rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: An
    title: Introduction to Mathematical Proofs
  title info:
    title: MATHnetBASE
  name:
    name part: Loehr, Nicholas A.
    role:
      role term: creator
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: xx
    place:
      place term: Milton
    publisher: CRC Press LLC
    date issued: 2019
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (413 pages).
  abstract: An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra.
  table of contents: Logic Propositions; Logical Connectives; Truth Tables Logical Equivalence; IF-Statements IF, IFF, Tautologies, and Contradictions Tautologies; Quantifiers; Universes Properties of Quantifiers: Useful Denials Denial Practice; Uniqueness Proofs Definitions, Axioms, Theorems, and Proofs Proving Existence Statements and IF Statements Contrapositive Proofs; IFF Proofs Proofs by Contradiction; OR Proofs Proof by Cases; Disproofs Proving Universal Statements; