On the magnitude of Gauss's achievements
Carl Friedrich Gauss.
Widely agreed upon among mathematicians as, at worst, the third best mathematician of all time. The more I learn about him, the more I admire him. The more I admire him, the more astonished I become. The more astonished I become, the more sheer terror washes over me.
Gauss's influences span a significant proportion of mathematical fields: number theory, linear algebra, complex analysis, and, my favorite, statistics to name very few. Perhaps the most paramount principle in the realm of regression analysis was the result of Gauss's work. This was simply the tip of the iceberg as he was only nineteen when he arrived at this result.
Further agreed upon by the mathematical community is the uniformly highest esteem in which Gauss's doctoral dissertation is held. My breakdown of even the roughest outline of his abstract will not even begin to do him justice. Simply put: he made perhaps the most important contribution to pure mathematics to date.
As I study the Gauss-Markov theorem and practice the Gaussian elimination algorithm, I am left to ponder what he could achieve had he been born in the age of technology. I dare say, this hypothetical is pointless to speculate upon as technology could easily be argued to be the result of the types of things he and other analytical minds put their hands to with sticks and stones.
Why am I writing about all this?
1. Procrastination...finals are in a little over eighty hours.
2. I feel that our understanding of higher level mathematics has been obscured by computing power.
I quote R.R. Hocking:
"The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved."
Witness the motivation behind reason #2 for this particular blog entry.
As a side note, in undergraduate, a classmate of mine asked the professor, "What if Euler had Maple?" To which she jokingly responded, "There'd be nothing left to prove!"
As I am finishing my master's core courses, I find myself "bridging the gap" between technology and analytical methodology to which Hocking refers. When I first started in the program, I knew how to type in some code and interpret a small portion of computer output and, finally, fire off the bottom line.
"Yes, the data seem to indicate that when you imbibe copious amounts of caffeine and nicotine, you are significantly more likely to post jargon on the internet."
I feel as though this linear models course is tying everything together. Having a solid, complete and thorough understanding of the behind the scenes calculations is vital to being a statistician. Hocking said what needed to be said in perfect wording.
As I watch the undergraduate college algebra students in the computer lab operate the Microsoft Calculator that comes with Windows, I begin to understand why it is important to be one of these "educated end-users."
Enough blabbering, back to studying...
Widely agreed upon among mathematicians as, at worst, the third best mathematician of all time. The more I learn about him, the more I admire him. The more I admire him, the more astonished I become. The more astonished I become, the more sheer terror washes over me.
Gauss's influences span a significant proportion of mathematical fields: number theory, linear algebra, complex analysis, and, my favorite, statistics to name very few. Perhaps the most paramount principle in the realm of regression analysis was the result of Gauss's work. This was simply the tip of the iceberg as he was only nineteen when he arrived at this result.
Further agreed upon by the mathematical community is the uniformly highest esteem in which Gauss's doctoral dissertation is held. My breakdown of even the roughest outline of his abstract will not even begin to do him justice. Simply put: he made perhaps the most important contribution to pure mathematics to date.
As I study the Gauss-Markov theorem and practice the Gaussian elimination algorithm, I am left to ponder what he could achieve had he been born in the age of technology. I dare say, this hypothetical is pointless to speculate upon as technology could easily be argued to be the result of the types of things he and other analytical minds put their hands to with sticks and stones.
Why am I writing about all this?
1. Procrastination...finals are in a little over eighty hours.
2. I feel that our understanding of higher level mathematics has been obscured by computing power.
I quote R.R. Hocking:
"The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved."
Witness the motivation behind reason #2 for this particular blog entry.
As a side note, in undergraduate, a classmate of mine asked the professor, "What if Euler had Maple?" To which she jokingly responded, "There'd be nothing left to prove!"
As I am finishing my master's core courses, I find myself "bridging the gap" between technology and analytical methodology to which Hocking refers. When I first started in the program, I knew how to type in some code and interpret a small portion of computer output and, finally, fire off the bottom line.
"Yes, the data seem to indicate that when you imbibe copious amounts of caffeine and nicotine, you are significantly more likely to post jargon on the internet."
I feel as though this linear models course is tying everything together. Having a solid, complete and thorough understanding of the behind the scenes calculations is vital to being a statistician. Hocking said what needed to be said in perfect wording.
As I watch the undergraduate college algebra students in the computer lab operate the Microsoft Calculator that comes with Windows, I begin to understand why it is important to be one of these "educated end-users."
Enough blabbering, back to studying...