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Math at Work Monday: Mary Helen the History Museum Curator

I’ve known Mary Helen Dellinger my whole life. That’s because she’s my cousin, born a whole two months before I was (a fact she never let me forget when we were kids). Growing up in Virginia as we both did, it was darned near impossible to avoid a history lesson at every turn. And while I never really caught the bug, Mary Helen got it bad.

She’s been a history museum curator for 22 years now, the last year in a new position as curator for the City of Manassas Museum System, where she has overseen exhibits that include photographs of the Civil War and a collection that features a rare, surviving “John Brown Pike,” or spear, with which abolitionist Brown had intended to arm sympathizers in an aborted raid at Harper’s Ferry.

Yeah, this is cool stuff. And much to Mary Helen’s chagrin, her job includes quite a bit of math. She’s not shy about expressing her disdain for the Queen of Sciences, but like most grownups, she has learned to get along just fine.

Can you explain what you do for a living? 

There are two major aspects to my with the Manassas Museum System. First, I am in charge of maintaining the Museum’s collection of objects. This includes meeting with prospective donors and accepting new donations for the collection, making sure the collection is properly stored and that a proper environment is maintained at all times (stable temperature and humidity at acceptable levels), and that adequate security is always in place. There is a lot of paperwork that goes along with this – Deed of Gift forms for donors, thank you letters, conservation reports, tax forms for those objects that are really valuable. Everything has to be photographed and entered into the Museum’s collection database. The entire collection numbers over 10,000 pieces – most of it in off site storage. Much of the work I described above is backlogged from the past eight years, so there is always something to keep me busy.

The second aspect of my job is running the Museum’s exhibition program. Exhibit schedules are usually created 2-3 years out. So right now, I am scheduling shows for 2015. For exhibits that we do “in-house” I select objects from our collection and negotiate loans from private collectors and other museums. I also have to write labels, work with exhibit designers and (if necessary) conservators, and do things like select paint colors, make object mounts, etc. – basically come up with the look and feel of the gallery space. The final step in all of this is the installation process – which is the most fun of all.  It’s a very creative process and neat to see it all come together in the end. On occasion, I will rent a traveling exhibition that was put together by another museum. When I do that, it is just a matter of unpacking it and installing it.

When do you use basic math in your job? (And what kind of math is it?) If you can offer a very specific situation when math is important, that would be great.

Math is very important when creating any exhibition. First, I have to keep in mind what the square footage is in the gallery, and how much space the objects in the exhibits will take up. This includes spaces on the floor, inside cases, and on the walls. Large objects take up lots of floor space but also cover the wall space behind them. Cases have to hold the objects AND the labels. Framed pieces go on the walls. My design must include measurements of all the major components that include height, width and depth. This allows me to make sure everything will fit and yet allow space for visitors to move through the exhibit. During the design process we are constantly measuring, re-measuring and moving things around to get the most out of the space. For complicated exhibits we use floor plans and sketch in everything including measurements to help us understand the relationships between the pieces and if we are leaving enough space. You don’t want to get to installation and realize you don’t have enough room for a key piece of the exhibit. There is some geometry involved here (understanding angles and lines) but most of it is basic addition, subtraction, etc.

Secondly, each exhibit has an individual budget that I am responsible for creating at the outset of the project. I have to include designer time, materials, the cost of creating graphics, prepping the gallery space, etc. Each budget has a contingency built in for those unexpected things that inevitably crop up. I have to carefully track expenses to make sure I don’t overrun my budget.

In addition to the exhibitions, I am in charge of the annual budget for my part of the department. In fact, we are in the middle of creating the budget for FY 2014 right now. Using last years’ budget as a base, I have to project (using the aforementioned two-year exhibition schedule) how much money I am going to need in the next fiscal year. This requires me to know how much contractors charge per hour and how many hours I am going to need them, the cost of supplies, shipping schedules, etc. The math used here is addition/subtraction/multiplication/division – but it can be complicated because you are working with a lot of assumptions.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

I use calculators when doing the budget. For exhibit design, we use basic rulers and calculators. Nothing fancy.

How do you think math helps you do your job better?

Math enables me to design exhibits that are affordable, and work within the spaces that we have.

How comfortable with math do you feel? Does this math feel different to you? (In other words, is it easier to do this math at work or do you feel relatively comfortable with math all the time?)

I have NEVER been comfortable with math, not even today, 22 years into my career. Budgets, especially, make me nervous because if we don’t get it right, that will impact future expenditures and our ability to do other projects. So while the math I use in my job is familiar to me, because it is something I do every day, I don’t think I will ever be comfortable with it.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

In high school I took Algebra I and II (barely passing both) and Geometry (did okay in this). I absolutely hated math, and only took it because I had to. Despite my best efforts, going to all the extra tutorials, studying every night, etc. I never could get it. The abstract concepts were not something I could ever wrap my mind around. Put me in a history class with definable dates, facts, and people to learn about and I was fine. I never had to “show my work” in history.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pick up using the skills you learned in school?

