December 4, 2024

Memories - a beautiful campus and an abstract - 27 years ago

I vividly remember that talk. 

People were great! Added bonus: the campus and the nature were amazing. 

I could recover my abstract from https://scholarworks.umt.edu/mathcolloquia/7/

 

So... about 27 years years ago:

 

Presentation Date 10-23-1997 

Abstract A classical problem considered by Davenport asks for the number of occurrences of a certain pattern of quadratic residues and nonresidues among the set of integers modulo a prime p. We will take this problem as a starting point of an itinerary revealing the interplay between quasirandom structures over finite fields, definable subsets of finite fields, character sums and coding theory. 

Additional Details Thursday, October 23, 1997 4:10 p.m. in MA 109 Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

November 4, 2024

The eternal paradox of neuroscience

"If the human brain were so simple that we could understand it, we would be so simple that we couldn't."

Emerson Pugh

Pictured: Cross-section of a human head, showing location of the hypothalamus (source)

Kenneth A. Ribet, "A 2020 View of Fermat's Last Theorem"

 

October 26, 2024

Are these the same proof?

In his blog, Timothy Gowers presents two proofs of the fact that the product of k consecutive positive integers is a multiple of k! and asks  

"whether there is some sophisticated perspective from which it is possible to regard them as sort of the same"

There are many interesting answers from the readers, among them being Terence Tao.


October 14, 2024

My book among the best 20 prime numbers books of all time (10/10/2024)

As of October 10, I noticed that Sequential Experiments with Primes is ranked 6th in the list of best 20 prime numbers books of all time (maintained by bookauthority - here). 

The evaluations in the rubrics New Mathematical Ideas and High Impact Learning make me happy because these were the primary objectives and the spirit in which I wrote the book.

October 12, 2024

Earl Llhamon at the Schoonover Observatory 60th Anniversary Dinner

 


Earl will soon turn 90! 

It was an extraordinary event. 

Lima Astronomical Society 

October 11, 2024

https://limaastro.com/

September 18, 2024

1 proton per 4 cubic meters...

"More than 95% of the energy density in the universe is in a form that has never been directly detected in the laboratory! The actual density of atoms is equivalent to roughly 1 proton per 4 cubic meters."

Source: WMAP- Content of the Universe - NASA https://wmap.gsfc.nasa.gov/universe/uni_matter.html

Image - CMB Timeline300 no WMAP.jpg

Be grateful for the complex life on Earth...

August 19, 2024

Raison d'ĂȘtre - Capstone projects

 

A Capstone Research project is a wonderful experience for a Mathematics educator engaged in Undergraduate Research. That's our raison d'ĂȘtre! Here are the Capstones that I advised at ONU. With many thanks to all those amazing students.


  1. Julia DeVore, Carmichael Numbers 2024 
  2. Kaleb Swieringa, On the Alternating Sum of Divisors 2023 
  3. McKinley Britton: Fibonacci Numbers and Domino Tilings 2023 
  4. Alexander Hare: Experiments with Greatest Prime Factor Sequences 2023 
  5. Rachael Harbaugh: Extending a Putnam Problem to Fields of Various Characteristics 2022 
  6. Benjamin Morris: Fibonacci Periods 2022 
  7. Greg Hassenpflug: The Golden Ratio 2021 
  8. Aaron Kemats: An Investigation of the Square Grid Graph 2021 
  9. Travis Maenle: A linear complexity analysis of quadratic residues and primitive roots spacings 2020 
  10. Bryan Peck: Bell's Inequalities 2020 
  11. Kaity Kelly: Gaussian Integers 2020 
  12. Kenneth Eaton: The Fundamentals of Automated Theorem Proving 2019 
  13. Megan Meyer: An Experimental Approach to Sophie Germain Sequences 2019 
  14. Addison Carter: An Introduction to Partitions and Compositions 2019 
  15. Rachel Liebrecht: Special Topics on Graph Theory and Ramsey Numbers 2019 
  16. Shannon Tefft: Processing Quadratic Residues with Ducci Iterations 2019 
  17. Jenna Holler: American Mathematics Competitions – Variations and Generalizations 2018 
  18. Joseph Stomps: American Mathematics Competitions AMC 10 - analogies and generalizations 2018 
  19. Matthew Golden: The Baker-Campbell-Hausdorff Formula 2017 
  20. Michelle Haver: Poissonian Character and Chebyshev Bias for GPF Sequences: A Computational Analysis 2017 
  21. Amanda Marco: Fibonacci Numbers and Some of Their Properties 2014 
  22. Matthew R. Zirkle: Finding Square Roots in a Prime Field 2013 
  23. Jonathan C. Schroeder: Small Special Pairs of Primitive Roots 2013 
  24. Donald J. Pleshinger: On a Congruence of Ohtsuka 2013 
  25. Ashley Risch: An Euler-Fibonacci Sequence 2011 
  26. Lauren Sutherland: Multidimensional Greatest Prime Factor Sequences 2011 
  27. Greg Back: The Greatest Prime Factor and its Applications 2010 
  28. Jenna Brace: Traffic Flow Simulation with Cellular Automata 2010 
  29. John Holodnak: The Perron-Frobenius Theorem and Applications 2010 
  30. Sharon Binkley: The One Time Pad and Text Visualization 2009 
  31. Joshua Somerlot: The Affine Cipher 2009 
  32. Andrew Homan: An Overview of Model Theory and Completeness 2007 
  33. Allison Mackay: Elementary Number Theory and Classical Cryptography 2006 
  34. Lisa Scheckelhoff: GPF Sequences 2006 
  35. Brandon Bucholtz: The Euclidean Algorithm 2006 
  36. Jacob L. Johanssen: Fibonacci-Lucas Densities 2006 
  37. Nathan Baxter: Finite Fields 2005  
  38. Sara Miller: Fibonacci Numbers 2003


