Mathematical Processes and Models
Additional Resource
Video Series: What is Math Modeling?
Society for Industrial and Applied Mathematics has published a series of modeling videos that describes the "Modeling Cycle".
Video Series Part 1: What is Math Modeling?
Mathematical modeling provides answers to real-world questions like “Which recycling program is best for my city?” “How will a flu outbreak affect the US,” or “Which roller coaster is the most thrilling?” In math modeling, you’ll use math to represent, analyze, make predictions, or otherwise provide insight into real-world phenomena. This is the first episode in this new math modeling video series and introduces the modeling process, setting the stage for the next six videos which dive into the specific steps of modeling.
Video Series Part 2: Defining the Problem
Mathematical modeling provides answers to real-world questions. The process begins by defining the problem statement. Because real-world problems are often open-ended, defining the problem statement upfront will help modelers decide exactly what information they’re looking to solve. At the end of this step, modelers will have a clear understanding of the next steps in the modeling process. This is the second episode in this new math modeling video series.
Video Series Part 3: Making Assumptions
Mathematical modeling uses math to represent, analyze, make predictions, or otherwise provide insight into real-world phenomena. After defining the problem statement, modelers must make assumptions to reduce the number of factors affecting the model. This episode brings us one step closer to building an effective model and is the third segment in this new math modeling video series.
Video Series Part 4: Defining Variables
Mathematical modeling uses math to represent, analyze, make predictions, or otherwise provide insight into real-world phenomena. After defining the problem statement and making assumptions, defining variables tells modelers exactly the units they are looking for. This creates the basis for the next part of the process – getting a solution! This is the fourth episode in this new math modeling video series.
Video Series Part 5: Getting a Solution
Mathematical modeling uses math to represent, analyze, make predictions, or otherwise provide insight into real-world phenomena. This episode, number five in this new seven-part series, guides you through the process of finding a solution to your mathematical model. Here’s where you’ll first discover if you’ve really answered your original real-world problem.
Video Series Part 6: Analysis
By the time you’ve reached the analysis step of the math modeling process, you’ve built a mathematical model -congratulations! Now it’s time to analyze and assess the quality of the model. In this step and number six in this seven-part series, modelers take an honest look at the body of work, discerning the model’s accuracy, sensitivity, strengths, and weaknesses. When you know all this, you’ve got one step left in the process: report it to the world!
Video Series Part 7: Reporting the Results
It’s exciting to see the results of a successful model that predicts, analyzes, and otherwise provides insight into real-world phenomena. Once modelers have built and fully assessed the quality of the model, it’s time to tell the world what you’ve found! This episode, the final in this seven-part video series, explains the various aspects of a report and gives helpful guidelines to ensure a successful paper.