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Introduction to the MATHEMATICS MAJOR in THE DEPARTMENT OF MATHEMATICS & STATISTICS at JAMES MADISON UNIVERSITY Fact and Fiction; The Real Truth about Mathematics 1. The computer revolution has lessened the need of mathematics in modern society. 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 graduate school. 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 environment. 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 classes. FALSE: At JMU men and women are equally successful in mathematics. Women actually form a majority in most JMU mathematics classes. 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 different settings. 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 site (http://www.math.jmu.edu) 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 rewarding career. 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 classroom. Informal Settings 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. Organizations 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 involved. Competitions 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. Awards 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 investing. 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 currently enormous. 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 experience. MANDY WHITE 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 PAUL DOSTERT 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. KATHLEEN BELLINO 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.

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posted: | 9/19/2010 |

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