How is applied math research done

In summary, the conversation discusses the process of research in applied math and the role of mathematical modeling in various scientific fields. It is suggested that research often starts with an original idea that can benefit individuals, companies, or government agencies. However, it is also noted that many other fields, such as physics, biology, and geology, also utilize mathematical modeling. The conversation also mentions the pairing of advisors, one in math and one in another field, for PhD students at the University of Michigan.
  • #1
ObHassell
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I was curious how research in applied math is done, the reason I'm curious is because I can't seem to believe that research is started with a question...like "what temperature will a cell freeze without killing the cell" for example. All I've ever seen is math modeling of a phenomenon. thank you
 
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  • #2
It seems like it would pretty much be along those lines. If you're looking for funding you would attempt to come up with an original idea that could benefit someone/some company/Govt.
But remember a lot of the "easier" stuff will be done by people directly in those fields. You'd be surprised at how often mathematical modeling is used by Physicists/Biologists/Geologists/ALL SCIENTISTS with/without the aid of an Applied Mathematician.

Check out UofMichigans applied math page:
http://www.math.lsa.umich.edu/aim-grad/faculty.html

They pair advisors (one math, one something else) for every PhD student.
 
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  • #3


Applied math research is typically done by first identifying a real-world problem or phenomenon that can be described and analyzed using mathematical principles. This can involve observing and gathering data, conducting experiments, or consulting with experts in the field. The research then involves applying mathematical models and techniques to analyze and understand the problem or phenomenon in question. This may include developing new mathematical models or adapting existing ones to fit the specific situation.

While it is true that some research may start with a specific question, such as the example you provided, this is not always the case. In applied math research, the focus is on using mathematical tools and techniques to solve practical problems and gain insights into real-world situations. This can involve exploring various scenarios and analyzing different factors to understand the underlying mechanisms at work.

Additionally, applied math research often involves collaboration with other disciplines, such as biology, engineering, or economics. This allows for a more holistic approach to problem-solving and can lead to innovative solutions.

In summary, applied math research is a multidisciplinary process that involves identifying a real-world problem, applying mathematical tools and techniques to analyze and understand it, and potentially collaborating with other fields to find practical solutions. It is a dynamic and constantly evolving field that contributes to advancements in various industries and technologies.
 

1. How do you choose a research topic in applied math?

Choosing a research topic in applied math typically involves identifying a problem or gap in knowledge that you are interested in solving or exploring. This can be done by reading current literature, attending conferences, and discussing with colleagues and mentors. It is important to choose a topic that is both relevant and feasible in terms of available resources and expertise.

2. What is the process for conducting applied math research?

The process for conducting applied math research typically involves the following steps:

  1. Identifying a research question or problem
  2. Gathering and reviewing relevant literature
  3. Developing a hypothesis or research approach
  4. Collecting and analyzing data
  5. Interpreting and drawing conclusions from the data
  6. Communicating the findings through publications and presentations

3. How do you determine the validity of results in applied math research?

Determining the validity of results in applied math research involves several steps. These can include conducting statistical analyses, replicating the study, and peer-review by other experts in the field. It is important to also consider the limitations of the study and potential sources of bias. Reproducibility and transparency are key factors in ensuring the validity of research results.

4. What are some common challenges in applied math research?

Common challenges in applied math research can include obtaining funding, data collection and analysis, and collaboration with other researchers. It can also be challenging to balance theoretical and practical considerations, and to communicate findings to a non-technical audience. Staying up-to-date with advancements in technology and methods is also important in keeping research relevant and impactful.

5. How does applied math research contribute to society?

Applied math research contributes to society in a variety of ways. It can lead to advancements in technology, improved understanding of complex systems, and development of new solutions to real-world problems. Applied math research also has applications in fields such as medicine, economics, and engineering. By informing decision making and solving practical problems, applied math research can have a positive impact on society as a whole.

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