thnik again!

Obstructing the teachers causes delay and can be dangerous. – Jan Nordgreen

Ice cream cones come in three cone types: plain, sugar, and waffle, and in fourteen flavours: vanilla, chocolate, rocky road, mint chocolate chip, strawberry, pralines and cream, bubble gum, butter pecan, mud pie, peanut butter crunch, almond fudge, coffee, chocolate chip, and banana royale.

You want to buy a two-scoop cone. How many are there to choose from?

Warning: only 16% of the submitted answers were correct (297 out of 1841) when it was presented as Problem of the Week at Columbus State University.

It’s all right letting yourself go as long as you can let yourself back. – Mick Jagger

Find four consecutive natural numbers. When you have found them, ask them to be quiet so you can multiply them. If the answer is a square number, jump up and down in joy.

Problem source: Wisconsin Mathematics Science & Engineering Talent Search.

Like I always say, there’s no ‘I’ in “team”. There is a ‘me’, though, if you jumble it up. – David Shore

If the solid lines mean multiply and the dotted ones means add, can you add numbers in the empty circles? How do you do it?

Problem source: The Number Warrior. The diagram is borrowed from the same source.

Most people ignore most poetry / because / most poetry ignores most people. – Adrian Mitchell

- What are you reading?
- You will like this. The author says the soft maximum of 1 and 2 is 2.31.
- Is he still loose or in an asylum?
- I think he is an assistant professor.
- Why will you never answer my questions?
- On the other hand, the soft maximum of 10 and 20 is 20.000005.
- That is better, but every kid under 5 knows the answer is 20.
- You need to work on your listening skills. The maximum, what the author calls the hard maximum is 20, but the soft maximum is 20.000005.
- What is soft maximum? I thought it was the bigger number of the two.
- The soft maximum of two numbers a and b is sm(a,b) =  ln(e^a + e^b).
- You mean the natural logarithm and its inverse function? I thought this blog could be read by anyone!?

- Another definition is sm(a,b,k) = ln(e^(ka) + e^(kb))/k.
- Light, can we have some light please!?
- sm(1,2,1) = 2.31 while sm(1,2,10) =  20.000005.
- So when k increases the soft maximum approaches the hard maximum?
- That’s today’s question.

Problem source: The blog of John D Cook.

Money doesn’t always bring happiness. People with ten million dollars are no happier than people with nine million dollars. – Hobart Brown

… there are programs that can perform mathematics at the symbolic level, and some of them are free. This fact leads to an objection, heard with increasing frequency, that people will use programs like Maxima to avoid learning anything about mathematics at all, instead depending on symbolic math software to conceal their ignorance.  - More

“Determine which of (x – 3), (x – 1), (x + 2) are factors of P(x) = 2x^3 + 7x^2 + 7x + 2, and hence factorise P(x) completely.”

This was the first question on a recent test I gave. The students could have asked Maxima:

(%i1) factor (2*x^3 + 7*x^2 + 7*x + 2);

(%o1)                      (x + 1) (x + 2) (2 x + 1)

or asked the web site  QuickMath which uses WebMathematica:

http://www.calc101.com/ is a similar site.

Most of the problems we deal with in class can be instantly solved by free symbolic math software. So why don’t we allow the students access? Why do we insist they should learn what machines are far better at than humans and instead use the time to what the machines are poor at, namely problem discovery and problem solving?

There is a risk that we will use math software to become intellectually lazy. But the possibility exists that, in partnership with computer math software, people will learn much more about mathematics than they would be likely to do while using the older methods. Because we have computers to perform low-level computations, we can spend our time acquiring mathematical knowledge at a higher level. - More

I believe several universities now allow this kind of software, but at the pre-university level it is unheard of. At IB there is even an exam where calculators are banned. I fail to grasp why.