Roger B. Nelsen

Mathematical Sciences Dept
Lewis & Clark College
0615 SW Palatine Hill Rd
Portland, OR 97219
Office: 503-768-7565
Email: nelsen(at)lclark[dot]edu


Books:

Charming Proofs

(with Claudi Alsina)

Proofs Without Words

The Calculus Collection

(with Caren L. Diefenderfer)

Proofs Without Words II

When Less is More

(with Claudi Alsina)

An Introduction to Copulas, 2nd Edition

Copulas book errata

Math Made Visual

(with Claudi Alsina)

Icons of Mathematics

(with Claudi Alsina)


Some recent publications:

2013

1. "A new index to measure positive dependence in trivariate distributions" (with J. E. García and V. A. González-López), Journal of Multivariate Analysis, 115 (2013), pp. 481-495. PDF

2012

1. "Directional dependence in multivariate distributions" (with M. Úbeda Flores), Annals of the Institute of Statistical Mathematics, 64 (2012), pp. 677-685. PDF

2. "Proof without words: The triple angle sine and cosine formulas" (with C. Alsina), Mathematics Magazine, 85 (2012), p. 43. PDF

3. "Proof without words: The Pythagorean theorem with equilateral triangles" (with C. Alsina), The College Mathematics Journal, 43 (2012), p. 226. PDF

4. "How close are pairwise and mutual independence?" (with M. Úbeda Flores), Statistics and Probability Letters, 82 (2012), pp. 1823-1828. PDF

5. "Proof without words: An alternating series," The College Mathematics Journal, 43 (2012), p. 370. PDF

6. "Proof without words: Runs of triangular numbers" (with H. Unal), Mathematics Magazine, 85 (2012), p. 373. PDF

2011

1. "Proof without words: Inequalities for two numbers whose sum is one" (with C. Alsina), Mathematics Magazine, 84 (2011), p. 228. PDF

2. "Multivariate copulas, quasi-copulas and lattices" (with J. Fernández Sánchez and M. Úbeda Flores), Statistics and Probability Letters, 81 (2011), pp. 1365-1369. PDF

2010

1. "An invitation to proofs without words" (with C. Alsina), European Journal of Pure and Applied Mathematics, 3 (2010), pp. 118-127. PDF

2. "Teaching Tip: The limit of (sin t)/t" (with C. Alsina), The College Mathematics Journal, 41 (2010), p. 192 PDF

3. "Quasi-copulas and signed measures" (with with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Fuzzy Sets and Systems, 161 (2010), pp. 2328-2336. PDF

4. "Proof without words: New Pythagorean-like theorems" (with C. Alsina), The College Mathematics Journal, 41 (2010), p. 370. PDF

2009

1. "Kendall distribution functions and associative copulas" (with with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Fuzzy Sets and Systems, 160 (2009), pp. 52-57. PDF

2. "Letter to the editor: Isosceles dissections", Mathematics Magazine, 82 (2009), p. 77. PDF

3. "Worst VaR scenarios with given marginals and measures of association" (with R. Kaas and R. J. A. Laeven), Insurance; Mathematics and Economics, 44 (2009), pp. 146-158. PDF

4. "Proof without words: Steiner's problem on the number e", Mathematics Magazine, 82 (2009), p. 102. PDF

5. "Teaching tip: Partial sums of geometric series", The College Mathematics Journal, 40 (2009), p. 278. PDF

6. "Proof without words: Squares in Circles and Semicircles," Mathematics Magazine, 82 (2009), p. 359. PDF

7. "Proof without words: A reciprocal Pythagorean theorem," Mathematics Magazine, 82 (2009), p. 370.PDF

2008

1. "Euler's triangle inequality via proofs without words," Mathematics Magazine, 81 (2008), pp. 58-61. PDF

2. "On the construction of copulas and quasi-copulas with given diagonal sections" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Insurance: Mathematics and Economics, 42 (2008) pp. 473-483. PDF

3. "A sampler of visual proofs in first-year calculus," available at the AP Central website (http://apcentral.collegeboard.com).

4. "Visual gems of number theory." Math Horizons, February 2008, pp. 7-9, 31. PDF

5. "Geometric proofs of the Weitzenböck and Hadwiger-Finsler inequalities" (with C. Alsina), Mathematics Magazine, 81 (2008), pp. 216-219. PDF

6. "Proof without words: Carnot's theorem for acute triangles" (with C. Alsina), The College Mathematics Journal, 39 (2008), p. 111. PDF

7. "Symmetries of random discrete copulas" (with A. Erdely and J. M. González-Barrios), Kybernetika, 44 (2008), pp. 846-863. PDF

2007

1. "Extremes of nonexchangeability," Statistical Papers, 48 (2007) pp. 329-336. PDF

2. "Proof without words: The area of a right triangle," Mathematics Magazine, 80 (2007), p. 45. PDF

