Highlight how symbolic operations on a system of linear equations do (or do not) change the graphic or tabular representations of the system. Note that the System Solver is a tool intended to illustrate the rationale behind the symbolic operations used to solve systems of linear equations, and not a way to learn what procedures to follow.
The Proportioner was developed to support your learning and your students’ learning of proportion. It allows you to manipulate images and compare their dimensions to the dimensions of other images. Using the Proportioner, you can: •Specify image dimensions graphically, numerically or using a scale factor •Duplicate images and modify copies for comparisons •Use one image to "paint" another
Concord.org Five Lessons: A Taste of the Future, Today
This issue of @Concord features five ready-to-use “Lessons” that illustrate how interactive models and tools can fit into real classrooms today. Each of these lessons addresses important content that can be found in all the standards and frameworks, and does it by giving students tools with which to explore and interact. The lessons illustrate how sophisticated math and science content can be taught earlier and how generative the resulting understanding can be.
CK-12 Geometry (CA Textbook)
CK-12's Geometry delivers a full course of study in the mathematics of shape and space for the high school student, relating the ancient logic and modern applications of measurement and description to its essential elements, processes of reasoning and proof, parallel and perpendicular lines, congruence and similarity, relationships within triangles and among quadrilaterals, trigonometry of right triangles, circles, perimeter, area, surface area, volume, and geometric transformations. This digi
Advanced Algebra II (CA Textbook)
Advanced Algebra II provides three complementary resources for teachers and students that combine to provide a friendly, easy-to-understand explanation of Algebra II concepts. The main text, "Activities and Homework", consists of a series of worksheets for both in-class group work as well as homework assignments. The concepts behind those activities are described in detail in the "Conceptual Explanations" text. The third book, the "Teacher's Guide", provides instructors with guides and suggestio
CK-12 Trigonometry (CA Textbook)
This textbook covers topics such as Trigonometry and Right Angles, Circular Functions, Trigonometric Identities, Inverse Functions, Trigonometric Equations, Triangles and Vectors, as well as Polar Equations and Complex Numbers. It can also be used in conjunction with other directed courses in Mathematical Analysis or Linear Algebra as a full course in Precalculus. This digital textbook was reviewed for its alignment with California content standards.
Linear Systems and Optimization: The Fourier Transform and its Applications
The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both.
Linear Systems and Optimization: Introduction to Linear Dynamical Systems
Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-outp
Linear Systems and Optimization: Convex Optimization II
Continuation of Convex Optimization I. Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Course requirements include a substantial project.
Linear Systems and Optimization: Convex Optimization I
Concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, control, digital and analog circuit design, computational geometry,
Artificial Intelligence: Natural Language Processing
This course is designed to introduce students to the fundamental concepts and ideas in natural language processing (NLP), and to get them up to speed with current research in the area. It develops an in-depth understanding of both the algorithms available for the processing of linguistic information and the underlying computational properties of natural languages. Wordlevel, syntactic, and semantic processing from both a linguistic and an algorithmic perspective are considered. The focus is on m
Artificial Intelligence: Machine Learning
This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include: supervised learning (generative/discriminative learning, parametric/non-parametric learning, neural networks, support vector machines); unsupervised learning (clustering, dimensionality reduction, kernel methods); learning theory (bias/variance tradeoffs; VC theory; large margins); reinforcement learning and adaptive control. The course will also discuss recent applications of machi
Copyright for Educators
This course is for educators and learners who wants to understand how copyright affects use of learning materials, and how to use copyright to facilitate education. The course is focused on developing practical solutions. The reading won't always give these to you, its up to you to devise practical solutions based on the reading.
This animation shows how velocity and position of an aircraft are resolved in a 3-D Cartesian coordinate system.
Elementary Statistics is an introduction to data analysis course that makes use of graphical and numerical techniques to study patterns and departures from patterns. The student studies randomness with emphasis on understanding variation, collects information in the face of uncertainty, checks distributional assumptions, tests hypotheses, uses probability as a tool for anticipating what the distribution of data may look like under a set of assumptions, and uses appropriate statistical models to
A Sense of Place
Place and Location are two of the five themes of geography and a natural starting point for a study of the Arctic and Antarctica. Location answers the question, "Where am I?" while the study of place asks, "What kind of a place is it?" and, "How does this place connect to my hometown?" This issue of Beyond Penguins and Polar Bears examines how you can introduce the Arctic and Antarctica and use science, geography, literacy, and technology to help your students compare and contrast these two dram
Using the macro tabletop AFM simulators, students will investigate the surface features of various samples using contact, tapping and magnetic modes. The students will measure the amplitude of oscillation of reflected LASER light at known coordinates to map out the surface features of the sample. Data is then analyzed through Microsoft Excel to construct a surface plot of the sample for comparison.
Introduction to Nanoscale Science: Surface Area to Volume Ratio Module
Many intriguing phenomena observed in the "nanoworld" can be attributed to the increase in the surface to volume ratio ( SVR ) at the nanoscale. Understanding the surface area effects to volume changes is thus crucial to the understanding of nanoscale phenomena and nanotechnology applications. As an introduction to the nanoworld, the major goals of this module are to (1) give students a feel for just how small the nanoscale is, (2) give students practice in mathematically communicating nanoscale