This course is designed to expand the basic concepts of elementary algebra with more sophisticated techniques and in-depth applications. The distance formula, for example, is extended to define and explore the algebra of conic sections: circles, ellipses, parabolas, and hyperbolas. The last third of the year is devoted to topics such as logarithms and natural logarithms, and exponential and logarithmic functions, and trigonometric and inverse trigonometric functions, with special emphasis on the solution of equations and practical applications.