Biological Models for Finite Mathematics

References

• Abalo, K., S. Clayton, F. Cuffney, P. Ryan, and P. Schuette. 2004. Biodiversity ESTEEM module. https://www.bioquest.org/esteem/esteem_details.php?product_id=2769.
   Google Scholar
• Aikens, M. L. and E. L. Dolan. 2014. Teaching quantitative biology: Goals, assessments, and resources. Molecular Biology of the Cell. 25(22): 3478–3481. doi:https://doi.org/10.1091/mbc.e14-06-1045.
   PubMed Web of Science ®Google Scholar
• Arganbright, D. 2005. Enhancing mathematical graphical displays in excel through animation. Spreadsheets in Education (eJSiE). 2(1). Article 8: 24. http://epublications.bond.edu.au/ejsie/vol2/iss1/8.
   Google Scholar
• Arai, K., T. Harayama, S. Sunada, and P. Davis. 2012. Randomness in a Galton board from the viewpoint of predictability: sensitivity and statistical bias of output states. Physical Review E. 86(5): 056216.
   Web of Science ®Google Scholar
• Baum, D. A., S. Smith, and S. Donovan. 2005. The tree-thinking challenge. Science. 310(5750): 979–980. http://www.tree-thinking.org/
   PubMed Web of Science ®Google Scholar
• Benacka, J. and S. Ceretkova. 2014. Modeling harvesting animal population at high school with spreadsheets – the case of Moby Dick. Spreadsheets in Education. 7(3), Article 3, 9.
   Google Scholar
• Ben-Jacob, E., I. Cohen, and H. Levine. 2000. Cooperative self-organization of microorganisms. Advances in Physics. 49: 395–554.
   Web of Science ®Google Scholar
• Berkowitz, A. R., M. E. Ford, and C. A. Brewer. 2005. A framework for integrating ecological literacy, civics literacy, and environmental citizenship in environmental education. In E. Johnson, E. A. Johnson, and M. J. Mappin (Eds.), Environmental Education and Advocacy: Changing Perspectives of Ecology and Education, pp. 227–266. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Biehler, R. 1991. Computers in probability education. In R. Kapadia and M. Borovcnik (Eds.), Chance Encounters: Probability in Education. Vol. 12, pp. 169–211. Dordrecht: Springer Science & Business Media.
   Google Scholar
• Biró, P., D. F. Manlove, and R. Rizzi. 2009. Maximum weight cycle packing in directed graphs, with application to kidney exchange programs. Discrete Mathematics Algorithms Applications. 1(04): 499–517.
   Google Scholar
• Bliss, P. and D. Brown. 2009. Geometric properties of three dimensional fractal trees. Chaos, Solitons and Fractals. 42(1): 119–124.
   Web of Science ®Google Scholar
• Bodine, E., R. Panoff, E. Voit, and A. Weissstein. 2020. Agent-based modeling and simulation in mathematical biology education. Bulletin of Mathematical Biology. 82(8): 1–18.
   Web of Science ®Google Scholar
• Brambila, F., ed. 2017. Fractal Analysis: Applications in Health Sciences and Social Sciences. BoD–Books on Demand.
   Google Scholar
• Brown, D. 2014. Experimental mathematics for the first year student. PRIMUS. 24(4): 281–293.
   Google Scholar
• Carlton, M. 2005. Pedigrees, prizes, and prisoners: The misuse of conditional probability. Journal of Statistics Education. 13(2): 12.
   Google Scholar
• Carvajal-Rodríguez, A. 2012. Teaching the fluctuation test in silico by using mutate: a program to distinguish between the adaptive and spontaneous mutation hypotheses. Biochemistry and Molecular Biology Education. 40(4): 277–283.
   PubMed Web of Science ®Google Scholar
• Ceccherini-Silberstein, T. and M. Coornaert. 2010. The garden of Eden theorem. In T. Ceccherini-Silberstein, and M. Coornaert (Eds.), Cellular Automata and Groups. Springer Monographs in Mathematics, pp. 111–149 Berlin, Germany: Springer.
   Google Scholar
• Cevri, M. and D. Üstündağ. 2016. Prediction of the probabilities of the transmission of genetic traits within Bayesian logical inference. Acta Physica Polonica, A. 130(1): 45–50.
   Web of Science ®Google Scholar
• Chen, M. M., S. M. Scott, and J. D. Stevens. 2018. Technology as a tool in teaching quantitative biology at the secondary and undergraduate levels: a review. Letters in Biomathematics. 5(1): 30–48. doi:https://doi.org/10.1080/23737867.2017.1413432.
   PubMedGoogle Scholar
• Cohen, J. E. 1978. Food Webs and Niche Space. Princeton, NJ: Princeton University Press.
   Google Scholar
• Cohen, J. E., F. Briand, and C. M. Newman. 2012. Community Food Webs: Data and Theory. New York, NY: Springer Science and Business Media.
