Math320 Paper
Coding Theory:
1. Introduction (background, history, etc);
2. How it is related to group theory;
3. Possible research direction in the future.
To start, please read pages 32-35, 52-55, 134-135 on text. May use some of the exercises
as exampl
Prateek Gaur
Term Paper
Math 320
Term Paper: Conjugate Root Theorem
Introduction:
The purpose of this paper is to show a proof of a theorem listed below by using the Conjugate
Root Theorem. The Conjugate Root theorem states that if P is a polynomial in on
Prateek Gaur
Term Paper
Math 320
Term Paper: Conjugate Root Theorem
Introduction:
The purpose of this paper is to show a proof of a theorem listed below by using the Conjugate
Root Theorem. The Conjugate Root theorem states that if P is a polynomial in on
Appendices 1 Appendix I: Matrix Algebra
Here we give a quick summary of matrix algebra needed. Matrices
appear frequently throughout the text in examples and in exercises. For
details, the interested reader is referred to either A Short Course in Matrix
T
Chapter II
Complex Numbers 1 Operations With Complex Numbers-
The cubic polynomial1 originally investigated by Bombelli showed
that complex numbers were not just mathematical “toys”; they have an
important role to play in mathematics. But even after the t
Chapter 111
Basic Background:
Sets, Logic and Induction 1 Set Theory
In this Section we discuss the basic language of abstract (or modern
algebra. We start with the concept of “set”. It is well known among logicians
that every logical system must have som
Chapter IV
Basic Background:
Mappings and Bijections 1 Mappings
In this Chapter we Will discuss the second principal object in modern
mathematics: mapping. (The ﬁrst is: set.) Essentially, mapping is just
another word for the concept of function. The impo
Chapter V
The Fathers of Modern Algebra, In this Chapter we discuss brieﬂy mathematicians of the eight—
teenth and nineteenth centuries who solved the question of ” solving poly-
nomials by radicals”. In doing so they found the connection between that 1
p
Chapter VI:
Binary Algebras: An Introduction In this Chapter we study sets with procedures for combining two
elements at a time to get a third. We are interested in abstracting those
properties common to the various additions —~ for example, of numbers,
o
Math 320 practice Testl
Spring 2013
1. Mark each If the following true of false.
1) An operation * on a set S is commutative if there exist a,b e S such that
a * b = b * a .
2) A group may have more than one identity element.
3) Any two groups of three
Math 320 practice Testl
Spring 2013
1. Mark each If the following true of false.
E 1) An operation * on a set S is commutative if there exist a,b e S such that
a * b = b * a.
I E 2) A group may have more than one identity element.
I 3) Any two groups of
Math 320 Practice Final (ch14-18)
Spring 2013
Mark each lf the following true of false.
_ An equation of the form a x = b always has a unique solution in a ring.
_ Every Ring has a multiplication identity (unity).
_ Let R be the set of all real numbers an
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Math 320 Test Name_
Spring 2013
l. (3pts each part) Mark each of the following true or'false.
Fug/Any element in a group may have more than one inverse.
IKE/Any two groups of seven elements are isomorphic.
/ ,
iaj/Any cychc group may have more than on