**Reading Assignment:**

- [Cox et al]
**Cox, Little, & O'Shea, "Ideals, Varieties, and Algorithms," (second Edition), Springer-Verlag, (1996), Chapters 1.** - [Heck]
**Heck, "Introduction to Maple," (Second Edition) Springer-Verlag, (1997), Chapter 15.**

Problem 1. Exercise 5 on page 5 of [Cox et al] Problem 2. Use Maple to draw the affine varieties found in Exercise 4 page 12 of [Cox et al]. Be sure to used the CONSTRAINED option. Also make sure to use Maple to label your drawings with a brief text description. Be sure to show the coordinate axes in your drwaings. Problem 3. Exercise 13, page 13 of [Cox et al] Problem 4. The 3-sphere S^{3}= V(x^{2}+ y^{2}+ z^{2}+ t^{2}- 1) "lives" in 4-space. Use Maple to visualize this hypersurface by viewing 3 dimensional cross-sections parameterized by t, i.e., draw S^{3}_{t}= V(x^{2}+ y^{2}+ z^{2}+ t^{2}- 1) for t = 1.0,0.9,0.8,0.5,0.0,-0.5,-0.8,-0.9,-1.0 Be sure to use Maple to label each drawing with the appropriate value of t. Also be sure to use the CONSTRANED option and to show the coordinate axes. Finally, use Maple's animate3d procedure to view a "movie" of the hyperserface. Problem 5. Repeat problem 4 with the hypersurface M^{3}= V(x^{2}- y^{2}- z^{2}+ t - 1) using an appropriate set of values for the parameter t.