Elements of algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Chelsea Publ. Co.
1961
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 189 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Elements of algebra |
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| 264 | 1 | |a New York |b Chelsea Publ. Co. |c 1961 | |
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Record in the Search Index
| _version_ | 1804116913597448192 |
|---|---|
| adam_text | CONTENTS
Preface to the Fourth Edition 5
Preface to the Second Edition 6
Preface to the First Edition 9
Preface to the Preliminary Edition 11
I. Sets, Statements, and Variables
Introduction, 19—Sets and their Members, 19 — Construction of Sets, 21
Variables and Statement forms, 23 — Functions, 25 — Rules of Inference
and Proofs, 28 — Beliefs, Validity, and Sets, 31 — Exercises, 32.
II. Cardinal Numbers
Introduction, 35 — Standard Sets and Cardinal Numbers, 35 — Addition
of Cardinal Numbers, 36 — The Commutative and Associative Laws
of Addition, 37 — Multiplication of Cardinal Numbers, 40 — The Com¬
mutative and Associative Laws of Multiplication, 41 — The Distributive
Law, 42 — Comments on the Five Basic Laws, 43 — Cancellation
Laws, 43 — Special Properties of Zero and One, 44 — The Addition
and Multiplication Tables for Cardinals, 46 — Exercises, 48.
III. Expressions
Introduction, 50 — Parentheses, 50 — Expressions, 51 — Evaluation of
Expressions, 52 — Equal Expressions, 53 — The Algebra of Expres¬
sions, 53 — Parentheses and the Generalized Addition Law, 55 —
Parentheses and the Generalized Multiplication Law, 57 — Parentheses
and the Generalized Distributive Law, 58 — Exercises, 61.
IV. Polynomials
Introduction, 63 — Expressions with No Parentheses, 63 — Expon¬
ents, 65 — Monomials, 67 — Multiplication and Addition of Mono¬
mials, 68 — Polynomials, 69 — Exercises, 71.
13
14 Contents
V. Number Systems in General
Introduction, 72 — Operations on a Set, 72 — Commutative and Associ¬
ative Operations, 74 — Distributive Operations, 75 — Numbers and
Number Systems, 76 — Zero Element and One Element of a Number
System, 76 — Inverses, Negatives, and Reciprocals, 78 — Some
Remarks About Numbers in General, 80 — Exercises, 80.
VI. Construction of the Integers
Introduction, 83 — Definition of Integers, 83 — Relations Among the
Sets l{x,y), 84 — Definition of Addition for Integers, 86 — The
Commutative and Associative Laws for Addition of Integers, 88 —
Definition of Multiplication for Integers, 90 — The Commutative and
Associative Laws for Multiplication of Integers, 91 — The Distributive
Laws for Integers, 93 — Relation Between Cardinals and Integers;
Isomorphisms, 94 — Exercises, 96.
VII. Properties of the Integers
Introduction, 99 — The Generalized Laws and Expressions, 99 — The
Zero Element and One Element of the Integers, 100 — The Negative of
an Integer, 101 — Standard Notation for the Integers, 103 — The Can¬
cellation Laws for Integers, 105 — Expressions Over the Integers, 107 —
Subtraction, 107 — Exercises, 108.
VIII. The Rational Number System
Introduction, 111 — The Set of Rational Numbers, 111 — Addition and
Multiplication of Rationals, 113 — One Element, Zero Element and
Negatives, 116—Relation Between Rationals and Integers, 117—Recip¬
rocals, 118 — Traditional Notation for Rationals, 119 — Standard
Forms, 120 — Expressions Over the Rationals, 120 — Exercises, 123.
IX. Equations
Introduction, 125 — Definitions, 125 — Classification and Solution of
Equations, 127 — Equations in One Variable, 127 — Equations of the
First Degree, 131 — Quadratic Equations, 132 — Equations with More
than One Variable, 136 — Simultaneous Equations, 137 — Additional
Comments, 139 — Exercises, 140.
X. Order
Introduction, 143 — Order for the Cardinals, 143 — Order for the
Integers, 145 — Order in General, 147 — Order for the Rationals, 150
— Exercises, 152.
Contents 15
XI. The Real Number System
Introduction, 155 — Finite Decimals, 155 — The Rationals as Infinite
Decimals, 157 — Repeating Decimals, 160 — Construction of the Real
Number System, 162 — Order Properties of the Real Number System,
163 — The Reals as an Extension of the Rationals, 165 — Extraction
of Roots, 166 — Exponents, 168 — Logarithms, 169 — Exercises, 170.
XII. Appendix
Introduction, 172 — Infinite Sets and the Cancellation Laws, 172 —
Equal and Unequal Infinities, 173 — Peano Axioms for Natural Num¬
bers, 175 — Proof by Mathematical Induction, 176 — Axioms, Groups,
Rings, and Fields, 178 — Exercises, 180.
Index 185
|
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV002507732 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:46:04Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001615303 |
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| physical | 189 S. |
| publishDate | 1961 |
| publishDateSearch | 1961 |
| publishDateSort | 1961 |
| publisher | Chelsea Publ. Co. |
| record_format | marc |
| spelling | Levi, Howard Verfasser aut Elements of algebra 4. ed. New York Chelsea Publ. Co. 1961 189 S. txt rdacontent n rdamedia nc rdacarrier Algèbre Algèbre ram Álgebra larpcal Algebra Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algebra (DE-588)4001156-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001615303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Levi, Howard Elements of algebra Algèbre Algèbre ram Álgebra larpcal Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4151278-9 |
| title | Elements of algebra |
| title_auth | Elements of algebra |
| title_exact_search | Elements of algebra |
| title_full | Elements of algebra |
| title_fullStr | Elements of algebra |
| title_full_unstemmed | Elements of algebra |
| title_short | Elements of algebra |
| title_sort | elements of algebra |
| topic | Algèbre Algèbre ram Álgebra larpcal Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algèbre Álgebra Algebra Einführung |
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