Analysis and partial differential equations. On sabbatical fall 2019.
Algebraic number theory and arithmetic geometry.
Survey statistics, statistical learning.
Algebraic topology and category theory. On leave fall 2019.
Algebraic geometry and combinatorics.
Algebraic geometry, number theory, and quantum computation.
Number theory and complex analysis.
Probability and statistics.
Since antiquity, mathematics has been a cornerstone of the liberal arts. It serves as a model of clear reasoning and expression of thought, and its focus on the study of patterns and structures ensures its continued wide-ranging relevance. Mathematics is the scaffolding of the physical sciences and has exciting new applications in areas such as information science, network theory, cryptography, biology, and theoretical and applied economics. Meanwhile, tools are being developed to solve some of the great long-standing problems of pure mathematics.
The mathematics department offers two mathematics programs: the mathematics major, and the mathematics major with concentration in statistics. The department offers a range of upper-division mathematics classes, including real analysis, algebra, and various topics courses, which vary year by year. Recent topics courses have covered elliptic curves, polytopes, modular forms, Lie groups, Galois theory, representation theory, functional analysis, and hyperbolic geometry. There are also upper-division classes in statistics, including probability, mathematical statistics, and a statistics practicum course. The yearlong senior thesis involves working closely with a faculty member on a topic of the student’s choice.
Mathematics majors have the opportunity to conduct summer research projects with the faculty, attend conferences and present papers, and participate in Research Experience in Mathematics (REU) programs. Many students from the department have enrolled in the Budapest Semester in Mathematics and AIT programs in Hungary or the Mathematics in Moscow program in Russia.
Graduates from the mathematics department have completed PhD 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 the software industry, finance, law, medicine, engineering, and architecture.
First-year students who plan to take a full year of mathematics can select among Calculus (Mathematics 111), Introduction to Analysis (Mathematics 112), Discrete Structures (Mathematics 113), Computer Science Fundamentals I (Computer Science 121), or Introduction to Probability and Statistics (Mathematics 141). 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 5 on the AB calculus AP exam or a 4 or 5 on the BC calculus AP exam. Students who intend to go beyond the first-year classes should take Introduction to Analysis in their first year. 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 Mathematics Major
- Mathematics 111 or the equivalent, 112, 113, 201, 202, 321, and 332.
- Four additional units in mathematics courses numbered higher than 300 (excluding Mathematics 470).
- Physics 101 and 102 or the equivalent.
- Mathematics 470 (Thesis).
- Mathematics 111 or the equivalent, 112, 113, 201, and 202.
- One data analysis course, either Mathematics 141, 241, or 243.
- Mathematics 321, 391, and 392.
- Two additional units in mathematics courses numbered higher than 300 (excluding Mathematics 470).
- Mathematics 470.
For students who wish to pursue the standing mathematics–computer science interdisciplinary major, please refer to the requirements in the interdisciplinary section of this catalog.
Mathematics 111 - Calculus
Full 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 Analysis
Full 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 113 - Discrete Structures
Full course for one semester. Sets, cardinality, number theory, combinatorics, probability. Proof techniques and problem solving. Additional topics may include graph theory, finite fields, and computer experimentation. Prerequisite: three years of high school mathematics. Lecture-conference.
Mathematics 141 - Introduction to Probability and Statistics
Full 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 laboratory.
Mathematics 201 - Linear Algebra
Full course for one semester. A brief introduction to field structures, followed by presentation of the algebraic theory of finite dimensional vector spaces. Topics include linear transformations, determinants, eigenvalues, eigenvectors, diagonalization. Geometry of inner product spaces is examined in the setting of real and complex fields. Prerequisite: Mathematics 112. Lecture-conference.
Mathematics 202 - Vector Calculus
Full course for one semester. The derivative as a linear function, partial derivatives, optimization, multiple integrals, change of variables, Stokes’s theorem. Prerequisites: Mathematics 112 and 201, or permission of the instructor. Lecture-conference.
Mathematics 241 - Data Science
Full course for one semester. Applied statistics class with an emphasis on data analysis. The course will be problem driven with a focus on collecting and manipulating data, using exploratory data analysis and visualization tools, identifying statistical methods appropriate for the question at hand, and communicating the results in both written and presentation form. Prerequisite: Mathematics 141 or equivalent. Lecture-conference.
Mathematics 243 - Statistical Learning
Full course for one semester. An overview of modern approaches to analyzing large and complex data sets that arise in a variety of fields from biology to marketing to astrophysics. The most important modeling and predictive techniques will be covered, including regression, classification, clustering, resampling, and tree-based methods. There will be several projects throughout the course, which will require significant programming in R. Prerequisite: Mathematics 141, or experience with linear regressions and programming. Lecture-conference.
Mathematics 311 - Complex Analysis
Full course for one semester. A study of complex valued functions: Cauchy’s theorem and residue theorem, Laurent series, and analytic continuation. Prerequisite: Mathematics 202. Lecture-conference.
