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Department Overview

Introduction

Mathematics embodies the spirit of the liberal arts: mathematics is an art, a pure science, a language and an analytical tool for the natural and social sciences, a means of exploring philosophical questions, and a beautiful edifice that is a tribute to human creativity.

Take the photo tour of the math department.

The Department of Mathematics offers its programs in modern classrooms and computer laboratories in the Center for Mathematics and Computing, a 42,500 square-foot building the department shares with the College's computing center.

The department is especially proud of the quality and diversity of its computer equipment available for student use. The department maintains four public labs including a mathematical computing lab, a statistical computing lab, an introductory computer science lab, and a research lab.

The Mathematics Major

Students can choose between a mathematics or a mathematics/statistics major. Both majors includes a common core of five courses -- Calculus I, II, and III, Linear Algebra, and Mathematical Structures. Students complete the major by taking six or more advanced courses beyond the core to insure both depth and breadth of mathematical or statistical knowledge. Students on the mathematics track can choose from courses such as Abstract Algebra, Real Analysis, Complex Analysis, Combinatorics or Topology, as well as many other courses offered on a regular basis. Students on the mathematics/statistics track will take courses such as Probability, Statistical Inference, and Applied Regression Analysis.

Students may plan a major in mathematics in preparation for work or further study in any of a variety of fields. In addition to traditional fields like pure mathematics, mathematical physics, statistics, operations research and actuarial science, there are a growing number of opportunities in interdisciplinary fields, such as mathematical economics, biostatistics, biomathematics, bioinformatics, environmental engineering, and scientific visualization. Students may prepare for teaching mathematics in secondary school through a sequence of courses in the department and in the Department of Educational Studies.

During the senior year, the mathematics major concludes with a capstone experience, known as "comps."  Students work in small groups, typically of size 2-4, on a research problem, an applied project, or directed reading.

Outside the classroom

In addition to regular coursework, students can enhance their mathematical experience in many other ways. The department features a colloquium series at which faculty, visitors and students present topics of current or historical interest. Over the past several years the speakers have included such distinguished visitors as Fred Brooks, Steven Krantz, Doris Schattschneider, Paul Erdös, Ron Graham, Carolyn Gordon, Richard Guy, Stephen Stigler, and Roger Penrose.

Students may also participate in seminars, independent study, or problem-solving groups. For decades Carleton has entered a team in the Putnam Mathematical Competition, a contest for undergraduates all across the United States and Canada. Often, our students have done quite well in this contest. Locally, Carleton teams compete with nearby colleges in the Konhauser problem-solving contest. Carleton students also have the opportunity to do research in mathematics.

The department also employs students as tutors, lab assistants, paper graders, and as research assistants.

Finally, majors in the department develop close relationships with departmental faculty not only through their academic work, but also at picnics and other special events.

Off-campus opportunities for majors

Many Carleton mathematics students participate in summer research programs (REU's), internships (for instance, at the Mayo Clinic in Rochester, Minnesota) or other enrichment programs (Carleton's Summer Mathematics Program for Women, George Washington University's Summer Program for Women). In addition, many students spend a term in Hungary on the Budapest Semester in Mathematics program.

Mathematics for non-majors

Since mathematics plays such a key role in the physical, biological, and social sciences, Calculus I, Calculus II, and Calculus III are all useful to students who plan careers in these areas. Diagnostic examinations are available during New Student Week to assist students in deciding at which level they should enter the calculus sequence. The department offers a course, Calculus with Review, for those students who require extra preparation.

Courses in probability and statistics are offered at several levels. For instance, Statistics: Concepts and Controversies, and Introduction to Statistics are of special interest to students seeking quantitative literacy in the social sciences or for students majoring in geology, biology, or economics. Two upper level courses, Probability Theory and Introduction to Statistical Inference, combine a rigorous introduction to probability and statistics with data analysis.

The department offers a general education course, Introduction to Mathematics, for those who wish to become acquainted, at an elementary level, with some modern mathematical ideas.

The department also offers Freshman Seminars on a regular basis. Recent topics have included Cryptography, Mathematics and Art, Chaos, Numbers, and Graph Theory. These seminars are independent of the calculus and introductory computer science sequences.

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Photo Tour

  • Entrance to the CMCThe entrance to the Center for Mathematics and Computing

  • Russ PetrickaMath Skills Center Director Russ Petricka with student.

  • Stats Lab: CMC 201Jenny Grover ('06) working in the Statistics Lab

  • Math Skills CenterJonah Ostroff in Math Skills Center

  • Paper ConstructionA paper construction in the Math Skills Center. Goodsell Observatory is in the background.

  • Mathematica Lab: CMC 301

  • Math Skills CenterStudents working on mathematics homework in the Math Skills Center.

  • PicnicEnd of term departmental picnic (2006)

  • Professors Appleyard, Nau, and Roosenraad RetireLongtime Mathematics Professors Dave Appleyard, Rich Nau, and Cris Roosenraad retired this spring. Dave Appleyard first came to Carleton as a student in 1957, graduating in 1961. He joined the Carleton faculty in 1966, after completing his PhD work at the University of Wisconsin-Madison. Rich Nau joined the Carleton faculty in 1970, and was instrumental in establishing first a major in computer science in the 1980s and eventually the Department of Computer Science. Cris Roosenraad came to Carleton in 1983 as the Dean of Students, a post he held for ten years before joining the Math department full time. In this photo Dave Appleyard teaches his last class, making use of both the CMCs outdoor classroom and his formal academic regalia. Dave also gave the honors convocation address this year, entitled ``'Remember Old Pete!' and Other Life Lessons.''