Ch 7. An algorithm for explicitly writing down polynomials in a given submodule of the space of polynomials. Further combinatorics of Young tableaux. Working with tensors in factored vs. expanded form.

§ 5.4, 5.5 Equations II: inheritance, and prolongation

finish Ch 4 (Littlewood-Richardson rule and other handy formulas, more decompositions of spaces of tensors)

Toric varieties, toric ideals, moment map, exponential families.

§ 4.3,4,5 - Representations of the symmetric group, Young diagrams, Young symmetrizers and wiring diagrams. Using these tools to decompose V^{\otimes d} as a GL(V) module. Schur-Weyl Duality.

Finish Ch. 2: skew-symmetric tensors, equations for rank at most r linear mappings, border rank, decomposing V^{\ot 3}., G-modules, isotypic components. § 4.1,2 Representations, Schur's Lemma, G-modules and decomposing spaces of tensors

Algebraic varieties § 3.1, 3.2. Basic definitions from algebraic geometry: projective space, variety, ideal, Zariski topology. Segre, Veronese, and other examples of varieties. Graphical models and motivating examples in statistics and information t