Dr. Kimichika Fukushima is currently the Chief Specialist at Toshiba Nuclear Engineering Service Corporation in Advanced Reactor System Engineering Department. He achieved his doctorate degree from Osaka University in the Molecular orbital study of helium atoms in fusion reactor materials. He then went on to be a Senior Researcher in the Theoretical study on the electronic state of antiferromagnetism as well as energy materials and systems.
Dr. Fukushima has written countless papers over the last 30 years for several publications including his paper “CaCuO2 antiferromagnetism using shallow well added solely to atomic potential for generating O2- basis set of periodic molecular orbitals with consideration of coulomb potential in solid in an LDA” recently published in the International Journal of Quantum Chemistry. He was also honored with the Science Award from the Society for DV(Discrete Variational)-Xa.
The following is the next interview in our Take Note and Promote series. Dr. Fukushima talks about self-promotion, how to get published, and some helpful resources.
WriteForWiley: What’s important for the self-promotion of your papers?
Dr. Fukushima: Through scientific studies, we can gain the deeper knowledge about nature and the technological potentiality. The expansion of recognition is straightforward in some cases, but is indirect in other cases with difficult problems. Previous studies help our study via communities, although the interest is not common to researchers. Information related to a specific theme in papers of journals and reports of meetings/conferences are useful. The information is, however, not easily obtained, because of the tremendous number of papers and reports from researches. Journals for scientific letters or rapid communications as well as abstract magazines have so far been useful, and recently, the search using web service is increasing its role. The problem is how to get the information simply and effectively. One of the important items for the self-promotion is the full consideration on the recognition of nature and the basic role in technology before and during the study. The revealing universal concept results in making strong influence on the self-promotion.
How can you find published articles?
The only certain way to find a published article is the DOI in the form like http://dx.doi.org/10.1002/qua.23146
which directly sends the researcher to the addressed website of the article.
The DOI written in the above form can be found if the author cites the DOI in an abstract of a conference/meeting and his own paper in his communities. Another way is the use of key words in the paper, which are commonly used primary terms in searching for articles. Anyway, what’s important is that the article is worthy to be read.
Did the above items influence on the promotion of your paper?
The Google Search using my full name finds the article published from Wiley with materials in the related international symposium. I have cited this article in abstracts of international conferences and meetings, as well as in subsequent papers. I have further studied concentrating on a basic concept expressed with the primary word appeared in the previous journal and cited the published papers using the primary word as a key word. These procedures are for the deeper study and the announcement of the study.
What do you hope for from publishers?
Short-time peer-reviews of manuscripts with sufficient number of positive referees and rapid publications; publications of mathematical books in front mathematical fields using physical and chemical words which are not for mathematicians; publications of annual reviews and symposium abstracts/proceedings of each scientific field emphasizing questions, answers and comments; publication of selected papers in biology with a note which explains long and complex terms in chemistry and biology.
What were useful books in your studies?
A book of selected problems in the mathematical contest in Hungary for high school students, which blushed up the mathematical sense; a mathematical textbook by Masayoshi Nagata, which gave a mathematical view from an abstract mathematical formalism like the Dirac’s book; a physical history written by Tomonaga, which teaches zigzag processes for advancing science; a book on quantum field theory by Tomonaga, which reviewed an essence of physics.
Let us know your thoughts by leaving us a relpy in the comments box below.
If you would like to participate in a guest post or interview contact us at firstname.lastname@example.org
New or Old 2 – Nanoputians
A few weeks ago Prof. Helena Dodziuk wrote a guest post on ‘Excessive Science,’ and the issues this creates. This guest post can be viewed here. As a follow up on this matter, Prof. Helena Dodziuk has written a second guest post again on ‘New or Old,’ specifically this time on nanoputians.
Do you like Prof. Helena Dodziuk find similar occurrences in your areas of research? Let us know your thoughts on the conflicts of ‘New or Old’ research by leaving a comment at the bottom of this page.
I have been always fascinated by molecules with unusual spatial structure2,3: the ones containing inverted 24 or planar 33,5,6 carbon atoms, planar 47 or unusually puckered 58 cyclohexane rings and other molecular “pathologies”. To name but a very few additional ones, olympiadane 69, knot 710, and endohedral fullerene complexes like 811 may be mentioned. They are fascinating, obtaining them presented a challenge but, as a rule, no applications were in sight when their syntheses were attempted. Cubane 9 is a good example: Eaton et al. published its synthesis in1964 without any hint to the applications, the researchers simply wanted to obtain this beautiful, highly symmetrical, and difficult to synthesize molecule. Much later we have learned that for ca 30 years polynitration of cubane was studied by US Army in the hope to get octanitrated cubane 1012 or that it could be used as HIV drug13.
