Do the Math

1.31.2006

Update on Mac Contest, Nearly $10,000 Up For Grabs

Colin Niederkoorn, a Mac enthusiast, has been running a contest to encourage the computer savvy to crack the new Intel-based Macs. The goal: run a dual boot Windows XP / Mac OS X system on Mac's newest line of MacBooks.

To date, no one has cracked the EFI interface, but donations have soared. As of 9:57pm EST, online donors have raised the prize to $9,569! Incredible.

Links:
Previous blog post
Contest page

1.28.2006

Get an MIT Education Free of Charge!

The Massachusetts Institute of Technology (MIT) has unleashed a set of free online courses to the public. According to their site, MIT's OpenCourseWare is
...a free and open educational resource for faculty, students, and self-learners around the world. OCW supports MIT's mission to advance knowledge and education, and serve the world in the 21st century. It is true to MIT's values of excellence, innovation, and leadership.
OCW offers a wide variety of subjects and courses. For the mathematically inclined, they provide anything from online exams for single-variable calculus to in-depth video lectures on differential equations and linear algebra.

1.27.2006

What's This E-Sports Thing Then?

A good friend of mine wrote an in-depth article on the history of professional gaming, or e-sports.

You can read it on her blog.

1.26.2006

Run Windows XP on a Mac and get $6000!

A Mac user's mistake has jumpstarted an online-donation fest. Colin Niederkoorn, an avid Mac user, told his boss that a new Intel based MacBook could dual boot Windows XP and would replace his IBM desktop. He was wrong.

Due to a modification in the new MacBook BIOS, no one has found a way to run Windows on the Intel Mac.

Enter Niederkoorn, who pledged $100 of his own money as a reward to the first person to provide him with a dual-boot solution. So far, online donations to the cause have rocketed the reward to nearly $7000!

Links:
The Donation Page
Colin Niederkoorn's Blog
Article on DailyTech.com

1.21.2006

Natural Geometric Tendencies in Humans

According to a recent article from MSNBC, people may have a natural talent for geometry. This realization comes from a study published in the journal Science. Researchers tested a set of Amazon villagers in a nonverbal picture-test. Villagers got about two thirds of the answers right, which is equivalent within acceptable uncertainties to the results from a set of 28 American children. American adults scored better than any other groups.

You can read the whole article here.

Take the test yourself by clicking here.

Math Trivia: Sets

A set is simply a collection of objects.
We represent common sets by scripted letters.
For example:
R is the set of all real numbers.
N is the set of all natural numbers. That is: N = { 1, 2, 3, ... }
C is the set of all complex numbers.
So far, the symbols make sense. R for Reals, N for Naturals. But what about the following sets?
Z is the set of all integers. Z = {..., -2, -1, 0, 1, 2, ... }
Q is the set of all rational numbers. Formally: Q = { p/q | p, q ∈ Z }
Most readers should be fairly perplexed by the unusual choice of symbols. Why Z and Q? After much delay, here is your math tip:

  • The set of all integers is denoted by Z for the german word for integers: Zahlen.
  • The set of all rationals is denoted by Q for the word Quotient. Rationals are simply quotients of integers.
Read more about set theory here, and here.

New Kit: Blackhawk For the Win!

After months of deliberation, I have finally decided on a new backpack. The verdict: Blackhawk Industries' 3-Day Assault Pack. I was torn between this and Maxpedition's Vulture-2.

The Vulture carries a lot more stuff, and is lined with MOLLE webbing for expandability, which is a plus. Unfortunately, this pack does not include a frame, making those heavy loads of books or supplies that much more cumbersome. Another negative, is that the Vulture is far too large for my needs.

Blackhawk's pack on the other hand, is not lined with any webbing whatsoever. It remains highly expandable though. The pack features attachment straps on either side, along with sleeping bag straps on the bottom. This pack also includes a sleave for an optional internal frame kit which I ordered with the backpack. The real selling point though, is in its durability. Blackhawk Industries is one of the most trusted brands in tactical gear, and this pack has been battle-tested and mother approved. Another plus, is that the 3-day assault pack features attachments to internally mount a 100 oz hydration pack. This may prove invaluable for long-duration hikes as well as endless days on campus.

Expect a full review when it arrives.

1.19.2006

First Impressions

Today marked my third day of classes. Here are my first impressons regarding each:

Calculus III:

An introduction to the world of 3-dimensional coordinate systems and multivariable calculus. Unfortunately, my professor has been out of town this week and I have yet to meet him. Since I am retaking this class to improve a previous grade, it is unlikely that I will have much difficulty. For a mathematics major, I am surprisingly weak in methods of integration, so if complex integrands come up, I may be in for a ride. This course will prove to be a much needed review and will greatly improve the stability of my mathematical foundation.

Differential Equations II:
DE2 will serve as an introduction to partial differential equations and boundary-value problems. The professor is Dr. Jan Zijlstra, one of my favorite teachers at MTSU, and the same instructor I took DE1 with. There are only seven students in the class, all of which are math majors. Resultingly, the atmosphere is very light at personable. Thus far, we have derived the heat equation from some basic facts from physics. The first hurdle will be to solve this equation. As a fan of applied mathematics, I am already enjoying this course.

