Careers in Math - Essay Example

Careers in Math The average national price of gas in May 2005 was approximately $2.10 per gallon (This Week in Petroleum 2005). The national average rose steadily for the next two months, and then dropped off slightly on July 25, 2005, when it reached about $2.27 per gallon (This Week in Petroleum 2005). This price remained constant for another two weeks and then proceeded to rise to record heights by September 5, 2005, when the national average reached $3.05 per gallon (This Week in Petroleum 2005).

Since that time, gas prices have steadily decreased to about $2.30 per gallon on October 31, 2005 (This Week in Petroleum 2005). This change in gas prices has been attributed to many things, including the war in Iraq, and Hurricanes Katrina and Rita. This is a real-life example of the pre-calculus concept of functions. The problems with modeling this situation are obvious. There are so many factors that could be involved it is difficult to tell which is the actual cause of the change, and then there is the difficulty with the rate of change.

Finally, there is the pesky problem of the spot price and the difficulties with assessing how spot prices affect retail prices. Retail prices usually follow the spot price shifts, but they sometimes lag behind (This Week in Petroleum 2005). These are the sorts of issues that must be analyzed and solved by mathematicians working out in the real world. One person who designs and runs numerous mathematical models for decision-making purposes is Amanda Peterson, who works in the Operations Research department of the Dynamic Research Corporation.

Often, decision problems can be solved using mathematical equations, but there are "cases, when the situation is too detailed for a math model alone or the customer, prefers a more visual product" (MAA Online 2005). Then she writes a computer program called a simulation model to simulate the different aspects of the problem. Decision-makers can use this model to test different scenarios. This helps them to quickly determine the best solution for the problem. She loves her job because: building a simulation model is similar to solving a puzzle or a math problem All of the pieces must fit together just right and after I've figured out how they fit together, I have a working simulation model which I can proudly present to my customer (MAA Online 2005).

Ellen Lentz combines her love of life sciences with her love of math in her job as a biostatistician for Hoffman La Roche Pharmaceuticals. Statistics and pre-calculus functions are very similar to each other. They both seek to analyze the results of changing a set of variables. Ellen Lentz uses her mathematical knowledge to: help clinicians find the best way to conduct an experiment to answer the most important questions to them. I calculate the number of subjects needed in each trial in order to make a conclusion with a given certainty on the effect of a new drug (MAA Online 2005).

Then the researchers know whether a drug is effective or not, and what changes they need to make within the formula in order to produce the desired results. Dr. Lentz provided me with a simple example of the kind of real-world math that she does every day: Suppose that you are trying to test the effectiveness of a certain drug. The effectiveness is measured by a positive difference between the pre-trial (A) and post-trial average test scores (B) between the two groups (X and Y). Group X is the experimental group (the group receiving the drug), and Group Y is the control group (the group that received a placebo, instead of a drug).

The pre-trial test score of Group X = 3. Their post-trial test score = 35. The pre-trial test score of Group Y = 5. The post-trial test score = 42. I see that this problem can be easily translated into a slope equation: m = (5 - 42) / (3 - 35). M, therefore, equals -37/-32, which equals 1.156. Since the slope is positive, the test scores rise as a function of the drug, so the drug is effective in this case. If the slope had been negative, we would have said that the drug was ineffective, and if the slope had been 0, we would have said that more tests would be necessary to test the drug's effectiveness because they were no changes in test scores due to treatment.

This is only one example of the many interesting situations in which professionals use pre-calculus concepts to solve real-world problems that can have a profound impact on all our lives. In the coming weeks, I will establish a free blog with BlogSpot.com in order to continue communications with Ms. Peterson and Dr. Lentz, and I will try to enlist the cooperation of other professionals who use math in the real world. This will facilitate networking and academic discussions and will enable an increased understanding of the broad expanse of careers that are available in the field of mathematics.