Guide for Math Majors

Mathematics as a Major

Mathematics is a means of dealing with order, pattern, and number as we see them in the world around us. Mathematics belongs to both the humanities and the sciences. At many universities, mathematics is located in a college of arts and sciences, but at BYU the Mathematics Department is located in the College of Physical and Mathematical Sciences. The traditional position of mathematics among the humanities is based on the fact that the study of mathematics has been one of the liberal arts for over 2000 years.

Every student who graduates from BYU must demonstrate some competence in mathematics. The abilities to compute, to think logically, and to take a reasoned approach to solving problems are highly valued by society and are considered characteristics of an educated person.

A mathematician's stock in trade is the ability to solve problems and to explain the solutions to others. Solving problems involves analyzing both abstract and concrete situations, relating them to mathematical ideas and using mathematical techniques to work toward solutions. Explaining the solution involves pointing out just what has been solved and why the solution is valid.

Today, our discipline offers more new and challenging frontiers than ever before. Totally new areas of investigation arise regularly, requiring creative and untried approaches and techniques. The applications of mathematics have expanded tremendously in recent years. Not only in the physical and engineering sciences, where mathematics has had a long association, but also in business and in the biological and social sciences are found increasingly useful applications for mathematics and its skills and reasoning.

In studying mathematics, you should remember that mathematics is not just a body of knowledge but also a process of analysis, reasoning, comparison, deduction, generalization, and problem solving. You will be deeply involved in this process, in which careful and rigorous thinking play the most prominent role. Mastering mathematics requires hard work, but few subjects repay genuine effort with such excellent skills and feelings of accomplishment.

Careers in Mathematics

Students decide to major in mathematics for many different reasons, and our program is flexible enough to accommodate a wide range of interests and abilities. Some students wish simply to pursue their interest in and enjoyment of mathematics, but most students have more specific career goals in mind.

Majors in Mathematics (seeking the BS degree) prepare for a wide variety of careers. Some enter graduate school and seek master's and doctor's degrees in mathematics, after which they enter careers in college teaching, consulting, and research and development, among others. Some majors enter professional schools and become lawyers, business administrators, actuaries, or professionals in other areas. Some take positions in government agencies, in industrial research and development laboratories, in various business organizations, or in a wide variety of other positions in both private and public sectors. All of them spend a good deal of their time communicating with others about the problems they are hired to solve. All of them continue to learn more about mathematical ideas and share those ideas with others as they work in their professions. Care is taken in training math majors to give them wide experience in mathematics and also exposure to statistics and computer applications.

Regardless of a student's reasons for studying mathematics, such preparation is especially appropriate at this time. Society is increasingly technologically oriented, and knowledge of mathematics provides a student with an exceptional degree of flexibility in career choice and in job mobility. A major in mathematics, coupled with an understanding of the applications of mathematics, is one of the most useful and potentially rewarding programs available at a university.

About the Department

The Department of Mathematics at Brigham Young University has been in existence since the 1950s; prior to its organization, mathematics was taught by the Physics Department. Departments of Statistics and Computer Science were spun off the Mathematics Department during the 1960s. The department has grown steadily, first in size and then in reputation, throughout its history.

The Department of Mathematics teaches about 500 majors, as well as about 8000 other students each year in a wide variety of service courses. The department also has graduate programs, in which about 40 students seek masters' degrees and 10 students seek doctoral degrees during a typical year.

The Mathematics Department sponsors two professional student organizations, a chapter of Pi Mu Epsilon, the National Honorary Mathematics Fraternity, and a student chapter of the Mathematical Association of America. Outstanding students are nominated for membership in these organizations each year by the faculty. Student members of these groups, as well as all other interested students, are invited to attend periodic "Math Club" meetings sponsored by the department and typically featuring topics of general interest. The department also sponsors a Putnam Exam team that competes nationally.

For more information about the department, see the Undergraduate Catalog or the Mathematics Department home page (https://www.math.byu.edu).

About the Faculty

Faculty in the BYU Mathematics Department number about 40 permanent faculty in the professorial ranks. During any given semester, the department will have three or four visiting professors of international status and a similar number of temporary and adjunct faculty, some of them on leave from high school teaching positions. There will also be two or three permanent faculty on leave at other universities, typically.

Major areas of research emphasis in the department are currently Algebra, Analysis, Applied Mathematics and Nonlinear Analysis, and Topology/ Geometry, and most permanent faculty are aligned with one of these areas. Most faculty have wide interests and expertise and teach a variety of the courses required for majors, as well as the service courses.

Individual information on each faculty member can be found in the Undergraduate Catalog or on the Mathematics Department home page (https://www.math.byu.edu).

Resources and Expectations

The purpose of academic advisement at BYU is to help students gain the most from their educational experiences. The philosophy is that you, the student, must take responsibility for your own education and the University will supply as much information as you need and as much advice as you want in order to do your best. Advisement resources include College Advisement Centers (CACs), Advisement by Computer (ABC), Academic Information Management (AIM), and departmental and faculty advisors.

