University teaching
Teaching
Making complex ideas accessible.
I developed the syllabuses, course materials and assessments for both courses.
Teaching materials for both courses are freely available.
Courses
Introduction to Astronomy
Saint Louis University · Madrid
For science and non-science majors
Making a broad subject accessible to students with very different backgrounds. Taught entirely in English.
Course outline & lectures
- How does science work? — Dropbox, opens in a new tab
The scientific method; peer review; Mog gameplay.
- The night sky — Dropbox, opens in a new tab
The night sky; celestial coordinates; a celestial-coordinates quiz.
- Time — Dropbox, opens in a new tab
Time and seasons.
- The Moon — Dropbox, opens in a new tab
The Moon and eclipses.
- The revolutions — Dropbox, opens in a new tab
The Copernican revolution; Kepler’s and Newton’s laws.
- The Solar System — Dropbox, opens in a new tab
Planets, moons and other Solar System objects.
- Observing the Universe — Dropbox, opens in a new tab
Waves and blackbodies; light spectra; telescopes.
- The stars — Dropbox, opens in a new tab
Stellar formation, classification and evolution.
- Nebulae — Dropbox, opens in a new tab
Emission, reflection and dark nebulae.
- Exotic objects — Dropbox, opens in a new tab
Black holes and other extreme objects.
- Astrobiology — Dropbox, opens in a new tab
Exoplanets and extraterrestrial life.
- Galaxies — Dropbox, opens in a new tab
Types of galaxies; the Milky Way.
- The expanding Universe — Dropbox, opens in a new tab
The Big Bang and the expanding Universe.
Exams
Bibliography
- Hannu Karttunen et al.Fundamental Astronomy.
- Bradley W. Carroll & Dale A. OstlieAn Introduction to Modern Astrophysics.
- Barbara Ryden & Bradley M. PetersonFoundations of Astrophysics.
Differential Geometry
UNIE Universidad
Abstract concepts, concrete examples
Connecting abstract mathematical concepts with real-world examples to build intuition.
Course outline & materials
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Curves in space
Arc length and reparametrisation; the Frenet–Serret frame; curvature and torsion; osculating, normal and rectifying planes; the fundamental theorem of curves.
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Surfaces and the first fundamental form
Scalar and vector products; charts and atlases; regular surfaces and tangent spaces; the first fundamental form; lengths, angles and areas on surfaces.
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Surface curvature
The second fundamental form; orientability and the Gauss map; principal, Gaussian and mean curvatures; classification of points; local isometries and Gauss’s Theorema Egregium; Weingarten equations and Christoffel symbols.
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Geodesics and parallel transport
Geodesic parametrisation and maximal geodesics; conformal maps; covariant derivatives; parallel transport; the Gauss–Bonnet theorem.
Exams
Bibliography
- Javier Lafuente LópezCuarenta y cinco sesiones de geometría diferencial de curvas y superficies.
- Manfredo P. do CarmoDifferential Geometry of Curves and Surfaces.
- Óscar A. Palmas Velasco & J. Guadalupe Reyes VictoriaCurso de geometría diferencial. Parte 1. Curvas y superficies.