The math skills I learned in elementary/high school are enough for me to do my job. I have not had to learn anything new.

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In Math for Teachers

The Mother of All Scientific Computing

Ada Lovelace was probably bound for greatness. The product of the brief marriage between Lord Byron (yes, that Lord Byron) and Anne Isabella (“Annabella”) Milbanke, she was born in 1815. But in true Romantic tragedy, her parents separated soon after her birth , and she never knew her father. Her mother, whom Lord Byron called “the Princess of Parallelograms,” was pretty quick with the calculations, and so Lovelace got a good education in math and science. This approach also served to protect Lovelace from the fiery passions of poetry (according to her prudish mother).

Seems Ada got the best of both parents. At age 13, she developed a design for a flying machine — quite a feat in 1828, a full 85 years before and an ocean away from the Wright Brothers at Kitty Hawk. But over time, her approach to mathematics was decidedly verbal. She called herself the poetic scientist, and her writings were imaginative and described in metaphors.

When she was 17 years old, Lovelace met Mary Somerville, the self-taught mathematician and scientist. The two became fast friends, attending lectures, demonstrations and concerts together. And it was Somerville who introduced Lovelace to the man who would help cement her name in history.

Charles Babbage was the inventor of the Difference Engine, a rudimentary calculator that wasn’t built until more than 100 years after his death. He and Lovelace met in 1834, when he was working out the design of his next invention, the Analytic Engine.

Unlike his Difference Engine, this new design was programmable, an idea that completely enthralled Lovelace. She and Babbage became good friends and colleagues, and in 1843, Babbage asked Lovelace to translate into English a French summary of a presentation he gave describing the Analytic Engine. And by the way, could she also expand upon the ideas, since she was so familiar with the design?

What Lovelace wrote was nothing less than prescient:

The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.

(I said she wrote in metaphors!)

Again Babbage’s machine was not built in his lifetime, but the design — featuring punch cards of the early mechanical computers — is still acknowledged as the precursor to the modern-day computer. And Lovelace is considered the first computer programmer because of what she suggested the machine could do: compute the Bernoulli numbers.

What the heck are they? Well, first off, Bernoulli numbers are a pretty big deal in number theory and analysis. Basically, they’re a sequence (or list) of rational numbers (or decimals that either repeat or terminate). These numbers show up in a variety of places that won’t matter to you. The important thing here is that they are darned difficult to compute. In the 19th century, folks who needed them typically depended on tables that listed these numbers. But Lovelace developed a program that would generate them automatically.

Thus, the first computer program program was born.

Unfortunately for all of us, Lovelace would never see her invention realized. She died of cancer in 1852, before publishing anything more. Still, her contribution is so great that computer geeks around the world still revere her. In 1977, the Department of Defense named its high-level computer programming language Ada. Heck, the IT guy at my last regular job named his first daughter Ada.

I wonder what Lord Byron would have written about his daughter, the poetic scientist?

Had you heard of Ada Lovelace? What do you think Lord Byron would have thought of her contributions? Share your feedback below.

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In Math for Teachers

The Cult That Changed Geometry

While the development of numbers continued for many, many centuries, even before the discovery or invention of zero, the Greeks were responsible for a long, long period filled with mathematical advances. By 600 B.C., a fellow named Thales of Miletus brought Babylonian mathematical discoveries to Greece, which were used to calculate distance and other measurements.

But the big player in Greece was Pythagoras. (Yes, you should recognize that name.) Born in 580 B.C. in Samos, he met old-man Thales when he was but a young lad. Perhaps Thales convinced him to travel to Egypt so that he could learn the mathematics of the Babylonians. At any rate, when Pythagoras returned from his journey, he settled in Croton (which is on the eastern coast of Italy) and this is where things get strange — at least by our modern standards.

Pythagoras established a philosophical and religious school that was made up of two societies: the akousmatikoi (hearers) and mathematikoi (learned). And while his followers look much like a cult to us, Pythagoras was in fact developing the world’s first intentional, philosophical society. Members — both men and women — were intent on living a contemplative and theoretical life, and as such divorced themselves from the culture at large, becoming completely devoted to philosophical and mathematical discovery.

But in order to do this, they had to follow a very strict set of rules, which included vegetarianism, giving up all personal possessions and absolute secrecy. And then there are the really strange orders: do not pick up something that has fallen; do not touch a white rooster; do not look in a mirror beside the light.

That’s not all. Mysticism infused almost all the Pythagoreans did, which led to some really off-the-wall mathematical ideas, like their understanding of numbers.

  1. Nothing exists without a center, and so the circle is considered the parent of all other shapes. It was called the monad or “The First, The Essence, The Foundation, and Unity” — or according to Pythagoras, “god and the good.”
  2. The dyad was a line segment and considered to be the “door between One and Many.” It was described as audacity and anguish, illustrating the tension between the monad and something even larger.
  3. And then there’s the triad, which of course represents the number 3. Continuing in their pseudo-anthropomorphism of numbers, the triad is considered the first born, with characteristics like wisdom, peace and harmony.

