Tufts University
Department of Mathematics

Opportunities for Undergraduate Students

Guide for Current and Potential Mathematics Majors and Minors

September 2005

Mathematics arose in antiquity in the needs of daily life. It has developed into a vast modern edifice of many interdependent disciplines that provide the foundation and the language of science. At its core are the three related areas of algebra, analysis, and geometry/topology, concerned with the concepts of abstract structures, functions, and shapes and spaces, respectively..
Many careers
One of the common misconceptions about a mathematics major is that the program is intended primarily for those interested in graduate studies in mathematics. In fact, most of our majors go on to many different careers, including law, business, medicine, teaching, and the government. At the undergraduate and graduate level, mathematics is studied for a variety of reasons: for its applicability, its aesthetics, intellectual challenge, enjoyment, and above all, as part of our cultural heritage. Moreover, the ability to think logically and rigorously, central to the experience of mathematics, is valued in many professions. Here are numerous links to career information.
Plan your program

In addition to the fundamental courses in linear algebra, abstract algebra, and analysis (Math 46, Math 135/136, and Math 145/146), the department frequently offers the following courses.

  • Math 22, Discrete Mathematics, can be taken at an early stage and simultaneously with another mathematics course. It covers topics that are essential in theoretical computer science and other applications areas.
  • Math 38, Differential Equations, gives an introduction to ordinary differential equations, that is, differential equations for functions of a single variable. Differential equations are of vast importance in both pure and applied mathematics. Most mathematical models in the sciences and engineering are differential equations.
  • Math 41, Number Theory, allows the student to sample the flavor of pure mathematics at an early stage. The course can be taken simultaneously with any calculus course.
  • Math 112, Topics in the History of Mathematics, gives an introduction to the evolution of mathematics from its roots in antiquity to modern times.
  • Math 126, Numerical Analysis, is a course about solving problems arising in calculus and linear algebra (for instance, integration, differential equations, systems of linear equations, and eigenvalue problems) by computer algorithms. This material is of great importance in many applications.
  • Math 128, Numerical Linear Algebra, is similar in spirit to Math 126, but focuses entirely (and in much greater depth) on linear algebra problems Ð systems of linear equations and computation of eigenvalues and eigenvectors.
  • Math 151, Applications of Advance Calculus, has recently evolved into an introductory course on partial differential equations, that is, differential equations for functions of several variables; see the comments about Math 38 concerning the wide importance of the topic. The course is cross-listed with ME 150.
  • Math 158, Complex Variables, is concerned with the extension of calculus and analysis to the complex plane; it is widely applicable to other areas of pure mathematics as well as to the natural sciences and engineering.
  • Math 161/162, Probability/Statistics, is a one-year sequence. Math 161 has been offered every fall, and Math 162 every spring. Probability is one of the great branches of pure analysis. In addition, this course sequence is of special relevance to students preparing for graduate study in statistics, applied mathematics, operations research, or actuarial science, as well as careers in industry.
  • Math 163, Computational Geometry, cross-listed as Computer Science 163, is an introduction to the design and analysis of computer algorithms for geometric problems.
  • Math 167, Differential Geometry, and Math 168, Algebraic Topology, are introductions to the third great core area of mathematics, geometry/topology (the other two are algebra and analysis). These courses present some of the major mathematical techniques of the twentieth century in a concrete and intuitive form. In recent years, they have only been offered occasionally. Students interested in taking them are encouraged to make their interest known to the mathematics faculty!
  • Math 171, Computational Mathematical Logic, provides a study of the logical foundation of mathematics. It has been offered sporadically only.
  • Special topics courses are regularly offered as "Math 50" and "Math 150" to complement and broaden the course offerings.

    • Engineers who are mathematically inclined do not need many additional courses to complete a double major in mathematics upon appropriate choice of curriculum. All engineers are required to take Math 13 and many are encouraged to take Math 46 anyway. Math 161-162 should be taken in place of CE102. Many engineers are required to take ME 150 (cross-listed with Math 151). The main additions to the curriculum would then be Math 135 and Math 145. To choose mathematics as a second area of concentration an engineering student must notify the dean of engineering through the Department of Mathematics at least one semester before graduation. The student must complete a program that simultaneously satisfies the requirements of the Engineering College and the Mathematics Department. Substantial overlap between the requirements in mathematics and computer science facilitates the double major. All mathematics majors are required to demonstrate knowledge of a computer language. The most common way of satisfying this requirement is to take an approved course in computer science (CS 10 is acceptable).

