1.26.2005
Confessions of a Reluctant Mathematician
For most of my life, I have avoided mathematics whenever and wherever possible. I hated math. It wasn’t so much that I couldn’t do it, but that I didn’t enjoy doing it. Public school math teachers seemed to believe teaching one way to do things was the only way to keep things simple, and any deviation from this was met with disdain. My natural curiosity led me to try experimenting with what I was learning, and my teachers didn’t have time to go off on my (pardon the pun) tangents. Math teachers always expect students to show work for their answers, if one didn’t, then the answer was not only wrong, but the person was suspected of cheating. As I got older, I simply refused to do math assignments. I didn’t do the homework, and my math grades reflected a lack of interest, enthusiasm, and knowledge as a result. When I was in high school, I was only required to pass two years of math and two years of the most often companion to math: science. After meeting these requirements, I never looked back.
My natural strengths have always been reading and writing. From the moment I learned to read, I devoured books. The library was my sacred refuge. I could bring home several books from the school library and read them all before going to bed that night. On those nights I couldn’t sleep, I would often use a flashlight to keep on reading after I was supposed to be asleep. I was a troubled child growing up. I often got grounded or restricted to my room. No matter how much trouble I got into, my parents did one thing right: they never took away my books. It was the only thing I had going for me in the dark years of my youth and adolescence. In the 7th grade, we took aptitude tests in math and reading. My reading score was in the 98th percentile. My math was in the 28th percentile. I could read and comprehend better than 98 out of 100 students, whereas I could solve math problems better than only 28 out of 100 students. This disparity would follow me for many years to come. In 9th grade, my teacher noticed me squinting to see the notes on the blackboard. It turned out I was nearsighted, so to add to the discomfort of being an awkward teenager, I added glasses. Now I could see better, but it still didn’t cure my negative attitude towards anything math-related. I failed the first semester of Introduction to Algebra, and as a result, I was transferred into the lower Introduction to High School Math, where I just managed to scrape by. My negative attitude towards school in my freshman and sophomore years of high school would live to haunt me when I struggled my junior and senior years to improve my GPA. Despite getting nearly all A’s and B’s the last two years, my GPA at graduation was a dismal 1.8, placing me close to 345 out of a class of 500.
After graduation from high school, I enlisted in the Navy. My ASVAB (Armed Forces Vocational Aptitude Battery) scores indicated I was on the high-end of their scale. I was by no means a “super genius,” but I scored better than 80% of my contemporaries taking the test. An opening in Electronics school because someone else failed to graduate gave me an opportunity to get more education than I had thought. Of course, the pre-school for electronics school just happened to be known as B/EE, or Basic Electricity and Electronics School, and it was nearly all mathematics. At the time, I had no idea about the men who pioneered what I was studying. Later I would discover they were the life works of people like Georg Simon Ohm, Andre Ampere, , Michael Faraday, James Maxwell, Rudolf Clausius, James Joule, and many others. The most important thing I remember from this time was Ohm’s Law, which allowed one to determine resistance, voltage, or current in a series circuit if one had at least two of the values. As many of my peers discovered, the calculations fell into a nice pattern that was easily remembered as a triangle:
I
E R
I = current measured in Amps
V = Voltage, measured in Volts
R = Resistance measured in Ohms
To find the current, cover up the I, and you know it’s V multiplied by R. To find either the Resistance or the Voltage, cover up the desired item and it is I over its opposite. This worked great in simple circuits, but they didn’t stay simple for long. Soon I was knee deep into circuits with values that changed depending on the state of gates, semi-conductors, and diodes. It got pretty complicated and I was nearly out of my depth on more than one occasion. I managed to pass BE/E with a 73%.
Electronics school proved too much for my brain. Despite spending a lot of time in extra-study, I just couldn’t keep up and I failed. Because of my extra study hours, I was given the opportunity to be reclassified into another rate. After careful consideration of the choices, I ended up in electro-mechanical calibration and repair. This presented another whole aspect of math and physics I was ill-prepared for, but it also provided me with an opportunity to shine. The school spent an entire month teaching what I had learned at BE/E in 7 months. I didn’t really need to pay attention because they were not presenting anything new. In the months that followed, I was able to grasp the concepts of machines, pressure, torque, temperature, mechanical revolution, precision instrument measurement, and several others. I graduated from this school with a 92%.
