SMSTC (2007/08)

Probability

                www.smstc.ac.uk

Contents

1 Probability spaces 1–1

1.1 Section heading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1

1.1.1 Subsection Heading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1 1.2 New section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1

SMSTC (2007/08) Probability

Lecture 1: Probability spaces

Stan Zachary, Heriot-Watt University^{a}

                  www.smstc.ac.uk

\underline{Contents}

1.1 Section heading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1 1.1.1 Subsection Heading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1 1.2 New section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1

1.1 Section heading

1.1.1 Subsection Heading

Subsubsection Heading

1.2 New section

Theorem 1.1 Theorem text comes here. Theorem 1.2 Theorem text comes here. Lemma 1.1 Lemma text comes here. Proof Because ℝ ≠ ℂ … … which completes the proof. □

Figure 1.1: Please write your figure caption here 1–1 SMST C: Probability 1–2

as.zachary@hw.ac.uk

Equations

Points on the circle satisfy

x^{2} + y^{2} = 4 ,  (1.1)

and the line is

y = m x + c .  (1.2)

Substituting for y from (1.2) into (1.1) gives …

Macros

Macros in smstc.sty include \aside and \cut:
\aside{text} gives [text]
\cut{text} gives

as well as the “logo” command \smstc which gives SMST C (with no extra space needed).

Citations

As shown by [2, Theorem 5.1] … We also refer to [1, 3]…

Exercises

1–1. For each …

1–2. If f : ℝ^{2} → ℂ is defined by …

References

[1] D. S. Jones, Theory of Electromagnetism, O. U. P., 1964.

[2] C. Lubich, On the multistep time discretization of linear initial–boundary value problems and their boundary integral equations, Numerische Mathematik, 67 (1994), pp. 365–389.

[3] A. Pujols, Time–dependent integral method for Maxwell equations, in Mathematical and Numerical Aspects of Wave Propagation Phenomena, G. Cohen, L. Halpern, and P. Joly, eds., SIAM, 1991, pp. 118–126.