This is the Teacher's Guide for Kenny Felder's course in Advanced Algebra II. This guide is *not* an answer key for the homework problems: rather, it is a day-by-day guide to help the teacher understand how the author envisions the materials being used. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Homework and Activities" collections (coming soon) to make up the entire course.

" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

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.

This lesson is about trying to get students to make connections between ideas about equations, inequalities, and expressions. The lesson is designed to give students opportunities to use mathematical vocabulary for a purpose to describe, discuss, and work with these symbol strings.The idea is for students to start gathering global information by looking at the whole number string rather than thinking only about individual procedures or steps. Hopefully students will begin to see the symbol strings as mathematical objects with their own unique set of attributes. (7th Grade Math)

" 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 research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.

Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.

In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

This final lesson in the unit culminates with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they have learned throughout the unit to answer the grand challenge question in a writing assignment.

Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976. Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems. The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface below. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

The CyberSquad tries to figure out a table arrangement for 20 workers in this video from Cyberchase.

In this video segment from Cyberchase, Matt tries for a second time to arrange tables and chairs to accommodate 20 workers.

Matt's third table arrangement helps fit all 20 workers at five tables in this video segment from Cyberchase.

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

This real world task requires students to answer questions about equations for calculating compound interest.

The consideration of cord length is very important in a bungee jump‰ŰÓtoo short, and the jumper doesn't get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbieĺ¨ doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)