MAT 300-02L                         FINAL EXAM            Name:

Spring 2006                             Take-Home                  E-mail:

 

Due:  6:00pm on Tuesday, May 16, 2006

 

Please do the work on separate paper, except for the matching question,   Over the weekend, I will post a copy of that question separately for you to download and turn in.

 

You may use your book and your notes to do the exam.

 

 

 GOOD LUCK!

 

 

1.         (8 points)  Identify two of the following by giving one mathematically significant fact about each.  Your answer should be several sentences.  Do not just give general statements; cite specific accomplishments or works.   If you cite a work, write a sentence describing its contents or why it was historically or mathematically significant.  Dates, nationalities, and geographical locations are not acceptable answers.

 

a.       al-Khwarizmi (You may not use his method of solving quadratics.)

b.      al- Biruni

c.       Fibonacci

 

 

2..        (12 points)  Identify each of the following by giving one mathematically significant fact about each.  Your answer should be several sentences.  Do not just give general statements; cite specific accomplishments or works.   If you cite a work, write a sentence describing its contents or why it was historically or mathematically significant.  Dates, nationalities, and geographical locations are not acceptable answers.

 

a.  Cardano

b.      Fermat

c.       Newton 

 

 

3.         (18 points/6 points each) The history of Western mathematics may roughly be broken up into six periods:

 

i. Ancient (Egyptians and Babylonians)

ii. Greek

iii. Medieval  (including the Arabic)

iv. Renaissance (1300-1600 CE)

v. Early modern (1600 - 1825 CE)

vi. Modern (1825-present)

 

a.                   List one (1) major work from the Medieval period.  Include the name, the author, and two or three sentences on either the contents of the work or the significance of the work historically.

b.         List one (1) major work from the Renaissance period.  Include the name, the author, and two or three sentences on either the contents of the work or the significance of the work historically.

 

c.         List one (1) major work from the Early Modern period.  Include the name, the author, and two or three sentences on either the contents of the work or the significance of the work historically.

 

4.         (18 points --  6 points each)  Do three of the following five problems, except that you may NOT do both (d) and (e). 

 

a.         Solve the equation   x2 + 8x = 84, using the “geometric” method of
al-Khowarizmi.  Draw the accompanying picture and identify relevant magnitudes.

b.                  Multiply the numbers 458 and 76 using the lattice method.        

c.                   Viete might have written the following equation:

  3Acubus + 8Cplano in A aequetus Dsolido.

Express this equation as we would write it.

d.                  Using the method of Leibniz, find dy when  .

e.                   Find the fluxion of y, , for the function , using the method of Newton.






 

5.         (28 points  2 points each)   MATCHING:  For each person, concept, or thing in the first column I, determine which item in the second column II matches it.  Then put the number of the item in II in front of the corresponding item in I.  There may be more than one correct answer for a given item in I; you need only give me one.  However, you may not use any item in II more than once, so if you use one of those answers twice, one will be immediately wrong. 

 

 

Column I

 

 

Column II

_____ A.

 

Treviso Arithmetic

 

 

1.

 

Considered one of the creators of modern analytic geometry, even though his was not the same as ours.

_____ B.

 

Cardano

 

2.

Considered one of the founders of the theory of probability

_____ C.

 

Stevin

 

3.

Included methods for finding areas and volumes.

_____ D.

 

Napier

 

4.

An early Renaissance textbook on performing common calculations

_____ E.

 

Fibonacci

 

5.

Lost a competition with Tartaglia

_____ F.

Pascal

 

6.

European who helped to introduce the Hindu-Arabic numerals to Europe.

_____ G.

 

Fermat

 

7.

Used the method of infinitesimals

_____ H.

Kepler

 

8.

Trigonometry

_____ I.

Fibonacci

 

9.

Got in trouble with the Church for supporting a heliocentric model of the universe

_____ J.

 

Leibniz

 

10.

Introduced Hindu-Arabic numerals to Western Europe

_____ K.

 

Galileo

 

11.

Logarithms

_____ L.

 

Recorde

 

12.

Decimal fractions

_____ M.

New Solid Geometry of Wine Barrels

 

13.

Elliptical orbits for the planets

______N.

Al-Biruni

 

14.

Connected integral and differential calculus

 

 

 

15.

Invented the “equals” sign, =.

 

 

 

16.

Games of chance

 

 

6.         (6 points)  List three areas of mathematics in which Pierre de Fermat worked.



7.         (6 points)  Through the ages many mathematicians have carried on mathematical correspondence with other mathematicians.  List two pairs of mathematicians who carried on such a correspondence with each other.

 

8.         (12 points)   Sometimes important mathematical “discoveries/creations” are made almost simultaneously.  List three cases in which this happened.  List the discovery/theory  and at least two of the “discoverers”.

 

9.         (6 points)  List two non-Babylonian works in which the writer would have described one of the quadratic equations as a case of  “Squares and roots equal numbers” and give a modern example of such an equation.

10.       (6 points)  List three mathematicians, but no more than one of them Greek, who were involved in the development of trigonometry.

 

11.       (6 points)  List three mathematicians other than Fermat, Newton, and Leibniz who worked on the development of the calculus between 1600 and 1710.





The End!