Last night, I submitted the grades for the summer session of MATH 106, Finite Mathematics, at UMUC. Teaching Finite Mathematics is kind of a mixed bag and this term, was my first hybrid 106 session. So I began the first night with a warning to my students that this would be the worst class they would ever take. It is an eight-week class and we cover several broad topics pretty quickly:
- Personal finance
- Linear equations and inequalities
- Linear programming
- Sets, counting, and probability
- Statistics focusing on the normal distribution
Each of these lines alone could merit a full semester-long course. To hit the highlights and move on requires a stamina a lot of students do not have.
Finite mathematics is one of two ways to meet the mathematics distribution requirement at UMUC. The other is to take a traditional college algebra course, MATH 107, that moves from functions to quadratics to polynomials to exponentials at the normal pace. This course is also equivalent to the first half of our MATH 115, Pre-Calculus, course. UMUC does not offer a mathematics major and only students majoring in computer science or environmental management require any other mathematics. Many majors have a statistics requirement, but that is for a different post.
I have begun introducing MATH 106 as the hardest course they will ever take. It is a great and fun course to teach because you can bounce from topic to topic almost weekly. But because the professor can bounce from topic to topic almost weekly, the class is very difficult for students. There’s no continuity. Even where there’s natural continuity in the material, from sets to probability, we don’t have the time to present it well. And student who get lost and frustrated early in the course never come back, despite the lack of continuous building so common in other math courses.
Generally, I have not met a lot of students who consider MATH 106 to be a good experience. I will keep teaching it and I will keep warning students about the pace and effort required to keep up. But I would rather see students who will not make it switch classes early in the semester, when there is no penalty, than to continue in a class where they cannot succeed. This provides students the best outcome when they can actively engage, learn, and master the material.
When American businesses want to do business in other countries, they take on several types of risk that are unfamiliar to domestic operations. Some are easy to manage. For instance, foreign exchange risk is the risk that a sale denominated in a foreign currency may be worth less later than it is now. Compared to some risk types, the risk premium is relatively easy to calculate. Purchasing insurance, in the form exchange rate swaps, is also relatively easy and the risk is transferred to a financial institution that specializes in managing risk. Of course, foreign exchange risk goes both directions and it is also possible the sale in a foreign currency is worth more later than at the time of sale.
Other types of risk, such as political risk are more difficult to manage. Political risks are the risks that stem from political instability and include war, regulatory changes, expropriation, and other legal and extralegal changes that affect in-country business operations. These types of risks are much harder to estimate and therefore harder to price. Accordingly, it is harder to purchase insurance against these types of risks. When risk is hard to price, it is not unusual for the government to step in and provide a risk insurance regime using the best risk estimation feasible.
One agency that provides this service is the Export-Import Bank of the United States (Ex-Im Bank). Due for reauthorization by September, the Ex-Im Bank is under attack as a government giveaway to big business. The Ex-Im Bank specifically provides insurance to American manufacturers that are exporting durable goods to foreign counties. For instance, the Bank’s largest customer is Boeing and Ex-Im absorbs the risk of exporting American-made airplanes to risky customers. Since the Ex-Im Bank only provides risk financing to sales that no commercial bank will finance, these planes would not be otherwise exported or manufactured.
The Ex-Im Bank is one of many organizations that provide this service. In the United States, there is also the Overseas Private Investment Corporation (OPIC) that provides risk support and financing to in-country projects (as opposed to commercial goods sales). Other countries also provide such risk financing. Finally, the United States participates in numerous international development organizations that provide similar services including the Multilateral Investment Guarantee Agency (MIGA), a component of the World Bank Group. Nevertheless, the fight over the Ex-Im Bank is expected to be intense.
A few weeks ago, the family flew to Columbus for my sister’s graduation from law school. On the way back, we bought a bottle of Fiji water.
Which I drank.
Because the flight path from Columbus to Baltimore is kind of a rainbow, we went up an down quickly. I finished the bottle of water at the peak of the flight path. I twisted the cap on as hard as possible.
After we hit the ground, my bottle looked like this:
I fairly well sealed the bottle when I screwed the cap on. But the plane is not pressurized to the same pressure as the air at sea level. There, the air pressure is roughly 14.7 pounds per square inch. However, the airplane is pressurized only to between 8 and 11 pounds per square inch.1 The outside air pressure is between 3 and 4 psi. By using a lower pressure on the plane than 14.7, there is less stress placed on the airframe extending its lifetime and it is high enough to not be completely uncomfortable, though your ears may disagree. But as the pressure increases, it grows higher outside the bottle than inside, which was sealed between 8 and 11 psi. So the bottle’s sides cave in as far as the shape of the bottle will permit. And when opened, there’s a delightful whoosh, but instead of carbonation leaking, the bottle is refilling with air.
- Thank you Al Romack for this information. ↩
I’ve done this before:
But I might have a real problem. Apparently MEININGER Hotels posted this:
I’ve not verified it was actually posted, mostly because I am afraid of the answer. But when presented with an opportunity at the Château Laurier in Ottawa, I did this: