Senior Capstone Presentations in Math/Stat at Ohio Northern UPDATE

Capstone presentations by ONU math/stat majors 1998 - Spring 2020

NOTE: Starting Fall 2020, the Mathematics and Statistics Department is replaced by two programs in the School of Science, Technology, and Mathematics: the Mathematics program, and the Statistics program. The records for The Mathematics and Statistics Department cease here. From here on, our records will involve the Mathematics program only.

1. Kaleigh Cummins: The Birthday Problem - an Expanded Look [Rahrig] 2020
2. John Mullin: What Makes a Successful Hire for A College Library [Wang] 2020
3. Hannah Ray: Heel Spur Surgery: Evaluating the Outcomes [Wang] 2020
4. Travis Maenle: A linear complexity analysis of quadratic residues and primitive roots spacings [Caragiu] 2020
5. Bryan Peck: Bell's Inequalities [Caragiu] 2020
6. Kenneth Eaton: The Fundamentals of Automated Theorem Proving [Caragiu] 2019
7. Megan Meyer: An Experimental Approach to Sophie Germain Sequences [Caragiu] 2019
8. Corey Thrush: Two Person Zero Sum Games [Robinson] 2019
9. Kayla Rieman:  Flipping Coins [Rahrig] 2019
10. Bradley Lockhart: Force Propagation in Multi-Rod Drumsticks [Fuller] 2019
11. Takumi Kijima: Naive Bayes Classifier [Wang] 2019
12. Addison Carter: An Introduction to Partitions and Compositions [Caragiu] 2019
13. Emma Talley: Multivariate Analysis of Variance [Wang] 2019
14. Rachel Liebrecht: Special Topics on Graph Theory and Ramsey Numbers [Caragiu] 2019
15. Grant McConnel: Problem Posing Using the Mathematical Game Qubic [Robinson] 2019
16. Dylan Battison: SAS Base Programmer Certification [Rahrig] 2019
17. Shannon Tefft: Processing Quadratic Residues with Ducci Iterations [Caragiu] 2019
18. Andrew Kurdys: The Autoregressive Model and Real Life Time Series Applications [Rahrig] 2019
19. Jenna Holler: American Mathematics Competitions – Variations and Generalizations [Caragiu] 2018
20. Joseph Stomps: American Mathematics Competitions AMC 10 - analogies and generalizations [Caragiu] 2018
21. Ian Simpson: Passive Scalar Transport of Contaminants via Traveling Waves [Fuller] 2018
22. Andrew Tomkins: Statistical Analysis of Library Surveys Using SAS [Wang] 2018
23. Gia Saturday: Myth Busting the Sophomore Slump [Wang] 2018
24. Zachary Goodchild: Three Dichotomous Variables: There is more to it than you think [Robinson] 2018
25. Lindsely Black: Player Efficiency Ratings for Basketball Players [Rahrig] 2018
26. Jennifer Point: Brownian Motion & Its Application to Stock Evaluation [Rahrig] 2017
27. Kyle Thomas: Performance Evaluation of Selected Normality Tests, a Simulation Study [Wang] 2017
28. Jessica Lewe: Analysis of Fall Preventions Outreach Survey Using Nonparametric Statistical Methods" [Wang] 2017
29. Meredith Eichenlaub: Variation of Probability: Baseball and the Binomial Distribution [Robinson] 2017
30. Matthew Golden: The Baker-Campbell-Hausdorff Formula [Caragiu] 2017
31. Michelle Haver: Poissonian Character and Chebyshev Bias for Greatest Prime Factor Sequences: a Computational Analysis [Caragiu] 2017
32. Andrew Harden: The Capital Asset Pricing Model & Markowitz Problem" [Jaki] 2017
33. David Zirkle: The Lognormal Distribution as a Model for Stock Prices [Rahrig] 2017
34. Kaila Bollinger: Kruskal-Wallis versus Classical One-Way Analysis of Variance: Who's the Winner? [Rahrig] 2016
35. Brandon Wilson: Black-Scholes Formula [Jaki] 2016
36. Jeffrey Hancock:  Optimal Strategy for an Obscure Game Show" [Robinson] 2016
37. Nathan Knodel: Exact Solutions of Cubic-Quintic Duffing Oscillators [Fuller] 2016
38. Abigail Thayer: Computer Solutions of the One Dimensional Diffusion Equation [Johns] 2015
39. Brian Slabe: Contingent Payment Methods [Rahrig] 2015
40. James Rader: Analysis of Points After Touchdown in the NFL [Putt] 2015
41. Ashley Ernst: A Group Theoretic Development of Isospin and Low Isospin Multiplets [Fuller] 2015
42. Benjamin McKinnis: The Square Wheel Problem [Hunt] 2014
43. Brandon Guillen: A Look at Bayesian Statistics [Robinson] 2014
44. Amanda Marco: Fibonacci Numbers and Some of Their Properties [Caragiu] 2014
45. Kerry DuLaney: Exploring Gears and Watchmaking [Hunt] 2014
46. Kate Klopp: Wheel of Fortune: From a Statistical Standpoint [Robinson] 2014
47. Lacey Hittle: Progression on Regression: A Look at Multicollinearity [Rahrig] 2014
48. Matthew R. Zirkle: Finding Square Roots in a Prime Field [Caragiu] 2013
49. Thomas E. Steinberger: Arithmetic Functions of Several Variables on the Gaussian Integers  [Jaki] 2013
50. Jonathan C. Schroeder: Small Special Pairs of Primnitive Roots [Caragiu] 2013
51. Devin F. Kisor: Eploration of the Regression to the Mean Phenomenon [Robinson] 2013
52. Morgan Hammer: Applications of Direct Products to Molecular Spectroscopy [Putt] 2013
53. Kelsie E. Zumberger: Did You Cheat In School This Year? [Robinson] 2013
54. Donald J. Pleshinger: On a Congruence of Ohtsuka [Caragiu] 2013
55. Matthew J. McCandless: Picturing Eigenfaces [Retterer] 2013
56. Joanna Snyder: Analyzing the "Hot Hand" Effect [Rahrig] 2012
57. David Mangus: "Let's Get Paradoxical: A Statistical Major's Quest to Solve Some Common Problems [Robinson] 2012
58. Jennifer Krauss: In the World of a Taxicab Driver: an Exploration of Conic Sections in Taxicab Geometry [Putt] 2012
59. Hannah (DePriest) Barnaba: How Much Does One Point Matter: A Study on the Probability of Winning a Tennis Match and the Generalized Case of Winning by n  [Rahrig] 2012
60. Lauren Cassell: Guarding a Koch Fractal Art Gallery [Fuller] 2012
61. Ashley Risch: An Euler-Fibonacci Sequence. [Caragiu] 2011
62. Molly Eickholt: Simplifying Ford Links [Hunt] 2011
63. Lauren Sutherland: Multidimensional Greatest Prime Factor Sequences [Caragiu] 2011
64. Lucas Witt: Sometimes Two Wrongs Do Make a Right [Robinson] 2011
65. Lindsey Miller Walch: Chordal Geometries and Their Axioms [Fuller] 2011
66. Joshua Szekely: The Quantum Harmonic Oscillator and the Hermite Polynomials [Boyadzhiev] 2011
67. Greg Back: The Greatest Prime Factor and its Applications [Caragiu] 2010
