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THE  CORUNDUMINIUM

   
 

MATHEMATICAL  PATTERN  AND  DISCOVERY     (062815)

   
 

     This is a work in progress, often intended to lead the viewer through his own investigations to seek a pattern which will solve a problem instead of just giving the answer.  The first page below will tell you more about where I hope to go with this as it develops over the next several months.  At this time (June 28, 2015), we are probably done with this until after the summer (September or October), when I return from gold mining in Montana. 

     If you are mathematically inclined and like to solve "brain teasers", this might give you insights into how to discover the often strange properties of mathematical constructions which the problems rely on for their existence.  

     If I find minor typos, I will probably not change the pages, but major errors and lies will be corrected and the changes will be published.  The date of publication or most recent revision appears after the title of each lesson.

   
       Pages are thumbnailed scans.  Left click on one to open the full resolution image.
   
   Introductory Remarks, Biographical Remarks, Table of Contents, Indices of abbreviations and Symbols   (060615)
 
   
  Lesson 1:  The Postage Stamp Problem   (060615)
 
   
  Lesson 2:  The Potato Weighing Problem   (060615)
 
 
   
  Lesson 3:  Logic and Reasoning   (060615)
 
   
  Lesson 4:  Classes of Numbers, Summation and Product Notation  (060915)
 
 
   
  Lesson 5:  Divisors and Multiples   (060915)
 
 
   
  Lesson 6:  Greatest Common Divisor   (060915)
 
 
   
  Lesson 7:  Least Common Multiple    (060915)
 
 
   
  Lesson 8:  The Euclidean Algorithm and its Unwinding    (060915)
 
 
   
  Lesson 9:  Integer solutions od Equations  X =  MA + NB ,  Axy  +Bx  +Cy = D     (061115)
 
 
   
  Lesson 10: Solutions of the Postage Stamp and Potato Weighing Problems    (061115)
 
 
   
  Lesson 11:  A Problem about Finite Sequences     (061215)
 
 
   
  Lesson 12:  Prime Numbers     (062315)
 
 
   
  Lesson 13:  Prime Factorizations, Fundamental Theorem of Arithmetic     (062315)
 
 
   
  Lesson 14:  Boolean Algebra     (062315)
 
 
   
  Lesson 15:  Bunch Algebra     (062415)
 
 
   
  Lesson 16:  Introduction to Counting Theory     (062415)
 
 
   
  Lesson 17:  Applications to Fractions     (062415)
 
 
   
  Lesson 18:  Rational and Irrational Numbers     (062815)
 
 
   
  Lesson 19:  Number Bases, Repeating Decimals     (062815)
 
 
   
   
  Lesson 96:  Supplemental Problems     (062815)
          
       
   
  Lesson 97:  Selected solutiions to problems not solved in the lessons where they were proposed     (062815)
   
   
  Lesson 98:  Selected Solutions to Problems in Lesson 96
 
   
   
   
  Remarks:    (062815)     
       A second series of notes is planned, which will be more related to precalculus math and elementary calculus, intended to reveal relationships and display techniques not often presented in texts.  These will probably not begin to appear until the fall of 2015 or early 2016.  A new website may be created to hold all the math material, but it will be linked and easy to find. 
       Please let me know what you think of this effort - worthwhile?  Fun?  Educational?  And please let me know if there are any typos, errors, or lies that should be corrected, by email to me at wheierman@corunduminium.com
       Lesson 99 will be devoted to remarks about provenance and bibliographic source information.  It is at this time vacant, but in the fall we will do the research.