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