68. Jenna Brace: Traffic Flow Simulation with Cellular Automata [Caragiu] 2010
69. Andrew Caldwell: Misuses of Statistics [Robinson] 2010
70. Kevin Earnest: Perturbations in the Aerospace Sequence of Attitude Determination Using Quaternions [Fuller] 2010
71. John Holodnak: The Perron-Frobenius Theorem and Applications [Caragiu] 2010
72. Kyle Meyer: Parity in Professional Sports [Robinson] 2010
73. Matt Rader: Quantifying Defensive Ability in Baseball [Putt] 2010
74. Sharon Binkley: The One Time Pad and Text Visualization [Caragiu] 2009
75. Joshua Stoffel: Maxwell's Equations through the Major Vector Theorems [Boyadzhiev] 2009
76. Joshua Somerlot: The Affine Cipher [Caragiu] 2009
77. Brock Prater: Transmission and Reflection Holograms [Hovis] 2009
78. Eric Gossett: Behavior of Particles in Circular Vertical Floe with Magnus Effect" [Fuller] 2009
79. Axel Brandt: Classification of Ford Links [Hunt] 2009
80. Andrew Magyar: The Einstein's Field Equations [Fuller] 2009
81. Amanda Stype: Holy Voley! How Should We Allocate Those Traps? [Robinson] 2009
82. Michael Gabrieli: The Exploration of Time Series and Forecasting [Robinson] 2009
83. Michael Garee: Solitary Waves and KdV Theory [Fuller] 2008
84. Steven Garofalo: Relational Model for Database Management [Retterer] 2008
85. Brittany Metz: Latin Squares, Probability, and their involvement in the Sudoku [Robinson] 2008
86. Heather Schimmoeller: B2 or not B2. That is the Question [Robinson] 2008
87. Ashley Yontz: Mathematics and Stocks: Risk Analysis of a Portfolio [Putt] 2008
88. Lorelei Rautsaw: The Geometry of Flowers [Raiti] 2008
89. Christopher Lemon: Markov Chains and the Heat Bath Monte Carlo Algorithm for the Ising Model of Ferromagnetism [Johns] 2008
90. Stacy Nagel: Symmetry and Quilting [Raiti] 2008
91. Brian Henderson: A Probability Distribution Associated with the Minehunt Game [Hovis] 2008
92. Katie Milligan: The Underlying Mathematical Patterns of Tessellations [Schroeder] 2008
93. Gretchen Deeg: Projective Geometry and the Art of Perspective [Hovis] 2008
94. Rachel Fye: An Analysis of Stock Portfolios: Random vs. Non-Random [Putt] 2007
95. Tyler Dunlap: Ford Links [Hunt] 2007
96. Andrew Homan: An Overview of Model Theory and Completeness [Caragiu] 2007
97. Aaron Piper: Given two fractions, what is the fraction between the two that has the smallest denominator? [Robinson] 2007
98. Greg Snyder: March Madness Probabilities [Robinson] 2007
99. Mark Bierkan: To Deal or Not to Deal - is that the Question? [Robinson] 2007
100. Matthew Shonkwiler: Conflict: A Game Theory Approach [Putt] 2007
101. Megan Reese: The Golden Section and Design [Raiti] 2007
102. Charise Kazmierczak: Geometry of Rose Windows [Raiti] 2007
103. Katie Miklovic: The Truth Behind the Witch of Agnesi [Schroeder] 2007
104. Anthony Gerdeman: A Venture Into the World of Obstructed Random Walks [Robinson] 2006
105. Allison Mackay: Elementary Number Theory and Classical Cryptography [Caragiu] 2006
106. Lisa Scheckelhoff: GPF Sequences  [Caragiu] 2006
107. Brandon Bucholtz: The Euclidean Algorithm [Caragiu] 2006
108. Kara Stechschulte: Braids and Music [Fuller] 2006
109. Michael Paulus: Predicting Winning Percentage: An Application of Mathematics to Sports [Putt] 2006
110. Adam Hibbard: Predicting Movie Ratings [Robinson] 2006
111. Dan Gudorf: Mary Had a Little Paradox: Whose fleece was and was not as white as snow... [Fuller] 2006
112. Jason Bockey: Ford Circles [Hunt] 2006
113. Jacob L. Johanssen: Fibonacci-Lucas Densities [Caragiu] 2006
114. Kristine Patton: An investigation of Continued Fractions [Schroeder] 2006
115. Kara S. Lewis: A look at Confounding [Robinson] 2005
116. Matt Katschke: San Gaku Problems in Hyperbolic and Spherical Geometry [Hunt] 2005
117. Nathan Baxter: Finite Fields [Caragiu] 2005
118. Jennifer Szippl: Platonic solids [Raiti] 2004
119. Julie Holda: Monte Carlo simulations [Robinson] 2004
120. Tyler Betts: Applications of Group Theory in Chemistry [Putt] 2004
121. Clinton Louiso: Tic-Tac-Toe: an in-depth analysis [Robinson] 2004
122. Molly Neer: Mathematics and Arts at Ohio Northern University [Fuller] 2004
123. Mark Clausing: Advanced Compass and Straightedge Constructions [Hunt] 2004
124. Michael Hewit: The Ehrenfest Model, Analysis via Markov Chains and Recurrent Events [Johns] 2004
125. Sara Miller: Fibonacci Numbers [Caragiu] 2003
126. Julia Gould: Fear of Crime, An Investigative Analysis [Putt] 2003
127. Matthew Suchan: Is Hitter Performance Affected by Free Agency? [Putt] 2003
128. Ann Boerger: The Value of a Bond [Putt] 2002
129. Reid Moore: Analysis of Interest and Basic Annuities [Putt] 2002
130. Stacey Stillion: Covariates of Pancreas Transplant Survival in Recipients of Combined Kidney-Pancreas Grafts [Putt] 2002
131. Laura DiMarco: Classification of Compact, Connected Topological Surfaces Without Boundary [Raiti] 2001
132. Kimberly Myers: Bond Valuation [Putt] 2001
133. Stephanie Osgood: Statistics Reveal the True "Best Hitters" in Baseball [Putt] 2001
134. Ivan Tornes: The Circular Vibrating Membrane [Boyadzhiev] 2001
135. Jason Kline: The Fourier Series and Some Applications [Boyadzhiev] 2000
136. Rachel Kahlenberg: Confidence Intervals for One Pupulation Mean [Song] 2000
137. Ryan Snivley: Analysis of Categorical Data [Song] 2000
138. Sarah Ruppert: Rubik's Cube [Retterer] 2000
139. Lindsay Nicholson: Fourier Series [Lhamon] 2000
140. Tim Thompson: Solutions to the Shortest Path Problem [Putt] 1999
141. Nathan Hyatt: Hypothesis Testing [Song] 1999
142. William Anthony: Recurrent Events [Hovis] 1999
143. Justin Reckner: Differential Geometry of Curves in 3-Space [Raiti] 1999
144. Bodi Kauffman: The Stieltjes Integral [Boyadzhiev] 1999
145. Chris Finney: The Mathematics of Annuity Valuation [Putt] 1999
146. James Conine: Fuzzy Sets [Hovis] 1998
147. Lee Koratich: Functions of Matrices [Boyadzhiev] 1998
148. Jason McCartney: Game Theory [Shult] 1998
149. Amanda Pater: Regression Analysis [Song] 1998
150. Michelle Schlauch: Random Walks [Roepke] 1998

