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Jostin Alcívar | Undergraduate Mentee
Jostin Alcívar | Undergraduate Mentee
Undergraduate student at the School of Mathematical and Computational Sciences at Yachay Tech University. His academic interests lie in pure and applied mathematics, particularly functional analysis, spectral theory, and the calculus of variations. His current thesis research explores the existence of normalized ground state solutions for a class of nonlinear elliptic systems. This work involves an in-depth study of Sobolev spaces, nonlinear analysis, and the variational formulation of elliptic boundary value problems. Methodologically, his research heavily relies on variational techniques such as min-max methods, the mountain pass theorem, and direct minimization on Nehari and Pohozaev constraints.
Beyond theoretical mathematics, he integrates technological tools into his academic training. He actively collaborates with Leonardo Medina, M.Sc., to develop university-level resources, including comprehensive solution manuals for Functional Analysis and other ongoing projects. Additionally, he serves as a Calculus Teaching Assistant, dedicating his time to supporting undergraduate students and contributing to the academic community.
Functional Analysis: Preliminaries
Functional Analysis: Preliminaries
Author: Juan Mayorga-Zambrano
Author: Juan Mayorga-Zambrano
This project offers a detailed, step-by-step solutions manual for the textbook's first chapter. Its goal is to make rigorous mathematical proofs more accessible, helping students build the analytical foundation needed to confidently solve complex variational problems. Developed under the guidance of Leonardo Medina, M.Sc., this material is freely available to promote collaborative learning and accessible education.
Designed to help students move beyond rote memorization, these tutoring sessions used Stewart's Calculus as a foundational guide but deliberately avoided standard mechanical exercises. The approach prioritized complex, real-world problems that demand deep analytical thinking. The provided link gives access to all the session exercises in PDF format, organized chronologically by date. These resources are made available to support students in connecting abstract theory with applied problem-solving.
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