Assistant Professor

Universidad Técnica Federico Santa María

Department of Mathematics

📅 March 2024 – July 2024

📍Santiago, Chile


  • MAT021 - Matemática I (2024-S1) 1

    Foundations of mathematical language, real numbers, basic analytic geometry, functions, trigonometry, limits and continuity, derivatives in real variables, induction and applications, complex numbers, and polynomials.

  • MAT022 - Matemática II (2024-S1)

    Differential and Integral calculus, linear algebra.

  • MAT051 - Matemática II Para Arquitectura (2024-S1)

    Linear transformations, geometric transformations, functions of one variable, limits and continuity of functions of one variable, differentiation of one variable and applications, primitive functions.

  • MATE08 - Complementos de Álgebra y Cálculo (2024-S1)

    Algebraic expressions, simplifying algebraic expressions, linear equations, quadratic equations, real numbers, order axioms, inequalities, absolute value, intervals, linear and quadratic inequalities, more general inequalities, basic analytic geometry, trigonometry, natural numbers, and real functions.

1 S: Semester

Senior Tutor

Universidad de Santiago

PAIEP - Mathematics

📅 April 2025 - July 2025

📍Santiago, Chile


Teaching Assistant

Universidad Técnica Federico Santa María

Department of Mathematics

📅 March 2018 - July 2024

📍Santiago, Chile


  • FIS100 - Introducción a la Física (2018-S1)2

    Time and distance, measurements, rate of change, vectors, description of motion, mass and density, forces.

  • FIS119 - Física Básica II (2019-S1),(2019-S2),(2020-S1),(2020-S2),(2021-S1),(2021-S2)

    Thermodynamics and Electromagnetism.

  • FIS120 - Física General II (2019-S1),(2019-S2),(2020-S1),(2020-S2),(2021-S1),(2021-S2)

    Advanced Electromagnetism.

  • MAT022 - Matemática II (2022-S1)

    Differential and Integral calculus, linear algebra.

  • MAT023 - Matemáticas III (2022-S1),(2023-S1)

    Linear algebra, multivariable calculus, ordinary differential equations, Fourier series.

  • MAT024 - Matemáticas IV (2019-S1),(2020-S1),(2022-S2)

    Vector calculus and partial differential equations.

  • MAT225 - Análisis 1 (2021-S1)

    Metric spaces, normed vector spaces, differential calculus in Banach spaces, and topological spaces.

  • MAT410 - Análisis Convexo (2023-S1),(2025-S1)

    Properties of Convex sets: Convexity and topology, relative interior, Hahn-Banach separation Theorems, Mazur’s Theorem, recession cone, Krein-Milman Theorem. Convex Functions: Continuity and lower semi-continuity, Weierstrass-Hilbert-Tonelli’s Theorem, Fenchel-Legendre’s Conjugate, subdifferential, subdifferential calculus, optimality conditions, recession function, Moreau-Yosida’s approximation, Differential Inclusions. Duality in Convex optimization: Perturbation functions, strong duality Theorem, Fenchel-Rockafellar’s Theorem, Lagrangian duality, Fritz John’s Theorem, Minmax Theorem.

  • MAT279 - Optimización no Lineal (2023-S2)

    Introduction to abstract optimization, convex optimization, smooth and non smooth convex optimization, unconstrained and constrained nonlinear optimization.

  • MAT043 - Teoría de Probabilidad y Aplicaciones (2023-S2)

    Elements of probability theory, random variables, discrete and continuous random variables useful in the analysis of electronic systems, continuous random variables in multiple dimensions, moment generating function, notions of stochastic processes.

  • MAT227 - Análisis 3 (2024-S1)

    Hahn-Banach, Banach-Steinhaus, and open mapping theorems; Unbounded operators, adjoint operator, and orthogonality relations; Weak topologies, reflexive spaces, separable spaces; Hilbert spaces; Stampacchia’s theorem; Lax-Milgram theorem; Riesz-Fredholm theory and spectral decomposition of compact operators.

  • MAT425 - Álgebra II (2024-S2)

    Field and extensions: Finite and Algebraic extensions. Transcendental extensions and transcendence degree. Algebraic closure: splitting field and normal extensions. Separable extensions and finite fields. Inseparable extensions. Galois extensions: Fundamental theorem of Galois theory. Solvable and radical extensions. Complements of commutative algebra. Module theory. Valuations, local fields. Exterior algebra. Dedekind rings in algebraic number theory.

  • MAT403 - Topología (2024-S2)

    Topological spaces. Topologies. Sub-bases. Bases. Open and closed sets, interior, closure, boundary. Equivalence of topologies. Continuity. Open maps. Closed maps. Homomorphisms. Subspaces. Relative topologies. Product topology. Identification topology. Quotient topology. Connectedness. Local connectedness, path connectedness. Separation. $T_0$, $T_1$, $T_2$, Hausdorff spaces, regular spaces. Normal and completely regular spaces. Urysohn’s and Tietze’s theorems. Metric spaces. Second-countable spaces. Separable spaces. Compactness. Tychonoff’s theorem. Compact metric spaces. Sequential compactness. Fréchet spaces. Locally compact spaces. Compactifications. Homotopy. Fundamental group of the circle. Covering spaces. Van Kampen’s theorem.

2 S: Semester

Teaching Assistant

Universidad Diego Portales

Faculty of Science and Engineering

📅 March 2021 - July 2021

📍Santiago, Chile


  • Electricidad y Magnetismo (2021-S1)3

    Advanced Electromagnetism.

    3S: Semester