## Posts Tagged ‘archaeology’

### Why I Blog about Archaeology (and Math)

November 28, 2013

The upcoming 2014 Society for American Archaeology meetings in Austin will include a session on blogging and archaeology. As part of that session, Doug’s Archaeology is hosting a monthly blogging carnival, in which participating blogs post on the same topic. I’ve been invited to join this group. The first topic is “why blog about archaeology”. This question has a couple answers.

The primary reason is that the blog provides some small motivation to continue to write and research. In this format, I can post pieces of a larger project. Those pieces get posted as they are completed. Each post thus feels like an accomplishment but also contributes to the goal of finishing the project. The first series of posts that I wrote, on the intensification of fishing, did eventually get formally published as a single piece. The blog was very helpful in developing that paper during the long slog toward publication.

My experience working on that paper and the blog led me to identify some other, related benefits of blogging. Due to space constraints, some material that I developed for the intensification paper was dropped from the final version. The blog provided a venue in which to share those thoughts, if someone should be interested in that aspect of the topic or greater details on the topic. For example, I used the blog to post R code that I wrote to perform some of the analyses for the intensification paper. This experience led me to the realization that the blog was also a great place for small projects that would likely never get formally published. The next series of posts that I wrote concerned variation in burial monument size. It’s possible that some of this material will resurface as a part of another project, but for now those posts were just a fun little diversion.

Other professions, such as economics, have a more well-developed tradition of posting working papers, papers that are pre-publication. Blogs are a great way to develop and further this tradition and to share data and insights that might not otherwise fit within the strictures of academic publishing.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013

### Identification of Lithic Reduction Strategies from Mixed Assemblages

November 11, 2013

This post is the first in a series that will try to characterize lithic debitage assemblages formed from more than one reduction strategy. The primary goals are to estimate the proportions of the various reduction strategies represented within these mixed assemblages and to quantify the uncertainty of these estimates. I plan to use mixture models and the method of maximum likelihood to identify the distinct components of such assemblages.

Brown (2001) suggests that the distribution of debitage size follows a power law. Power law distributions have the following probability density function:

$f(x\vert \alpha) = C*x^{\alpha}$,

where C is a constant that normalizes the distribution, so the density integrates to one. The value of C thus depends entirely on the exponent $\alpha$.

Based on analysis of experimentally-produced assemblages, Brown further suggests that the exponent, $\alpha$, of these power law distributions varies among different reduction strategies. Thus, different reduction strategies produce distinctive debitage size distributions. This result could be very powerful, allowing reduction strategies from a wide variety of contexts to be characterized and distinguished. The technique used by Brown to estimate the value of the exponent, however, has some technical flaws.

Brown (2001) fits a linear regression to the relationship between the log of flake size grade and the log of the cumulative count of flakes in each size grade. In its favor, this approach seemingly reduces the effects of small sample sizes and can be easily replicated. The regression approach, on the other hand, also produces biased estimates of the exponent and does not allow the fit of the power law model to be compared to other probability density functions.

Maximum likelihood estimates, using data on the size of each piece of debitage, produce more reliable estimates of the exponent of a power law. Maximum likelihood estimates can also be readily compared among different distributions fit to the data, to evaluate whether a power law is the best model to describe debitage size distributions. The next post will illustrate the use of the linear regression approach and the maximum likelihood approach on simulated data drawn from a power law distribution.

Reference cited

Brown, Clifford T.
2001 The Fractal Dimensions of Lithic Reduction. Journal of Archaeological Science 28: 619-631.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013

### More Thoughts on Mound Size Variability

June 29, 2013

This post begins to explore additional patterning in mound size, refining some of my earlier observations and offering some hypotheses for evaluation. Suppose mound-building groups occupied stable territories over the span of several generations or longer. Within the territory held by such groups, they built burial mounds. Many burial mounds within a given area may thus have been produced by the same group or lineage. Under these circumstances, burial mounds located in close proximity should be more likely to be the product of a single group or lineage. If the group traits that influenced mound volume were also relatively stable through time, burial mounds located near to each other should be similar in size. As an initial attempt to evaluate these claims, I looked at the relationship in mound size between mounds that were nearest neighbors and between randomly-paired mounds.

