Category Archives: Math Explorations

I work out a problem or propose a new solution method.

Changing the Limits of Integration

It is possible to change the limits of a definite integral to any limits you want by using a linear u-substitution.  To go from the integral from a to b to the integral from a’ to b’, use a u-substitution of u = mx + … Continue reading

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Machine Learning – So, Explain Yourself

We humans are not giving up without a fight. Though computers are clearly outthinking us, see AlphaGo for example, we aren’t listening.  Cynthia Rudin, my latest hero, describes the issue in this video. Humans need reasons. In the paper, A … Continue reading

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An Optimization Excursion

A student, Emily Wimmer, walked into my office.  She was trying to make sense of an optimization algorithm.  We worked it out and off she went to write a MATLAB program to test the algorithm on a well-behaved function. Of … Continue reading

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Rubrics as Data – Part IV

Rubric data is ordered categorical data and, as such, can not be used to find averages or other numerical statistics.  See this post for details.  And yet, our (my) instincts are that measures of human behavior must lie on some … Continue reading

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Rubrics as Data – Part III

It has been a long time since I have addressed this topic.  I was going to add, “for good reason.”  Is utter discouragement and temporarily quitting a good reason?  Anyway here is the saga. I first worked my way steadily … Continue reading

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Slide and Divide

One of our student tutors sent me this link, Slide and Divide , to a method of factoring trinomials.  It is essentially the one I explained extensively in https://jrh794.wordpress.com/2011/12/20/the-best-way-to-factor-trinomials/   I just argue to keep the fractions in the factored form since it is … Continue reading

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This Is What “Power = .006” Looks Like.

My current screen saver is this graphic: I found it on Andrew Gelman’s blog here.  The red areas are based on an alpha (probability of rejecting a null hypothesis) of 0.05.  A recent paper (preprint) endorsed/authored by a fat paragraph of … Continue reading

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