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• Explanation of the set of numbers.
• Intervals on the real line.
• Set notation.
  • Is a subset of.
  • Is a superset of.
• Mapping of domains to ranges.
• Real polynomials.
• Polynomial properties
  • Continuous
  • Differentiable
  • Integrable
• Explanation of functions
  • Constant
  • Linear,
• Completing the square.
• Jacobi theorem for polynomials of degree > 5
• Group theory.
  • Group representations.
  • Creating groups by division with other groups.
• Field extensions.
• Automorphisms.
• Vector space.
• Matrices.
• Calculus.
• Trignometric definitions.
  • Taylor series of trignometric functions.
• Stereographic projections.
• Quadratic equation form
  • Standard
  • Vertex
  • Y-intercept form.
• Shifting and stretching graphs of functions.
  • Reflecting around the y=x line.
  • Partial rotations.
• Diophantine Equations
• Gauss -> Algeberically closed field C.
• Difference between ring and field.
  • The multiplicative identity.
• Algebraic geometry.
  • Differential geometry.
• Manifolds.
  • Related to projection.
  • Patches.
• Definition of a function.
  • Injective
  • Surjective
  • Bijective functions.
• Trancendental numbers.
  • Not root of any polynomial.
• Natural exponential and logs.
• Fourier analysis/Harmonic analysis.