Martin Helsø

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STORM –– Stochastics for Time-Space Risk ModelsFunded by the Research Council of Norway, project no. 274410, and the University of Oslo

Ordinary table of contents1 Introduction

2 MathematicsTheoremExample

3 Highlighting

4 Lists

5 References

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1 Introduction

2 MathematicsTheoremExample

3 Highlighting

4 Lists

5 References

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MathematicsTheorem (Fermat’s little theorem)

For a prime p and a ∈ Z it holds that ap ≡ a (mod p).

Proof.

The invertible elements in a field form a group under multiplication. Inparticular, the elements

1,2, . . . , p − 1 ∈ Zp

form a group under multiplication modulo p. This is a group of orderp − 1. For a ∈ Zp and a 6= 0 we thus get ap−1 = 1 ∈ Zp. The claimfollows. �

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MathematicsExample

The function φ : R → R given by φ(x) = 2x is continuous at the pointx = α, because if ε >0 and x ∈ R is such that |x − α| <δ = ε

2 , then

|φ(x)− φ(α)| = 2|x − α| <2δ = ε.

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References IR. Hartshorne.Algebraic Geometry.Springer-Verlag, 1977.

M. Artin.On isolated rational singularities of surfaces.Amer. J. Math., 80(1):129–136, 1966.

R. Vakil.The moduli space of curves and Gromov–Witten theory, 2006.http://arxiv.org/abs/math/0602347

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References III M. Atiyah og I. Macdonald.

Introduction to commutative algebra.Addison-Wesley Publishing Co., Reading, Mass.-London-DonMills, Ont., 1969

[5] J. Fraleigh.A first course in abstract algebra.Addison-Wesley Publishing Co., Reading, Mass.-London-DonMills, Ont., 1967

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Martin Helsø

Beamer exampleShowcasing the theme STORM