billy-mosse / classes

13+ talks/classes I gave during the last years. Keywords: quaternions, numerical methods, ordinals, topology, logic.

classes

Here you will find:

• Some class notes for my final exam of Numerical Calculus.
• Classes I gave for Numeric Calculus (as a TA):
  • Best approximation theorems and baricentric formula.
  • Some methods for finding fixed points of functions.
• One of the exercises I solved in detail for Numerical Methods (as a TA; this subject is similar to Numerical Calculus, but with a more "Computer Sciency" approach). The exercise is about Singular Value Decomposition.
• Some lectures I gave:
  • A talk about 2D and 3D rotations using complex numbers and quaternions for a game company called NGD Studios. To describe 3D rotations, I'm proud to say that I brought - it has an axis and an angle!
  • A talk about ordinal notations I gave for the 2017 Logic and Computablity Summer School in Göttingen. Ordinal notations (for countable ordinals) are used to measure the strength of some logic theories. What's fun is that there are uncountable countable ordinals. These notations get convoluted quite fast. There isn't any systematic way for defining increasing notation systems for all countable ordinals (it can be argued that it can't be done in ZF, but yes in ZFC). I talk a little bit about that in my thesis!
  • Another talk about ordinal notations, this time about regarding Cut Elimination Theorem for an infinitary proof system, for the 2018 Logic and Computability Summer School in Göttingen.
  • A Computability Theory presentation I gave about a nice concept called Learnability Theory: "Can you guess my recursive function if you can only ask me about finite values?" For e.g., if you know you are only dealing with linear (mathematical) functions, you only need 2 values. But there are really interesting questions regarding this topic.
  • 2 Logic and Computability classes (2016, 2017) I prepared for my (successful!) qualifying exams for being a TA.
  • A presentation I gave as a part of an Automatic Program Analysis course. It was about using group theory for optimizing constraint satisfaction problems.

Any questions, feel free to email me to gmosse at dc.uba.ar.