You’re standing in the kitchen, watching your coffee cool on the counter. How long until it’s drinkable? That’s mathematical modeling. You ignore the shape of the mug’s handle, the exact color of the liquid, and the conversation happening in the next room. You keep only what matters—temperature, time, and the air around it—and turn those into a simple equation. The math exists to answer your question, not the other way around. Pure mathematics works differently. It starts with an idea and asks, “What is true here, and how far does it go?” No coffee. No cooling rate. Just structure, proof, and generality. One path asks, “Does this work in the real world?” The other asks, “Is this true no matter what?”
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Both are valid. One builds the habit of checking results against messy reality—traffic patterns, phone battery drain, how long leftovers stay safe in the fridge. The other builds the habit of asking whether something holds in every possible case. The difference shows up fast, and it shapes how you think more than raw talent does. The real question isn’t which one is better. It’s which question you actually want to keep asking.
What Is Mathematical Modeling? (A Student-Friendly Definition)
You’re running late and staring at the subway map. The designers deliberately straightened the lines and spaced the stations evenly, so the distances no longer match reality. However, you still know exactly which train to take and where to change. In other words, the map throws out the real geography and keeps only the connections and order that matter to you. Mathematical modeling works in exactly the same way. You keep the structure you need and drop the rest. For example, when you model a bouncing ball, you can ignore air resistance and still solve the equations by hand. If you include every tiny detail—temperature, the ball’s exact shape, or the wind from a nearby window—you create equations that no one can actually use. On the other hand, if you leave out too much, the answer stops matching what you see in front of you.
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That balance requires real skill and judgment. Beginners often include every factor they can think of, much like someone who tracks every coffee and bus fare down to the cent until the spreadsheet collapses under its own weight. Experts, by contrast, strip variables away until the model is only just holding together, the way a cook decides which ingredients truly change the taste of a dish and which ones they can leave out. As a result, developing this kind of judgment takes years of deliberate practice. Ultimately, the patience to keep simplifying usually matters more than how quickly you can write equations.
Standing at Bus Stop
You stand at the bus stop and start calculating without even thinking about it. People keep joining the line, the bus runs late, and you estimate whether you will still make it to work on time. In other words, that quiet calculation already functions as a model. You translate the messy scene—arrivals, waiting times, and available seats—into a rough mental picture, then carry the answer back to the street in front of you. Researchers, Krawitz and his colleagues, who study modeling education treat this skill as a core competency. Across different national frameworks, the same two-way process appears: you take a real situation, turn it into mathematics, and then return with a solution that fits the original setting. Therefore, this translation in both directions defines the entire field.
Everyday Examples of Mathematical Modeling
You already practice a simpler version of the same skill every day. For example, biologists use identical reasoning when they look for mathematical patterns in living systems—how cells divide, how animals move in groups, or how a population grows. Concrete examples from biology make the abstract ideas clearer. Formal study simply sharpens the instinct you already use while standing in line or deciding whether to switch lanes in traffic. As a result, effective teaching turns that everyday habit into a deliberate method. The shift usually requires about a year of steady practice. Ultimately, seeing modeling this way—starting from something as ordinary as a bus queue—helps newcomers find the whole process far less mysterious.
You double a recipe for six people instead of four and instantly adjust the sugar, flour, and baking time. In the same way, you check a savings app and watch the balance grow with interest, or you leave coffee on the counter and guess how long it will take to cool. Meanwhile, you stand in a grocery line and estimate whether the three people ahead of you will finish before your bus arrives. Each time, you start with a real situation and end with numbers.
These everyday calculations already contain the core patterns of mathematical modeling. Proportional reasoning handles the recipe and the savings plan, exponential decay describes the cooling coffee, and probability guides the queue. In fact, these two families of patterns—proportional and probabilistic—cover most of the situations you meet in ordinary life.
