Proofs 101 : an introduction to formal mathematics / Joseph Kirtland.
Material type:
TextPublisher: Boca Raton : Chapman & Hall/CRC, 2021Edition: 1stDescription: 1 online resource : illustrations (black and white)Content type: text | still image Media type: computer Carrier type: online resourceISBN: 9781000227383; 1000227383; 9781000227345; 1000227340; 9781000227369; 1000227367; 9781003082927; 1003082920Subject(s): Proof theory | MATHEMATICS / Set Theory | MATHEMATICS / LogicDDC classification: 511.36 LOC classification: QA9.54Online resources: Taylor & Francis | OCLC metadata license agreement Summary: Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies. Features Designed to be teachable across a single semester Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses Offers a balanced variety of easy, moderate, and difficult exercises
<P><STRONG>1. Logic.</STRONG> 1.1 Introduction. 1.2. Statements and Logical Connectives. 1.3 Logical Equivalence. 1.4. Predicates and Quantifiers. 1.5. Negation. <STRONG>2. Proof Techniques</STRONG>. 2.1. Introduction. 2.2. The Axiomatic and Rigorous Nature of Mathematics. 2.3. Foundations. 2.4. Direct Proof. 2.5. Proof by Contrapositive. 2.5. Proof by Cases. 2.6. Proof by Contradiction. <STRONG>3. Sets.</STRONG> 3.1. The Concept of a Set. 3.2. Subset of Set Equality. 3.3. Operations on Sets. 3.4. Indexed Sets. 3.5. Russel's Paradox. <STRONG>4. Proof by Mathematical Induction.</STRONG> 4.1. Introduction. 4.2. The Principle of Mathematical Induction. 4.3. Proof by strong Induction. <STRONG>5. Relations.</STRONG> 5.1. Introduction. 5.2. Properties of Relations. 5.3. Equivalence Relations.<STRONG> 6. Introduction.</STRONG> 6.1. Definition of a Function. 6.2. One-To-One and Onto Functions. 6.3. Composition of Functions. 6.4. Inverse of a Function.<STRONG> 7. Cardinality of Sets.</STRONG> 7.1. Introduction. 7.2. Sets with the same Cardinality. 7.3. Finite and Infinite Sets. 7.4. Countably Infinite Sets. 7.5. Uncountable Sets. 7.6 Comparing Cardinalities. </P>
Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies. Features Designed to be teachable across a single semester Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses Offers a balanced variety of easy, moderate, and difficult exercises
OCLC-licensed vendor bibliographic record.