 

August 12, 2024

Ada, Ohio - brief historical highlights

 Brief history Ada, OH, from https://en.wikipedia.org/wiki/Ada,_Ohio

"Ada is a village in Hardin County, Ohio, United States, located about 69 miles (111 km) southwest of Toledo. The population was 5,334 at the 2020 census. It is the home of Ohio Northern University and Ada High School. 

History 

Following the 1817 Treaty of Fort Meigs, the Shawnee Indians held reservation land at Hog Creek near Ada. Ada itself was originally called Johnstown, platted in 1853 by S. M. Johnson when the railroad was extended to that point. When a post office was established it was called Ada Post Office, named after the postmaster's daughter, Ada. The post office has been in operation since 1854.The growth of the village is due in large part to the founding of the Ohio Normal School, now known as Ohio Northern University. The University was founded in 1871 by Henry Solomon Lehr, just eighteen years after Ada was first settled. Today, Ada is the second largest incorporated community in Hardin County. In 1910, President William Howard Taft visited Ada, to give the fall commencement speech at Ohio Northern University. To date, Taft is the only president to visit the village. Ada welcomed Martin Luther King Jr. to the village in January of 1968, just three months before his assassination. Ada has been noted for having one of the shortest place names in Ohio. The National Arbor Day Foundation has qualified Ada as a Tree City USA since 1981."

August 10, 2024

Brief history of Kenton, Ohio

Brief history of the local county seat - Kenton, OH, from https://en.wikipedia.org/wiki/Kenton,_Ohio

"Kenton is a city in and the county seat of Hardin County, Ohio, United States, located in the west-central part of Ohio about 57 mi (92 km) northwest of Columbus and 70 mi (113 km) south of Toledo. Its population was 7,947 at the 2020 census. The city was named for frontiersman Simon Kenton of Kentucky and Ohio. 

History

Kenton was originally the site of Fort McArthur, erected in 1812 by Colonel Duncan McArthur as one of the forts along the line of General William Hull's march against the British headquarters at Fort Detroit during the War of 1812. 

In 1845, Kenton was incorporated as a village; it became a city in 1886. The city was named after frontiersman Simon Kenton. The city began as a center for agricultural trade, then in the late 19th century, developed industry common to America of the time.

From 1890 to 1952, Kenton was home to the Kenton Hardware Company, manufacturers of locks, cast-iron toys, and the very popular Gene Autry toy cap guns. International Car Company, a manufacturer of rail cabooses, operated in Kenton for many years. In 1975, it was purchased by Paccar, a manufacturer of medium- and heavy-duty trucks. In 1983, Paccar closed down the business, noting a decrease in demand for rail equipment. The 2001 CSX 8888 incident involving an unmanned freight train ended in Kenton."


 

August 3, 2024

Math Education: "more than good grades and test scores..."