Modeling: Recognizing the Pattern in Front of You
You already reason this way without calling it modeling. Therefore, the first real skill is simply recognizing the pattern in front of you. Once you spot it, formal study becomes much easier. Intuition alone rarely solves a completely new problem, yet formal methods extend what your instinct can already do. As a result, the two approaches reinforce each other. Teachers can build on this foundation quickly because most students already think like modelers.
The Mathematical Modeling Process — A 7-Step Framework
You try a new pasta recipe and taste it halfway through. The sauce is too thin, so you reduce the heat and add a little more tomato paste. After another few minutes you taste it again, adjust the salt, and only then serve it. In other words, you do not follow a single straight path from ingredients to plate; you cycle through small improvements until the result matches what you want.
Mathematical modeling works the same way. You begin with a real question that needs an answer. Next, you turn that question into mathematical terms and solve the equations you have written. You then compare the solution with what actually happens in the real world. As a result, the comparison usually reveals flaws, and those flaws send you back to an earlier stage to revise the model. Each trip around the cycle improves the model slightly.
A Typical Textbook Definition
Textbooks describe this process as the modeling cycle and list anywhere from five to nine stages. Nevertheless, the basic logic stays the same. Newcomers often expect one clean pass from question to answer. Experienced modelers, however, anticipate several go-throughs. It is entirely normal to iterate; returning to an earlier step is not a sign of failure. Ultimately, the seven steps that follow simply give that recurring cycle a clear structure.
A diagram is useful in this case since the cycle is truly circular. Specifically, the chart illustrates how each step leads on to the next. There are two habits that distinguish good modelers from poor ones. First, they clearly set out their assumptions. Secondly, they check the results against independent data. Moreover, a 2022 review noted that the WHO guidelines had weak reporting. These guidelines did not include detailed modeling information. In effect, Lo and colleagues called for clearer documentation standards. At the same time, all fields gain from keeping honest records of their assumptions.
You should document everything, even the decisions you later throw away. For this reason, a brief log is helpful for your future work. Six months later you will no longer remember why you picked a constant. Briefly put, that written record immediately provides the answer to the question. Proper documentation means that every model can be more easily defended.
Stage-by-Stage: Inside the Mathematical Modeling Cycle
The first step is to pose a well-defined question that can be answered. Broad objectives always lead to vague equations. The second step is just as important in practice; in fact, each assumption that you record turns into a testable statement. The third step involves turning those words into symbols. Following that, the fourth step usually requires a computer. The fifth step consists of finding out what the numbers really mean. In contrast, the sixth step involves comparing the predictions with the measurements. The seventh step then involves revising anything that didn’t match.
To sum up, many teams go through steps two to six again and again. With each repetition, one further weakness is eliminated. At the same time, the cycle functions like a spiral: spirals move forward even as they continue to turn. This kind of motion is exactly how real projects advance. In fact, lessons learned from false starts are more valuable than those from smoothly running projects. This insight applies to every project that I supervise.
Types of Mathematical Models — A Quick Overview
You decide how to plan tomorrow’s commute. If you simply check the distance and speed limit, you get one fixed travel time. However, if you also factor in traffic that varies from day to day, you get a range of possible arrival times instead. In the same way, you can look at your bank balance right now as a single snapshot, or you can track how it changes over months as interest and spending alter it. These choices already point to different kinds of mathematical models.
Modelers classify models along two main axes. One axis separates certainty from chance: a deterministic model produces a single output for each input, whereas a stochastic model produces a range of possible outputs. The other axis separates snapshots from change: a static model ignores time completely, while a dynamic model follows how things evolve. As a result, these two axes create four basic combinations. Linearity and continuity then extend the range further. The table below lists the six common families; each row gives a short definition and a typical example so you can use it as a quick reference when you choose an approach.
Ultimately, these families function as tools rather than fixed labels. Begin with the six listed here, then explore the broader taxonomy later if you need it. The complete classification deserves its own dedicated guide, yet this starting set already covers most everyday questions.