Abstract Algebra:
So far, nothing has been covered in this class, but I did get the chance to look over the book. Abstract is certainly the right word for this course. Fans of mathematical theory and logical thinking will love this one. Over the course of the semester, I will get a thorough treatment of group theory, a touch of Galois theory, and a brief introduction to ring theory. All of these are very interesting as they are active fields of contemporary mathematics. Even better, Dr. Krishnamani, my professor, encourages student research by allowing an optional research project to be substituted in place of a test.

Number Theory:
Even more abstractions. This will be my first advanced course in pure mathematics. In our first class meeting, Dr. Sinkala presented the one fact that we are allowed to know: the well-ordering principle. The well ordering principle states that every nonempty set of positive integers contains a smallest number. Using this principle, we will presumably construct everything else. I am still a little unclear as to what number theory is really all about, but I'm sure that will change over the course of the semester.

Microeconomics:
Yet another general education class. I believe this will be the last one. There really isn't much to be said about this one. Markets, supply, demand, etc. Fortunately for me, economics is one of the most scientific and mathlike areas of business, so I should feel quite at home.

1.16.2006

Back to school.

The winter break has come to a close, and I'm glad for it. Although I've been flying a little more over the winter, I've been a little bored. Maybe I'm just excited. This semester marks my first full load of upper division mathematics, which should prove to be both exciting and challenging.

My schedule for the semester is as follows:
Abstract Algebra
Calculus III
Diferential Equations II
Number Theory
Microeconomics

In addition to this, I am drawing up plans for a new ground school program to combat the scheduling difficulties encountered with my previous attempt. Expect further details in the near future (that is, unless school swats me off the web for a while).

Engine Failure

At my nine to five the other day, I heard some rather sad news. A coworker's husband had died in a paraplane accident. Apparently, the engine quit. Shortly thereafter, the plane and pilot plummeted 200 feet to the ground. I can not claim to know much about the operation of paraplanes, but I do know that a failed engine is a perfectly survivable event in an airplane. Perhaps we all could use a little review in that pilot's worst fear: the emergency engine-out.

There you are all alone in the sky. With the magnificent view beneath you, you can't help but feel a little godlike. You turn left, when suddenly the engine gets quiet. Your engine, that lifeline that was keeping you in the air, just died. Now, you are faced with a grim reality: one of your worst nightmares has come true.

Don't panic, so you've lost an engine. The airplane still has wings, right? OK then, since you can still fly the plane, the only thing that changed is that you have to start coming down. But remember: you are still in control.

Lets break down the procedure step by step.
Recite your ABC's...
A is for Airspeed. Immediately pitch up (or down) for best glide speed. Before flying any airplane, you should know this number by heart. If you don't, go get your POH and look it up now. Now trim the airplane to hold best glide.
B is for Best Field. Look out that window and finalize your decision on the best field to land. Remember, the field needs to be close enough to get to, large enough to land in, and needs to be clear of trees, power lines, and other hazardous obstacles. If possible, try to choose a field facing into the wind, but don't get too picky. Remeber, you don't have an engine, which makes time a commodity. Pick your field, and begin manuevering towards it.
C is for Checklist. Now that we're all set for that landing, lets try to restart the engine. Go through your engine out checklist in a smooth and orderly fashion. Ideally, you want to practice this frequently enough to make it second-nature. Remember, move quickly, but don't rush through this. You can always make things worse by going too fast. Keep your cool.
D is for Declare the emergency. So that engine wouldn't start up after all. Keep setting yourself up for the landing while you switch your transponder over to the emergency code of 7700. While your at it, you'ld better tune into the emergency frequency of 121.5 and make your may-day call.

Once you are certain that the engine will not restart, go ahead and shut down the fuel system. Your engine-out checklist should dictate this to you, but typically you will turn the fuel pump, fuel selector, mags, and master off. Ensure that the seat belts are buckled and tightened, and crack the door open on approach. Before you land, it is advisable to turn the ELT on as well. Now land the plane.


OK, so you've got the checklist down, but just how do you go from cruise to landing in your field without an engine? Easy. Fly to the field of intended landing. If you have excessive altitude, simply circle the field, and KEEP YOUR EYE ON IT to bleed off that altitude. Ideally, you want to manuever the plane to be on the downwind, abeam the intended touchdown point, 1000' agl. From then on, it is simply a judgement game. Based on your rate of descent and groundspeed, make your turns to base / final. Don't worry about squaring off the pattern. This is an emergency, so do what you have to do to make the plane land at that perfect patch of grass you picked out. Remember, its always better to be a little high than low. Without an engine, you can't reclaim lost altitude. If you are too high though, you can always drop some flaps, slip the airplane, or make S-Turns to get her down. In a pinch, you can always do all three.

If you are a pilot, and you do not feel 100% confident in your ability to land without an engine, it is advisable that you spend some time with a CFI building experience and confidence in engine-out procedures.

1.10.2006

First Post

Until I can put something more professional together, this will be a temporary home for the blog/news feature of my future site. If blogger proves to be more useful than expected, I may include mathematical and aviation related sections. We shall see.