Tuesday, November 24, 2009

"I don't use fractions in my daily life" ... Really?!

1/2 by Leo Reynolds, on Flickr
Creative Commons Attribution-Noncommercial-Share Alike 2.0 Generic License by Leo Reynolds

In a recent discussion about fractions in one of my online math courses, a student claimed s/he does not use fractions in her/his daily life but only in math courses. This student's response was a precious "teaching moment" to promote math awareness of how math is embedded in our lives. Below, you will find my reply to this student's post:

Thank you for your response, though I may have to respectfully disagree with
your assessment that you do not use fractions in your daily life. We are
constantly working with portions or making decisions out of a set of choices
in our daily lives, which is the same as working with fractions. Here are a
few examples:

-- When pouring milk, juice, or soda in a cup, we are using a portion (fraction!) of the milk, juice, or soda available in the container.
-- When we receive our paycheck, a part (fraction!) of our money is used to pay the bills.
-- When we stop at an intersection and decide to make a left turn, your decision
(fraction!) was based on 4 posibilities: go straight, turn left, turn right, or go back (U-turn).
-- When we go shopping and take advantage of the sale of 25% off (fraction!) on every item.
-- When we type our name in the computer, we only use a few keys (fraction!) of the
keyboard.
-- When we have a headache, we take 1 or 2 Tylenol tablets (fraction!) out of the bottle.

These are only a few examples. There will be many more in this discussion, which I hope it will help you gain awareness that we all use fractions (and math!) every day in our lives.

I hope this helps.


Help me add more examples to this list, so I can share them with my students.

No "Wiggle" in Rowing!

I recently read this interesting article of how math was used to solve an issue that rowing athletes often need to overcome during races: "the wiggling boat." Once again, Math is in places that you least expect! Read this interesting article from "Technology Review" by clicking the link below. Enjoy!
Mathematician Solves Rowing Boat "Wiggle" Problem
A mathematician has discovered two entirely new arrangements of rowers in a racing eight in which the rowing forces cancel to make the boat wiggle-free.

The placement of the rowers, the "rig" of the boat, obviously has consequences for the motion of the boat. The question is how best to arrange an even number of crew members in a coxless racing boat in a way that minimizes or eliminates wiggle.

The traditional way of rigging a boat places rowers alternately pulling oars on each side of the boat. "The traditional rig appears symmetrical and simple in ways that might tempt you into thinking it is in every sense optimal. However, this is not the case," says Barrow who goes on to show that the balance of forces in this rig as the oars are pulled through the water always produces a wiggle.

What's the betting that that we'll see at least one of the new rigs at the 2012 Olympics in London?

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Wednesday, October 14, 2009

Financial Mathematics

I always find interesting when business major students claim they do not need to learn algebra or any mathematics course for their career because it only involves basic arithmetic. Well, I hope they read this interesting article from Plus Magazine about "Financial Mathematics." Click the link below to read the full article.
clipped from plus.maths.org
What is financial mathematics?
icon
I was drawn into financial maths not because I was interested in finance, but
because I was interested in making good decisions in the face of uncertainty.
Cardano, famously, commented that knowing that the chance of a fair dice coming
up with a six is one in six is of no use to the gambler since probability does
not predict the future. But it is of interest if you are trying to establish
whether a gamble is fair or not; it helps in making good decisions.
Financial mathematicians investigate markets on the basis of a simple premise;
when you price an asset it should be impossible to make money without the risk
of losing money, and by symmetry, it should be impossible to lose money without
the chance of making money.
Financial mathematics needs to tell not only what people ought to do, but
also what people actually do.
Banks need high level maths skills because that is how the bank makes
money.
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Saturday, October 10, 2009

The Story of Mathematics (Video)

Thanks to the people I follow on Twitter, I found this awesome video about mathematics. If you are one of those students who constantly question the reasons for learning mathematics, then renting the documentary "The Story of Mathematics" (see previews below) from your favorite video store will be worth each penny! Enjoy!


