Class 1.5: about algorithms vs
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
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.
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
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
How do we choose confidence intervals (Neyman
(Following section 18.104.22.168 in [PDG-Stat].)
Find intervals for each value of the parameter such that
P (1 < < 2 ) = 1 =
f (; )d.
Programming and Numerical Methods for Scientists
What every computer has to have
At least one input device.
Central Processing Unit.
At least one output device.
almost always some
Programming and Numerical Methods, class #2 (notes only)
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
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
f ( xi ) = V < f >
Class 9: Fitting data
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+ 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):
Class 2.5: more on integers and floating point
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.
(T-32.0)*(5/9) always gives zero (because
Class 4: C+ Part II
Explicit type conversion (casting)
Usefulness of arrays and references:
An algorithm for DrawAllBalls()
Many things demonstrated by DrawAllBalls()
A more CPU-efficient algorithm
Class 5: C+ part III, and using APIs
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
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
The basic n-dimensional ODE equation
y = f (y , t)
where t is the independent variable, y are the dependent variable, and underlines
This looks like a first-order ODE, but it can rep