Works
Two books with the American Mathematical Society, and my research articles in number theory and arithmetic geometry.
An Introduction to Arithmetic Geometry
An introduction to number theory in which geometry motivates the theorems: finding the integer and rational points on lines, conics and cubic curves leads to the fundamental theorem of arithmetic, quadratic reciprocity, continued fractions and Pell's equation, and finally elliptic curves. For a first course in number theory, or a junior–senior course in arithmetic geometry.
An introductory survey of the three families of objects in the title and the surprising connections between them, told with the number theory in front: the modularity theorem and Fermat's Last Theorem, the Birch and Swinnerton-Dyer conjecture, and many concrete examples. Written for advanced undergraduates; it motivates definitions and explains the main theorems rather than proving them.
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Each PDF is the more recent of the copy on my UConn website and the copy on arXiv. These are author versions, not publisher typeset versions: please cite the journal of record.
Abstracts are the authors’ own, taken from arXiv, from the publisher’s record, or from the PDF itself. Three articles (a Notices column, a short story and an essay) have no published abstract; for those a short Summary is given instead.
An HTML link appears where arXiv has rendered the submitted LaTeX as a web page, with real MathML: the mathematics reflows, scales without blurring, and can be read aloud by a screen reader.