Recall that most mounds have been affected by modern plowing and other disturbances, but some mounds have been largely spared such damage. The museum records that I used characterized these undamaged mounds as “whole”. The museum records documented 287 whole mounds. To make sure that the comparisons were fair, I limited the sample of nearest neighbors to just those whole mounds that had another whole mound as its nearest neighbor. I eliminated duplicate pairings, so each pair of nearest neighbors was only considered once. The imposition of these constraints shrunk the nearest neighbor sample size to 49. Finally, I ran a simple linear regression to evaluate the relationship between the size of the mounds in these nearest neighbor pairings. Because the distribution of mound volume can be modeled as an exponential distribution, I used the log of mound volume in the regression analysis. Without this transformation, any relationship in
mound size between the nearest neighbors would be unlikely to be well approximated by a straight line.

I then sampled without replacement from the 287 whole mounds to obtain 49 randomly-selected pairs. As with the nearest neighbors, I performed a simple linear regression, using log volume. I repeated this procedure 500 times. The repeated sampling and analysis allowed me to develop a null hypothesis for the values of the regression coefficients.

I expected that the randomly-selected pairs would not have a meaningful relationship. The slope of the regression line should be close to zero for these samples. In contrast, the size of the nearest neighbor pairs should be positively correlated, so the slope of the regression line should be significantly larger than zero. The following two figures show the distribution of the regression coefficients, the intercept and slope, for the randomly-selected pairs.

Notice, in particular, that the distribution of the slope clusters near zero as predicted. This result indicates that the randomly-selected pairs do not have a meaningful relationship with each other, at least with respect to size.

These distributions contrast with the regression coefficients calculated for the nearest neighbors. The intercept is 0.90, and the slope is 0.75. These values are completely beyond the range of values estimated for the randomly-selected pairs. This experiment shows that the size of nearest neighbors is significantly and positively correlated. The results lend some support to the notion that stable groups produced these mounds. At the very least, the results provide encouragement to further explore the relationship between mound size and mound spatial distribution. Such work should probably make use of the spatial analysis tools available in GIS programs.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

### A Very Preliminary Interpretation of Mound Size Variability

May 11, 2013

Monumental architecture, by virtue of its scale, implies something about the organizational capabilities of the groups that produced it. The previous analysis of burial mound size further implies something about the variation in those capabilities. I explore some of those implications at greater length here.

The following thoughts should be considered preliminary. The original goal of this particular analysis was very modest, concerned with establishing a reliable measure of monument scale or prominence. My hope was that mound volume had stayed reasonably constant despite the effects of weathering and other processes. The analysis was being done as part of a project regarding monument function and social organization. While the analysis showed that many mounds lost volume as a result of modern plowing, it also showed that the volume of plowed mounds and whole mounds varied in very similar fashion. Variation in mound volume can be modeled with the exponential distribution. I did not expect this result at the outset.

I have often regarded mounds as potentially reflecting the “strength” of the groups that built them. Group strength might be a function of many different factors, such as group size, the productivity of the territory that the group occupies, the group’s organizational capabilities and the size of the social network upon which the group could call. Groups that scored higher on these variables should have been capable of building larger mounds. Groups that scored lower on these variables should have been limited to building smaller mounds. A large list of qualities could thus contribute to group strength and to burial mound size. I assumed that each factor would have a small additive effect on strength. Consequently, I supposed that variation in group strength and mound size should take the form of a normal distribution.

Clearly, this intuition was wrong. Upon further reflection, I think that I’ve underestimated the contribution of social networks. Their contribution is probably not minor. Ethnographic studies of leadership in small-scale societies illustrate the hard work and emphasis that group leaders often put on the maintenance of their networks. The effect of each additional ally is probably not merely additive, since each ally that gets incorporated has the potential to contribute their own unique allies to the network. Modern studies of social networks indicate that variability among individuals in network size has a heavy-tailed distribution, where most individuals have a relatively small network and a few individuals have very large networks. The mound data is suggestive of similar processes at play.

Before getting too carried away, let me emphasize again that this interpretation is very preliminary. It is, nevertheless, consistent with other archeological evidence for the operation of long-distance exchange networks at the time. The results also illustrate the potential value of this form of statistical modeling. The type of probability model which can be fit to the data — whether normal, exponential, or some other model — reflect the type of processes which operated in the past. The modeling thus constrains the set of possible interpretations that should be considered.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

### On Monument Volume IV

April 29, 2013

This post evaluates burial mound volume, fitting various probability models to the data. As noted previously, the exponential distribution seems like an appropriate model to fit to the mound volume data. This model is not the only possibility, of course, so I will also consider an alternative, the gamma distribution. The exponential distribution is a simplified version of the gamma distribution.

