How I Beat Parkinson's
 
Math And Such

Mathematical Books, Games and Apps
 
   
Mathematical Vignettes

Now available on Amazon.com.

Mathematicians Don't Work with Numbers!

Upon hearing that I am a mathematician people often say to me, "You must be good with numbers." There is really no response to this, for how do I explain that numbers are not the subject of modern mathematics? Sometimes mathematicians do indeed work with numbers but in such cases the numbers themselves are never the point.

Mark Kac was a mathematician recruited to work on the Manhattan Project, the secret WWII project that developed the atom bomb. Everyone working on the Manhattan Project had to reduce their theoretical results to numbers, for otherwise a machinist would not know what to make nor how big to make it. No general methods would suffice here, numbers were paramount. Kac captured this sense of mathematicians getting their hands dirty, figuratively speaking, by humorously commenting that he was reduced to working with numbers and, even worse, some of them actually had decimal points!

The Manhattan Project was an important special case and no one working on it chose to do anything else, but that is not what professional mathematicians otherwise do. The next time (the first time?) you meet a mathematician say something different like, "What branch of mathematics do you work in?" Any mathematician worth his salt will answer by saying, "I work in _____, which has applications to _____." Yours will be a much better opening statement than if you say what comes across as, "Golly gee whiz, you must be good with numbers!"

In the meantime, this book is my answer to the question, what do mathematicians work with? It consists of mathematical "vignettes", most being an elementary and brief description of one part of mathematics. Some vignettes use numbers but you will see they are incidental to the general principles involved.
 
 
   
The First Seven Days
Limits and Continuity: Bridging the Gap between Algebra and Calculus

Now available on Amazon.com.

Calculus is often called Infinitesimal Calculus, even when it is developed using limits and there are no infinitesimals. The historical confusion between the two formulations is finally untangled.

These seven chapters can be covered in seven lectures in a formal course or in seven sessions for self-instruction.

The opening chapter "All the Preliminaries" lays the groundwork for the rest of the book.

The next chapters. "What is the Problem?" and "Developing a New Intuition", make plain the mathematical obstacles that caused a two- century delay between the invention of calculus and the first rigorous formulation of the subject.

The succeeding chapters, "Limits: A First Attempt at Rigor" and "Limits: Rigor That Works" show why the more obvious definition does not work and why the modern definition solves that problem.

The final chapters, "Continuity: The Key to Everything" and "Derivatives: Putting It All Together", launch the student into calculus with a solid understanding of the limit-based formulation and how it differs from the infinitesimal-based formulation.
 
 
List - A Handy Utility
Program List.exe is a free Windows utility for viewing the contents of any file in hex and ASCII. It contains its own documentation. It is highly recommended that you put a link to List.exe in folder shell:sendto.
 
Explore Chaos Theory
Program Chaos.exe is a free download. Its documentation is Chaos.docx.
 
Morley's Theorem
Program Morley.exe is a free download that needs no documentation. Just try it!
 
Helpful Sudoku for Windows
(Because what the world needs is yet another Sudoku app :)
  • Easiest to play Sudoku app (and we know there are so many out there)
  • Introducing the Expanded Cell providing an easier to use user interface
  • 50,000 minimal puzzles (17 cells specified in each)
  • Visual Import - simply paste an image of a Sudoku game captured with the Windows Snipping Tool from any source
  • Visual Scaling - board size scales with the window size
  • Choice of managing notes yourself or being managed automatically
  • Deep undo/redo
  • Optional auto-complete of singleton chains
  • Four levels of hints with explanations and visual indicators
  • Detection of invalid imported puzzles (produced by a few popular web sites) and display of their multiple solutions
  • Highlight cells with a selected note
  • Optionally fill in the solution for selected cell(s) for difficult puzzles
  • Optionally restart a puzzle
  • Print a puzzle
  • Maintains scoring: numbers of moves, hints, hint explanations, and elapsed time
  • Save to a file and restore with all features including cell highlighting, current hint, and undo/redo history
  • Optionally highlight cells in error
  • Text file import in various formats
  • Define your own puzzle
 
While free to download, you are not permitted to distribute Helpful Sudoku in any form. Anyone desiring this app must download it from this site.

Helpful Sudoku scores your game but imposes a point penalty for every bit of help you use. You incur a Penalty mark if you do anything that would otherwise allow you to circumvent this scheme. Anyone with a low score has achieved that legitimately.

The one and only "freebie" is that there is no penalty for highlighting errors - the errors themselves are the penalty.

The lowest score theoretically possible is 64.
How low can you go?

I will put the top ten players and their low scores below.
 
 
Contact me at richard.poulo@mathandsuch.com.