PreCalcI – Pre-Calculus I

Prerequisite

• A sufficient score on the SAT, or
• a sufficient score on the Old Dominion University ALEKS Placement Test, or
• a grade of C or higher in Math 102M/103M (College Algebra).

Textbook

• Precalculus: A right triangle approach by Ratti/McWaters, 5th Edition; Pearson/Addison–Wesley ISBN-13: 9780137519415

Learning outcome, core skills

• Students will learn about quadratics, higher-order polynomials, radicals, logarithms, and exponentials. The successful student will be able to:
  • Analyze and manipulate algebraic expressions, equations, and inequalities.
  • Interacts with graphs of functions and determine their properties.
  • Recognize formulas and identities such as the quadratic equation, difference quotient, and log/exp rules.
  • Transform relevant real-world applications into mathematical problems, then solve them using the topics covered in the course, and translate them back into words.
  • Reflect on the content learned and be able to determine their own preferred methods from the topics of this course.

Reading Guide: How to Read Mathematics?

Mathematics has a reputation for being a tough subject. However, mathematics enjoys the ability to be broken down into much smaller building blocks. Addition, subtraction, multiplication, and division are fundamental operations that can be applied to build more complicated operations, such as computing the difference quotient of a function. The more building blocks are utilized, the more concepts are understood that build up mathematical topics. When reading a mathematical text:

• Annotate and highlight concepts, notation, or variables you cannot immediately identify. Try to find them within the text first, or in related sections second. Then write their meaning on the side or in your note.
• Recognize that there are multiple ways to represent functions and equations. Expressions such as x^2-4, and equations such as y=x^2 are not rigid. They can be manipulated to be viewed from different perspectives, the first can be factored into (x-2)(x+2), and the second can be written as x equals the positive or negative square root of y. These forms are equivalent to the original, respectively.

Understanding math is all about the engagement. To engage with the mathematical text, you should apply the algebraic operations you learn throughout the course on the expressions, functions, and equations you are reading in the lecture note, book, and even assignments so you feel comfortable with them and be in control of your learning experience.

AI Policy

• Generative AI tools are common nowadays. I use LLM tools far less than the average user, primarily as a search engine (e.g.: duck ai) to find credible primary references and transforming and interacting with text.
• Know that they are language simulators and not thinking machines. Generative AI is of lower credibility that Wikipedia. The generated text is not guaranteed to be accurate, but more conforming to the average knowledge online. It is bound to reiterate common mistakes and misconceptions.
• Know that they were trained on primary, secondary, and anonymous, credible, and non-credible sources that are not typically cited or referenced.
• The use of AI for answering homework, quizzes, or tests are prohibited in this class (unless explicitly stated in an assignment). However, using them as an additional learning tool is permitted under the following conditions:
  • continue to question the reasoning and confirm the derivations independently.
  • ask for explicit references and focus on the highest credible sources first: textbooks, peer-reviewed articles, credible online sources such as Khan academy, etc.