I’ll write more about such unusual molecules later but here I would like to present for pure fun a synthetic paper on nanoputians, including nanokid 1 shown above, nanoballetdancers, and nanoputian chain forming a monolayer on a support.
Chanteau and Tour1 synthesized what they call anthropomorphic molecules 11 – 14 (and some other, for instance nanoputians dancing in pairs) not because they wanted to use them for any application. They made it for fun! Running 11 and dancing 12 individual nanoputians and a group 13 as well as another group 14 forming a layer put on a support using thiol links. With the syntheses and compounds identification meticulously described it is an example of very good craftmanship. Carried out by sheer curiosity, earlier in French one called it “acte gratuit”.
The next submission will be about 3D printing. It is a very interesting technique promising to revolutionize not only industry but also the whole everyday life.
(1) Chanteau, S. H., Tour, J. M. J. Org. Chem. 2003, 68, 8750-8766.
(2) Strained Hydrocarbons. Beyond van’t Hoff and Le Bel Hypothesis. With Foreword by Roald Hoffmann; Dodziuk, H., Ed., Ed.; Wiley-VCH: Weinheim, 2009.
(3) Dodziuk, H. In Modern Conformational Analysis. Elucidating Novel Exciting Molecular Structures; Wiley-VCH: Weinheim, 1995; pp 157-211.
(4) Wiberg, K. B. Chem. Rev. 1989, 89, 975.
(5) Hoffmann, R., Alder, R., Wilcox, J., C. F., J. Am. Chem. Soc. 1970, 92, 4992.
(6) Hoffmann, R., Alder, R. W., Wilcox, C. F. J. Am. Chem. Soc. 1979, 92, 4992.
(7) Dodziuk, H., Ostrowski, M. Eur. J. Org. Chem. 2006, 5231.
(8) Dodziuk, H., Nowinski, K. Bull. Pol. Acad. Sci., Chem. 1987, 35, 195.
(9) Amabilino, D. B., Ashton, P. R., Reder, A. S., Spencer, N., Stoddart, J. F. Angew. Chem, Int. Ed. Engl. 1994, 33, 1286.
(10) Dietrich-Buchecker, C.-O., Sauvage, J.-P. Angew. Chem. Int. Ed. 1989, 28, 189-192.
(11) Dodziuk, H. J. Nanosci. Nanotechnol. 2007, 7, 1102-1110.
(12) http://en.wikipedia.org/wiki/Octanitrocubane Octanitrocubane.
(13) http://www.chm.bris.ac.uk/webprojects2004/hook/applications/#Pharmaceuticals Applications of cubane: Pharmaceuticals; 2004.
Today we have a guest post from Prof. Helena Dodziuk on ‘Excessive Science.’ Prof. Helena Dodziuk studied Physics at Warsaw University before completing her Masters in Physical Chemistry and her PhD in Organic Chemistry. She then went on to work in chemical institutes throughout her career. Helena Dodziuk was presented her ‘Professor’ title from the President of Poland in 2002. More about this can be read in an interview with Prof. Helena Dodziuk on ChemistryViews. More details about Prof. Helena Dodziuk scientific activity can also be viewed on her webpage.
She has authored/edited the following books; ‘Modern Conformational Analysis’, ‘Cyclodextrins and Their Complexes’, ‘Strained Hydrocarbons’, ‘Introduction of Supramolecular Chemistry’ and its Polish updated version. At present, Prof. Helena Dodziuk submits articles in Polish to the site of physicists from the Toruń University.
In addition to Chemistry and Popularization, Prof. Helena Dodziuk loves singing, traveling and sightseeing.
New or old but always hot
First of all I would like to specify what I am going to write about. The only criteria will be my fascination by phenomena, discoveries or simple results. Their actuality would not be decisive, today one forgets about important or simply appealing yesterday’s findings. In addition to new ones, I would like to remind you what caught my attention earlier. Today “Excessive science” will be presented. With it, I would like to start a serious discussion of inflated and overspecialized science, in which we all suffer of too much information. Since I studied Physics and carried research in Chemistry, my texts will be often related to these domains. However, more general topics like that discussed today as well as those related to health will also be covered. To stay not only in a very serious mood, in the next part I am going to discuss nanoputians, molecules with formulae resembling humans that have been synthesized without any practical aim, simply to have fun.