Matrix Models

Journeys into Theoretical Physics - 2019, Speaker: Pedro Vieira (Perimeter/ICTP-SAIFR/IFT-UNESP) 

  

  

  

  

 

 

covid-19 era whiteboards (11)

 

ONU-SOLVE data (UPDATE MARCH 2021)

1. Problem 12126 – The American Mathematical Monthly Vol. 128 (3), March 2021, recognizes correct solution of ONU-SOLVE
2. Problem 1126 – College Mathematics Journal Vol. 50 (3), May 2019, recognizes correct solution of Shannon Tefft. 
3. Problem 1115 – College Mathematics Journal Vol. 49 (5), November 2018, recognizes correct solution of Noah Pinkney.
4. Problem 2025 – Mathematics Magazine Vol. 91 (3), June 2018, recognizes correct solution of ONU-SOLVE.
5. Problem B-1166 – The Fibonacci Quarterly Vol. 54 (2), May 2016, recognizes correct solution of ONU-SOLVE. 
6. Problem 1956 – Mathematics Magazine Vol. 89 (1), February 2016, recognizes correct solution of ONU-SOLVE. 
7. Problem 1951 – Mathematics Magazine Vol. 88 (5), December 2016, recognizes correct solution of Ashley Ernst and Matthew Golden.
8. Problem 1921 – Mathematics Magazine Vol. 87 (3), June 2014, recognizes correct solution of ONU-SOLVE.
9. Problem 1920 – Mathematics Magazine Vol. 87 (2), April 2014, published solution of Tommy Steinberger. 
10. Problem 1916 – Mathematics Magazine Vol. 87 (2), April 2014 - recognizes correct solution of Tommy Steinberger.
11. Problem 1896 – Mathematics Magazine Vol. 86 (3), June 2013 - recognizes correct solution of Tommy Steinberger.
12. Problem 965 – College Mathematics Journal Vol. 43 (5), November 2012, recognizes correct solution of Tommy Steinberger. 
13. Problem 961 – College Mathematics Journal Vol. 43 (5), November 2012, recognizes correct solution of Tommy Steinberger.
14. Problem B-1120 – The Fibonacci Quarterly Vol. 50 (4), November 2012, recognizes correct solution of Matt Zirkle
15. Problem B-1106 – The Fibonacci Quarterly Vol. 51 (2), May 2013, recognizes correct solution of ONU-SOLVE. 
16. Problem 11596 – The American Mathematical Monthly Vol. 120 (5), May 2013, recognizes correct solution of ONU-SOLVE
17. Problem B-1103 – The Fibonacci Quarterly Vol. 51 (1), February 2013, publishes solution of ONU-SOLVE  
18. Problem B-1102 – The Fibonacci Quarterly Vol. 51 (1), February 2013, recognizes correct solution of ONU-SOLVE. 
19. Problem B-1101 – The Fibonacci Quarterly Vol. 51 (1), February 2013, recognizes correct solution of ONU-SOLVE.  
20. Problem 1873 – Mathematics Magazine, Vol. 84 (3), June 2011, recognizes correct solution of ONU-SOLVE. 
21. Problem 1872 – Mathematics Magazine, Vol. 84 (3), June 2011, recognizes correct solution of ONU-SOLVE. 
22. Problem B-1078 – The Fibonacci Quarterly Vol. 49 (4), November 2011, recognizes correct solution of ONU-SOLVE. 
23. Problem B-1074 – The Fibonacci Quarterly Vol. 49 (3), August 2011, publishes solution of ONU-SOLVE.
    

Mihai Caragiu CV

 See here

covid-19 era whiteboards (10)

 

covid-19 era google meet videos (2) Discrete Mathematics - Boolean Algebra

covid-19 era google meet videos (1) Calculus 3 Harmonic Functions Examples

covid-19 era whiteboards (9)

 

covid-19 era whiteboards (8)

 

covid-19 era whiteboards (7)

 

covid-19 era whiteboards (6)

 

Pi Day

Memories... 

Pi Day 2003

 

covid-19 era whiteboards (5)

 

covid-19 era whiteboards (4)

 

covid-19 era whiteboards (3)

 

covid-19 era whiteboards (2)

 

covid-19 era whiteboards (1)

 

Amazing Resonance Experiment

The Heisenberg and Witt algebras

Here - a nice introduction by Akhil Mathew @ Climbing Mount Burbaki

The attractiveness of primes for experimental mathematics...

