About

The provided page text does not contain specific information about Professor Andrew Bruckner's research focus, background, or key contributions. It primarily describes the structure and activities of the UCSB Directed Reading Program (DRP), including mentoring, awards, and organizational details. Therefore, there is no detailed professional biography available for Professor Andrew Bruckner in the given content.

Research topics

• Computer Science
• Mathematical analysis
• Pure mathematics
• Mathematics
• Geometry
• Discrete mathematics

Selected publications

• Can One Visualize a Continuous Nowhere Differentiable Function?

  American Mathematical Monthly · 2023

  1st authorCorresponding
  • Computer Science
  • Computer Science
  • Mathematics

  When students first encounter an example of a continuous nowhere differentiable function in a real analysis course, what do they visualize? It is not easy to visualize an infinite sum of functions when the partial sums get increasingly complicated. We offer a geometric approach via the graph of such a function.Our theme is based on the fact that, if the graph of a function intersects all non-vertical lines in a special way, then that function cannot have a derivative at any point. We will require that at each point P on the graph G of the function there must be many lines L through P having P as a limit point of the intersection G∩L. This picture is easy to imagine but impossible to represent graphically: it avoids all of the computational complications that faced nineteenth-century mathematicians when they first attempted to describe these functions.

  PublisherDOI

• Umgebungslärmrichtlinie in Schleswig-Holstein/Environmental Noise Directive in Schleswig-Holstein

  Lärmbekämpfung · 2019-01-01

  articleSenior author

  Die dritte Runde der Umgebungslärmrichtlinie 2002/49/EG [1] wird mit der Lärmkartierung 2017 und der aktuellen, in Schleswig-Holstein (SH) noch nicht vollständig abgeschlossenen Aufstellung der Lärmaktionspläne umgesetzt. Die Zuständigkeit für die Ausarbeitung der Lärmkarten und für die Aufstellung der Aktionspläne liegt in SH gemäß § 47 e Bundes-Immissionsschutzgesetz [2] bei den Gemeinden. Dem Land obliegt die Berichterstattung an die Bundesregierung.   The third round of the Environmental Noise Directive 2002/49/ ED [1] will be implemented with noise mapping 2017 and the current list of noise action plans, which has not yet been completed in Schleswig-Holstein (SH). The responsibility for the development of the noise maps and for the preparation of the action plans lies in SH according to § 47 e Federal Immission Control Act [2] in the municipalities. The country is responsible for the reporting to the Federal Government.

  PublisherDOI

• Memories about Solomon Marcus

  WORLD SCIENTIFIC eBooks · 2018-04-24

  book-chapter1st authorCorresponding
  PublisherDOI

• On the Composition of Derivatives

  Real Analysis Exchange · 2018-01-01 · 1 citations

  article1st authorCorresponding

  We show that there exists a derivative \(f\colon [0,1]\to[0,1]\) such that the graph of \(f\circ f\) is dense in \([0,1]^2\), so not a \(G_\delta\)-set. In particular, \(f\circ f\) is everywhere discontinuous, so not of Baire class 1, and hence it is not a derivative. %neither of Baire class 1 nor a derivative.

  PublisherDOI

• To Develop the Colonial Estate:The Reasons for British West African Railways

  2011-09-23

  dissertation1st authorCorresponding

  This Dissertation is a history of reasons and motivations behind building the first railways in British West Africa. It analysis Sierra Leone, the Gold Coast, Lagos and Northern Nigeria from the early 1890s to 1906. This is a history not only of the railways but of British imperialism, and helps illustrate its economic nature. This work uses a variety of sources such as government papers, speeches, newspapers, books and journals written around the time of lobbying, planning and construction of these first railways. One of the goals of this paper is to shed more light on a region of the British Empire that has not been dealt with in great quantity and to do so with the intention to further both railway and British imperial history. This dissertation also highlights the different nature of the railways built in British Africa and the importance of studying all of them in order to have the best possible understanding of railway imperialism.

  Publisher

• Periodic and regional variations in the appearance of certain eye conditions.

  PubMed · 2008-10-20

  article1st authorCorresponding
  Publisher

• Recollections of Working With Caspar Goffman

  Real Analysis Exchange · 2007-01-01

  article1st authorCorresponding
  Publisher

• Applications of the Baire Category Theorem to Real Analysis

  Elsevier eBooks · 2003-01-01

  book-chapter1st authorCorresponding
  PublisherDOI

• Real variable contributions of G. C. Young and W. H. Young

  Expositiones Mathematicae · 2001-01-01 · 13 citations

  article1st authorCorresponding
  PublisherDOI

• The space of 𝜔-limit sets of a continuous map of the interval

  Transactions of the American Mathematical Society · 1996-01-01 · 55 citations

  articleOpen access

  We first give a geometric characterization of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega"> <mml:semantics> <mml:mi> ω </mml:mi> <mml:annotation encoding="application/x-tex">\omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -limit sets. We then use this characterization to prove that the family of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega"> <mml:semantics> <mml:mi> ω </mml:mi> <mml:annotation encoding="application/x-tex">\omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -limit sets of a continuous interval map is closed with respect to the Hausdorff metric. Finally, we apply this latter result to other dynamical systems.

  PublisherOA PDFDOI

Frequent coauthors

• R. Biskner

  University of California, Davis

  18 shared

• S. J. Agronsky

  California Polytechnic State University

  18 shared

• Jan Mařík

  17 shared

• Brian S. Thomson

  14 shared

• Casper Goffman

  11 shared

• Miklós Laczkovich

  Eötvös Loránd University

  11 shared

• David Preiss

  University of Oxford

  10 shared

• S. J. Agronsky

  California Polytechnic State University

  10 shared