Prerequisites for Beginning Math Courses

Five levels of pre-university mathematical competence are described below. These descriptions are intended to describe the knowledge needed for the beginning university-level courses: Intermediate Algebra 101, College Algebra 112, Trigonometry 113, and Calculus 221. If you have a question about the prerequisites for higher-level university courses, contact the Director of Mathematics by e-mail or at 608-262-2152.

Students with minimal or intermediate mathematical competence (as described below) who are planning to register in University of Wisconsin System campus programs are strongly advised to enroll in appropriate Independent Learning courses before their freshman year. The following descriptions imply that the student is able to use the listed mathematical tools in problem-solving situations, and to select and combine techniques appropriate to a problem. The ability to solve problems that are almost exactly the same as examples previously studied, perhaps with the numbers changed, is not sufficient. (Note: While it's possible to achieve advanced competence in algebra without achieving it in trigonometry, or in trigonometry without achieving it in algebra, advanced competence in both is required for most courses at the 200 level or higher.)

1. Minimum Mathematical Competence

This level of competence is equivalent to successful completion of one unit each of high-school algebra and geometry, which is less than the requirement for admission to a UW System campus. It is a prerequisite for Mathematics 101: Intermediate Algebra. Students who do not meet this standard are advised to consult the listings of high-school courses.

From algebra and arithmetic: an understanding of the axioms that underly arithmetic, the decimal system and its use in calculation, and the definition and elementary properties of rational numbers; basic algebraic skills, including special products,September 5, 2006 algebraic fractions; setting up and solving linear equations and inequalities. From geometry: axioms, theorems, and proofs of theorems concerning striaght lines, triangles, and circles; graphs of linear equations and the solutions and geometric significance of systems of two linear equations; measurement formulas for the perimeter, circumference, area, and volume of common two- and three-dimensional figures.

2. Intermediate Mathematical Competence

A student normally can achieve this level of competence with successful completion of three units of high-school mathematics. Intermediate mathematical competence is the prerequisite for Mathematics 112 or 114.

All the competencies of Level 1, together with equations, laws of rational exponents and radicals; additional topics in factoring; zero product rule; setting up and solving quadratic equations; complex numbers; algebra of polynomials and rational expressions; setting up and solving simultaneous linear equations and inequalities; graphing, including linear and quadratic polynomials; definition and application of absolute value and of scientific notation; definition and elementary properties of logarithms.

3a. Advanced Mathematical Competence - Algebra

This level of competence is recommended for Math 113

The competencies of levels 1 and 2 above, together with functions: definition, domain, range, algebraic combinations, composition, inverse, symmetries, translations, graphs; theory of polynomial equations, including the remainder and factor theorems; equivalent and partially equivalent equations and systems of equations; equations solvable by linear and quadratic techniques; exponential and logarithmic functions, equations and inequalities; analytic geometry of conic sections; representation of plane curves and regions by equations or inequalities; sequences, sums, and series, including arithmetic and geometric sequences and series; mathematical induction.

3b. Advanced Mathematical Competence - Trigonometry

Students who have attained both levels 3a and 3b are normally prepared for a course in calculus and analytic geometry.

The competencies of levels 1 and 2 above, together with functions: definition, domain, range, algebraic combinations, composition, inverse and graphs; trigonometric functions of a real number, including their basic properties and graphs; trigonometric equations and identities; geometric significance of the trigonometric functions and elementary applications; polar form of complex numbers and DeMoivre's theorem.

Superior Mathematical Competence

Some high schools may offer topics to students with advanced mathematical preparation. For example, courses in probability and statistics, analytic geometry, calculus, or topics in modern algebra are suitable for high school students of superior ability. Students who have completed a program of study beyond advanced mathematical preparation should decide in consultation with their high school teachers on an appropriate course.

Independent Learning courses in mathematics offer challenges not always available in the classroom. Students studying mathematics on their own have an opportunity to use their ingenuity and initiative. They are also challenged to develop the creative abilities that are so greatly needed today.