2024 MathWorks Math Modeling Challenge - A Tale of Two Crises

It has been my pleasure to once again register our math team at CAVA to participate in the M3 Mega Math Challenge. I am happy to announce that this year - for the first time - our team was successful in triage. Our students are to be commended for this achievement. I must also express my congratulations to those students and teams who advanced further, including those who attained finalist, semi-finalist, and honorable mention prizes. In these trying times, it is especially important that the M3 Math Challenge continue in its mission to involve our top high school students in using math modeling to tackle aspects of our current, pressing crises. I would make the case that our country needs more activities of this nature. I would go further yet and declare that this is a model of how we might pivot and redirect our focus away from the excessive standardized Testing, Testing, Testing, and emphasis on Standards, Standards, Standards, and - instead - challenge our students to tackle problems in a way that their results might be utilized by our leaders to improve conditions in this country. Climate change, conversion to electric vehicles, and short- and long-term trends in telecommunication are among the topics from recent years. This year, the topic is that of solving the problem of homelessness in major cities. Here you go, young scholars- take the raw data on population and homeless figures, extrapolate a mathematical model encompassing the next 50 years, and give us the Answer to homelessness. Good luck! Ah - one of the crises facing humanity throughout this planet - homelessness. Though we often think of it as a modern urban issue, we find references to this "problem" dating as far back as the early 17th century Many of us recall having read, as required high school reading, "A Modest Proposal," the satirical essay by Irish author Jonathan Swift, suggesting that utilizing Irish babies as a food source (more bluntly, resorting to cannibalism) would be a logical remedy to poverty in Ireland. This particular essay may be especially worthwhile for my fellow left-brained readers - mathematicians, scientists, economists - who resort primarily to quantitative, math-based considerations, perhaps at the expense of missing aspects of the situation which someone with "common sense" would consider obvious. Hence, as referenced in previous posts, we have the stereotype of the "absent-minded mathematician," reminiscent of the "Wise Men of Chelm" stories. Most of us in America are also familiar with Charles Dickens' A Christmas Carol, a work which - while frequently read in school, and/or viewed (in movie version) in November and December - might be too closely associated with the holiday of Christmas in particular, and having the possible liability of missing the main point: economic inequality in Victorian England, and the plight of England's poverty-stricken and homeless citizens in particular. Ebeneezer Scrooge represents the successful British businessman, an affluent and law-abiding citizen, yet lacking in empathy and charity. His perception is that homelessness was an issue which had been resolved some time prior - in the 17th century - with the poorhouses. It is worthwhile to contemplate the exchange which occurs when he is approached by 2 men seeking charity on behalf of the poor. Scrooge replies by asking - whether with genuine or feigned surprise - whether the poorhouses are still in operation. The men reply in the affirmative. Scrooge presses them further: for those poor individuals who refuse to go there, are the prisons still opened? (The latter must surely be intended as sarcasm). The alms collectors again reply in the affirmative. In that case, declares Scrooge, he already provides for the poor through his paying his taxes (he is law-abiding, after all). The taxes he pays go to the aforementioned institutions, and those who are badly off must go there- end of discussion. The men collecting alms reply that many of the poor cannot go to these places, and many would rather die. One would think that this reply would be immune to rebuttal, but somehow Ebeneezer is sufficiently cold-hearted to press further: "If they would rather die, then they had better do it, and reduce the surplus population....." Goodness gracious, we think (hopefully); can a problem of this nature be solved with purely quantitative considerations? Is this reminiscent of the movie "Field of Dreams," in which the main character is told - referencing a baseball field he wishes to build on his ranch: "If you build it, they will come?" Build the baseball field, and somehow (magic! Or perhaps time travel coupled with teleportation?) the famous baseball players pop onto the field from the past, or from some parallel universe, and through some unspecified instantaneous transmission of information, the surrounding residents are somehow made aware of everything that is happening. Cars jam the entryway to the stadium with fans who will clearly suffice to pay off the main characters' debtors- and the financial crisis is solved. Perhaps my above digression was excessive, but hopefully it will suffice to demonstrate that mathematical models of some sort have previously been attempted by intelligent scholars for over 3 centuries (albeit with much lesser technological resources, no computers at all prior to World War II), and their results implemented. The poorhouses were a product of prior such efforts. History tells us that despite good intentions, poorhouses were ultimately discontinued due to the unsafe, unsanitary, etc. conditions in these institutions. We now have "homeless shelters" to support some of our homeless citizens, but these are usually temporary, with residents being compelled to vacate within 6 months. Also, how safe are these shelters in terms of protection from pickpockets and the like? Is there any degree of security? That being said, it is worthwhile to peruse the results and conclusions of many of the teams' solutions this year. Most of the winning teams seem to have used a logistic growth model, after first having considered linear regression, and noted a much stronger correlation of the raw data with a logistic growth function. I have previously discussed logistic growth with regard to the early part of our COVID pandemic; such a model is very useful for bacterial, viral, or human population growth. Both human population and land use have fixed carrying capacities; hence, the usefulness of a logistic growth curve is evident. As mentioned above, I am hopeful that our leaders - in government and industry - will have the wisdom to peruse the hard work of our country's motivated advanced students, who were willing to take the time and effort to provide some viable mathematical models of our homeless population and project accommodations needed for this population over the coming 50 years. At the same time, while scrutinizing students' solutions, I would strongly recommend noting their solutions for covering the cost of housing for the homeless (such as "affordable housing" solutions), as well as ensuring safe, secure, and sanitary conditions for this community.