Watch The Story of Maths Part 1 in Educational View More Free Videos Online at Veoh.com



Watch the story of maths part 2 of 4 The Genius of the East in Educational & How-To View More Free Videos Online at Veoh.com

Tuesday, August 18, 2009

Algorithms - Logical Thinking

In the article below, you will find out how learning mathematics is important to develop the ability of working effectively and efficiently. When learning mathematics, you are learning to think in a logical manner, which will allow you to solve problems using step-by-step processes known as algorithms. Complex real-life problems can only be solved if individuals know how to apply algorithms to vast amount of data with the aid of computers, which are then analyzed and interpreted to make informed decisions. I encourage you to read the article below and learn more how mathematics play an important role in decision-making.

Your Friend the Algorithm

With exponential trends of data growth and computational power colliding, the
world is literally drowning in data. There’s too much data, and not enough
analysis.
magnifying glass

Fortunately, companies are using technology to capture and integrate data and
sophisticated mathematical procedures to analyze data and make better
decisions—decisions that ultimately improve the customer experience.


An article from The Economist,href="http://www.economist.com/business/displaystory.cfm?story_id=9795140"
target=_blank>Business by the Numbers
”, highlights how companies are using
algorithms to make book recommendations, choose optimum delivery routes for
packages and even route calls to agents that can best diagnose a particular
problem.

Algorithms help tackle complicated challenges—especially necessary as companies
race to take care of their “best” and/or most profitable customers.  I am
sure you will agree that our world is becoming more—not less—complex. As data
volumes and decision options increase, algorithms and the systems that run them
take on added importance.
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Monday, August 17, 2009

Shoelaces and Math



I found this interesting article of how we use math when tying our shoes. Another example how math is an integral part of our lives, even in the simplest tasks such as tying our shoes. Once again, Math is Everywhere!

Tying Shoes: Math May Make Case for How We Lace

Math-phobes of the world, take heart! You might not have realized it, but you've been acing at least one math problem each morning since the day you gave up Velcro.

"Tying shoelaces is a simple, familiar example of a geometrical optimization problem," said Ian Stewart, a professor of mathematics at the University of Warwick in England.

"We learn nothing of practical value about shoelaces that couldn't be found by
experiment—but we learn some interesting things about how to tackle other
problems of a similar kind, and those are often of practical value."
The bows that people make while tying shoelaces have nothing to do with making
the knot stronger, and serve only to make the knot easier to untie.
The ideal lacing should create uniform tension along the length of the lace.
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Thursday, August 6, 2009

For Today's Graduate, Just One Word: Statistics!

Interesting article! Learning mathematics, in particular statistics, is essential in times where everything is measured or quantified. We need people capable of analyzing data to identify trends and make accurate predictions. Click the link below to learn more about how learning statistics could lead you to a lucrative career.

For Today’s Graduate, Just One Word: Statistics


“People think of field archaeology as Indiana Jones, but much of what you
really do is data analysis,” she said.

“We’re rapidly entering a world where everything can be monitored and measured,”
said Erik Brynjolfsson, an economist and director of the Massachusetts
Institute of Technology
’s Center for Digital Business. “But the big problem
is going to be the ability of humans to use, analyze and make sense of the
data.”
The new breed of statisticians tackle that problem. They use powerful computers
and sophisticated mathematical models to hunt for meaningful patterns and
insights in vast troves of data.
Computing and numerical skills, experts say, matter far more than degrees. So
the new data sleuths come from backgrounds like economics, computer science and
mathematics.
The data surge is elevating a profession that traditionally tackled less visible
and less lucrative work, like figuring out life expectancy rates for insurance
companies.
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Sunday, August 2, 2009

How Algebra is going to help me be or become ...?

Today, a student asked one of the typical questions that students ask in a developmental math course: "How Algebra is going to help me be or become ...?" Unfortunately, today this question irked my normal coolness and patience with students. Why students continue having a narrowed mind about knowledge in general? Why they consider course content as useless when they cannot find an immediate application of this content to their lives? Why shut down the unlimited ramifications of what they are learning to focus it only to the present they live in?

