UTK Biology Degree Learning Objectives and Math151 Students seeking a degree in Biological Sciences (whether the concentration is in Biochemistry, Cellular, and Molecular Biology, Ecology and Evolutionary Biology, or Microbiology) are expected to be able to do the following by the time they graduate: Explain and provide examples of each the five big ideas in Biology, using their knowledge of biological concepts gained from their course of study: 1. Evolution: Populations of organisms and their cellular components have changed over time through both selective and non-selective evolutionary processes. 2. Structure and Function: All living systems (organisms, ecosystems, etc.) are made of structural components whose arrangement determines the function of the systems. 3. Information Flow and Storage: Information (DNA, for example) and signals are used and exchanged within and among organisms to direct their functioning. 4. Transformations of Energy and Matter: All living things acquire, use, and release and cycle matter and energy for cellular / organismal functioning. 5. Systems: Living systems are interconnected, and they interact and influence each other on multiple levels. Note that these biological concepts are more fully explained in the AAAS/NSF report “Vision and Change in Undergraduate Biology Education” (available at visionandchange.org) and the course instructor is one of the authors of this report. In addition to the above, Biology students are expected to demonstrate the ability to perform the following scientific practices: Formulate empirically-testable hypotheses Interpret visual representations (figures and diagrams) Evaluate data and come to a conclusion (with evidence) (formulate an argument) Math151 contributes to each of the above learning objectives and abilities by covering the key mathematical methods that are used to investigate each of the above five "Big Ideas" and emphasizing the applications of these methods to the Ideas. For example, we will analyze the basic mathematical models of population genetics, which is a key topic in evolutionary biology. We will develop matrix modeling methods that are used to investigate the structure of biological systems at various hierarchical levels (cell size distributions, population age distributions, etc.). The discrete dynamical systems and matrix models we develop are among the simplest methods to analyze systems of interacting biological entities and the probability ideas we develop are essential to analyze information flow within and between biological levels.