Course Description

Welcome to this engaging and comprehensive pre-Calculus course designed to bridge the gap between high school mathematics and university-level calculus. This interactive course will deepen your understanding of functions, graphs, and equations, providing you with the essential foundation needed to excel in advanced mathematical studies. Unlike traditional math courses that focus solely on mechanics, this program emphasizes conceptual understanding and logical reasoning, encouraging you to actively participate in the "doing" of mathematics.

What Students Will Learn

• Making conjectures and constructing logical arguments
• Function concepts, characteristics, and properties
• Modeling common relations and functions using statistical regression and matrix methods
• Connections between algebra and geometry in analytic geometry
• Properties and applications of exponential and logarithmic functions
• Trigonometric functions, identities, and applications
• Limits and rates of change as precursors to calculus
• Alternative coordinate systems, including parametrization and polar coordinates
• Sequences and series, including the Method of Induction
• Basic probability and combinatorics, leading to the Binomial Theorem

Prerequisites

To succeed in this course, students should have a strong foundation in mathematics, specifically:

• Mastery of Algebra II or College Algebra
• Solid understanding of high school geometry concepts

Course Coverage

• Functions, Rates, and Patterns
• Algebra and Geometry
• Exponential and Logarithmic Functions
• Trigonometry
• Limits and Rate of Change of Functions
• Exploring Other Coordinate Systems
• Sequences and Series

Who This Course Is For

• High school students preparing for college-level mathematics
• College students looking to strengthen their mathematical foundation before tackling calculus
• Anyone seeking to deepen their understanding of advanced mathematical concepts
• Lifelong learners interested in developing critical thinking and logical reasoning skills

Real-World Applications

• Engineering: Applying mathematical modeling to solve complex problems
• Finance: Utilizing exponential and logarithmic functions for financial analysis
• Computer Science: Implementing algorithms based on mathematical concepts
• Physics: Understanding and applying trigonometric functions and vectors
• Data Science: Using statistical regression for data analysis and prediction
• Research: Developing logical arguments and proofs for scientific studies

Syllabus

The course is organized around the following seven units:

1. Functions, Rates, and Patterns
2. Algebra and Geometry
3. Exponential and Logarithmic Functions
4. Trigonometry
5. Limits and Rate of Change of Functions
6. Exploring Other Coordinate Systems
7. Sequences and Series

By enrolling in this course, you'll not only prepare yourself for success in calculus but also develop critical thinking skills that will serve you well in any future academic or professional endeavor. Don't miss this opportunity to elevate your mathematical prowess and unlock new realms of problem-solving potential!