Remote Work- M3 MathWorks Math Modelling Challenge 2022

The joke is told of a frustrated farmer who relates his troubles to a friend of his, who happens to be a prominent physicst. The farmer bemoans the fact that none of his hens will lay eggs. "Ah," the physicist replied, "give me a few days, and I shall discover a solution for you." The physicist departs. Two days later, the physicst returns, and excitedly declares, "Eureka! I have your egg problem solved!" Incredulous, the farmer replies, "Really?!" To which the physicist replies, "Most definitely! There is one small detail, however; my solution assumes that all of the hens are spherical, with all of their mass concentrated at their centers." The relevance here? For the past 7 years, (this year being the exception), high school students from my school - with my encouragement- have formed a team to compete at SIAM's annual M3 Math Challenge. (SIAM is the Society of Industrial and Applied Mathematics). Even without having a team to coach this year, the nature of the competition - coupled with recent concerning world developments- are of extreme interest to me. The problems posed each year are not purely abstract math problems, but involve the application of mathematics to real world problems, usually of strong relevance to current events; thus, we adults would be well advised to examine the conclusions presented by the winning teams, and hopefully apply these conclusions for the purpose of improving our circumstances and future prospects as a civilization. For those unfamiliar with the competition, teams of 3-5 students each are challenged to complete a real-world, relevant, multi-part math problem. Viable solutions must include a lengthy report- akin to a major research paper in an advanced high school class, or perhaps a work project normally expected to take a few weeks to complete- all within the span of 14 hours. To clarify how this works, if the team members download the project at 9 AM on Saturday or Sunday, they must complete and submit all parts of their solution by 11 PM that same day. While they break for lunch, dinner, etc., the clock continues ticking. SIAM very recently released the solutions of the winning teams in this year's competition. The challenge this year was to investigate the percentage of jobs which are "remote-ready," meaning that they could be done online from home, within several specified cities in the United States and Great Britain, and ultimately design a model enabling the prediction of percentage of workers who would be working online from home, projecting up to 5 years in the future. Raw data is broken down by gender, age range, level of education, and occupation categories. However, this problem also requires students to take into account workers' preferences in terms of remote versus in-person work, as well as employers' preferences concerning their employees' working virtually as opposed to in-person, coupled with their flexibility in terms of considering their employees' preferences in this regard. This problem is of interest for a number of reasons. Young people who are entering or approaching adulthood- including college students and perhaps high school juniors and seniors- are likely planning their careers, and may well consider the potential of work flexibility and the possibility of working from home. Their decision on where to reside may hinge on this possibility. The need- or lack of need- to commute to and from work everyday are important considerations. There is the individual workers' consideration of arranging daily commute (if applicable). We - as a world human commmunity- should, however, consider the impact on society at large. As we see increasing impact of global climate change driven by continued use of fossil fuels, remote work can be seen as a way to buy us some time by reducing the emissions from our still-mostly gasoline-powered cars. Hopefully, we eventually switch to 100% clean energy vehicles (electric, etc.), with the electricity powered 100% from renewable resources, but even optimistic projections recognize we are at least a few decades from achieving this. In any event, I wanted to address the issue of assumptions. A major consideration in any mathematical model is the assumption(s) as initially stated, and validity of such assumptions- hence, the joke about the farmer's hens. It is only fair, however, that I precede these comments by praising all of the students who submitted viable solutions- and especially those winning teams whose solutions are presented. This is definitely a non-trivial problem. It would be a challenge to solve within a month- let alone within a 14-hour period. The winning teams' solutions and mathematical methodologies are quite ingenious, and I would certainly not be inclined to critique these. However, if the reader will forgive perhaps a mild trace of impudence, I cannot resist the urge to comment a wee bit upon some of the assumptions. In defense of the students making certain assumptions, it should be acknowledged that experience of age is likely the primary consideration. This does not diminish the remarkable potential of these gifted young scholars, and enormous value they offer to society as they apply their talents. That being said..... One of the problematic assumptions was the notion that choice of profession is independent of gender. My own profession would seem to immediately refute this point. According to the OECD, the percentage breakdown of elementary teachers in the U.S. is 86.8% female, 13.2% male. There is a steady decrease in this imbalance as we increase in students' age levels: In junior high, this breakdown decreases to 66.8% female, 33.2% male. By high school (my own student body), the breakdown is 58.2% femaile, 41.8% male. It is only when we examine tertiary (post-secondary) U.S. education that we finally see a virtual parity, at 50.2% female, 49.8% male. Okay- enough with the education example.... How about technicians, electricians, plumbers, auto