Leonard Susskind gives a brief introduction to the mathematics behind physics including the addition and multiplication of vectors as well as velocity and acceleration in terms of particles. The notions of configuration, reversibility, determinism, and conservation law are introduced for simple systems with a finite number of states. Topics covered: - Allowable laws of physics - Configurations of a coin - Equations of motion of a coin and a die - The concept of conserved quantities and conservation laws - Systems with infinite number of configurations - Laws of physics that are not allowable - Non reversibility - Predictability in the real world - Determinism in the past and future - System of point particles in space - Mathematics: coordinate systems, vector algebra, vector dot-product, triangle law of cosines - Motion of a particle: position, velocity and acceleration - Circular motion and centripetal acceleration Recorded on September 26, 2011.

1. State diagrams and the Nature of Physical Laws
2. Newton's Law, Phase Space, Momentum and Energy
3. Lagrangian, Least Action & Euler-Lagrange Equations
4. Symmetry and Conservation Laws
5. The Hamiltonian
6. Hamilton's Equations
7. Liouville's Theorem & Phase Spaces
8. Poisson Brackets
9. Lagrangian of Static Electric and Magnetic Fields
10. Particles in Static Electric and Magnetic Fields

This is the first course in a collection of 6 core physics courses by renowned physicist Leonard Susskind's series, The Theoretical Minimum. Our exploration of the theoretical underpinnings of modern physics begins with classical mechanics, the mathematical physics worked out by Isaac Newton (1642--1727) and later by Joseph Lagrange (1736--1813) and William Rowan Hamilton (1805--1865). We will start with a discussion of the allowable laws of physics and then delve into Newtonian mechanics. We then study three formulations of classical mechanics respectively by Lagrange, Hamiltonian and Poisson. Throughout the lectures we will focus on the relation between symmetries and conservation laws. The last two lectures are devoted to electromagnetism and the application of the equations of classical mechanics to a particle in electromagnetic fields.