Course Overview

Course Description

This College Algebra course covers fundamental and advanced algebraic concepts, including polynomial and rational functions, inverse, exponential and logarithmic functions, systems and matrices, analytic geometry, sequences and series, the binomial theorem, mathematical induction, counting theory, and probability. The course is designed to prepare students for further studies in mathematics and related fields.

• Polynomial and Rational Functions: Study of their properties, graphs, and methods for finding zeros.

• Inverse, Exponential, and Logarithmic Functions: Analysis, graphing, and solving related equations.

• Systems and Matrices: Methods for solving linear and nonlinear systems, matrix operations.

• Analytic Geometry: Geometric definitions and graphing of conic sections.

• Sequences, Series, and Probability: Arithmetic and geometric sequences, binomial theorem, and basic counting theory.

Course Objectives

Polynomial and Rational Functions

Students will learn to analyze and graph polynomial and rational functions using various algebraic techniques.

• Quadratic Functions: Graph using the vertex formula and completing the square.

• Polynomial Evaluation: Apply synthetic division and the remainder theorem.

• Finding Zeros: Use the factor theorem, rational zeros theorem, fundamental theorem of algebra, conjugate zeros theorem, and Descartes' rule of signs.

• Graphing: Sketch graphs, locate turning points, describe end behavior, and apply the intermediate value theorem.

• Rational Functions: Find asymptotes and zeros; determine types of variation (direct, inverse, combined, joint).

Inverse, Exponential, and Logarithmic Functions

Students will explore the properties and applications of inverse, exponential, and logarithmic functions.

• Inverse Functions: Determine existence and calculate inverses.

• Exponential Functions: Graph and solve exponential equations; calculate compound and continuous compound interest.

• Logarithmic Functions: Graph and solve logarithmic equations; change the base of logarithms.

• Applications: Model exponential growth and decay.

Systems and Matrices

Students will solve systems of equations and perform matrix operations.

• Linear Systems: Solve by substitution, elimination, and Gauss-Jordan methods.

• Cramer's Rule: Apply to square linear systems.

• Partial Fraction Decomposition: Decompose rational functions.

• Matrix Operations: Add, subtract, multiply matrices; find inverses; use matrix inversion to solve systems.

Analytic Geometry

Students will study conic sections and their properties.

• Conic Sections: Geometric definitions and graphing of parabolas, ellipses, and hyperbolas.

• Eccentricity: Determine for ellipses and hyperbolas.

• Applications: Solve problems involving conics.

Sequences, Series, and Binomial Theorem

Students will analyze sequences and series, and apply the binomial theorem.

• Arithmetic and Geometric Sequences: Identify and find the nth term.

• Convergence/Divergence: Determine for infinite sequences.

• Summation: Find sums of finite series; use summation notation.

• Binomial Theorem: Expand binomials raised to a power.

Course Learning Outcomes

• Factoring Polynomials: Use long or synthetic division to factor polynomials of degree given a zero.

• Zeros of Polynomials: Determine zeros, including complex zeros, given one zero.

• Rational Functions: Find equations for vertical and horizontal asymptotes.

Grading and Assessment

Grading Breakdown

Grading Scale

Homework and Exams

• Homework: Assigned via MyMathLab, covering chapters 1-7. Practice is essential for success.

• Exams: Three tests (20% each), lowest test score may be replaced by final exam score if higher. No make-up exams.

• Final Exam: Cumulative, comprehensive, worth 25% of final grade.

Attendance and Classroom Policies

• Attendance: Required; four unjustified absences may result in being dropped.

• Classroom Conduct: Proper behavior, no eating/smoking, no electronic devices during class.

• Academic Honesty: Individual and original work required; cheating results in an F grade.

Support and Resources

• Math Tutoring Center: Free tutoring available; see schedule for hours and locations.

• Disabled Student Program: Accommodations available for students with disabilities.

Suggested Schedule of Events

Key Algebraic Concepts (Preview)

Polynomial Functions

• Standard Form:

• Vertex Formula for Quadratics:

• Synthetic Division: Efficient method for dividing polynomials.

• Remainder Theorem: is the remainder when is divided by .

• Factor Theorem: is a factor of if .

Rational Functions

• Vertical Asymptotes: Occur at zeros of the denominator.

• Horizontal Asymptotes: Determined by degrees of numerator and denominator.

Exponential and Logarithmic Functions

• Exponential Function:

• Logarithmic Function:

• Change of Base Formula:

• Compound Interest:

• Continuous Compound Interest:

Systems and Matrices

• Matrix Addition: Add corresponding elements.

• Matrix Multiplication: Multiply rows by columns.

• Inverse of a Matrix: exists if is nonsingular.

• Cramer's Rule:

Analytic Geometry

• Parabola:

• Ellipse:

• Hyperbola:

• Eccentricity: (ellipse)

Sequences and Series

• Arithmetic Sequence:

• Geometric Sequence:

• Sum of Arithmetic Series:

• Sum of Geometric Series:

• Binomial Theorem:

Academic Honesty and AI Policy

• Academic Honesty: All work must be original; cheating results in disciplinary action.

• AI Policy: AI tools are not permitted during in-person assessments; unauthorized use may result in a grade of zero.

Additional info:

• These notes summarize the syllabus and course structure, previewing key algebraic concepts. For detailed explanations and practice, refer to the textbook and MyMathLab assignments.