Deterministic and Stochastic Mathematical Modeling
You set a kitchen timer and the clock’s pendulum swings at a steady rate. Give it the same starting position and length, and it always finishes in exactly the same number of seconds. A deterministic model works the same way: identical inputs always produce the identical output, with no variation at all.
A stochastic model behaves differently. Imagine two identical neighborhoods facing the same flu season. Even though the population size, the weather, and the number of people who stay home are the same, one neighborhood can end up with far more cases than the other. Random patterns of contact—who sits next to whom on the bus, who forgets to wash their hands—drive the difference. As a result, a stochastic model returns a range of possible outcomes rather than a single number.
What is the difference?
This distinction changes how you read the results. With a deterministic model you can report one precise answer. With a stochastic model you need a confidence interval or a distribution, because the process itself contains chance. Therefore, the choice between the two shapes the entire analysis. Choosing the wrong family can waste months of careful work. Ultimately, you must decide according to the final question you actually need to answer: do you want the single exact result, or do you need to understand the spread of possible results?
There is a useful rule of thumb which can help students make sensible choices. Generally speaking, deterministic models should be used if the amount of variation remains small whereas stochastic models should be used when the variation is what determines the answer. Moreover, randomness is necessary in the case of financial risk and disease spread but is not needed in structural engineering or in orbital mechanics. In fact, Cevikbas and his colleagues looked at how researchers assess competence. Their 2022 review showed a great deal of disagreement regarding assessment (Cevikbas et al., 2022).
At the same time, Hidayat and his colleagues reached agreement in 2022 (Hidayat et al., 2022). The consistent measurement of modeling skill is still an open issue. Most importantly, this lack of agreement has an impact on teaching, hiring, and research. Progress in the development of standardized assessment tools is proceeding very slowly. To sum up, the field still does not have a common standard. Teachers are most acutely aware of this absence. At the same time, researchers continue to suggest new frameworks. Improved measurement would benefit both teaching and hiring.
Where Is Mathematical Modeling Used? — Industry Applications
You check the weather app before you leave the house and decide whether to carry an umbrella. In the same way, a climate model takes different emission scenarios and projects how much the planet will warm. You also glance at your bank app, notice an unusual charge, and wonder whether it is fraud—just as financial models flag suspicious transactions and price risk. These everyday decisions already follow the same logic that industries use at a much larger scale.
Healthcare models forecast disease spread and decide how many nurses a hospital needs on a given night. Engineers run simulations that test a bridge long before anyone pours concrete. Manufacturing teams adjust production lines so fewer products leave the factory with defects. Sports analysts evaluate players and estimate the chance that one team will beat another. Although the questions differ, the fundamental approach stays the same.
Any model begins with a real decision, and that decision determines which variables matter most. Therefore, the table below shows how these six industries typically apply models. Treat it as a starting guide rather than a complete list. Many smaller specialties exist outside these six, yet the same cycle appears in every case: you start with a concrete choice, translate it into mathematics, and use the result to act.
Modeling as Regulatory Evidence
Modeling is now regarded as substantial evidence. The FDA actually issued official guidance in 2023 on the subject, outlining the way in which sponsors can justify the reliability of their models (FDA, 2023). Meanwhile, another report lists the agency’s achievements (FDA, n.d.). Taken together, these documents demonstrate how far modeling has developed. To put it briefly, regulators now routinely accept evidence from simulation. This change sets a higher standard for all practicing modelers. Most importantly, the standards for documentation are continually increasing year by year. Those teams that make early adjustments gain a clear benefit. Furthermore, inadequate documentation currently causes delays in obtaining approvals.
Thorough records, on the other hand, accelerate the process. By contrast, careless records lead to costly inquiries. Good practice thus saves both time and money. In fact, regulators are now more and more asking for the actual model code. Transparency has become a necessary requirement, not an extra advantage. Honest reporting is now what distinguishes credible work.
