In Part One of this lesson, students are introduced to apartheid in South Africa. They watch clips from Steven Van Zandt and Arthur Baker's Sun City documentary to learn about apartheid, and attempt to experience what life might have been like during apartheid through a classroom activity. Then, students consider ways in which apartheid could be fought, and whether elements of apartheid in South Africa also existed in the history of the United States.

In Part 2 of this lesson, students view clips from the Sun City documentary and explore how musicians united to challenge apartheid. In a group setting, students will consider the various strategies activists, corporations, and other governments used to isolate the South African government and hasten the end of apartheid. Finally, students consider how apartheid relates to segregation in the United States.

With Reading Progress, learners build fluency through independent practice and educators save time for active instruction with intuitive grading features and progress data through Insights.

This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.

A focus on the organization, development, and refinement of technical communications.  Internal and external communications, including letters, memos, reports, and presentations are included.

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.   

This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

Resource used and updated by the Utah Board of Education for 3rd grade integrated science.

The course provides a survey of the theory and application of time series methods in econometrics.

The course provides a survey of the theory and application of time series methods in econometrics.

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

Topics vary from year to year. Fall Term: Numerical properties and vanish theorems for ample, nef, and big line bundles and vector bundles; multiplier ideals and their applications

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

Content varies from year to year. Introduces new and significant developments in algebraic topology with the focus on homotopy theory and related areas. Spring 2003: An introduction to higher algebraic K-theory.

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.

This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor.

This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc.

Geometry of pseudoconvex domains, the Monge-Ampere equation, Hodge theory on Kaehler manifolds, the theory of toric varieties and (time permitting) some applications to combinatorics.