IDS 101-30

IDS 101-30 Reading assignments

Last updated 11/12/07

Date Assigned
Date Due
Assignment
Questions
8/23/07 8/24/07 Aaboe Intro - 1.2
  • On page 4, Aaboe talks about "...discovering the patterns of thought of great minds of the distant past." What mind from the distant past would you like to communicate with if you could? Since this is the "ancient" world, consider only people who lived BC.
  • How does the number system on pages 7 and 8 work? How is it similar to or different from ours?
  • Why would the Babylonians use 60 as a base instead of 10?
  • What role does zero play?
8/24/07 8/25/07 Aaboe 1.3, 1.4
  • Confirm that the error in the table on page 12 is really an error.
  • Work problem 1.1 on page 16.
  • Write out numbers from 1 to 30 in base 5.
8/25/07 8/27/07 Aaboe 1.5-1.7
  • On page 22, Aaboe refers to a 20\% annual interest rate as "exorbitant." How does that compare to typical interest rates on credit cards?
  • Why did the Greeks use the Babylonian number system for astronomy?
  • Interpret (2) on page 24. What is going on? Why does the solution work?
  • Page 30 induces me to ask: Why do we call it the Pythagorean Theorem?
8/27/07 8/29/07 Aaboe 2.1, 2.2
  • Why would it have been impossible for Thales to predict a solar eclipse?
  • What is the famous "Pythagorean Theorem"?
  • Try to understand the proof that the square root of 2 is irrational.
  • What was the significance to the ancient Greeks of the existence of irrational numbers?
8/29/07 8/31/07 Aaboe 2.3
  • What do Euclid's axioms mean? That is, try to interpret what they are saying.
  • What is the significance of the "fifth" postulate of Euclid?
  • Try to understand Euclid's proof that there are infinitely many prime numbers.
8/31/07 9/5/07 Aaboe 2.4
  • Try to understand the construction of a 36 degree angle. We will do this construction in class.
9/10/07 9/12/07 Continuing Aaboe 2.4
9/12/07 9/14/07 Crossley 2-10
  • We have evidence that Palaeolithic humans counted. Why did they bother?
  • Based on the evidence in Crossley, do you believe that counting is "instinctive"? Why or why not?
9/14/07 9/17/07 Crossley 1.4-1.6
  • How does one "separate the number from the objects numbered"? (Crossley, p. 11)
  • Chol has words for numbers up to 159,999. Why go that high? Why stop there?
  • Consider the quote from Codrington on page 12. Does English have number words that are attached to specific objects?
  • Page 13: "The Jahai do not count above one." Does that qualify as "counting"?
9/17/07 9/19/07 Crossley, sections 1.9, 2.1, 2.2
  • How large a number can we describe in English?
  • Try to understand Euclid's proof on page 32.
9/21/07 9/24/07 Crossley 3.1, 3.2
  • Decipher the paragraph at the bottom of page 62.
  • What does the quote at the top of page 64 mean?
9/24/07 9/26/07 Crossley 3.3, 3.4, 5.1, 5.2
  • Decipher the "rule" on page 64 for solving quadratic equations.
  • Determine the relationship between the figure on page 67 and the rule.
  • Figure out the long examples on pages 67 and 68.
  • Were irrationals problematic for the ancient Greeks? (See Chapter 5.)
9/26/07 10/3/07 Crossley, section 3.5
10/3/07 10/5/07 Crossley, sections 5.3-5.4
10/5/07 10/8/07 Crossley, sections 5.5-5.7
10/8/07 10/10/07 Crossley, sections 5.8, 5.9
  • Draw figures for the first four pentagonal numbers.
  • Page 127 gives a rather foreign way (to our minds) of thinking of numbers and magnitudes. Decipher these descriptions.
  • How does the "Euclidean Algorithm" work?
  • What is the significance of the figures at the bottom of page 130?
10/10/07 10/12/07 Crossley, sections 6.1, 6.2, 6.9, Epilogue
  • Explain Archimedes' axiom.
  • What does Proclus mean by "infinite divisibility"?
  • Work through the algorithm for determining a decimal approximation of the square root of 3. (See page 135.)
  • Consider the largest paragraph on page 152. What is Crossley saying?
10/12/07 10/15/07 Martzloff, forewords, preface, and pp. 13-16
  • What differences do you notice immediately between "Western" and "Eastern" mathematics?
  • What similarities are there?
  • What does your book smell like?
10/15/07 10/17/07 Martzloff, chapters 4, 5
  • What properties characterize ancient Chinese texts?
  • What further similarities and differences do you observe (compared to western mathematics of the time)?
10/24/07 10/26/07 Martzloff, chapter 8 and pages 89-101
  • What distinguishes mathematicians from non-mathematicians?
  • What distinguishes Chinese mathematicians from European mathematicians?
  • page 90, number 6: What does he mean?
  • page 91: "The negative numbers of the Chinese are not the same..." What is the difference?Interpret the problems and solutions on pages 94-95.
  • What does the table on page 99 mean?
10/26/07 10/29/07 Martzloff, pages 123-136
  • What is the relationship between the problem on page 127 and the Pythagorean Theorem?
  • What is in the JZSS?
  • Continued theme: what differences do you notice from European mathematics?
10/29/07 10/31/07 Martzloff, pages 179-190
  • Try to represent 37165 using the pictograms on pages 180-181.
  • Try to understand the series on page 187. When are they used? Why?
  • Continued theme: what differences do you notice from European mathematics?
10/31/07 11/2/07 Martzloff, pages 191-200
  • Why are ancient Chinese units defined the way they are?
  • page 194: "...should be afraid..." Why?
  • Understand the algorithm beginning at the bottom of page 194.
  • What are "joker units"?
  • What do you think of the words behind the unit names? (See page 198, for example.)
11/2/07 11/5/07 Martzloff, pages 200-208
  • How does the Chinese view of negative numbers differ from the European view? Why?
  • How does zero appear in ancient Chinese mathematics?
11/7/07 11/9/07 Martzloff, pages 209-216
  • What else were counting rods used for?
  • What can one compute with an abacus?
11/12/07 11/14/07 Martzloff, pages 273-282