Modular Algorithms in Symbolic Summation and Symbolic Integration

1. Introduction.- 2. Overview.- 3. Technical Prerequisites.- 4. Change of Basis.- 5. Modular Squarefree and Greatest Factorial Factorization.- 6. Modular Hermite Integration.- 7. Computing All Integral Roots of the Resultant.- 8. Modular Algorithms for the Gosper-Petkovsek Form.- 9. Polynomial Solutions of Linear First Order Equations.- 10. Modular Gosper and Almkvist & Zeilberger Algorithms.