David Ruch

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David Ruch

Professor of Mathematics

Mathematics & Statistics

Bio

After growing up in Colorado Springs, I went out to California for some fun, sun, smog and an undergraduate education at Pomona College. Then I went to Lesotho with the Peace Corps. I missed mathematics quite a bit, so I went to graduate school at New Mexico State, followed by a decade of hard time in Huntsville, Texas. I made it back to Colorado in 1989.

Degree

PhD in Mathematics

New Mexico State University

MS in Mathematics

New Mexico State University

BA in Mathematics

Pomona College

Published Works

  • Ruch, K. D., Barnett, H. J., Scoville, A. n. (2023). Teaching Undergraduate Mathematics with Primary Historical Sources: Projects for Real Analysis, Topology, and Complex Variables. American Mathematical Society, https://bookstore.ams.org/view?ProductCode=CLRM/71
  • Barnett, H. J., Klyve, D., Ruch, K. D. . Learning Mathematics from the Master: A Collection of Euler-based Primary Source Projects for Today’s Students, Part II. Euleriana, 2(Volume 2, Issue 2 (2022)). https://scholarlycommons.pacific.edu/euleriana/.
  • Ruch, K. D. (2020). Euler's Square Root Laws for Negative Numbers. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2020). Gauss and Cauchy on Complex Integration. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2020). Riemann's Development of the Cauchy-Riemann Equations. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2018). Euler's Rediscovery of e: A Mini-Primary Source Project for Introductory Analysis Students. Convergence, MAA Press, 15 - 2018 www.maa.org/press/periodicals/convergence/eulers-rediscovery-of-e-a-mini-primary-source-project-for-introductory-analysis-students.
  • Ruch, K. D. (2017). Abel and Cauchy on a Rigorous Approach to Infinite Series. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2017). An Introduction to a Rigorous Definition of Derivative. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2017). Bolzano's Definition of Continuity, his Bounded set Theorem, and an Application to Continuous Functions. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2017). Euler's Rediscovery of e. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2017). Investigations Into d'Alembert's Definition of Limit. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2017). The Definite Integrals of Cauchy and Riemann. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2017). The Mean Value Theorem. , https://blogs.ursinus.edu/triumphs/
  • Ruch, K. D. (2014). "Creating a Project on Difference Equations with Primary Sources: Challenges and Opportunities". Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Volume 24( Issue 8, 2014), pages 764-773. https://doi.org/10.1080/10511970.2014.896836.
  • Alejano-Steele, A., Worthy, C. S., Tull, T., Paul, E., Ruch, K. D., Anderson, M., Schwab, N. (2013). Institutional Processes Designed to Promote Diversity and Equity at Metropolitan State University of Denver. Cuaderno de Investigacion en la Educacion, 28 .
  • Ruch, K. D., Van Fleet, P. (2013). "Nonnegative Scaling Vectors on the Interval". Axioms/MDPI, 2(3), 371-389. www.mdpi.com/2075-1680/2/3/371.
  • Ruch, K. D., Van Fleet, P. (2009). "Wavelet Theory, An Elementary Approach with Applications". Wiley, www.wiley.com/WileyCDA/WileyTitle/productCd-0470388404.html
  • Ruch, K. D. (2007). "Solving a Wavelet Problem using Groebner Bases". Denver Metropolitan Journal of Mathematics & Computer Science,
  • Ruch, K. D. (2006). "Comprehensive Backward Biorthogonalization". International Journal of Mathematics and Mathematical Sciences,
  • Ruch, K. D., Van Fleet, P. (2004). "Gibbs' Phenomenon for Nonnegative Compactly Supported Scaling Vectors". Journal of Computational and Applied Mathematics,
  • Ruch, K. D. (2004). "Vanishing Moments for Scaling Vectors". International Journal of Mathematics and Mathematical Sciences,
  • Ruch, K. D. (2002). "Java Applets in the Teaching and Learning of Mathematics, Tools With Great Potential". Denver Metropolitan Journal of Mathematics & Computer Science,
  • Ruch, K. D. (2002). "The nth Derivative Test and Taylor Polynomials Crossing Graphs". College Mathematics Journal,