repair? Without researching each of these professions individually, I presume we can all agree that when we call upon any of these professionals, we are far more likely to be serviced by a male than a female. Thus, hopefully we have sufficiently refuted the notion of gender being uncorrelated with profession. Another problematic assumption made by competitors included the notion that parents are fully able to supervise their kids while working remotely from home. Ah! Speaking as a father of 3, please let me assure you of the invalidity of this assumption. We can start from infancy (the relatively "easy" age) and advance from there. Infants are easy, right? All they do is eat, drink, sleep, and release waste. That being so, all you need to do is structure your day based upon the regular pattern of meals, waste, naps, etc. Seriously- how much consistency do you expect, and how much anticipation of unanticipated interruptions can you truly work around? If you have a live meeting at 1 PM, and your baby wakes up and needs you at 1:15? How would your boss likely respond to the defense "Oh- my apologies, the baby was supposed to nap until 2:30. I suppose I miscalculated." Even supposing all of your work is extremely flexibile, with all interactions asynchronous- have you noticed how inefficienctly work tends to progress when there are frequent interruptions? You are in the midst of one task, the baby suddenly needs your attention, and you expect- after meeting the kid's needs- that you will be able to smoothly get back on task? (More realistically, "Uh... where exactly was I when the baby started flipping out? Oh, that page- uh oh, what line was I up to" is the more likely scenario. Oh, that's just the beginning. The baby eventually gets older. At the toddler stage (1-3 years), you need to be frequently monitoring that he or she is not causing trouble of some sort- risking his or her own safety when playing, damaging items in the home, including flushing bath toys down the toilet (at a cost of at least $250 to replace as of about 7 years ago. God knows what the cost would be in 2022), etc. Oh, and then when there are siblings? In addition to the aforementioned items, you then will have the fun of mediating disputes of all sorts. You can anticipate having your work duties interrupted by all-pressing issues, including- but by no means limited to- "He went into my room!", "She played with my _______ (fill in name of toy)," "I can't find my _________ (fill in name of lost item)", resolving property disputes such as the following: Kid A outgrew toy x, and Kid B took possession in advance of toy x being thrown into the trash. Months having passed, Kid B takes out toy x, and now Kid A is demanding the right to repossess toy x. By the time you are finished admonishing Kid A (hopefully), you have no clue what you were just working on. I have not even mentioned the issue of transporting kids to and from school and/or other activities. So much for the notion of simultaneously working and caring for young children- or shall I say, successfully working and properly caring for young children. Much like Heisenberg's Uncertainty Principle, one - but not both - of these can be managed at any particular time. There is a 3rd commonly asserted assumption in the winning entries- namely, the assumption that workers are sufficiently flexible about their place of residence that they would freely - without any hesitation or vacillation - relocate anywhere solely based on job opportunities as applied to their professional goals. In other words, to take it to an extreme, this implies that any American would happily relocate to Antarctica provided he or she received a sufficiently lucrative job opportunity that was compatible with his or her professional goals. At a certain level, perhaps, I am being facetious here. However, when we consider that very example in the context of this (erroneous) assumption, it is evident that refuting it is accomplished quite easily- and we should surely discard the example. I should be fair on this point, and grant that these students are quite possibly making this assumption based on their own short-term projections. They may well perceive that in their own near-term future - which may not necessarily involve a spouse and/or kids- their plan is to complete their schooling, whether at the Bachelor's or (more likely) graduate level, they will happily move to whatever location may be required for them to secure their most preferred job opportunity. Speaking as a middle-aged man- with wife and kids - I would point out that over the long-term, this assumption becomes increasingly invalid. Suppose, as an example, I were to somehow receive an extremely lucrative job opportunity, with extremely favorable working conditions- on the other end of the country. Imagine I were to then declare to my wife, "Honey, I just received an outstanding job offer in Tumakeeki, an isolated, tiny town in South Carolina. We're moving there in 3 weeks. We'll have to pull the kids out of their current school, move everything...." I have never tested this- even as a (bad) joke; however, I assure you the response would NOT be "Mazel Tov! Let's get ready." Honestly, I am not sure I want to know the exact response, but suspect someting more along the lines of "Are you _______ kidding me?" - perhaps with some colorful adverbs thrown in for emphasis. In any event, can we dispense with this 3rd assumption? I believe I have made my point sufficiently. This was- by the way - intended in part in the spirit of some light-hearted humor, something needed all the more urgently given current world circumstances. Again, this is not to diminish the accomplishments of the participants in this year's M3 Mega Math Challenge. I would like to encourage all of our gifted young people- whether in math, science, or any other field - to please continue applying your full potential, both in your classes and in tackling problems which, like this one, impact our country and society.

