Jeffrey T. Hoag  Office: Howley Hall 200  TEL: (401) 865-2464  Email: jhoag@providence.edu    Department Chairperson

Research Interests:

Non-linear difference equations of order two or more
Functional differential equations
Conditions for Uniqueness of solutions to ODE initial value problems

Teaching interests:

GEOMETRY (MTH 309)
 

This course is required for students in the Mathematics/Secondary Education major and is taken as an elective by many Mathematics majors. The course begins with a brief look at the geometry that was known to the ancient Greeks and how they used it not only in engineering problems, but to determine such quantities as the size of the earth and the distance to the moon. We then study systems of axioms in general and the Euclidean Axioms in particular. Other topics: Classical results about triangles and circles, Construction (Can a line segment be trisected using only straight edge and compass? Can an angle be trisected using only these tools?), Transformations of the plane and Non-Euclidean Geometries. Other topics as time permits. Prerequisite: MTH 132 (Calculus & Analytic Geometry II)

 

REAL ANALYSIS I & II (MTH 323-324)

 

This two semester sequence is taught each year by me or other members of the department. It is required for Mathematics and Mathematics/Secondary Education majors. In this course we look at the theory of calculus. Many of the ideas (limit, derivative, integral etc.) will be familiar to you from the introductory calculus sequence, but there the focus was on problem solving and applications. In this course the emphasis is on proving theorems and the logical foundation of the subject.

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