M425 Assignments/Study Guide 2 - Spring 2002

Here L1, L2, etc. refer to lectures (i.e. chapters) in the text. The dates shown are when assignments are made. The assigned readings, problems, and questions may be discussed at the next class meeting.

Day 12 - Monday February 11 -- Ptolemy
- Read L10
- Write up exercises 10.1, 10.2, think about term project
- Study questions:
  - Describe the early history of trigonometry. Why was trigonometry important?
  - What is Ptolemy's theorem? How is it proved?
  - What important trig results follow from Ptolemy's theorem?
Day 13 - Wednesday February 13 -- Diophantus
- Read L11
- Write up exercises 11.6(a,d,e,f), 11.7(a,d), think about term project
- Study questions:
  - Define and contrast the terms arithmetic, logistic, and number theory.
  - Describe some sets of special integers.
  - What was the most famous problem in the Arithmetica of Diophantus, and why?
Day 14 - Friday February 15 -- Descartes, Euler
- Read L12 and L13
- Write up exercises 13.2, 13.3, think about term project
- Study questions:
  - Describe three stages in the development of algebra.
  - Show how we can now solve typical early algebra problems, such as distribution, age, work, cistern, mixture problems.
  - Describe some of the strange notational conventions used in early algebra.
  - Describe some contributions of Descartes and Euler to our modern notation.
  - How, where, and when did our modern number system come into existence? How and when did it come into widespread use in the West?
  - How were computations carried out before the modern system?
  - Describe the history, structure, and function of the abacus.
Day 15 - Monday February 18 -- Omar Khayyam
- Read L14
- Write up exercises 14.1, 14.2, 14.3, think about term project
- Study questions:
  - When and where did Omar Khayyam live, and what is he most famous for?
  - What is Omar Khayyam famous for in mathematics?
  - Describe the importance of Arab mathematicians during the dark ages. When was that?
  - What is the rule of false position? Give an example of its use.
  - Describe the process followed to solve cubic equations geometrically.
Day 16 - Wednesday February 20 -- al-Khowarizmi, Fibonacci
- Read L15
- Write up exercises 15.3, 15.7, think about term project
- Study questions:
  - Who wrote the first Arab arithmetic known to us? What mathematical terms stem from that author and book?
  - What is Fibonacci known for? When and where did he live?
  - What is the Fibonacci sequence? Where does it turn up?
Day 17 - Friday February 22 -- Cardano, Tartaglia
- Read L16
- Write up exercises 16.1, 16.2, think about term project
- Study questions:
  - Why do we have another chapter about solving cubic equations?
  - Who was involved? When? Where?
  - Describe in a general way the solutions given. What other problems were solved this way?
  - What general theory was developing in these efforts? What was the final outcome?
Day 18 - Monday February 25 -- Briggs, Napier
- Read L17
- Write up exercises 17.2, 17.3, 17.7, think about term project
- Study questions:
  - What important computing tool was invented in Scotland around 1600? By whom?
  - What does the word logarithm mean?
  - Who helped make logarithms into the form we have today?
  - Why were logarithms important?
  - Explain mantissa, characteristic, and operation of a slide rule.
  - Describe the operation of Napiers rods. (See ex.17.6, Fig. 58)
Day 19 - Wednesday February 27 -- Galileo, Kepler
- Read L18
- Write up exercises 18.1, 18.7, 18.10, think about term project
- Study questions:
  - Describe some of the discoveries of Galileo. What field were they mostly in?
  - Describe some of the discoveries of Kepler. What field were they mostly in?
  - What information did Kepler use to make his discoveries?
Day 20 - Friday March 1 -- Cavalieri
- Read L19
- Write up exercises 19.1, 19.7, think about term project
- Study questions:
  - When and where did Cavalieri live?
  - What are Cavalieri's principles? Why are they important?
  - Give examples of their use.
  - Explain Cavalieri congruence.
Day 21 - Monday March 4 -- DO FOR FRIDAY -- Descartes
- Read L20
- Write up exercises 20.5, 20.7, think about term project
- Study questions:
  - Explain what is meant by transform-solve-invert.
  - Describe the invention of analytic geometry.
  - List the steps in a typical analytic geometry proof.
  - Give analytic proofs of several geometry theorems.
Day 22 - Wednesday March 6 - EXAM 2 (NOTEBOOKS DUE TODAY)
- No new assignment.
Day 23 - Friday March 16
- We will discuss L20. No new assignment. Enjoy Spring Break.

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