• Prove/Disprove that every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. (MATH 544/FREN 544)

    Required Reading: Introduction to Topological Manifolds, John M. Leehttps://gallica.bnf.fr/ark:/12148/bpt6k4337198/f7.imagehttps://zenodo.org/record/2063679#.YknrXuiZNrUhttps://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s1-32.1.277http://www.numdam.org/numdam-bin/feuilleter?id=BSMF_1902__30_ (Page inexistante)https://gallica.bnf.fr/ark:/12148/bpt6k1074672/f170.image.r=Journal%20math%C3%A9matiques%20pures%20appliqu%C3%A9es.langFRTranslating these papers satisfies the foreign language requirement, solves the statement and will grant you a phd. Good luck!Proof: For Stevie Wonders Eyes Only [learn_press_profile]

  • Complex Manifolds (Thesis)


  • Polar Coordinates and Coxeter Groups (MATH 127)

    Course Textbook: Reflection Groups and Coxeter Groups, James E. Humphreys,Preparing for this Section (Review)Rectangular CoordinatesDefinition of the Trigonometric FunctionsThe Distance FormulaInverse Tangent FunctionCompleting the SquareAngles; Degree Measure; Radian Measure [learn_press_profile]

  • Schrödinger’s cat (Reinterpreted)

    One can even set up quite ridiculous cases. A cat is locked up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of an hour only one of the atoms decays,…

  • Persistent Homology (MATH 528)

    Required Reading (Lectures): https://mrzv.org/Course Website: http://graphics.stanford.edu/courses/cs468-09-fall/Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space rather than artifacts of sampling, noise, or particular choice of…

  • Who is Hamilton? (MATH 436)

    Required Reading: https://www.ria.ie/hamilton-did-it/who-hamilton [learn_press_profile]

  • Physics Survey (PHYS 538)


  • Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance (FREN 102)

    Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power is a book published in 1824 by French physicist Sadi Carnot.[1][2][3][4][5] The 118-page book’s French title was Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. It is a significant publication in the history of thermodynamics about a generalized theory of heat…

  • I’m sorry this statement is so blatantly wrong that’s probably why he italicized it. The physical object in question is not a four-dimensional Riemann manifold it doesn’t even sound right. [learn_press_profile]

  • Stone–Weierstrass theorem

    In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation. The original version of this result was established by Karl Weierstrass in 1885 using the Weierstrass transform.…