MARC details
| 000 -LEADER |
|---|
| fixed length control field |
05268cam a2200361 i 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
|---|
| control field |
CUTN |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
|---|
| control field |
20231215150929.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
210526s2022 riu 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781470465148 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Cancelled/invalid ISBN |
9781470467616 |
| 041 ## - LANGUAGE CODE |
|---|
| Language |
English |
| 042 ## - AUTHENTICATION CODE |
|---|
| Authentication code |
pcc |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
510 |
| Edition number |
23 |
| Item number |
SET |
| 084 ## - OTHER CLASSIFICATION NUMBER |
|---|
| Classification number |
00-01 |
| -- |
00A05 |
| Source of number |
msc |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Sethuraman, B. A., |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Proofs and ideas : |
| Remainder of title |
a prelude to advanced mathematics / |
| Statement of responsibility, etc |
B. Sethuraman. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xiii, 334 pages ; |
| Dimensions |
26 cm |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Volume number/sequential designation |
v.68 |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Includes index. |
| 505 ## - FORMATTED CONTENTS NOTE |
|---|
| Title |
Title page<br/>Copyright<br/>Contents<br/>Preface<br/>Chapter 1. Introduction<br/>1.1. Further Exercises<br/>Chapter 2. The Pigeonhole Principle<br/>2.1. Pigeonhole Principle (PHP)<br/>2.2. PHP Generalized Form<br/>2.3. Further Exercises<br/>Chapter 3. Statements<br/>3.1. Statements<br/>3.2. Negation of a Statement<br/>3.3. Compound Statements<br/>3.4. Statements Related to the Conditional<br/>3.5. Remarks on the Implies Statement: Alternative Phrasing, Negations<br/>3.6. Further Exercises<br/>Chapter 4. Counting, Combinations<br/>4.1. Fundamental Counting Principle<br/>4.2. Permutations and Combinations<br/>4.3. Binomial Relations and Binomial Theorem<br/>4.4. Further Exercises<br/>Chapter 5. Sets and Functions<br/>5.1. Sets<br/>5.2. Equality of Sets, Subsets, Supersets<br/>5.3. New Sets From Old<br/>5.4. Functions Between Sets<br/>5.5. Composition of Functions, Inverses<br/>5.6. Examples of Some Sets Commonly Occurring in Mathematics<br/>5.7. Further Exercises<br/>Chapter 6. Interlude: So, How to Prove It? An Essay<br/>Chapter 7. Induction<br/>7.1. Principle of Induction<br/>7.2. Another Form of the Induction Principle<br/>7.3. Further Exercises<br/>7.4. Notes<br/>Chapter 8. Cardinality of Sets<br/>8.1. Finite and Infinite Sets, Countability, Uncountability<br/>8.2. Cardinalities of Q and R<br/>8.3. The Schröder-Bernstein Theorem<br/>8.4. Cantor Set<br/>8.5. Further Exericses<br/>Chapter 9. Equivalence Relations<br/>9.1. Relations, Equivalence Relations, Equivalence Classes<br/>9.2. Examples<br/>9.3. Further Exercises<br/>Chapter 10. Unique Prime Factorization in the Integers<br/>10.1. Notion of Divisibility<br/>10.2. Greatest Common Divisor, Relative Primeness<br/>10.3. Proof of Unique Prime Factorization Theorem<br/>10.4. Some Consequences of the Unique Prime Factorization Theorem<br/>10.5. Further Exercises<br/>Chapter 11. Sequences, Series, Continuity, Limits<br/>11.1. Sequences<br/>11.2. Convergence<br/>11.3. Continuity of Functions<br/>11.4. Limits of Functions<br/>11.5. Relation between limits and continuity<br/>11.6. Series<br/>11.7. Further Exercises<br/>Chapter 12. The Completeness of R<br/>12.1. Least Upper Bound Property (LUB)<br/>12.2. Greatest Lower Bound Property<br/>12.3. Archimedean Property<br/>12.4. Monotone Convergence Theorem<br/>12.5. Bolzano-Weierstrass Theorem<br/>12.6. Nested Intervals Theorem<br/>12.7. Cauchy sequences<br/>12.8. Convergence of Series<br/>12.9. 𝑛-th roots of positive real numbers<br/>12.10. Further Exercises<br/>Notes<br/>Chapter 13. Groups and Symmetry<br/>13.1. Symmetries of an equilateral triangle<br/>13.2. Symmetries of a square<br/>13.3. Symmetries of an 𝑛-element set<br/>Groups<br/>13.4. Subgroups<br/>13.5. Cosets, Lagrange’s Theorem<br/>13.6. Symmetry<br/>13.7. Isomorphisms Between Groups<br/>13.8. Further Exercises<br/>Chapter 14. Graphs: An Introduction<br/>14.1. Königsberg Bridge Problem and Graphs<br/>14.2. Walks, Paths, Trails, Connectedness<br/>14.3. Existence of Eulerian Trails and Circuits: Sufficiency<br/>14.4. Further Exercises<br/>Index |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
AMS/MAA Textbooks<br/>Volume: 68; 2021; 334 pp<br/>MSC: Primary 00;<br/>Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts.<br/><br/>The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine.<br/><br/>This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
General and overarching topics; collections -- Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
General and overarching topics; collections -- General and miscellaneous specific topics -- Mathematics in general. |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Department Name |
Mathematics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Project book |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Relator term |
author. |
| 490 0# - SERIES STATEMENT |
|---|
| Series statement |
AMS/MAA textbooks, |
| International Standard Serial Number |
2577-1205 ; |
| Volume number/sequential designation |
Volume 68 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Source of heading or term |
msc |
| 9 (RLIN) |
4 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Source of heading or term |
msc |
| 9 (RLIN) |
4 |
| 906 ## - LOCAL DATA ELEMENT F, LDF (RLIN) |
|---|
| a |
7 |
| b |
cbc |
| c |
orignew |
| d |
1 |
| e |
ecip |
| f |
20 |
| g |
y-gencatlg |