Human Behavior and Mathematical Modeling COVID-19- another addendum

In my recent posting, I had estimated the expected end of “1st wave” and total estimated deaths as of that point in time. Based on data at that time, it seemed we had passed an inflection point, and would enjoy a basically contained situation with roughly 70,000 cumulative deaths by mid-May. Sadly, I was quite incorrect. In my own defense, so was the CDC. I believe our mutual error was the assumption of rational behavior from our citizens, who- during April- seemed to be mostly adhering to scientific expert recommendation with the required shutdowns aside from essential services. By early May, increasing irrational behavior was evident. As individuals, we observed people socializing unprotected, holding parties despite advice, and so on. And then our local governments allowed restaurants to reopen- for indoor dining. “Yes- we’re open!” (No charge for extra protein in viral form!) signs abounded. CDC and other scientific experts warned that they expected an increase in transmission and fatalities. And the reaction to this advice- denial. The old joke tells us, “De Nial is not just a river in Egypt.” Somehow, individual decisions were based on the incorrect assumption that mathematical and scientific models can be nullified by edict. Highly illogical. Recall the Inquisition of the 15th-16th century, during which the Church rejected all evidence of a heliocentric solar system as heresy, decreeing the geocentric model was the only permissible model- on penalty of death. As we now all realize (hopefully), such decrees may be unpleasant for those who adhere to mathematical and scientific truth, but as we can see, the planets still orbit the sun. Similarly, those who declare COVID-19 to be hyped, political, not especially dangerous, etc. do so not based on mathematical and scientific evidence, but rather based on their own desired conclusion- namely, “We want everything opened NOW NOW NOW!” (stamping feet) Do I dare project future COVID-19 figures at this time? With the daily transmission rate having surpassed 71,000, and still increasing, perhaps we shall see no letup, and one long wave for the next several months? Projection becomes quite complicated when human behavior is a factor. We had recently 4th of July celebrations (despite recommendations to the contrary), theme parks reopening, schools perhaps reopening next month, all such events tending to shift the curve in an undesirable direction. And speaking as a teacher, it is expected that students will not necessarily retain every nitty gritty detail from math and science classes. However, key concepts should be retained, especially logical deduction, algebraic, exponential, and logistic growth functions, the scientific method, etc. We see here that many citizens- in other countries as well- while they covered these in secondary grades, they seem to have either forgotten all of this, or are arbitrarily discarding this because they do not like the conclusions reached therefrom. It is an accomplishment to graduate from high school, college, and so on, but if- and only if- the knowledge acquired is actually applied in our everyday decisions.

