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The exhaustive list of topics in Algebraic Techniques and Semidefinite Optimization in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Root Bounds and Sturm Sequences
  • Counting Real Roots
  • Nonnegativity
  • Sum of Squares
  • Positive Semidefinite Matrices
  • Discriminants
  • The set of Nonnegative Polynomials
  • Hyperbolic Polynomials
  • SDP Representability
  • Convex Sets in R2
  • Hyperbolicity and the Lax Conjecture
  • Relating SDP-representable Sets and Hyperbolic Polynomials
  • Binomial Equations
  • Newton Polytopes
  • The Bézout and BKK Bounds
  • Application: Nash Equilibria
  • Nonegativity and Sums of Squares
  • Sums of Squares and Semidefinite Programming
  • Multivariate Polynomials
  • Duality and Density: SOS Applications
  • Gröbner Bases
  • Zero-dimensional Ideals
  • Hilbert Series
  • Generalizing the Hermite Matrix
  • Recovering a Measure from its Moments
  • A Probabilistic Interpretation
  • Duality and Complementary Slackness
  • Multivariate Case
  • Density Results
  • Polynomial Ideals
  • Algebraic Varieties
  • Quotient Rings
  • Monomial Orderings
  • Parametric Versions
  • Cylindrical Algebraic Decomposition (CAD)
  • Psatz Revisited
  • Copositive Matrices and Pólya's Theorem
  • Positive Polynomials
  • Schmüdgen's Theorem
  • Groups and their Representations
  • Infeasibility of Real Polynomial Equations
  • The Zero-dimensional Case
  • Quantifier Elimination
  • Tarski-Seidenberg
  • Algebra Decomposition: Sums of Squares Programs and Polynomial Inequalities