Class 1.5: about algorithms vs
programming
There are several steps to computing, and the
most important are not done on the computer:
1) Recognize and clarify a problem to solve.
2) Devise a method for solving it.
3) Carry out the solution.
4) Test, corre
Class 0x0C: Hypothesis testing and significance
tests
Different cases of hypothesis and significance testing
Comparison of two hypotheses H0 and H1 :
The classic simple hypothesis test.
Characterized by the significance level of the test.
Comparison o
Class 0x0B: Statistics
Quick non-review of probability
Im going to assume you already know about the following:
Definition of probability in terms of frequency of occurrence in a large
sample.
Probability density function (p.d.f.) for a continuous varia
Class 0x0D: Confidence regions
What is a confidence region?
Given a parameter or parameters fit to data according to a model:
The confidence region is an interval or area around the best fit point which
has a certain probability of containing the true va
Class 13.5 (0xD.8): Feldman-Cousins confidence
regions
How do we choose confidence intervals (Neyman
construction)
(Following section 32.3.2.1 in [PDG-Stat].)
Find intervals for each value of the parameter such that
P (1 < < 2 ) = 1 =
2
f (; )d.
1
Here f
Class #1
Programming and Numerical Methods for Scientists
and Engineers
1
What every computer has to have
Input
CPU
Output
At least one input device.
P ermanent
Storage
Central Processing Unit.
At least one output device.
Memory:
almost always some
Random
Programming and Numerical Methods, class #2 (notes only)
Introduction
This class is going to cover some aspects of the compiled languages C and C+. I'm not going to
attempt to teach everything about these languages in the classroom. I will attempt to teac
Class 0x0A: Monte Carlo integration and
simulation
Simple Monte Carlo integration
Suppose we have some function f (x) of the n-dimensional parameter x. Pick N
random points xi , uniformly distributed in volume V . Then
IMC
V
N
N
f ( xi ) = V < f >
i=1
is
Class 9: Fitting data
General problem
We have some model with one or more adjustable parameters ai and a function
that describes how well the model fits some set of measurements. Lets call
this goodness-of-fit function F . This function depends on the par
Class 3: C+ part I
C-inherited syntax
C+ has become very complicated (or rich), but its based on C.
C and C+ have a nested syntax structure.
At the top level, C has two main possibilities:
Define a function, or
Declare something (say what it is):
a
Class 2.5: more on integers and floating point
Integer math
The most important thing to keep in mind here is that division of two integers
gives an integer:
1/3 = 0, 2/3 = 0, 3/3 = 1, 4/3 = 1, etc.
In particular:
(T-32.0)*(5/9) always gives zero (because
Class 4: C+ Part II
Contents
Contents
Contents
1
Explicit type conversion (casting)
1
Usefulness of arrays and references:
1
An algorithm for DrawAllBalls()
1
Many things demonstrated by DrawAllBalls()
2
A more CPU-efficient algorithm
2
New DrawAllBalls()
Class 5: C+ part III, and using APIs
Pointers
Pointers are just values that indicate memory addresses and the type of data
that the programmer thinks is there.
Declaration syntax: type * pointer_variable ;
Dereference operator (get the value at this addre
Class 8: Roots and minima, more C+, and
using external libraries
Overview
Root-finding algorithms in 1-d and multiple dimensions
Minima-finding algoritms in 1-d and multiple dimensions
A little more C+: derived classes
Two examples of external librari
Class 6: Numeric ODE integrators; API design
and testing
The basic n-dimensional ODE equation
y = f (y , t)
where t is the independent variable, y are the dependent variable, and underlines
denote vectors.
This looks like a first-order ODE, but it can rep