Math 660 GEOMETRY I
SOLUTION FOR EXTRA CREDIT HOMEWORK I (09/12)
September 24 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (20pts)
(1)
Consider the system
x1 x6 = 0,
x8 + x9 = 0,
x3 x8 =
Math 660 GEOMETRY I
CRASH COURSE ON THE COMPLEX NUMBER FIELD I
December 3 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
31. Introduction to Complex Numbers. Arithmetic. Commutativity.
As you m
Math 660 GEOMETRY I
FINAL EXAM (Take-home)
December 10 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
ID # :
Name :
This take-home part of Final Exam is worth 200 points and is
due Monday, Dece
Math 660 GEOMETRY I
REVIEW OF LECTURES II
August 26 (Wed), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
2. Models.
Today, I want to talk about models. Models, as in geometric models. Not
supermodels
Math 660 GEOMETRY I
REVIEW OF LECTURES III
August 31 (Mon), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
3. Projective geometry.
How are you, everyone? Last time I told you there is actually a plane
Math 660 GEOMETRY I
FINAL EXAM (Take-home)
December 10 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
ID # :
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Name :
This take-hom
Math 660 GEOMETRY I
SOLUTION FOR QUIZ VI (10/19)
October 26 (Mon), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
[I] (10pts)
(1)
The equation of the tangent line to the curve
XY + 3 Y Z Z 2 = 0
insid
Math 660 GEOMETRY I
REVIEW OF LECTURES VI
September 14 (Mon), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
6. Intersection of two lines in P2 .
Intersection of two lines.
Here we go, finally:
In P2
Math 660 GEOMETRY I
REVIEW OF LECTURES IX
September 16 (Wed), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
9. Projective 3-space.
Projective 3-space.
Today I would like to show you how the picture
Math 660 GEOMETRY I
REVIEW OF LECTURES VII
September 14 (Mon), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
7. Duality.
Duality.
Last time we have proved that two lines always intersect in P2 . Tod
Math 660 MODERN GEOMETRY I
REVIEW OF LECTURES IV
September 2 (Wed), 2015
Yasuyuki Kachi
Instructor:
Line #: 25941.
4. Homogeneous coordinate.
Last time we were examining how a line in an xy-coordinate
Math 660 GEOMETRY I
REVIEW OF LECTURES V
September 9 (Wed), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
5. P2 as a completion of an xy-plane.
We are in the process of building a geometry where a ra
Math 660 GEOMETRY I
REVIEW OF LECTURES VIII
September 16 (Wed), 2015
Instructor:
Yasuyuki Kachi
Line #: 25941.
8. Incidence.
Incidence.
Now we have addressed two major questions that naturally arose
Math 660 GEOMETRY I
REVIEW OF LECTURES XXIX
November 21 (Thu), 2013
Yasuyuki Kachi
Instructor:
Line #: 26471.
29. Linear span III.
Now it is almost clear how to generalize the notion a linear span for
Math 660 GEOMETRY I
SOLUTION FOR MIDTERM EXAM I (In-class; 10/22)
October 22 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (20pts)
(1)
Let
y, z
be the ane coordinate of A2 inside P2 (X :Y
Math 660 GEOMETRY I
SOLUTION FOR QUIZ I (09/12)
September 17 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (4pts)
(1)
Homogenization of
X:Y :Z
(2)
=
=
1:
:Z
x , z
Homogenization of
1
,
2
Math 660 GEOMETRY I
SOLUTION FOR QUIZ II (09/24)
September 26 (Thu), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (20pts)
(1)
In P2 (X :Y :Z ) :
Identify the point of intersection of the two lin
Math 660 GEOMETRY I
SOLUTION FOR QUIZ III (09/24)
September 26 (Thu), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (20pts)
(1)
In P2 (X :Y :Z ) :
The dening equation of the line that passes thro
Math 660 GEOMETRY I
SOLUTION FOR QUIZ IV (10/03)
October 8 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (20pts)
In P3 (X :Y :Z :W ) :
1 :
4X 2Y +
(1)
X+
7X +
Z 3W
Y + 2Z
= 0,
W
= 0,
Y +
Math 660 GEOMETRY I
SOLUTION FOR QUIZ VI (10/17)
October 22 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (10pts)
(1)
The equation of the tangent line to the curve
XY + 3 Y Z Z 2 = 0
insid
Math 660 GEOMETRY I
SOLUTION FOR QUIZ VII (10/29)
October 31 (Thu), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (20pts)
(1) The two lines and , both residing in P3 (X :Y :Z :W ) , whose
Plcker
Math 660 GEOMETRY I
SOLUTION FOR QUIZ VIII (10/31)
November 5 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
[I] (15pts)
(1)
True or false :
In P3 , two lines always intersect.
The answer is
Math 660 GEOMETRY I
REVIEW OF LECTURES XXVII
November 19 (Tue), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
27. Linear span I.
The end of the semester is approaching. It was quite a journey. At the
Math 660 GEOMETRY I
REVIEW OF LECTURES XXVIII
November 21 (Thu), 2013
Instructor:
Yasuyuki Kachi
Line #: 26471.
28. Linear span II.
Last time we covered the notion of a linear span for three distinct
Math 660 GEOMETRY I
REVIEW OF LECTURES XXX
November 26 (Tue), 2013
Yasuyuki Kachi
Instructor:
Line #: 26471.
30. Linear span IV.
Lets review the formal denition of the linear span from last time:
Assu