As you can see, I was annoyed by the question since I cannot comprehend how students invest so much in a college education to just come out the same way they got in: with a narrowed mind attitude. I thought the purpose of earning a college education is to come out a better person than when we got in. Anyway, here is my response to my student's discussion post:

Students,

Learning Algebra will help you in the following way:

(1) To earn a college degree since it is part of your degree plan. The college degree diploma will open many opportunities that you may have never expected. Once you earn your degree, employers will see this as a person who is persistent, hard worker, self-disciplined and capable of overcoming whatever challenges s/he may face. Isn't this what you experienced in this course?

(2) To make you think in a structured, logical and critical manner. This is what Algebra is all about! When difficult situations arise in your life, you will methodically think and reflect how to solve it instead of just making wild guesses or reactive decisions that most likely you will regret at a later time.

(3) To develop the habit of working smarter, not harder. I am certain there have been times in your life that you are responsible for completing a task that is tedious and repetitive, and you wonder if there is a better way to do it. The ability of analyzing if there is a pattern on what you do and find a better-efficient way of doing it is what Algebra is all about.

In my humble opinion, and with all due respect, it is time to stop seeing Algebra as a manipulation of variables, such as x + y = z, and start realizing that Algebra is about understanding how the world around you works, so you can take control and make it better. Isn't this why you are pursuing a college degree?

Thursday, July 30, 2009

Math Court!

Today, a student told me she 'hates math.' My response to her was 'At some point, everyone use math in some way or another in their lives.' She responded back to me with 'I'm going to be a lawyer, so I only need to know the basics: add, subtract, multiply and divide.' Interestingly, too many students majoring in Criminal Justice have the same belief as the previous student: 'They don't need math to enforce the law.' Here is a humorous video showing an example of how mathematics play an important role also in the field of law and order.

Friday, July 3, 2009

The Secret of Productivity

Another reason to learn mathematics. Just watch the video and find out. The ramifications for learning mathematics are unknown to most of us. Complicated problems in real-life are often solved by applying mathematical concepts that for many of us at first seem to be useless. The examples in this video just prove it. Great quote in the video: 'The secret of productivity is...the work done by dead people (mathematicians).'


Thursday, June 25, 2009

Do you know what doing mathematics mean?

Decisions Decisions by Garrettc, on Flickr
Creative Commons Attribution-Noncommercial-Share Alike 2.0 Generic License by Garrettc


Unfortunately, many students believe that mathematics is what they only do in the math classroom instead of the processes they naturally use in their daily lives to make decisions and/or choices. The article below (click the link for full article) shows 9 basic mental abilities we all have and it represents doing mathematics. We are mathematical beings by nature!

doing mathematics makes use of nine basic mental
abilities
1. Number sense
Child psychologists have
demonstrated conclusively that we are all born with
number sense
2. Numerical ability
The Sumerians are the first people we know of who
used abstract numbers
3. Spatial-reasoning ability
ability to recognize shapes and to judge
distances


4. A sense of cause and effect. Much of
mathematics depends on "if this, then that"
reasoning, an abstract form of thinking about
causes and their effects.


5. The ability to construct and follow a causal
chain of facts or events. A mathematical proof
is a highly abstract version of a causal chain of
facts.


6. Algorithmic ability. This is an abstract version
of the fifth ability on this list.

7. The ability to handle abstraction
8. Logical-reasoning ability
9. Relational-reasoning ability
Much of mathematics deals
with relationships among abstract objects
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My students showing how geomtery is everywhere!

The videos below were created by students in my Geometry for Educators course (i.e. MAT 165) at St. Thomas University. The purpose of the assignment was to promote awareness among students on how geometry is embedded in those things they like most to do. To many, doing this project made the course content relevant and meaningful. Enjoy a sample of my students' videos.