A colleague told me that the new version of the Gaussian program suite contains more than 300 functionals1 while a special website “Basis set exchange,” provides, as of 19 June 2013, 490 of them. According to the latter there are 250 published basis sets for the hydrogen and 310 for the carbon atom. Too much to reasonably deal with, even for someone involved only in the DFT quantum calculations who should also be able to analyze reliability of experimental data to compare with and to know specific properties of the molecules under study. I am interested in molecular properties determined by a combined application of experimental and theoretical methods2-4 and this immensity of the computational methods is unbearable for me. I also believe it is for many others. But this is only one facet of the crisis situation experienced by science today. Some specific manifestations of the crisis are discussed in journals and the Web. Proposals for the cure of the problems are given however no general discussion on the whole has been published. As it will be shown below in one example, the curing procedures themselves can also be problematic.
Most of the problems can be summarized by saying too much: too many experimental and computational methods, too much data and too many papers they create.
The abundance of experimental and computational methods and narrow specializations is typical for all areas of science, in particular chemistry. Note that this abundance is accompanied by the interdisciplinary character of most studies today. In addition, new methods replace the old ones. In 1990’s Prof. Kenneth Wiberg from Yale University told me that almost no one carried out calorimetric measurements at that time. Certainly, this was an exaggeration, but some basic information seems to be increasingly difficult to find even if it exists. To a great extent this is due to too much data which is difficult to handle.5 For instance, the flood of publications (analyzed by Bauerlein et al.6) according to Michael Mabe (as cited in ref. 6), the number of publications grows at a rate of 3.26% per year doubling in about 20 years. As presented in7a, doctors/practitioners who 20 years ago refused to accept any clinical guidelines from the British National Institute of Health and Clinical Excellence concerning the drugs and procedures to be used, today have changed their minds; unable to face 18 – 20 papers that they should read every day seven days a week to cope with the data.
The growing number of scientists competing for grants and the pressure to publish, especially in high impact journals, is to blame for the surfeit of scientific information. A significant percentage of the published articles in science are not only not cited but also not read at all. According to Bauerlein et al.6, “the amount of redundant, inconsequential, and outright poor research has swelled in recent decades,” raising the cost of publishing, reviewing, and simple reading of scientific literature.
On the other hand, a dangerous opinion that “anything more than a few years old is obsolete,” becomes more and more accepted. Thus, there is neglect of older papers independently of their real value.
Decreasing the number of published papers and limiting them to only high-quality and short ones, e.g. “stopping the over publication,” and taking into account impact factors, IF, of only few articles for a position is presented by Bauerlein and collaborators as a wonder drug which will heal science.6 In the same way as favoring the candidates for the academic positions “with high citation scores, not bulky publications,” in our opinion, will not help significantly.
A concern for high citations is they are prone to manipulation8, to fight it down, the owner of Institute of Scientific Information, Thomson Reuters, every year bans from its listing journals for self-citations9. Not only single journals but also “citation cartels” of journals and individuals do exist10. On the other hand, even in the same scientific domain, if you produce outstanding works in an important but very specialized area, you will never reach high scores.
Another burden difficult to fight with is publishing of results that cannot be reproduced. (Of course, we are not talking about the Journal of Irreproducible Results11) Some of them deliberately produced frauds, others contain simple errors or misconceptions. The most famous from the former category was the case of a rising star aspiring to the Nobel Prize in Physics, Jan Hendrik Schön (whose numerous articles were withdrawn by highly respected journals after the publication5) and Hwang Woo-suk who claimed to succeed in cloning human embryonic stem cells12. Wikipedia even gives a list of experimental errors and frauds in physics5. In 2009 an article13 with the intriguig title “How many scientists fabricate and falsify research? A systematic review and meta-analysis of survey data” appeared.
Closer to applications, Begley and Ellis14 analyzed preclinical cancer data published in top-tier journals, 90% of which could not be reproduced even by the investigators themselves. As a result, Nature recently published a special comment by Begley14, presenting criteria allowing one to specify papers reporting preclinical cancer research “that don’t stand up to scrutiny.”