An interesting article at The Conversation:

Real equity in math education is about more than good grades and test scores - by Megan Staples, Associate Professor of Mathematics Education, University of Connecticut

"With more than three decades of experience as a researcher, math teacher and teacher educator, I advocate for expanding what equity means in mathematics education. I believe policymakers and educators should focus less on test scores and grades and more on developing students’ confidence and ability to use math to make smart personal and professional decisions. This is mathematical power – and true equity."

Read the full article at  

https://theconversation.com/real-equity-in-math-education-is-about-more-than-good-grades-and-test-scores-215518  

July 3, 2024

With Fifth Busy Beaver, Researchers Approach Computation’s Limits (Quanta Magazine)

Turing Machines


With Fifth Busy Beaver, Researchers Approach Computation’s Limits

After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get.

QUANTA MAGAZINE - https://www.quantamagazine.org/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702/

June 24, 2024

AI Will Become Mathematicians’ ‘Co-Pilot’

AI Will Become Mathematicians’ ‘Co-Pilot’ 

Fields Medalist Terence Tao explains how proof checkers and AI programs are dramatically changing mathematics 

By Christoph Drösser - https://www.scientificamerican.com/article/ai-will-become-mathematicians-co-pilot/ (June 8, 2024)

June 20, 2024

A Position of the National Council of Teachers of Mathematics - AI and Mathematics Teaching

 A Position of the National Council of Teachers of Mathematics

Artificial Intelligence and Mathematics Teaching

https://www.nctm.org/standards-and-positions/Position-Statements/Artificial-Intelligence-and-Mathematics-Teaching/

NCTM Position 

Artificial Intelligence (AI)-driven tools can respond to students’ thinking and interests in ways that previous tools could not. By drawing from large language sets, AI has the potential to adjust application-based problems to student interests and identify the sense students have made even in their incorrect answers. Students will continue to need teachers’ mathematical, pedagogical, and relational expertise, though teachers are also likely to benefit from AI-driven tools. In some cases, AI may serve as a teaching assistant, but students will need teachers to help them create a bridge between prior knowledge, new knowledge, and shared knowledge. Teachers must tell students to be very skeptical about AI results, especially about the unique challenges of using tools that may have been trained on biased datasets. This skepticism can be woven into existing pedagogical and assessment techniques. Knowing this, educators need to be involved in developing and testing AI tools in math education to stay up to date with current AI trends to best prepare students for an AI future. Contrary to some popular opinions, this effort will require teachers with even deeper knowledge of math instruction and assessment—math teachers with more experience, not less.

June 7, 2024

Mark Twain on cats

“That's the way with a cat, you know -- any cat; they don't give a damn for discipline. And they can't help it, they're made so. But it ain't really insubordination, when you come to look at it right and fair -- it's a word that don't apply to a cat. A cat ain't ever anybody's slave or serf or servant, and can't be -- it ain't in him to be. And so, he don't have to obey anybody. He is the only creature in heaven or earth or anywhere that don't have to obey somebody or other, including the angels. It sets him above the whole ruck, it puts him in a class by himself. He is independent. You understand the size of it? He is the only independent person there is. In heaven or anywhere else. There's always somebody a king has to obey -- a trollop, or a priest, or a ring, or a nation, or a deity or what not -- but it ain't so with a cat. A cat ain't servant nor slave to anybody at all. He's got all the independence there is, in Heaven or anywhere else, there ain't any left over for anybody else. He's your friend, if you like, but that's the limit -- equal terms, too, be you king or be you cobbler; you can't play any I'm-better-than-you on a cat -- no, sir! Yes, he's your friend, if you like, but you got to treat him like a gentleman, there ain't any other terms. The minute you don't, he pulls freight.” 

Mark Twain, ‘The Refuge of the Derelicts’

Agrocybe praecox

 


May 3, 2024

Carl Sagan - food for thought


The cosmos is within us. We are made of star-stuff. We are a way for the universe to know itself.” 

~Carl Sagan

May 1, 2024

Way More Animals Than Assumed (Including Insects) May Have Consciousness, Scientists Argue

“There is sufficient evidence out there such that there’s a realistic possibility of some kinds of conscious experiences in species even quite distinct from humans.” 

