Archive for the ‘Mathematical’ Category

Mathematical Colors and Codes, Episode Six — Binary Codes and Booktalks

Tuesday, July 28th, 2020

Episode Six of Mathematical Colors and Codes, my Virtual Program Series for the library is up!

Episode Six now looks at the Base Two number system, binary, and puts that into a code. To finish up the series, I talk about more books that play with mathematical ideas.

Like all the other videos in the series, this one has a downloadable coloring page. This one has a chart for a Binary Code.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Codes
Episode Three, Nondecimal Bases
Episode Four, Color Codes with Nondecimal Bases
Episode Five, More Codes with Nondecimal Bases
Episode Six, Binary Codes and Booktalks

Mathematical Colors and Codes, Episode Five — More Codes with Nondecimal Bases

Monday, July 20th, 2020

Episode Five of Mathematical Colors and Codes, my Virtual Program Series for the library is up!

Episode Five looks at more ways you can use nondecimal bases to make coded messages.

This video, like all the others has a downloadable coloring page. This one has charts for a Base Six Code and a Base Five Code.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Codes
Episode Three, Nondecimal Bases
Episode Four, Color Codes with Nondecimal Bases
Episode Five, More Codes with Nondecimal Bases
Episode Six, Binary Codes and Booktalks

Mathematical Colors and Codes, Episode Four — Color Codes with Nondecimal Bases

Tuesday, July 14th, 2020

Episode Four of Mathematical Colors and Codes, my Virtual Program Series for the library is up!

Episode Four now takes the Nondecimal Base systems we talked about in Episode Three and uses them to make

This video, like all the others has a downloadable coloring page. This one has a chart for choosing your own colors and making your own coded messages with nondecimal bases.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Codes
Episode Three, Nondecimal Bases
Episode Four, Color Codes with Nondecimal Bases
Episode Five, More Codes with Nondecimal Bases
Episode Six, Binary Codes and Booktalks

Mathematical Colors and Codes, Episode Three – Nondecimal Bases

Tuesday, July 7th, 2020

Episode Three of Mathematical Colors and Codes, my Virtual Program Series for the library is up!

Episode Three is the longest episode. (They do get shorter!) I talk about various bases and look at them together with prime factorization color charts. I’m hoping it gives kids a feel for how other bases work.

This video, like all the others has a downloadable coloring page. [Right now this is the incorrect link. I’ll fix it with the correct one tonight.] This one will let you see for yourself how prime factorization patterns change in other bases, as well as giving you a feel for how counting works in other bases.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Codes
Episode Three, Nondecimal Bases
Episode Four, Color Codes with Nondecimal Bases
Episode Five, More Codes with Nondecimal Bases
Episode Six, Binary Codes and Booktalks

Mathematical Colors and Codes, Episode Two: Prime Factorization Codes

Thursday, July 2nd, 2020

Episode Two of my Mathematical Virtual Program Series is up!

In Episode Two, I talk more about prime factorization and ways to show it with colors. Then I show how you can use that idea to make a prime factorization code.

This video has a downloadable coloring page to help you make your own prime factorization code.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Codes
Episode Three, Nondecimal Bases
Episode Four, Color Codes with Nondecimal Bases
Episode Five, More Codes with Nondecimal Bases
Episode Six, Binary Codes and Booktalks

Mathematical Colors and Codes

Monday, June 22nd, 2020

My Mathematical Virtual Program Series is up!

This program is a series of six videos with downloadable coloring pages. New videos will post on Mondays at 3 pm.

They will show kids how to use math to make colorful patterns and coded messages, learning about prime factorization and nondecimal bases along the way.

They’ll post on Fairfax County Public Library’s website, but I’ll post them here as well.

These will be best for kids who already understand multiplication.

And this week, Episode One is up! It covers Prime Factorization, with an explanation of my Prime Factorization Sweater. And it explains how you can color your own chart, using this downloadable coloring page.

I hope you enjoy it!

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Code
Episode Three, Nondecimal Bases
Episode Four, Color Codes with Nondecimal Bases
Episode Five, More Codes with Nondecimal Bases
Episode Six, Binary Codes and Booktalks

Review of One Fox: A Counting Book Thriller, by Kate Read

Wednesday, February 5th, 2020

One Fox

A Counting Book Thriller

by Kate Read

Peachtree, 2019. 32 pages.
Starred Review
Review written December 9, 2019, from a library book
2019 Sonderbooks Stand-out: #4 in Picture Books

I always enjoy counting books. Nothing helps a kid learn numbers better. But it’s nice when the book adds a little something to make it more interesting than just the numbers. This “Counting Book Thriller” actually tells an exciting story.