I could go on. Seriously. But while the ideas of the Pythagoreans were kind of kooky, this band of deep-thinking brothers and sisters advanced mathematics in some pretty significant ways. First of all, they began classifying numbers as even and odd, prime and composite, triangular, square, perfect and irrational. Through their strange ideas of numbers, they popularized geometric constructions. They are also attributed with the discovery of the five regular solids (tetrahedron, hexahedron, octahedron, iscosahedron and dodecahedron).

But their biggest discovery is the theorem named for Pythagoras. The Pythagorean Theorem states that the in a right triangle, the square of the longest side is equal to the sum of the squares of the remaining two sides. In other words:

This is more than just a silly formula you needed to memorize in high school. Carpenters use it to be sure that they have right angles (in other words that their door frames, decks, and walls are “square”). It’s useful to find the diagonal of a television set (which is how those contraptions are measured for some reason), if you only know its length and width. And it’s the basis of a great deal of additional math discovery, like the distance formula and various area formulas.

It’s a big, honkin’ deal. And in some ways, we’re lucky it survived the secrecy of the Pythagoreans. Pythagoras wrote nothing down. (If tin foil had been invented, he might have been wearing a hat of the stuff.) But despite its closed society, this cult of nutty mathematicians and philosophers is considered one of the most important influences in all of history.

What do you remember of Pythagoras from your high school geometry class? Have you used the Pythagorean theorem in your everyday or work life? If so, how?

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In Math for Teachers

The Number that Changed the World: History of numbers, part 3

Things were moving right along in the invention and use of number systems. The Sumerians started things off sometime during the 3rd millenium, when their budding commerce system helped them invent the first set of written numbers. The Egyptians systematically engineered a formal base-ten system that morphed from hieroglyphics to the much-easier-to-write hieratic numbers.

But something was missing. Something really important — and really, really small.

The Greeks advanced geometry considerably. (More on that next week.) But in the Roman Empire, mathematical invention and discovery virtually stopped — with the exception of Roman numerals. These were widely used throughout Europe in the 1st millenium, but like the number systems that came before, it was positional and did not use place value.

But why weren’t these systems using place value? It all comes down to zero. Up to this point, this seemingly inconsequential number was absent.

There is some debate about this, of course. Some historians assert that sometime around 350 B.C. Babylonian scribes used a modified symbol to represent zero, which astronomers found useful to use this placeholder in their notations. And on the other side of the world, the Mayans used a symbol for zero in their “Long Count” calendar. But there is no evidence that zero was used for calculations.

Along came the Indian mathematician and astronomer, Brahmagupta, who was the first person in recorded history to use a symbol for zero in calculations. But India’s relationship with zero started well before that.

In ancient and medieval India, mathematical works were composed in Sanskrit, which were easily memorized because they were written in verse. (I am not kidding.) These beautiful sutras were passed down orally and in written form through the centuries. Thus the idea of zero — or śūnya (void), kah (sky), ākāśa (space) and bindu (dot) — was first introduced with words. Eventually, an actual dot or open circle replaced these words, as Indians began using symbols to represent numbers.

Brahmagupta used zero in arithmetic — adding, subtracting, multiplying and even dividing using the all-important number. All of that was well and good, except for division. It wasn’t until Sir Isaac Newton and his German counterpart Gottfried Wilhelm Leibniz came along that it was established that dividing by zero is undefined.

But really, the big deal here was not doing arithmetic. Nope, it was place value. This is so important that we all take it for granted. It’s the difference between $65 and $605 or the difference between 0.02% and 2%. See, zero isn’t just a place holder — in our number system it can represent a place value. You think math is hard now? Imagine doing calculations with Roman Numerals! Without place value and our humble zero, this work is exceedingly difficult.

This is a relatively new idea in the scheme of things. Almost 3,000 years had passed, since the Sumerians developed the first written number. Zero was introduced in India sometime around 400 A.D., though it didn’t show up in a text until around 600 A.D. Through trade routes, zero began showing up in the Middle East and China, but it took a very long time — the middle of the 12th century! — for Europeans to begin using zero and place value.

And that’s pretty much it — the very long history of our current number system, without which most other major discoveries, like calculus, trigonometry or geometry, could not be developed.

Of course there is much, much more to say about numbers themselves. For example, they’re arranged in a system based on their particular characteristics, kind of like the way we categorize animals or plants. Positive whole numbers are called natural numbers;positive and negative numbers are called integers; fractions and terminal decimals are rational numbers, and so on. This is connected to a fascinating (to me) branch of mathematics, called abstract algebra. But that’s a story for another day.

What surprised you about the history of numbers? And how about that zero? Ask your questions or make comments here.

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In Math for Teachers

A Mathematical Time Machine

Was mathematics invented or discovered?

(I’ll give you a second or two to really think about that.)

Most non-mathematicians have never really given that question much thought. Math has just always been there. An isosceles triangle has always had two congruent sides, and 3 + 8 has always equalled 11. But the reality is this: since the beginning time, human kind has struggled to find ways to describe its world. And one important outcome of this struggle is what I call the language of mathematics. Whether math was invented or discovered, the people involved were fascinating and scary and funny and sometimes sad. And that’s why I’ve decided to devote the remainder of November to the history of mathematics. Here are a few of the stories I hope to share with you.