'Although the prime numbers are rigidly determined, they somehow feel like experimental data'

Timothy Gowers. Mathematics: A Very Short Introduction (Oxford Univ. Press, 2002) p.118; as cited in "surprising connections between number theory and physics"

All primes in terms of one: non-associative algebra and Google cloud computing

Under addition, the positive integers 1, 1+1, 1+1+1,.... form a cyclic (semigroup) structure generated by 1. We will explore a way of representing prime numbers in terms of the single generator g = 2, under a non-associative, non-commutative binary operation "o" on the set A of all primes, defined by setting x o y:=P(2x+y) where P is the greatest prime factor function. For example, 3 = 2 o 2, 5 = 2 o (2 o (2 o (2 o 2)))), etc. In a joint work with Paul A. Vicol from Simon Fraser University, we managed to verify that all primes up to 7259167 can be expressed as non-associative products involving the symbols 2, o, and parentheses ),(. This computational evidence points towards a cyclicity conjecture for the (magma) structure (A, o). Moreover, we searched for other similar non-associative algebraic structures on A (prime magmas) that might be cyclic, established a set of fairly restrictive necessary conditions for cyclicity, formulated a more general cyclicity conjecture for special prime magmas, and found computational evidence (after days of running Julia programs on a GCE platform) for the cyclicity of the structures in a representative set. (October 24, 2014 - MAA Ohio Fall Meeting)

Love and Tensor Algebra - from "The Cyberiad" by Stanislaw Lem

"Come, let us hasten to a higher plane
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n
Commingled in an endless Markov chain!

Come, every frustrum longs to be a cone
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in our bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Bools or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?

Cancel me not - for what then shall remain?
Abscissas some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.

Ellipse of bliss, converge, O lips divine!
the product o four scalars is defines!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.

I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a^2 cos 2 phi!"

SOURCE: http://www.aleph.se/Trans/Cultural/Art/tensor.html

The OEIS Movie. Experimental Mathematics

Experimental mathematics channel - You Tube

Erdős' discrepancy problem - recently solved

Blog comment, collab help man attack old maths problem 
Phys.Org - September 26, 2015 by Nancy Owano 

The Erdos Discrepancy Problem - Terrence Tao - http://arxiv.org/abs/1509.05363

The Singular Mind of Terry Tao

The Singular Mind of Terry Tao 
A prodigy grows up to become one of the greatest mathematicians in the world. 
New York Times
By GARETH COOK, July 24, 2015

Vox: Emmy Noether revolutionized mathematics - and still faced sexism all her life

http://www.vox.com/2015/3/23/8274777/emmy-noether

Mihai Raileanu - o amintire

De fapt una dintre multele amintiri ce nu se pot sterge. M-a introdus in lumea congruentelor si a lucrului cu 'numere mari'. In stilul problemelor ce le primeam la inceput de clasa a IX-a, sa se afle toate numerele naturale N astfel incat 1249^N  ≡ 1948441249 (mod 311920921441)...

Roger Penrose lecture at Penn State: Faith, Fashion, and Fantasy: How Big is Infinity?

OEIS - The Movie!

N. J. A. Sloane Article

The unexpected math behind Van Gogh's "Starry Night"

The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair

Beauty in Math and Art Activate Same Brain Area

Beauty in Math and Art Activate Same Brain Area 
Elegant equations evoke the same activity in mathematicians' brains as gorgeous art or music 
Scientific American, Aug 14, 2014 
By Seth Newman

Maryam Mirzakhani - first woman to be awarded the Fields Medal - ICM 2014 Seoul

Maryam Mirzakhani - Iranian mathematician, full Professor of Mathematics at Stanford, first woman to be awarded the Fields Medal, at The International Congress of Mathematicians 2014 (Seoul, August 13-21)

"for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces" - see presentation and video @  http://www.icm2014.org/en/awards/prizes/f4

Joint Statistical Meetings Proceedings - not peer-reviewed

"If you give a presentation at JSM, you may submit a corresponding paper to be published in the conference proceedings. Papers are not peer-reviewed in the same manner as for journals, but authors are encouraged to have others examine their paper before submission. The proceedings are published online around November. Authors retain the right to publish their research later in a peer-reviewed journal."

SOURCE: "What Happens at JSM Should Not Stay at JSM / How to get the most out of the Joint Statistical Meetings"  AMSTAT News - May 2014
http://magazine.amstat.org/wp-content/uploads/2014/02/AN_May2014.pdf

Eu si... Antonin Scalia

Pe o scara personal/academica, momentul cel mai interesant al anului care a trecut a survenit atunci cind am fost comparat (la o conferinta, deci in public) cu... Antonin Scalia (!). Intentia nu a fost magulitoare, iar motivul fiind inistenta mea pe cercetarea intreprinsa de profesori, (nici vorba de "publish or perish" la un 4 years college, insa macar "publish involving undergraduates" - pentru un 4 years college ar fi minunat). Insistenta mea a trezit reactii mixte: unii s-au bucurat ("it's about time!"), altii au subliniat ceva in genul "teaching is paramount" (so?... does this exclude engaging students in research?), altii au fost relativ ostili, negind orice rol special acordat publicatiilor cu sau fara studenti co-autori. In sfirsit, ma bucur ca macar aceasta atitudine i-a pus pe ginduri pe unii.

Nature's secrets

"Nature conceals her secrets because she is sublime, not because she is a trickster" 
Albert Einstein, in a letter to Oscar Veblen

Cosmic inflation: 'Spectacular' discovery hailed

17 March 2014
Cosmic inflation: 'Spectacular' discovery hailed
By Jonathan Amos Science correspondent, BBC News


NY Times - Space & Cosmos 
Detection of Waves in Space Buttresses Landmark Theory of Big Bang 
By DENNIS OVERBYE, MARCH 17, 2014

RAMANUJAN: Letters from an Indian Clerk

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Why the brain sees maths as beauty (BBC News)

Mathematics: Why the brain sees maths as beauty 
By James Gallagher
Health and science reporter, BBC News
12 February 2014

"What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating." (P. A. M. Dirac)

'On Ducci Sequences with Primes' - Fibonacci Quarterly

http://www.fq.math.ca/Abstracts/52-1/caragiu.pdf
Mihai Caragiu, Alexandru Zaharescu, and Mohammad Zaki 
On Ducci Sequences with Primes 
Fibonacci Quart. 52 (2014), no. 1, 32-38.

An analogue of the Proth-Gilbreath conjecture (new paper)

O fenomenologie a numerelor prime - in gen fantasy cu demonstratii plus "experiment" (computer).

Far East Journal of Mathematical Sciences (FJMS)

Volume 81, Issue 1, Pages 1 - 12 (October 2013)
AN ANALOGUE OF THE PROTH-GILBREATH CONJECTURE 
Mihai Caragiu, Alexandru Zaharescu and Mohammad Zaki
Communicated by Juliusz Brzezinski

Miami University Fall Conference on Undergraduate Research in Mathematics

Abstract of my presentation:

More than twelve years ago, a talk on "Ducci games" delivered jointly by two Ohio Northern University students at the 2001 Ohio MAA Spring meeting initiated a fairly long streak of undergraduate research in the area of number theory at our school. Since then, Ohio Northern University students presented 40 talks and posters in the broad area of number theory at various mathematics meetings, and were co-authors of 11 research articles in number theory which appeared in peer-reviewed mathematics journals. We were especially pleased to see our research on "greatest prime factor sequences" (published in Fibonacci Quarterly in 2010) featured alongside other "noteworthy variations on the Fibonacci numbers" in the keynote talk at the 15th International Conference on Fibonacci Numbers held in Budapest (June 25-30, 2012), and cited in various other journals. In the light of the speaker's experience as an undergraduate research advisor, we will try to address some issues of interest regarding the impact of undergraduate research in the outside mathematical community. This "impact" may be viewed as a long-sought fulfillment or closure of the combined efforts of faculty and students engaged in undergraduate research, which ultimately takes a life of its own. We will explore open-ended difficult questions such as: What does it mean to make an impact? Are there specific strategies for smaller schools? Can presentations make an impact? What is the relationship between undergraduate research and faculty research? Is it harder for pure mathematics?

Alba Iulia 2013

My talk (abstract) at the 2013 RMS-AMS Special Session of Discrete Mathematics and Theoretical Computer Science in Alba Iulia:
Uniform distribution for a class of k-paradoxical oriented graphs 
By using estimates for incomplete character sums with polynomial arguments, we provide uniform distribution results for the dominating sets in a class of k-paradoxical regular oriented graphs, including the Paley tournaments. Moreover, we will explore a method of quasi-random tournament generation from fi nite sets of natural numbers, by using the greatest prime factor function.

Work on Stirling numbers honored with an Allendoerfer Award (2013)

Khristo N. Boyadzhiev (Ohio Northern University) - 2013 Carl B. Allendoerfer Award for the paper "Close Encounters with the Stirling Numbers of the Second Kind" - Mathematics Magazine, 85:4 (2012), pp. 252-266.
More at: http://www.maa.org/news/2013-maa-awards-recipients-announced

UNIFORM DISTRIBUTION FOR A CLASS OF k‑PARADOXICAL ORIENTED GRAPHS

Mihai Caragiu, Donald Pleshinger and Jonathan C. Schroeder, UNIFORM DISTRIBUTION FOR A CLASS OF k‑PARADOXICAL ORIENTED GRAPHS, JP Journal of Algebra, Number Theory and Applications, Volume 29, Issue 2, Pages 107-117 (June 2013)

A major breakthrough on primes: Yitang Zhang

Bounded gaps between primes - by Yitang Zhang - Ann. Math. (forthcoming)

Mandelbrot set, zoom, matlab

http://www.youtube.com/watch?v=EQGGnIyIoDM

A parametric curve with... Bach's Prelude in G major

http://youtu.be/IvNQbTYSON8

A Uniform Distribution Result for k-Paradoxical Directed Graphs

The research I am conducting with two students of mine was presented at the 2013 MAA Undergraduate Poster Session in San Diego.

The Legacy of Srinivasa Ramanujan

Srinivasa Ramanujan: Going Strong at 125 (Krishnaswami Alladi, Editor - Notices of the AMS - Part I and Part II).

The Legacy of Srinivasa Ramanujan-An International Conference, University of Delhi, India

Mysterious WWII encrypted message found in UK

UK spies unable to crack coded message from WWII carrier pigeon (CNN)

A nice picture

A nice "Paley digraph" picture - with outgoing edges from x to x+1, x+2, x+3, x+4, x+6, x+8, x+9, x+12, x+13, x+16 and x+18 (modulo 23) for x = 0,1,...,22.

October 23 - ONU Mathematics Seminar on a-T-menability

The Role of Research at Undergraduate Institutions

An excellent article by Robert Gavin, in "Academic Excellence - The role of research in the physical sciences at undergraduate institutions" (Michael P. Doyle, Editor - published in the year 2000 by Research Corporation - a foundation for the advancement of science). Even if the paper, which emphasizes the role of publishing in a research-based education, refers to physical sciences, the ideas in there are even better suitable for mathematical sciences, where there is not an excessive need for laboratories and equipment.
Straight to the point: "Publishing research articles, especially those done in collaboration with undergraduate students, should be expected, encouraged and supported both before and after the tenure decision".

GPF sequences in Rutgers' Experimental Mathematics Seminar

Apparently the sequences introduced in the Fibonacci Quarterly paper by Greg Back and myself have been discussed in the RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR (Neil J. A. Sloane's presentation was on February 17, 2011

GPF sequences - a forum discussion

A discussion of the paper "The Greatest Prime Factor and Related Sequences" (JP Journal of Algebra, Number Theory and Applications 6(2), 403-409 (2006), by Mihai Caragiu and Lisa Scheckelhoff), with neat pictures, can be found here (Mathematical Oddities Thread - The Something Awful Forums)

An Euler-Fibonacci Sequence

An Euler-Fibonacci Sequence
by Mihai Caragiu and Ashley Risch
Far East Journal of Mathematical Sciences, Volume 52, Issue 1, Pages 1 - 7 (May 2011)
abstract - here

Undergraduate research: what is that ?

The Council on Undergraduate Research defines it as follows:

``An inquiry or investigation conducted by an undergraduate student that makes an original intellectual or creative contribution to the discipline.''

