ضير 242 ررقم
هتاقيبطتو يطخلا ربجلا
Other sources:
ELEMENTARY LINEAR ALGEBRA
By Howard Anton
هتاقيبطتو يطخلا ربجلا :ررقملا باتكلا
ناحمس نمحرلا دبع فورعم .د : نوفلؤملا
ينابيحسلا الله دبع يلع .د
ريكذلا دمحأ يزوف .د
:تايوتحملا
تافوفصملا: لولأا لصفلا
اهيلع تايلمعلاو تافوفصملا )
ةيلولأا ةيفصلا تايلمعلا )
1,1
1,2
(
(
ةفوفصملا سوكعم ) 1,3 (
ةصاخ تافوفصم ) 1,4 (
تاددحملا:يناثلا لصفلا
ددحملا فيرعت ) 2,1 (
تاددحملا صاوخ )
ةقفارملا ةفوفصملا )
2,2
2,3
(
(
ةماع نيرامت ) 2,4 (
ةيطخلا تلاداعملا ةمظنأ :ثلاثلا لصفلا
نادروج سواجو سواج ايقيرط ) 3,1 (
ةسناجتملا ةيطخلا تلاداعملا ةمظنأ ) 3,2 (
رمارك ةدعاق ) 3,3 (
تاهجتملا تاءاضف : عبارلا لصفلا
تاهجتملا ءاضف فيرعت ) 4,1 (
ةيئزجلا تاءاضفلا ) 4,2 (
ةدلوملا تاعومجملاو ةيطخلا تابيكرتلا) 4,3 (
يطخلا للاقتسلااو طابترلاا ) 4,4 (
دعبلاو ساسلأا ) 4,5 (
ساسلأا رييغتو تايثادحلاا )
ةفوفصملا ةبتر )
رشابملا عمجلا )
4,6
4,7
4,8
(
(
(

يلخادلا برضلا تاءاضف:سماخلا لصفلا
يلخادلا برضلا فيرعت ) 5,1 (
دماعتلا ) 5,2 (
ةيرايعلا تاساسلأا ) 5,3 (
يدومعلا طاقسلااو يدومع لا ممتملا) 5,4 (
ةيطخلا تلايوحتلا :سداسلا لصفلا
ةيساسأ صاوخ ) 6,1 (
يطخلا ليوحتلا ةروصو ةاون ) 6,2 (
ةيطخلا تلايوحتلا ربج ) 6,3 (
يطخلا ليوحتلا ةفوفصم ) 6,4 (
راطقتسلااو ةزيمملا تاهجتملاو ميقلا :عباسلا لصفلا
ةزيمملا تاهجتملاو ميقلا : ) 7,1 (
راطقتسلاا ) 7,2 (
ةلثامتملا تافوفصملا راصقتسا) 7,3 (
ييطخلا تارثؤملا راطقتسا ) 7,4 (
SYLLABUS OF 242 MATH ( ELEMENTARY LINEAR ALGEBRA)
CONTENTS
THAPTER ONE
MATRICES
1.1 MATRICES AND MATRIX OPERATIONS
2.1 ELEMENTARY ROW OPERATIONS
3.1 INVERSE OF MATRIX
4.1 SPECIAL MATRICES
CHAPTER TWO
DETERMINANTS
1.2 DEFINITION OF DETERMINANT
2.2 PROPERTIES OF DETERMINANTS

3.2 ADJOINT MATRIX
4.2 REVIEW EXERCISES
CHAPTER THREE
SYSTEMS OF LINEAR EQUATIONS
1.3 GAUSS AND GAUSS _JORDAN METHODS
3.2 HOMOGENEOUS SYSTEMS OF LINEAR EQUTIONS
3.3 CRAMER , S RULE
CHAPTER FOUR
VECTOR SPACES
1.4 DEFINITION OF A VECTOR SPACE
2.4 SUPSPACES
3.4 LINEAR COMBINATION AND SPANNIG SETS
4.4 LINEAR DEPENDENCE AND LINEAR INDEPENDENCE
5.4 BASIS AND DIMENSION
6.4 COORDINATES AND CHANGE OF BASIS
7.4 RANK OF A MATRIX
8.4 DIRECT SUM
CHAPTER FIVE

INNER PRODUCT SPACES
1.5 DIFFENITION OF INNER PRODUCT
2.5 ORTHOGONALITY
3.5 ORTHONORMAL BASIS
4.5 ORTHOGONAL COMPLEMENT AND ORTHOGONAL PROJECTION
CHAPTER SIX
LINEAR TRANSFORMATIONS
1.6 BASIC PROPERTIES
2.6KERNEL AND IMAGE OF LINEAR TRANSFORMATION
3.6 MATRIX OF LINEAR TRANSFORMATION
CHAPTER SEVEN
EIGENVALUES , EIGENVECTORS AND DIAGONALIZATION
1.7 EIGENVALUES , EIGENVECTORS
2.7 DIAGONALIZATION
3.7 DIAGONALIZATION OF SYMMETRIC MARTICES
4.7 DIAGONALIZATION OF LINEAR OPERATORS

