MATH 147 Generic Syllabus

Department of Mathematics Generic Syllabus
Boise State University Updated August 22, 2007
Math 147
Precalculus
5 semester credits

Catalog Description

MATH 147 is the union of MATH 143 and MATH 144. Accordingly, the catalog descriptions for all three courses are included here:
MATH 147 PRECALCULUS (5-0-5)(Area III) (Formerly MATH 111). A single course equivalent to College Algebra (MATH 143) plus Analytic Trigonometry (MATH 144). Credit cannot be granted for both MATH 143 and MATH 147, nor for both MATH 144 and MATH 147. PREREQ: MATH 108 or satisfactory placement score.
MATH 143 COLLEGE ALGEBRA (3-0-3)(Area III). Emphasis on the concept of functions as mathematical entities; domain, range, algebraic operations, composition, inverses, graphing. Polynomial functions, division of polynomials, roots, factor theorem, complex numbers, fundamental theorem of algebra. Rational functions and asymptotes. Logarithmic and exponential functions. Multi-level algebraic manipulation of functional expressions - eg., difference quotients. Conic sections and other topics from analytic geometry as time permits. Credit cannot be granted for both MATH 143 and MATH 147. PREREQ: MATH 108 or satisfactory placement score.
MATH 144 ANALYTIC TRIGONOMETRY (2-0-2). Right-triangle and circular-function approaches to trigonometry. Trigonometric Identities. Graphs of trigonometric functions; amplitude, frequency, phase shift. Inverse trigonometric functions and their graphs. Polar coordinates, polar representation of complex numbers. Credit cannot be granted for both MATH 144 and MATH 147. PREREQ: MATH 143 or satisfactory placement score.

Prerequisites

MATH 108, with a grade of "C" or better; or sufficient score on COMPASS placement exam; or an 85th-percentile score on the ACT or SAT. The rationale for these prerequisite 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 how much time should be allotted to each. Exams, homework, and grading system are left to the instructor.

Objectives

The objectives of MATH 147 reflect all four of the Department's teaching goals:
  1. Appreciation of mathematical patterns:
    MATH 147 presents several mathematical patterns:
    1. elementary proof patterns;
    2. an almost-axiomatic pattern of trigonometry;
    3. elementary duality patterns such as function inverses and the great geometry-algebra pattern;
    4. elaboration of the Pythagorean pattern to circular trigonometry.
  2. Awareness of applications:
    MATH 147 presents the following applications while laying groundwork for study of further applications in subsequent courses:
    1. compound interest and exponential growth and decay;
    2. trigonometric applications such as surveying and circular or oscillatory motion;
  3. Mastery of some mathematical tools:
    1. geometric effects of algebraic transformations;
    2. algebraic effects of geometric transformations;
    3. algebraic address of exponential and trigonometric phenomena;
    4. use of "appropriate technology" to investigate problems.
  4. Mathematics as a language:
    1. algebraic language and its geometric consequences;
    2. geometric language and its algebraic consequences;
    3. grammar of communication with computers and calculators.
MATH 147 relates to the General Learning Outcomes of the University Core-Curriculum Philosophy as follows:
  1. Critical Thinking/Problem-Solving Skills This course promotes critical thinking and problem-solving skills on a very narrow class of abstract problems. It is not a "problems" course: for each mathematical topic covered, the course presents an array of problems which can be addressed successfully using the insights and techniques appropriate to the topic.
    Periodically, the students must have some problems presented free of any particular context, in hopes that they break down the "topic-to-problem" structure of the course's presentation to arrive at a successful "problem-to-topic" solution.
  2. Communication Skills An ongoing battle is to encourage the student to document problem solutions with appropriate prose, mnemonic variable names and labeled diagrams.
    This eventually aids the student in communicating problem descriptions and solutions to others as well as in communicating about problems with the student's own self.
    Student who have attained these communication skills and habits exhibit the ability to solve non-routine problems, problems not immediately transparent, problems whose solution may require time spent several different days.
  3. Cultural Perspective Persons lacking the minimal algebra and geometry perspectives of MATH 147 are at a disadvantage if life ever requires coping with scientific exposition or argument. That is, such persons are walled off from any appreciation of the basis of the scientific part of our culture.
  4. Breadth of Knowledge and Intellectual Perspective MATH 147 aims to promote a sensitivity toward numeric inputs and quantitative relationships in general. Thus, MATH 147 is at the launch point of an acculturation effort which can lead to membership in the western scientific-technical subculture.
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. Particular trigonometric knowledge and skills:
    1. a working knowedge of right-triangle trigonometry and the trigonometric functions in this setting: sin, cos, tan, arcsin, arccos, and arctan.
    2. a working knowedge of the unit-circle
      1. circle geometry: tangent lines, arc length, radian measure.
      2. trigonometry and the circular functions in this setting: sin, cos, tan, arcsin, arccos, and arctan. This includes the famous "by-heart" values of the functions: at 30° 45°, 60°, 90°, 120°, 315°, -540° and their radian-measure versions.
    3. a working knowledge of trigonometric graphs: sinusoids, tan, sec, and the inverse-trigonometric graphs.
    4. a working knowledge of the basic identities: the Pythagorean identities, the sum formulas and the multiple-angle formulas.
    5. skill at writing proofs of trigonometric or logarithmic identities.
    6. skill at solving trigonometric equations and the use of graphs or symmetry to find all their solutions.
  5. Have skill in translating problems to relevant prose, graphical, diagrammatic, or algebraic form.
  6. Exhibit a working understanding of reflection, symmetry, and translation of graphs.
  7. Be able to solve "routine" problems efficiently and have at-least-occasional success with more challenging problems.
  8. Be able to cope with the problems inherent in solving equations for polynomials with degree greater than 2 and elementary transcendental equations.
  9. Be able to avoid calculator-generated gaffes. Although MATH 147 does not teach calculator or computer skills as an alternative to algebraic techniques, it does bear some responsibility to study use of powerful graphing and algebraic calculators and attendant pitfalls.

Assessment of Learning Objectives

These objectives are periodically assessed via input from client departments and from instructors in MATH 147 and subsequent courses. Although the objectives have not changed in many years, their realization has changed over the time in response to learning research and technological progress.

Assessment of Student Progress

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:

Topics and Approximate Timeline

The following table is based on a typical semester schedule- 74 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.
Number of
Topic Meetings
Algebra Background for Precalculus 9
Functions 12
Polynomials and Roots of Polynomial Equations 8
Exponential and Logarithmic Functions 6
Trigonometric Functions of Angles 7
Trigonometric Functions of Real Numbers 7
Additional Topics in Trigonometry 14
Systems of Equations 4
Exams/Review 7

Text

As of fall, 2007, Precalculus, 5th edition, Stewart (Brooks/Cole) and Graphing Calculator Manual with Exercises, Kenny, (Brooks/Cole website ).

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion, and sometimes small group activity; the instructor chooses the appropriate mix.
Homework is an important part of the course: the students are striving both for manipulative skill as well as habits of thought. This requires practice.
The instructor chooses the exact grading scheme, but a typical distribution would be:
Homework 10%
4 Exams 65%
Final Exam 25%
Total 100%
Letter grades are usually based on a standard scale in which 90% of the total possible points guarantees an A , 80% a B, and 70% a C, with the instructor having the discretion to raise or lower these cutoffs if warranted.
Using the plus/minus system, one may further refine grades within these cutoffs, but should not expand the grade ranges. For example, if a C is normally 70 - 79, then the C- should not be lower than 70.


File translated from TEX by TTH, version 3.66.
On 23 Aug 2007, 10:09.