1. There was the 1st Century Roman who, while taking a bath, figured out the idea of displacement. What did he do? Well, naturally, he shouted “Eureka!” and went running down the streets in his birthday suit. (Or so the story goes.)

2. Then there was the 5th century, mystical cult that demanded complete loyal and secrecy from its members. And by the way one of its members discovered one of the most useful and important facts about right triangles.

3. In the 1600s, the surrogates of two mathematicians — one in England and the other in Germany — held heated debates over who had actually invented (or discovered) calculus.

4. A child prodigy born in 1777 was confounding his teachers and managing his father’s business accounts at the tender age of five. He went on to make a staggering number of contributions in number theory, statistics and algebra, including normal distribution and the bell curve. He also apparently chose work over being at his wife’s deathbed, saying, “Ask her to wait a moment; I’m almost done.”

5.  A girl (gasp!) made significant contributions to the fields of abstract algebra and physics in 19th and 20th century Germany.

6. After cracking World War II German codes for the Brits and playing a major role in the birth of computer science, one fellow was arrested for the crime of homosexuality, chose chemical castration over prison and is said to have killed himself by cyanide poisoning at the age of 42.

Clearly, the history of mathematics is full of comedy and tragedy. The stories weave in and out of major world developments and the histories of other sciences. At the least, some of these stories are entertaining. Others help us make connections between ideas that lead to our own personal revelations. Still others remind us that while these contributions have provided the underpinning of how we understand our world today, the people behind them were just that — people.

So climb aboard this mathematical time machine. I’m still trying to decide whether to take it chronologically or by subject or perhaps even with a more random approach. Let’s just see what happens, shall we?

Do you have a question about the history of mathematics? If so, please share it in the comments section. I’m happy to take suggestions of topics I should consider.

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In Math for Grownups

Engineering tops highest-earning degrees — again

With the economy still struggling along and a price of a college degree outpacing ordinary inflation, more and more personal finance experts are suggesting that students choose a major based on its earning potential. And true to form, this year’s American Community Survey data shows that STEM (science, technology, engineering and mathematics) degrees continue to promise much higher incomes than even business degrees. And so today, instead of interviewing someone about how they use math in their job, I thought I’d take a look at this data.

In 2011, 59 million Americans (25 years and older) held bachelor’s degrees. The most popular degree is business (20%), with education coming in second (12%). In fact, those with business degrees were the most likely to be employed. But here’s where the rubber hits the road: those with engineering degrees continue to out-earn business majors by about $25,000 a year (based on median salaries).

Yes, you read that right.

And the hits keep coming (again, based on median salaries): those with mathematics, computer science or statistics degrees earn $13,000 more each year, as do those with physical science degrees. Even if a STEM degree holder was not working in that humanities degree holders were (naturally) at the low end of the earning potential, along with education,

But money isn’t everything. Those in STEM careers are more likely be employed in full-time, year-round jobs. (Curiously, teachers aren’t considered year-round employees, which I think skews the data somewhat.) The mathy/sciencey types are also less likely to be unemployed.

I am not one to suggest that someone get a degree merely for the earning potential. If you don’t want to be an engineer, don’t major in that field. It sounds a little woo-woo, but I firmly believe in the general idea that we should all be following our bliss (and being smart about what that means financially).

Where I think this data matters — big time — is much farther down the educational ladder. Students who learn to love (or at least appreciate) STEM subjects are much more likely to consider these as a field of study. On the other hand, many of you can personally attest to the fact that it’s hard to fall in love with these subjects — and play catch up with the concepts and foundation needed to excel in them — when you’ve learned to hate them or have zero confidence in your abilities.

In other words, the work starts in elementary and middle school. For students reach their real earning potential and for employers to find qualified experts for the jobs that they do have, we really must make STEM a priority in these grades. That doesn’t mean more testing or introducing concepts at a younger age. (In my opinion, those strategies are counterproductive.) It means finding truly gifted STEM teachers who are able to motivate their students and overcome our epidemic of mathematics anxiety and general apathy towards the subject.  It means approaching STEM subjects with excitement and a sense of discovery. It means encouraging, not discouraging, exploration in these subjects.

So I ask you: What are you doing to help with this?

Interested in how things broke down numerically? Here are a few median salaries from the American Community Survey:

  • Engineering, $91,611
  • Computers, mathematics, statistics, $80,180
  • Physical and related sciences, $80,037
  • Business, $66,605
  • Literature and languages, $58,616
  • Education, $50,902
  • Visual and performing arts, $50,484

What do you think? Should college students choose a degree based on earning potential? Or should they “follow their bliss”? How can schools help students develop an interest in the fields that offer a higher earning potential? Share your comments!