Mathematical Modeling of COVID-19 addendum

We are now over a month into the pandemic crisis in the U.S., and - with more data now to work with- it is becoming possible to more easily and accurately extrapolate the end result of this cycle. We seem to have just a few days ago- around April 10- reached the inflection point in terms of total cases, and are just now reaching the inflection point in terms of total deaths. Insofar as that marks the halfway point of the cycle, we can thereby project a total of 1 to 1.1 million total cases in this country, with a resulting 50,000-60,000 American deaths by the time the virus is contained. We can likely anticipate containment around mid-May. Most mathematicians - if asked to project given current data- would likely offer a similar projection. However, we would need the medical professionals and other scientists to provide further data to consider the future beyond that. What is the potential of subsequent waves of infection? How long until there is a vaccine to protect the public from this virus? We can only work with the data we are given.

2020 MathWorks Math Modeling Challenge- Electric Vehicles and the Environment

As mentioned in an earlier post, I (and probably many others with a math background) have a keen interest in the annual math modeling challenge managed by the Society for Industrial and Applied Mathematics. We have had math teams representing our school (California Virtual Academies) competing in this event during the last 5 consecutive competitions. My interest in the topics chosen is not merely as a math team coach, but in considering the major challenges facing our civilization which are hopefully surmountable via a combination of mathematical and scientific knowledge, coupled with proper ethical conduct and implementation by our leadership. The topics covered are tackled by our country's teams, representing some of the most gifted high school students in the United States. Their mathematical modeling yields results which are worthy of our government's serious consideration. Do they have the wisdom to examine these results, or at least consider the basic conclusions of the winning teams? Or will they brush aside the results, and simply develop the legislation based on their party lines' positions? This year's competition- like that of 3 years ago- is related to the oft-covered issue of global climate change. We see this issue in the news almost daily. Climate change is unfolding before our eyes. Very bizarre weather patterns are increasingly manifesting themselves- record heat waves, increasing intensity of severe storms, wildfires, rising ocean levels as our ice caps are melting. Meanwhile, extinction of numerous species is acceleration Long-term concerns include a continuation of the above, coupled with rising sea levels, flooding of human coastal communities. While this is occurring, we are also depleting our nonrenewable resources- especially fossil fuels, the primary culprit of climate change (via increased carbon dioxide in the atmosphere). These facts are undeniable. The argument is no longer one of environmentalism versus denial of the threat of climate change. Instead, the argument is between ardent environmentalism versus those who concede the threat of climate change but quite ironically portray the situation as too hopeless to address, owing to the financial cost of addressing these issues. Moderation and pragmatism - as exemplified (hopefully) by mathematicians- is all too lacking. Whereas the problem of 2017 examined the evidence of climate change as exhibited by rising sea levels, this year's competition instead focuses on a major piece of the solution- namely, conversion of gasoline-powered diesel trucks to electric-powered ones. The competitors were challenged to examine the speed at which diesel-powered trucks would be converted to electric. Next, they were instructed to determine the number of charging stations needed, and the number of chargers needed at each station, to accommodate the needs of semi-trucks along 5 major corridors. These corridors were San Antonio, TX, to/from New Orleans, LA; Minneapolis, MN, to/from Chicago, IL; Boston, MA, to/from Harrisburg, PA; Jacksonville, FL, to/from Washington, DC; Los Angeles, CA, to/from San Francisco, CA. Lastly, they were challenged to prioritize which corridor was most important to develop first. This problem is not a mere theoretical exercise. For those who have been following, the Doomsday Clock- which represents the danger of humanity's self-destruction- this January was moved forward from 11:58 PM to 11:58:20. It is now 100 seconds to midnight. The primary danger to our civilization is nuclear war, followed by climate change. These are interrelated, insofar as climate change would likely lead to competition for resources, leading to a situation in which war is increasingly likely to occur. This is a grave long-term danger that we need to tackle in a reasonable and pragmatic way. It is not a Democratic issue, or Republican issue, but rather an American issue and, indeed a Human issue. At the moment, we are witnessing how humans behave during a comparatively minor crisis. Hoarding and human indecency are manifesting themselves, even as shortage of supply begins to occur. It is not my intention in any way to minimize the impact of tens of thousands of deaths, millions of seriously ill people, and social isolation over a period of many months. Eventually- within the next 12-18 months- this situation will resolve. However, climate change looms ahead as a much bigger crisis which should be regarded as an existential threat. We have resources- not merely financial and technological resources, but also brilliant students to figure out the best methodology to tackle these issues. God willing, our leaders should have the wisdom to turn to our scientists and mathematicians (of all ages) and figure out a pragmatic set of policies to implement their recommendations. Of course, we need policies that will stick permanently, not ones that will be implemented by one party, dismantled by the next administration, while we find ourselves sinking deeper and deeper into a hole. If we learn just one thing from this present crisis, it should be the need for proper planning and working together with our scientists and mathematicians who have been charged with the task of tackling society's greatest threats.

