Stanley Chang
Professor of Mathematics
Research on positive scalar curvature and rigidity of manifolds, noncommutative geometry, tools of surgery theory
I am engaged in the study of the curvature and rigidity of high-dimensional manifolds, using such tools that appear in algebraic topology, differential geometry, index theory and C*-algebras. The examination of such properties has been of classical interest, but recent developments have reanimated the subject in both the compact and noncompact contexts. Currently I am co-authoring an advanced textbook on surgery methods and applications which will describe the many topological theorems proved in the 1970s and 1980s.
In the past years I have taught a wide variety of courses at all levels of the mathematics curriculum, including calculus, linear algebra, abstract algebra, real and complex analysis, topology and Galois Theory. More recently I have developed courses in Advanced Number Theory, Functional Analysis and Stochastic Processes. Many of our advanced students request independent study courses and research opportunities, and I have overseen such efforts in the study of modular forms, advanced analysis, representation theory and logic. In the Fall of 2016 I will be offering an Applied Calculus course that motivates theory and calculation with real-world problems in the life and social sciences.
At Wellesley I have served both on the 2015 Commission, the Academic Planning Committee and the Presidential Search Committee in 2016. In these campus bodies I am interested in helping the College maintain high academic standards for all of its students. In my own department I am very much involved in the effort to build our curricular offerings and to prepare our students for graduate studies. Along with Professor Oscar Fernandez, I co-created the Wellesley Emerging Scholars Initiative in the hopes to increase the participating by underrepresented minorities in the mathematical sciences.
I am an amateur fencer and have competed in some regional tournaments. Currently I hold a national E ranking. I play both piano and harpsichord and have performed some ensembles on campus. My love of mathematics extends to a love of language, and I spend some of each week reading Classical works written in Greek and Latin. Also I am a member of the Metropolitan Chorale, a Boston-area choir that performs choral works three times a year.
Education
- B.A., University of California (Berkeley)
- M.A., Cambridge University (England)
- Ph.D., University of Chicago
Current and upcoming courses
Abstract Algebra
MATH305
In this course, students examine the structural similarities between familiar mathematical objects such as number systems, matrix sets, function spaces, general vector spaces, and mod n arithmetic. Topics include groups, rings, fields, homomorphisms, normal subgroups, quotient spaces, isomorphism theorems, divisibility, and factorization. Many concepts generalize number theoretic notions such as Fermat's little theorem and the Euclidean algorithm. Optional subjects include group actions and applications to combinatorics.
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Combinatorics and Graph Theory
MATH225
Combinatorics is the art of counting possibilities: for instance, how many different ways are there to distribute 20 apples to 10 kids? Graph theory is the study of connected networks of objects. Both have important applications to many areas of mathematics and computer science. The course will be taught emphasizing creative problem-solving as well as methods of proof, such as proof by contradiction and induction. Topics include: selections and arrangements, generating functions, recurrence relations, graph coloring, Hamiltonian and Eulerian circuits, and trees. -
This course is designed to examine the degree to which a function can be determined by an algebraic relationship it has with its derivative(s) --- a so-called ordinary differential equation (ODE). For instance, can one completely catalog all functions which equal their own derivative? In service of developing techniques for solving certain classes of differential equations, some fundamental notions from linear algebra and complex numbers are presented. Â Differential equation topics include modeling with and solving first- and second-order ODEs, separable ODEs, and a discussion of higher order and non-linear ODEs; linear algebra topics include solving systems via elementary row operations, bases, dimension, determinants, column space, and eigenvalues/vectors.
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This course is a first-year seminar for students in the Wellesley Plus program. It will introduce students to important basic mathematical concepts as set theory, proof techniques, propositional and predicate calculus, graph theory, combinatorics, probability, and recursion.