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In Math at Work Monday

Math at Work Monday: Wendy the astronaut

Meet Wendy Lawrence, a real, live astronaut who has logged more than 1,225 hours in space. Cool, huh? From 1995 until 2005, Lawrence took four trips into space, including the last Shuttle-Mir docking mission on Discovery. She also took rides in Endeavor and Atlantis. 

And, duh, she used lots and lots of math as an astronaut. She breaks it down below.

Wendy Lawrence

Can you explain what you do for a living?

As a NASA astronaut, first and foremost, your job is to support NASA’s human spaceflight program. For example, one of my jobs in the Astronaut Office was to oversee the training of astronauts who would spend five to six months on the International Space Station (ISS). In this job, I had to work closely with representatives of the other participating space agencies to determine the specific content and length of the training flow.

Certainly, the highlight of being an astronaut was having the opportunity to be assigned to a mission! I was very fortunate to have the opportunity to fly on the space shuttle four times. On my first flight, STS-67, we performed astronomical observations with the three telescopes that we had in the payload bay. My next two flights, STS-86 and 91, went to the Russian space station Mir. My last flight, STS-114, was the first shuttle flight after the Columbia accident and we went to the ISS.

When do you use basic math in your job?

Astronauts use math regularly. We often fly in the T-38 jet for crew coordination training and to travel to other locations for mission training and support. Before every landing, the crew (front seat pilot and back-seater) needs to calculate the landing speed. This requires basic addition, subtraction and division. We subtract 1000 from the current amount of fuel and then divide that number by 100. We then add the result to the basic landing speed (155 kts or knots). Here’s an example:

2000-1000 = 1000

1000 ÷ 100 = 10

Landing speed is 155 + 10 = 165 kts

We also have to use math when we fly the space station robotic arm. This arm was built by the Canadian space agency. They used centimeters to measure distances and centimeters are displayed on the control panel. When NASA astronauts ride on the arm during a spacewalk, they typically measure distances in inches and feet. For example, the space-walker may say that he or she needs to move 12 inches to the right. Knowing that there are 2.5 centimeters per inch, the robotic arm operators can make the conversion to 30 centimeters (typically done in our heads) and then fly the arm to that new location (based on the numbers displayed on the control panel).

Do you use any technology to help with this math?

Typically, we when fly in the T-38 jet or fly the station robotic arm, we don’t use calculators or computers to help us with this math. When your hands are on the controls of the jet or the robotic arm, it is hard to use a calculator!

How do you think math helps you do your job better?

When we fly the T-38, it is a matter of safety. We could quickly get ourselves into trouble if we don’t land the jet at the proper speed.

How comfortable with math do you feel?

I studied engineering in college, so I do feel very comfortable with math.

What kind of math did you take in high school?

I took geometry, algebra II, trig and pre-calculus in high school. I did enjoy math, but I did feel like I needed to work hard to be good at it.

Did you have to learn new skills in order to do the math you use in your job?

Basically, for the situations that I have already described, I could use the math skills that I learned in school.

No surprise that Wendy uses lots of math, right? But I was a little surprised that she used so much mental math. And I didn’t expect her to say that she had to work hard at math in high school. What surprised you? Share in the comments section.

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In Math at Work Monday

Math at Work Monday: Greg the weightlifting coach

I’m of the age when I should be lifting weights — to help manage my increasingly decreasing metabolism and ward off bone density loss. And actually, I like strength training. But not as much as Greg Everett, founder of Catalyst Athletics and Olympic-style weightlifting coach. The author of  Olympic Weightlifting for Sports, Greg is considered an expert on this sport, which requires quite a bit of calculations. Take a look.

Can you explain what you do for a living? 

As a coach for my competitive weightlifting team, most of my time is spent creating training programs for my weightlifters and coaching them during their daily training. I also write and edit books, as well as program our website.

When do you use basic math in your job?  

I use math every day. Most commonly, I use it to calculate training weights based on percentages of a lifter’s maximum lift, or to calculate a percentage based on the weight used. I also have to convert pounds to kilograms often; the sport of weightlifting uses kilograms officially, but sometimes individuals only know weights in pounds. During program design, I also use math to calculate other figures like volume (in this case, the number of repetitions performed in a given time period) to allow me to track and plan a lifter’s training. And of course, I have to be able to add the weights on the barbell quickly to know what a lifter is lifting. In weightlifting, weight plates are color coded to make this easier.

Do you use any technology to help with this math?

I do use a calculator frequently during program design for calculating percentages because I need it to be accurate. Calculations of volume are done with functions in the Excel spreadsheets I use to write programs. I normally do pound/kilo conversions in my head as much as possible just for the sake of practice.

How do you think math helps you do your job better?

Understanding some fundamental math concepts allows me to design better training programs and develop my weightlifters more successfully. Without math, there would be too much guesswork, and training athletes to high levels of performance requires accuracy.

How comfortable with math do you feel?  

I didn’t particularly enjoy math as a student, although I never struggled with it. I’m comfortable with the math I use frequently in my work and am fairly comfortable with basic algebra, geometry and the like. I feel like I have the math tools to be able to solve problems in life well, but certainly any more complex math I learned as a student has been forgotten simply because I don’t use it often enough.