Despite this early success, my thinking was not very clear, nor was my problem-solving skills very sharp. I would manage to pass promotion tests by a narrow margin, and I was able to perform most of the duties I was assigned to, but I was not the best technician in the world, mostly because I lacked the necessary patience, forethought, and discipline. As my Navy career winded down, I began to look at college. As a sailor, I was afforded an opportunity to take the SAT’s at no cost to me. I scored a 970. Again, this was my abilities as a reader and writer that allowed me to score high on the verbal, and rather dismal on the math. To nobody’s surprise I looked towards earning a degree in a Liberal Arts field.
My college entrance exams indicated I had the necessary skills in English, but lacked math skills. I was enrolled to take Introduction to College Algebra against my wishes. I did try hard, but my frustration, lack of patience, and lack of interest led me to drop the class and seek a degree program that had no math requirement for graduation. I had neatly side-stepped the problem for the time being. However, again and again, I would find myself in situations where math skills were crucial, and I would be unprepared.
By this time, my affinity for all things computing had made itself evident. I had a “knack” for figuring out how to make them work, how to fix basic problems with them, and how to get the most out of them. As a result, I began looking into graduate coursework in computing, where, not surprisingly, I ran into math once more. My first programming class was in C programming . I worked very hard at this, but I never quite felt like I knew what I was doing. The people around me chattered in what seemed to me to be some sort of foreign “techno-babble.” The only reason I passed this class with a “B” was because I had help on my final exam. My program worked really well until it got to the very end when it was supposed to output the results of a mathematical problem. For whatever reason, I couldn’t resolve the error, but a friend of mine saw the issue in a moment and fixed the one or two lines of code needed to make the program work. If this hadn’t happened, I don’t know if I would have passed the class. At the time I was just so relieved to have gotten by this obstacle that I really didn’t consider the fact that no matter how one slices it, I cheated to pass a class. I am not prone to cheating in anything, but in a subject I desperately wanted to learn more about despite my perceived struggles and handicaps, I let it slide. Of course, my lack of understanding would have dire consequences on the next programming class I took.
The next class took C programming several steps further. We were looking at how to use the language to solve more “real world” problems, most of which were purely mathematical in nature. I withdrew from this class twice to avoid failing it outright and I never got a chance to take a programming class at this school again. I got a job teaching computers at a local high school and dropped out of graduate school all together.
My very first teaching job paid very little. My fiancée had been trying to get hired by any district in the area with little or no success, so we both applied to districts outside where we lived and landed interviews with the Clark County School District in Las Vegas Nevada. As luck would have it, both of us got hired, so we packed up and moved across the country to better paying teaching jobs in Nevada.
I taught for a year and found teaching was not what I thought it was going to be. I was not as well-prepared for a more “traditional” classroom as I had thought from a year teaching computers. The rules had changed and I didn’t adjust with them very well. Within a year I was politely told my contract would not be renewed. I was out of a job. I took refuge in the realm that I loved so much: computers. By the time the school year ended, I was on the phones doing technical support for Dell Computers.
My first tech job did not pay very well, but it did have regular bonuses for good call times and resolutions. I quickly gained a reputation for being able to help people with their problems and resolve calls efficiently. My monthly bonuses were among the top 10 for the six months I remained a phone technician. Then I was promoted. My career as a tech would take many unusual twists and turns, sometimes I was out in the field, sometimes I was on the phones, still other times, I was given very non-specific duties to support computing efficiency. All of these jobs were sub-contracting. All of them carried little in the way of benefits and stability. Most of them ended up with my contract being terminated after my services were no longer needed.
In an attempt to improve my chances of landing a more stable position, I decided to go back to school and pursue a Masters in computing. I ended up at the University of Phoenix in their Computer Information Systems Management degree program. Here I began to see what it takes to really run technology projects, how to understand the very uncertain nature of the business world’s take on computing. Technology projects are rarely cheap and more business-minded individuals have a hard time seeing what they call a “return on investment” from them. Technology projects often bolster the infrastructure of a business, but rarely do they have an immediate or direct impact on the bottom line, rather, their benefits are realized in very small increments over a much longer term. This has a tendency to make men and women who are responsible to shareholders nervous and reluctant to allocate funding and resources to IT departments.
As I am now coming to the end of my masters program, a new fire has begun to burn brightly within me. My field has many organizations, journals, conventions, and resources that I have become more aware of. As the industry changes at the speed of light, so must I continually keep up with it through research, reading, and communicating with my peers. As with so many others, my career field often “brushes up against” the fields of science, math, and engineering, so much so that I have become far more aware of the implications they have upon my future. As a result, I have come to read far more technically-oriented materials. I have successfully programmed computers using a variety of programming languages. I have come to see my lack of math skills as a detrimental flaw in my abilities. I have also begun to understand what I never understood before. My lack of understanding of math and science was just that, a lack of understanding. Now that I understand the underlying principles of both, I find myself drawn to the very problems and theories I used to repel from. I want to learn them. I want to be able to apply them. I want to know more. In essence, maturity and a new sense of myself have driven me full circle, and I am no longer afraid.
One day, I was reading what I thought was a fascinating article in Scientific American, where astonishing new theories concerning black holes were just coming to light. These new theories were causing scientists to look at the universe in a radical new way, as one big giant computer. It was once believed that nothing escaped the gravitational forces of a black hole, but brilliant astrophysicist Stephen Hawking, helped prove that some energy did escape from a black hole. Thus it was theoretically possible to input physical matter into a black hole and measure the output energy in a similar way to how one would enter data into a computer program and measure the output. This speculation does not answer whether or not the output would make sense in relation to the input, but the theory is none-the-less fascinating. The article also mentioned something called quantum information theory, which caused me to do a web search on that subject, and that led me to information theory, and a man named Claude Shannon.
In 1948, a mathematician working for Bell Labs named Claude Shannon proposed a mathematical theory for calculating the most efficient means of transmitting a message over a noisy channel. This theory was so revolutionary at the time that it led to breakthroughs in all aspects of communication, electronics, digital electronics, computing, and more. Shannon’s breakthrough paper, A Mathematical Theory of Communication, became the foundation upon which most of our Information Age would be built upon. Here is a man who more than likely died not knowing just how much impact his work would have upon the future. Here I was reading the paper and actually understanding the basic principles of it. Since then, I have ordered more books on this subject, and after that, I began ordering books on subjects such as discrete math, physics, Scientific math, and so on. I have joined the Institute of Electrical and Electronics Engineers, so I could get more access to the “bleeding edge” of technology today. I am looking towards finishing my masters and going on for a PhD. in Information Systems at Nova Southeastern University.
Along with all these developments, I began working as a junior Satellite Hub Technician for Hughes Network Systems, which again has required I learn the finer points of the engineering necessary to keep major satellite communications systems operating, troubleshooting remotely, and understanding the principles of electronic satellite communications. Once again, the marriage of science, math, and technology are demonstrating to me that I cannot hope to pursue a career in this field without all three of them. This time, I’m ready.
©2004, J.S.Brown
0 comments
My natural strengths have always been reading and writing. From the moment I learned to read, I devoured books. The library was my sacred refuge. I could bring home several books from the school library and read them all before going to bed that night. On those nights I couldn’t sleep, I would often use a flashlight to keep on reading after I was supposed to be asleep. I was a troubled child growing up. I often got grounded or restricted to my room. No matter how much trouble I got into, my parents did one thing right: they never took away my books. It was the only thing I had going for me in the dark years of my youth and adolescence. In the 7th grade, we took aptitude tests in math and reading. My reading score was in the 98th percentile. My math was in the 28th percentile. I could read and comprehend better than 98 out of 100 students, whereas I could solve math problems better than only 28 out of 100 students. This disparity would follow me for many years to come. In 9th grade, my teacher noticed me squinting to see the notes on the blackboard. It turned out I was nearsighted, so to add to the discomfort of being an awkward teenager, I added glasses. Now I could see better, but it still didn’t cure my negative attitude towards anything math-related. I failed the first semester of Introduction to Algebra, and as a result, I was transferred into the lower Introduction to High School Math, where I just managed to scrape by. My negative attitude towards school in my freshman and sophomore years of high school would live to haunt me when I struggled my junior and senior years to improve my GPA. Despite getting nearly all A’s and B’s the last two years, my GPA at graduation was a dismal 1.8, placing me close to 345 out of a class of 500.