Mathematical Modeling in Healthcare and Finance
You check the weather and flu forecasts before you decide whether to get a shot this year. In the same way, epidemiologists simulate outbreaks so hospitals can prepare extra beds and staff before a winter surge hits. Pharmacists model how quickly a drug clears the body so doctors can set a safe dose. These quiet calculations already shape decisions that protect people’s health.
A model must be validated before anyone acts on it. Bad healthcare models cost lives. As a result, standards have tightened and careful testing has become standard practice. Ultimately, trust is earned only with evidence. That same principle applies wherever quantitative models guide real decisions.
Tools & Software for Mathematical Modeling
You should choose modeling software based on the problem you need to solve, not on current popularity. Five tools handle the majority of professional work. Python gives you free, flexible libraries that cover almost any application. MATLAB handles matrices and control systems especially well. Mathematica excels at symbolic algebra. R dominates statistical modeling and visualization. Julia delivers high performance when the computation grows heavy. Each tool brings genuine strengths and real limitations.
Therefore, learn one of them deeply before you sample the others. Switching later is easy, but switching too early disrupts your progress. Depth matters more than variety at the start. Once you master one tool, that mastery transfers surprisingly easily to the next. What matters most is the mathematics itself; although the syntax changes from one program to another, the underlying concepts stay stable. Some ecosystems simply fit certain tasks better than others.
Free Tools, Paid Licenses, and Community Support
The importance of cost and community is just as great. Specifically, Python and R are entirely free, while MATLAB and Mathematica demand paid licenses. Julia is also free and is developing rapidly. Universities usually give MATLAB licenses without any extra charge. Generally, it’s a good idea to check with your institution before making a purchase. The best initial point of reference is the tool’s specific documentation, since it clearly explains the main functions. This applies to the Python manuals, the MATLAB docs, and the R guides.
To sum up, you should read the official documentation before relying on random tutorials. Official documentation remains accurate and up to date; in contrast, the quality of answers on forums varies greatly. The size of the community also affects how quickly you receive help. Most importantly, larger communities provide more worked examples. In short, select a tool that has an active community because this decision brings long-term benefits.
Choosing Your First Modeling Tool
There’s one good reason why beginners should start with Python: it’s applicable in almost every field. If a student learns Python, they can use it to model subjects such as biology or physics. It’s then relatively easy to switch over to MATLAB later on, whereas switching in the opposite direction is a lot more difficult. To sum up, choose a real-world problem for your first project and go for something small and personal. Once you’ve done that, rebuild it using a second tool. The act of comparing the two versions teaches you more than any tutorial does.
Most importantly, you should complete one project before beginning another. Completing a project quickly builds your confidence. Moreover, having a finished project gives you something to share. When you share it, you get feedback, and that feedback speeds up your growth. Indeed, this cycle causes beginners to improve rapidly. Keep your projects small and well focused. In brief, momentum is more important than perfection.
How to Learn Mathematical Modeling — A Roadmap for Students
The process of learning modeling is different from that of learning calculus. Broadly speaking, having a well-structured plan stops you from wasting your time. No one is able to master the subject simply by reading. On the contrary, you have to construct models, break them, and then rebuild them. The approach mentioned here consists of three stages, each one being based on the one that came before. If you skip the basic stages you will end up with serious gaps later on. Furthermore, if you omit practice your knowledge will be weak.
Many students tend to move too quickly into more advanced topics. To sum up, patience in this case brings enormous rewards. Slow progress is still progress. In contrast, rushing through the material leaves you with nothing firm. Regular practice leads to real skill. Most importantly, consistency is better than intensity throughout the entire year. In effect, short daily sessions are better than marathons. This habit makes challenging topics easier to deal with. Of course, just as much importance is given to rest as to repetition.
