math

Mathematical Curriculum and Resources for EEPsters.

All EEPsters are expected to take the following sequence of courses their freshman year: #102 College Algebra in the first quarter, followed by #103 Algebra and Trigonometry in the second quarter, and #206 Calculus I-Differentiation (highly recommended, but not required for non-science majors) in the third quarter.

It is realized that the EEPsters have had varying math preparation for these courses. Furthermore, it was found that there were some "gaps" most EEPsters had upon entering a college mathematics curriculum, having skipped several years of high school math. To meet these diverse needs, a special (free) 5-session review course was designed and implemented (see below) prior to the start of the Freshman Fall Quarter.

If a student has taken AP or college courses, and wishes to opt out of Algebra and/or Algebra&Trigonometry, please see Richard Maddox with the appropriate paperwork. Even with the AP credits, it is not a good idea to skip too much university math, as the pace, depth and complexity of university math classes, as well as the faculty interactions, can't be experienced by skipping these classes. If the student conversely feels that his/her preparation is not sufficient for College Algebra, there are several additional resources available to bring the student up to speed, including tutoring and taped courses. Freshmen EEPsters must realize that their required minimum ELM test scores qualified them for Math 102, so it is expected that while they might need brush-up on some of these math skills, remediation should not be required.

EEPsters should note that EEP provides tutoring, free-of-charge, to all students. The tutors are (usually upperclass) EEPsters, who recently mastered these same courses. Note that these EEPsters are anxious to tutor, as they do receive a stipend for their services from the EEPClub. EEP Director Rich Maddox initiated the tutoring program himself, and considers it an important and essential part of the EEP success. Freshman EEPsters should keep in mind that many upperclass EEPsters received tutoring themselves, and it should be no embarrassment -- in fact, it is expected and encouraged. Furthermore, it is imperative that Freshmen EEPsters seek help BEFORE it becomes a major problem; so, as soon as there is some concern, please see the current EEP Academic Chair. Virtually all Freshmen are surprised at how quickly a 10-week quarter passes, so do not wait until it is too late.

Some EEPsters have found supplemental taped courses useful, such as the following courses on dvd (usually 30-half-hour classes each) from the Teaching Company (website: http://www.teach12.com/) helpful:
               • High School Level - Algebra I
               • High School Level - Geometry
               • High School Level - Algebra II
               • High School Level - Basic Math
               • Change and Motion: Calculus Made Clear, 2nd Edition
               • Joy of Mathematics
               • Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas

Note: we have several of these dvds available in the EEP Lounge for viewing, or to borrow for at-home use -- click here.

It is felt that the 5-session course should be sufficient for virtually all EEPsters. While CSULA does offer lower level mathematics courses (#089 Introduction to Algebra, #090 Elementary Algebra, #091 Intermediate Algebra, #100 Introduction to College Mathematics, #101 Supplemental Instruction-College Algebra), these are considered remediation classes. EEPsters are not expected to need such remediation classes; if the EEPster is not prepared to take Math 102, the EEPster probably belongs in High School and not college; only under some very special circumstances do a very few EEPsters start with a lower class such as these. The minimum ELM score required for EEP qualifies students for Math 102; students should review the subjects covered in the Teaching Company dvds above to see if refresher studying prior to the start of the Fall Quarter freshmen year is adviseable.

Preparatory Mathematics for EEP Students
Prospectus June, 2004
Department of Mathematics CSULA
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The purpose of this 5-segment series is to give self-contained modules to supplement the background of EEP students who are authorized to enroll in College Algebra but who, nevertheless, lack the formal background to be truly successful in this and subsequent mathematics courses. Both the SAT-1 and the ELM are inadequate barometers of math readiness, especially the latter, which has been dumbed-down to increase the pass rate.

As forcing EEP students to attend academic activities for which they do not receive credit is likely to be viewed as unwelcome coercion, it is important to try to minimize the time commitment involved. Thus, coverage must be kept to mathematical ideas and procedures, omitting contextual problems. Each segment requires a 2-hour class period. Together, they are intended to present a quick overview of certain relevant areas of precollegiate mathematics. Students should be given a 1 or 2 page problem sheet relative to each class period whose solutions are not meant to be discussed within the series itself. Instead, they should be viewed as a resource for students to be considered leisurely as their time permits. While working problems is critical for subject mastery, going through these problems sheets in class would make the series too long.

Module 1 - Exponents and Radicals

1. Exponents: positive intergers first, then negative integers, then fractions. aº=1.
2. Laws of exponents. Simplifying expressions with exponents. Scientific notation. Multiplication and division of numbers in scientific notation.
3. Radical expressions. Laws of radicals as special cases of laws of exponents.
4. Simplifying and combining radical expressions (assume all variables are positive)
5. If time permits: equations involving radicals.

Module 2 - Quadratic equations

1. The principle of zero products and solution by factoring.
2. Completing the square. Quadratic equations with no real solutions, i.e., those of the form a(x + d)² = -k where k>0. Introduction of i and general complex numbers a + bi. Addition, subtraction and multiplication of complex numbers. Solution of quadratic equations of the form a(x + d)² = -k revisited.
3. Use of the quadratic formula (don't derive QF, just say that it can be derived by completing the square on ax² + bx + c = 0). The discriminant and the nature of zeros.
4. Equations of the quadratic type, e.g., x²² + 2x² - 15 = 0. (note, x²² is supposed to be x to the fourth power, but there is no html coding for "fourth power.")
5. If time permits: Equations that involve a product of linear and quadratic factors, e.g., (x³ - x)(2x² + 18) = 0

Module 3 - Rational expressions

1. Definition of polynomials in one or more variables. Rational espressions as quotients of polynomials. Simplest or reduced form.
2. Multiplication and division of rational expressions.
3. Addition and subtraction of rational expressions.
4. Equations with rational expressions, including those reducible to quadratic equations.

Module 4 - Equations in two variatles I

1. Graphs of equations of the linear equation ax + by = c. Slope and intercepts. The slope-intercept form of the equation of a line. Parallel and perpendicular lines.
2. Systems of two linear equations in two unknowns.
3. Distance in the plane. General equations of circles: (x - h)² + (y - k)² = r²
4. If time permits: completing the square and equations of circles.
5. If time permits: linear inequalities.

Module 5 - Equations in two variables II

1. Graphing quadratic equations y = ax² + bx + c naively by plotting points. Note that (1) whether it is upturning or downturning depends on the sign of the lead coefficient; (2) vertex occurs at x = -b/2a; (3) one can obtain the solutions to ax² + bx + c = 0 or determine their nonexistence from the graph.
2. The standard form of the quadratic equation in 2-variables: y = a(x-k)² + h.
3. Points of intersection of a linear and a quadratic equation, two quadratic equations, or of a linear and a circular equation.
4. The inverse of an equation f(x,y) = g(x,y) and the graph of the inverse as a reflection in the line y=x. Horizontal parabolas as a special case.
5. If time permits: reflections in the x-axis and y-axis. Symmetry in the x-axis, the y-axis, and the diagonal y=x.