Interactive Exercises

These interactive pages allow you to practice certain mathematical techniques (e.g. calculus of fractions). Javascript needs to be activated in your browser; usually this is the default setup. You can use these pages from mobile devices. So start practicing!

• Union, intersection, set differences
• Power sets
• Injective, surjective and bijective
• Fractions
• Zeros of quadratic polynomials
• Division of polynomials
• Complex numbers
• Finite fields
• Products of vectors
• Matrix multiplication
• Inverting matrices
• Basis transformation
• Matrices representing linear maps
  
• Determinants
• Orientations
• Volume of a parallelotope
• Characteristic polynomials
• Minimal polynomial
• Eigenvalues
• Diagonalizing matrices
• Jordan normal form
• Sylvester's theorem
• Gram-Schmidt process
• Euclidean triangles
• Spherical triangles
• Hyperbolic triangles

These pages use the open source computer algebra system SageMath. The computations are performed on the Sage Cell Server.