Class, College, and Life
spring 2011 course description
spring 2011 syllabus
instructions for the TI-84
study tips
Modeling and Statistics are two branches of applied mathematics. Modeling involves fitting equations to data, usually just approximately. Statistics is the science of uncertainty.
Both of these fields got their starts during the Renaissance, the period during the 14th to the 17th centuries in which European science and culture were "reawakened" from the Dark Ages. Modeling began as physicists attempted to predict the motions of the planets, the phases of the moon, and other natural phenomena. Eventually other disciplines, such as biology, sociology, and business, learned the methods, so that today mathematical modeling is an integral part of research in many fields. Statistics was initially developed to analyze errors in measurements. When different measurements for the same quantity (time between full moons, large distances on the earth's surface) were compared, it was quickly discovered that they formed a pattern, the now-familiar bell curve. Not long afterward, probability was invented to understand games of chance, and then greatly enhanced the understanding and applicability of statistics. Today, the two are intertwined in the area called inferential statistics.
In this beginning course, we study three kinds of mathematical models: linear, exponential, and power. The main idea is to collect data that relates two variables, say x and y, graph the data, and use the shape of the graph to pick a likely family of possible equations. Each family has infinitely many members (think of all the possible lines there are: different slopes, different y-intercepts), and one of these members will be the best fit for the data. The fit might not be exact; in fact, it might be very poor (not all data is remotely linear). Using mathematical analysis, we can judge just how useful that particular equation is. After we decide on the appropriate equation, the model, we can use it to make predictions about the variables.
We will see two kinds of statistical analysis: descriptive and inferential. Descriptive statistics assigns numerical values to data sets so that we can gain a quick and rough understanding of the numbers. For example, the mean tells us approximately how large the numbers are and the variance describes how spread out from each other they are. Inferential statistics allows us to test hypotheses about data. For example, we might hypothesize that male and female Stetson students get the same grades. We take random samples of male and female GPA's, and perform a hypothesis test, which will tell us how likely that hypothesis is.
Class, College, and Life
spring 2011 course description
spring 2011 syllabus
instructions for the TI-83/84
study tips
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