Mathematics Seminars 2020

Mathematical modeling of annual plants

Speaker: Tomoatsu Sugiyama

Abstract

Mathematical model is a representation in mathematical terms of the behavior of real devices and objects. It is used in many contexts such as physics, engineering, biology, finance and others. In this presentation, I show an example from a mathematical model of biology. It shows the population number at (n+1)-th generation by using the population information at n-th and (n − 1)-th generations.

What we should know about a mathematical model is that it is not necessary a tool which guess correct number of something. Some of them might be a such tool. But many are different. That is because we use parameters and approximation. For example, I use four parameters in the mathematical model given in my presentation. Among those parameters, I use ∂ to mean the probability that seeds can survive through a winter. Although I always multiply ∂ to the population when the time in the figure comes to next spring from the winter, I do not believe it is always the same number because ∂ would have many factors which make ∂ to change, such as temperature, humidity, place and others. Not to mention, other winters and other places may have different values of ∂. Nonetheless, we use ∂ in a mathematical model.

Mathematical model is even useful even if it cannot lead to an accurate number. Mathematical model is abstract and treat just important parts which affect the result. In this meaning, mathematical model is useful to grasp the core. Also, mathematical model tell us a method for solving a problem. Consider an easy mathematical model, y = ax. If we want to raise y, we can know what we should do is raising a or x. Although it is sometimes clear before making a mathematical model, we can know the way with evidence.

This was a great topic for a 380 presentation. The details could have been clearer, but it’s great to see yet another application of probability to gardening. A quick suggestion: to number your equations, you can use the \begin{align} command rather than \begin{align*}. This will provide easy reference for equations throughout the presentation!

Who would have thought annual plants could also be modeled mathematically. Interesting to say the least. There are some minor issues with the slides via organization but overall for just learning Latex they are really nothing. This presentation was executed very well.

This was a nice presentation. I wish the results were explained in a little more detail, but overall it was a nice topic for a 380 presentation. I would have never thought of this. It is very interesting and you did a nice job with formatting and organizing the presentation. Great job.

Good presentation on a topic that probably no one has ever done before. The graphic on the first slide was done very nicely. I found the notation a bit confusing to follow, so I’d recommend making sure you use the same notation throughout, or redefine as necessary. Overall it was an interesting topic and a cool introduction into how mathematics can be used in the natural sciences.

Really cool 380 topic! I really like when mathematicians give the definitions immediately and up front, because it helps to frame the discussion in context. Definitely a good stepping stone for your next two presentations!

Hello! This was a very interesting seminar topic! I never thought about plant populations having a recurrence relation. It’s funny how math models can be applied to so many situations around us, but we never really think about them that way! Your visual demonstration that you included on your fourth slide was very nicely done, and it really helped clarify your main idea. Great job!

Unique seminar topic! If you asked me to create a real-life example of mathematical modeling, my first example definitely would not have been modeling annual plants! I myself tend to plant perennials in my garden for the sole fact that they grow back every year. I wonder if the growth of perennials could be mathematically modeled as well? I think that this is a topic with a lot of potential for growth (pun intended) into a 381 presentation as well.

Pretty cool topic and some nice looking mathematics. I think we could have used a bit more explanation in the introduction, but other than that, looks really good!

Interesting topic, I always appreciate real-world applications of mathematics! As was previously mentioned, there’s some confusing notation that could use clarification and some standardization of notation due, but nonetheless very neat! I suppose that there are lots of factors guiding the growth and dissemination of plants from year-to-year; I’d be curious to see the non-recursive form of this problem and how it would ultimately oscillate based on the carrying capacity of the environments monitored.

Good work, I hope you expand upon this topic further in a later presentation.

This was a good 380 presentation. I would have never thought of giving a math presentation on plants. I liked the use of the visual on the fourth slide because I think it helps the audience get a better picture of the situation. I think you could have given more explanation at the beginning and the end, but overall, great job.