Mathematics 321 - Real Analysis
Full course for one semester. A careful study of continuity and convergence in metric spaces. Sequences and series of functions, uniform convergence, normed linear spaces. Prerequisite: Mathematics 202. Lecture-conference.
Mathematics 322 - Ordinary Differential Equations
Full course for one semester. An introduction to the theory of ordinary differential equations. Existence and uniqueness theorems, global behavior of solutions, qualitative theory, numerical methods. Prerequisite: Mathematics 202. Lecture-conference. Offered in alternate years.
Mathematics 332 - Abstract Algebra
Full course for one semester. An elementary treatment of the algebraic structure of groups, rings, fields, and/or algebras. Prerequisite: Mathematics 331, or Mathematics 201 and one of Mathematics 113, 131, or 138. Lecture-conference.
Mathematics 341 - Topics in Geometry
Full course for one semester. Topics in geometry selected by the instructor. Possible topics include the theory of plane ornaments, coordinatization of affine and projective planes, curves and surfaces, differential geometry, algebraic geometry, and non-Euclidean geometry. Prerequisite: Mathematics 202. Lecture-conference. May be repeated for credit. Offered in alternate years.
Mathematics 342 - Topology
Full course for one semester. An introduction to basic topology, followed by selected topics such as topological manifolds, embedding theorems, and the fundamental group and covering spaces. Prerequisite: Mathematics 202 and 332, the latter of which may be taken concurrently. Lecture-conference.
Mathematics 343 - Statistics Practicum
Full course for one semester. In this course, students will participate in a team-based, semester-long research project. Class time will be divided between supervised research time and a seminar focused on providing students with skills to facilitate their research. Seminar topics will include reproducible workflows, effective strategies for collaborative work, technical writing, statistical consulting, and scientific presentations. The course covers several components of the research process, such as literature reviews, technical writing, and scientific presentations. Emphasis is placed on developing a reproducible workflow. Prerequisite: Mathematics 243, or Mathematics 241 with permission of the instructor. Conference-laboratory. May be repeated for credit.
Mathematics 361 - Number Theory
Full course for one semester. A study of integers, including topics such as divisibility, theory of prime numbers, congruences, and solutions of equations in the integers. Prerequisite: Mathematics 201. Concurrent Mathematics 332 is recommended. Lecture-conference. Offered in alternate years.
Not offered 2019–20.
Mathematics 372 - Combinatorics
Full course for one semester. Emphasis is on enumerative combinatorics including such topics as the principle of inclusion-exclusion, formal power series and generating functions, and permutation groups and Pólya theory. Selected other topics such as Ramsey theory, inversion formulae, the theory of graphs, and the theory of designs will be treated as time permits. Prerequisite: Mathematics 113 and 201. Lecture-conference. Offered in alternate years.
Mathematics 382 - Algorithms and Data Structures
See Computer Science 382 for description.
Mathematics 387 - Computability and Complexity
See Computer Science 387 for description.
Mathematics 388 - Cryptography
See Computer Science 388 for description.
Mathematics 391 - Probability
Full course for one semester. A development of probability theory in terms of random variables defined on discrete sample spaces. Special topics may include Markov chains, stochastic processes, and measure-theoretic development of probability theory. Prerequisites: Mathematics 113 and 202. Lecture-conference.
Mathematics 392 - Mathematical Statistics
Full course for one semester. Theories of statistical inference, including maximum likelihood estimation and Bayesian inference. Topics may be drawn from the following: large sample properties of estimates, linear models, multivariate analysis, empirical Bayes estimation, and statistical computing. Prerequisite: Mathematics 391 or consent of the instructor. Lecture-conference.
Mathematics 393 - Stochastic Processes
Full course for one semester. A brief introduction to calculus-based probability theory, as well as a study of the main discrete- and continuous-time stochastic processes. Topics include Markov chains, martingales, Poisson processes, renewal processes, continuous-time Markov chains, and Brownian motion. A portion of the course is devoted to modeling stochastic processes using computer software. Prerequisites: Mathematics 202 and one of Mathematics 113, 141, or 391. Lecture-conference.
Mathematics 411 - Topics in Advanced Analysis
Full course for one semester. Topics selected by the instructor. Prerequisite: Mathematics 321 or consent of the instructor. Lecture-conference. May be repeated for credit.
Mathematics 412 - Topics in Algebra
Full course for one semester. Topics selected by the instructor, for example, commutative algebra, Galois theory, algebraic geometry, and group representation theory. Prerequisite: Mathematics 332 or consent of the instructor. Lecture-conference. May be repeated for credit.
Mathematics 441 - Topics in Computer Science Theory
See Computer Science 441 for description.
Mathematics 470 - Thesis
Full course for one year.
Mathematics 481 - Independent Study
One-half course for one semester. Independent reading primarily for juniors and seniors. Prerequisite: approval of the instructor and the division.