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If you’re new here, you may want to subscribe to my RSS feed. Thanks for visiting! Today’s post is a guest-post by Barbara Jolie. I think you will find it interesting and inspiring. I did. It fits in well with the Math Mojo philosophy:
This post is for all you math gurus out there who really love your field of study but are having trouble finding a practical place for that love in the modern job market (which, granted, shouldn’t be that hard in the first place in less you, say, strictly studied chaos theory and refuse to work on anything else … even then). The most marketable and out-branching aspect of your mathematical expertise is probably so embedded into your brain that it’s really just an extension of who you are: your logic.
Essentially, mathematics is a formal codification of logic. Using high levels of problem solving for mathematics involves a great deal of abstraction. In topology, you will be abstracting shape from numbers, and in algebra, you are dealing with structure. Many people don’t see math in this way, but this has to do more with their own shallow grasp of the study, understanding primarily arithmetic and not much else.
This is how many of the concepts that you learn in mathematics can apply to computer science and even philosophy and semantics. Now granted, if you actually write a computer program, you probably won’t be using much if any applied mathematics. In fact, you probably won’t be using much computer science to simply write a program (particularly a simple one at that).
It’s only once you begin attempting to solve especially difficult programming problems that your mathematical mindset really begins to bloom. As you go further into the specifics of a program and try to flesh it out, you will be using lower levels of abstraction. These lower levels will begin to reveal the values behind the programming and the significance of what their variation represents.
I’m not definitively calling computer science a subset of math, but the two are definitely related. And having a flexible mind that can give shape to dynamic abstract concepts and problems is a must for both fields of study. In this same vein of thought, you can also reason that having that mental perspicacity could easily lend itself to the sciences and even language. After all, what is language but a series of abstractions arranged to represent a bigger “problem,” or meaning. The only difference is that, while computer science and mathematics are interpreted by a strict and robust system, the interpretation of language is left to the whims of any nitwit with ears or eyes.
So, in the spirit of this post, please make ever attempt you can to branch out your mathematical mind to new levels of abstraction. Seek out relationships between the field of study you love and other topics you might find interesting. Who knows, you may create a whole new career from it.
This guest post is contributed by Barbara Jolie, who writes for online classes. She welcomes your comments at her email Id: barbara.jolie876@gmail.com.
This is a guest-post. I’ve never had a guest-post on the Math Mojo Chronicles before, but I’m open to anything that fits in with the Math Mojo Manifesto, and had real value for readers. Jeremy Fordham has written just such an article, and I’m happy to present it to you here:
A Look at 9 Awesome Careers that Use Math
Many students have the same question when they have to study math in high school: “When am I going to use this?” The answer to that question is multifaceted. First of all, math is one way that students can learn logic, problem solving and critical thinking skills, which are all extremely important for furthering one’s education, especially if a student is considering getting an advanced degree like an online Ph.D. Second, basic principles of math are important in everyday life, even if it is just as simple as keeping financial records, calculating costs and estimating simple probabilities. Third, and finally, more advanced mathematics can be directly useful in many different careers involving mathematics and science. As such, when determining how their math degree will best serve them, students might want to consider the following nine possibilities.
Computer Scientist
Computer science is a practical field that requires some knowledge of math. In fact, computer programming in general requires the same step-by-step logical thinking involved in mathematics. Some areas of computer science require knowledge of advanced mathematics; and math and computer science are often so integrated that universities combine their math and computer science departments. Computer scientists solve problems, program computers, develop new technology and may work in fields such as robotics and artificial intelligence.
Physicist
Of the “hard sciences,” physics is the most math-heavy. It is often the case that abstract, or “pure” mathematicians will work on an entirely theoretical problem that they think has no real-world application, and it will turn out to have an application later in quantum mechanics or some other field in physics. Physics is a difficult subject, but for those who are interested in the fundamental principles of the universe, being a physicist can be an extremely rewarding career. Physics has both theoretical and applied divisions.
Chemist
Chemists require knowledge of mathematics both for theoretical and research calculations. In chemistry research, different types of mathematics such as statistics, algebra and calculus may be utilized. Students in basic chemistry classes are required to know algebra and basic mathematical operations, but in some areas of chemistry, the mathematical calculations can get much more advanced. Like physicists, chemists can work in the chemical industry as applied chemists or do research as theoretical chemists.
Biologist
The biological sciences are also great career option for those that like math. This is due to the fact that all scientific researchers need to be familiar with statistics, as well as basic math to perform tasks in the laboratory and for biochemical calculations. Likewise, some occupations in biology such as ecology and population genetics have a heavy theoretical foundation in math. Not all fields in biology require the knowledge of advanced math, but this knowledge is beneficial and useful.
Social Scientist
Social scientists and anthropologists study populations of people, their traits and how they interact. All researchers in the social sciences need a solid background in statistics. Statistics help researchers determine whether a trend they are observing is significant or if it is due to chance alone. Believe it or not, this is not easy to determine without using math to account for observer biases. People who do research in psychology also need to know statistics for the same reason.
