In many of the fields of science the task of "coordinating, arranging, and systematizing" the knowledge can be difficult precisely because mathematics cannot easily be applied. Although mathematics has the reputation of being a difficult subject, it is tremendously efficient at compressing information. If a picture is worth a thousand words, an equation is worth a thousand pictures. Consider, for example, the effect of temperature, volume, and composition on the total pressure of a mixture of three solvents in equilibrium with its vapor, or the shape of the cone of depression around a well as it depends on soil permeability and water flow. We cannot easily visualize high-dimensional relationships, so they must be represented by a family of curves. Alternatively, the information could be contained concisely in a single mathematical representation. However, biological systems often are not described so compactly.

This leads us to discuss how to approach the study of biology. The method usually first thought of is to apply memorization. This is laborious and unproductive. It is extremely difficult to keep numerous unconnected facts in your head for any amount of time. The key, then, is to establish connections, to seek out relationships. This recovers some of the efficiency of the mathematical equation. We can think graphically about concepts, mentally plotting developmental trends, sequences, patterns, and networks of relationships.

Make studying an active process by keeping notes: Outline the reading and write lists, even lists of lists, under a unified topic. See if you can create an explanation of the concepts in each section of this book in your own words. If you have trouble with this at some point, you should formulate the difficulty as a question and seek the answer in the references or from your instructor. To learn a complex relationship from a figure such as the oxidation of glucose in Figure 5.5 or the nitrogen cycle in Figure 14.7, try copying it (possibly with less detail), and then try reproducing it again with the book closed.

Create what are known as concept maps. These are graphical representations of the relationships among information. For example, Figure 1.3 shows a concept map for science and engineering science topics in environmental engineering education, emphasizing the place of biology and leading to the twin roles of environmental engineers: design and prediction. To create a concept map, start with a list of related concepts. Then, state an organizing principle, which is a concept or idea used to arrange and connect items appropriately. The organizing principle behind Figure 1.3 is that connections lead from one topic to others that require their application. Another arrangement of

Mathematics

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