Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
PSYCHGA.2211/NEURLGA.2201 Fall 2012
Mathematical Tools for Cognitive and Neural Science
Homework 3
Due: 12 Oct 2012
(late homeworks penalized 10% per day)
Save the solution for each numbered problem in a separate MATLAB le, with a lename of
Yourlastname
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
The population includes all objects of interest whereas the sample is only a portion of
the population. Parameters are associated with populations and statistics with .
Parameters are usually denoted using Greek letters (mu, sigma) while statistics are
us
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
PSYCHGA.2211/NEURLGA.2201 Fall 2012
Mathematical Tools for Cognitive and Neural Science
Homework 2
Due: 28 Sep 2012
24
(late homeworks penalized 10% per day)
Save the solution for each numbered problem in a separate MATLAB le, with a lename of
Yourlastn
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
PSYCHGA.2211/NEURLGA.2201 Fall 2012
Mathematical Tools for Cognitive and Neural Science
Homework 1
Due: 17 Sep 2012
(late homeworks penalized 10% per day)
Save the solution for each numbered problem in a separate MATLAB le, with a lename of
Yourlastname
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
G80.2207/G89.2211 Fall 2011
Math Tools for Cognitive Science and Neuroscience
MATLAB Homework 0
This homework is optional. If you would like to submit answers, they should be in the form of a
MATLAB le (please make the lename follow the form of yourlastna
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
PSYCHGA.2211/NEURLGA.2201 Fall 2012
Mathematical Tools for Cognitive and Neural Science
Homework 4
Due: 5 Nov 2012
(late homeworks penalized 10% per day)
Save the solution for each numbered problem in a separate MATLAB le, with a lename of
YourlastnameH
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
Linear shiftinvariant (LSI)
systems
Linearity (covered previously):
linear combination in, linear combination out
Shiftinvariance (new):
shifted vector in, shifted vector out
Some examples
Monday, 29 October2012
[on board]
LSI system
Input
v
v1 x
v1
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
Least Squares Optimization
The following is a brief review of least squares optimization and constrained optimization
techniques. Broadly, these techniques can be used in data analysis and visualization to examine the relationships between variables.
Leas
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
Math Tools
Simoncelli/Maloney
1
HOMEWORK 6: DUE DECEMBER 17, 2012
ESTIMATION AND HYPOTHESIS TESTING
1. The Psychometric Function. Write a simulation program
C = simpsych(mu,sigma,I,T)
that simulates a psychophysical experiment used to measure a psychometr
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
A Geometric Review of Linear Algebra
The following is a compact review of the primary concepts of linear algebra. I assume the
reader is familiar with basic (i.e., high school) algebra and trigonometry. The order of presentation is unconventional, with em
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
The range is the simplest measure of variation to find. It is simply the highest value
minus the lowest value.
RANGE = MAXIMUM  MINIMUM
Since the range only uses the largest and smallest values, it is greatly affected by
extreme values, that is  it is n
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
A sample space is the set of all possible outcomes. However, some sample spaces are
better than others.
Consider the experiment of flipping two coins. It is possible to get 0 heads, 1 head, or
2 heads. Thus, the sample space could be cfw_0, 1, 2. Another
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
int (N*rand+S)
INT is found under the MATH menu (math num 4). RAND is also found under
the MATH menu (math prb 1).
Simulate the rolling of a die (16): int (6*rand+1)
Simulate the flipping of a coin (01): int (2*rand)
This works because the rand function
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
Mean
This is what people usually intend when they say "average"
Population Mean:
Sample Mean:
Frequency Distribution:
The mean of a frequency distribution is also the weighted mean.
Median
To find the depth of the median, there are several formulas that c
Mathematical Tools for Cognitive and Neural Science
MATH GA 2207

Fall 2011
G80.2207/G89.2211 Fall 2012
Mathematical Tools for Cognitive and Neural Science
Background Poll
Name:
Email Address (print clearly):
School/Department:
Program (masters, PhD, postdoc):
Credit or Audit:
For each of the topics in the table, indicate
Your c