Mathematical Foundation

Robotics heavily relies on a robust mathematical foundation. To succeed in this course, familiarity with the following areas is recommended:

  • Trigonometry: Fundamental for analyzing angles, rotations, and transformations in robotic systems.

  • Linear Algebra: Essential for understanding robotic motion, kinematics, and system modeling.

  • Calculus: Used extensively for analyzing dynamics, motion planning, and control.

  • Probability and Statistics: Critical for interpreting sensor data, uncertainty modeling, and robotics perception.

  • Optimization: Important for control strategies, path planning, and decision-making in robotics. You can find a brief introduction to optimization in the Optimization chapter.

This section provides brief overviews and key concepts from these mathematical fields to refresh your knowledge and support your learning experience.

To start your journey in these topics, we recommend exploring the following resources:

Supervised Online Course:

  • Khan Academy: A nonprofit organization offering free, standards-aligned educational content. This platform provides engaging courses with numerous instructional videos and exercises complete with solutions, ideal for structured learning.

📚 Explore Trigonometry on Khan Academy

Quick and Visual Introduction:

  • 3Blue1Brown: Known for intuitive and engaging visual explanations with short videos, these series are ideal for a conceptual understanding (scroll down on the site of each chapter to find additional practice questions!).

▶️ Watch the Linear Algebra Series

Useful chapters for us:
  1. Vectors, Chapter 1
  2. Linear combinations, span, and basis vectors, Chapter 2
  3. Linear transformations and matrices, Chapter 3
  4. Matrix multiplication as composition, Chapter 4
  5. Three-dimensional linear transformations, Chapter 5
  6. Dot products and duality, Chapter 9
  7. Cross products, Chapter 10

▶️ Watch the Calculus Series

Useful chapters for us:
  1. The essence of calculus
  2. The paradox of the derivative, Chapter 2
  3. Integration and the fundamental theorem of calculus, Chapter 8
  4. Higher order derivatives, Chapter 10

▶️ Watch the Probability Series

Useful chapters for us:

In-depth Theory and Practice:

  • MIT Linear Algebra Course (by Professor Gilbert Strang): Covers comprehensive matrix theory and linear algebra, emphasizing applications in various fields including physics, engineering, economics, social sciences, and natural sciences. It parallels the approach of Prof. Strang’s textbook, Introduction to Linear Algebra.

Course Format:

Designed for independent study, this course provides:

  • Complete Lecture Videos by Professor Gilbert Strang
  • Summary Notes for all videos with suggested textbook readings
  • Problem-Solving Videos on every topic by an experienced MIT recitation instructor

▶️ MIT Linear Algebra YouTube Playlist

📚 MIT Official Course Website (Lectures, Problems & Solutions)

We recommend initially engaging with 3Blue1Brown’s videos to quickly grasp key concepts visually. For those seeking deeper theoretical understanding and problem-solving practice, exploring the MIT course materials is highly beneficial.