Prof. Aaron A. King, Ph.D.

Departments of Ecology & Evolutionary Biology and Mathematics

Email: kingaa@umich.edu

Tel: +1 734 936 7861

Office: 2051 Kraus Natural Science Building

Office Hours: Mondays 14:00-15:00, Fridays 11:00-12:00

Tuesdays & Thursdays 14:30–17:00 in 2015 Ruthven Museums

The course will make extensive use of its Canvas site. You should check it regularly for assignments, updates, and to receive feedback on your performance.

All branches of modern biology are fundamentally quantitative. To be successful in biology, it is increasingly important to have strong quantitative skills. Especially important are the concepts and methods of dynamics, probability, statistics, and logic. In this course, students will learn the elements of these fields as they pertain to biology. Students will work with biological examples, analyze data, construct models, and formulate arguments. Emphasis will be placed on constructing clear and valid arguments rather than on correctness of conclusions alone.

Students completing this course will be able

- To understand and communicate the integral role of mathematics and quantitative reasoning in science generally, and in the biological and biomedical sciences in particular.
- To display a sophisticated understanding of the nature of biological data and a working knowledge of tools for the display, analysis, and interpretation of data.
- To understand the concept of a mathematical model in biology and the relationships among mathematical models, scientific hypotheses, and data.
- To approach any given problem from four directions: symbolic, numerical, graphical, and verbal.
- To develop valid quantitative arguments, both written and oral.
- To criticize and improve others’ quantitative arguments by identifying hidden assumptions, isolating unwarranted conclusions, and clarifying obscure reasoning.
- To understand key elements of mathematics especially relevant to biology, including
- discrete-time dynamics
- continuous-time dynamics
- matrix algebra and matrix models
- probability and probabilistic models

- To use the
**R**environment for scientific computing.

Math 115 (Calculus I) or equivalent, and a sense of humor.

The course will be taught using a mixture of in-class and homework exercises, short lectures, readings, in-class discussions, and writing assignments. Attendance at all class meetings is critical and therefore mandatory: there is nothing you can afford to miss! Most of the work in class will use **R**: you will need to bring your laptop, with **R** and **Rstudio** installed, to every class meeting. You are expected to complete assigned readings before class meetings, keep up with assigned homework, participate fully in discussions, and work on course activities during class meetings.

Erin N. Bodine, Suzanne Lenhart & Louis J. Gross. Mathematics for the Life Sciences. Princeton University Press, 2014. ISBN: 9780691150727.

**Errata:** See the textbook website and on the course website.

- the nature of biological data
- scientific programming in
**R** - manipulation and visualization of data
- modeling in discrete time
- modeling with differential equations
- compartmental models
- matrix models
- probability models
- Markov processes
- population dynamics
- population genetics
- genetic substitution models

Numerical computation is an important tool in scientific work and it is a goal of the course to familiarize students with the free, open-source **R** computing environment for such computation. The course assumes no programming experience or background: we will teach you what you need to learn.

The text makes much use of **Matlab**, a commercial software package, but the authors have provided an **R** supplement with translations of the exercises for **R** is available on the textbook’s website (accessible via the CTools site). The **R** scripts mentioned in the text can be accessed here. Whenever the text refers to **Matlab**, you should look up the corresponding portion of the **R** supplement.

There will be no exams. Your course grade will instead be based on routine homework Exercises, periodic short quizzes, class participation, and your work on a series of “Challenges”.

*It is impossible to learn quantitative reasoning without lots of practice.* For this reason, you will be assigned Exercises with every reading. Your work on these Exercises will be handed in regularly and graded. Exercises must be written up *in hardcopy*, stapled, and handed in on time. *No late work will be accepted.* However, the lowest several scores will be dropped at the end of term to accommodate the unavoidable vicissitudes of life.

Your Exercise write-ups must be self-contained, legible, intelligible, and clear. These are not records of your work, notes to yourself, or responses to the instructor; **they must be written to be read as stand-alone documents**. Feedback on your early Exercise write-ups will help you acheive this goal rapidly.

On each Exercise, 7 points will be awarded for *completeness and correctness* and 3 points for *clarity of writing*, for a total of 10 points.

Challenges are problems that are intended to be more interesting, realistic, and therefore more open-ended than Exercises. You can turn in up to three drafts of the solution to each Challenge and receive feedback from the instructor. Your grade will be based on the final version. Again, because it is very important you not fall behind, there will be strict due dates for each draft. Drafts handed in late will be penalized at a rate of 10% per day per draft.

Challenge write-ups must be handed in in hardcopy. Codes and other electronic materials can be uploaded via the Canvas site.

An important goal of the course is to improve your powers of written and spoken communication. Consequently, in-class discussions are a very important part of the course, and you will be rewarded for your participation.

Life is full of conflicting demands. To help you to give the demands of this course their due, there will be brief quizzes over the reading material from time to time. These will be held at the beginning of class.

Your grade in the course will be determined by your average score on graded work, weighted as follows:

Exercises | 40% |

Challenges | 40% |

Participation | 10% |

Quizzes | 10% |

- This classroom is a safe space: treat everyone with respect and courtesy at all times.
- Importantly, we are learning to criticize reasoning and to hear criticism. Criticize the idea, not the person.
- Listen carefully to what others are saying even when you disagree. Let your comments reflect that you understand another’s point of view.
- Respect the subject. Quantitative reasoning requires concentration. Avoid distractions by silencing your personal electronics and putting them away. The action is here, now: no social media during class meetings.
- Be self-aware. If you have a lot to say, try to make sure that others have a chance to speak too. If you find yourself hesitating to speak, look for opportunities to contribute.
- Be self-confident. This is a safe space: don’t be afraid to take risks.
- This is
**your**education: seize it! If something isn’t clear, ask about it. If you catch a mistake, speak up. If you see another solution, propose it. If see something excellent, say so.

Because we have no exams in the course, there is no need for formal accommodations for learning disabilities, physical requirements, medical needs, etc. However, students with such needs should contact the instructor within the first two weeks of the term to discuss any issues that are anticipated.

There are no exams, but the instructors will make every reasonable effort to allow students to observe their religious holidays without academic penalty. Absence from class for religious reasons does not relieve you from responsibility for any part of the course work. If you expect to miss classes or assignment due dates due to religious observance, be sure to contact Prof. King in advance.

Students in good standing (i.e., grade of B or better), forced by circumstances beyond their control to withdraw entirely from school after the withdrawal deadline may request a grade of Incomplete. The instructor may request proof of the necessitating circumstances and will, in consultation with the student, set the terms for the timely completion of course requirements.

We follow the university’s academic integrity policy for undergraduates. **Students should bear in mind that the ideas, writings, or other works of others (including information obtained from the internet) must be attributed appropriately in all written work.** *Failure to do so will not be tolerated!*