MATH 108 Generic Syllabus

Department of Mathematics Generic Syllabus
Boise State University Updated November 28, 2005

• Math Learning Center
• Hybrid Math 108

Catalog Description

MATH 108 INTERMEDIATE ALGEBRA (4-0-4). Radicals, negative and rational exponents, completing the square, quadratic formula. Linear and absolute-value inequalities; simple systems of equations. Multiplication of polynomials; basic factorization techniques. Manipulation of rational expressions, compound fractions, rationalization of denominator (or numerator). Introduction to the concept of function, graphs of functions and equations. Introduction to exponential and logarithmic expressions. MATH 108 is NOT a Core course, and cannot be taken for credit after any MATH course numbered MATH 143 or higher. PREREQ: MATH 025 or satisfactory placement score.

Prerequisites

Sufficient score on COMPASS placement exam; or recent beginning algebra from high school with strong grades; or remedial math courses, such as MATH 025, with strong grades; or a 70^th-percentile score on the ACT or SAT. The rationale for these prerequisites is to ensure that students have an adequate level of ``mathematical maturity'' as well as specific background knowledge.

Jurisdiction

This course is controlled by a departmental committee, whose members may or may not be teaching the course. All sections use the same text, which is chosen by the committee. The committee also writes a syllabus detailing which sections should be covered and approximately how much time should be allotted to each.

The multiple sections of the course are monitored through a monthly progress report. A faculty member is designated to canvas the MATH-108 instructors as to how far along they are with the course material. This report is sent to the department chairman and made available to the MATH-108 instructors.

Instructors are responsible for all exams, homework, and grading. University final-exam scheduling problems have forced the abandonment of the former common-final system.

Objectives

1. Appreciation of mathematical patterns:

   MATH 108 presents several mathematical patterns:

   1. elementary proof patterns;
   2. elementary duality patterns such as function inverses and the great geometry-algebra pattern;

2. Awareness of applications:

   MATH 108 presents the following applications while laying groundwork for study of further applications in subsequent courses:

   1. use of one- and two-variable linear equations to solve simple story problems having to do with finance, geometry, mixtures, and graphs.
   2. compound interest and exponential growth and decay;

3. Mastery of some mathematical tools:

   1. geometric effects of algebraic transformations;
   2. algebraic effects of geometric transformations;
   3. algebraic address of exponential and geometric phenomena;

4. Mathematics as a language:

   1. algebraic language and its geometric consequences;
   2. geometric language and its algebraic consequences;

Upon completion of this course, students should:

1. Be able to use the concepts of function, relation, and graphs.
2. Be able to use the algebraic and geometric language of mathematics correctly and effectively.
3. Have skill with manipulative algebra and the basic properties of elementary polynomial, rational, and transcendental functions.
4. Have skill in translating problems to relevant prose, graphical, diagrammatic, or algebraic form.
5. Exhibit a working understanding of reflection, symmetry, and translation of graphs.
6. Be able to solve ``routine'' problems efficiently and have at-least-occasional success with more challenging problems.
7. Be able to cope with the problems inherent in solving equations for polynomials with degree greater than 2 and elementary transcendental equations.

Students are not required to have calculators. Nevertheless, instructors are encouraged to include some instruction in calculator usage in their classes. Students should underestand how to use calculators to find reasonable approximations to quantities such as ln(6), e^3.7, log₃(7), 4.2^5.6.

Assessment of Learning Objectives

Assessment of Student Progress

• Constant and frequent homework serves as both a learning and an assessment tool.
• Routine classroom student assessment can be based upon discussion contributions and contributions to group activities.
• In-class exams are designed to give students the opportunity to demonstrate their ability to work mostly-routine problems.

Topics and Approximate Timeline

The following table is based on a typical spring semester schedule- 58 class meetings of 50 minutes each. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.

Text

Intermediate Algebra, Functions and Graphs; R. Larson, R.  Hostetler, and C. Neptune; D.C. Heath; (1994).

Format, Student Activities, and Grades

The individual instructors choose the format that seems most effective. The lecture format is still the dominant method, although when class sizes are small, group activities are used by some instructors. Instructors are encouraged to collect homework on a regular basis and to give quizzes. The instructor chooses the exact grading scheme, but a typical distribution would be: