1. Concerning These Notes 2 2. Introduction (First Day) 2 3. Algebraic Numbers and Integers 5 4. Linear Algebra for Number Theory 10 5. Review of Field Theory; Traces/Norms 10 6. Units: Some Notes Missing Here 16 7. Diophantine Approximation 16 8. The Trace Pairing 18 9. Linear Algebra and Discriminants 21 10. The Ring of Integers Inside the Number Field 26 11. Some Computational Aspects of Dis...

The Hahn-Banach theorem is one of the most fundamental theorems in the functional analysis theory. This theorem is well known in the case where the range space is the real number system as follows. Let p be a sublinear mapping from a vector space X into the real number system R, Y a subspace of X, and q a linear mapping from Y into R such that q ≤ p on Y. Then there exists a linear mapping g fr...

Recapitulation The origin of the representation theory of finite groups can be traced back to a correspondence between R. Dedekind and F. G. Frobenius that took place in April of 1896. The present article is based on several lectures given by the author in 1996 in commemoration of the centennial of this occasion. In Part I of this article we recounted the story of how Dedekind proposed to Frobe...

We discuss a trinity, i.e., three distinct expressions, of the Borcherds Φ-function on the analogy of the trinity of the Dedekind η-function.

A complete classification is obtained for all second-order linear recurring sequences uniformly distributed modulo an ideal of a Dedekind domain.