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before getting into robotics, strengthen your math.
robotics is applied mathematics running on motors. without the math, you are wiring components and copying code.
linear algebra
• vectors and coordinate frames
• matrix multiplication
• eigenvalues, eigenvectors
• transformations and rotations (SO(3), SE(3))
every pose estimate, every sensor fusion step, every neural network layer is linear algebra.
calculus
• derivatives as rates of change
• integrals as accumulation
• differential equations
• gradients and optimization
control systems are calculus. trajectory generation is calculus. learning algorithms are calculus.
probability and statistics
• random variables and distributions
• bayes’ rule
• expectation and variance
• gaussian noise models
real sensors are noisy. state estimation is probabilistic. kalman filters, particle filters, SLAM; all statistics.
tools like ROS 2 and Gazebo are interfaces.
the math is the substance....

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