The ramifications of learning mathematics

Question often asked by students: 'Why I need to learn mathematics?' You never know the ramifications for using such knowledge. Just check how the basic concept of a math game is making an impact in the field of medical genetics. Click the link below to read the article.
DNA Sudoku: Logic Of 'Sudoku' Math Puzzle Used To Vastly Enhance
Genome-sequencing Capability
A math-based game that has taken the world by storm with its ability to delight
and puzzle may now be poised to revolutionize the fast-changing world of genome
sequencing and the field of medical genetics, suggests a new report by a team of
scientists at Cold Spring Harbor Laboratory (CSHL). The report will be published
as the cover story in the July 1st issue of the journal Genome
Research.

Combining a 2,000-year-old Chinese math theorem with concepts from
cryptology, the CSHL scientists have devised "DNA Sudoku." The strategy allows
tens of thousands of DNA samples to be combined, and their sequences – the order
in which the letters of the DNA alphabet (A, T, G, and C) line up in the genome
– to be determined all at once.

"In theory, it is possible to use the Sudoku method to sequence more than a
hundred thousand DNA samples," says CSHL Professor Gregory Hannon, Ph.D.
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Monday, May 18, 2009

The price of lacking quantitative skills

Venta de Automobiles by Telstar Logistics, on Flickr
Creative Commons Attribution-Noncommercial 2.0 Generic License by Telstar Logistics

The price of not acquiring quantitative skills (which are developed in math courses) could be cost prohibitive. Recently, I watched the news a report on how people are getting into financial troubles when purchasing a new car. The problem is that more people are taking car loans in which they owe a lot more than the real value of the car. This is called an upside-down loan. People are making decisions of buying a new car based on no-down payment deals and longer terms to payback the loan to allegedly save a few bucks. Unfortunately, if they would have done the math, they would have realized they are not saving at all! Click the link below to read an article about the incresed trend of upside-down loans.

In a hole with an upside-down auto loan

"Upside down" means owing more on a car than it's worth. When a dealer knocks
down the value of your used car even further, the financial hole you're in gets
that much deeper.
"It's an alarming statistic that 40 percent of consumers are upside down."
How could this happen? It's easy. Just combine a low down payment or no down
payment with an auto loan with a longer term -- say five, six, even seven years.
Toss in the rapid depreciation that hits every new car in the first couple of
years and presto, you're upside down on your auto loan. Try to trade in your car
and you'll find yourself awash in negative equity.
Some folks make matters worse by rolling the old car's remaining debt into a new
loan. They're forced to pay interest and make payments on a car they don't even
own anymore. And tacking the extra debt on their new auto loan puts them upside
down all over again.
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Monday, May 11, 2009

STOP! The traffic light is turning red!

There are so many people driving vehicles on the streets but you rarely see chaotic events due to traffic. Why? Mathematics play an important role controlling traffic lights by helping traffic controllers optimizing the signal changes of traffic lights. Click the link below to learn more about this interesting application of mathematics and traffic lights.
clipped from news.bbc.co.uk

Welcome to the red light district
Traffic light
There's nothing more frustrating than sitting at a red light, watching
smiling drivers on the other side of the road speed past.
HOW ARE TRAFFIC LIGHTS CONTROLLED?
The first uses data collected on traffic flow in a certain area to calculate
timings for the lights, running the red lights to a strict timetable.

The other method is a little more hi-tech.

Coiled under the tarmac at junctions and crossroads across the UK, are loops
of cable which act as metal detectors as cars pass over them.

This information is passed to a central computer, which uses complex
algorithms to calculate the optimal time each light should spend on each colour,
ideally creating a smooth flow of traffic throughout the network.

Mathematical algorithms, and futuristic operations centres can only get you so
far.
"There is no way of getting down to a neat mathematical formula.
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Sunday, May 10, 2009

Remarkable Coincidences...Hmmm!

Have you experienced remarkable coincidences in your daily life? Maybe these were not remarkable after all. Watch the video below to learn how probability explains logically how typical or common are many events in our lives that we may have considered as remarkable coincidences.

Down You Go!


Down You go
Originally uploaded by Flashheart HP



Things around our lives are more than what meets the eye. If you oberve carefully, the simple staircase above is more mathematical than what you think. Compare the spiral staircase to the mathematical spiral. Can you see the resemblance? Learn more about this spiral and others by visiting the site 'Visual Dictionary of Special Plane Curves.'