The word "original" is very important. An original contribution to knowledge rules out works of a severely expository or textbook nature, results that follow immediately from previous work (as in... use the previously obtained A=B to "discover" that 2A=2B, or something like that), or trivial derivations in existent or made-up ad hoc formal systems. The original contribution to the discipline must also go through a rigorous, external, peer-review process. Ideally, a rigorous, solid peer-review is a process which does not accept works simply because they are formally correct, indeed it demonstrates a pattern of rejecting a significant percentage of logically correct but otherwise not interesting enough (as judged by the reviewers) works. Also, note that being "peer-reviewed" is not the same with "being made public/disseminated" (a confusion that is still circulating). A valuable original contribution will be able to generate 'participative waves', engaging others in the area. Thus, when it comes to goals and assessment, 'undergraduate research' is not (and shouldn't be, in my opinion) different from good old 'research'. So it is a serious matter, and competitive universities recognize that. I found interesting the following straight-to-the-point statement (due to Jim Coleman, vice chancellor for research and professor of biology at the University of Missouri) on the central place of undergraduate research in the life of a good university:

``There is nothing more central to the mission of a university than activities associated with discovery, creation, innovation and scholarship. So, I think that what defines a great university is the integration of these activities into the entire fabric of the undergraduate experience.''

Integrating the research/scholarship into the undergraduate life is a challenging enterprise. There are no clear recipes, since there are students and students. Each individual case is unique and interesting in itself. The faculty's essential asset is their own involvement and demonstrated proficiency in research. Indeed the undergraduate research is driven, after all, by faculty research. Or, if you want, faculty research is a necessary condition for undergraduate research. One may ask, is it also a sufficient condition? This is not true, mainly because the student is a person, not a machine or a notebook on which the faculty mentor writes a paper. In the end, note that the complexities of (undergraduate) research that even an otherwise well prepared academic (mentor) faces, ultimately point to persons (as in real persons, and not ``the idea of a person''), and their participative experience.

Ion Barbu: matematică, poezie şi arte (un citat concis...)

Matematicile pun în joc puteri sufleteşti care nu sunt cu mult diferite de cele solicitate de poezie şi de arte.
(Ion Barbu; sursa - citatepedia.ro)

music and computation

Gottfried Wilhelm Leibniz's view on music ('the hidden arithmetical exercise of a mind unconscious that is calculating') has (at least) two straightforward interpretations. The first one is essentially reductionist (a 'fallacy of the misplaced concreteness' according to Alfred North Whitehead) and tends to suggest that music is nothing but computation (albeit in the background/unconscious, in a less obvious way). The second interpretation of the music-calculating connection runs somehow in the opposite direction, and tends to suggest that there is more to computation than meets the eye, an ethereal/ineffable/musical/higher-order quality. At this point, one might try to revisit the spirit of some traditional Gödelian themes...
Image source: http://en.wikipedia.org/wiki/File:FortranCardPROJ039.agr.jpg

Fractals and partitions

A recent major breakthrough is announced here (Emory University's site, eScienceCommons). Looks like ultimately periodic sequences made the news. Also see here a recent article by Ken Ono (The Last Words of a Genius, Notices of the AMS Volume 57, Number 11, 1410-1419), and here a relevant abstract by John Webb (An improved “zoom rate” for the Folsom-Kent-Ono l-adic fractal behavior of partition values).

Image source.

A relevant video - Ken Ono talk (Emory University YT Channel):

http://youtu.be/aj4FozCSg8g
New Theories Reveal the Nature of Numbers

New paper. GPF-Tribonacci sequences

Starting with 5, 13, 7, each subsequent term is the greatest prime factor of the sum of the previous three terms. More about this type of sequences - in a new Fibonacci Quarterly article by Greg Back and Mihai Caragiu ("The Greatest Prime Factor and Recurrent Sequences" - Fibonacci Quarterly 48 (2010), no. 4, 358–362) - abstract here. 

In the main result on GPF-Fibonacci sequences (Theorem 3) we prove that all GPF-Fibonacci sequences (that is, prime sequences in which each subsequent term is the greatest prime factor of sum of the previous two terms) that are non-constant eventually enter the same 4-cycle 7,3,5,2.

The "phi-bonacci" sequence - an update

More data on the "phi-bonacci" sequence introduced previously here, after computing the first 500 terms:

• a plot of the sequence of quotients X(n+1)/X(n) for n = 1,2,...,499:

X(n) is a multiple of 4 for n between 13 and 500.
Here is the updated raw data (last previously calculated term marked in red):

GPF stability?...

A visual on the behavior of the same recurrence as before, only with a different initial condition (an 8-digit prime, picked at random)

L[1] = 11631013

L[N] = P(26390*L[N-1] + 1103)

The limit cycle is the same. The choice

L[1] = 7654237825827857857221111238572389123865443346789678979

leads, again to the same limit cycle. This raises an interesting question of "stability" (that is, assuming ultimate periodicity holds, are there finitely many - if not a single one - limit cycles?*) Note that in this particular case, the limit cycle is not unique: for example, the choice

L[1] = 2250957258971258907129712971234237484736596896123596812363

leads to a different limit cycle, of period 18:

A recurrence with primes inspired by a formula of Ramanujan

Inspired by the linear component appearing in the numerators of the terms of the Ramanujan's formula for pi, I looked into the recurrent sequence of primes defined as follows:   

L[1] = 2

L[N] = P(26390*L[N-1] + 1103)

where P is the greatest prime factor function. The prime sequence (L[N]) turns out to be ultimately periodic, with period