When you declare your major as mathematics, you are assigned a mentor who is a member of the faculty of the Mathematics Department. Your mentor becomes your faculty advisor, and can answer your questions regarding your career as a math major. The undergraduate coordinator in the Mathematics Department can also advise you relative to mathematics requirements and courses. You can receive assistance on general University require-ments at the CAC for the College of Physical and Mathematical Sciences in N179 ESC. The CAC can assist you in learning to use ABC and AIM.

Printed advisement material is also provided, but you must take the responsibility to read it. You should study this Guide for Math Majors, the New Student Registration Guide, the Class Schedule for each term, and the Undergraduate Catalog for information concerning requirements, registration procedures, and graduation information.

While you can receive advisement at any time, you are expected to meet with advisory personnel at least three or four times during your undergraduate experience:

At the beginning of your first year here, you should meet your mentor and prepare an outline of courses that you plan to take during the first two years. It is important to your success to follow the prerequisite structure (see the Course Descriptions) as you plan your sequence of courses.

1. If at any time during your first two years, you find yourself needing to make adjustments in your plan, you should meet with your advisor who will suggest and approve alterations.
2. During the first semester of your junior year, you are required to file with the College Advisement Center a graduation plan, listing all the courses you have taken or plan to take, leading to graduation from the University. This plan requires the signature of your advisor or of the Mathematics Department undergraduate coordinator. If you do not file a graduation plan, a hold can be placed on your registration.
3. During the first semester of your senior year, you are required to file an application for graduation with the College Advisement Center. No application, no graduation!

Of course, all students are expected to excel in their mathematics courses. This normally requires hard work and dedication, qualities that help you succeed in all of life's endeavors. If you are like most students, however well motivated, you will find that you need help mastering mathematical concepts at some point in your classwork. The following resources are available to you for help in math classes:

• The Math Lab. Individual help is available in the Math Lab to all students taking math classes at BYU. The greater part of the Math Lab effort is geared to students at the lower levels, but graduate and advanced undergraduate students also serve as tutors for upper division classes. (You may want to consider being a tutor in the Math Lab at some point in your stay here.)
• Your Instructor. Professors post office hours, at which times you can consult with them about the classes you are taking. If a professor's office hour is not possible for you, set up an appointment for another time. Professors will assist you in any way they can to gain the skills and information you need to succeed at mathematics.
• Your Peers. You will be surprised at how much you can learn, simply by trying to explain your difficulty to a classmate. Others see problems from points of view you never thought of, and your point of view may be a real revelation to a classmate. Talk about what you are learning, and assist in teaching each other.
• Your Advisor. Sometimes you need a broader view; it is easy to get lost among the trees and not be able to see the forest. A chat with your advisor can often give you renewed perspective on your career in mathematics.

Many students at BYU need financial assistance to remain in school. The BYU Financial Aid Office, A-41 ASB, administers scholarships for new freshmen, transfer students, and continuing students. In general, you must have a GPA close to 3.8 or above to be considered for a scholarship. The Financial Aid Office also handles federal grants and loans available at the University.

The Mathematics Department has a limited amount of funds for departmental scholarships. If you want to apply for a departmental scholarship, write a letter to the Chairman of the Mathematics Department outlining your needs and qualifications. More information can be obtained at the departmental office, 292 TMCB. There are also research grants sponsored by the University that are available to undergraduates on a competitive basis; inquire at the Mathematics Department office.

Many students help defray the cost of their education by working for the Mathematics Department. The department hires some of our best undergraduate majors to tutor in the Math Lab, serving thousands of students across the university who are studying mathematics. In addition, many undergraduate majors grade papers for faculty. A few math majors become Teaching Assistants in mathematics honors courses. Occasionally there are limited research funds available to students who assist professors on research projects. Applications and further information can be found at the Mathematics Department office, 292 TMCB.

Students with AP Credit

If you are an entering freshman and took AP Calculus in high school, you may have advanced standing upon entrance at BYU. Here are the rules:

• If you took AP Calculus but did not take the AP exam, or if you took the Calculus AB exam and scored 1, 2, or 3, or if you took the Calculus BC exam and scored 1 or 2, then you have no credit in calculus and must start with Math 112H, ideally followed by Math 113H and Math 190 the following semester.
• If you took the Calculus AB exam and scored 4 or 5, then you have credit in Math 112 and may take Math 113H and Math 190 your first semester. If you feel unsure of yourself, you may take Math 112H and Math 190 instead. You may not skip Math 113H.
• If you took the Calculus BC exam and scored 3, 4, or 5, then you have credit in Math 112 and 113 and you should take Math 113H and Math 190 your first semester. If you scored 5 on the exam, you may take Math 190 and Math 343 instead, realizing that you may need extensive review of calculus when you get to Math 316.