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Mathematical Proofs: A Transition to Advanced Mathematics 4th edition [Kietas viršelis]

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  • Formatas: Hardback, 512 pages, aukštis x plotis x storis: 234x188x23 mm, weight: 807 g
  • Išleidimo metai: 03-Nov-2017
  • Leidėjas: Pearson
  • ISBN-10: 0134746759
  • ISBN-13: 9780134746753
Kitos knygos pagal šią temą:
Mathematical Proofs: A Transition to Advanced Mathematics 4th editionDidesnis paveikslėlis
  • Formatas: Hardback, 512 pages, aukštis x plotis x storis: 234x188x23 mm, weight: 807 g
  • Išleidimo metai: 03-Nov-2017
  • Leidėjas: Pearson
  • ISBN-10: 0134746759
  • ISBN-13: 9780134746753
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780134746753.html
Raktažodžiai:

For courses in Transition to Advanced Mathematics or Introduction to Proof.

Meticulously crafted, student-friendly text that helps build mathematical maturity

Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity.  They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs.



0134746759 / 9780134746753 Chartrand/Polimeni/Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, 4/e


0 Communicating Mathematics
1(13)
0.1 Learning Mathematics
2(1)
0.2 What Others Have Said About Writing
3(2)
0.3 Mathematical Writing
5(1)
0.4 Using Symbols
6(2)
0.5 Writing Mathematical Expressions
8(2)
0.6 Common Words and Phrases in Mathematics
10(2)
0.7 Some Closing Comments About Writing
12(2)
1 Sets
14(24)
1.1 Describing a Set
14(4)
1.2 Subsets
18(5)
1.3 Set Operations
23(4)
1.4 Indexed Collections of Sets
27(4)
1.5 Partitions of Sets
31(2)
1.6 Cartesian Products of Sets
33(5)
Chapter 1 Supplemental Exercises
35(3)
2 Logic
38(43)
2.1 Statements
38(3)
2.2 Negations
41(2)
2.3 Disjunctions and Conjunctions
43(2)
2.4 Implications
45(4)
2.5 More on Implications
49(4)
2.6 Biconditionals
53(4)
2.7 Tautologies and Contradictions
57(3)
2.8 Logical Equivalence
60(2)
2.9 Some Fundamental Properties of Logical Equivalence
62(3)
2.10 Quantified Statements
65(11)
2.11 Characterizations
76(5)
Chapter 2 Supplemental Exercises
78(3)
3 Direct Proof and Proof by Contrapositive
81(24)
3.1 Trivial and Vacuous Proofs
82(3)
3.2 Direct Proofs
85(4)
3.3 Proof by Contrapositive
89(5)
3.4 Proof by Cases
94(4)
3.5 Proof Evaluations
98(7)
Chapter 3 Supplemental Exercises
102(3)
4 More on Direct Proof and Proof by Contrapositive
105(22)
4.1 Proofs Involving Divisibility of Integers
105(5)
4.2 Proofs Involving Congruence of Integers
110(3)
4.3 Proofs Involving Real Numbers
113(4)
4.4 Proofs Involving Sets
117(3)
4.5 Fundamental Properties of Set Operations
120(2)
4.6 Proofs Involving Cartesian Products of Sets
122(5)
Chapter 4 Supplemental Exercises
123(4)
5 Existence and Proof by Contradiction
127(25)
5.1 Counterexamples
127(4)
5.2 Proof by Contradiction
131(7)
5.3 A Review of Three Proof Techniques
138(3)
5.4 Existence Proofs
141(5)
5.5 Disproving Existence Statements
146(6)
Chapter 5 Supplemental Exercises
149(3)
6 Mathematical Induction
152(29)
6.1 The Principle of Mathematical Induction
152(10)
6.2 A More General Principle of Mathematical Induction
162(8)
6.3 The Strong Principle of Mathematical Induction
170(4)
6.4 Proof by Minimum Counterexample
174(7)
Chapter 6 Supplemental Exercises
178(3)
7 Reviewing Proof Techniques
181(19)
7.1 Reviewing Direct Proof and Proof by Contrapositive
182(3)
7.2 Reviewing Proof by Contradiction and Existence Proofs
185(3)
7.3 Reviewing Induction Proofs
188(1)
7.4 Reviewing Evaluations of Proposed Proofs
189(11)
Exercises for
Chapter 7
193(7)
8 Prove or Disprove
200(24)
8.1 Conjectures in Mathematics
200(5)
8.2 Revisiting Quantified Statements
205(6)
8.3 Testing Statements
211(13)
Chapter 8 Supplemental Exercises
220(4)
9 Equivalence Relations
224(27)
9.1 Relations
224(2)
9.2 Properties of Relations
226(4)
9.3 Equivalence Relations
230(5)
9.4 Properties of Equivalence Classes
235(4)
9.5 Congruence Modulo n
239(6)
9.6 The Integers Modulo n
245(6)
Chapter 9 Supplemental Exercises
248(3)
10 Functions
251(27)
10.1 The Definition of Function
251(5)
10.2 One-to-one and Onto Functions
256(3)
10.3 Bijective Functions
259(4)
10.4 Composition of Functions
263(4)
10.5 Inverse Functions
267(11)
Chapter 10 Supplemental Exercises
274(4)