What kind of math did you take in high school?  

Just the standard algebra and geometry; I didn’t take any advanced math courses in high school and was an English major in college. I felt that I was good at math to the degree that I was interested. That is, I never struggled with the concepts or the execution, but I also didn’t push myself beyond what I needed to learn. In retrospect, I wish I had put more time and effort into math and the sciences in school to build a better foundation.

Did you have to learn new skills in order to do the math you use in your job? 

I didn’t need to learn anything new for my job; what I learned in school was adequate. As I mentioned previously, I wish now that I had more exposure to more advanced math and science as a young student. At that time, I wasn’t interested enough to pursue it beyond basic requirements, but at that age you can’t predict well what you’ll end up doing in life. My advice to students would be to put as much time and effort into your schooling as possible because that time will be your greatest opportunity to learn. You can certainly regret not knowing enough, but you’ll never regret knowing more than you need.

Even jocks use math! Do you use math in your exercise program? Share your experiences in the comments sections — along with any questions you have for Greg. I’ll ask him to swing by and respond!

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In Math for Grownups

Math at Work Monday: Joe the Platform Consultant

In the IT field, there are many machines and programs that are really confusing and difficult to understand. Not only do we have to trust and depend on these machines, but also the people who service them. Joe Thompson is one of the good guys. He provides assistance to the users and companies when they need it most. From consulting to maintenance, Joe and his colleagues are there for us when our technology isn’t working quite right. (Joe is also one of my former geometry students. It’s been great to reconnect with him and see how accomplished he is now!)

Can you explain what you do for a living?

Red Hat’s consultants help customers get our products working when they have specific needs that go beyond the usual tech support.  We are essentially advanced computer system administrators on whatever our customers need us to be to get Red Hat’s products to work for them.  Common consulting gigs are setting up Red Hat Satellite to manage the customer’s servers, or doing performance tuning to make things run faster or a “health check” to verify things are running as efficiently as possible.

We just put out a marketing video about our consulting for public-sector clients, actually:

https://www.youtube.com/watch?v=eMzANG3Yhlk(We do more than just public sector and cloud, of course.)

When do you use basic math in your job?

The most common is when tuning a system to perform well, or configuring various things.  Unit conversions and base conversions are especially important.

IT has a long-running math issue actually: does “kilo” mean “1000” (a round number in base 10), or “1024” (a round number, 10000000000, in base 2)?  There are various ways people try to indicate which is intended, like using a capital K vs. a lowercase k, or using KiB vs. KB.  This matters in a lot of cases because when you get up into large data sizes, the difference between round numbers in base 10 and base 2 gets pretty big.  A 1-TB hard drive (a typical size today, maybe even a little small) is a trillion bytes — 1000 to the fourth power, not 1024 to the fourth power.  The difference is about 10% of the actual size of the drive, so knowing which base you’re dealing with is important.

Then there are units that have to be converted.  A common adjustment for better performance is tweaking how much data is held in memory at a time to be transmitted over the network, which is done by measuring the delay between two systems that have to communicate.  Then you multiply the delay (so many milliseconds) by the transmission speed (so many megabits or gigabits per second) and that gives the buffer size, which you have to set in bytes (1 byte = 8 bits) or sometimes other specified units.Sometimes software writers like to make you do math so they can write their code easier.  If a program has options that can either be on or off, sometimes a programmer will use a “bitfield” — a string of binary digits that represent all the options in a single number, which is often set in base 10.  So if you have a six-digit bitfield and want to turn off everything but options 1 and 6, you would use the number 33: 33 = 100001 in binary.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

I’ve always done a lot of arithmetic in my head and I can at least estimate a lot of the conversions without resorting to a calculator.  I’ll break out the calculator if the math is long and tedious though, like averaging a long column of numbers, or if I need a precise answer quickly on something like how many bytes are in 1.25 base-10 gigabits — I can do the billion divided by 8 and come out with 125 million bytes per base-10 gigabit, and then multiplying by 1.25 I know I’m going to be in the neighborhood of 150 million bytes, but I need the calculator to quickly get the exact answer of 156250000 bytes.  If I’m on a conference call about that kind of thing I’ll use the calculator more than otherwise.Google introduced a new feature a couple of years ago that will do basic math and unit conversions for you, so if I’m deep into things or just feeling lazy I can also just pull up a web browser and type “1.25 gigabits in bytes” in the search bar, and Google does it all for me.  But recently I noticed I was reaching for the calculator more, and arithmetic in my head was getting harder, so I’ve been making a conscious effort to do more head-math lately.

How do you think math helps you do your job better?

Without math, I couldn’t do my job at all 🙂 Even so little a thing as figuring out how long a file will take to transfer takes a good head for numbers.  As soon as you dig under the surface of the operating system, it’s math everywhere.

How comfortable with math do you feel? Does this math feel different to you ?

