Additional Useful Resources
Books:
There is no required textbook for this course, but the following books or lecture notes are suggested if you want to deepen your knowledge on the subject.
- [vzGG] von zur Gathen, Gerhard Modern Computer Algebra
- [BCS] Buergisser, Clausen, Shokrollahi Algebraic Complexity Theory
- [CLO'15] Cox, Little, O’Shea Ideals, Varieties and Algorithms
- [CLO'05] Cox, Little, O’Shea Using Algebraic Geometry
- [S'08] Sturmfels, Bernd Algorithms in Invariant Theory
- [BC'13] Buergisser, Cucker Condition: the geometry of numerical algorithms
- [S] Shoup Algorithms in Number Theory
Other web resources:
- Arne Storjohann’s version of CS 487
- Ramprasad’s course on Computational Group Theory and Computational Algebra
- Shpilka and Yehudayoff survey on arithmetic circuits
- Madhu Sudan’s 2012 course on Algebra and Computation
- Madhu Sudan’s 1998 course on Algebra and Computation
- Eugene Luks’ 1990 Lectures on Polynomial Time Computation in Groups
- Richard Borcherds’ commutative algebra lectures
- Richard Borcherds’ algebraic geometry lectures
Further reading:
- Avi Wigderson’s new book, Math and Computation
- Ramprasad Saptharishi’s survey, Lower Bounds in Algebraic Complexity
- David Eisenbud’s Commutative Algebra with a View Toward Algebraic Geometry