We aim to encourage and support women in the specific discipline of mathematics. In particular, we would like to bring together women undergraduates, graduates and members of faculty in the mathematics department, to provide mutual support and to increase the visibility of women in mathematics. Some planned activities of our organization include having speakers, either from the U of C community or elsewhere, to discuss issues relating to women in math, running a mentoring program for women in math, and providing online resources for women in math.
Divvying up tasks between the left and right hemispheres of the brain is one of the hallmarks of typical brain development. The left hemisphere, for instance, is involved in analyzing specific details of a situation, while the right hemisphere is more important for integrating all the various streams of information coming into the brain. A new study by neuropsychologists at San Diego State University suggests that in children and adolescents with autism spectrum disorder (ASD), the brains’ hemispheres are less likely to specialize one way or another. The finding gives further insight into how brain development in people with ASD contributes to the disorder’s cognitive characteristics.
The Development of Correlation and Association in Statistics Jake D. Brutlag fifth revision 12/15/07 The object of statistical science is to discover methods of condensing information concerning large groups of allied facts into brief and compendious expressions suitable for discussion --Sir Francis Galton (1822-1911) One historical motivation for the field of statistics was to capture the meaning of data in "brief and compendious expressions." It is one thing to glance at a table of numbers and claim "I see some meaning here"; it is quite another to demonstrate such a table constitutes evidence for a particular conclusion. In the study of two random variables measured in the same sample, correlation measures the degree to which the two measures are linearly related. A related concept is the regression model, in which the goal is to find a linear equation that best predicts the value of one variable (or measurement), given the value of the other variable. The best estimate of the slope in the regression model, y = b(x) + a, is related to the correlation coefficient, r, by:
The most common question students have about mathematics is “when will I ever use this?” Many math teachers
would probably struggle to give a coherent answer, beyond being very good at following precise directions. They
will say “critical thinking” but not much else concrete. Meanwhile, the same teachers must, with a straight face, tell
their students that the derivative of arccosine is important. (It goes beyond calculus, in case you were wondering)
So here is my list. The concrete, unambiguous skills that students of mathematics, when properly taught, will
practice and that will come in handy in their lives outside of mathematics. Some of these are technical, the
techniques that mathematicians use every day to reason about complex, multi-faceted problems. Others are
social, the kinds of emotional intelligence one needs to succeed in a field where you spend almost all of your time
understanding nothing. All of them are studied in their purest form in mathematics. The ones I came up with are,
Coming up with counterexamples
Being wrong often and admitting it
Evaluating many possible consequences of a claim
Teasing apart the assumptions underlying an argument
Scaling the ladder of abstraction
Let p(x) = a0 + a1x + a2x2 + … + anxn and suppose at least one of the coefficients ai is irrational for some i ≥ 1. Then a theorem by Weyl says that the fractional parts of p(n) are equidistributed as n varies over the integers. That is, the proportion of values that land in some interval is equal to the length of that interval. Clearly it’s necessary that one of the coefficients be irrational. What may be surprising is that it is sufficient. If the coefficients are all rational with common denominator N, then the sequence would only contain multiples of 1/N. The interval [1/3N, 2/3N], for example, would never get a sample. If a0 were irrational but the rest of the coefficients were rational, we’d have the same situation, simply shifted by a0. This is a theorem about what happens in the limit, but we can look at what happens for some large but finite set of terms. And we can use a χ2 test to see how evenly our sequence is compared to what one would expect from a random sequence.