   Google Scholar
• Courant, R. and H. Robbins. 1941, Six editions. What is Mathematics? An Elementary Approach to Ideas and Methods. London: Oxford University Press. page 240. (Revised edition: Courant, Richard, Herbert Robbins, and Ian Stewart. (1996). What is Mathematics?: an elementary approach to ideas and methods. Oxford University Press: USA).
   Google Scholar
• Cozzens, M. 2015. Food webs and graphs. In R. Robeva (Ed.), Algebraic and Discrete Mathematical Methods for Modern Biology, pp. 29–49. New York, NY: Elsevier.
   Google Scholar
• Crooks, G. E., G. Hon, J. M. Chandonia, and S. E. Brenner. 2004. Weblogo: A sequence logo generator. Genome Research. 14: 1188–1190.
   PubMed Web of Science ®Google Scholar
• Dahlquist, K. D., M. L. Aikens, J. T. Dauer, S. S. Donovan, C. D. Eaton, H. C. Highlander, K. P. Jenkins, J. R. Jungck, M. D. LaMar, G. Ledder and R.L. Mayes. 2017. An invitation to modeling: building a community with shared explicit practices. PeerJ Preprints 5: e3215v1.
   Google Scholar
• Daud, M. and A. Aslah. 2017. An improved mathematical model of Galton board with velocity-dependent restitution. Journal of Computational and Nonlinear Dynamics. 12(6): 3.
   Web of Science ®Google Scholar
• Donovan, S. 2005. Tree thinking and reasoning about change over deep time. In J. Cracraft and R. W. Bybee (Eds.), Evolutionary Science and Society: Educating a New Generation, pp. 87–90. Colorado Springs, CO: BSCS.
   Google Scholar
• Dreyfus, A., B. Feinstein, and J. Talman. 1997. The electronic spreadsheet and cognitive skills in inquiry oriented biology. In D. Passey and B. Sammways (Eds.), Information Technology: Supporting Change Through Teacher Education, pp. 278–284. London, UK: Chapman and Hall.
   Google Scholar
• Drummond, A. J. and A. Rambaut. 2007. BEAST: Bayesian evolutionary analysis by sampling trees. BMC Evolutionary Biology. 7(1): 1–8.
   PubMedGoogle Scholar
• Eaton, C. D., H. C. Highlander, K. D. Dahlquist, M. Drew LaMar, G. Ledder, and R. C. Schugart. 2019. A “rule-of-five” framework for models and modeling to unify mathematicians and biologists and improve student learning. PRIMUS. 29(8): 799–829.
   Google Scholar
• Ekici, C. and C. Plyley. 2019. Inquiry-Based modeling of population dynamics with logistic differential and difference equations. PRIMUS. 29(6): 1–18. (Their students used EXCEL for a finite model.).
   Google Scholar
• Ekici, C., C. Plyley, C. Alagoz, R. Gordon, and N. Santana. 2018. Integrated development and assessment of mathematical modeling practices for Culturally Responsive STEM education: Lionfish case study. The Eurasia Proceedings of Educational & Social Sciences. 9: 1–10.
   Google Scholar
• El-Hajj, A. and K. Y. Kabalan. 1991. A spreadsheet simulation of logic networks. IEEE Transactions on Education. 34(1): 43–46. (This method may be used to simulate combinational, sequential, synchronous and asynchronous networks).
   Web of Science ®Google Scholar
• Espigule, B. 2019 checked. Fractal Trees Project. http://pille.iwr.uniheidelberg.de/~fractaltree01/.
   Google Scholar
• Fisher, L. 2008. Rock, Paper, Scissors: Game Theory in Everyday Life. New York: Basic Books.
   Google Scholar
• Fitch, W. M. and E. Margoliash. 1967. Construction of phylogenetic trees. Science. 155: 279–284.
   PubMed Web of Science ®Google Scholar
• Friedler, Y. and H. Greensfeld. 1994. Integrating electronic spreadsheets as part of the biology curriculum – A model for inservice teacher education. Journal of Computers in Mathematics and Science Teaching. 13(4): 415–432.
   Google Scholar
• Frongillo, R., E. Lock, and D. Brown. 2009. Symmetric fractal trees in three dimensions. Chaos, Solitons, & Fractals. 32(2): 284–295.
   Web of Science ®Google Scholar
• Fulkerson, D. R. and O. A. Gross. 1965. Incidence matrices and interval graphs. Pacific Journal of Mathematics. 15(3): 835–855.
   Web of Science ®Google Scholar
• Gale, D. and L. S. Shapley. 1962. College admissions and the stability of marriage. The American Mathematical Monthly. 69(1): 9–15.
   Web of Science ®Google Scholar
• Gammack, D. 2015. Using NetLogo as a tool to encourage scientific thinking across disciplines. Journal of Teaching and Learning with Technology. 4: 1. June 2015, pp. 22–39.
   Google Scholar
• Gammack, D., E. Schaefer, and H. Gaff. 2013. Global dynamics emerging fromlocal interactions: Agent-based modeling for the life sciences. In R. Robeva (Ed.), Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models, pp. 105–141. Boston, MA: Academic Press.