Mathematical Modelling and the Coronavirus covid-19 Pandemic

It would be safe to say that Americans are presently living in a state of anxiety and fear. I am admittedly far from immune to this from my end- on behalf of my entire household and family (and, incidentally, myself). However, it is worthwhile to step back a bit (in many ways) and tackle this- as mathematicians do- from a mathematical perspective. Perhaps then, the conflicting news reports will begin to make some sense. This is the current U.S. data on Coronovirus numbers. This virus- as with any virus - can be modeled as a logistic growth function. A logistic growth function is most commonly used in biology, as any population will initially grow exponentially, but the rate of increase will slow, eventually to 0; at that point, we reach the "carrying capacity." In the case of viruses, that "carrying capacity" would actually be the total number of people infected. After all, viruses needed human hosts to remain "alive" (insofar as viruses are technically not considered alive); once there are no further non-immune hosts available, they would theoretically cease to operate- so to speak. Any physicians reading this are probably cringing at my medical terminology (or lack thereof). Back to the math.... So what is a logistic growth function? And right now, we are still on the first half (or leg, if you prefer) of the graph, during which dP/dT, the rate of increase, is still increasing. As of today, Coronovirus cases are increasing at a rate of 7500 per day. The "inflection point" would represent the midway point of this crisis. At that inflection point, the rate of increase would stabilize, and the daily rate of new cases would begin to decrease. You see, then, that even if today is the inflection point (which seems unlikely), we would still have another 3 weeks until the graph finally plateaued, and the total Coronavirus cases in our country maxed out at 65,000, with the virus declared contained at that point. That would appear be the best case scenario as of this point. Until we actually reach that inflection point, we would extend our estimate of the crisis' duration, as well as the maximum expected number of Coronavirus cases. UPDATED 3/26/2020- The number of Coronavirus cases in the U.S. is now 85,268, with dP/dT of over 17,000 and climbing. We are poised to reach P of 100,000 within hours. The function now resembles an exponential function of the form P = P0r^t, where r is between 1.2 and 1.25. We are evidently not approaching an inflection point. Prepare for reported Coronavirus cases to exceed 200,000 in the best-case scenario. Worst case, we may conceivably head into 7 figures. This happens normally, by the way- with colds, etc. We hear the expression "There's a cold going around." Within a few weeks, much of the population is infected. Why? Because normally we do not shut the country. Colds are normally of minimal danger (aside from for those with severe immune deficiencies); hence, there is no reason to stop business as usual. However, this virus is different. It is far nastier, and with a mortality rate of 4%, allowing 1/2 the population to become infected (which is a figure we hear commonly) in the absence of a shutdown, amounting to roughly 10 million American deaths, would be unacceptable to us. We hear the expression "flattening the curve." This is precisely what is accomplished by this shutdown. Minimizing human interaction (aka “social distancing”) slows the rate of transmission so that the maximum number of Coronacases- and, more importantly, deaths resulting from such, is minimized. There is a price paid, however- increased duration. To save lives, this shutdown increases the duration before the "carrying capacity" point is reached. Hopefully we all would concur that increasing the duration is worth saving many millions of lives. Also, we hear about hospitals' capacity. By slowing the spread, this also - hopefully- decreases the cases of severe Coronavirus patients who are unable to receive adequate treatment due to shortages of beds, medical supplies, etc. We hear many officials indicating figures of 9-11 more weeks. This is a probably fairly accurate estimate of the time remaining until containment is attained. One official grimly indicated 18 months, punctuated by multiple waves. This would make sense when considering the expectation that a vaccine to eliminate COVID-19 would likely take 18 months to develop, and meanwhile- even after containment is achieved- some people might potentially bring the virus back into our country, and it would then resume spreading to Americans not previously infected, and then another round of this. Hopefully, with our government wiser from the experience, the response would be more prompt, decisive, and hence more effective than this round. And this, in a nutshell, is the mathematical representation of the Coronavirus pandemic. If you prefer to hear the non-mathematical details- regarding food shortages, people acting irrationally, the occasional touching story of people reaching out to help others, etc., this will pop up in front of you in today's headlines. No reason for me to provide more of this here. However, if you are reading this, please stay safe. And as Mr. Spock would say, "Live long and prosper!"

