http://www.oercommons.org/browse/keyword/linear daily 1 2000-01-01T12:00+00:00 http://www.oercommons.org/courses/abstract-algebra-i The study of abstract algebra grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted. The student will begin this course by reviewing basic set theory, integers, and functions in order to understand how algebraic operations arise and are used. The student then will proceed to the heart of the course, which is an exploration of the fundamentals of groups, rings, and fields. Upon successful completion of this course, the student will be able to: Describe and generate groups, rings, and fields; Relate abstract algebraic constructs to more familiar number sets and operations and see from where the constructs derive; Identify examples of specific constructs; Identify and differentiate between different structures and understand how changing properties give rise to new structures; Explain the theory behind relations and functions and identify domains and images of functions, based on the structures given; Explain how functions may relate seemingly dissimilar structures to each other and how knowing properties of one structure allows us to know the same properties in the related structure, if certain functions exist between them. (Mathematics 231) Mathematics and Statistics 2011-11-11T11:22:52 Course Related Materials http://www.oercommons.org/courses/abstract-algebra-ii This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232) Mathematics and Statistics 2011-11-11T11:22:52 Course Related Materials http://www.oercommons.org/courses/array-signal-processing-an-introduction An introduction to the principles of array signal processing and to our project. Claiborne McPheeters Edward Rodriguez James Finnigan Jeremy Bass Science and Technology 2007-08-20T04:24:00 Course Related Materials http://www.oercommons.org/courses/bacteria-populations This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal. Mathematics and Statistics 2013-03-14T23:55:18 Course Related Materials http://www.oercommons.org/courses/beamforming-basics Discusses the basics of beamforming concerning our project. Claiborne McPheeters Edward Rodriguez James Finnigan Jeremy Bass Science and Technology 2007-08-20T05:11:00 Course Related Materials http://www.oercommons.org/courses/carbon-14-dating The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances. Mathematics and Statistics 2013-03-14T23:55:18 Course Related Materials http://www.oercommons.org/courses/carbon-14-dating-in-practice-i In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base. Mathematics and Statistics 2013-03-14T23:55:18 Course Related Materials http://www.oercommons.org/courses/carbon-14-dating-in-practice-ii This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function. Mathematics and Statistics 2013-03-14T23:55:18 Course Related Materials http://www.oercommons.org/courses/carbon-14-dating-variation-2 This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time. Mathematics and Statistics 2013-03-14T23:55:18 Course Related Materials http://www.oercommons.org/courses/collaborative-statistics Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. The textbook is also available in printed form from Qoop.com. Dr. Barbara Illowsky Susan Dean Mathematics and Statistics 2008-09-12T23:38:27 Course Related Materials http://www.oercommons.org/courses/collaborative-statistics-custom-version-modified-by-r-bloom Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom textbook collection has been modified by R. Bloom for her classes at De Anza College; the homework content for the custom collection is now contained in a separate homework collection. Roberta Bloom Mathematics and Statistics 2009-06-17T01:07:02 Course Related Materials http://www.oercommons.org/courses/collaborative-statistics-homework-book-custom-version-modified-by-r-bloom This is a custom collection (by R. Bloom) of homework and review problems to accompany Collaborative Statistics textbook custom collection by R. Bloom. Content is derived from Collaborative Statistics written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook by S. Dean and B. Illowsky was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom version of their collection has been modified by R. Bloom for her classes at De Anza College. Roberta Bloom Mathematics and Statistics 2009-06-17T01:07:02 Course Related Materials http://www.oercommons.org/courses/15-063-communicating-with-data-summer-2003 Introduces students to the basic tools in using data to make informed management decisions. Covers introductory probability, decision analysis, basic statistics, regression, simulation, and linear and nonlinear optimization. Computer spreadsheet exercises and examples drawn from marketing, finance, operations management, and other management functions. Restricted to Sloan Fellows. Carroll, John S. Business 2006-03-20T23:57:00 Course Related Materials http://www.oercommons.org/courses/comparing-exponentials This task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations. Mathematics and Statistics 2013-03-14T23:55:18 Course Related Materials http://www.oercommons.org/courses/coordinate-geometry-of-st-lines-revision-practice Self generating, interactive practice sheet with questions and answers provided dynamically. Drag Points A & B to change the values of given Points Mathematics and Statistics 2012-07-13T14:53:35 Course Related Materials http://www.oercommons.org/courses/data-concepts-linear-functions This module discusses the concept of modeling data with linear functions in Algebra. Kenny Felder Mathematics and Statistics 2009-06-17T01:07:02 Course Related Materials http://www.oercommons.org/courses/developing-the-array-model-and-processing-techniques A discussion of the ULA, its properties, the array that we used for our project, and an introduction to beamforming. Claiborne McPheeters Edward Rodriguez James Finnigan Jeremy Bass Science and Technology 2007-08-20T04:18:00 Course Related Materials http://www.oercommons.org/courses/discrete-time-filtering-example Average stock price as an example of discrete-time filtering. Don Johnson Science and Technology 2007-08-20T04:26:00 Course Related Materials http://www.oercommons.org/courses/do-two-points-always-determine-a-linear-function-ii This task is designed as a follow-up to the task F-LE Do Two Points Always Determine a Linear Function? Linear equations and linear functions are closely related, and there advantages and disadvantages to viewing a given problem through each of these points of view. This task is intended to show the depth of the standard F-LE.2 and its relationship to other important concepts of the middle school and high school curriculum, including ratio, algebra, and geometry. Mathematics and Statistics 2013-03-14T23:55:19 Course Related Materials http://www.oercommons.org/courses/do-two-points-always-determine-an-exponential-function This problem complements the problem ``Do two points always determine a linear function?'' Mathematics and Statistics 2013-03-14T23:55:19 Course Related Materials