The gamma probability density function (pdf) is:

$f(x\vert \alpha , \lambda) = \frac{\lambda ^{\alpha} x^{\alpha - 1}e^{- \lambda x}}{\Gamma (\alpha)}$,

where:

$\alpha$ is the shape parameter,

$\lambda$ is the rate parameter,

and $\Gamma$ is the gamma function.

The gamma function typically takes the following form:

$\Gamma (\alpha) = \int_{0}^{\infty} t^{\alpha -1} e^{-t} dt$

Depending on the parameter values, the graph of the gamma pdf can take a wide variety of shapes, including forms that resemble the bell-shaped curve of the normal distribution. The following illustration shows some of the possible variation.

To evaluate the relationship between mound volume and mound condition (plowed and whole) under the gamma and exponential distributions, I analyzed model fit using the maximum likelihood method. The following R code details the analysis.

>library(bbmle)
>mdvol_g.mle=mle2(Allmds$Mound.Volume~dgamma(shape=shape, rate = gvar), start=list(shape = 1, gvar = 1/mean(Allmds$Mound.Volume)), data=Allmds, parameters = list(gvar~Allmds$Condition)) >mdvol_g.mle >mdvol_e_cov.mle=mle2(Allmds$Mound.Volume~dexp(rate = avar), start=list(avar = 1/mean(Allmds$Mound.Volume)), data=Allmds, parameters = list(avar~Allmds$Condition))
>mdvol_e_cov.mle

>mdvol_e.mle= mle2(Allmds$Mound.Volume~dexp(rate = bvar), start=list(bvar = 1/mean(Allmds$Mound.Volume)), data=Allmds)
>mdvol_e.mle

In this code, Allmds refers to an R data frame containing the variables Mound.Volume and Condition. The code uses the maximum likelihood method to evaluate the fit of an exponential distribution to the data and to estimate parameter values. I performed the analysis three times. In the first analysis, I fit the gamma distribution, using Condition as a covariate. In the second and third analyses, I fit the exponential distribution to the data, once with the covariate Condition and once without the covariate.

The models are “nested”. The gamma distribution can be reduced to the exponential distribution by setting the gamma’s shape parameter to one. The exponential model without the covariate is a simplified version of the model with the covariate. Nested models can be compared using an ANOVA test to see whether the more complex model gives a significantly better fit to the data, justifying the extra complexity. The following two tables show the results of the analysis.

The initial results suggest that the exponential distribution with the covariate provides a significantly better fit to the data than the simpler model without the covariate. The gamma distribution does not provide a significantly better fit. Notice that the gamma’s shape parameter is estimated to be one, which reduces the gamma to the exponential distribution.

From this preliminary analysis, I offer the following conclusions. The exponential distribution appears to be an appropriate model for mound volume. In addition, plowed mounds may be distinctly smaller than whole mounds, contradicting my initial hypothesis. In subsequent posts, I will consider some archaeological implications and address some additional considerations that may help to explain these results.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

### On Monument Volume III

April 20, 2013

For my study area, the distribution of burial mound volume for plowed and whole mounds looks similar. This distribution is also quite different from the normal distribution that characterizes so many traits in the natural world. The distribution of burial mound volume resembles the form of an exponential distribution. Exponential distributions have a peak at the extreme left end of the distribution and decline steadily and rapidly from that point. The exponential distribution has a single parameter, the rate, typically denoted by $\lambda$. The following function gives the probability density (sometimes called the pdf) of the exponential distribution.

$f(x\vert \lambda) = \lambda e^{-\lambda x}$

The pdf defines a curve. For a continuous distribution such as the exponential distribution, the area under this curve provides the probability of a sample taking on the value within the interval along the x-axis under the curve. The following illustration depicts these relationships. In the illustration, the shaded area under the curve represents the probability of a given sample falling between the two values of x.