Why Problem Framing Matters More Than Calculations
I learned a difficult lesson from my own classroom. Specifically, while the students were able to solve equations they failed to formulate questions. For example, one group worked on modeling the time students had to wait in the coffee queue around the campus and at the same time another group tried to estimate rainfall from a tank. Observing them struggle gave me an important insight. To put it briefly, it is the hardest part to frame a problem. Once the problem has been well framed, the mathematics then follows easily. Indeed, this observation is the basis for the roadmap that follows. Experience in solving problems is more effective than theory at every single stage. Moreover, students need to receive honest feedback regarding their assumptions.
Three Stages of Learning Mathematical Modeling
If you only mark the arithmetic you overlook the real difficulties. On the other hand, marking the way in which the problem is framed reveals weaknesses at an early stage. This method has changed the way I teach the subject. Certainly, students improve more quickly with this kind of feedback. In effect, giving feedback on how a problem is framed has a quick effect on beginners.
Stage One — Build the Foundations
Begin with algebra and some basic calculus, and then include linear algebra and probability. Learn how to read a differential equation without feeling afraid. At the same time, get used to converting word problems into symbolic form. Take a good deal of time studying units and carrying out dimensional analysis. In fact, the units attached to every physical quantity must balance. If a model has incorrect units, it is immediately wrong. Briefly put, NIST issues the authoritative guidance on units (NIST, 2019). Read this early on since unit errors can waste weeks. Most importantly, dimensional checks pick up those errors instantly. Such mistakes occur frequently in students’ work. In contrast, careful students catch them before handing in their work.
Developing good habits in this area saves a lot of time later on. In short, the foundations support the whole structure that comes above them and if the foundations are weak they will collapse when subjected to pressure. Of course, revision is always less expensive than rebuilding.
Stage Two — Move to Hands-On Practice
Build small models for yourself. Begin by studying population growth and cooling laws, then move on to simple optimization problems. At the same time, learn one programming language properly; Python is still the easiest option for students. Furthermore, do five or ten small projects first. Exponential functions occur all the time in the early models. In fact, exponential and logarithmic functions form the foundation of all such models.
A good understanding of them makes the rest of the work much easier. Briefly put, carry out one project using genuinely messy data since real data teaches you humility more quickly than textbooks do. Above all, make sure that the data is properly cleaned before modeling it; if the data is dirty, it will produce confident nonsense, whereas clean data leads to defensible results. Take the time to put real effort into the cleaning process. In effect, the quality of the data determines the quality of the model; no algorithm can compensate for poorly prepared inputs. To be sure, professionals allocate time to the cleaning stage.
Stage Three — Reach Advanced Work
Advanced modeling requires both a wide range of knowledge and a deep understanding. You should also study partial differential equations and numerical methods, learn stochastic simulation and Monte Carlo techniques, and at the same time incorporate machine learning when there is a large amount of data. It is necessary to take part in competitions in order to assess your abilities under pressure. In fact, it is the current research papers that show where the true frontier lies. You should eventually specialize, but should first maintain a broad knowledge base.
To put it briefly, the majority of breakthroughs result from linking together different fields. Nowadays, climate scientists are using methods from finance. Most importantly, this kind of cross-fertilization leads to real advances. Yet deep expertise remains of enormous importance. On the other hand, having only a superficial breadth achieves nothing in terms of solving difficult problems. If you achieve a balance between the two, then opportunities increase. As an example, hybrid modeling combines physics and machine learning. Basically, the frontier favors those who are flexible in their thinking. That kind of flexibility has to be developed over many years. Certainly, curiosity keeps the entire process going.
Mathematical Modeling Competitions & Career Pathways
Competitive contests teach modeling skills more effectively than almost any course. Every year, COMAP organizes the Mathematical Contest in Modeling and the Interdisciplinary Contest in Modeling; high-school students enter the related HiMCM event. In each contest, a team receives a real-world problem and has ninety-six hours to model it, produce a solution, and defend the reasoning. Judges reward clear assumptions and honest statements of limitations rather than perfect arithmetic alone.
