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Algebra
Sarah Eichhorn, Ph.D. and Rachel Cohen Lehman, Ph.D.
This course is taught so that students will acquire a solid foundation in algebra. The course concentrates on the various functions that are important to the study of calculus.
About the Course
This course is taught so that students will acquire a solid foundation in algebra. Emphasis is placed on understanding the properties of linear, polynomial and rational functions, including inequalities and complex numbers. Students will learn to work with various types of functions in symbolic, graphical, numerical and verbal form.
About the Instructor(s)
Sarah Eichhorn is the Assistant Vice Chair of Undergraduate Studies in the 
Department of Mathematics at the University of California, Irvine. Dr. Eichhorn received her Ph.D. in Applied Mathematics from the University of Arizona in 2004. Her research interests include dynamical systems, planetary physics and undergraduate mathematics education.
Rachel Cohen Lehman is a Lecturer at the Department of Mathematics at the University of California, Irvine, (UCI) since her Ph.D. in 1997. Dr. Lehman received a B.S. (1988), and M.S. (1992), and a Ph.D. (1997) from UCI, all in mathematics. Her Ph.D. thesis was titled, "The Acquisition of Stable Percepts via Bayesian Directed Convergence."
CONTACT INFORMATION:
algebra.coursera@unx.uci.edu
Due to the large number of enrolled students and the open online nature of this course, the instructors will likely not be able to respond to individual student emails. There will be ample forums for content question answers once the course begins.
Department of Mathematics at the University of California, Irvine. Dr. Eichhorn received her Ph.D. in Applied Mathematics from the University of Arizona in 2004. Her research interests include dynamical systems, planetary physics and undergraduate mathematics education.
Rachel Cohen Lehman is a Lecturer at the Department of Mathematics at the University of California, Irvine, (UCI) since her Ph.D. in 1997. Dr. Lehman received a B.S. (1988), and M.S. (1992), and a Ph.D. (1997) from UCI, all in mathematics. Her Ph.D. thesis was titled, "The Acquisition of Stable Percepts via Bayesian Directed Convergence."
CONTACT INFORMATION:
algebra.coursera@unx.uci.edu
Due to the large number of enrolled students and the open online nature of this course, the instructors will likely not be able to respond to individual student emails. There will be ample forums for content question answers once the course begins.
Course Syllabus
This course is self-paced. The following is a suggested order, but your actual path may vary depending on your prior knowledge of the subject. Each of the modules has an introductory video and each subtopic has its own associated video.
Week One. Introduction, Algebra and Real Numbers. Exponents and Radicals.
Week Two. Polynomials: Basic Operations and Factoring. Rational Expressions: Basic Operations.
Week Three. Linear Equations. Linear Inequalities.
Week Four. Absolute Value in Equations and Inequalities. Complex Numbers. Quadratic Equations. Additional Equation Solving Techniques.
Week Five. Cartesian Coordinate System. Distance in the Plane.
Week Six. Equations of a Line. Linear Equations and Models. Functions.
Week Seven. Graphing Functions. Transforming Functions.
Week Eight. Quadratic Functions. Operations on Functions, Composition. Inverse Functions. Polynomial Functions and Models
Week Nine. Real Zeros and Polynomial Inequalities. Complex Zeros and Rational Zeros of Polynomials. Rational Functions and Inequalities.
Week Ten. Review and Final.
Week One. Introduction, Algebra and Real Numbers. Exponents and Radicals.
Week Two. Polynomials: Basic Operations and Factoring. Rational Expressions: Basic Operations.
Week Three. Linear Equations. Linear Inequalities.
Week Four. Absolute Value in Equations and Inequalities. Complex Numbers. Quadratic Equations. Additional Equation Solving Techniques.
Week Five. Cartesian Coordinate System. Distance in the Plane.
Week Six. Equations of a Line. Linear Equations and Models. Functions.
Week Seven. Graphing Functions. Transforming Functions.
Week Eight. Quadratic Functions. Operations on Functions, Composition. Inverse Functions. Polynomial Functions and Models
Week Nine. Real Zeros and Polynomial Inequalities. Complex Zeros and Rational Zeros of Polynomials. Rational Functions and Inequalities.
Week Ten. Review and Final.
Recommended Background
High school algebra and geometry is recommended.
Suggested Readings
We highly recommend ALEKS software be used in conjunction with the course. Though not required, this software will allow students more algebra practice opportunities and a more individualized course experience in which you focus just on those topics you have yet to master.
Assessment and LEarning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained.
Students may purchase ALEKS directly from www.aleks.com. You will want at least a 10 week access licence. Do not activate your licence until the start of the course. You will use Course Code K3UAW-JUFD9 to link your software into this specific course. (Note: This code will not be active until the start of the Coursera class.)
The above ALEKS licence will also enable you limited access to an electronic version of the textbook "Precalculus" by Barnett, Ziegler, Byleen and Sobecki. Some students may prefer a physical version of this textbook. You can purchase that from any online textbook retailer. (Any edition of this text is fine!)
Assessment and LEarning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained.
Students may purchase ALEKS directly from www.aleks.com. You will want at least a 10 week access licence. Do not activate your licence until the start of the course. You will use Course Code K3UAW-JUFD9 to link your software into this specific course. (Note: This code will not be active until the start of the Coursera class.)
The above ALEKS licence will also enable you limited access to an electronic version of the textbook "Precalculus" by Barnett, Ziegler, Byleen and Sobecki. Some students may prefer a physical version of this textbook. You can purchase that from any online textbook retailer. (Any edition of this text is fine!)
Course Format
This course is divided into topical sections. Each student may work through the material at his or her own pace and not every student will follow the topics in exact order.
FAQ
Yes. Students who successfully complete the class will receive a Statement of Accomplishment from Coursera.
ALEKS software licence is highly recommended, but not required. Please see the Suggested Readings section for more information.
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