## Resources

*Ideals, Varieties, And Algorithms*by David A. Cox, John Little and Donal O'Shea

*Using Algebraic Geometry*by David A. Cox, John Little and Donal O'Shea

*Introduction to Tropical Geometry*by Diane Maclagan and Bernd Sturmfels

*Invitation to Nonlinear Algebra*by Mateusz Michałek and and Bernd Sturmfels

if you are a person who prefers shorter reading, there is a nice expository article about nonlinear algebra*Matroid Theory*by James Oxley

anything shorter than this? there is also a nice article about a matroid*The Numerical Solution of Systems of Polynomials Arising in Engineering and Science*by Andrew J. Sommese and Charles W. Wampler

*Lectures on Polytopes*by Günter M. Ziegler

*A Course in Convexity*by Alexander Barvinok

### Introductory level articles

These are research papers all examine various aspects of nonlinear algebra. Most of them are papers that I

1) enjoyed reading during my earlier years of my graduate studies,

2) found useful to study an introduction of a specific topic or,

3) think worth to read because they are cited frequently.

Many of these papers are available at arXiv.

**Caveat :**The meaning of "introductory level" can be (seriously) personal and interpreted in various way ;)- A Polyhedral Method for Solving Sparse Polynomial Systems by Birkett Huber and Bernd Sturmfels

- Algebraic Matroids in Action by Zvi Rosen, Jessica Sidman and Louis Theran

- Computing the multiplicity structure in solving polynomial systems by Barry H. Dayton and Zhonggang Zeng

- Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems by Jonathan D. Hauenstein and Frank Sottile

- The Bergman complex of a matroid and phylogenetic trees by Federico Ardila and Caroline J. Klivan

- Algebraic matroids and set-theoretic realizability of tropical varieties by Josephine Yu

- Algebraic Degree of Polynomial Optimization by Jiawang Nie and Kristian Ranestad

- What is a matroid? by James Oxley
- Macaulay2

- HomotopyContinuation.jl

- Bertini

- alphaCertified

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