This seminar will allow you to solve a system of linear equations by graphing. It will help you to understand what it means when the lines in a system of equations are parallel, and also what it means for the graphs to be the same line. You will learn how to visually identify information about the system of equations simply by examining the graphs of the lines that make up the system.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra.

Students analyze how two different calculators get different values for the same numerical expression. In the process, students recognize the need for following the same conventions when evaluating expressions.Key ConceptsMathematical expressions express calculations with numbers (numerical expressions) or sometimes with letters representing numbers (algebraic expressions).When evaluating expressions that have more than one operation, there are conventions—called the order of operations—that must be followed:Complete all operations inside parentheses first.Evaluate exponents.Then complete all multiplication and division, working from left to right.Then complete all addition and subtraction, working from left to right.These conventions allow expressions with more than one operation to be evaluated in the same way by everyone. Because of these conventions, it is important to use parentheses when writing expressions to indicate which operation to do first. If there are nested parentheses, the operations in the innermost parentheses are evaluated first. Understanding the use of parentheses is especially important when interpreting the associative and the distributive properties.Goals and Learning ObjectivesEvaluate numerical expressions.Use parentheses when writing expressions.Use the order of operations conventions.

This book presents 49 space-related math problems published weekly on the SpaceMath@NASA site during the 2011-2012 academic year. The problems utilize information, imagery, and data from various NASA spacecraft missions that span a variety of math skills in pre-algebra and algebra.

This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

This course is a continuation of 18.014 Calculus with Theory. It covers the same material as 18.02 Multivariable Calculus, but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

This course offers an advanced introduction to numerical analysis, with a focus on accuracy and efficiency of numerical algorithms. Topics include sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems), floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) are also surveyed.

This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

An overview of the STEM 9 program at Pequea Valley High School in Lancaster County, PA. Most 9th grade learners take this course which teaches Algebra I math concepts via physics concepts and tech ed building.

Students express the lengths of trains as algebraic expressions and then substitute numbers for letters to find the actual lengths of the trains.Key ConceptsAn algebraic expression can be written to represent a problem situation. More than one algebraic expression may represent the same problem situation. These algebraic expressions have the same value and are equivalent.To evaluate an algebraic expression, a specific value for each variable is substituted in the expression, and then all the calculations are completed using the order of operations to get a single value.Goals and Learning ObjectivesEvaluate expressions for the given values of the variables.

Students will learn about NASA's Radiation Belt Storm Probes (RBSP), Earth's van Allen Radiation Belts, and space weather through reading a NASA press release and viewing a NASA eClips video segment. Then students will use simple linear functions to examine the scale of the radiation belts and the strength of Earth's magnetic field. This activity is part of the Space Math multimedia modules that integrate NASA press releases, NASA archival video, and mathematics problems targeted at specific math standards commonly encountered in middle school textbooks. The modules cover specific math topics at multiple levels of difficulty with real-world data and use the 5E instructional sequence.

CK-12 Middle School Math Concepts for seventh grade provides a complete textbook. It presents topics including algebraic thinking, patterns, decimals, decimal operations, fractions, fraction operations, integers, integer operations, ratios, rates, proportions, percents, percent applications, equations, solving equations, inequalities, functions, graphing functions, geometry, plane geometry, solid geometry, area, perimeter, surface area, volume, statistics including mean, median, mode and range, graphing and types of graphs, and probability.

This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.

Mathematicians often argue that anything which can be represented numerically or algebraically can also be represented geometrically. This is perhaps true even to the extent that simple numeric calculations can be demonstrated geometrically. This example illustrates one such geometric process of addition. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

This is a project that generally follows the PBL framework that can be used to help students master the concept of qudratics in their study of intermediate algebra. Specifically, it was designed to help students master the concept of quadratic functions, equations, and inequalities, including the parts of both standard & vertex equations, as well as how to identify the domain & range of a quadratic function; how to apply quadratics as the square of binomials; how to make decisions about a specific quadratic problem or application relative to the significance of the vertex and roots; and how to transform a quadratic by manipulating its parent equation. Note that the project was designed and delivered per the North Carolina Math 2 curriculum and it can be customized to meet your own specific curriculum needs and resources.

A java code for computing permutation algebra using standard cycle notation (right to left). The first version was produced during Fall 2017 and the second version was produced during Spring 2018. Version 2.0 is available for download (Readme can be found at https://drive.google.com/file/d/1-Mz6-6lMd2kL6WiWI4VnBuhclZ3C1dAw/view).

In this course, we will present the theory of Probabilistically Checkable Proofs (PCPs), and prove some fundamental consequences of it as well as more recent advances. More specifically, the first half of the course will be devoted to the (algebraic) proof of the basic PCP Theorem and basic relation to approximation problems. We will then move on to more advanced topics, such as hardness amplification, the long-code framework, the Unique-Games Conjecture and its implications, and the 2-to-2 Games Theorem.

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: Numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed.

Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.