11 Cardinalities of Sets
278(25)
11.1 Numerically Equivalent Sets
279(1)
11.2 Denumerable Sets
280(8)
11.3 Uncountable Sets
288(5)
11.4 Comparing Cardinalities of Sets
293(3)
11.5 The Schroder-Bernstein Theorem
296(7)
Chapter 11 Supplemental Exercises
301(2)
12 Proofs in Number Theory
303(24)
12.1 Divisibility Properties of Integers
303(2)
12.2 The Division Algorithm
305(5)
12.3 Greatest Common Divisors
310(2)
12.4 The Euclidean Algorithm
312(3)
12.5 Relatively Prime Integers
315(3)
12.6 The Fundamental Theorem of Arithmetic
318(4)
12.7 Concepts Involving Sums of Divisors
322(5)
Chapter 12 Supplemental Exercises
324(3)
13 Proofs in Combinatorics
327(38)
13.1 The Multiplication and Addition Principles
327(6)
13.2 The Principle of Inclusion-Exclusion
333(3)
13.3 The Pigeonhole Principle
336(4)
13.4 Permutations and Combinations
340(8)
13.5 The Pascal Triangle
348(4)
13.6 The Binomial Theorem
352(5)
13.7 Permutations and Combinations with Repetition
357(8)
Chapter 13 Supplemental Exercises
363(2)
14 Proofs in Calculus
365(35)
14.1 Limits of Sequences
365(8)
14.2 Infinite Series
373(5)
14.3 Limits of Functions
378(8)
14.4 Fundamental Properties of Limits of Functions
386(6)
14.5 Continuity
392(3)
14.6 Differentiability
395(5)
Chapter 14 Supplemental Exercises
397(3)
15 Proofs in Group Theory
400(30)
15.1 Binary Operations
400(5)
15.2 Groups
405(6)
15.3 Permutation Groups
411(3)
15.4 Fundamental Properties of Groups
414(4)
15.5 Subgroups
418(5)
15.6 Isomorphic Groups
423(7)
Chapter 15 Supplemental Exercises
428(2)
Answers to Odd-Numbered Section Exercises 430(53)
References 483(1)
Credits 484(2)
Index of Symbols 486(1)
Index 487
Gary Chartrand is Professor Emeritus of Mathematics at Western Michigan University. He received his Ph.D. in mathematics from Michigan State University. His research is in the area of graph theory. Professor Chartrand has authored or co-authored more than 275 research papers and a number of textbooks in discrete mathematics and graph theory as well as the textbook on mathematical proofs. He has given over 100 lectures at regional, national and international conferences and has been a co-director of many conferences. He has supervised 22 doctoral students and numerous undergraduate research projects and has taught a wide range of subjects in undergraduate and graduate mathematics. He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He was the first managing editor of the Journal of Graph Theory. He is a member of the Institute of Combinatorics and Its Applications, the American Mathematical Society, the Mathematical Association of America and the editorial boards of the Journal of Graph Theory and Discrete Mathematics.



Albert D. Polimeni is an Emeritus Professor of Mathematics at the State University of New York at Fredonia. He received his Ph.D. degree in mathematics from Michigan State University. During his tenure at Fredonia he taught a full range of undergraduate courses in mathematics and graduate mathematics. In addition to the textbook on mathematical proofs, he co-authored a textbook in discrete mathematics. His research interests are in the area of finite group theory and graph theory, having published several papers in both areas. He has given addresses in mathematics to regional, national and international conferences. He served as chairperson of the Department of Mathematics for nine years.



Ping Zhang is Professor of Mathematics at Western Michigan University. She received her Ph.D. in mathematics from Michigan State University. Her research is in the area of graph theory and algebraic combinatorics. Professor Zhang has authored or co-authored more than 200 research papers and four textbooks in discrete mathematics and graph theory as well as the textbook on mathematical proofs. She serves as an editor for a series of books on special topics in mathematics. She has supervised 7 doctoral students and has taught a wide variety of undergraduate and graduate mathematics courses including courses on introduction to research. She has given over 60 lectures at regional, national and international conferences. She is a council member of the Institute of Combinatorics and Its Applications and a member of the American Mathematical Society and the Association of Women in Mathematics.