After graduation from high school, I enlisted in the Navy. My ASVAB (Armed Forces Vocational Aptitude Battery) scores indicated I was on the high-end of their scale. I was by no means a “super genius,” but I scored better than 80% of my contemporaries taking the test. An opening in Electronics school because someone else failed to graduate gave me an opportunity to get more education than I had thought. Of course, the pre-school for electronics school just happened to be known as B/EE, or Basic Electricity and Electronics School, and it was nearly all mathematics. At the time, I had no idea about the men who pioneered what I was studying. Later I would discover they were the life works of people like Georg Simon Ohm, Andre Ampere, , Michael Faraday, James Maxwell, Rudolf Clausius, James Joule, and many others. The most important thing I remember from this time was Ohm’s Law, which allowed one to determine resistance, voltage, or current in a series circuit if one had at least two of the values. As many of my peers discovered, the calculations fell into a nice pattern that was easily remembered as a triangle:
I
E R
I = current measured in Amps
V = Voltage, measured in Volts
R = Resistance measured in Ohms
To find the current, cover up the I, and you know it’s V multiplied by R. To find either the Resistance or the Voltage, cover up the desired item and it is I over its opposite. This worked great in simple circuits, but they didn’t stay simple for long. Soon I was knee deep into circuits with values that changed depending on the state of gates, semi-conductors, and diodes. It got pretty complicated and I was nearly out of my depth on more than one occasion. I managed to pass BE/E with a 73%.
Electronics school proved too much for my brain. Despite spending a lot of time in extra-study, I just couldn’t keep up and I failed. Because of my extra study hours, I was given the opportunity to be reclassified into another rate. After careful consideration of the choices, I ended up in electro-mechanical calibration and repair. This presented another whole aspect of math and physics I was ill-prepared for, but it also provided me with an opportunity to shine. The school spent an entire month teaching what I had learned at BE/E in 7 months. I didn’t really need to pay attention because they were not presenting anything new. In the months that followed, I was able to grasp the concepts of machines, pressure, torque, temperature, mechanical revolution, precision instrument measurement, and several others. I graduated from this school with a 92%.
Despite this early success, my thinking was not very clear, nor was my problem-solving skills very sharp. I would manage to pass promotion tests by a narrow margin, and I was able to perform most of the duties I was assigned to, but I was not the best technician in the world, mostly because I lacked the necessary patience, forethought, and discipline. As my Navy career winded down, I began to look at college. As a sailor, I was afforded an opportunity to take the SAT’s at no cost to me. I scored a 970. Again, this was my abilities as a reader and writer that allowed me to score high on the verbal, and rather dismal on the math. To nobody’s surprise I looked towards earning a degree in a Liberal Arts field.
My college entrance exams indicated I had the necessary skills in English, but lacked math skills. I was enrolled to take Introduction to College Algebra against my wishes. I did try hard, but my frustration, lack of patience, and lack of interest led me to drop the class and seek a degree program that had no math requirement for graduation. I had neatly side-stepped the problem for the time being. However, again and again, I would find myself in situations where math skills were crucial, and I would be unprepared.
By this time, my affinity for all things computing had made itself evident. I had a “knack” for figuring out how to make them work, how to fix basic problems with them, and how to get the most out of them. As a result, I began looking into graduate coursework in computing, where, not surprisingly, I ran into math once more. My first programming class was in C programming . I worked very hard at this, but I never quite felt like I knew what I was doing. The people around me chattered in what seemed to me to be some sort of foreign “techno-babble.” The only reason I passed this class with a “B” was because I had help on my final exam. My program worked really well until it got to the very end when it was supposed to output the results of a mathematical problem. For whatever reason, I couldn’t resolve the error, but a friend of mine saw the issue in a moment and fixed the one or two lines of code needed to make the program work. If this hadn’t happened, I don’t know if I would have passed the class. At the time I was just so relieved to have gotten by this obstacle that I really didn’t consider the fact that no matter how one slices it, I cheated to pass a class. I am not prone to cheating in anything, but in a subject I desperately wanted to learn more about despite my perceived struggles and handicaps, I let it slide. Of course, my lack of understanding would have dire consequences on the next programming class I took.
The next class took C programming several steps further. We were looking at how to use the language to solve more “real world” problems, most of which were purely mathematical in nature. I withdrew from this class twice to avoid failing it outright and I never got a chance to take a programming class at this school again. I got a job teaching computers at a local high school and dropped out of graduate school all together.
My very first teaching job paid very little. My fiancée had been trying to get hired by any district in the area with little or no success, so we both applied to districts outside where we lived and landed interviews with the Clark County School District in Las Vegas Nevada. As luck would have it, both of us got hired, so we packed up and moved across the country to better paying teaching jobs in Nevada.
