Class meeting time and location: MWF 12:00-12:50 p.m. in S 143
Units: 3
Prerequisites: Math 76, or consent of instructor
The required textbook is E. K. Yeargers, R. W. Shonkwiler, and J. V. Herod, An Introduction to the Mathematics of Biology: With Computer Algebra Models, Birkhauser, Boston, 1996.
The main purpose of this course is to introduce the student to scientific research using mathematical modeling while teaching some of the latest computer software tools. The student will be led through the steps of selecting a topic of interest, collecting the background information and data, and using tools such as Maple, LaTeX, and PowerPoint to analyze the data and present results. An introduction to mathematical modeling using populations will be presented in order to illustrate the development of a mathematical model from first principles. Additionally, topics related to working with data sets and curve fitting will be explored. Please note that even though the course focuses on applied mathematical topics in lecture, research topics in pure mathematics and fields related to mathematics are strongly encouraged.
The object of this course is to become familiar with various aspects of performing research using mathematical modeling. Among the areas in which you will gain experience are selection of a topic, obtaining information, and use of software research tools such as Maple and LaTeX. The primary goals of this course are to prepare a research paper, give presentations, and prepare a poster based on your research. Additional skills will be learned, including using LaTeX to write papers, using Maple for numerical investigations, and using PowerPoint to prepare presentations. Furthermore, this course develops communication, critical reasoning, and problem solving skills.
Upon completion of this course, students should be able to:
The starting point for your research is to select a topic. This is not as easy as it might sound. You need to determine an open problem that you find interesting, since this is your project. In other words, your research should be something that has not been done already. Part of the research process is determining what has been done already. The scope of your research should be clearly defined in terms of the ultimate goal of the project. Keep in mind that your are NOT expected to complete your project in the span of the semester; however, you are expected to make weekly progress towards this goal. Work that does not lead to advancing your goal (i.e., time spent getting nowhere, invalid results, or other setbacks) is to be expected; this is part of the research experience that all researchers go through at some point in their work.
All students are encouraged to find a faculty mentor for their project. Your mentor should be able to help direct you in pursuing your research objectives and can help in selecting your topic. The mentor does not need to be in the math department, but should be someone who is knowledgeable about your topic. Please inform me as soon as possible who your faculty adviser will be and provide contact information for them. Please keep in mind that, if you select a topic because you are interested in it, then working on your project should be enjoyable. If you are not sure of a topic, feel free to come and discuss with me the selection of a topic. Some topics chosen by students in the past have included:
The following is an approximate schedule for the course and is subject to change. Skills, like using Maple, will be developed throughout the semester. Class time will also be set aside to discuss the experiences of students. Additionally, outside researchers may present their own experiences so that students can see how others approach their research.
Discussion of the basic concepts of research, finding sources, and using LaTeX, Maple, and PowerPoint. By the end of the second week, you are required to select your topic and turn in a draft of your project using LaTeX that includes only a title, abstract, all authors (include a faculty mentor, if not me), and several relevant sources in a reference section. Please note that you are expected to continually obtain new sources throughout the course of the semester. Additionally, Chapters 1, 2, and 3 of the text will be covered during these five weeks.
Each student in the class will be responsible for preparing a presentation of an assigned topic to the class. The length of these presentations will be about ten to twelve minutes, with three minutes for questions. The presentations will be made using PowerPoint. Equation Editor should be used to format all mathematics presented. You should also include plots generated by Maple to illustrate the results of the model studied. Make sure that the material is presented in such a way that those not familiar with the topic will understand the material and the mathematics presented.
Material will be presented showing the development of population models from first principles. These models include single and interacting populations, and we will utilize Maple to explore them. Much of this material will come from Chapters 4 and 5 of the text.
You will give a short PowerPoint presentation of about seven minutes on your topic to the class. You should make sure to clearly present the goals of your project to the class. Again, make sure that the material is presented in such a way that those not familiar with the topic will understand the material and the mathematics presented.
You will need to submit an advanced draft of your paper. It should include the title, authors, abstract, an introduction, development of your topic, future directions, conclusions, and references. This is the basic shell for the final paper and should represent your work to date.
More complex models for physical systems will be explored. For example, infectious diseases may be presented using compartmental models from a historical viewpoint. An advanced model for the spread of HIV/AIDS may also be presented, using an advanced compartmental model. Other topics may be presented depending on the desires of the class. I will avoid presenting material that is too closely related to any student project.
You will give a short PowerPoint presentation of about seven minutes on your latest developments of your topic to the class. You should make sure to clearly present the goals of your project to the class. Again, make sure that the material is presented in such a way that those not familiar with the topic will understand the material and the mathematics presented.
You will need to submit a more advanced draft of your paper. It should incorporate new results obtained since the last draft of the paper, and should incorporate feedback obtained from the previous draft.
The focus of the last week is on your final presentation and written paper. The poster session will be held during the fifteenth week. Your final presentation (about fifteen minutes, with an additional five minutes for questions) will be held during the final exam time (to be determined), at which time your written paper is due. You will also need to turn in a disk(s) that contains all of the work done in the class. This should include all of your presentations, poster, and any codes that you have used in your project.
Your grade will be based on your presentations, written paper, and poster, as well as attendance. After the final presentations, students will go through an exit interview for this class. Keep in mind that you earn your grade based on the work that you have done. This includes all work, whether productive or not. This course is non-traditional, and therefore the policies used to determine the grades are not standard, but are based on an individual's performance and development of his/her research topic. Feel free to see me if you have any concerns regarding grading in this class.
Talking, whispering, or any other student conduct which disrupts the learning process will not be tolerated and may lead to removal from class and/or other disciplinary action. University policies on disruptive behavior are followed and enforced in every instance.
Academic dishonesty will not be tolerated in any form. For more information on the University's policy regarding cheating and plagiarism, refer to the Class Schedule (Legal Notices on Cheating and Plagiarism) or the University Catalog (Policies and Regulations).
University student disability policies are followed. Contact the Disabled Student Services office (located in the Madden Library) for specific arrangements and information.
For required syllabus statements referring to the use of computers and copyright policy, please see required syllabus policy statement page Required Syllabus Policy Statements