Part Five : Advanced Topics

The goal of this part is to look more how SageMath connects to other software packages and to cover some advanced topics, and to deepen our knowledge about earlier issues. We start by making interactive web pages. Then we cover sympy, numpy, and scipy. The last lectures are spent on GAP, PARI/GP, Singular, and R.

• Lecture 34: Building Interactive Web Pages
  • Drawing Tangent Lines to a Curve
  • Making the Web Page
  • Drop Down Menu
  • Assignments
• Lecture 35: an Application of Interact
  • Turning a Crank
  • Computing Coordinates of the Connector Point
  • Adding the Coupler and Fourth Bar
  • Deploying the Interactive Web Page
  • Assignments
• Lecture 36: Symbolic Computation with sympy
  • sympy outside SageMath
  • sympy inside SageMath
  • Pattern Matching
  • Solving Recurrence Relations
  • The Nearest Algebraic Number
  • Assignments
• Lecture 37: Numerical Computation with numpy and scipy
  • Numerical Solving of Systems of Linear Equations
  • Numerical Integration
  • Rational Approximations
  • Numerical Solving of Ordinary Differential Equations
  • Assignments
• Lecture 38: Introduction to Julia
  • Getting Started
  • Implicit Differentiation with SymPy.jl
  • Implicit Differentiation with Symbolics.jl
• Lecture 39: Parallel Computing in Julia
  • Parallel Symbolic Computing
  • Parallel Computing with Julia
  • Parallel Numerical Integration
• Lecture 40: Computational Group Theory with GAP
  • Permutation Groups
  • Decomposition of Permutations
  • Rubik’s Cube
  • Assignments
• Lecture 41: Higher Arithmetic with Pari/GP
  • Calculating with GP in Sage
  • The Cauchy Integral Formula
  • Expansions and Series
  • Integer Relation Detection
  • Assignments
• Lecture 42: Computing with Polynomials in Singular
  • Polynomials
  • Reducing Polynomials with a Groebner basis
  • Assignments
• Lecture 43: Statistical Computing with R
  • Computations with R
  • Plotting Data
  • Fitting Linear Models