It’s all simple – and will give little ones so much to talk about to tell the adult reader about all the subtext. You can even think of this as a wordless picture book – with numbers, though there are a few words. But the story is in the pictures.

The first numbers are:

One famished fox

Two sly eyes

Three plump hens

Four padding paws

Five snug eggs

Oh, but the pictures! There’s nothing routine about them.

I’m going to save this book for a preschool storytime. You want the kids to be interested in the counting and also be able to infer what the famished fox wants with those plump hens.

There is a surprise ending, and a note at the book reassures us: “No hens or foxes were harmed in the making of this book.”

kateread.co.uk
peachtree-online.com

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Picture_Books/one_fox.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Disclaimer: I am a professional librarian, but I maintain my website and blogs on my own time. The views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

What did you think of this book?

Review of How Many? by Christopher Danielson

Wednesday, January 29th, 2020

How Many?

A Different Kind of Counting Book

by Christopher Danielson

2019, Charlesbridge. First published in 2018 by Stenhouse Publishers. 39 pages.
Starred Review
2019 Sonderbooks Stand-out: #2 in Children’s Nonfiction Picture Books

I already loved Christopher Danielson’s earlier book, Which One Doesn’t Belong? It came to my attention when it won a Mathical Book Prize. Now Charlesbridge has taken on his books to hopefully reach a wider audience.

Here’s how the book explains that it is different from other counting books:

This book doesn’t tell you what to count.

It doesn’t start with small numbers and end with big ones.

Instead you decide what to count on each page. You have many choices.

The longer you look, the more possibilities you notice.

And that’s what you get. The illustrations are photographs. The pictures show things like an apple being cored and two shoes in a shoebox. The text asks, “How many do you see?”

After that first picture, the narrator says:

If you thought, “how many what do I see?” then you get the idea.

It does give examples of things you can count: shoes, pairs of shoes, shoelaces, holes for the laces, yellow stitches. And it asks, “What other things can you count?”

The pictures get interesting in different ways. There’s a picture of an egg carton with one egg in it. There’s a picture of eggs frying, one of which has a double yolk. The eggshells are by the stove, and the eggs that were not used are still in the carton next to the stove.

In other pictures, some fruit gets cut in half. We’ve got pictures of pizza, and then pizza in slices. Pictures toward the end show kitchen scenes with many of the things we already looked at – including shoes on the floor.

Questions at the back give you ways to extend the ideas. I do love that there are no answers anywhere in this book.

This is a wonderful book for curious children! It builds sophisticated mathematical ideas into preschool and early elementary school children. Anyone who has learned to count will have something to think about with this book.

As the author says at the end, “When you count carefully and clearly state what you’re counting, you’re doing some great math!”

talkingmathwithkids.com
charlesbridge.com
Stenhouse.com

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/how_many.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on my own copy, purchased via Amazon.com.

Disclaimer: I am a professional librarian, but I maintain my website and blogs on my own time. The views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

What did you think of this book?

Baby Martin’s Normal Distribution Blanket

Saturday, January 11th, 2020

I finished a Normal Distribution Blanket for my new little nephew, Martin!

This is the same idea I used to make a blanket for my little niece Kara, but that one was in shades of pink.

Unfortunately, I didn’t get to try the blanket out on Martin in person, but I gave the blanket to my brother, his Daddy, to give to Martin.

Here’s the method. The blanket is simply a series of entrelac squares (diamonds). I knit one row of squares in one direction, then pick up stitches along an edge to make another row of squares in the other direction, and knit back and forth, with squares in between the squares of the previous row. The nice thing about it is that each square is knitted completely before you move on to the next square, so you don’t have to carry different yarns across the row.

I used Tahki’s Cotton Classic yarn because they have many, many shades, and I already had some spare yarn from previous projects — Cotton Classic is my go-to yarn for mathematical knitting projects. All those shades!

Choosing the shade of the yarn for each square is where the normal distribution math comes in.

I simply generated a list of random numbers from the normal distribution (using google to find a random number generator). The normal distribution is a bell-shaped curve, so I’ll get more numbers in the middle of the distribution.

I took five shades of purple and labeled them A through E. For numbers in the middle, I used lighter colors, and got gradually darker as the numbers went out from the middle. For numbers that were outliers, I added a sparkly silver yarn to color E — because it’s the outliers that make life beautiful. And aren’t we all outliers in some way?

Here’s the specific math for those who care or who want to reproduce the method:

I set the middle of the distribution as zero, with a standard deviation of one. For positive numbers, I did a garter stitch square, and for negative numbers I did a seed stitch square.