As a result, students who participate report a sharp rise in confidence. Employers treat the experience as a genuine signal of ability because the work develops skills that ordinary classrooms rarely demand. Unlike timed exams, these contests require open-ended thinking; they credit both technical accuracy and creativity, and they place equal weight on teamwork and mathematics. Ultimately, the combination prepares students for real professional work and gives them concrete stories to tell in job interviews. COMAP remains the recognized authority on these contests.
Careers Built on Modeling: From Markets to Public Health
Modeling skills open doors across many different careers. Quantitative analysts design trading strategies that move real money. Epidemiologists build models that help public-health agencies prepare for outbreaks. At the same time, simulation engineers test aircraft designs long before anyone leaves the ground. Data scientists create predictive models in nearly every industry, operations researchers optimize supply chains so goods arrive on time, and actuaries quantify the risks that shape insurance and pension plans.
In most markets these roles pay above the national average. The common thread is quantitative thinking, so the core skills transfer easily from one field to another. Each sector, however, adds its own domain knowledge, and that knowledge multiplies a modeler’s value. Combining strong modeling ability with deep subject expertise creates rare, durable skill sets. By comparison, generalists who never develop real depth often find fewer interesting opportunities. Deep specialization opens the most rewarding doors, while curiosity and continuous learning keep those doors open over the long term.
Advanced Topics & Research Frontiers
Frontier modeling now reaches into new areas every year, and uncertainty quantification sits at the center of the work. In 2022 Simmonds and his colleagues examined how different disciplines treat uncertainty and found major inconsistencies (Simmonds et al., 2022). Meteorology, ecology, and economics each handle the same problem in their own way. As a result, researchers struggle to compare findings across fields. A shared vocabulary and standardized reporting would let teams place results side by side. Yet long-standing habits change slowly, so widespread adoption has lagged. Credibility, however, depends on comparable reporting. Journals now require uncertainty statements, and reviewers examine those claims carefully. This steady scrutiny improves published work. Unverified claims, by contrast, erode trust quickly. Honest reporting of uncertainty protects both authors and readers, and the practice is gradually spreading.
Other frontiers also deserve attention. Digital twins track physical systems in real time. Hybrid models combine physical equations with machine learning. Agent-based simulations capture human behavior, while multiscale models link molecular details to bulk properties. Measurement science underpins all of these approaches. The Joint Committee for Guides in Metrology (JCGM, 2008) sets the rules that govern uncertainty. Without common rules, researchers cannot compare results reliably. Standards turn individual findings into shared knowledge and thereby enable cumulative progress. Disciplines that lack them tend to repeat past mistakes. Shared methods reduce that waste and quietly accelerate discovery. Metrology rarely receives awards, yet it makes the rest of the work possible.
Image credits – Grok AI and Google NotebookLM
Frequently Asked Questions about Mathematical Modeling
A model, in fact, represents reality through equations, and the cooling of coffee proceeds along a curve that is exponential.
It is difficult yet something that can be learned; begin with small, concrete problems.
People such as actuaries, epidemiologists, engineers, and data scientists make use of it every day.
Python is best for most beginners, MATLAB is suitable for engineering, and R is appropriate for statistics.
No. Algebra and basic calculus are enough to start.
Expect six to twelve months for working competence.
Simulation solves a model numerically. Modeling builds it first.
Yes, but programming greatly expands what you can build.
How This Guide Was Compiled
The guide uses a method that is well documented and starts with evidence. The author, in fact, has a degree in physics and gives lessons on modeling. All of the claims can be traced to named and verifiable sources. Furthermore, five of the journal articles were published by open-access publishers. The sourcing is completely auditable so that you can check it yourself. Most importantly, transparency enables readers to assess the evidence for themselves. In short, readers should be given the direct links. The resources section contains all of the links. By contrast, a great many articles completely conceal their sources. We have deliberately avoided adopting that practice. Of course, any requests for correction are always welcome.
