Dear friends,

this is to share with you what a joy it was to work with Maple on the problem of enumerating non-isomorphic graphs. This problem goes back to Polya and Harary and it is a beautiful example of Polya counting, while also being of notable simplicity, so that a high school student or an undergraduate can follow it easily.

I have worked on this problem over the years, adapting my solutions in Cocoa and Lisp as I gained insights. My first attempt used...

The Maple dsolver is very powerful, but everything has advantages and disadvantages. I was recently asked the following question.
Let us consider the system of ODEs
>restart; sys := [diff(y(x), x) = -(4*cos(x)*y(x)+z(x)*cos(x)^2+3*z(x))/(sin(x)*(cos(x)^2-9)),
>diff(z(x), x) = -(y(x)*cos(x)^2+3*y(x)+4*z(x)*cos(x))/(sin(x)*(cos(x)^2-9))]:
The functions
>y1 := C[1]*(cos(x)+1)^(1/2)/(cos(x)+3)^(1/2)+C[2]*(1-cos(x))^(1/2)/(3-cos(x))^(1/2):
>z1 := -C[1...

Clock:=proc(H, M)  # H and M - time in hours (0 <= H <= 23) and minutes (0<=M<60)

local A1,A2, A, B, B1, C1, C, E, F,alpha,t, T, T1, T2, P, G;

uses plottools, plots; 

A1:=(irem(H,12)+M/60)*30;  A2:=M*6;

A:=circle([0,0], thickness=5);

P:=disk([0,0], 1, color=grey);

Here are two procedures associated with a clock with hands. I think they are interesting not only for fun, but will be useful for teachers in schools in the preparation of such tasks.

The first procedure called  ClockHandsAngle  finds the angle between the hands of the clock at any time.

The second procedure called  TimeFromAngle , for a given angle finds all times in a given time range. The first procedure  is...

    A powerful approach to the teaching and learning of mathematics for students of science and engineering has been made practical through the development of powerful general mathematical software, of which Maple provides the least steep learning curve.  Accordingly, it is timely to produce an interactive electronic textbook that, for students of chemistry -- also biochemistry and chemical engineering, has as its objective in part I,
Mathematics for...

Fridays Killer Questions 7city Learning:

Question) The number sequence is: 2 1 3 6 5 11 18 17 which number should come after 17?
Answer) 35

Fridays Killer Questions 7city Learning:

Question) You're the captain of a pirate ship and your crew gets to vote on how the gold is divided up. If fewer than half of the pirates agree with you, you die. How do you recommend apportioning the gold in such a way that you get a good share of the booty, but still survive?

Answer) You divide the booty evenly between the top 51% of the crew.

Fridays Killer Questions 7city Learning:

Question) Calculate the number of degrees between the hour hand and the minute hand of a clock (non digital) that reads 3:15.

Answer) The minute hand will be horizontal and the hour hand will also almost be horizontal but it will have moved ¼ of an hour 12 hours=360 degrees, 6 hours = 180 degrees, 3 hours =90 degrees, 1 hour = 30 degrees, ¼ of an hour=7.5 degrees

Fridays Killer Questions 7city Learning:

Question) You have two containers, one holds five gallons, the other holds three. You can have as much water as you want. Measure exactly four gallons of water into the five gallon container.

Answer) Fill up the three-gallon container and pour it into the five-gallon container. Do it again – there will be one gallon left in the three-gallon container. Empty the five, pour in the one,...

Fridays Killer Questions 7city Learning:

Question) You have 100 kg of berries. 99% of the weight of berries is water. Time passes and some amount of water evaporates, so our berries are now 98% water. What is the weight of berries now?

Answer) The unexpected, yet correct, answer is 50 kg. It seems like a tiny amount of water has evaporated so how can the weight have changed that much? There is clearly 1 kg of solid matter in the...

Fridays Killer Questions 7city Learning:

Question) There are eight balls, one of which is slightly heavier than the others. You have a two-armed scale, which you are allowed to use only twice. Find the ball that’s heavier.

Answer) Put three balls on each side of the scale. If the arms are equal, you know the heavy ball is one of the two remaining. If the arms are unequal, take the three balls on the heavier side, pick two and weigh them against each other.

Fridays Killer Questions 7city Learning:

Question)  You’re trying to get to Truthtown. You come to a fork in the road. One road leads to Truthtown (where everyone tells the truth), the other to Liartown (where everyone lies). At the fork in the road is a man from one of those towns -- but which one? You get to ask him one question to discover the way. What’s the question?

Daniel Kahneman - Thinking Fast and Slow

1) A bat and ball cost $1.10.
2) The bat costs one dollar more than the ball.
3) How much does the ball cost?

x+y=1.1; x=cost of the bat, y=cost of the ball.
y=x+1; substituting for y
x+(x+1)=1.1;
2x=0.1;
x=0.05; the cost of the ball
y=1.05; the cost of the bat

The right answer is 5 cents.
The intuitive, appealing, and wrong number is, of course 10 cents.

dicing-with-death-chance-risk-and-health (Stephen Senn)

Mr Brown has exactly two children. At least one of them is a boy. What is the probability
that the other is a girl?

What could be simpler than that? After all, the other child either is or is not a girl.
I regularly use this example on the statistics courses I give to life scientistsworking
in the pharmaceutical industry. They all agree that the probability is one-half.

So they are all...

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