Completeness of the real numbers; topology of the real line including the Bolzano-Weierstrass and Heine-Borel theorems; sequences, properties of continuous functions on sets; infinite series, uniform convergence.
MATH 211 and either MATH 271 or 272, or consent of the instructor is required. Students with a grade of B+ or lower in linear algebra are encouraged to take another 200-level course with proofs before taking MATH 355.
Limited to 25 students per section.
Completeness of the real numbers; topology of the real line including the Bolzano-Weierstrass and Heine-Borel theorems; sequences, properties of continuous functions on sets; infinite series, uniform convergence.
MATH 211 and either MATH 271 or 272, or consent of the instructor is required. Students with a grade of B+ or lower in linear algebra are encouraged to take another 200-level course with proofs before taking MATH 355.
Limited to 25 students per section.
A brief consideration of properties of sets, mappings, and the system of integers, followed by an introduction to the theory of groups and rings including the principal theorems on homomorphisms and the related quotient structures; integral domains, fields, polynomial rings.
MATH 211 and either MATH 271 or 272, or consent of the instructor is required. Students with a grade of B+ or lower in linear algebra are encouraged to take another 200-level course with proofs before taking MATH 350.
Limited to 25 students per section.
A brief consideration of properties of sets, mappings, and the system of integers, followed by an introduction to the theory of groups and rings including the principal theorems on homomorphisms and the related quotient structures; integral domains, fields, polynomial rings.
MATH 211 and either MATH 271 or 272, or consent of the instructor is required. Students with a grade of B+ or lower in linear algebra are encouraged to take another 200-level course with proofs before taking MATH 350.
Limited to 25 students per section.
An introduction to analytic functions; complex numbers, derivatives, conformal mappings, integrals. Cauchy’s theorem; power series, singularities, Laurent series, analytic continuation; special functions.
MATH 211 and either MATH 271 or 272, or consent of the instructor is required. Limited to 25 students.
How to handle overenrollment: Preference is given to seniors.
The first half of the course covers continuous and discrete Fourier transforms (including convolution and Plancherel’s formula), Fourier series (including convergence and the fast Fourier transform algorithm), and applications like heat conduction along a rod and signal processing. The second half of the course is devoted to wavelets: Haar bases, the discrete Haar transform in 1 and 2 dimensions with application to image analysis, multiresolution analysis, filters, and wavelet-based image compression like JPEG2000. Three class hours per week plus a weekly one-hour computer laboratory.
This course emphasizes enumerative combinatorics, a classical subject in mathematics related to the theory of counting. Problems in this area often pertain to finding the number of possible arrangements of a set of objects under some particular constraints. This course incorporates a wide set of problems involving enumerative combinatorics, as well as theory and applications.
The study of vector spaces over the real and complex numbers, introducing the concepts of subspace, linear independence, basis, and dimension; systems of linear equations and their solution by Gaussian elimination; matrix operations; linear transformations and their representations by matrices; eigenvalues and eigenvectors; and inner product spaces. This course will feature both proofs and applications, with special attention paid to applied topics such as least squares and singular value decomposition.
The study of vector spaces over the real and complex numbers, introducing the concepts of subspace, linear independence, basis, and dimension; systems of linear equations and their solution by Gaussian elimination; matrix operations; linear transformations and their representations by matrices; eigenvalues and eigenvectors; and inner product spaces. MATH 271 will feature both proofs and applications, with special attention paid to the theoretical development of the subject.
The study of vector spaces over the real and complex numbers, introducing the concepts of subspace, linear independence, basis, and dimension; systems of linear equations and their solution by Gaussian elimination; matrix operations; linear transformations and their representations by matrices; eigenvalues and eigenvectors; and inner product spaces. MATH 271 will feature both proofs and applications, with special attention paid to the theoretical development of the subject.
