MAT 300                                        

Spring 2004                            Review for the Final Exam   

The final examination for both sections is Tuesday,  May 18, from 6:00-8:00 pm,  in our regular classroom.   The closed-book part of the exam will be drawn from this review sheet.  There will be no essay questions on the in-class part of the final exam; there is a take-home part to the final consisting of one-three essay questions. 

There will also be an open-book and open-note part to the exam, which will be done after the closed book part of the exam on Tuesday.   This part of the exam may include material not on the review sheet.

You may bring and use on the closed-book part two 3²´5² cards with the following information.

One 3²´5² card with the names and dates of any person you want.

One 3²´5² card with the names only of any works that you want.  The names of the works should be written in one color, equally spaced, with no additional lines drawn to separate and/or group the names.  I will accept either the original names of the work or an accepted English translation.  Dates and associated mathematicians should NOT be included.

I will check the cards during the exam, so do not write any additional information on the cards before or during the exams.  Please put your names on the cards, as I may collect them.

In general, dates within 40 years will be accepted for dates after 1350 CE and dates within 75 years for dates before 1350 CE; more leeway will be given when we are talking about things occurring over a period of centuries rather than events occurring over periods of less than a century.  However, incorrect chronological ordering of events, dates when people lived, etc., will be penalized.

            GOOD LUCK!

1.         IDENTIFICATIONS.  Be able to give two different mathematically significant facts about each of the following.  Do not just give general statements, e.g., "He was an astronomer."; cite specific  accomplishments or works.  If you cite a work, be able to write a sentence describing its contents or why it was historically or mathematically significant.  Also, be able to give the approximate dates of the person's life.   

a.                   Pythagoras

b.                  Archimedes

c.                   al-Khwarizmi

d.                  Leonardo of Pisa (Fibonacci) – (Do not use the Fibonacci sequence unless you state the entire problem.from Liber Abaci.)

e.                   Cardano

f.                    Kepler

g.                   Fermat

h.                   Newton

2.         IDENTIFICATIONS.  Be able to give one mathematically significant fact about each of the following.  Do not just give general statements, e.g., "He was an astronomer"; cite specific accomplishments or works.  If you cite a work, be able to write a sentence describing its contents or why it was historically or mathematically significant.  Also, be able to give the approximate dates of the person's life.

a.         Euclid

b.           Apollonius

c.            Stevin

d.           Viete

e.            Napier

f.             Descartes

g.            Pascal

h.            Leibniz

i.              Euler

j.             Gauss

3.                  IDENTIFICATIONS for the non-L section only.  Be able to give one mathematically significant fact about each of the following.  Do not just give general statements, e.g., "He was an astronomer"; cite specific accomplishments or works.  If you cite a work, be able to write a sentence describing its contents or why it was historically or mathematically significant.  Also, be able to give the approximate dates of the person's life.

 

a.                   Eudoxus

b.                  Diophantus

c.                   Brahmagupta

d.                  al-Biruni

e.                   al-Khayyami

4.         The history of Western mathematics may roughly be broken up into six periods:

 i.         Ancient (Egyptians and Babylonians)

 ii.         Greek (Hellenic and Roman)

 iii.        Medieval (including the Arabic and Hindu)

 iv.        Renaissance ( 1300 - 1600 CE)

 v.        Early modern ( 1600 - 1825)

 vi.        Modern (1825-present)

Know and be able to briefly discuss two major works from each of the periods except for the Ancient and the Modern (1825-present), and know the historical and mathematical significance of each of your chosen works.  The works should be of major mathematical significance, either with respect to content or historically, or be characteristic of the time period, or both.  These may be works that will be used in the answers of other questions on the test.

5.         Students in Section 01, the non-L section, should be able to do the following problems as part of their required material on the closed-book part of the exam.   Also, some of these questions will appear as an EXTRA  CREDIT question on the exams for BOTH sections, but except  for that, these problems will not appear as required  problems on the L-section final unless they are part of the open-book part of the exam.  I reserve the right to give additional questions of this type of the open-book part of the exam, in particular if you are given the option to choose another question.

A.        Multiply using the Egyptian method, but you can use our number system.

B.         Give geometric interpretations of       a(b+c) = ab + ac
                                                      and      (a+b)² = a² +2ab + b².

C.        Know the geometric statement of the Pythagorean Theorem and the geometric proof of the Pythagorean Theorem discussed in class.

D.        Solve an equation of the form x² + ax = b, using the completing-the-square method of al-Khwarizmi.

E.         Multiply two numbers using the lattice method.

F.                  Interpret cubic polynomial expressions written using the notation of Viete.  I will give you the expressions in the historical form; you will only need to translate them into modern notation.  However, on the open-book part of the exam, I may ask you to go in the opposite direction.

 

G.                 For an expression of the form y=xⁿ for n=1,2,3 or 4, be able to find either the fluxion using the method of Newton or the differential dy using the method of Leibniz.

 

THE END!!