(1459, 30011, 15529243, 409816723873, 292299009270529, 701251895877205583, 15696384675317604187, 451826639233, 109391789076697, 151939437564949207, 74396630251, 29303389139179, 26646743, 2111734381, 55728670315693, 70865191, 18516162293, 487831, 12873861193, 1132987, 1921687, 330167, 968123137, 2901559, 14505047, 2091738751, 675347, 5940802811, 57192517, 137210047703, 938359, 24763295113, 6250999, 2795997707, 6922448587, 30040009, 46632696389, 3290305727, 282788861, 24151449977, 212452254964711, 5606615008518724393, 4871183188935589, 733134419023, 19347417318018073, 29451120121, 218661017, 242650193, 36178184149, 16311737023, 6797093683, 179375302295473, 29858734728029, 1862817989297131, 4993054962517, 15723597697, 311287129201, 13424039, 6946282163, 252731, 741063577, 106787, 26293, 10356319, 23227, 612961633, 511873, 4640443, 346915841, 3511741099, 33101671, 3527213, 6883, 20719, 433, 57427, 1529263, 510851287, 4456663, 117611337673, 999421747, 33078701, 2389547, 2335560979, 4285298911, 113089038262393, 30741542832733, 1801335599663, 688945601088517, 4790671, 7790117, 769966999, 239280127, 8821951, 756227, 34513, 4289, 37729271, 914302537, 11594639093, 39465611, 11110373, 478571, 11549, 859, 22670113, 176369, 1551459671, 40453493, 6714262147, 14927447, 43770591937, 70138194257, 2603300909203, 51190093, 942712181, 8292724819231, 24011017, 168928483, 6954793553, 270216913, 16301459, 1158523, 30573423073, 21129377, 5023461803, 1979, 17408971, 70381, 1798021, 88289, 467017, 540149, 39929, 4231837, 223803967, 5906186690233, 155864266755249973, 144041128039, 604427630617, 8896176894581, 1577342687387, 17151245784979, 452621376265596913, 878711663, 19359229, 2829679, 12128509, 8627, 41177, 65371, 1663589, 4878012757, 207798167, 609310403137, 1409652983, 1377805267499, 526960594337677, 86463252140809, 8419797874523803, 15369684199, 10962323405749, 1278583667, 132525119, 129531033019, 1221680363, 7825861, 206524472893, 5450180839647373, 24708859707660913, 652066807685171495173, 1941559636106473627171, 193285868819, 100015962316363, 1111967795377, 29344830120000133, 81694832084891, 718642206240091531, 18964967822676015504193, 4407663528935561, 857965267921, 42742695533, 20327255503, 11413537717559, 250324962137, 1275058048793, 11216260635882791, 857911268779, 13341354380129, 39119815787956157, 209783083, 325657385969, 72031783, 2035949, 163601, 72953, 7247, 21249937, 560785838533, 1345376207171543, 1075893275977485481, 9099479420859497, 98635636088557, 320878911329, 2822664823324471, 110249906411, 14055531546799, 499608015161, 548195730743, 160630728871, 385367721355163, 32609594737, 1641473, 83465267, 122840243, 140682811, 161071, 4250664793, 153443, 449929097, 26904379, 116579, 405499, 7715299, 3579647, 33083, 2881391)

Here is a logarithmic plot of this sequence:

This special case illustrates a general conjecture on the ultimate periodicity of GPF sequences. For this, and related sequences and algebraic structures, see

• Greg Back and Mihai Caragiu, The Greatest Prime Factor and Recurrent Sequences, Fibonacci Quarterly (accepted for publication);
• Mihai Caragiu and Greg Back, The Greatest Prime Factor and Related Magmas, JP J.of Algebra, Number Theory and Appl. 15 (2), 127-136 (December 2009);
• Mihai Caragiu and Lisa Scheckelhoff, The Greatest Prime Factor and Related Sequences, JP J.of Algebra, Number Theory and Appl. 6(2), 403-409 (2006);

A "phi-bonacci" sequence and its consecutive quotients

A most interesting sequence:
"phi-bonacci" ?...

X(0)=0, X(1)=1
X(n)=phi (X(n-1)+X(n-2)+1) 
if n is at least 2, where phi is the Euler's totient function.

This ensures that X(n) is never greater than the 'regular' Fibonacci number F(n)
 
Plotted - the sequence of quotients X(n+1)/X(n) for n = 1,2,...,324

The raw list of the first 325 non-zero terms follows:

1, 1, 2, 2, 4, 6, 10, 16, 18, 24, 42, 66, 108, 120, 228, 348, 576, 720, 1296, 2016, 3312, 5256, 7200, 12456, 17860, 25200, 40256, 37368, 39600, 72900, 112500, 185400, 282204, 364800, 517600, 805392, 1133988, 1939380, 2788176, 4727556, 6819120, 11539840, 18324852, 28220080, 46471680, 70297856, 77663160, 98640672, 173595168, 256221952, 408844800, 613907760, 1020322800, 1598868000, 2614401972, 3650502240, 6204873360, 9219832128, 14163287040, 23375208496, 37533203556, 59869153008, 77921885248, 136242824256, 171331767600, 280988047872, 412648088320, 492483317760, 759235553856, 1248565926960, 1825274073460,

Eadem mutata resurgo

Commemorating Jacob Bernoulli...

Eadem mutata resurgo
"Though changed I shall rise the same"

Inscribed on Jacob Bernoulli's tombstone (he died on August 16, 1705 in Basel), this motto refers to the logarithmic (equiangular) spiral (N.B. the spiral that was actually imprinted on the tombstone is not equiangular). Through this self-similar object Jacob Bernoulli symbolically points to the ‘fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self ’ - as quoted in Mario Livio's book "The Golden Ratio..." (via here).

Jacob Bernoulli at the Mathematics Genealogy Project.

The Whirlpool Galaxy...

Beauty in Mathematics

Michael Atiyah - Beauty in Mathematics

Structure and Randomness in the Prime Numbers (Terence Tao)

Terence Tao: Structure and Randomness in the Prime Numbers, UCLA
Slides: pdf, powerpoint

Lecture for a general audience: Terence Tao is UCLA's Collins Professor of Mathematics, and the first UCLA professor to win the prestigious Fields Medal.

Johann Bernoulli (1667 - 1748) anniversary

Johann Bernoulli (1667 - 1748) was born on July 27, 7^3 years ago, in Basel, Switzerland. He was Euler's "mathematical parent".

And here is the... "sophomore's dream" - neat identities due to Johann Bernoulli (1697):

A traffic flow simulation

This traffic flow educational project with Matlab features a gradually increasing car density starting from an initial value of 0.2. There are 250 cells. The update rule (describing the transition from time t to time t + 1): apply rule 184, after which randomly select a position - if occupied, nothing happens, while if empty, introduce a car at the selected place with probability 0.7. The image follows the first 500 time units. Notice the transition to a congested regime happening at some point (emerging shock waves). In the picture, free cells are blue, while cells occupied by "cars" are red.

Lothar Collatz anniversary

Lothar Collatz, who proposed (in 1937) the celebrated "3n+1 problem", was born 100 years ago in Arnsberg, Germany.

Mac Tutor Biography

Lothar Collatz at MGP

A Thermodynamic Classification of Real Numbers

I just found a very interesting paper presentation (JNT on YT - link) by Thomas Garrity (Williams College) - "A Thermodynamic Classification of Real Numbers":


On arXiv - A Thermodynamic Classification of Real Numbers.

