Course Syllabus

MATH 1080 Pre-Calculus

Course Description

In this course students will study polynomial, rational, exponential, logarithmic, and trigonometric functions, relations, and applications; additional topics include sequences and series, conic sections, matrices, the binomial theorem, modeling, and graphing technology. This course prepares students for calculus.

Justification

Math 1080 fulfills the Quantitative Literacy General Education requirement and is the College Algebra/Trigonometry course that prepares students for future quantitative work in their majors. It is similar to courses offered by other colleges and universities in the state. This course is also a useful semester-long review for students returning to school after an extended period of time.

General Education Outcomes

1. A student who completes the GE curriculum has a fundamental knowledge of human cultures and the natural world. In pre-calculus, students acquire significant problem-solving skills through algebra and trigonometry. This course provides students with fundamental knowledge to apply critical-thinking to a variety of topics in human cultures and the natural world. This ability to problem-solve in the natural world will be assessed through homework, exams, quizzes, student projects and/or presentations.
2. A student who completes the GE curriculum can read and research effectively within disciplines. In the field of mathematics, students must be able to carefully examine a given problem then determine and execute a plan for solving the problem. Often the information given is presented using symbols and variables the student must be able to read and interpret mathematically within the context of the given problem. In addition to learning new concepts, pre-calculus students are taught many new ways to express their new understanding using various mathematical symbols. This ability to read, retrieve, evaluate, interpret, and deliver mathematical information will be assessed through homework, exams, quizzes, student projects and/or presentations.
3. A student who completes the GE curriculum can draw from multiple disciplines to address complex problems. A typical pre-calculus course provides multiple opportunities to examine math as it manifests itself in the world. By the end of the course, successful students will be proficient at using such skills. Problems to analyze potentially come from a variety of areas, such as business, human behavior, natural and social sciences, and medicine. Mastery of these skills will be assessed through homework, exams, quizzes, student projects and/or presentations.
4. A student who completes the GE curriculum can reason analytically, critically, and creatively. The mathematical principles and methods taught in this course will help students critically approach intricate, multifaceted, real-world problems. This ability will be assessed through homework, in-class activities, exams, quizzes, student projects and/or presentations.
5. A student who completes the GE curriculum can reason quantitatively.  The pre-calculus course consists of algebra and trigonometry, which are of themselves logical processes of solving and analyzing problems. Therefore, this course gives students an increased ability to critically approach situations which call for numerical and logical solutions. In addition, students can propose creative, new solutions. Proficiency of these skills will be assessed through homework, exams, quizzes, student projects and/or presentations.

General Education Knowledge Area Outcomes

1. Given graphs or equations representing real world information, students will be able to identify critical values such as zeros, intercepts, maximum and mininum values and explain what they mean in terms of the situation given. This outcome will be assessed through homework, exams, quizzes, student projects and/or presentations. Given graphs or equations representing real world information, students will be able to identify critical values such as zeros, intercepts, maximum and mininum values and explain what they mean in terms of the situation given. This outcome will be assessed through homework, exams, quizzes, student projects and/or presentations.
2. Convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, and tables). Students will be asked to make, recognize and write equations for graphs given. They will also be asked to identify properties of graphs given an equation or table. This outcome will be assessed through homework, exams, quizzes, student projects and/or presentations.
3. Demonstrate the ability to successfully complete basic calculations to solve problems. Students will be given problems to complete that involve using calculations learned in previous classes and in the current course as they apply to polynomial, rational, exponential, logarithmic, and trigonometric equations. The ability to solve problems using these calculations will be assessed through homework, exams, quizzes, student projects and/or presentations.
4. Demonstrate the ability to problem solve using quantitative literacy across multiple disciplines. Make judgments and draw appropriate conclusions based on quantitative analysis of data, recognizing the limits of this analysis. Examples and applications used in this course will come from multiple disciplines such as economics, nutrition, and various areas of science. Students are asked to analyze information from these areas using techniques taught in Pre-Calculus. This outcome will be assessed through homework, exams, quizzes, student projects and/or presentations.
5.  Students will demonstrate their ability to express quantitative evidence in support of their conclusions to questions presented in this class by showing their step-by-step calculations used to solve given problems. This outcome will be assessed through homework, exams, quizzes, student projects and/or presentations.

Student Learning Outcomes

1. Demonstrate an ability to solve problems using methods resulting from theorems used in this course.
   Throughout mathematics, theorems are used to understand why a process will achieve the desired outcome. Students will learn various theorems as they go through this course and will learn new methods of solving problems that result.
2. Be familiar with many common functions as well as their graphs.
   
3. Apply mathematical knowledge to real world problems.
   
4. Understand and use mathematics as a language to communicate.
   
5. Explore and analyze mathematical concepts using technology as appropriate.
   

Course Content

Through lecture, class discussions, and homework this course will include:
• Linear Equations and Inequalities
• Relations (Conic Sections and Inequalities)
• General Functions
• Polynomial and Rational functions
• Exponential and Logarithmic functions
• Trigonometric functions
• Systems of Equations and Inequalities
• Matrices
• Sequences and Series
• Binomial Theorem

This content (through its history references and extensive word problems) provides many opportunities for students of all backgrounds to explore and hopefully come to value the contributions made to the maths and sciences from many cultures and through many centuries.