This art history video examines the "Alexander Mosaic" c. 100 B.C.E., tessera mosaic from the House of the Faun, Pompeii. This Roman floor mosaic may be based on a lost Hellenistic painting by Philoxenos of Eretria, The Battle of Issus, c. 315 B.C.E.). Museo Archeologico Nazionale, Naples.

"Democracy in America" by Alexis de Tocqueville is one of the most influential books ever written about America. While historians have viewed "Democracy" as a rich source about the age of Andrew Jackson, Tocqueville was more of a political thinker than a historian. His "new political science" offers insights into the problematic issues faced by democratic society.

The problem statement describes a changing algae population as reported by the Maryland Department of Natural Resources. In part (a), students are expected to build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth (F-LE.2).

Students are introduced to biofuels, biological engineers, algae and how they grow (photosynthesis), and what parts of algae can be used for biofuel (biomass from oils, starches, cell wall sugars). Through this lesson, plants—and specifically algae—are presented as an energy solution. Students learn that breaking apart algal cell walls enables access to oil, starch, and cell wall sugars for biofuel production. Students compare/contrast biofuels and fossil fuels. They learn about the field of biological engineering, including what biological engineers do. A 20-slide PowerPoint® presentation is provided that supports students taking notes in the Cornell format. Short pre- and post-quizzes are provided. This lesson prepares students to conduct the associated activity in which they make and then eat edible algal cell models.

This site teaches Arithmetic with Polynomials and Rational Expressions to High Schoolers through a series of 4333 questions and interactive activities aligned to 26 Common Core mathematics skills.

This site teaches High Schoolers how to create equations through a series of 298 questions and interactive activities aligned to 5 Common Core mathematics skills.

Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and techonolgy to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.

This site teaches Structure in Algebraic Expressions to High Schoolers through a series of 3482 questions and interactive activities aligned to 26 Common Core mathematics skills.

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

This is a textbook for first year Computer Science. Algorithms and Data Structures With Applications to Graphics and Geometry.

This textbook is an introductory coverage of algorithms and data structures with application to graphics and geometry.

This web page contains a free electronic version of my self-published textbook Algorithms, along with other lecture notes I have written for various theoretical computer science classes at the University of Illinois, Urbana-Champaign

In-depth study of an active research topic in computer graphics. Topics change each term. Readings from the literature, student presentations, short assignments, and a programming project. Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today's animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robotics, biomechanics, physics, applied mathematics and scientific computing.

In this game activity students practice comparing shapes and naming something that is alike or different about them.