I’m pretty comfortable with math.  A lot of my off-time hobbies touch on computers too so it’s a lot of the same math as work even when I’m not working.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

I took the standard track for an Advanced Studies diploma from grades 8-11 (Algebra I, Geometry, Algebra II, Advanced Math), plus AP Calculus my senior year, and always did well. I didn’t expect to like Geometry going in because it’s not one-right-answer like a lot of math, but I ended up enjoying the logical rigor of proofs.  (Though I do recall giving my Geometry teacher fits on occasion when my proofs took a non-standard tack…)

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pickup using the skills you learned in school?

Most of it was learned in school, although base conversion isn’t something we spent a lot of time on.  I got good at it through long, frequent practice as you might guess…

Do you have a question for Joe? Send me your question and I will forward it to him.

Photo Credit: Dan Hamp via Compfight cc

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In Personal Finance

Real Savings Has Curves: The difference between simple and compound interest

What’s the most common math question I get from grownups? Easy: What’s the big deal about compound interest? For some reason, this idea stumps some very smart people. But the whole thing is pretty simple really. (Ha!) It all comes down to one concept — curves vs. lines.

You probably know that simple interest is, well, simple. That’s because it’s linear. (Stay with me here. I promise it’s not too hard.) In other words, simple interest can be described as a line. Now in mathematics, lines are very specific things. They go on forever, for one thing. For another, they’re straight. So while I might casually use the word “line” to describe a squiggly while I’m doodling, that’s a huge no-no in math. Among the Pythagorii and Sir Isaac Newtons, there’s no such thing as a “straight line.” By definition, a line is straight, not curved.

Because simple interest is linear, it increases (and decreases) steadily. Remember graphing linear equations? Take a look:

Graph courtesy of MoneyTipCentral

The graph above is an example of simple interest. As time goes on (or as you look to the right on the “time” axis), the money, $, increases. And it increases very steadily. If you can remember back to your algebra class, you know that each point on this line is found by taking the same steps — x number of “steps” to the right and y number of “steps” up. This is consistent. In other words, you don’t take 2 steps to the right and 1 step up and then 2 steps to the right and 4 steps down. (If you were really paying attention in algebra class, you might remember that this is a way of describing slope, which indicates the steepness of the line.)

Now curves are different. And, yep, you guessed it, compound interest is a curve. Here’s a general example:

Graph courtesy of MoneyTipCentral

If you looked at three points on this graph, you would find that the way to get from the first to the second to the third is not a consistent series of steps. There would be a pattern, yes, but it wouldn’t be the same each time. This is what we call a non-linear equation, because, well, it’s not linear. (Duh.)

But what can these graphs tell us? It’s not as hard as you might think. Take a look at the graphs themselves. As time increases, so does the money, right? (In other words, as you move to the right along “time” the graph moves up along “$.”) But with the curve, the $ gets bigger faster. It takes less time for the money to increase along the curve than it does along the line. (Follow me? If not, take a closer look at the graphs.)

That’s because of one simple fact: with compound interest, the interest is accrued on the principal (or original amount) and the interest. Each time the interest is calculated, the interest from the previous time period is added to the amount. On the other hand, with simple interest, the interest is accrued on the principal alone. That translates to a steady increase over time, rather than a sharp increase, like with the curve.

So what does this matter? Well, it depends on whether your spending or saving. Since with compound interest, the amount accrues faster over time, this is a good thing for savings or investments — but a bad thing for credit. And it’s the other way around for simple interest.

(Of course that is all moot, since unless you’re borrowing from good old dad, simple interest is pretty hard to come by.)

The point is this: if you can remember that simple interest is a line and compound interest is a curve, you will likely remember how simple and compound interest are figured — slow and steady or speedy quick.

Do you have questions about compound or simple interest? Is there another way that you remember the difference? Share your ideas in the comments section.

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In Math at Work Monday

Math at Work Monday: Robert the veterinarian

With a blind, deaf, 18-year old toy poodle who has dementia (canine cognitive disorder), I’ve gotten to know our friendly neighborhood veterinarian very, very well. Dr. Robert Z. Berry, DVM at The Village Vet has helped us manage some strange symptoms and supported us in the last year since Roxie was diagnosed with dementia. Just like people doctors, vets must have excellent bedside manner, and Dr. Berry has it in spades.

I also noticed that he does quite a bit of math in his work. Roxie has been on a variety of medication, as we’ve looked for the right combination to keep her happy and healthy. And she’s only 6 pounds. That means converting measurements like crazy. At a recent visit, I finally got the idea to ask Dr. Berry to answer my Math at Work Monday questions. If your kid aspires to be a vet, read on!

Can you explain what you do for a living? 

I examine sick and healthy animals, provide preventative care such as vaccinations or parasite (intestinal and blood born worms) screening and offer early disease detection, blood tests or imaging (xrays and ultrasound). In the case of sick animals, we can hospitalize and provide medical care or medical surgical care to help return them to normal health. Additionally we provide routine surgical and dental services such as spaying , neutering, tumor removal, dental cleaning and extractions.

When do you use basic math in your job?

