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

Master Essential Math Skills for STEM Success

This free course provides a foundational understanding of the mathematical skills crucial for success in college-level science, technology, engineering, and mathematics (STEM) disciplines. Designed as a valuable resource for both classroom support and independent review, this course covers key concepts in geometry, algebra, and trigonometry.

This course is not a complete curriculum, but rather a guide to reinforce concepts learned in class or to brush up on essential skills. It aims to provide a deeper understanding of the mathematical principles underpinning many STEM applications.

Course Highlights:

• Parallel Lines & Triangles: Explore the fundamental relationships between parallel lines and transversals, leading to the proven sum of interior angles of a triangle = 180 degrees. This foundational knowledge is essential for solving problems in science, technology, engineering, and mathematics (STEM).
• Triangles: Properties & Area: Delve into the characteristics of different triangle types – scalene, isosceles, equilateral, and right triangles. Learn to prove the area of a triangle formula and understand the role of right triangles in defining trigonometry (sine, cosine, tangent).
• The Equation of a Line: Review the equation of a line and its properties, essential for understanding quadrilaterals and geometric transformations.
• Quadrilaterals: Classify various quadrilaterals based on their angles, sides, and diagonals. Learn to represent these figures in Cartesian space and apply the concept of slope to prove their defining properties.
• Transformations (2D): Understand geometric transformations like translation, rotation, and reflection. Learn how these transformations affect the coordinates of points and how they can be combined to create complex shapes.
• Pythagorean Theorem Proof: Discover an engaging proof of the Pythagorean theorem using transformations. Understand its application in calculating distances and defining a circle.
• The Unit Circle & Trigonometry: Explore the unit circle and its connection to sine and cosine. Visualize how these functions create waves and understand their fundamental role in trigonometry.
• Wave Equations: Learn how the unit circle can be used to derive the formula for a wave.
• Triangulation: Apply the law of sines and tangent function to calculate distances and heights in triangulation problems.

Course Structure:

The course consists of approximately 10 lectures, with about half of the video time completed. Lectures are designed to be concise and focused, under 2 hours in total.

Note: Some lectures are currently pending, but exercises and answers are available for many topics. External resources are provided for further practice.

This course is ideal for:

• STEM students seeking a review of fundamental math concepts.
• Students preparing for standardized tests.
• Anyone looking to strengthen their understanding of geometry, algebra, and trigonometry.