Sebastián Fernández Rivera

Two further sets of personal class notes from the University of Costa Rica are now available under Notes:

• 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.

• 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.

I have published a set of personal class notes from two advanced calculus courses I took at the University of Costa Rica, now available under Notes:

• Single Variable Real Analysis (MA-0350) — Cálculo en una Variable 2, taught by Dr. Pedro Méndez Hernández. Twelve chapters covering sequences and series of real numbers, the Riemann integral and its applications, improper integrals, and pointwise and uniform convergence of function sequences.

• Multivariate Real Analysis (MA-0450) — Cálculo en varias variables, taught by Dr. Juan Gabriel Calvo Alpízar. Five chapters covering the topology of \(\mathbb{R}^n\), differentiation in several variables, multiple integration, and an introduction to vector calculus.

The notes are available in Spanish and English, and shared as-is. They may contain errors and are not affiliated with the instructors.

New working paper out! “The Gap Between Mandate and Execution: An Evaluation of the Inflation Target in Costa Rica” finds empirical evidence supporting the existence of a contractionary bias in Costa Rica’s monetary policy. Read it on my Research page.

I am happy to announce the launch of my personal website! This platform will serve as my personal academic hub.

The site is organized into three main sections:

• About: An overview of my research agenda.

• CV: A current curriculum vitae detailing my coursework, research assistantships, and teaching experience.

• Research: A consolidated archive of my working papers, non-academic writings and fact-checking articles.

I built this site using the al-folio Jekyll template. I will be updating the website regularly.