I taught for a year and found teaching was not what I thought it was going to be. I was not as well-prepared for a more “traditional” classroom as I had thought from a year teaching computers. The rules had changed and I didn’t adjust with them very well. Within a year I was politely told my contract would not be renewed. I was out of a job. I took refuge in the realm that I loved so much: computers. By the time the school year ended, I was on the phones doing technical support for Dell Computers.
My first tech job did not pay very well, but it did have regular bonuses for good call times and resolutions. I quickly gained a reputation for being able to help people with their problems and resolve calls efficiently. My monthly bonuses were among the top 10 for the six months I remained a phone technician. Then I was promoted. My career as a tech would take many unusual twists and turns, sometimes I was out in the field, sometimes I was on the phones, still other times, I was given very non-specific duties to support computing efficiency. All of these jobs were sub-contracting. All of them carried little in the way of benefits and stability. Most of them ended up with my contract being terminated after my services were no longer needed.
In an attempt to improve my chances of landing a more stable position, I decided to go back to school and pursue a Masters in computing. I ended up at the University of Phoenix in their Computer Information Systems Management degree program. Here I began to see what it takes to really run technology projects, how to understand the very uncertain nature of the business world’s take on computing. Technology projects are rarely cheap and more business-minded individuals have a hard time seeing what they call a “return on investment” from them. Technology projects often bolster the infrastructure of a business, but rarely do they have an immediate or direct impact on the bottom line, rather, their benefits are realized in very small increments over a much longer term. This has a tendency to make men and women who are responsible to shareholders nervous and reluctant to allocate funding and resources to IT departments.
As I am now coming to the end of my masters program, a new fire has begun to burn brightly within me. My field has many organizations, journals, conventions, and resources that I have become more aware of. As the industry changes at the speed of light, so must I continually keep up with it through research, reading, and communicating with my peers. As with so many others, my career field often “brushes up against” the fields of science, math, and engineering, so much so that I have become far more aware of the implications they have upon my future. As a result, I have come to read far more technically-oriented materials. I have successfully programmed computers using a variety of programming languages. I have come to see my lack of math skills as a detrimental flaw in my abilities. I have also begun to understand what I never understood before. My lack of understanding of math and science was just that, a lack of understanding. Now that I understand the underlying principles of both, I find myself drawn to the very problems and theories I used to repel from. I want to learn them. I want to be able to apply them. I want to know more. In essence, maturity and a new sense of myself have driven me full circle, and I am no longer afraid.
One day, I was reading what I thought was a fascinating article in Scientific American, where astonishing new theories concerning black holes were just coming to light. These new theories were causing scientists to look at the universe in a radical new way, as one big giant computer. It was once believed that nothing escaped the gravitational forces of a black hole, but brilliant astrophysicist Stephen Hawking, helped prove that some energy did escape from a black hole. Thus it was theoretically possible to input physical matter into a black hole and measure the output energy in a similar way to how one would enter data into a computer program and measure the output. This speculation does not answer whether or not the output would make sense in relation to the input, but the theory is none-the-less fascinating. The article also mentioned something called quantum information theory, which caused me to do a web search on that subject, and that led me to information theory, and a man named Claude Shannon.
In 1948, a mathematician working for Bell Labs named Claude Shannon proposed a mathematical theory for calculating the most efficient means of transmitting a message over a noisy channel. This theory was so revolutionary at the time that it led to breakthroughs in all aspects of communication, electronics, digital electronics, computing, and more. Shannon’s breakthrough paper, A Mathematical Theory of Communication, became the foundation upon which most of our Information Age would be built upon. Here is a man who more than likely died not knowing just how much impact his work would have upon the future. Here I was reading the paper and actually understanding the basic principles of it. Since then, I have ordered more books on this subject, and after that, I began ordering books on subjects such as discrete math, physics, Scientific math, and so on. I have joined the Institute of Electrical and Electronics Engineers, so I could get more access to the “bleeding edge” of technology today. I am looking towards finishing my masters and going on for a PhD. in Information Systems at Nova Southeastern University.
Along with all these developments, I began working as a junior Satellite Hub Technician for Hughes Network Systems, which again has required I learn the finer points of the engineering necessary to keep major satellite communications systems operating, troubleshooting remotely, and understanding the principles of electronic satellite communications. Once again, the marriage of science, math, and technology are demonstrating to me that I cannot hope to pursue a career in this field without all three of them. This time, I’m ready.
TANSTAAFL!
©2004, J.S.Brown
0 comments
0 Comments:
