Ge-Alge-Trig: Elements of Geometry, Algebra, & Trigonometry

👩‍🏫 Course Title: Essentials of Mathematics for Science & Engineering

Course Description

Welcome to "Essentials of Mathematics for Science & Engineering," a comprehensive course designed to bridge the gap between fundamental mathematical concepts and their practical applications in scientific and engineering fields. This course, led by expert instructor [Instructor's Name], will guide you through the core principles of geometry, algebra, and trigonometry with a focus on transformational geometry, coordinate systems, and the application of these concepts to real-world problems.

Course Structure:

1. Geometry & Transformations:

   • Understand and apply translations, rotations, and reflections in 2D space.
   • Master the rules of transformations and learn how they affect coordinate pairs.

2. Coordinate Geometry & Linear Equations:

   • Review the basics of plotting points in Cartesian coordinates.
   • Solve linear equations and understand their graphical representation.

3. Quadrilaterals & Proofs:

   • Identify different types of quadrilaterals and their properties.
   • Engage with interactive exercises to prove geometric theorems.

4. Transformations in Practice:

   • Explore real-world applications of transformational geometry.
   • Learn how transformations are applied in various fields, including engineering and computer science.

5. The Pythagorean Theorem & The Unit Circle:

   • Discover the Pythagorean theorem's significance beyond right triangles.
   • Understand the role of the unit circle in defining trigonometric functions like sine, cosine, and tangent.

6. Trigonometry & Wave Forms:

   • Explore the relationship between the unit circle and wave forms.
   • Learn how to derive equations for waves and their applications in signal processing.

7. Triangulation & Height/Distance Calculations:

   • Apply trigonometry to solve problems involving height and distance measurements.
   • Use practical examples, such as triangulation with a baseline and an observed peak, to understand the law of sines and its applications.

Course Highlights:

• Interactive Learning: Engage with Google Forms exercises that offer immediate feedback on your understanding of key concepts.
• Real-World Applications: Learn how mathematical principles are applied in scientific research, engineering design, and technology development.
• Comprehensive Coverage: From the basics to more complex topics like transformations and trigonometry, this course ensures a solid foundation in mathematics.
• Expert Instruction: Benefit from the expertise of an instructor with a deep understanding of both mathematics and its applications across various disciplines.

Course Progress:

• Completed Sections:

  • Transformations (4 Lectures)

• Pending Sections:

  • Quadrilaterals & Proofs
  • The Unit Circle: the Core of Trigonometry
  • An Equation for a Wave
  • Triangulation

• Currently Available Resources:

  • Review exercises and their answers for an interesting proof (Pythagorean theorem) are available.
  • A video following the exercises/proof is pending completion.

What You'll Learn:

By the end of this course, you will have a deeper understanding of the fundamental principles of geometry, algebra, and trigonometry, and how these principles can be applied to solve complex problems in science and engineering. You will learn to think mathematically and critically, enhancing your problem-solving skills and preparing you for further study or professional practice in these fields.

Join us on this mathematical adventure, where every concept unveils a new application that bridges theory and practice. Let's dive into the beauty of mathematics together! 🧮✨

Note: The course content marked as "pending" will be released shortly, providing a full spectrum of learning opportunities for students enrolled in the course. Stay tuned for updates and new lectures that will complement the existing material and enhance your learning experience.