Read the full article at

https://www.iflscience.com/way-more-animals-than-assumed-including-insects-may-have-consciousness-scientists-argue-73907

April 26, 2024

Asimov on belief adjustment

 

"So the universe is not quite as you thought it was. You'd better rearrange your beliefs, then. Because you certainly can't rearrange the universe" ~Isaac Asimov

April 1, 2024

March 24, 2024






Always in my heart, Fluffy!
At our other house, March 24 2024

March 23, 2024

February 7, 2024

130 years of mind games and quantum challenges

 A wonderful article by Laurie Wurth-Pressel (source)

130 years of mind games and quantum challenges

graphic showing Benjamin Finkel, a mathematic trailblazer

2024 marks the 130th anniversary of The American Mathematical Monthly. 

The trailblazer who launched this premier academic journal in 1894 and inspired the establishment of the American Mathematical Association (AMA) graduated from Ohio Northern University in the late 1800s—Benjamin Franklin Finkel, BS 1888, BA 1896.

Mathematical problems fascinated Finkel from a young age, and his eagerness to solve them impelled his ambition to “publish a journal devoted solely to mathematics and suitable to the needs of teachers of mathematics.”

He once stated: “Many dormant minds have been aroused into activity through the mastery of a single problem.” 

Over a century later, Finkel’s statement still rings true. 

While much has changed at Ohio Northern since Finkel’s days, the University continues to attract brilliant problem-solvers molded in Finkel’s character who graduate to become leading mathematicians and physicists. 

Read about three outstanding alumni from ONU’s School of Science, Technology, and Mathematics, housed in the Getty College of Arts & Sciences, who are making a mark in the world of physics and mathematics.

Photo of Tommy SteinbergerFrom algebra to plasma physics

Thomas (Tommy) Steinberger, BS ’14, Ph.D., is breaking new ground in experimental plasma physics at West Virginia University in Morgantown, W.V.

A research assistant professor in the Department of Physics and Astronomy, he explores charged gas systems (plasmas), investigating gas particle motion and temperature. His work aims to enhance electronics manufacturing, space travel, and our understanding of space phenomena, such as magnetic reconnection.

“I come into the lab and can work on 10 different projects before lunch,” he said. “I have a lot of ongoing projects that are unique. Most of my effort is helping all these projects move forward.”

Steinberger’s journey began in freshman Algebra class in high school. While his classmates bellyached about having to solve 50 of the 100 algebra problems listed in the final exam, he felt a burst of excitement.

 “I completed nearly all 100 in a couple of days, almost obsessively,” he recalled. 

His ONU experience further ignited his passion for problem solving. He joined ONU-SOLVE, a problem-solving group of students that tackle the challenging problems found in leading math magazines such as Fibonacci Quarterly, Mathematics Magazine, The College Mathematics Journal, and Finkel’s own The American Mathematical Monthly.

ONU-SOLVE has been recognized multiple times in recent years for submitting correct solutions, and several have been published in leading journals as the most well-written solutions, according to Mihai Caragiu, Ph.D., professor of mathematics.

According to Steinberger, several solutions he worked on with the assistance of ONU professors received honorable mentions in academic magazines.

“My time at ONU really fostered my interest in math and its application to other fields,” he said. “I received fantastic instruction from professors who truly cared about their students.” 

After graduating from ONU with a double major in mathematics and physics, and minor in astronomy, Steinberger received a master’s degree in physics and astronomy, and a Ph.D. in experimental plasma physics from West Virginia University. 

“The challenge of the subjects (math and physics) resonates with my stubborn nature,” he added. “It leads me to be ever more persistent in my studies.”

Photo of Ashley ErnstFrom jigsaw mastery to national defense

Ashley Ernst, BS ’15, Ph.D., is a senior physicist at Arcfield in Colorado Springs, Colo, where she helps to solve complex challenges in support of the United States’ most critical national security missions.

Arcfield is a leading provider of mission-focused systems engineering and integration capabilities to the U.S. Intelligence Community, Department of Defense, and other agencies.

Ernst is currently working primarily with simulation and modeling of radiation in both vacuum and in atmosphere or material. She develops technical documentation, presents work to clients, and performs calculations with the aid of software.

“There is always another problem on the horizon,” she says. “The quest for the solution to the next problem is what drives me every day.”

Growing up, Ernst loved to solve jigsaw puzzles with her mom. As her skill increased, so did her hunger for harder challenges.

“They became larger in puzzle number, smaller in puzzle piece size, and more complex in shape and design,” she said. “When that wasn’t enough, I started solving puzzles without guide pictures.”