   Google Scholar
• Ganter, S. L. and W. E. Haver. 2012. CRAFTY tools for revitalizing college algebra. MAA Focus. 32(3): 6–7.
   Google Scholar
• Gerhardt, M., H. Schuster, and J. J. Tyson. 1990. A cellular automaton model of excitable media: III. Fitting the Belousov-Zhabotinskii reaction. Physica D: Nonlinear Phenomena. 46(3): 416–426.
   Google Scholar
• Grace, M. and M.-T. Hütt. 2015. Regulation of spatiotemporal patterns by biological variability: general principles and applications to Dictyostelium discoideum. PLoS Computational Biology. 11(11): e1004367.
   PubMed Web of Science ®Google Scholar
• Griffiths, A. K. and B. A. Grant. 1985. High school students’ understanding of food webs: Identification of a learning hierarchy and related misconceptions. Journal of Research in Science Teaching. 22(5): 421–436.
   Web of Science ®Google Scholar
• Hall, B. M., C.-X. Ma, P. Liang, and K. K. Singh. 2009. FALCOR: fluctuation AnaLysis CalculatOR: A web tool for the determination of mutation rate using Luria–Delbrück fluctuation analysis. Bioinformatics (Oxford, England). 25(12): 1564–1565.
   PubMed Web of Science ®Google Scholar
• Hamming, R. W. 1984. Calculus and discrete mathematics. The College Mathematics Journal. 15(5): 388.
   Google Scholar
• Hartman, C., M. J. Heule, K. Kwekkeboom, and A. Noels. 2013. Symmetry in Gardens of Eden. The Electronic Journal of Combinatorics. 20(3), 1- [They assert that “free will can never be proven or disproven”].
   Web of Science ®Google Scholar
• Head, B., R. Grider, and U. Wilensky. 2017. NetLogo Rock Paper Scissors model. http://ccl.northwestern.edu/netlogo/models/RockPaperScissors. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Heitz, J., M. Wolansky, and B. Adamczyk. 2012. Using Classical Genetics Simulator (CGS) to teach students the basics of genetic research. Proceedings of the Association for Biology Laboratory Education. 33: 85–94.
   Google Scholar
• Hidayat, E. W., I. K. G. D. Putra, I. A. D. Giriantari, and M. Sudarma. 2019. Visualization of a two-dimensional tree modeling using fractal based on L-system. IOP Conference Series: Materials Science and Engineering. 550(1): 012027. IOP Publishing,.
   Google Scholar
• Hong, F. T. 2003. Towards physical dynamic tolerance: an approach to resolve the conflict between free will and physical determinism. Biosystems. 68(2–3): 85–105.
   PubMed Web of Science ®Google Scholar
• Hornbach, D. 1993. Biometrics. BioQUEST Library (I–III: ePress of the University of Maryland; IV–VI: Academic Press; VII ff: (https://bioquest.org/BQLibrary/library_details.php?product_id=166#)).
   Google Scholar
• Howard, P., A. O'Hanlon, and D. Brown. 2004. Path length and height in asymmetric binary branching trees. Missouri Journal of Mathematical Sciences. 16(2): 86–103.
   Google Scholar
• Huelsenbeck, J. P. and F. Ronquist. 2001. MRBAYES: Bayesian inference of phylogeny. Bioinformatics (Oxford, England). 17: 754–755.
   PubMed Web of Science ®Google Scholar
• Ito, K. and Y.-P. Gunji. 1992. Self-organization toward criticality in the game of life. BioSystems. 26(3): 135–138.
   PubMed Web of Science ®Google Scholar
• Jones, T. C. and T. F. Laughlin. 2009. Learning to measure biodiversity: two agent-based models simulate sampling methods and provide data for calculating diversity indices. The American Biology Teacher. 71: 406–410.
   Web of Science ®Google Scholar
• Jones, T. C. (T. J.), T. Laughlin, H. Miller, and B. Van Nes. 2019. Virtual Ecology Lab. http://faculty.etsu.edu/jonestc/Virtualecology.htm; .
   Google Scholar
• Jungck, J. R. 2012. “If Life Is Analog, Why Are We Being So Discrete?: Middle-Out Modeling. In Rubem Mondani, ed., BIOMAT 2011, World Scientific, pp. 371–395. http://www.worldscientific.com/doi/abs/ArtFormshttps://doi.org/10.1142/9789814397711_0025.
   Google Scholar
• Jungck, J. R. 2012. Mathematics make microbes beautiful, beneficial, and bountiful. Advances in Applied Microbiology. 80: 37–80.
   PubMed Web of Science ®Google Scholar
• Jungck, J. R. 2012. Incorporating quantitative reasoning in common core courses: mathematics for The Ghost Map. Numeracy: Advancing Education in Quantitative Literacy. 5, 1 Article 7. http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=1097&context=numeracy.
   Google Scholar
• Jungck, J. R. 2013. Genesis of what Is life?: A Paradigm shift in Genetics history. CBE Life Science Education. 9: 201–211. (Fall). Reprinted in “Highlights of 2013” hardcopy printed issue: pages 31-32.