Moody's Mega Math Challenge

Some of us who completed our secondary-level education in the 1980s and 1990s (myself included) had the pleasure of competing in local math competitions. The Greater San Diego Math Field Day was one such example. I personally competed in this event- and later the high school equivalent of the same- in every grade from 6th through 12th grade. The setup was fairly consistent. On one particular Saturday morning in spring, students representing teams from all competing schools would show up at one specified location, usually a public school campus. Students would be ushered into rooms and would be given a challenging timed math test. These tests contained challenging isolated math problems, which tested math skill and knowledge. Then, while students cleared their heads and waited- attending lectures and perhaps having lunch- the tests would be quickly graded. In early afternoon, students and families would assemble in an auditorium and the awards ceremony would ensue. Winning students would receive a ribbon and/or trophy, perhaps a small prize (one year, my 2nd place prize was the game of Helix). Flash forward to the present. The "low stakes" competitions of the kind described above are increasingly rare, perhaps regarded as obsolete. The "old-fashioned" problems are an intellectual challenge, but how does society benefit from tackling such isolated and seemingly random problems? Over the past several years, a new and high-stakes math competition-which draws thousands of competitors nationwide- has emerged. I refer specifically to Moody's Mega Math Challenge, organized by the Society for Industrial and Applied Mathematics. This competition is held online over the last weekend in February. Students have a 2- to 3-day window in which to compete, but must submit the team's solution within 14 hours of accessing the problem. Once any team member downloads the problem, the clock starts ticking for the entire team. Our math team from California Virtual Academy just competed in this competition- for the 2nd consecutive year! Regardless of the results, the students found this an enjoyable and interesting experience. The problems from past years have been posted. As seen on their website, this year's problem involved investigation of environmental impact and climate change, specifically considering historical sea levels at major national parks and extrapolating future levels via mathematical modeling. Surely the results of students' work on this problem is of enormous value to our country. Indeed, ther are many who scoff at the notion of environmentalism and global warming and the like. However, if the gifted students throughout our country consistently arrive at similar conclusions, this would be something our political leaders should consider. (Yes? At least I would hope so. For our sake as a species....). This is a high-stakes competition. The prizes awarded to winners reflect this. While there is no cost to register to compete, a total of up to $150,000 of prizes are awarded, with prizes ranging from $1000 to $20,000 split amongst team members, to be paid to their future colleges. It should be pointed out, however, that all teams submitting viable solutions are deserving of commendation. As noted above, these problems are not isolated abstractions, but are relevant matters that impact our entire country- and world. Successful students need a well-rounded academic background for this competitions, since they must not only tackle the math, but also write a lengthy, detailed research paper containing all specfied components within the time allotted. Such a feat is indeed impressive.