Extension of Fields: Norm and Valuation

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Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Competitiveness of the 'Factory of the World'

Explores China's competitiveness as the 'Factory of the World' and recent developments in its economy and stock market.

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.

Matrix Calculations: Basis Change and Extensions

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Principles of Finance: Stock Valuation and Investment Strategies

Explores stock valuation, risk-return relationship, and portfolio returns based on weights.

Decomposition & Inertia: Group Actions and Galois Theory

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

Algebras and Field Extensions

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

P-adic Expansion and Hensel's Lemma

Covers the p-adic expansion theorem and Hensel's Lemma in Qp.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Valuation of Priceless Resources and Impacts

Explores preference-based assessment methods for valuing priceless resources and impacts.