In an effort to fight frauds, the Journal of Cell Biology adopted a special screening procedure to detect image manipulations10. As the result, 1% of the publications accepted by the journal are revoked after the positive referee reviews. Moreover, 25% of all accepted articles were found to contain at least one figure that should be corrected because of “inappropriate” manipulation. Similarly, the Organic Letters journal has just hired a data analyst to inspect the submitted data (in articles as well as in the Supporting Information) for evidence of manipulation15. The scientific misconduct is a great problem but it is only the tip of the iceberg of severe problems the science faces today and, in my opinion, there is no simple method to solve the problems.
Let us know your views by writing a comment in the ‘Leave a reply’ box below
(1) http://www.gaussian.com/g_tech/g_ur/k_dft.htm functionals in Gaussian; 2013.
(2) Dodziuk, H. In Modern Conformational Analysis. Elucidating Novel Exciting Molecular Structures; Wiley-VCH: Weinheim, 1995; pp 157-211.
(3) Bernatowicz, P., Ejchart, A., Ruszczynska-Bartnik, K., Dodziuk, H., Kaczorowska-Molchanow, E., Ueda, H. J. Phys. Chem. B 2010, 114, 59-65.
(4) Dodziuk, H., Korona, T., Lomba, E., Bores, E. J. Chem. Theor. Comput. 2012, 8, 4546-4555.
(5) http://en.wikipedia.org/wiki/List_of_experimental_errors_and_frauds_in_physics Errors and frauds in physics; 2013.
(6) Bauerlein, M., Gad-el-Hak, M., Grody, W., McKelvey, B., Trimble, S. W., http://chronicle.com/article/We-Must-Stop-the-Avalanche-of/65890/ stop the overpublishing; 2013.
(7) http://www.nature.com/news/assessing-the-value-of-health-treatment-1.12701#auth-1 Assessing the value of health treatment; 2013.
(8) Harzing, A.-W., http://www.harzing.com/esi_highcite.htm How to become an author of ESI Highly Cited Papers?; 2012.
(9) van Noorden, R., http://blogs.nature.com/news/2012/06/record-number-of-journals-banned-for-boosting-impact-factor-with-self-citations.html, Record number of journals banned for boosting impact factor with self-citations; 2012.
(10) http://jcb.rupress.org/site/misc/about.xhtml manipulated figures; 2013.
(11) http://www.jir.com/ Journal of Irreproducible Results.
(12) https://en.wikipedia.org/wiki/Hwang_Woo-suk Hwang Woo-suk scandal.
(13) Fanelli, D. PLOS one 2009, 4, e5738.
(14) Begley, C. G., Ellis, L. M. Nature 2012, 483, 531-533.
(15) Smith, A. B., III, Org. Lett. 2013, 15, 2893-2894.
This is the second in our series of posts by Bernd Schroeder, Wiley author and academic director and program chair of Mathematics and Statistics at Louisiana Tech University.
In this post, he talks about how we can expertly teach non-expert students in a manageable way.
Click here to read his previous post about preparing STEM and non-STEM students for a workplace that demands mathematical skill sets.
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How to Teach Analysis?
As with my other post, the question mark should indicate that this is not a “How To” manual but food for thought instead. I will not claim to be right, but your reaction to what follows can tell you a bit about your own comfort level with change.
At my institution, the sooner students are ready for work in Numerical Partial Differential Equations or Physics, the better. This should be common because by the time most people know all the mathematical details they need for Numerical Partial Differential Equations or Physics, they’re old.
We can make the case that much of the requisite theory builds on pretty deep functional analysis, which builds on measure theory and linear algebra, which is best taken after a first proof class in analysis. So, assuming that these concepts also need time to settle in your mind, a time of 3 years between the first analysis proof and the end of a functional analysis class may not be unrealistic, possibly even too fast.
It is typically the case that a mathematics graduate student who invests 3 years into these fundamentals should have had some of them as an undergraduate. But even if 2 years of graduate school are spent on fundamentals, graduation in a total of 4 years becomes a challenge.
For non-mathematics students, investing 3 years into the mathematical background for the work they do seems unreasonable. Unsurprisingly, many of them do not take “our” (that is mathematics departments’) classes.
In summer 2013, I taught the spectral theorem for unbounded self-adjoint operators on dense subspaces of infinite dimensional Hilbert spaces to a group of 5 students most of whom started their first proof class in analysis in December 2012. (Disclaimer: As I recall it, students asked about the mathematical background for quantum mechanics and I decided to provide it to those who would volunteer for the ride.) The net exposure to analysis for most of my students was two 10-week quarters in which we had a semester’s worth of instructional time, plus the 5 week summer session (another semester’s worth of instructional time). The pace and density of material were quite murderous, as there was nary a result in the early part of the development that was not quoted later.