Friday, May 1, 2009

Searching for Information in the Internet?!

Most of us are always looking for information in the Internet and we use popular search engines, such as Google, Yahoo, etc. However, there will be a new search engine starting May 2009 that will interpret your questions. Is this search engine will be more powerful than Google? I'm not sure yet but I believe it will be! How is this possible? ... it uses Mathematics! Click the link below to learn more about this new search engine.
clipped from blog.wolfram.com
WolframAlpha

Fifty years ago, when computers were young, people assumed that they’d
quickly be able to handle all these kinds of things.

And that one would be able to ask a computer any factual question, and have
it compute the answer.

But it didn’t work out that way. Computers have been able to do many
remarkable and unexpected things. But not that.

But armed with Mathematica and NKS I realized there’s another way:
explicitly implement methods and models, as algorithms, and explicitly curate
all data so that it is immediately computable.
All one needs to be able to do is to take questions people ask in natural
language, and represent them in a precise form that fits into the computations
one can do.

I wasn’t at all sure it was going to work. But I’m happy to say that with a mixture of many clever algorithms and heuristics, lots of linguistic discovery and linguistic curation, and what probably amount to some serious theoretical breakthroughs, we’re actually managing to make it work.

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Wednesday, April 29, 2009

Fast and Furious!

Jeff Gordon Dupont Chevy Impala by The Freewheeling Daredevil, on Flickr
Creative Commons Attribution 2.0 Generic License by The Freewheeling Daredevil


Have you seen the movie 'Fast and Furious?' Are you a Nascar or Indy fan? Many people enjoy watching or driving very fast cars. There is a thrill for speed that is difficult to describe. I encourage you to click the link below to discover how mathematics is applied in every aspect of racing cars.
The Math Used in Professional Auto Racing
The math used in professional auto racing covers virtually every mathematical
concept taught in school today. The successful professional racing teams use
every mathematical advantage they can to win.
Along with the cars, drivers have their own mathematical statistics to calculate
and define their level of performance in numbers.
Everything that a professional driver does on the race course is measured to
compare where improvements are not needed.
When the tires are removed during a pit stop, the depth of the remaining tread
is measured to determine how the car is handling.
Another use of math in professional auto racing is to using electronic timing as
cars go up and down the pits, so they do not speed.
Math is everywhere in professional auto racing.
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Tuesday, April 28, 2009

Baseball Predictions!

Dodger Stadium by penner42, on Flickr
Creative Commons Attribution-Noncommercial-Share Alike 2.0 Generic License by penner42


Recently, one of my students (an avid Marlin fan and knowing that I am also a baseball fan) asked me which teams were making the playoffs this year. Making the clarification that is too early to make such predictions, I chose the following teams: Phillies, Cubs, Dodgers, and Cardinals from the National League and Blue Jays, Indians, Athletics and Red Sox (this hurts since I am a Yankees' fan!). However, my predictions were based on gut instincts, but if I would have read professor Bruce Bukiet's mathematical model to make baseball predictions, I probably would feel more confident about my predictions. His mathematical model to make baseball predictions have been pretty much accurate every year. Predicting certain events or behaviors based on particular data is one of the most practical applications for learning mathematics. Learn more about Bukiet's mathematical model by clicking the science daily web site link below.

Tight Races In Major League Baseball's Eastern Divisions, Mathematician Predicts
The National League (NL) should see another very tight race in the Eastern
Division as has occurred in recent years.

Bukiet, an associate professor of mathematical sciences and associate dean of
the College of Science and Liberal Arts at NJIT, once again provides the number
of games each Major League Baseball team should win in 2009 based on the
mathematical model he developed in 2000.

His model computes the probability of a team winning a game against another team
with given hitters, bench, starting pitcher, relievers and home field advantage.
Bukiet, an avid Mets fan, has used this mathematical model to determine whether
it is worthwhile to wager on games during the baseball season.
These picks have produced positive results for six of the eight years he has
posted them.
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