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IntMath Newsletter: Putnam, review, Captive, cipher

By Murray Bourne, 12 Dec 2019

12 Dec 2019

0. Season's greetings
1. New on IntMath: Putnam
2. The year in review
3. Math movies: Captive
4. Math puzzle: Cipher
5. Final thought: Imagine

0. Season's greetings

'Tis the season for special days. If you celebrate any of these, enjoy.

Festival 2019/20 date Notes
Bodhi Day 8 Dec, 2 Jan "8th day of the 12th month" - so there's 2 of them
Pancha Ganapati Hindu festival celebrated from 21 through 25 Dec Based on the solstice
Solstice 22 Dec Celebrated in many cultures
Hannukah 22 Dec to 20 Dec Movable. Could be late November to early January.
Christmas 25 Dec "12 Days" finish on 6 Jan
Chinese New Year 25 Jan (new moon) to 8 Feb (full moon) Movable. Could start 21 Jan to 20 Feb

1. New on IntMath: Solving a word problem (Putnam solution)

The William Lowell Putnam Mathematical Competition is held each year in early December. It's aimed at undergraduate students and has quite a reputation. Reader Pat Lachapelle participated in the competition this year and kindly provided a series of guest articles outlining the solution for an earlier competition question.

 See how to go about solving a word problem. Most of the concepts involved are around the grade 9 school level (age 15). There are 7 parts to the solution.

2. The year in review

Thousands of readers have found the following useful or interesting during 2019. In case you missed any of them...

5 Most popular external resources, 2019

1. Mathematical Symbols (by RapidTables)
2. How to Study (MyDegreeGuide)
3. Essence of Calculus (3Blue1Brown)
4. MathGraph (online graphing tool)
5. Breakthrough Junior Challenge (Explain a big scientific idea with a short video.)

6 Most popular blog posts, 2019

I wrote some of these years ago, but they are still popular - and/or causing controversy.

6 Most popular math lessons, 2019

1. Domain and range (Functions and graphs)
2. Convert polar to rectangular interactive (Complex Numbers_
3. Derivative of sine, cosine and tangent (Differentiation)
4. Solving DEs (Differential Equations)
5. Singapore Toto (Counting and probability)
6. Poisson Probabillity Distribution (Counting and Probability)

6 Most popular Tweets, 2019

1. How to overcome fear of math tests
3. The way math is written is (often) silly: Towards more meaningful math notation
4. "Kindness is the language which the deaf can hear and the blind can see." [Mark Twain]
5. "That man is richest whose pleasures are cheapest." [Henry David Thoreau]
6. "Who you become is not about the traits you have. It's what you decide to do with them." [Adam Grant]

3. Math Movie - Device allows users to manipulate 3-D virtual objects more quickly

Here's an approach that could make quite a difference when students are learning about 3-D graphs.

 The device, called CAPTIVE, offers six degrees of freedom (6DoF) for users - with applications ranging from video gaming to medical diagnostics to design tools.

The article includes a video of the process in action. (It's a 2017 article, but nonetheless interesting.)

4. Math puzzles

The puzzle in the last IntMath Newsletter asked whether median or mean would be the best way to describe a typical value.

There were two parts to the puzzle, and correct answers with sufficient explanation were given by Dritan, Danish and Bob (who gets a special mention for pointing out it could be different depending on who the audience for the statistic is!).

A good way to see what's happening in this puzzle is to draw graphs.

Person A "typically" could expect to earn around $90 (the median) per day. Clearly the mean (just over$75) is not "typical" of his earnings, so we would take the median to be the best statistic.

Person A's data

Person B, on the other hand, usually earns around $82 (the mean), not$72 (the median), so in this case, the mean would represent the "typical" earnings.

Person B's data

New math puzzle: Substitution cipher

A popular article at this time of the year is: The 12 Days of Christmas - How many Presents?

This cryptogram also involves 12. What is the value of each letter?

          T W O
T H R E E
+ S E V E N
-----------
T W E L V E

You can leave your responses here.

5. Final thought - Imagine

Next year marks the 40th anniversary of John Lennon's murder.

John Lennon [Image source]

My hope for 2020 is that more of us will get out of our echo chambers, start to listen to each other, and "live life in peace".

Imagine there's no countries

It isn't hard to do
Nothing to kill or die for
And no religion, too

Imagine all the people
Living life in peace

John Lennon, Imagine

All the best to everyone for the holidays, and for 2020.

Until next time, enjoy whatever you learn.

1. ranjith says:

Dear friend,

Throughout the last year I was enjoyed.

Most of the time I couldn't understand everything.

Even-though I was managed to learn many things over the presentations itself.

thanks

wish you all the best

2. Thomas A Buckley says:

0=W, 1=T, 2=E, 3=L, 4=N,
5=V, 6=O, 7=R, 8=S, 9=H

Values for O and N can be swapped. All others the same.
So 4=N and 6=O, or 4=O and 6=N , are both correct.

Worked this out a month ago.
No record, so had to start again.
But may not have posted then, sorry!

Thomas

3. Trevor Down says:

I used a spreadsheet, and trial and error, and came up with
102 + 19633 + 83739 = 103473

4. Lidia says:

Solution to cryptogram.
To start with deduced that T=1 and W=0, then S=8 and H= 9 or vice versa. By trial and error worked on column H + E + E and found that 4 worked well.

Value of each letter: T=1 , W=0 , H=9 , S=8 , R=6 , E=4 , V=5 , L=2 , O=7 and N=3 (or O=3 and N=7)

TWO 107
+ THREE + 19644
SEVEN 84543
TWELVE 104254

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