# Volume II, Issue 1

# Bounding the Fat Shattering Dimension of a Composition Function Class Built Using a Continuous Logic Connective

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The paper deals with an important combinatorial parameter of a function class, the Fat
Shattering dimension. An important known result in statistical learning theory is that a function class
is distribution-free Probably Approximately Correct learnable if it has finite Fat Shattering dimension
on every scale.

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# Integers With A Predetermined Prime Factorization

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A classic question in analytic number theory is, given integers x and k, to find asymptotics for the numbers n less than or equal to x with exactly k prime factors. This problem was originally resolved by Landau in 1900, and much work was subsequently done where k is allowed to vary. In this paper we look at a similar question about integers with a specific prime factorization. Download the article

A classic question in analytic number theory is, given integers x and k, to find asymptotics for the numbers n less than or equal to x with exactly k prime factors. This problem was originally resolved by Landau in 1900, and much work was subsequently done where k is allowed to vary. In this paper we look at a similar question about integers with a specific prime factorization. Download the article

# Rotterdam Must Die: Triangular Finite Volume Methods Applied To The Shallow Water Equations

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In this paper we apply the method of finite volumes using a triangular mesh with a Roe solver to solve the
shallow water wave equations. In order to demonstrate the advantages of using a triangular mesh, we solve
two problems that are not easily solved using rectangular finite volume methods. We first solve the classic
problem of a broken circular dam and then apply the scheme to the Maeslantkering, a movable barrier
along the Nieuwe Waterweg in Holland used to regulate water flow from storms into the shipping canal, to
demonstrate the complicated geometry that triangular meshes are able to model.

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Volume I, Issue 2 of The Waterloo Mathematics Review is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Canada License.