The standards documents originated with three official organizations. Specifically, NIST gave guidance regarding measurement uncertainty. The Joint Committee for Guides in Metrology formulated the metrology rules. At the same time, the FDA offered advice on modeling. There was also a separate agency report which dealt with modeling successes. Furthermore, each URL was checked before being published, and the live article links were verified individually. To sum up, the editorial board carefully examined the draft.
The classroom examples are drawn from the author’s own teaching. Most importantly, none of the content here is based on unverified claims. Corrections can be sent via the nycstem.in’s contact page. In effect, this guide is based on published evidence. Readers are able to carry out every step described in it. On the other hand, unsourced guides provide little that can be checked. This distinction is important when it comes to trust. Of course, verification does take time, and we are aware of that.
Verified Resources
- iScience — open access, CC BY
- Epidemics — open access, CC BY
- Educational Studies in Mathematics — open access
- Eurasia Journal of Mathematics, Science and Technology Education
- ZDM – Mathematics Education — open access
- U.S. Food and Drug Administration — modeling credibility guidance
- U.S. Food and Drug Administration — modeling and simulation report
- National Institute of Standards and Technology — TN 1297
- Bureau International des Poids et Mesures — JCGM guides
References
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modeling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 109(2), 205–236. https://doi.org/10.1007/s10649-021-10104-6
COMAP. (2026). Mathematical Contest in Modeling (MCM/ICM) and High School Mathematical Contest in Modeling (HiMCM). Consortium for Mathematics and Its Applications. https://www.comap.com/
Hidayat, R., Adnan, M., Abdullah, M. F. N. L., & Safrudiannur. (2022). A systematic literature review of measurement of mathematical modeling in mathematics education context. Eurasia Journal of Mathematics, Science and Technology Education, 18(5), em2108. https://doi.org/10.29333/ejmste/12007
Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data — Guide to the expression of uncertainty in measurement (JCGM 100:2008). Bureau International des Poids et Mesures. https://doi.org/10.59161/JCGM100-2008E
Krawitz, J., Schukajlow, S., Yang, X., & Geiger, V. (2025). A systematic review of international perspectives on mathematical modeling: Modeling goals and task characteristics. ZDM – Mathematics Education, 57(2–3), 193–212. https://doi.org/10.1007/s11858-025-01683-2
Lo, N. C., Andrejko, K., Shukla, P., Baker, T., Sawin, V. I., Norris, S. L., & Lewnard, J. A. (2022). Contribution and quality of mathematical modeling evidence in World Health Organization guidelines: A systematic review. Epidemics, 39, 100570. https://doi.org/10.1016/j.epidem.2022.100570
Simmonds, E. G., Adjei, K. P., Andersen, C. W., Aspheim, J. C. H., Battistin, C., Bulso, N., Christensen, H. M., Cretois, B., Cubero, R., Davidovich, I. A., Dickel, L., Dunn, B., Dunn-Sigouin, E., Dyrstad, K., Einum, S., Giglio, D., Gjerløw, H., Godefroidt, A., González-Gil, R., … O’Hara, R. B. (2022). Insights into the quantification and reporting of model-related uncertainty across different disciplines. iScience, 25(12), 105512. https://doi.org/10.1016/j.isci.2022.105512
Taylor, B. N., & Kuyatt, C. E. (1994). Guidelines for evaluating and expressing the uncertainty of NIST measurement results (NIST Technical Note 1297). National Institute of Standards and Technology. https://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf
U.S. Food and Drug Administration. (2023). Assessing the credibility of computational modeling and simulation in medical device submissions: Guidance for industry and Food and Drug Administration staff. Center for Devices and Radiological Health. https://www.fda.gov/media/154985/download
U.S. Food and Drug Administration. (n.d.). Successes and opportunities in modeling & simulation for FDA: A report prepared by the Modeling & Simulation Working Group of the Senior Science Council. Office of the Commissioner, Office of the Chief Scientist. https://www.fda.gov/media/163156/download