   Google Scholar
• Jungck, J. R. and J. N. Calley. 1986. Genetics: Strategic Simulations in Mendelian Genetics. Part A: Elementary Genetics; Part B: Intermediate Genetics: Diskette 1: Automsal Linkage, Sex Linkage, & Multiple Alleles, Diskette 2: Pleiotropy, Gene Interaction, Lethality & Penetrance, Diskette 3: Multifactorial Inheritance; Part C: Genetics Construction Kit. Five Apple Computer Disks and Associated Manual. Wentworth, New Hampshire: COMPress, Inc. Later distributed by QUEUE: Bridgeport, CT.
   Google Scholar
• Jungck, J. R. and J. Spangenberg. 2005. ESS: Evolutionary Stable Strategies Game Theory Module. A module of the Biological ESTEEM Collection, published by the BioQUEST Curriculum Consortium. http://bioquest.org/esteem/esteem_details.php?product_id=262
   Google Scholar
• Jungck, J. R., G. Dick, and A. G. Dick. 1982. Computer- assisted sequencing, interval graphs and molecular evolution. BioSystems. 15(3): 259–273.
   PubMed Web of Science ®Google Scholar
• Jungck, J. R., H. Gaff, and A. E. Weisstein. 2010. Mathematical manipulative models: In defense of beanbag biology. CBE—Life Sciences Education. 9: 201–211.
   PubMed Web of Science ®Google Scholar
• Jungck, J. R. and J. Manon. 2019. Brave spaces: Augmenting Interdisciplinary STEM education by using quantitative data explorations to engage Conversations on Equity and social justice. Numeracy: Advancing Education in Quantitative Literacy. 12(1): Article 4. 36. https://scholarcommons.usf.edu/numeracy/vol12/iss1/art4/.
   Google Scholar
• Jungck, J. R. and R. Roy. 2014. 3P's ∪ MMM in Finite Mathematics: A Union of the BioQUEST Curriculum Consortium's Problem Posing, Problem Solving, Peer Review/Publication Pedagogy with the Modified Moore Method. Proceedings of the Symposium on BEER, 2014.
   Google Scholar
• Jungck, J. R. and V. Streif. 1986. Deletion mapping of genetic “fine structure”: Supplementing ad hoc problem solving approaches with algorithms and heuristics. Bioscene: Journal of College Biology Teaching. 12(2): 13–27.
   Google Scholar
• Jungck, J. R., V. Streif, S. Everse, and P. Jungck. 2004. “javaBenzer.” http://bioquest.org/ESTEEM.
   Google Scholar
• Jungck, J. R., V. Streif, and A. Telerski. 1995. Complex Food Webs Maintain Strong One-Dimensional Connectedness: Software for Visualizing Interval Graph Complexity. Abstracts, International Meeting, Society for Mathematical Biology, Oaxtepec, Morelos, Mexico, pages 53–54.
   Google Scholar
• Jungck, J. R., J. Galovich, and J. Reistetter. 2004. BioBayes. BioQUEST ESTEEM Collection. http://bioquest.org/esteem/esteem_details.php?product_id=422#.
   Google Scholar
• Jungck, J. R. and R. Viswanathan. 2015. Graph theory for systems biology: interval graphs, Motifs, and pattern Recognition. In R. Robeva (Ed.), Algebraic and Discrete Mathematical Methods for Modern Biology, pp. 1–27. Chennai: Elsevier. plus electronic supplement.
   Google Scholar
• Jungck, J. R. and A. E. Weisstein. 2013. Mathematics and evolutionary biology make bioinformatics education comprehensible. Briefings in Bioinformatics. 14(5): 599–609. doi:https://doi.org/10.1093/bib/bbt046.
   PubMed Web of Science ®Google Scholar
• Jungck, P., R. Duncan, and D. Mulcahy. 2011. Packet C Programming. New York: Apress of Springer Science + Business Media.
   Google Scholar
• Just, W., H. Callender, M. D. LaMar, and N. Toporikova. 2015. Transmission of infectious diseases: data, models, and simulations. In R. Robeva (Ed.), Algebraic and Discrete Mathematical Methods for Modern Biology, pp. 193–215. New York, NY: Academic Press.
   Google Scholar
• Just, W., H. L. Callender, and D. M. Lamar. 2015. “Exploring transmission of infectious diseases on networks with NetLogo.” In: https://www.qubeshub.org/IONTW, https://qubeshub.org/resources/365/download/ModelsQ.pdf, and http://www.ohiouniversityfaculty.com/just/IONTW/PosterIONTW.pdf.
   Google Scholar
• Just, W. and H. C. Highlander. 2017. Vaccination strategies for small worlds. In A. Wootton, V. Peterson, and C. Lee (Eds), A Primer for Undergraduate Research: From Groups and Tiles to Frames and Vaccines, pp. 223–264. Cham, Switzerland: Birkhäuser.
