Because of the importance of algebra--as well as the results of recent international studies that show American students are weak compared to Europeans and Asians in this important area--several states, including California, Texas, and Virginia, have put into effect new mathematics standards that have an increased emphasis on a rigorous algebra course. These standards also call for more algebra to be taught in the middle schools. This requires that more middle and high school teachers have a firm knowledge of the techniques and concepts of algebra and its applications both to higher levels of mathematics and to the natural and social sciences.

This course is intended to cover two quarters. (5 units).

A sample lecture from Topics in Algebra

• ratios and proportionality
• linear equations and inequalities
• systems of linear equations, including their graphical representation as intersections of lines and planes
• techniques for solving quadratic equations (factoring, completing the square, the quadratic formula)
• applications to conic sections: parabolas, ellipses and hyperbolas, including a study of how the algebra of their equations is related to the geometry of their graphs

Professors
Gunnar Carlsson and Ralph L. Cohen, Department of Mathematics, Stanford University
Professors Carlsson and Cohen are internationally known research mathematicians and teachers of university mathematics. Both have been involved in K-12 education for many years, and have served as consultants to the Texas State Board of Education for the development of the TEKS mathematical standards, and to the California State Board of Education for the development of California's Framework and Standards for K-12 mathematics education.