SYLLABUS OF 344 MATM ( RINGS AND FIELDS)
CONTENTS
CHAPTER ONE
1.1 DEFINITION AND EXAMPLES OF RING
2.1 SPECIFIED TYPES OF RINGS
3.1 DEFINITION OF A UNIT AND THE GROUP OF UNITS
4.1 DEFINITION OF ZERO DIVISORS AND NON ZERO DIVISORS
5.1 DEFINITION OF INTEGRAL DOMAIN , DIVISION RING AND FIELD
6.1 THE TEN TYPES OF RINGS
7.1 THE RELATIONSHIP BETWEEN THE TEN TYPES OF RINGS
8.1 IDEMPOTENT AND NILPOTENT ELEMENTS OF A RING
9.1 BOOLEAN GING
10.1 SUBRING AND THE CHARACTERISTIC OF THE RING
CHAPTER TWO
1.2 DEFINITION OF IDEALS AND EXAMPLES

2.2 CONSTRUCT NEW IDEALS OF GIVEN ONES
3.2 DEFINITION OF FINITELY GENERATED IDEAL AND THE
PRINCIPALIDEAL
4.2 DEFINITION OF CERTAIN BINARY OPERATIONS ON THE IDEALS
OF A RING
5.2 DEFINITION OF THE INTERNAL DIRECT SUM
6.2 FEFINITION OF RING HOMOMORPHISM AND EXAMPLES
7.2 SOME PROPERTIES OF RING HOMOMORPHISM
8.3 DEFINITION OF KERNEL AND IMAGEOF THE RING
HOMOMORPHISM AND SOME APPLICATIONS
8.2 DEFINITION OF AN IMBEDDED RING IN ANOTHER RING
9.2 DEFINITION OF AN EXTERNAL DIRECT SUM
10.2 RELATIONSHIP BETWEEN THE INTERNAL AND EXTERNAL
DIRECT SUM
CHAPTER THREE
1.3 QUOTIENT GING
2.3 FACTORIZATION OF HOMOMORPHISMS
3.3 CLASSICAL ISOMORPHISM THEOREMS
3.3.A FIRST ISOMORPHISM THEOREM
3.3 B SECOND ISOMORPHISM THEOREM
3.3 C THIRD ISOMORPHISM THEOREM
CHAPTER FOUR
INTEGRAL DOMAIN AND FIELDS

1.4 A. EVERY FINITE INTEGRAL DOMAIN IS A FIELD
1.4 B. EVERY INTEGRAL DOMAIN WITH ONLY A FINITE NUMBER
OF IDEALS IS A FIELD
2.4 DEFINITION OF A SUBFIELD
3.4 THE RELATION BETWEEN A SUBRING OF A FIELD AND THE
SUBFIELD GENERATED BY THE SUBRING
4.4 CONSTRUCT THE QUOTIENT FIELD OF AN INTEGRAL DOMAIN
CHAPTER FIVE
MAXIMAL AND PRIME IDEALS
CHAPTER SIX
DIVISIBILITY THEORY IN INTEGRAL DOMAIN
1.6 DEFINITION OF UNIQUE FACTORIZATION DOMAIN
2.6 EVERY PRINCIPAL IDEAL DOMAIN IS A UNIQUE FACTORIZATION
DOMAIN
3.6 DEFINITION OF AN EUCLIDEAN DOMAIN
4.6 SOME PROPERTIES OF AN EUCLIDEAN DOMAIN
5.6 EVERY EUCLIDEAN DOMAIN IS A PRINCIPAL IDEAL DOMAIN
CHAPTER SEVEN
POLYNOMIAL RINGS
1.7 ROOTS OF POLYNOMIALS OVER A FIELD
2.7 DEFINITION OF A PRIMITIVE POLYNOMIAL

3.7 GAUSS , S LEMMA
4.7 THE EISENSTEIN CRITERION
CHAPTER EIGHT
1.8 FIELD EXTENTIONS
2.8 FINITE AND SIMPLE EXTENTION OF FIELDS
3.8 ALGEBRIC CLOSURE OF A FIELD
4.8 SPLITTING FIELDS
5.8 FINITE FIELDS

FIRST MID TERM EXAM FIRST SEMESTER (2007-1428 ) KING SAUD UNIVERSITY
FOR 344 MATH TIME : ONE HOUR AND THIRTY MINUTES
___________________________________________________________________________________________
QUESTION ONE
Let R be a ring with identity a) Define the unit element in R . b) List the units of R = Z
10 c) Prove the following :
(i) No unit in R is a zero divisor .
(ii) The set of units in R form a group with respect to multiplication .
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QUESTION TWO
Let S
 
be the set of ordered pairs of real numbers .
Define addition and multiplication on S by
(a,b) + (c,d) = (a+c,b+d)
(a,b) (c,d) = (ac-bd,ad+bc)
Prove that S is a field under these operations .
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QUESTION THREE a) Define the characteristic of a ring R . b) Define the characteristic of Z
6

Z
15
C ) Let R be an integral domain , Prove the following :
(i) The only idempotent elements in R are o and 1 .
(ii) If the charR = n 0 then 0

a

R has additive order equals n .
(iii) If charR = 0 then 0

a

R has an infinite order .
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(242 رابتخلاايلصفللاولاا )