   Google Scholar
• Karperien, A. L. and H. F. Jelinek. 2016. Box-Counting fractal analysis: A Primer for the Clinician. In D. Ieva A (Ed.), The Fractal Geometry of the Brain. Springer Series in Computational Neuroscience. New York, NY: Springer. doi:https://doi.org/10.1007/978-1-4939-3995-4_2.
   Google Scholar
• Kehle, P. 2015. Drawing lines: spatial arrangements of biological phenomena. In F. Roberts and M. Cozzens (Eds.), BioMath, pp. T1–T129. Boston, MA: CoMap. (Teachers Edition). (https://www.comap.com/undergraduate/projects/biomath/PDF/Drawing_Lines_SE.pdf).
   Google Scholar
• Kemeny, J. G. 1959. Mathematics without numbers. Daedalus. 88(4): 577–591.
   Web of Science ®Google Scholar
• Kemeny, J. G., J. Laurie Snell, and G. L. Thompson. 1974. Introduction to Finite Mathematics. Saddle River, NJ: Prentice-Hall, Inc.
   Google Scholar
• Khiripet, N., W. Khantuwan, and J. R. Jungck. 2012. Ka-me: a Voronoi image analyzer. Bioinformatics (oxford, England). 28(13): 1802–1804.
   PubMed Web of Science ®Google Scholar
• Khiripet, N., R. Viruchpintu, J. Maneewattanapluk, J. Spangenberg, and J. R. Jungck. 2010. Morphospace: measurement, modeling, mathematics, and meaning. Mathematical Modelling of Natural Phenomena. 6(2): 54–81. https://eudml.org/doc/197624.
   Web of Science ®Google Scholar
• Ko, R. L. and C. P. Bean. 1991. A simple experiment that demonstrates fractal behavior. The Physics Teacher. 29(2): 78–79.
   Google Scholar
• Koirala, P. 2018. Food webs, competition graphs, and a 60-year old unsolved problem. In E. W. Hart and J. Sandefur (Eds), Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research, pp. 165–181. Cham, Switzerland: Springer.
   Google Scholar
• Kozlov, V. V. and M. Y. Mitrofanova. 2003. Galton board. Regular and Chaotic Dynamics. 8(4): 431–439.
   Web of Science ®Google Scholar
• Krashniak, A. and E. Lamm. 2017. Was regression to the mean really the solution to Darwin’s problem with heredity?: Essay Review of Stigler, Stephen M. 2016. The Seven Pillars of Statistical Wisdom. Cambridge, Massachusetts: Harvard University Press. Philica 32: 749–758.
   Google Scholar
• Langton, C. G. 1984. Self-reproduction in cellular automata. Physica D: Nonlinear Phenomena. 10(1–2): 135–144.
   Google Scholar
• Lesser, L. M. 2007. Critical values and transforming data: teaching statistics with social justice. Journal of Statistics Education. 15(1): 21.
   Google Scholar
• Levy, S. and U. Wilensky. 2008. Inventing a “Mid level” to make ends meet: reasoning between the levels of complexity. Cognition and Instruction. 26: 1–47.
   Web of Science ®Google Scholar
• Malley, C. (lead developer), A. McGarry (lead designer), W. Adams, M. Hoffman, O. Nix, J. Olson, A. Paul, K. Perkins, N. Podolefsky, and M. Lai (graphic arts). 2012, 2020. PheT Natural Selection Module. https://phet.colorado.edu/en/simulation/natural-selection.
   Google Scholar
• Maxim, B. R. and R. F. Verhey. 1991. Using spreadsheets to introduce recursion and difference equations in high school mathematics. In M. J. Kenney and C. R. Hirsch (Eds), Discrete Mathematics Across the Curriculum, K-12, pp. 158–165. Reston, VA: National Council of Teachers of Mathematics, Inc.
   Google Scholar
• McGuire, M. 1991. An Eye for Fractals: A Graphic/Photographic Essay. Reading, MA: Addison-Wesley Longman Publishing Co., Inc.
   Google Scholar
• Meinhardt, H. 2009. The Algorithmic Beauty of Seashells. Berlin, Germany: Springer Science and Business Media.
   Google Scholar
• Montgomery, R. J. 2016. Kidney paired donation: Optimal and equitable matchings in bipartite graphs. Rose Hulman Undergraduate Mathematics Journal. 17(1): 158–179.
   Google Scholar
• Morris, C. C. and R. M. Stark. 2015. Finite Mathematics: Models and Applications. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Neal, D. 2018. Simulations in population biology: htttp://publications.usask.ca/population/spreadsheets.htm.] {Accompany his textbook: Introduction to Population Biology, 2nd ed., Cambridge: Cambridge University Press.
   Google Scholar
• Norton, H. W. III. 1937. General formulae for homozygosis. Iowa Academy of Science. XLIV: 139–143.
   Google Scholar
• Nowak, M. 2006. Five rules for social cooperation. Science. 314: 1560–1563.