3. "On the relationship between Spearman's rho and Kendall's tau for pairs of continuous random variables" (with G. A. Fredricks), Journal of Statistical Planning and Inference, 137 (2007), pp. 2143-2150. PDF

4. "A visual proof of the Erdös-Mordell inequality" (with C. Alsina), Forum Geometricorum, 7 (2007), pp. 99-102. PDF

5. "On Candido's identity" (with C. Alsina), Mathematics Magazine, 80 (2007), pp. 226-228. PDF

6. "On the diagonals of a cyclic quadrilateral" (with C. Alsina), Forum Geometricorum, 7 (2007) pp. 147-149. PDF

7. "Robust fits for copula models" (with B. V. M. Mendes and E. F. L. de Melo), Communication in Statistics--Simulation and Computation, 36 (2007), pp. 997-1017. Website

2006

1. "Proof without words: Every fourth power greater than one is sum of two nonconsecutive triangular numbers," Mathematics Magazine, 79 (2006) p. 44. PDF

2. "Proof without words: Padoa's inequality," Mathematics Magazine, 79 (2006) p. 53. PDF

3. "Proof without words: Right triangles and geometric series," Mathematics Magazine, 79 (2006) p. 60. PDF

4. "Proof without words: Inclusion-exclusion for triangular numbers," Mathematics Magazine, 79 (2006) p. 65. PDF

5. "Proof without words: A weighted sum of triangular numbers," Mathematics Magazine, 79 (2006) p. 317. PDF

2005

1. "Proof without words: Candido's identity," Mathematics Magazine, 78 (2005), p. 131. PDF

2. "Proof without words: Sums of triangular numbers," Mathematics Magazine, 78 (2005), p. 231. PDF

3. "Dependence modeling with Archimedean copulas," Proceedings of the Second Brazilian Conference on Statistical Modelling in Insurance and Finance, (N. Kolev and P. Morettin, editors), Institute of Mathematics and Statistics, University of São Paulo (2005), pp 45 - 54. PDF

4. "Copulas with fractal supports" (with G. A. Fredricks and J. A. Rodríguez Lallena), Insurance: Mathematics and Economics, 37 (2005), pp. 42-48. PDF

5. "The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas" (with M. Úbeda Flores), C. R. Acad. Sci. Paris, Ser I, 341 (2005) pp. 583-586. PDF

6. "Proof without words: A triangular sum," Mathematics Magazine, 78 (2005), p. 395. PDF

7. "Some properties of Schur-constant survival models and their copulas," Brazilian Journal of Probability and Statistics, 19 (2005) pp. 179-190. PDF

2004

1. "Best-possible bounds on sets of bivariate distribution functions" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Journal of Multivariate Analysis, 90 (2004), pp. 348-356. PDF

2. "The symmetric footrule is Gini's rank association coefficient" (with M. Úbeda Flores), Communications in Statistics - Theory & Methods, 33 (2004), pp. 195-96. PDF

3. "Proof without words: Four squares with constant area," Mathematics Magazine, 77 (2004), p. 135. PDF

4. "Proof without words: Every octagonal number is the difference of two squares," Mathematics Magazine, 77 (2004), p. 200. PDF

5. "A comparison of bounds on sets of joint distribution functions derived from various measures of association" (with M. Úbeda Flores), Communications in Statistics - Theory & Methods, 33 (2004), pp. 2299-2305. PDF

6. "Proof without words: A triangular identity," Mathematics Magazine, 77 (2004), p. 395. PDF

2003

1. "Kendall distribution functions" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Statistics & Probability Letters, 65 (2003), pp. 263-268. PDF

2. "Paintings, plane tilings, and proofs," Math Horizons, November 2003, pp. 5 - 8. PDF

3. "An improved remainder estimate for use with the integral test," The College Mathematics Journal, 34 (2003), pp. 397-399. PDF

4. "Properties and applications of copulas: A brief survey," Proceedings of the First Brazilian Conference on Statistical Modelling in Insurance and Finance (J. Dhaene, N. Kolev, and P. Morettin, eds.), Institute of Mathematics and Statistics, University of São Paulo (2003), pp. 10 - 28. PDF

5. "Proof without words: The cube as an arithmetic sum," Mathematics Magazine, 76 (2003), p. 136. PDF

2002

1. "Concordance and copulas: A survey," Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 169-178. PDF

2. "The Bertino family of copulas" (with G. A. Fredricks), Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 81-92. PDF

3. "Some new properties of quasi-copulas" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 187-194. PDF

4. "Multivariate Archimedian quasi-copulas" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 179-186. PDF

5. "Proof without words: The area of a salinon," Mathematics Magazine, 75 (2002), p. 130. PDF

6. "Proof without words: The area of an arbelos," Mathematics Magazine, 75 (2002), p. 144. PDF

7. "Proof without words: Lunes and the regular hexagon," Mathematics Magazine, 75 (2002), p. 316. PDF


Updated: February 2012
By: Anne Boal