At the same time, we only left a small number of logical gaps in the presentation: Fubini’s theorem and products of measure spaces, the density of the compactly supported infinitely differentiable functions in Lp, and the Stone-Weierstrass Theorem were discussed, but not proved. We also spent the last day discussing how the powerful functional calculus leads to the Spectral Theorems for Unitary and for Self-Adjoint Operators and did not go through all the technical parts of the proofs, which would have taken two days. Overall, given another 3 weeks, maybe less, we could have done it all without gaps.
Given the short time of exposure, we cannot expect the students to have the same deep connection to the content that an expert has. However, I feel that these students can construct a decent proof in analysis and elementary functional analysis on a regular basis. That is not a bad outcome for being 8 months removed from being first exposed to analysis proofs. Moreover, these students have seen a lot of content that will be useful in their applied classes (spectral theorems, the elements of complex and functional analysis needed to prove them, Lp spaces, convergence of Fourier series in L2 and plenty of in-class remarks attempting to make connections to numerical analysis, physics, etc.). To me, this is preferable to spending a lot of time in training exercises, which leads to students not even seeing the Lebesgue integral in their first year.
Are there gaps? Certainly. Anything that did not directly contribute to progress towards the spectral theorem for self-adjoint operators was omitted. The students have not proved, using ε and N, that the limit of the nth root of n is 1 as n goes to infinity, they have not proved the limit comparison test for series, etc. Is that acceptable? Personally, I find Lp spaces much more important than lots of details on series (just about everything that we needed went back to facility with the geometric series). Similarly, ε-N type training can be provided by analyzing the Dirichlet kernel rather than with training exercises. So, overall, I feel reasonably good about the job we did. Further iterations of this sequence can always be improved by picking the right exercises (and by slowing down a little).
How do you define success? How do you assess it? Here is where judgment calls are needed. It is a virtual certainty that there are problems from a first analysis proof class that would be a lot harder for my students than for students who went the usual route. I also noticed that, although I did not need specifics from the topology classes I took, I was a lot more comfortable with “continuity means inverse images of open sets are open” than my students were: For them, that was one theorem among many with the importance slowly emerging in the course this summer. If that is considered to be a problem, then my experiment (if you will) failed. On the other hand, these students are developing a feel for Hilbert spaces and L2 at a time when other students just learn the definition of an open set.
Is it hard to design such a new approach? Well, let’s say that I was surprised when I thought that I could avoid using the Hahn-Banach Theorem. So I designed the course without proving the Hahn Banach Theorem and the surprise lasted until I ran into a proof (the Cauchy Integral Theorem for Banach space valued functions) that is best done by using a consequence of the Hahn-Banach Theorem. That result could also be proved by simply reworking the proof from complex analysis with the range being a Banach space instead of the complex numbers, but nonetheless …
Along the lines of creating new approaches, the challenge for this sequence of classes is the same as for any change to canonical approaches: First of all, because we are supposed to model logical thought, we have to create something that is logically consistent. After this first step in our student-centered approach, we then have to figure out if it does what we intended to do. For example, the mind can be overchallenged by an approach that is too dense or too fast. You may rightly say that the class was both and, if so, I will not argue against you. However, my experience shows that the mind can stand up to much stricter rigors than we may give it credit for.
Overall, I certainly recommend approaching change with care. The “race to the spectral theorem” above is the product of about 10 years tinkering with the structure of fundamental analysis. Abject failure at any stage would have likely diverted the project from the result described above.
So be careful, and when something does not quite work, learn from it. As long as the bumps in the road can be navigated and you have at least half as much fun as I had with my spectral theory class, you’ll do fine. Just make sure your department head knows and supports what you’re doing. I had a slight advantage there, because I am the department head
I do answer to a dean, though…
The following is a guest post from Bernd Schroeder, the current academic director and program chair of Mathematics and Statistics at Louisiana Tech University. His specialties include discrete mathematics, harmonic analysis, and probability theory. He has about 20 years of teaching experience and wrote a few titles including Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers (2010) and A Workbook for Differential Equations (2009).
Below, he talks about the difficult task of providing both STEM and non-STEM students with the skills they need to succeed in this increasingly analytic workplace. He says that he does not to have all of the answers but wanted to share some observations with fellow authors.
This is his first of two posts. Check back next week for a piece on how to teach analysis to the varied levels of those seeking this skill set.
If you have any comments or thoughts on this topic, feel free to reply to the post below.