   PubMed Web of Science ®Google Scholar
• Nowak, M. and R. Highfield. 2011. Super Cooperators: Altruism, Evolution, and Why We Need Each Other to Succeed. New York: Free Press of Simon and Schuster.
   Google Scholar
• Ohtsuki, H., C. Hauert, E. Lieberman, and M. A. Nowak. 2006. A simple rule for the evolution of cooperation on graphs and social networks. Nature. 441(7092): 502–505.
   PubMed Web of Science ®Google Scholar
• Peitgen, H.-O., H. Jürgens, and D. Saupe. 2013. Fractals for the Classroom: Part one Introduction to Fractals and Chaos. Berlin, Germany: Springer Science & Business Media.
   Google Scholar
• Petropoulou, E. N. 2010. A discrete equivalent of the logistic equation. Advances in Difference Equations. 2010(1): 457073. (15 pages).
   Google Scholar
• Porkess, R. and S. Dudzic. 2013. A World Full of Data. Statistics Opportunities Across A Level Subjects. London: Royal Statistical Society and the Institute and Faculty of Actuaries.
   Google Scholar
• Prusinkiewicz, P. and A. Lindenmayer. 2012. The Algorithmic Beauty of Plants. Berlin, Germany: Springer Science & Business Media.
   Google Scholar
• Price, F. 1993. Data Collection and Organization. BioQUEST Library (I-III: ePress of the University of Maryland; IV-VI: Academic Press; VII ff: https://bioquest.org/BQLibrary/library_details.php?product_id=167#].
   Google Scholar
• Radakovic, N. and D. McDougall. 2012. Using dynamic geometry software for teaching conditional probability with area-proportional Venn diagrams. International Journal of of Mathematical Education in Science and Technology. 43: 7.
   Google Scholar
• Ralston, A. 1981. Computer science, mathematics and the undergraduate Curricula in both. Am. Math. Monthly. 88: 472–485.
   Web of Science ®Google Scholar
• Ralston, A. 1986. Views: discrete mathematics: The new mathematics of science: The computer revolution has made discrete mathematics as indispensable as the calculus to science and technology. American Scientist. 74(6): 611–618.
   Google Scholar
• Ralston, A. 1991. Calculators for teaching and testing mathematics: A mathematician's view. College Board Review. 160: 18–21. 26.
   Google Scholar
• Ralston, A. 1992. The impact of computers and computer science on the mathematics Curriculum. In B. Cornu and A. Ralston (Eds.), The Influence of Computers and Informatics on Mathematics and Its Teaching, pp. 19–24. Paris, (France): United Nations Educational, Scientific, and Cultural Organization. Div. of Science, Technical and Environmental Education.REPORT NOED-92/WS/17.
   Google Scholar
• Ralston, A. and G. S. Young, eds. 1983. The Future of College Mathematics. New York: Springer-Verlag.
   Google Scholar
• Resnick, M. 1992. Beyond the Centralized Mindset–Explorations in Massively Parallel Microworlds. PhD dissertation, Cambridge, MA: Massachusetts Institute of Technology.
   Google Scholar
• Resnick, M. 1993. Learning about life. Artificial Life. 1(1–2): 229–241.
   Google Scholar
• Resnick, M. 1995. New paradigms for computing, new paradigms for thinking. In L. D. Edwards (Ed.), Computers and Exploratory Learning, pp. 31–43. Berlin, Germany: Springer.
   Google Scholar
• Resnick, M. 1996. Beyond the centralized mindset. The Journal of the Learning Sciences. 5(1): 1–22.
   Web of Science ®Google Scholar
• Resnick, M. 1999. Decentralized modeling and decentralized thinking. In W. Feurzeig and N. Roberts (Eds), Modeling and Simulation in Science and Mathematics Education, pp. 114–137. New York, NY: Springer.
   Google Scholar
• Resnick, M. 1999. Turtless, Termites, and Traffic Jams: Explorations in Massively Parallel Microworlds. MIT Press. Cambridge: Mass. and London.
   Google Scholar
• Robertson, C. J. 2011. FrakOut!: an application to explore the fractal dimension of shapes. https://code.google.com/archive/p/frakout]. Both Windows and Mac OS downloads are available as well as a tutorial manual.
   Google Scholar
• Robeva, R. and R. Laubenbacher. 2009. Mathematical biology education: beyond calculus. Science. 325(5940): 542–543.
   PubMed Web of Science ®Google Scholar
• Ronquist, F., M. Teslenko, P. Van Der Mark, D. L. Ayres, A. Darling, S. Höhna, B. Larget, L. Liu, M. A. Suchard, and J. P. Huelsenbeck. 2012. Mrbayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space. Systematic Biology. 61(3): 539–542.
   PubMed Web of Science ®Google Scholar
• Rosche, W. A. and P. L. Foster. 2000. Determining mutation rates in bacterial populations. Methods. 20(1): 4–17.
   PubMed Web of Science ®Google Scholar
• Rossman, A. J. and T. H. Short. 1995. Conditional probability and education reform: Are they compatible? Journal of Statistics Education. 3(2): 9.
