Solution Manual for Mathematical Proofs: A Transition to Advanced Mathematics, 3/E 3rd Edition Gary Chartrand, Albert D. Polimeni, Ping Zhang digital download immediately after payment is complete.

Product details:

ISBN-10 ‏ : ‎ 0321797094
ISBN-13 ‏ : ‎ 978-0321797094
Author: Gary Chartrand, Albert D. Polimeni

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Table contents:

SETS
1.1  Describing a Set 13
1.2  Special Sets  15
1.3  Subsets  16
1.4  Set Operations  18
1.5  Indexed Collections of Sets 21
1.6  Partitions of Sets 23
1.7  Cartesian Products of Sets 24
Exercises for Chapter 1 24



LOGIC
2.1  Statements 29
2.2  The Negation of a Statement 31
2.3  The Disjunction and Conjunction of Statements 32
2.4  The Implication  33
2.5  More On Implications 35
2.6  The Biconditional 36
2.7  Tautologies and Contradictions 38
2.8  Logical Equivalence  39
2.9  Some Fundamental Properties of Logical Equivalence 41
2.10 Characterizations of Statements 42
2.11  Quantified Statements and Their Negatiors  44
Exercises for Chapter 2 46
DIRECT PROOF AND PROOF BY CONTRAPOSITIVE
3.1  Trivial and Vacuous Proofs 51
3.2   Direct Proofs 53
3.3  Proof by Contrapositive  56
3.4  Proof by Cases 60
3.5  Proof Evaluations 63
Exercises for Chapter 3 64
MORE ON DIRECT PROOF AND PROOF
BY CONTRAPOSITIVE
4.1  Proofs Involving Divisibility of Integers 67
4.2  Proofs Involving Congruence of Integers 70
4.3  Proofs Involving Real Numbers 73
4.4  Proofs Involving Sets 74
4.5  Fundamental Properties of Set Operations 77
4.6  Proofs Involving Cartesian Products of Sets 79
Exercises for Chapter 4 80
PROOF BY CONTRADICTION
5.1  Proof by Contradiction  83
5.2  Examples of Proof by Contradiction  84
5.3  The Three Prisoners Problem  85
5.4   Other Examples of Proof by Contradiction  87



5.5  The Irrationality of /2  87
5.6  A Review of the Three Proof Techniques 88
Exercises for Chapter 5 90
PROVE OR DISPROVE
6.1  Conjectures in Mathematics 93
6.2  A Review of Quantifiers 96
6.3  Existence Proofs 98
6.4  A Review of Negations of Quantified Statements  100
6.5  Counterexamples  101
6.6   Disproving Statements  103
6.7  Testing Statements  105
6.8  A Quiz of "Prove or Disprove" Problems  107
Exercises for Chapter 6 108
EQUIVALENCE RELATIONS
7.1  Relations  113
7.2  Reflexive, Symmetric, and Transitive Relations  114
7.3  Equivalence Relations  116
7.4  Properties of Equivalence Classes  119
7.5   Congruence Modulo n  123
7.6  The Integers Modulo n  127
Exercises for Chapter 7 130
FUNCTIONS
8.1  The Definition of Function  135
8.2  The Set of All Functions From A to B  138
8.3  One-to-one and Onto Functions  138
8.4  Bijective Functions  140
8.5  Composition of Functions  143
8.6  Inverse Functions  146
8.7  Permutations  149
Exercises for Chapter 8 150
MATHEMATICAL INDUCTION
9.1  The Well-Ordering Principle  153
9.2  The Principle of Mathematical Induction  155
9.3  Mathematical Induction and Sums of Numbers  158



9.4  Mathematical Induction and Inequalities  162
9.5  Mathematical Induction and Divisibility  163
9.6  Other Examples of Induction Proofs  165
9.7  Proof By Minimum Counterexample  166
9.8  The Strong Form of Induction  168
Exercises for Chapter 9 171
CARDINALITIES OF SETS
10.1  Numerically Equivalent Sets  176
10.2  Denumerable Sets  177
10.3  Uncountable Sets  183
10.4  Comparing Cardinalities of Sets  188
10.5  The Schr6der-Berstein Theorem  191
Exercises for Chapter 10 194
PROOFS IN NUMBER THEORY
11.1  Divisibility Properties of Integers  197
11.2  The Division Algorithm  198
11.3   Greatest Common Divisors 202
11.4  The Euclidean Algorithm  204
11.5  Relatively Prime Integers 206
11.6  The Fundamental Theorem of Arithmetic  208
11.7  Concepts Involving Sums of Divisors 210
Exercises for Chapter 11 211
PROOFS IN CALCULUS
12.1  Limits of Sequences 215
12.2  Infinite Series 220
12.3  Limits of Functions 224
12.4  Fundamental Properties of Limits of Functions 230
12.5  Continuity  235
12.6  Differentiability  237
Exercises for Chapter 12 239
PROOFS IN GROUP THEORY
13.1 Binary Operations 243
13.2  Groups 247



13.3  Permutation Groups 252
13.4  Fundamental Properties of Groups 255
13.5  Subgroups 257
13.6  Isomorphic Groups 260
Exercises for Chapter 13 263

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