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How to Prepare Mathematics Majors and STEM Undergraduates for Jobs and for Work with Non-Mathematicians?
Labor statistics suggest that there is an impending shortage of STEM talent but not at the Ph.D. level. Therefore, the mathematical community needs to (re)focus on students whose final degree will be a bachelor’s or a master’s degree. Moreover, we need to focus on students whose degree will not be in mathematics. This is a substantial task even if your program’s focus is already wider than the stereotype in which “the courses get you ready for your Mathematics Ph.D. qualifying exams.”
So how can mathematics and the job relevant “mathematics abilities” (see page 57 of this document) be made “more accessible” without “watering down” the students’ preparation?
For some student populations, changes in the first two years may well turn out to be minimal.
For engineering, physics, and mathematics majors, there does not seem to be a replacement for calculus. Multivariable calculus is the mathematical basis for the theories of fields and flows, which are central to subjects like Physics, Electrical Engineering, Mechanical Engineering, and more.
For mathematics majors, the case can be made that calculus is the “applied version” of mathematical analysis. When I surveyed the AMS subject classification, in my judgment, I found that analysis is the indispensable foundation for 38 of the 62 branches of mathematics. In addition, another 9 branches were closely related to analysis. This means that less than one fourth (15/62) of all branches of mathematics might get by without analysis. If you go through the same exercise, I’m quite confident that your count will be similar to mine. For many disciplines, the question is not if to teach calculus, but how. Similarly, at a more advanced level, the question is not if to teach analysis, but how.
Although the populations above are sizable, for other students, changes are possible, maybe even desirable.
A calculus prerequisite for Discrete Mathematics helps assure that students have “mathematical maturity.” But questions arise like:
- What parts of an introductory Discrete Mathematics class truly need calculus content?
- Can these parts be replaced with content that is similarly beneficial?
- Would it be sacrilege to consider a hypothetical computer science graduate who has not had calculus?
My only constraint in this regard is that I would want this graduate to have developed/trained certain overall cognitive abilities (ability to concentrate, ability to think about a problem in different ways, ability to correctly follow a procedure, deductive reasoning, etc.) to the same level as would have been gained through calculus.
The situation gets muddier in disciplines that do not require the (whole) calculus sequence and need STEM skills, such as business and biology. One reason STEM majors are considered useful is because they can analyze data. However, data analysis appears to be fundamentally different from proving theorems. For example, I proofread a proof of the Central Limit Theorem as a graduate student, but I only developed an understanding of the Central Limit Theorem when I wrote this simulation.
So how can we authors help with the changes that will either be made by the mathematical community or that someone else will make for us?
First of all, we face a paradox that affects something publishers care about: sales. Take a calculus book as an example. If you write a calculus book that is similar to the standard texts in the field (10 years ago, sequences and series was always Chapter 8), then why would people buy your book? On the other hand, if you write a text that is very different from the standard texts, will people dare adopt your book?
Personally, I have no interest in writing a book that’s already been written by someone else. The above remarks on future needs also indicate that there is little to be gained from incremental changes. That is, unless you write an incrementally changed text that sells millions of copies, in which case at least one person has gained substantially: you; and (without sarcasm or envy) congratulations. The market leaders are market leaders because their products are good. Specific users will always find certain things that they wish would be different, but the texts satisfy the needs of many quite well.
So here is the hard questions are when you write something that radically departs from the canonical setup:
What do you include? What do you drop and what will be the effect?
For the above examples, we immediately obtain some specific questions:
Can you design a reasonably deep Discrete Mathematics book that does not need to touch upon calculus (definitely) and would students who have not been vetted by calculus respond to the presentation (There is a lack of data available)?
Can you teach the deep data analysis skills needed in the working world without touching upon the theory of continuous distributions (probably, as long as you’re okay using tables and computers and simply quoting results) and would students who have not been vetted by calculus respond well to the presentation (There is a lack of data available to me but a colleague told me about positive experiences with graduate students in biology)?
Finally, once you have answered these (and other) questions in a convincing fashion, how do you get other people to agree that your answer is convincing?
I have not tackled the questions above yet, but I would be interested in doing so. Discrete Mathematics and its connection to computer science should be well within my competence. However, I have never let a lack of education stop me from exploring other areas. Every book of mine has at least one chapter of which I knew little when I started writing. (Replies of the nature “All chapters read so poorly, which one is the one you had no clue about?” are not needed. ) So, despite my shortcomings, data analysis would be interesting, too.