Rice university math games

Description: Concrete mathematics is a blend of continuous and discrete mathematics. Major topics include sums, recurrences, integer functions, elementary number theory, binomial coefficients, generating functions, discrete probability and asymptotic methods. Cross-list: COMP Description: This course will cover graduate level topics in group theory, ring theory, and module theory.

The course will also include an introduction to category theory as time permits. Tensor and exterior algebra, introductory commutative algebra, structure of modules, and elements of homological algebra. Additional advanced topics may include representations of finite groups and affine algebraic geometry. Description: Varieties as solution sets of systems of polynomial equations, varieties in projective space, rational and regular functions, maps of varieties, local properties and singularities.

Description: This course deals with miscellaneous special topics not covered in other courses. Description: Mathematical models of quasicrystals, whose discovery in the early 's led to a paradigm shift in materials science.

Topics include: classical theory of ordered structures i. Contact department for current semester's topic s. Description: In depth investigation of a particular area of mathematics of mutual interest to the student and the faculty adviser. Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics.

The course may be repeated multiple times for credit. Restrictions: Enrollment is limited to Graduate level students. Description: A graduate course in smooth and Riemannian manifolds. Description: Topic to be announced.

Additional course work is required beyond the undergraduate course requirements. Description: A graduate course on the topology of fiber bundles, especially vector bundles and principal bundles, as well as their characteristic classes.

If time allows, other topics may be included. In particular, the student should be familiar with smooth manifolds, the tangent spaces, homotopy groups, covering spaces, and homology groups. Description: This course will cover graduate level topics in field theory, Galois theory, and advanced topics in commutative algebra and in multilinear algebra. Specific topics include various algebraic field extensions; fundamental theorem of Galois theory; solvable and radical extensions; transcendental extensions; tensor, symmetric, and exterior algebras; projective, injective, and flat modules; advanced ideal theory; localization; and chain conditions for rings and modules.

The course will also additional advanced topics, such as homological algebra, as time permits. Description: Possible topics include rational points on algebraic varieties, moduli spaces, deformation theory, and Hodge structures.

Description: Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Description: Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Restrictions: Enrollment is limited to Graduate or Visiting Graduate level students. Description: Topics and credit hours vary each semester. Description: Presentations of research topics in mathematics and related fields. Description: Presentations of research in topology and related areas.

Description: Presentations of research in algebraic geometry and related areas. Description: Presentations of research in geometric analysis, mathematical physics, dynamics and related areas. Enrollment limited to students in a Doctor of Philosophy degree.

Can be repeated for credit. Note: Internally, the university uses the following descriptions, codes, and abbreviations for this academic program. The following is a quick reference:. Course Level: Undergraduate Lower-Level Description: Provides transfer credit based on student performance on approved examinations in calculus, such as the AB Calculus Advanced Placement exam or the International Baccalaureate higher-level calculus exams.

Course Level: Undergraduate Lower-Level Description: Provides transfer credit based on student performance on approved examinations in calculus, such as the BC Calculus Advanced Placement exam or the International Baccalaureate higher-level calculus exams. Course Level: Undergraduate Lower-Level Description: Math is intended primarily for students majoring in non-STEM fields seeking knowledge of the nature of mathematics as well as training in mathematical thinking and problem-solving.

Course Level: Undergraduate Lower-Level Description: A rigorous introduction to the study of ordinary differential equations, including results about the existence, uniqueness and stability of solutions. Course Level: Undergraduate Lower-Level Description: In this course, undergraduates who have previously excelled in MATH courses will develop teaching skills while supporting faculty as teaching assistants TAs in a particular MATH course for the benefit of the students taking that particular course.

Course Level: Undergraduate Upper-Level Description: Vector spaces, linear transformations and matrices, theory of systems of linear equations, determinants, eigenvalues and diagonalizability, inner product spaces; and optional material chosen from: dual vector spaces, spectral theorem for self-adjoint operators, Jordan canonical form. Course Level: Undergraduate Upper-Level Description: Linear transformations and matrices, solution of linear equations, inner products eigenvalues and eigenvectors, the spectral theorem for real symmetric matrices, applications of Jordan canonical form.

Course Level: Undergraduate Upper-Level Description: Topics chosen from Euclidean, spherical, hyperbolic, and projective geometry, with emphasis on the similarities and differences found in various geometries. Course Level: Undergraduate Upper-Level Description: Laplace transform: inverse transform, applications to constant coefficient differential equations.

Course Level: Undergraduate Upper-Level Description: Study of the Cauchy integral theorem, Taylor series, residues, as well as the evaluation of integrals by means of residues, conformal mapping, and application to two-dimensional fluid flow. Course Level: Undergraduate Upper-Level Description: Lectures by undergraduate students on mathematical topics not usually covered in other courses.

Course Level: Undergraduate Upper-Level Description: Existence and uniqueness for solutions of ordinary differential equations and difference equations, linear systems, nonlinear systems, stability, periodic solutions, bifurcation theory. Course Level: Undergraduate Upper-Level Description: Varieties as solution sets of systems of polynomial equations, varieties in projective space, rational and regular functions, maps of varieties, local properties and singularities. Course Level: Undergraduate Upper-Level Description: This course deals with miscellaneous special topics not covered in other courses.

Course Level: Undergraduate Upper-Level Description: In depth investigation of a particular area of mathematics of mutual interest to the student and the faculty adviser. Course Level: Undergraduate Upper-Level Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics.

Course Level: Graduate Description: Topic to be announced. Course Level: Graduate Description: First order of partial differential equations.

Course Level: Graduate Description:. Course Level: Graduate Description: Varieties as solution sets of systems of polynomial equations, varieties in projective space, rational and regular functions, maps of varieties, local properties and singularities. Course Level: Graduate Description: Possible topics include rational points on algebraic varieties, moduli spaces, deformation theory, and Hodge structures. Course Level: Graduate Description: Mathematical models of quasicrystals, whose discovery in the early 's led to a paradigm shift in materials science.

Course Level: Graduate Description: Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Course Level: Graduate Description: Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Course Level: Graduate Description: Topics and credit hours vary each semester. Course Level: Graduate Description: Presentations of research topics in mathematics and related fields.

Course Level: Graduate Description: Presentations of research in topology and related areas. Course Level: Graduate Description: Presentations of research in algebraic geometry and related areas.

Course Level: Graduate Description: Presentations of research in geometric analysis, mathematical physics, dynamics and related areas. Course Level: Graduate Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. A guided research project: Students will also have the opportunity to conduct a research project in STEM fields ranging from mathematics to biology.

Students will be matched to a virtual lab and work closely with mentors. For schedule and plans of this semester, please check Schedule. However, when a course is taken at both Rice and another institution, the grade in the Rice course will be used for departmental GPA calculations.

Students who wish to take advantage of this option must inform the Director of Undergraduate Studies in the Economics Department. In some cases, transfer credit may be awarded for courses completed at other schools after the student has matriculated at Rice. Students may present a maximum of two such transfer courses in fulfilling requirement 2a.