Strong coupling from an improved <math display='inline'> <mi>?</mi> </math> vector isovector spectral function

Math 206: Banach Algebra and Spectral Theory

Math 241b Functional Analysis - Notes Spectral Theorem

We present the material in a slightly different order than it is usually done (such as e.g. in the course book). Here we prefer to start out with an abelian C∗-algebra A (say, the algebra C∗(a) generated by a normal operator a ∈ B(H)) and construct from it the spectral measure. This is done as follows: We know that A is isomorphic to C(X), the algebra of continuous functions on a compact set X....

FrameIT Reloaded: Serious Math Games from Modular Math Ontologies

Serious games are an attempt to leverage the inherent motivation in game-like scenarios for an educational application and to transpose the learning goals into real-world applications. Unfortunately, serious games are also very costly to develop and deploy. For very abstract domains like mathematics, already the representation of the knowledge involved becomes a problem. We propose the FrameIT ...

Math 108b: Notes on the Spectral Theorem

For a general vector space V , and a linear operator T , we have already asked the question “when is there a basis of V consisting only of eigenvectors of T?” – this is exactly when T is diagonalizable. Now, for an inner product space V , we know how to check whether vectors are orthogonal, and we know how to define the norms of vectors, so we can ask “when is there an orthonormal basis of V co...

Math Games: An Alternative (Approach) to Teaching Math

Getting students to read, digest and practice material is difficult in any discipline, but even more so for math, since many students have to cope with motivational problems and feelings of inadequacy, often due to prior unsuccesful training and teaching methods. In this paper we look at the opportunities offered by computer graphics, visual programming and game design as an alternative for tra...