Chapter Zero; Carol Schumacher; 2000
Chapter Zero; Carol Schumacher; 2000

Chapter ZeroUpplaga 2

av Carol Schumacher

  • Upplaga: 2a upplagan
  • Utgiven: 2000
  • ISBN: 9780201437249
  • Sidor: 256 st
  • Förlag: Pearson
  • Format: Häftad
  • Språk: Engelska

Om boken

0. Introduction-an Essay Mathematical Reasoning. Deciding What to Assume. What Is Needed to Do Mathematics? Chapter Zero 1. Logic. True or False. Thought Experiment: True or False. Statements and Predicates. Quantification. Mathematical Statements. Mathematical Implication. Direct Proofs. Compound Statements and Truth Tables. Learning from Truth Tables. Tautologies. What About the Converse? Equivalence and Rephrasing. Negating Statements. Existence Theorems. Uniqueness Theorems. Examples and Counter Examples. Direct Proof. Proof by Contrapositive. Proof by Contradiction. Proving Theorems: What Now? Problems. Questions to Ponder 2. Sets. Sets and Set Notation. Subsets. Set Operations. The Algebra of Sets. The Power Set. Russell's Paradox. Problems. Questions to Ponder. 3. Induction. Mathematical Induction. Using Induction. Complete Induction. Questions to Ponder. 4. Relations. Relations. Orderings. Equivalence Relations. Graphs. Coloring Maps. Problems. Questions to Ponder. 5. Functions. Basic Ideas. Composition and Inverses. Images and Inverse Images. Order Isomorphisms. Sequences. Sequences with Special Properties. Subsequences. Constructing Subsequences Recursively. Binary Operations. Problems. Questions to Ponder 6. Elementary Number Theory. Natural Numbers and Integers. Divisibility in the Integers. The Euclidean Algorithm. Relatively Prime Integers. Prime Factorization. Congruence Modulo n. Divisibility Modulo n. Problems. Questions to Ponder. 7. Cardinality. Galileo's Paradox. Infinite Sets. Countable Sets. Beyond Countability. Comparing Cardinalities. The Continuum Hypothesis. Problems. Questions to Ponder. 8. The Real Numbers. Constructing the Axioms. Arithmetic. Order. The Least Upper Bound Axiom. Sequence Convergence in R. Problems. Questions to Ponder. A. Axiomatic Set Theory. Elementary Axioms. The Axiom of Infinity. Axioms of Choice and Substitution. B. Constructing R. From N to Z. From Z to Q. From Q to R. Index.

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Mer om Chapter Zero (2000)

I november 2000 släpptes boken Chapter Zero skriven av Carol Schumacher. Det är den 2a upplagan av kursboken. Den är skriven på engelska och består av 256 sidor. Förlaget bakom boken är Pearson som har sitt säte i London.

Köp boken Chapter Zero på Studentapan och spara pengar.

Referera till Chapter Zero (Upplaga 2)

Harvard

Schumacher, C. (2000). Chapter Zero. 2:a uppl. Pearson.

Oxford

Schumacher, Carol, Chapter Zero, 2 uppl. (Pearson, 2000).

APA

Schumacher, C. (2000). Chapter Zero (2:a uppl.). Pearson.

Vancouver

Schumacher C. Chapter Zero. 2:a uppl. Pearson; 2000.