As a check on my intuition regarding the applicability of the exponential distribution, I generated a random sample of 2000 from an exponential distribution with a mean of 500. The following figure shows what such a distribution may look like. The simulation does not provide definitive proof, but it may nevertheless indicate whether a more rigorous analysis that employs the exponential distribution is worth pursuing.

At least superficially, the histogram of the simulation results resembles the histograms of mound volume shown in the previous post. This simulation did not produce the apparent outliers seen in the mound data, but the resemblance suggests that burial mound volume can be modeled with an exponential distribution. I thus modeled mound volume with an exponential distribution, using mound condition (plowed or whole) as a covariate. I performed this analysis in R with the bbmle module. In the next post, I’ll present the code and initial results.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

### On Monument Volume II

April 10, 2013

The previous post suggested that mound shape could be modeled as a spherical cap. I then proposed that the shape of those mounds may change through time, due to weathering and repeated plowing by modern agricultural equipment, but mound volume might remain the same. As illustrated in the following figure, mounds might become shorter but wider as they are weathered and plowed. In the figure, A represents the original mound shape, while B reflects mound shape after weathering and plowing. The height, h, has decreased over time, while the radius, a, has increased.

Other hypotheses are possible, but I will evaluate this scenario first.

I have compiled museum data on mound condition and mound size for all recorded mounds in my study region. The museum records characterize mound condition as either “whole” or “plowed”. The records did not disclose the basis for this characterization. These records also document mound height and width. For each mound, I calculated a volume, assuming that mound shape resembles a spherical cap. The following two histograms illustrate the distribution of mound volume for plowed mounds and for whole mounds.

As you can see, the distributions of mound size for plowed and whole mounds look very similar. A few outliers may occur at the right tail of both distributions. These outliers represent unusually large mounds. The similarity of the histograms suggest that a single probability distribution could be used to model monument volume. The next post will evaluate monument volume more rigorously.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

### On Monument Volume I

March 26, 2013

This post introduces an approach for evaluating the original size of round burial mounds. In one of the places where I’ve worked, burial mounds comprise a prominent feature of the landscape, as illustrated in the following photograph.

This prominence may be amenable to explanation through formal high-level theory. Mound size, for example, may reflect the labor used to produce it, suggesting something about the size and organizational capabilities of the group that produced the mound. In order to use this feature of the monuments to evaluate high-level theory, the modern size should be an accurate reflection of the original size.

Such monuments may erode over time, making them less conspicuous and also less reliable as an index of the characteristics of the group that produced them. Natural weathering may take its toll, but modern agricultural practices probably affected burial mounds to a greater extent. Burials mounds were sometimes plowed repeatedly. These modern practices came later to the region where my case study is located, by which time laws protecting them had been enacted. Nevertheless, various processes leveled many mounds, perhaps decreasing their height and increasing their diameter. Despite these depredations, the original volume of the mounds may be preserved.

Mound shape can be modeled as a spherical cap, a geometric form representing the portion of a sphere above its intersection with a plane. Spherical caps are thus dome-shaped. The following figure illustrates a spherical cap. In the figure, h is the height of the dome, a is the radius of the dome’s base, and R is the radius of the sphere.

The total volume of a spherical cap depends on the maximum dome height, h, and on the radius of the circle where the plane intersects with the plane, a. The formula for the volume, V, of a spherical cap is:

$V=(\frac{1}{6})\pi h(3a^2+h^2)$

Importantly, the calculation of the volume of a spherical cap does not depend on the radius of the sphere of which it is a part. The maximum possible original height of a mound, however, should be equal to the radius of that sphere. This height can be calculated by holding the volume constant and finding this value of the height and radius. At that point, the height and radius will be equal. Subsequent posts will explore these ideas further and play with some data on mound size.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

### Off-topic: Career Paths in Archaeology

January 17, 2011

In this post, I will again digress, slightly, to discuss possible career paths in archaeology. I addressed an aspect of this issue in my earlier posts on graduate school,which gave some of my thoughts on preparing for an academic career. This time, I’ll talk more generally about possible career trajectories and ways to prepare for them. This discussion will serve as an introduction to subsequent posts, which will detail my own efforts to chart a particular career path.

I have observed a couple pathways to career “success” in archaeology. I define success in terms of acquiring a steady job doing something close to the kind of work for which you prepared yourself in graduate school and through subsequent work experience. One pathway I would consider a high risk, high reward strategy. The other pathway entails lower risks and commensurately lower rewards. I’ll discuss the high-risk strategy first.