Here’s how I assigned the colors:
Color A: Absolute values between 0 and 0.5
Color B: Absolute values between 0.5 and 1.0
Color C: Absolute values between 1.0 and 1.5
Color D: Absolute values between 1.5 and 2.0
Color E (with sparkles!): Absolute values greater than 2.0

Now, I didn’t have a perfect progression from light to dark. Color D was the reddish purple. And it’s not obvious in the photo that E was definitely much darker than Color C. Making D the reddish purple seemed to get the weight of the colors to progress better. I should have done a close-up of the sparkles, but didn’t think of it this time.

One thing I like about visualizing a normal distribution this way is you get a more visceral feel for how the colors are distributed than just looking at the curve. There are almost as many B-colored squares as A squares — and there really are a lot of outliers. (It might be a better representation if I had gone out one more level and used six colors. But this worked.)

I’ve also done scarves this way (with stripes) and of course the pink blanket. And it always comes out pleasing to the eye. The normal distribution really is the way so much of nature is arranged.

You can find links to explanations of all my mathematical knitting at sonderbooks.com/sonderknitting!

Review of Prime Suspects, by Andrew Granville & Jennifer Granville, illustrated by Robert J. Lewis

Saturday, November 9th, 2019

Prime Suspects

The Anatomy of Integers and Permutations

by Andrew Granville & Jennifer Granville
illustrated by Robert J. Lewis

Princeton University Press, 2019. 230 pages.
Starred Review
Review written 9/19/19 from a library book

Okay, now I’ve seen everything! This is a graphic novel murder mystery about research mathematics!

The characters have names that play off of the names of distinguished mathematicians. The lead detective uses ideas from his namesake.

The most interesting part is that when the detective team goes to the autopsy of recent victim Arnie Int, lieutenant of the Integer Crime Family, they found everything inside his body has decomposed – except for prime numbers! The apprentice detective pulls a bloody number out of his body and says, “It’s a prime, sir!”

They find the body is similar to a previous victim, Daisy Permutation. I like the scene where the detectives discuss it while playing billiards:

“It’s not a similarity, but in both victims, the internal organs were completely decomposed.
Except that in Arnie Int there was a smattering of primes, and in Daisy permutation, a smattering of cycles.”

“But that’s only to be expected.
Cycles are the fundamental constituent parts of a permutation, just like primes are the fundamental constituent parts of an integer.”

And it’s all done in a dark style, with some clueless videographers to explain things to, and mathematical puns in the background.

The math itself – where they compare the set of integers to the set of permutations – went over my head, and I’ve got a Master’s in Math. I read the back matter where it’s explained, and it still went over my head – though I at least understood what basic concepts were at work. And I did, after reading, understand at least that cycles are the building blocks of permutations as primes are the building blocks of integers.

And I’m still tickled to death that someone made a graphic novel thriller about higher math.

There are fun ads on the inside cover, such as: “Are you looking to get away from it all? Why not come and stay at Hilbert’s fabulous “Infinite Hotel”? There is ALWAYS room for as many guests as want to stay.” And: “RIEMANN’S ROOTS: We’ll plant your organic roots in straight rows. Guaranteed to have at least 41.69% of the roots in a straight line!” And: “Fermat’s Dreams: Truly remarkable ideas for the future which this inside cover is too small to contain!”

The back matter takes up 50 large pages, so it takes as long to read as the 180 pages of the graphic novel part. Yes, it includes the math, but also you’ve got notes on the mathematicians referred to, notes about the references in the art, and an explanation of how the book came to be – beginning as a screenplay (which has been performed in live readings).

Here’s the beginning of that section:

Integers and permutations are fundamental mathematical objects that inhabit quite distinct worlds though, under more sophisticated examination, one cannot help but be struck by the extraordinary similarities between their anatomies. This comic book stemmed from an experiment to present these similarities to a wider audience in the form of a dramatic narrative. In these after-pages, we will clarify some of the mathematical ideas alluded to in the comic book, giving the details of Gauss’s lectures and Langer’s presentation at the police precinct. We will also break down the content of some of the background artwork, explaining how some of it refers to breakthroughs in this area of mathematics, some of it to other vaguely relevant mathematics, while some content is simply our attempt at mathematical humor.

Our goal in Prime Suspects has been not only to popularize the fascinating and extraordinary similarities between the fine details of the structure of integers and of permutations, but also to draw attention to several key cultural issues in mathematics:

— How research is done, particularly the roles of student and adviser;
— The role of women in mathematics today; and
— The influence and conflict of deep and rigid abstraction.

I’m not sure everyone will love this book, but I sure do! Sure to be all the rage in graduate wings of math departments across the nation!

press.princeton.edu

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Fiction/prime_suspects.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Disclaimer: I am a professional librarian, but I maintain my website and blogs on my own time. The views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

What did you think of this book?