Medical Professional
Pharmacists, doctors, medical technicians and others in the health care industry are required to understand math. This is incredibly important when calculating dosages for medications and the parameters for the treatment of certain patients. Anesthesiologists, for example, are required to calculate the correct dosages of anesthesia that a patient receives before surgery. Pharmacists are also required to calculate and measure correct dosages of medications. Similarly, people who work in a medical laboratory need to use math during certain lab tests.
Financial Analyst/Business Person
Mathematics is extremely important in the financial world. People with a background in math can work in any field of financial mathematics, from banking to becoming a tax professional on Wall Street. Likewise, people with a background in mathematics are very qualified to run a business or work for a large or small company. Having a degree in math shows that you are capable of logical and critical thinking.
Epidemiologist
People with degrees in math may choose to specialize in statistics or epidemiology. Statisticians are hired to analyze data, and statistics is an important part of any scientific research. Epidemiology is basically statistics as applied to health care. As such, epidemiologists may study outbreaks of infectious diseases, risk factors for certain health conditions or transmission of genetic diseases.
Bioinformatician
A relatively new field that has formed in the past few decades is called bioinformatics . Bioinformatics is basically a combination of the biological sciences, computer science and mathematics. This type of discipline may appeal to someone with a wide variety of scientific interests. People who work in bioinformatics help to develop databases to store biological information and create algorithms to analyze this data. Bioinformatics is, at its heart, a way to make scientific research more efficient and informative. It is useful in many fields, such as genome mapping, protein folding and evolutionary biology.
People who get a degree in math may want to stay within the field of mathematics, as opposed to one of the careers described above. These people may teach in at a high school or college, or they may do mathematics research of their own.
Contrary to popular belief, mathematics is actually a very useful subject. All scientists and businesspeople need to have some degree of mathematical knowledge. Plus, the critical thinking skills learned in solving math problems are applicable in all careers and in everyday life.
Jeremy Fordham, a contributing writer for onlinephdprograms.com, is an engineer who addresses issues at the boundary of many fields with the hope of inspiring dialogue in unique niches. He is an advocate of process optimization and renewable energy.
An interested reader asked:
“Why is it that when you multiply a negative number by another negative number, you get a positive number? Is there any way to show this; any examples?”
Professor Homunculus answers:
I love this question because it makes so much sense. It makes sense to question the premise.
But keep an open mind, because the answer, too, will make sense to you in a moment.
OK, let’s assume Lenny the Fish owes Vinny the Shark $5. So Lenny is down five bucks. That means Lenny has, in effect, negative 5 dollars.
Now, along comes Lenny’s friend, Sammy the Clam. Sammy is loaded, so he gives Lenny the five buck to pay off Vinny. In other words, he has NEGATED Lenny’s negative sum. Lenny is now even. So the negation of a negative is it’s opposite positive.
Sammy has negated that negative five bucks, one time, by giving Lenny the five. Had he negated it twice, by giving him another five, he would have given him ten. If he had negated it another time, he would have given him fifteen dollars, four times would have been twenty, and had Sammy negated Lenny’s negative five dollars five times, he would have given him a cool twenty-five slimmolians.
In other words, multiplying something by a negative is the same thing as negating something that many times.
Got it? Does this make any sense to you, because it is starting to make sense to me, and I hate to be alone with my delusions.
Here is another way to look at multiplying by negatives, (in case the above analogy is too weird).
Multiplication of integers can be seen as repeated addition. (That is not a good definition of multiplication – I repeat, that is NOT the definition of multiplication, for many reasons. To understand that, and get a great lesson in mathematical thinking, see Keith Devlin’s article. )
Although it’s not the definition, sometimes it’s useful to see a simple multiplication problem as being able to be represented as repeated addition. (I may catch hell for saying this by some math puritans. I think sometimes they miss the bigger point, though.)
So multiplying by -n can be accomplished by adding that thing -n times. (And even the puritans will have a hard time arguing with that.)
That needs and example to make it more clear.
Let’s take -6 x -3. That can be accomplished by adding -6 negative three times. So you take the negative of -6 three times.
The negative of -6 means positive six, right? (Because you should know that the negative of a negative is a positive). So, if you add positive six 3 times, you get what? Positive 18, of course!
That, in a nutshell, is why a negative times a negative gives you a positive.
I think you probably get it by now, a bit.
Remember, though, having something explained to you is not the same as really understanding it. If you just say, “I get it,” that means you will probably forget it by the time you need it again.
Go over what you have just read, until you have it “in your bones.” By that, I mean until you can really explain it to someone else who doesn’t get it, and make them understand it.
That is one of the secrets to learning math. Teachers only care if you can answer quizzes and pass some tests.
The real test is if you can have a discussion with someone and use your knowledge when you need it.
So take my advice, and re-read all the above, then go out and try to make someone else understand it. If you have no family member, friend or teacher who gives a hoot, you can write your explanation for why a negative equals a negative in comment below.
Today a thoughtful reader left a comment on a previous post (Why You Suck at math Pt. I) Dan Marks commented:
I love it! OK, generally, I feel the same way, but there is a lot more going on deep down. I run into a lot of kids who are, yes, lazy and irresponsible.
