The lectures will cover chapters from these two texts

1. Introduction to nonlinear algebra by Mateusz Michalek and Bernd Sturmfels
2. Solving polynomial systems by Bernd Sturmfels

and have applications in

1. Nash equilibria,
2. Kinematics,
3. Algebraic statistics, and
4. Reaction networks.

Additional references:
(A) Ideals, varieties, and algorithms by Cox, Little, and O'Shea.
(B) Algebraic Statistics by Sullivant
(C) Numerically solving polynomial systems with Bertini by Bates, Hauenstein, Sommese, Wampler
(D) The Numerical Solution of Systems of Polynomials Arising in Engineering and Science by Sommese and Wampler

Software:
PHC pack
Bertini
Macaulay2
Matlab/Maple/Mathematica

Tentative Outline
Week 1-2: 	Problems: Nash Equilibria, Algebraic kinematics, reaction networks, Algebraic statistics
Week 2: 	Chapter 1 INA: 	Polynomial Rings
Week 2-3: 	Chapter 2 INA: 	Varieties

Week 3-4: 	Chapter 3 CBMS: Bernstein’s Theorem and Fewnomials
Week 4-5:	Chapter 6 CBMS: Polynomial systems in economics [Nash Equilibria]

Week 5-6:	Chapter 4 INA:	Mapping and Projecting
Week 6-7:	Chapter 6 INA:	Nullstellensatze
Week 7-8: 	Chapter 8 INA: Toric Varieties (Algebraic Statistics and Reaction networks)

Week 8: 	Chapter 9 INA: Tensors (if time permits)

Spring break

Week 9:		TBD.

Week 10: 	Homotopy methods / Regeneration / Equation by equation solving
Week 10-11: 	Algebraic Kinematics
Week 12: 	Chapter 12 INA: Semidefinite programming
Week 13-14: 	Final projects