the
Mathematical Association of America, and several departmental awards just
before graduation. Many of the academic activities outlined above, such as
conference presentations and national competitions may also lead to awards.
A Look at the Programs
The department‟s major in mathematics features a required core designed to
introduce you to many areas of mathematics. You may then choose the elective
part of your program to further your interests or to enhance studies in other
departments or divisions of the university.
The core consists of courses in differential, integral, and multivariate calculus;
linear algebra with differential equations; computer methods in mathematics;
probability and statistics; and introductory and advanced mathematical theory.
Formal concentrations that you may include within your mathematics major are
computational and applied mathematics, pure mathematics or statistics. You can
also minor in education and be certified to teach in public and private schools. In
addition, there are two interdisciplinary concentrations available, one in
computational sciences (taught jointly with physics faculty) and the other in
financial mathematics (taught jointly with finance faculty). There are actually
many other opportunities available – mathematics fits in with many disciplines. A
major in mathematics with a minor, or well-chosen concentration of courses from
another field often opens exciting and unusual career opportunities. One may
also major in mathematics and minor in statistics.
Here is some more detail about the concentrations described briefly above:
The computational and applied mathematics concentration combines
traditional methods of applied mathematics with laboratory experiences in
computational techniques to solve applied problems in both scientific and non-
scientific arenas. Students who elect this concentration often work on
independent studies with faculty members and/or participate in team projects that
utilize the powerful computational resources of the Center for Computational
Mathematics and Modeling (CCMM)
The computational science concentration - a collaborative effort by faculty in
the Departments of Physics and Mathematics and Statistics at JMU and the
Department of Mathematics and Computer Science at North Carolina Central
University - is designed to prepare students for either immediate employment or
graduate studies in the emerging “key technology'' of computational science.
Computational science involves a triad of high-level skills: 1) mathematical
modeling of physical phenomena, 2) numerical methods of solving the model
equations, and 3) scientific visualization. The concentration currently explores
aspects of fluid dynamics and provides students with both physical and
computational laboratory experiences in this exciting area.
If you think you might like to go on to graduate school in mathematics, the pure
mathematics concentration would be ideal for you. This concentration focuses
on the beauty and elegance of mathematics, "the queen of the sciences." While
this program provides a solid background for students who plan to continue their
study of mathematics in graduate school, it also provides the added benefit of
developing creative problem-solving skills and logical thinking abilities, two
attributes that potential employers desire. In fact, many students with pure
mathematics training go on to graduate school in other academic disciplines or
pursue careers in the private sector. Students in this concentration have various
research options: applying for NSF-sponsored "Research Experiences for
Undergraduates" summer programs at various institutions, working with
professors on individualized research projects at JMU, and applying to study
abroad at the "Budapest Semesters in Mathematics" program.
The statistics concentration will give you a good foundation in theoretical and
applied statistics. Continuation of your studies in a graduate statistics program or
a job in industry would be likely upon completion of this option. Students in this
program can work with faculty and students on “real-world” statistical consulting
in the Office of Statistical Consulting.
The financial mathematics concentration will give a foundation of mathematics
and finance. Students in this concentration will learn to use mathematics to
model the finance involved in income and investments. In particular, they will
study many of the models that are currently used in banking, insurance and
If you are interested in teaching mathematics at the pre-college level, our
mathematics major with a minor in education will certify you for these
positions. The demand for well-trained mathematics and statistics teachers is
You should note that with all the above choices, you will leave JMU with a
mathematics degree – you will be a mathematician. You will be just starting
down that road of continuous learning, but you will be a mathematician, with lots
of choices. If, for example, you trained to teach in a public school, but didn‟t like
it, you would still have available to you any of the jobs for which mathematicians
are normally hired. If you didn‟t like working in one type of industry, you could
switch to some of the many other places mathematicians and statisticians work.
Keep in mind that mathematical training can heighten and improve yo ur
involvement in almost any area, including those which are non-technical.
A Final Word of Advice
No matter what major you choose or what profession you enter, it is a fact that
the more mathematics you take, the more you will improve your chance for
landing that great first job or entering the graduate school of your choice. Take
your math placement result seriously. If you qualify to take calculus Math 235,
236 or 237, then by all means do so. Your future will be enhanced by that
Math has always been my favorite subject, but when I was in
high school, I was so involved with choosing a good
basketball school that I really didn‟t think much about what
career I would pursue. I began college undecided, and I took
a number of general education classes to see what interested
me. After my freshman year, I rediscovered my interest in
math, and I decided that I wanted to be a teacher. The math
program here is excellent. The professors are very
knowledgeable, and they are also extremely helpful. They
want students to succeed, and it shows in their enthusiasm
when they teach.
Credit: JMU Photography
I began college as a music major, but quickly became
bored. I skipped class all of the time, and just didn't care
about what I was learning. After my first semester, I
decided to try taking Calculus II. I immediately knew that I
wanted to be a math major. My professor just seemed to
have so much fun teaching us, and it really made me care
about the class, and mathematics in general. I've met
many other mathematics majors from different institutions,
and it's quite clear that the professors at JMU really care
about their students more than at any other university.
Being at JMU has been a wonderful experience, and I
hope many others can realize how great being a math
Credit: Irma Housden major can be.
I chose James Madison University mostly to be a
member of the gymnastics team. I had been in the
sport since the age of seven, and couldn‟t imagine
my life with out it. I had always had an interest in
mathematics, and declared it as my major when I
entered JMU as a freshman. I had never had
calculus, and didn‟t even know what a major in
mathematics involved, but I decided to give it a try.
Fortunately, I found great friends and professors in
the math department who showed me their
enthusiasm and love for mathematics. I enjoyed the
classes because they challenged me to think in a
new way; the problem solving, logic, and absolute
proof were fascinating and just seemed to make
sense. The professors are very personable and
always willing to help. Balancing school and
gymnastics was a challenge, but my professors were
always very supportive. Now that my gymnastics
career is over, I feel lucky to have discovered a love
for mathematics- something I can enjoy forever. Credit: JMU Photography
Next year, I plan on continuing my mathematics
studies in graduate school.