Two further sets of personal class notes from the University of Costa Rica are now available under Notes:
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Metric Spaces and Measure Theory (MA-0505) — Análisis I, taught by Dr. Pedro Méndez Hernández. Twenty chapters: metric space topology, compactness, completeness, the Arzelà–Ascoli theorem, connectedness and the Baire category theorems, followed by functions of bounded variation, the Riemann–Stieltjes integral, Lebesgue measure and measurable functions, the theorems of Egorov and Lusin, the Lebesgue integral and its convergence theorems, and Lebesgue’s characterisation of Riemann integrability.
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Groups and Rings (MA-0561) — Grupos y Anillos, taught by Dr. Samaria Montenegro Guzmán. Twenty-four chapters: subgroups, cyclic groups, permutation groups, cosets and quotient groups, the isomorphism theorems, group actions and the Sylow theorems, then rings and fields, the polynomial ring, ideals both maximal and prime, quotient rings, ring homomorphisms, characteristic and the Frobenius map, the field of fractions, and the factorization of homomorphisms.
These were written in Spanish and translated into English. Both versions are available for every course in the section — including the two published in April — and you can switch between them from any page. As before, they are shared as-is, may contain errors, and are not affiliated with the instructors.