Mathematics 152The Mathematics of Symmetry
Homework #1
Revised September 20, 2008
Required Problems due Thursday, October 2, 2008
Remember that the required problems are handed in Thursdays and the exploratory problems are to be done throughout the semest
Mathematics 152The Mathematics of Symmetry
Homework #4
Revised October 17, 2008
Required Problems due Thursday, October 23, 2008
Section 1. Required Problems
1. Consider the symmetry groups of the tetrahedron, the cube, and the icosahedron. For
each case,
Mathematics 152The Mathematics of Symmetry
Homework #3
Revised October 10, 2008
Required Problems due Thursday, October 16, 2008
Section 1. Required Problems
1. In Z13
(a) what is the additive inverse of [7]?
(b) for what m and n does 13m + 7n = 1?
(c) wh
Mathematics 152The Mathematics of Symmetry
Homework #2
Revised September 20, 2008
Required Problems due Thursday, October 9, 2008
Section 1. Required Problems
1. In the group S6 , how many permutations are of the form (12)(34)(56)? In the group
S7 , how m
Mathematics 152The Mathematics of Symmetry
Homework #6
Revised November 5, 2008
Required Problems due Thursday, November 13, 2008
Section 1. Required Problems
1. In the large ane faculty senate two triangles are Danny-Gavin-Viola (ABC ) and
Helen-Sally-Xe
Mathematics 152The Mathematics of Symmetry
Homework #7
Revised November 15, 2008
Required Problems due Thursday, November 13, 2008
Section 1. Required Problems
1. In a vector space there are two zeroes, the additive identity for the eld F , 0, and
the zer
Mathematics 152The Mathematics of Symmetry
Additional Exploratory Problems
Revised October 28, 2008
Section 1. Exploratory Problems
Exploratory Problems
1. Consider the ring R = F [x], where F is a eld. Suppose a(x), b(x) R are non-zero.
Show that deg (a(
In 1903 Hessenberg proved that Desargues' Theorem in the plane is a consequence of Pappus'
Theorem (which he called Pascal's Theorem). Given that Pappus' Theorem was known in
antiquity and so was Desargues' Theorem (though not by that name) it is remarkab
Mathematics 152The Mathematics of Symmetry
More Exploratory Problems
Revised November 24, 2008
Section 1. Exploratory Problems
1. Prove by induction that if a vector space V is spanned by n vectors v1 , v2 .vn , any
set of n + 1 vectors w1 , w2 ,.wn+1 in
Mathematics 152The Mathematics of Symmetry
Homework #8
Revised December 4, 2008
Required Problems due Tuesday, December 16, 2008
Section 1. Required Problems
1. With the two-component vectors over F4 arranged into lines as in the notes, i.e.
Line 1: multi