106 midterm
Instructor: Peter Petersen
Date: Feb 26, 2016
Place: MS 5200
Name
Student number
Section
Instructions:
(1) First read all questions.
(2) Each question carries a weight of 10 points.
(3) No
EXERCISES
1. Prove two theorems attributed to Thales and tell, with reasons, whether or not you think
he may have used similar reasoning.
Prove the Pythagorean theorem. Do you think Pythagoras used yo
1. Describe the sources Euclid probably used in writing the Elements; justify your presump.
tions.
2. Which of the thirteen books of the Elements do you regard as the most important? Justify
your answ
EXERCISES
l.
2.
3.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Describe the evidence on which our estimate of Egyptian mathematics is based. Do you
think that this is likely to be altered by the discovery of
EXERCISES
- 1, The names of Aristotle, Euclid, Archimedes, and Apollonius are associated respectfvély; I,
with those of four powerful rulers—Alexander, Ptolemy, Hiero, and Attalus. Tel
Chapter 10.8
James Gregory
Scotland (1638)
mathematician and astronomer
first achievement:invention of the reflecting telescope in his book Optica promota(failed),
Newton succeed
1664-1668 study m
DIFFERENCES AND INTERPOLATION
PETER PETERSEN
Consider a sequence
a0 , a1 , a2 , ., an , .
Define the sequence of first dierences as
a0 = a1
a0 ,
a1 = a2
a1 , .,
an = an+1
an , .
the second dierences
2
106 midterm
Instructor: Peter Petersen
Date: Jan 29, 2016
Place: MS 5200
Name
Student number
Instructions:
(1) First read all questions.
(2) Each question carries a weight of 10 points.
(3) No electro