Most books about fundamental quantum mechanics use results in the theory of Hilbert space operators without proving them, while most books about Hilbert space operators do not treat quantum mechanics.

Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing ...

Set theory remains the fulcrum of modern mathematical foundations, providing the language and axiomatic structure upon which much of mathematics is built. Predominantly formulated through the ...

The course will be a proof-based theoretical course and assume sufficient mathematical maturity, in particular in probability and linear algebra. Important concepts will be reviewed. A good ...

Familiarity with linear algebra is expected. In addition, students should have taken a proof-based course such as CS 212 or Math 300. Tensors, or multiindexed arrays, generalize matrices (two ...