The greatest excitement in archaeology generally comes from fieldwork which sheds new light on an old problem or fieldwork which identifies new problems to be solved. Fieldwork also provides opportunities to find the first, oldest, youngest, largest, smallest or whatever-superlative that’s-ever-been-found. In any case, fieldwork remains key to generating high levels of enthusiasm and support for the work that an archaeologist is doing. This simple fact is reflected in many (but, certainly, not all) of the job postings for academic jobs in archaeology. Most job descriptions for such positions will identify an ideal candidate as a person who, among many other things, has an active program of field research. The sad truth is that few people get famous (or secure academic positions) researching old collections. What makes this truth so sad is that a lot of archeological data already exists, is available for research, and has been incompletely reported. In some parts of the world, collection facilities don’t have room for many new collections. And yet the imperative exists to keep surveying and keep digging.

Thus, candidates for academic jobs would generally be wise to develop an active field research program. I consider this a high-risk strategy, however, because there’s little guarantee that the work will provide truly novel data that speaks to interesting problems or that leads to new questions or that results in the discovery of the first, oldest, youngest, largest, smallest or whatever-superlative that’s-ever-been-found. Certainly not if the archaeologist in question is working in a place like Mesoamerica, which can seem like an archaeological theme park, with hordes of professors, students and volunteers in tow, wafting through each field season. More likely, all that hard work (and fieldwork can be incredibly labor-intensive) will make a modest, incremental contribution. Such contributions will not likely move the meter sufficiently to impress an academic search committee, no matter how well-formed the underlying research design.

Taking this path therefore risks producing a highly competent but rather generic field archaeologist, destined to manage projects in the CRM world. Not that there’s anything wrong with that, as long as that the prospective candidate anticipated and planned for that career path. It’s unlikely, however, that an archaeological student who trained as a Mesoamerican/European/Andean/your-culture-area-here specialist will end up working solely in that particular area during the course of a CRM career. Frustration thus ensues.

The other, lower-risk career path is to specialize in a technical discipline, such as zooarchaeology, geophysical prospecting, underwater archaeology, chemical analysis, or quantitative methods. Sometimes academic jobs are posted specifically for these specialties, but such postings are relatively rare. A demand always exists for the services of these specialists, however, as consulting members of academic research programs or as suconsultants on CRM projects. For individuals with the appropriate training, opportunities exist to work in the exact specialty for which the archaeologist trained. Thus, this career path is likely to entail less frustrations: the specialist training provides appropriate additional research opportunities. Of course, such specialists also generally work in support of another archaeologist’s project and not on projects of their own devising.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2011.

### Off-topic: Archaeomath’s Guide to Success in Graduate School for Archeology II

January 19, 2010

In my previous post, I detailed some things that prospective graduate students should do to prepare themselves for graduate school. In this post, I tackle the graduate years. The tips are focused on things that you should do while you are still in graduate school to improve your future academic job prospects.

Tip Group 2 – Early Years of Graduate School. During these years, you will be satisfying course requirements, obtaining funding (if you didn’t already snag some), and developing and writing a Master’s thesis. If you are serious about an academic career, you will begin establishing your qualifications for such a career at this point. One of the more important credentials will be your publication record.

• Tailor your coursework to your thesis research. Work with each professor to tie your class paper or project to a chapter or portion of that thesis.
• Scale your thesis project to a level of effort sufficient to produce one publishable article. Save the book-length monograph for your dissertation. Anything longer than 50 double-spaced pages will require extensive trimming prior to publication in journal.
• Work with an existing artifact assemblage or data for your thesis. Ideally, you should only spend a couple years working toward your Master’s degree. To meet this schedule and produce a publishable thesis, you would be very hard pressed to acquire enough data through fieldwork to write a thesis worth publishing.
• Don’t waste your time going to a lot of conferences if you don’t have a paper to present. Conferences are a good way to catch up with people you haven’t seen in long time. Conferences are not terribly useful for networking, if you don’t have a paper to present. Let’s face it: many archeologists are not that good at this kind of interaction. If they really wanted to talk with people, they wouldn’t study human behavior through the lens of their garbage.
• Go to conferences if you are ready to present your thesis or if you will be giving a paper with your advisor.
• Give poster presentations rather than speaking at a session, unless you have been invited to speak at an organized session. General sessions are not likely to attract enough people interested in your research to make it worth your while. In addition, the main focus at many sessions is keeping the session on schedule. Discussion opportunities are inevitably more limited. With a poster, you will have a much greater opportunity to actually talk with people.
• Get some CRM training. You may need to go outside your own institution to get it. As noted previously, most archeologists ultimately work in CRM and not in academia. Scoff if you like, but that’s the reality. It’ll probably be your reality, if only for a couple years before you can land that sweet academic job. You’ll be much happier if you actually know what you’re supposed to be doing. Learn the regulatory process and how it applies to archeology.

