SYLLABUS
I. MATH 111-112 College Algebra I, II 3 credit hours
II. Fall, Spring, 2001-2002 INSTRUCTOR: Herman Matthews
Office: 207 Farr-Chinnock, Ext. 6226
e-mail: hmatthews@inetlmu.lmunet.edu
Office Hours: Hours are posted on the door of my office, together with my complete schedule.
III. COURSE PREREQUISITES: Math 100 or 2 years of high school algebra, ACT score 18 or higher
IV. COURSE DESCRIPTION/COURSE GOALS (includes topics covered in MATH 112): Major topics include sets, the real number system, exponents and radicals, polynomials, functions and graphs, exponential and logarithmic functions, equations and systems of equations, quadratic equations, elementary probability, and ratio and proportion. Major goals: 1) to develop respect for and a positive attitude toward mathematics; 2) to instill a respect for critical thinking and to nurture its development; 3) to develop algebraic skills needed in other courses or in real-life situations; 4) to learn how to express mathematical ideas clearly in written and oral forms.
V. RELATIONSHIP OF THIS COURSE TO CONTENT AREA KNOWLEDGE/SKILLS: This course is unrelated to the Tennessee Matrix with regard to the mathematics major. For other fields of study, it aids the student's awareness of information sources, the ability to analyze information and data, the awareness of the importance of mathematics to other fields of study, the understanding of how algebraic and geometric ideas are applied as models in problem-solving situations, and the ability to express and interpret information in graphical form.
VI. TEXT: Stewart, James, Precalculus, Third Edition,
Brooks/Cole Publishing Company, Pacific Grove, CA, 1993.
VII. COURSE OBJECTIVES: 1) to learn basic properties of the real numbers system and their applications; 2) to use set notation correctly; 3) to learn properties of exponents and radicals, and the application of exponents to polynomials; 4) to solve linear equations and systems of linear and quadratic equations using various standard methods; 5) to solve various types of inequalities; 6) to learn how to represent functions in terms of ordered pairs, formulas and graphs. 7) to solve practical (written) problems of various kinds, giving particular attention to the use of diagrams, commonly used literal equations (or formulas), and the thinking processes that should accompany problem-solving skills; 8) to learn about complex numbers and their connection to the Fundamental Theorem of Algebra; 9) to manipulate exponential and logarithmic functions for use in calculation and application; 10) to solve linear equations and systems of linear and quadratic equations using various standard methods; 13) to recognize the increasing importance of mathematics in all fields of human endeavor.
VIII. OUTLINE OF COURSE CONTENTS/UNITS OF INSTRUCTION:
1. Real Numbers, Exponents and Radicals: properties of real numbers; sets and intervals; absolute value and distance; integer exponents; scientific notation; radicals; rational exponents.
2. Algebraic and Fractional Expressions: polynomials and factoring; rational expressions and rationalizing.
3. Equations and Problem Solving: linear equations; quadratic equations; other equations; word problems.
4. Inequalities (in one variable): rules; linear and nonlinear inequalities; absolute-value inequalities.
5. Coordinate (Plane) Geometry and Lines: the Cartesian coordinate system; graphs of equations; circles; symmetry; slope and equations of lines; parallel and perpendicular lines; applications of linear equations.
6. Function Concept, Graphs, and Applied Functions: definition of a function; four representations; properties of graphs; piece-wise defined functions; formulating applied functions; direct and inverse variation.
7. Transformations and Extreme Values of Functions: shifting, reflecting, stretching and shrinking of graphs; even and odd functions; extreme values of quadratic functions; applied maximum and minimum problems.
8. Combining Functions and Inverses of Functions: algebra of functions; composition of functions; definition and properties of one-to-one functions and their inverses.
9. Polynomial Functions and Real Zeros: form of a polynomial function; zeros of a function; graphing and local extrema of polynomials; dividing polynomials; the remainder and factor theorems; rational zeros.
10. Complex Numbers and The Fundamental Theorem of Algebra: definition and arithmetic operations; graphical representation; fundamental, complete factorization, zeros, and conjugate root theorems.
11. Exponential and Logarithmic Functions: definition and graphs of exponential functions; the definition of e; compound interest; exponential growth; definition and graphs of exponential functions; the natural logarithm
12. Formulas and Applications of Exponentials and Logarithms: laws of logarithms; change of base; exponential and logarithmic equations; interest; growth; radioactive decay; Newton’s law of cooling; logarithmic scales.
13. Systems of Equations/Inequalities: substitution and elimination methods; applied linear systems; inequalities.
14. Matrices: matrix form of linear systems; Gaussian elimination; inconsistent and dependent systems; algebraic operations on matrices; matrix multiplication and inverses; matrix equations; determinants; Cramer’s rule.
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IX. REQUIRED READINGS: Textbook
X. SUGGESTED READINGS/BIBLIOGRAPHY: None.
XI. METHODS OF INSTRUCTION AND LEARNING: Lecture and problem-solving constitute the principal instruction methods . All students are expected to participate actively in class discussions, board work, and recitation. Homework is assigned or implied daily, based on material under discussion.
XII. COURSE REQUIREMENTS/METHODS OF ASSESSMENT AND EVALUATION: All students are expected to attend classes and to keep up with homework. Three or four major tests and a final exam are the main sources of evaluating subject comprehension and knowledge. Make-ups may be taken only with valid excuse for absence. The final exam will be taken only on the official date designated in the LMU current schedule of classes, excepting the requirements of early grades for graduating seniors. Grading will be scaled to the following scheme so that students can determine and interpret average grades easily:
A 90.0 and above
B 80.0 – 89.99
C 70.0 – 79.99
D 60.0 – 69.99
F below 60.0.
XIII. CLINICAL/LABORATORY/FIELD EXPERIENCES: None.
XIV. DATE OF REVISION: July, 2001