    Major

    To major in mathematics, a student must take ten courses in the department. Up to two of these courses may be replaced by certain courses in related fields approved by the department. The courses in mathematics may not include Mathematics 4 through 12, or 17, and must include Mathematics 13 or 18, 46, 135, and 145. For depth, students must complete at least one of the four major year-long sequences (Mathematics135/136, 145/146, 151/152, and 161/162), and for breadth, students must either complete a second one of these sequences or else take an additional course chosen from among Mathematics 126, 128, 151, 158, 161, 167, 168, 161. Majors are advised to complete Mathematics 13 or 18 and Mathematics 46 by the end of their sophomore year. Majors must demonstrate knowledge of a computer language by including an approved course in computer science in their program.

    Students in the School of Engineering may, with certain exceptions, choose mathematics as a second area of concentration. To do so a student must notify the dean of engineering through the Department of Mathematics at least one semester before graduation. The student must complete a program that simultaneously satisfies the conditions for a degree from the School of Engineering and the concentration recommendations of the Department of Mathematics.

    Minor

    To minor in mathematics, a student must take six courses in the department beyond the level of Mathematics 12 (or 17). These must include Mathematics 13 (or 18) and 46, as well as Mathematics 135 or 145 (or both).

    Courses in Related Fields

    Majors may substitute up to two courses chosen from the following list:
  • Chemistry 133, 134
  • Computer Science 15, 160, 170
  • Economics 107, 108, 154, 202
  • Electrical Engineering 18, 107, 108, 125
  • Engineering Science 151, 152
  • Mechanical Engineering 137, 138, 150, 165, 166
  • Philosophy 33, 103, 114, 170
  • Physics 12, 13, and any course numbered above 30
  • Psychology 108, 140

    Career Paths for Mathematics Majors

    The Mathematics Department is very much interested in assisting its students with the difficult decisions involved in choosing a career. We encourage you to discuss your career plans (including graduate school) with your advisor and professors. Prof. Quinto has a collection of information on careers and would be happy to talk to you. The bulletin board in the student study area on the third floor of Bromfield-Pearson is now devoted to information and announcements related to careers. Keep your eye on it! Here are a few pertinent links.

    Here are a few specifics. (For all these, the links to careers and other opportunities may be useful.

    Graduate school in mathematics: Information on the programs at many universities (including Tufts!) is available in the Department office. Your advisor and professors will be happy to give you their opinions about many of these programs.

    Service programs: Information about the Peace Corps, Teach for America, City Year and other programs will be posted.

    Accounting: Prof. Quinto has information (including a video) on careers in public accounting.

    Actuarial science: General information is available in the Department office. Information about internship programs and the exams will be posted.

    Law and business: The pre-law and pre-business advisors in the Office of Undergraduate Studies in Ballou can help you. In general, our majors feel that their mathematical background is a real advantage in these careers.

    Teaching: Prof. Teixidor is our liaison to the Education Department. See her for information about certification or talk directly with the members of the Education Department.

    Operations research, banking, civil service, computers and industry: Keep your eye on the bulletin board.

    The Career Counseling Center has information about writing resumes and job hunting in general. They also organize on-campus interviews. There are job fairs from time to time at various locations. Each January, for example, there is a fair organized by the Actuarial Society of Greater New York. Again, keep your eye on our bulletin board.

    Come to the career talks organized by the Department. These are informal sessions conducted by students, alumni and professionals eager to share their experiences with you. Please let us know if there are specific careers you would like to see presented. Last fall we had talks on the actuarial, teaching, and accounting professions.

    The Math Club

    The Math Club is a student-run organization that tries to involve students in mathematics beyond the classroom. Through faculty-student discussions and reviewing of articles and videos, the club seeks to present mathematics in a new and interesting light. The club is a resource for forming study groups and researching career options. You need not be a mathematics major to participate.