Tip Group 3 – Mid-Career Graduate School. During these years, you will be publishing your Master’s thesis, developing your dissertation project, finding funding for your research, and initiating your dissertation fieldwork. This time is the crucial period for establishing your academic credentials through a solid publication record.

• Focus your early solo publication efforts on niche or regional journals. Contributions to edited volumes are also an acceptable venue for your early efforts. Like it or not, your reputation (and lack thereof) will matter when people review your work. Everyone would love to have their first publication be in Current Anthropology or Nature, but that goal is not realistic for most people. Start small at first. Then build on that work in subsequent publications.
• In a similar vein, focus your early papers on presentations of new data. This kind of paper is easiest to generate and hardest to reject. Your work needs to be theoretically-informed, obviously. There will be reviewers, however, who scoff at the presumption of a newbie who’s trying to publish some Grand Theory of Stuff. Establish your track record as a diligent scholar before trying to impress the old silverbacks with your credentials as an innovative scholar.
• Collaborate with your advisor. Your Grand Theory of Stuff will be much more likely to gain acceptance if you co-author it with another established silverback.
• Work on a field project for your dissertation that can be spun into future field projects. In addition to a successful record of publications, prospective academic employers want to know that you can provide field and research opportunities for their students. I wouldn’t, for example, join an established field project at its tail end unless you’re confident that you can make a go of it on your own.
• Do a little CRM work on the side. If you’ve made it this far in school, you could probably use the money. As noted, you are also likely to end up working in CRM. The contacts and experience that you obtain working a few local CRM jobs will be valuable later, if your pursuit of an academic job is unsuccessful.

Tip Group 4 – End of Graduate School. During these years (which may last a long time), you will be analyzing field data, writing your dissertation, preparing for your future career,. and submitting job letters for open positions. If you haven’t already started to establish your publication record, you may have very little opportunity left to do so, depending on how long you take to write your dissertation.

• Don’t be in a rush to graduate, unless you have severe financial constraints. The clock on your viability as an academic job applicant will be ticking once you’ve graduated. If you haven’t landed that first academic job within the first three or four years of graduating, you aren’t likely to get one. At that point, most schools will figure that you’ve been rejected for other opportunities for good reason.
• Organize a session at a major conference around a topic that is central to your dissertation work. This session will give you a little extra visibility prior to graduation. If successful, you may also be able to organize an edited volume around the proceedings.
• Turn your dissertation’s “theory chapter” into a publishable article. At this point, you presumably have a publication record going for you. Hopefully you now also have enough credibility and a sufficiently strong paper to get your work accepted in a major journal. Having just one article in a major journal at this stage will provide a significant boost to your chances of getting interest on the academic job market.
• Try to find teaching opportunities available to ABD candidates and obtain a few part-time teaching gigs. Local community colleges may provide such opportunities, in addition to the spots available at your own university. Prospective academic employers will want to know what classes you’ve taught and are prepared to teach. If you can establish your ability to teach a diverse range of classes to a diverse audience, with documentation of teaching efficacy (good class evaluations), you will give your academic job chances another boost.
• Once you’ve graduated, apply for any limited (one-to-two-year) appointments as a university lecturer for which you are qualified. You can often turn this experience into a full-time gig somewhere. Of course, you need to be sufficiently mobile to make this kind of short-term move.
• Start dialing your friends at local CRM firms. You may need a place to hang your hat while applying for academic jobs. And you may need to settle on CRM as a long-term career path.

Hopefully, you find these suggestions useful. Maybe they seem obvious, but I certainly didn’t think strategically about my career while I was in graduate school. My lack of forethought definitely shaped my prospects once I was finished.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2010.