  • Ruch, K. D. (2000). "An Introduction to the Solution of Differential Equations Using Scaling Functions and Wavelets". Denver Metropolitan Journal of Mathematics & Computer Science,
  • Ruch, K. D., Van Fleet, P. (2000). "On the Construction of Positive Scaling Vectors". Proceedings of Wavelet Analysis and Multiresolution Methods,
  • Foley, G., Ruch, K. D. (1999). "Calculus Labs and Student Projects" Calculus Supplement Manual. Sam Houston University Press,
  • Ruch, K. D., Kissock, J., Reddy, T. (1999). "Model Identification and Prediction Uncertainty of Linear Building Energy Use Models with Autocorrelated Residuals". ASME Journal of Solar Engineering,
  • Ruch, K. D., Wang, J. (1998). "Connections Between the Support and Linear Independence of Refinable Distributions". Journal of Approximation Theory,
  • Ruch, K. D., So, W., Wang, J. (1998). "Global Support of a Scaling Vector". Applied and Computational Harmonic Analysis , 593-498. .
  • Reddy, T., Kissock, J., Ruch, K. D. (1998). "Uncertainty in Baseline Modeling and in Determination of Retrofit Savings". ASME Journal of Solar Engineering,
  • Ruch, K. D. (1997). "Solving Polynomic Operator Equations in an Ordered Banach Space". Numerical Functional Analysis and Optimization, 1835-445. .
  • Ruch, K. D. (1996). "Completely Continuous and Related Multilinear Operators". Circolo Matematico di Palermo, 44 .
  • Ruch, K. D., Van Fleet, P. (1996). "On Multipower Equations: Some Iterative Solutions and Applications". Zeitshrift fur Analysis und ihre Anwendungen, 1501-222. .
  • Massopust, P., Ruch, K. D., Van Fleet, P. (1996). "On the Support Properties of Scaling Vectors". Applied and Computational Harmonic Analysis, 329-238. .
  • Ruch, K. D. (1996). "A Statistical Method and SAS Program for Determining Operational Changes in Commercial Buildings from Energy Data". Energy Systems Laboratory Technical Report, Texas A&M University,
  • Foley, G., Ruch, K. D. (1995). "Calculus Reform for Comprehensive Universities and Two-Year Colleges". UME Trends, 6(6). .
  • Ruch, K. D. (1995). "On Uniformly Contractive Systems and Quadratic Equations in Banach Space". The Bulletin of the Australian Mathematical Society, 9541-455. .
  • Dhar, A., Claridge, D., Ruch, K. D. (1995). "An Artificial Neural Network with Wavelet Basis Functions to Predict Hourly Heating and Cooling Energy Use in Commercial Buildings". Proceedings of the 1995 ASME International Solar Engineering Conference,
  • Reddy, T., Kissock, J., Katimpaula, S., Ruch, K. D., Claridge, D. (1994). "An Overview of Measured Energy Retrofit Savings Methodologies Developed in the Texas LoanSTAR Program". Energy Systems Laboratory Technical Report, Texas A&M University,
  • Ruch, K. D., Chen, L., Haberl, J., Claridge, D. (1993). "A Change-Point Principal Component Analysis Method for Predicting Energy Usage in Commercial Buildings". ASME Journal of Solar Energy Engineering,
  • Ruch, K. D., Claridge, D. (1993). "A Development and Comparison of NAC Estimates for Linear and Change-Point Models for Commercial Buildings". Energy and Buildings, 207-95. .
  • Ruch, K. D., Chasteen, T. (1993). "Solving Equilibria Problems with a Graphing Calculator". Journal of Chemical Education,
  • Ruch, K. D. (1993). "Properties of NAC and CV (NAC) for Energy Models". Energy Systems Laboratory Technical Report, Texas A&M University,
  • Ruch, K. D. (1993). "A Matrix-Free Algorithm for Computing Prediction Error Bounds for the Hybrid Energy Model". Energy Systems Laboratory Technical Report, Texas A&M University,
  • Ruch, K. D., Claridge, D. (1992). "A Four Parameter Change-Point Model for Predicting Energy Consumption in Commercial Buildings". ASME Journal of Solar Energy Engineering,
  • Ruch, K. D., Weber, K. (1990). "A Four Parameter Change-Point Model for Predicting Energy Consumption". Energy Systems Laboratory Technical Report, Texas A&M University,
  • Ruch, K. D. (1989). "Characterizations of Compact Bilinear Maps". Lin. Multilin Alg., 2597-307. .

Research Interests

Wavelet Theory, History of Analysis

Teaching Interests

Teaching and Learning with Primary Source Projects

Office Hours

Mon, Wed: 12 - 12:30 pm, 1 - 1:50 pm
Tues, Thurs: 3 - 3:50 pm.

Additional Information

mcs.msudenver.edu/_u_/ruchwebsitehome