   Google Scholar
• Roth, A. E., T. Sönmez, and M. Utku Ünver. 2004. Kidney exchange. The Quarterly Journal of Economics. 119(2): 457–488.
   Web of Science ®Google Scholar
• Rueden, C. T., J. Schindelin, M. C. Hiner, B. E. DeZonia, A. E. Walter, E. T. Arena, and K. W. Eliceiri. 2017. Imagej2: ImageJ for the next generation of scientific image data. BMC Bioinformatics. 18(1): 529.
   PubMed Web of Science ®Google Scholar
• Saitou, N. and M. Nei. 1987. The neighbor-joining method: a new method for reconstructing phylogenetic trees. Molecular Biology and Evolution. 4(4): 406–425.
   PubMed Web of Science ®Google Scholar
• Schelling, T. 1978. Micromotives and Macrobehavior. London, NY: W. W. Norton.
   Google Scholar
• Schmickl, T. (Original date not given). StarLogo model of reaction-diffusion. http://zool33.uni-graz.at/schmickl/Self-organization/Pattern_formation/Reaction-diffusion/reaction-diffusion.html] Department for Zoology, Karl-Franzens-University Graz, Austria. (See Karsai I., Schmickl T., Kampis G. (2020) Understanding Ecosystem Stability and Resilience Through Mathematical Modeling. In: Resilience and Stability of Ecological and Social Systems. Springer, Cham. doi:https://doi.org/10.1007/978-3-030-54560-4_1].
   Google Scholar
• Schneider, T. D. and R. M. Stephens. 1990. Sequence logos: A new way to display consensus sequences. Nucleic Acids Research. 18: 6097–6100.
   PubMed Web of Science ®Google Scholar
• Schneider, C. A., W. S. Rasband, and K. W. Eliceiri. 2012. NIH image to ImageJ: 25 years of image analysis. Nature Methods. 9(7): 671.
   PubMed Web of Science ®Google Scholar
• Sen, S. I. and A. M. Day. 2005. Modelling trees and their interaction with the environment: A survey. Computers & Graphics. 29(5): 805–817.
   Web of Science ®Google Scholar
• Shaw, G. 1998. Spreadsheets in molecular biology. In G. Filby (Ed.), Spreadsheets in Science and Engineering, pp. 203–228. New York, NY: Springer-Verlag.
   Google Scholar
• Seibold, C. and H. L. Callender. 2016. Modeling epidemics on a regular tree graph. Letters in Biomathematics. 3(1): 59–74.
   Google Scholar
• Shkurba, V. V. 1965. Mathematical processing of a class of biochemical experiments. Cybernetics. 1(1): 63–69.
   Google Scholar
• Sinex, S. A. and B. A. Gage. 2006. Using Excel for Handling, Graphing, and Analyzing Scientific Data: A Resource for Science and Mathematics Students. (2019 download): http://academic.pgcc.edu/psc/Excel_booklet.pdf.
   Google Scholar
• Slipper, M. 1998. Fifty years of research on self-replication: An overview. Artificial Life. 4: 237–257.
   PubMed Web of Science ®Google Scholar
• Soderberg, P., J. Stewart, J. N. Calley, and J. R. Jungck. 1994. Genetics construction kit: A tool for open-ended investigation in transmission genetics. Journal of Computing In Higher Education. 5(2): 67–84.
   Google Scholar
• Sokal, R. R. and C. D. Michener. 1958. A statistical method for evaluating systematic relationships. University of Kansas Science Bulletin. 38: 1409–1438.
   Google Scholar
• Spreng, J. D. 2017. How the leopard got its spots. Eukaryon. 13: 19–20. [Biolog://www.lakeforest.edu/live/files/3728-28-29spreng.pdf].
   Google Scholar
• Stansfield, W. D. and M. A. Carlton. 2004. Bayesian statistics for biological data: pedigree analysis. The American Biology Teacher. 66: 177–182.
   Web of Science ®Google Scholar
• Stansfield, W. D. and M. A. Carlton. 2014. Biostatistics in the popular press. The American Biology Teacher. 76(7): 429–430.
   Web of Science ®Google Scholar
• Stanley, H. E. 2002. Exploring Patterns in Nature: Computer Simulabs and Hands on Activities. New York, NY: Springer.
   Google Scholar
• Stigler, S. M. 2016. Seven Pillars of Statistical Wisdom. Cambridge, MA: Harvard University Press.
   Google Scholar
• Stohl Drier [Lee], H. 2001. Teaching and learning mathematics with interactive spreadsheets. School Science and Mathematics. 101(4): 170–179.
   Google Scholar
• Stohl, H. and J. E. Tarr. 2002. Developing notions of inference using probability simulation tools. Journal of Mathematics Education. 21: 319–337.
   Google Scholar
• Stohl Lee, H., R. L. Angotti, and J. E. Tarr. 2010. Making comparisons between observed data and expected outcomes: students’ informal hypothesis testing with probability simulation tools. Science Education Research Journal. 9(1): 68–96.