Now, for me, it boils down to this: Does that mean that there is something bad or wrong with them? I think not.
Unfortunately, part of our country (at least my country) was founded on some ill-conceived Protestant work ethic. There is a pernicious myth about that ethic being some kind of moral thing.
Yeah, it’s good to work. Whoopie. It’s also good not to beat children, undermine their confidence (or, on the other end of the spectrum, overpraise them for no good reason); it’s not good to feed them coke and oreo cookies, chips and McDiabetes, send them to school without teaching them any work ethic, yet chastise them for what we have never helped them avoid.
I find it hard as hell to morally justify judging a fourteen year-old for his or her attitude, unless
Continue reading Why You Still Suck at Math →
The First ever KenKen Contest is going to be held on Oct 30, at the Chappaqua Library, in Westchester County, NY.
Sign up for the First Ever KenKen Contest I wish I could be there, but I’ll be rallying for sanity (imagine that!) in Washington that day.
Bone up on your KenKen at The Math Mojo Chronicles KenKen Page
 Recently, an interested reader wrote in this question:
Hi ,
I am doing a quiz and one of the questions asks what is the lowest number which divides evenly into 1,111,111.
What is the way to find the answer? Is there some sort of formula?
Thanks (hopefully!)
- A Reader
Professor Homunculus replied:
Continue reading Prime Factors and the Great Brain Quiz →
I just wanted to try this little experiment with readers. I came across this little problem recently, and I have to admit, it gave me pause. I wanted to know what readers think.
Is this problem correct or incorrect, and why? (Please don’t answer just yes or no, withouth the “why,” OK?)
Please leave your thoughts about this in a comment below.
A concerned parent wrote in:
Hello, I was never very good at algebra. I managed to get by,and it has haunted me ever since. My daughter is in the eighth grade and wants my help with homework. Now, I feel really dumb, any suggestions. Thanks.
Professor Homunculus replies:
Thanks for your question. It’s a problem a lot of parents come across, and I think your question will resonate with many people. And by the way, no need to feel dumb – it’s the people who don’t try to help their kids with learning that are dumb.
Continue reading Helping your Child Learn Algebra →
 Photo by selma90
If you’re a teacher, my condolences go out to you at the beginning of this semester.
With the nation polarized concerning just about any issue, the hate- and fear-mongers have pounced on teachers with a sick, perverted glee.
You may have the misfortune to have your local newspaper publish an alleged “comic” strip (an odd name for a propaganda-strip devoid of any comic relief at all) that will go unnamed here. No need to publicize the hate-filled, malevolent ravings of a malicious maladroit. If you don’t know the one I mean, I wouldn’t dream of sending you to his reactionary website, but you can see a copy of an offensive cartoon at http://cartoonistsgroup.com/store/add.php?iid=51181
For years, that malcontent has been spewing venom about how teachers are the bane of modern society because of constructionist education reforms.
A typical case of the debate around education reform is the “Math Wars.” The Math Mojo Chronicles have tackled this issue a bit in some of my posts about the math wars. In those writings I’ve tried to be open minded, and not lay blame at any one group’s doors. We’re all culpable to some degree. But to blame teachers for the things they have no control over is more than a little wrong, yet that is exactly what that foul creature does.
Alas, many people, like the questionable cartoonist, prefer simple answers to complex questions. They apparently never learned to think beyond scapegoating the easiest target, even if it’s the wrong one. It is apparent that they had bad teachers. Something has to explain their lack of logical thought. It’s a typical logical fallacy to assume that even though you are poorly educated and suffer from a lack of critical thinking, that everyone shares your ignorance because they had bad teachers, as well, but that is where this odd duck is at.
Let’s put it bluntly – teachers are up against some terrible odds today. They are expected to be babysitters, lawyers, nurses, bean-counters, crisis-negotiators – anything but teachers. They are often stuck with class-sizes that are over the legal limit, and can’t do anything about it. They deal with some parents who spend no time on their own children’s education, yet expect every teacher to be Annie Sullivan (“The Miracle Worker”)
Then along come some lobbyists for different curriculums and textbooks, both traditionalist and reform-minded, that fight for the administration’s budget (your tax dollars) and want to inculcate your kids with their ideology.
It is a canard that teachers are at fault for this. Teachers are more at the mercy of a treacherous industry that is bound by a bottom line that the student’s welfare plays no part in.
Continue reading Respect for Good Teachers →
Recently I read this question online:
The sum of two numbers is 91. And the difference is 31. What are the two numbers?
The first answer to it simply gave the answer as, “The two numbers are 66 and 25.”
I think the whole thing is a waste of time for all concerned, so far. The asker has learned nothing, and the answerer has taught nothing.
Just giving an answer is “show–and–tell” teaching. It serves no purpose except to show off that you have an answer. It doesn’t teach anything. It’s the old phenomenon of,”Give a man a fish and you make him dependent on you.”
Let’s see if we can make this meaningful with math, by figuring out how we could come up with this answer.
Continue reading Simple word problem puzzle →
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Seriously, students with bad grades in any class are generally (there’s that word) lazy and irresponsible.