Élie Cartan (1869-1951)

Élie Cartan had significant contributions in areas such as Lie theory, differential geometry, exterior differential forms, the theory of spinors (introduced by him in 1913), etc. Cartan died on May 6, 1951.

Dieudonné places Cartan right after Poincaré and Hilbert when it comes to the lasting influence in shaping modern mathematics. He was a speaker at the 1924, 1932 and 1936 International Mathematical Congresses. He lectured in Romania in 1931. The letters that he exchanged with Albert Einstein, Gheorghe Ţiţeica, Alexandru Pantazi and Gheorghe Vrânceanu, have been published (as mentioned in M. A. Akivis and B Rosenfeld - Élie Cartan (1869-1951), Providence R.I., 1993).

Paul Montel (1876-1975)

Paul Antoine Aristide Montel, Honorary Member of the Romanian Academy, advisor of Henri Cartan, Jean Dieudonné, Miron Nicolescu, Tiberiu Popoviciu and others (see Montel's entry at MGP), was born on April 29, 1876...

Max Planck on consciousness

"I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness." (Max Planck - born on April 23, 1858)

link to quotation source
link to top picture source/credits (grave of Max Planck in Göttingen)
link to  bottom picture source/credits (NGC7090)
Mac Tutor Biography
Mathematics Genealogy Project - Max Planck
Planck units

Marius Dabija (13 ianuarie 1969-22 iunie 2003)

De pe blogul lui Florin:

Un prieten căruia îi păstrez o vie amintire este Marius Dabija. Minte strălucită, scormonitoare, imprevizibil in acţiuni, căutând mereu soluţia surpriză. În clasele a VII-a şi a VIII-a am lucrat împreună la matematică, pregătindu-ne pentru Olimpiade. Ca să variem, jucam şah până nu mai ştiam de noi. Era talentat şi la fotbal, tenis de masă etc.

În liceu ne-am văzut mai rar. Eu eram la liceul I. L. Caragiale, el, la Mihai Viteazul. L-a avut profesor pe Eugen Onofraş. În clasa a XI-a, Marius a luat locul I la Olimpiada de matematică, faza Naţională şi la Olimpiada Internaţională de Matematică. După ce a absolvit Facultatea de matematică, a plecat la doctorat în America, unde munca de cercetare i-a fost încununată de reuşită. A luat doctoratul şi a scos nişte articole remarcabile.

Ca elev şi student, era în stare să-şi conducă profesorii de la agonie la extaz şi invers. Născocea pe loc soluţii din cele mai diverse la câte o problemă, după care, lăudat fiind de profesor, care nu reuşea totuşi să urmărească deplin şirul argumentărilor, revenea şi arătând că greşise într-un loc ştergea totul, scoţând ca din joben o altă demonstraţie fulger. Asta se putea întâmpla de câteva ori la rând...

Avea de regulă o deosebită poftă de viaţă, umor, voioşie, neastâmpăr, o doză sensibilă de nonconformism, atras de situaţii-limită, uneori fiind, e drept chinuit de gânduri şi întrebări, incertitudini existenţiale, întorcând lucrurile pe toate părţile în căutarea unei soluţii, construind şi deconstruind la nesfârşit.

Mie îmi părea câteodată, în unele momente ale sale de graţie, că regăsesc profilul unui Mozart al matematicii. Am aflat cu durere în inimă vestea că în America a trecut pe neaşteptate la cele veşnice, în plină activitate creatoare, la numai 34 de ani. Dumnezeu să-l ierte şi să-l odihnească!

Articole Publicate:

Dabija, M. "Algebraic and Geometric Dynamics in Several Complex Variables". PhD thesis, University of Michigan, 2000. ps.gz
Bonifant, A. and Dabija, M. "Contractive Curves". International Journal of Mathematics and Mathematical Sciences, 30(4), 2002. ps.gz
Bonifant, A. and Dabija,M. "Self-maps of P2 with invariant elliptic curves". Contemporary Mathematics, 311, 2002. ps.gz
Coman,D.and Dabija, M. "On the Dynamics of Some Diffeomorphisms of C2 near parabolic fixed points". Houston Journal of Mathematics, 24(1), 1998. pdf

Articole Nepublicate:

Dabija, M. "Bötcher divisors", 2000. ps
Dabija,M. "Self-maps of projective bundles on projective spaces",2000. ps
Dabija, M."Self-maps of ruled surfaces", 2000. ps
Dabija,M.and Jonsson, M. "Self-maps of P2 with an invariant curve of curves", 2002.

J.S. Bach - Crab Canon on a Möbius Strip

(YT link)

Ph.D. mathematician and NFL champion

In some sense, the stunning 2010 Super Bowl XLIV victory of New Orleans Saints led by Drew Brees against the Peyton Manning's Indianapolis Colts (my favorite team) may be analogue to a similar event that happened in 1964. Then the NFL quarterback Frank Ryan led the Cleveland Browns to the 1964 NFL Championship title in a 27-0 victory against Johnny Unitas' Baltimore Colts. To this one might add the impressive 1966 season in which the Cleveland Browns' legend Ryan threw for 2974 yards and scored 29 touchdowns.

What is especially relevant for this particular blog is that Frank Ryan is also the recipient of a Ph.D. in Mathematics awarded by Rice University in 1965, with a most interesting thesis, "A Characterization of the Set of Asymptotic Values of a Function Holomorphic in the Unit Disc", and that among the references cited in the thesis are Luzin's "Leçons sur les ensembles analytiques et leurs applications", Sierpinski's "General Topology" (University of Toronto Press, 1952), and Stoilow's "Les propriétés topologiques des fonctions analytiques d'une variable", Ann. Inst. H. Poincaré, 2 (1932), 233–266. In 1966 Frank Ryan also published two fundamental papers on the set of asymptotic values of a function holomorphic in the unit disc in Duke Mathematical Journal (he also published in Pacific Journal of Mathematics, Mathematische Zeitschrift, Michigan Mathematical Journal, etc).

I will conclude with mentioning a recent mathematical event - the amazing, super-entertaining after-dinner talk "Resolved, that a Football is a Mathematical Object" delivered by Frank Ryan at the 2007 Ohio MAA Meeting held at Wittenberg (a talk which I will never forget).