   Google Scholar
• Stonedahl, F. and U. Wilensky. 2008. NetLogo Virus on a Network model. http://ccl.northwestern.edu/netlogo/models/VirusonaNetwork. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Stultz, L. 2000. How to Excel in Finite Math: Spredsheet Mathematics – A Supplement for Finite Mathematics. Boston, MA: Pearson Custom Publishing.
   Google Scholar
• Taylor, R. and T. Timberlake. 2007. Tearing plastic: A laboratory exercise on fractals and hyperbolic geometry. PRIMUS. 17(4): 316–324.
   Google Scholar
• Thompson, D. W. 1917. On Growth and Form. Cambridge: Cambridge University Press.
   Google Scholar
• Thompson, K. V., T. J. Cooke, W. F. Fagan, D. Gulick, D. Levy, K. C. Nelson, E. F. Redish, R. F. Smith, and J. Presson. 2013. Infusing quantitative approaches throughout the biological sciences curriculum. International Journal of Mathematical Education in Science and Technology. 44(6): 817–833.
   Google Scholar
• Tucker, A. 1972. A structure theorem for the consecutive 1's property. Journal of Combinatorial Theory, Series B. 12(2): 153–162.
   Google Scholar
• Turnbull, B.. 2012. Longest kidney transplant chain in history had a Canadian connection. Toronto Star. https://www.thestar.com/life/health_wellness/2012/02/24/longest_kidney_transplant_chain_in_history_had_a_canadian_connection.html.
   Google Scholar
• Turnbull, L., M.-T. Hütt, A. Ioannides, and A. J. Parsons. 2018. Connectivity and complex systems: learning from a multi-disciplinary perspective. Applied Network Science. 3(11): 49.
   PubMedGoogle Scholar
• Viswanathan, R., S. Liang, Y. Yang, and J. R. Jungck. 2016. “BIOGRAPHER: Visualization of Graph Theoretical Patterns, Measurements, and Analysis In Mathematical Biology.” In BIOMAT 2015: International Symposium on Mathematical and Computational Biology, pp. 118–140.
   Google Scholar
• Weisstein, A. E. 2011. Building mathematical models and biological insight in an introductory biology course. Mathematical Modelling of Natural Phenomena. 6(6): 198–214.
   Web of Science ®Google Scholar
• Weisstein, A. E. 2012. Deme 2.0. A module of the Biological ESTEEM Collection, published by the BioQUEST Curriculum Consortium. http://bioquest.org/esteem/esteem_details.php?product_id=193.
   Google Scholar
• Wilensky, U. 2001. NetLogo Tree Simple model. http://ccl.northwestern.edu/netlogo/models/TreeSimple. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Wilensky, U. 2003. NetLogo B-Z Reaction model. http://ccl.northwestern.edu/netlogo/models/B-ZReaction. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Wilensky, U. 2003. NetLogo CA Continuous model. http://ccl.northwestern.edu/netlogo/models/CAContinuous. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Wilensky, U. 2005. NetLogo DLA Alternate Linear model. http://ccl.northwestern.edu/netlogo/models/DLAAlternateLinear. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Wilensky, U. 1999. NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
   Google Scholar
• Wilensky, U. and K. Reisman. 2006. Thinking like a wolf, a sheep or a firefly: learning biology through constructing and testing computational theories – an embodied modeling approach. Cognition & Instruction. 24(2): 171–209.
   Web of Science ®Google Scholar
• Wirth, E., G. Szabó, and A. Czinkóczky. 2016. Measure of landscape heterogeneity by agent-based methodology, ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci. III-8, 145–151. doi:https://doi.org/10.5194/isprs-annals-III-8-145-2016, 2016.
   Google Scholar
• Wolfram, S. 2018. Are all fish the same shape if you stretch them? The Victorian Tale of On Growth and Form. Mathematical Intelligencer. 40(4): 39–61.
   Web of Science ®Google Scholar
• Wolfram, S. 2002. A New Kind of Science. Champaign, IL: Wolfram Media Inc.
   Google Scholar
• Viswanathan, R. 2006. Biographer and WDisplay: Excel modules for data visualization. BioQUEST_Notes. 15(1): 6–7.
   Google Scholar
• Yunes, N. D. 2011. The decentralized mindset. https://nourdiab.wordpress.com/2011/10/03/the-decentralized-mindset/.
   Google Scholar
• Zheng, Q. 2010. The Luria–Delbrück distribution: early statistical thinking about evolution. Chance. 23: 15–18.
   Google Scholar
• Zheng, Q. 2017. Rsalvador: An R package for the fluctuation experiment. G3: Genes, Genomes, Genetics. 7(12): 3849–3856.
   Web of Science ®Google Scholar
• Zhu, J., K. Alderfer, B. Smith, B. Char, and S. Ontañón. 2020. Understanding Learners’ Problem-Solving Strategies in Concurrent and Parallel Programming: A Game-Based Approach. arXiv preprint arXiv:2005.04789.
   Google Scholar