Santiago, Santiago Metropolitan Region, Chile
Chilean/Italian From 2014-2026, interested in advanced Maths & learned by self teaching: -Groups,Rings,IntegralDomains,Ideals,Fields,Vector Spaces,Modules,Algebras;LieGroups -Topology,Homotopy;Quotient&HomogeneousSpaces,SeifertVanKampen theo -Topological/Smooth/Riemannian/Complex/Kähler/Hodge&SpinManifolds; Whitney embedding theo;Dehn twists -Simplicial/Singular&CechHomology,Differential&HarmonicForms,Poincare Lemma,Hodge Decomposition theo, DeRham/Doulbeaut/Alexander-Spanier/Cech/SheafCohomology -Cup/CapProduct,CohomologyRing,Short/Long ExactSequences,Mayer-Vietoris Seq, -Complexes,Riemann&SeifertSurfaces,KauffmannBracket,Alexander&JonesPolinomials,Skein Relations -CharacteristicsClasses,Total/Euler/Chern/Pontrjagrin/Stiefel-Whitney/Todd/A-genusClass/ChernCharacter -Maurer-Cartan Form,CartanStructure eqns,Calabi-Yau Manifolds,Orbifolds,FiberBundles -Elliptic-Modular-Morse Functions,Moduli &TeichmullerSpaces,(Pre)Sheaves,HodgeDiamonds, -TheUniversalCo/HomologyCoefficientTheorem-The Künneth Formula, -ProjectiveSpaces,Grassmanians,(Alexander)HornedSphere,HopfBundle,Poincare/SerreDuality,Foliations,Exotica, -Eisenstein Series,Modular Forms,the Modular discriminant,the modular j-invariant,L-functions,Elliptic Curves -Categories,Functors,Resultants,Divisors,Riemann-Roch theo,Affine/ProjectiveVarieties,Blow_ups -Elliptic/FredholmOperators,Analytic/Topological Index,Atiyah-Patodi-Singer Index Theorem -Zariski Topology,Maximal/Prime/Radical Ideals,Noetherian Rings|Hilbert's Basis theo|HilbertNullstellensatz -Spectrum of a Ring|Schemes|Bézout's theo,Kodaira embeddingtheo|KdVequation|Solitons -DonaldsonInvariants|RicciFlow|Algebraic-Topological K Theory -SurfaceClassifications|ThurstonGeometrizationConjecture:"the Eight 3-d Geometries”, non-linear forms -SobolevSpaces|SobolevTheorems|TopologicalQFT|FloerTheory|Seiberg-Witten -ThetaFunctions|Jacobi's Modular eq|GaloisGroup|SolivingoftheQuintic|Kronecker's Jugendtraum -DerivedFunctEXT&TOR|Taniyama-Shimura-Weil theo|The Twisted cubic,Birational Geometry -WittenIndex|WittenGenus|Elliptic-Abelian Integrals|Jacobian Variety|Darboux derivative|Klein & Cartan Geometries|IntersectionForm, Stable:Homotopy/Bundles,Bordism&Cobordism,h-s-Cobordism|Lie/Clifford-Algebras|The Whitney Trick|The Whitney Umbrella 2019 studied Supersymmetry/Supergravity|2022 got into Super String Theory & Branes Other Interests: -Electric Guitar-Sing-Charismatic-Praise -Dinosaurs/EarlyMammals -Socrates/Plato/Aristotle/Zeno/Epitectus/Seneca/MAurelio Defend:TheTruth|TheJustice|learningtolove Follow: YEHOVAH & YEHOSHUA Sinner by nature|Saved by Grace.
Dictating a course on Fundamentals of Mathematics and Physics. We start by exploring the different numbers systems like the Naturals, the Integers, the Rational, Irrational and Reals. We touch upon solving linear equations and doing graphs of the straight line equation. Then we explore the same for the quadratic. We introduce the basics of Trigonometry including trigonometric functions and fundamental identities. We introduce the concept of a set, Domain and Image set and of a Relation, in particular, of a Function. We explore the graphs of the linear, affine and quadratic functions. Study some basic functions like the exponential and the Logarithm and their graphs. Then we pass on to Physics, units and measurements. Kinematics, like motion with constant velocity and motion with constant acceleration. Dynamics with the three laws of Newton, Mechanical Energy and finally touch lightly upon waves and sound. The course includes doing Laboratories.
Teaching Pre-Calculus course at PUC for students of Civil Construction.
Theoretical Biophysics Course for Health Sciences and Related Laboratories with 6 experiences: Four of Classical Mechanics, such as human reaction time, carts with uniform acceleration and Mechanical Energy, one on Waves and Sound and finally an Electrostatics experience working with a Van Der Graaff particle accelerator.
Dissemination course "THE CURRENT STATE OF PHYSICS, FROM NEWTON, THROUGH EINSTEIN TO STRING THEORY" for students of law, journalism and commercial engineering.