Lecture notes and oral exam topics in mathematics, AI, and finance.
Practice sheet on constructing rigorous epsilon and delta proofs, covering sums and products of convergent sequences, continuity of x² and √x, preservation of sign, and the relationship between limits, lim sup, and lim inf.
Cheatsheet on the Cauchy-Schwarz inequality, including its proof in real and complex inner-product spaces, standard forms for vectors, series, integrals, random variables, and matrices, equality cases, classical applications, common pitfalls, and its extension to Hölder's inequality.
Reference sheet introducing norms, induced distances, metric spaces, and normed vector spaces, with the axioms of norms and distances and the relationship between these mathematical structures.
Cheatsheet comparing vector spaces, metric spaces, normed vector spaces, norms, and norm-induced distances, with their defining axioms, key properties, and relationships.
Method sheet covering the fundamentals of probability: expectation and its properties, independence of events and random variables, variance, covariance, and standard computation techniques. Document generated with the assistance of AI based on the information I provided.
Complete method sheet covering: standard antiderivatives, integration by parts, substitutions, Bioche's rules, partial fraction decomposition, improper integrals, and advanced techniques such as differentiation under the integral sign and the Gamma and Beta functions.
Assessment criteria used during oral examinations: presentation, rigor of reasoning, mastery of the course material, and quality of answers to questions.
Arithmetico-geometric sums ; Binomial coefficients, Vandermonde's identity ; Lagrange's identity and the Cauchy–Schwarz inequality
Course notes on fundamental electrical quantities: charge, current, voltage, resistance, power, and energy. Document generated with the assistance of AI based on the information I provided.