When she first arrived at ONU, however, she lacked focus and felt extremely homesick. Her ONU professors noticed her struggles and made special efforts to engage her in math conferences and ONU-SOLVE. Professor Caragiu spurred her mind into action by exposing her to Graph Theory and Discrete mathematics.

“Having a direction for my mental energy definitely helped me,” she said.

Within a short time, she says, she was on a better path forward. “I would not be where I am today without their help. The math and physics programs at ONU nurture the search for knowledge. No matter the level, the program meets the student at that level and pushes them to the next level.”

After graduating from ONU with a double major in physics and applied mathematics, Ernst earned a master’s degree in physics and a Ph.D. in hadronic physics from Florida State University. Her second year of graduate school, she received a highly-competitive National Science Foundation (NSF) Graduate Research Fellowship, which she credits to the quality of education and one-on-one mentoring she received at ONU.

“Each student that passes through the math program at ONU is instilled with a sense of excitement regarding a problem. While that problem may change, that excitement stays,” she said. 

Photo of Matthew GoldenFrom twisty puzzles to cosmic enigmas

Matthew Golden, BS ’17, Ph.D., is a postdoctoral fellow at the Georgia Institute of Technology in the Xtreme Astrophysics group. The group is led by two founding members of the Event Horizon Telescope Collaboration, which released the first image of a black hole in 2019.

“I am a full-time researcher,” he said. “My research focuses on the interface of machine learning and physics. Specifically, I work on using machine learning to accelerate human learning. Our goal is to produce physics equations directly from complex data with minimal human intervention.” His recent publication in Science Advances showed how machine learning learned the equations of a living fluid directly from a video of the experiment.

In high school, Golden became enthralled with solving “twisty puzzles”—think Rubik’s cube, only the more complicated versions. He had puzzles of every platonic solid and with hundreds of pieces. Some would take him mere minutes to solve, others weeks.

“I eventually went on to solve the four-dimensional 3x3x3x3 Rubik’s cube,” he said. “You can find my name in the 4D Hall of Fame as solver #196.”

At ONU, his obsession switched to General Relativity. He spent many late nights in the Mathile Center for the Natural Sciences working through derivations. Then, he’d head to the third floor of Heterick Memorial Library, pull a random math or physics book from the shelf, and read until he was “hopelessly confused.” 

“My schooling was significantly accelerated compared to the usual undergraduate,” he said. “That’s because the physics department was small and the teachers eager to teach at any pace.”

His professors allowed him to take courses in any order he desired. He completed Quantum Mechanics his first semester, then continued to grow his knowledge in leaps and bounds. He’ll never forget being the only student in Dr. Khristo Boyadzhiev’s Real Analysis class. Dr. Boyadzhiev, who obtained YouTube fame for his consistent classroom outfit and greeting, passed away in June 2023.

“It feels like half the people my age know Dr. Khristo Boyadzhiev because of his lovable appearance on Vine,” said Golden. “He was a micro celebrity, and I still remember him laughing about it in the hall.”

Golden also recalls leading a small group of students to first place in the 2017 Ohio MAA Leo Schneider Team Math Competition, dethroning Case Western Reserve University for the first time in many years. 

With accelerated learning and one-on-one attention, Golden says he was way ahead of his peers in graduate school. 

“The education I received was passionate and tailored to me,” he said. “There is no math program in the Midwest that could compete with the personal attention I received at ONU, and it paid off.”

He’s ecstatic that his professional career is centered on gravity research.

“I love that every day I get to think about machine learning and extreme astrophysical environments,” he said. “I get to interact with some of the greatest minds in physics.”

January 31, 2024

Fluffy is back. A genuinely zen cat.

Being still aware of the pervading impermanence, and still having Fluffy forever in our hearts whether alive with us, or alive in the forest, or traveling who knows where, or over the rainbow, the thing is that Fluffy IS BACK after ~10 days, yay. 

A very strange and wonderful cat. 

She was totally unfazed. A zen cat.

I took a photo after serving her a celebratory late dinner with whipped cream.


 

January 30, 2024

Fluffy, our sweet Norwegian forest cat

Unfortunately, it is possible that our sweet, proud, loving but strongly independent, Norwegian forest cat Fluffy (with us for more than 9 years) crossed the rainbow bridge. She disappeared on January 22, 2024. 

We can only hope, being aware at the same time that nothing is permanent. The love for her is and will remain forever in our hearts. 

Until we meet again.