Everyday, from basic math skills to algebra. Here’s an example : An animal weighs 22 pounds and needs medication which is dosed at a rate of 20 mg/kg and given three times a day. The animal’s weight is measured in pounds, so the first step is to convert to kilograms. Then I need to multiply the weight in kilograms by 20 mg/kg. Now we have a milligram dose of 200 mg. But things can get even more complex. Suppose the drug is supplied in 400 mg/ml strength? I use division or an algebraic formula to arrive at a milliliter (or cc, cubic centimeter) dose of 0.5 ml.

Do you use any technology (like calculators or computers) to help with this math?  

I really prefer not to use a calculator because I think it can make my brain become lazy. It is remarkable how much agility you lose (even basic math skills) when you don’t use basic math skills on a daily basis. I calculate in my head but verify with the calculator.

How do you think math helps you do your job better?

It’s absolutely necessary with any sort of drug therapy.

How comfortable with math do you feel?

I feel very comfortable with math and have all of my life. Vets must be mentally sharp and learn to rely on their most important assets — their brains! I took calculus in high school, and I felt very confident in the class. School prepared me very adequately for the nuts-and-bolts part of my job. I was fortunate to have good teachers and also to have been raised in the time period before calculators were allowed in school. A good primary education prepares one for the rest of his or her life.

So there you have it, a vet who is both compassionate and math-savvy — a great combination! Were you surprised by the math that Dr. Berry uses in his practice? Share your response in the comments section.

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In Math Education

The Problems with PEMDAS (and a solution)

If you’re on Facebook, you’ve probably seen one of a variety of graphics like the one above.

The idea is to solve the problem and then post your answer. From what I’ve observed, about half of the respondents get the answer correct, while the other half comes to the wrong answer. The root of this problem? The order of operations.

Unlike reading English, arithmetic is not performed from left to right. There is a particular order in which the addition, subtraction, multiplication, and division (not to mention parentheses and exponents) must be done. And for most of us old-timers, that order is represented by the acronym PEMDAS (or its variations).

P – parentheses
E – exponents
M – multiplication
D – division
A – addition
S – subtraction

I learned the mnemonic “Please Excuse My Dear Aunt Sally” to help me remember the order of operations.

The idea is simple: to solve an arithmetic problem (or simplify an algebraic expression), you address any operations inside parentheses (or brackets) first. Then exponents, then multiplication and/or division and finally addition and/or subtraction.


But there really are a lot of problems with this process. First off, because multiplication and division are inverses (they undo one another), it’s perfectly legal to divide before you multiply. The same thing goes for addition and subtraction. That means that PEMDAS, PEDMSA, and PEMDSA are also acceptable acronyms. (Not so black and white anymore, eh?)

Second, there are times when parentheses are implied. Take a look:

If you’re taking PEMDAS literally, you might be tempted to divide 6 by 3 and then 2 by 1 before adding.

Problem is, there are parentheses implied, simply because the problem includes the addition in the numerator (top) and denominator (bottom) of the fraction. The correct way to solve this problem is this:

So in the end, PEMDAS may cause more confusion. Of course, as long-time Math for Grownups readers should know, there is more than one way to skin a math problem. Okay, okay. That doesn’t mean there is more than one order of operations. BUT really smart math educators have come up with a new way of teaching the order of operations. It’s called the Boss Triangle or the hierarchy-of-operations triangle. (Boss triangle is so much more catchy!)

The idea is simple: exponents (powers) are the boss of multiplication, division, addition, and subtraction. Multiplication and division are the bosses of addition and subtraction. The boss always goes first. But since multiplication and division are grouped (as are addition and subtraction), those operations have equal power. So either of the pair can go first.

So what about parentheses (or brackets)? Take a close look at what is represented in the triangle. If you noticed that it’s only operations, give yourself a gold star. Parentheses are not operations, but they are containers for operations. Take a look at the following:

Do you really have to do what’s in the parentheses first? Or will you get the same answer if you find 3 x 2 first? The parentheses aren’t really about the order. They’re about grouping. You don’t want to find 4 + 3, in this case, because 4 is part of the grouping (7 – 1 x 4).  (Don’t believe me? Try doing the operations in this problem in a different order. Because of where the parentheses are placed, you’re bound to get the correct answer more than once.)

And there you have it — the Boss Triangle and a new way to think of the order of operations. There are many different reasons this new process may be easier for some children. Here are just a few:

1. Visually inclined students have a tool that suits their learning style.

2. Students begin to associate what I call the “couple operations” and what real math teachers call “inverse operations”: multiplication and division and addition and subtraction. This helps considerably when students begin adding and subtracting integers (positive and negative numbers) later on.

3. Pointing out that couple operations (x and ÷, + and -) have equal power allows students much more flexibility in computing complex calculations and simplifying algebraic expressions.

Even better, knowing about the Boss Triangle can help parents better understand their own child’s math assignments — especially if they’re not depending on PEMDAS.

So what do you think? Does the Boss Triangle make sense to you? Or do you prefer PEMDAS? What to learn to solve these and other problems, buy the book that will help grown-ups like you with these and other math problems here.

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