Critical Math

Sometimes I think about basic ideas in mathematics that that the general public would greatly benefit from. In particular, I think that mathematicians often take for granted that these things are natural to us, and that to most people it’s almost like having a super power. Please augment this list!
1. Computing how long it will take to pay off a balance on a credit card, with interest.
2. How to balance a checkbook.
3. The concept of instantaneous rate of change vs. average rate of change.
4. Basic laws of probability.
5. How to add and multiply fractions, and compare fractions (as in, is 5/9 larger than 9/45)?
6. Basic logical reasoning, in particular understanding “if-then” statements, and converse/contrapositives of such statements.
Good luck with the rest of your semester, and have a great holiday break!
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Contemplative education; math and meditation

“The faculty of voluntarily bringing back a wandering attention, over and over again, is the very root of judgment, character, and will. . . An education which should improve this faculty would be the education par excellence.” 

-William James, 1890

The ability to focus and refocus attention is obviously extremely important for a mathematician working on research, or a student learning in class.  There is a growing body of scientific evidence showing that meditation can improve this ability.  In fact, there is a range of different meditation techniques, with a range of potential benefits: e.g. increased focus, mindfulness, curiosity and creativity; better control of emotions, and stress reduction; improved interpersonal communication.  Sounds great, right?

In the last few decades, empirical evidence has been piling up, supporting the millenia-old subjective claims of meditators.  An incomplete but good research bibliography is maintained here; see also here or hereContinue reading

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Upcoming Breaks

It is becoming increasingly obvious that breaks from school is no longer a time to get some R&R. I will spend this Thanksgiving break with my parents and also working on my thesis. I just need to keep in mind, “I must write! I must write! I must write!”

Over Christmas break I will continue writing, but I will also begin studying for comprehensive exams. Today we set a date for when everyone will be taking their comps. We decided it will be the first and second week of classes starting back in January. Thankfully my university has a long winter break and we do not start back until LATE January. This should give me plenty of time to study. Does anyone have any advice on studying for comps (algebra, statistics, and probability)?

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Grad Blog on Twitter

AMSBlogTwitterWe are now on Twitter. Make sure you follow us, @AMSGradBlog.

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Sudoku

Web SudokuAs many of you may know, Sudoku is a logic-based, combinatorial number-placement puzzle.  I recently found an online database of Sudoku puzzles at http://www.websudoku.com/.

Sudoku has a great deal of math involved in it. If you are interested in reading about the mathematics behind Sudoku, you might want to check out Taking Sudoku Seriously: The Math Behind the World’s Most Popular Pencil Puzzle by Jason Rosenhouse and Laura Taalman. I have not yet read the book myself, but have heard great reviews on it. Let me know what you think about it if you have read it.

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