Reed College Catalog
James D. Fix
Algebraic geometry, number theory, and quantum computation.
V. Rao Potluri
Number theory and combinatorics.
Number theory and complex analysis. On sabbatical and leave 2010–11.
Thomas W. Wieting
Differential geometry and ergodic theory.
The mathematics curriculum emphasizes solving problems by rigorous methods that use both calculation and structure. Starting from the first year, students discuss the subject intensely with one another outside the classroom and learn to write mathematical arguments.
The major is grounded in analysis and algebra through the four years of study. A student typically will also take upper-division courses in areas such as computer science, probability and statistics, combinatorics, and the topics of the senior-level courses that change from year to year. In particular, the department offers a range of upper-division computer science offerings, while recent topics courses have covered elliptic curves, polytopes, modular forms, Lie groups, representation theory, and hyperbolic geometry. A year of physics is required for the degree. The yearlong senior thesis involves working closely with a faculty member on a topic of the student’s choice.
The department has a dedicated computer laboratory for majors. Mathematics majors sometimes conduct summer research projects with the faculty, attend conferences, and present papers, but it is more common to participate in a Research Experience in Mathematics (REU) program elsewhere to broaden experience. Many students from the department have enrolled in the Budapest Semester in Mathematics program to study in Hungary.
Graduates from the mathematics department have completed Ph.D.programs in pure and applied mathematics, computer science and engineering, statistics and biostatistics, and related fields such as physics and economics. Graduates have also entered professional careers such as finance, law, medicine, and architecture.
First-year students who plan to take a full year of mathematics can select among Calculus (Mathematics 111), Introduction to Computing (Mathematics 121), Introduction to Number Theory (Mathematics 131), Introduction to Combinatorics (Mathematics 132), or Introduction to Probability and Statistics (Mathematics 141) in the fall, and Introduction to Analysis (Mathematics 112) or Introduction to Probability and Statistics in the spring. The prerequisite for all of these courses except Analysis is three years of high school mathematics. The prerequisite for Analysis is a solid background in calculus, usually the course at Reed or a year of high school calculus with a score of 4 or 5 on the AP exam. Students who intend to go beyond the first-year classes should take Introduction to Analysis. In all cases, it is recommended to consult the academic adviser and a member of the mathematics department to help determine a program.
The mathematics department’s web page can be found at academic.reed.edu/math.
Requirements for the Major
- Mathematics 111 or the equivalent, 112, 211, and 212.
- Mathematics 321, 331, and 332.
- Four additional units in mathematics courses numbered higher than 300 (excluding Mathematics 470).
- Physics 100 or the equivalent.
- Mathematics 470.
Mathematics 111 - CalculusFull course for one semester. This includes a treatment of limits, continuity, derivatives, mean value theorem, integration—including the fundamental theorem of calculus, and definitions of the trigonometric, logarithmic, and exponential functions. Prerequisite: three years of high school mathematics. Lecture-conference.
Mathematics 112 - Introduction to AnalysisFull course for one semester. Field axioms, the real and complex fields, sequences and series. Complex functions, continuity and differentiation; power series and the complex exponential. Prerequisite: Mathematics 111 or equivalent. Lecture-conference.
Mathematics 121 - Introduction to ComputingFull course for one semester. An introduction to computer science, covering topics such as elementary data structures, algorithms, computability, floating point computations, and programming in a high-level language. Prerequisite: three years of high school mathematics. Lecture-conference and lab.
Mathematics 131 - Introduction to Number TheoryFull course for one semester. A rigorous introduction to the theorems of elementary number theory. Topics may include: axioms for the integers, Euclidean algorithm, Fermat's Little Theorem, unique factorization, primitive roots, primality testing, public-key encryption systems, Gaussian integers. Prerequisite: three years of high school mathematics or consent of instructor. Lecture-conference.
Mathematics 132 - Introduction to CombinatoricsFull course for one semester. Permutations and combinations, finite mathematical structures, inclusion-exclusion principle, elements of the theory of graphs, permutation groups, and the rudiments of Pólya theory will be discussed. Prerequisite: three years of high school mathematics. Lecture-conference. Not offered 2010–11.
Mathematics 141 - Introduction to Probability and StatisticsFull course for one semester. The basic ideas of probability including properties of expectation, the Law of Large Numbers, and the Central Limit Theorem are discussed. These ideas are applied to the problems of statistical inference, including estimation and hypothesis testing. The linear regression model is introduced, and the problems of statistical inference and model validation are studied in this context. A portion of the course is devoted to statistical computing and graphics. Prerequisite: three years of high school mathematics. Lecture-conference and lab.
Mathematics 211 - Multivariable Calculus IFull course for one semester. A development of the basic theorems of multivariable differential calculus, optimization, and Taylor series. Inverse and implicit function theorems may be included. Prerequisite: Mathematics 112 or consent of the instructor. Lecture-conference.
Mathematics 212 - Multivariable Calculus II
Full course for one semester. A study of line, multiple, and surface integrals, including Green’s and Stokes’s theorems and linear differential equations. Differential geometry of curves and surfaces or Fourier series may be included. Prerequisite: Mathematics 112 and 211 or consent of the instructor. Lecture-conference.