000			05268cam a2200361 i 4500
003			CUTN
005			20231215150929.0
008			210526s2022 riu 001 0 eng
020			_a9781470465148
020			_z9781470467616
041			_aEnglish
042			_apcc
082	0	0	_a510 _223 _bSET
084			_a00-01 _a00A05 _2msc
100	1		_aSethuraman, B. A.,
100	1		_eauthor.
245	1	0	_aProofs and ideas : _ba prelude to advanced mathematics / _cB. Sethuraman.
300			_axiii, 334 pages ; _c26 cm
440			_vv.68
490	0		_aAMS/MAA textbooks, _x2577-1205 ; _vVolume 68
500			_aIncludes index.
505			_tTitle page Copyright Contents Preface Chapter 1. Introduction 1.1. Further Exercises Chapter 2. The Pigeonhole Principle 2.1. Pigeonhole Principle (PHP) 2.2. PHP Generalized Form 2.3. Further Exercises Chapter 3. Statements 3.1. Statements 3.2. Negation of a Statement 3.3. Compound Statements 3.4. Statements Related to the Conditional 3.5. Remarks on the Implies Statement: Alternative Phrasing, Negations 3.6. Further Exercises Chapter 4. Counting, Combinations 4.1. Fundamental Counting Principle 4.2. Permutations and Combinations 4.3. Binomial Relations and Binomial Theorem 4.4. Further Exercises Chapter 5. Sets and Functions 5.1. Sets 5.2. Equality of Sets, Subsets, Supersets 5.3. New Sets From Old 5.4. Functions Between Sets 5.5. Composition of Functions, Inverses 5.6. Examples of Some Sets Commonly Occurring in Mathematics 5.7. Further Exercises Chapter 6. Interlude: So, How to Prove It? An Essay Chapter 7. Induction 7.1. Principle of Induction 7.2. Another Form of the Induction Principle 7.3. Further Exercises 7.4. Notes Chapter 8. Cardinality of Sets 8.1. Finite and Infinite Sets, Countability, Uncountability 8.2. Cardinalities of Q and R 8.3. The Schröder-Bernstein Theorem 8.4. Cantor Set 8.5. Further Exericses Chapter 9. Equivalence Relations 9.1. Relations, Equivalence Relations, Equivalence Classes 9.2. Examples 9.3. Further Exercises Chapter 10. Unique Prime Factorization in the Integers 10.1. Notion of Divisibility 10.2. Greatest Common Divisor, Relative Primeness 10.3. Proof of Unique Prime Factorization Theorem 10.4. Some Consequences of the Unique Prime Factorization Theorem 10.5. Further Exercises Chapter 11. Sequences, Series, Continuity, Limits 11.1. Sequences 11.2. Convergence 11.3. Continuity of Functions 11.4. Limits of Functions 11.5. Relation between limits and continuity 11.6. Series 11.7. Further Exercises Chapter 12. The Completeness of R 12.1. Least Upper Bound Property (LUB) 12.2. Greatest Lower Bound Property 12.3. Archimedean Property 12.4. Monotone Convergence Theorem 12.5. Bolzano-Weierstrass Theorem 12.6. Nested Intervals Theorem 12.7. Cauchy sequences 12.8. Convergence of Series 12.9. 𝑛-th roots of positive real numbers 12.10. Further Exercises Notes Chapter 13. Groups and Symmetry 13.1. Symmetries of an equilateral triangle 13.2. Symmetries of a square 13.3. Symmetries of an 𝑛-element set Groups 13.4. Subgroups 13.5. Cosets, Lagrange’s Theorem 13.6. Symmetry 13.7. Isomorphisms Between Groups 13.8. Further Exercises Chapter 14. Graphs: An Introduction 14.1. Königsberg Bridge Problem and Graphs 14.2. Walks, Paths, Trails, Connectedness 14.3. Existence of Eulerian Trails and Circuits: Sufficiency 14.4. Further Exercises Index
520			_aAMS/MAA Textbooks Volume: 68; 2021; 334 pp MSC: Primary 00; 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. 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. 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	_aMathematics.
650		7	_aGeneral and overarching topics; collections -- Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general.
650		7	_aGeneral and overarching topics; collections -- General and miscellaneous specific topics -- Mathematics in general.
650		7	_2msc _94
650		7	_2msc _94
690			_aMathematics
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cPROJECT
999			_c40968 _d40968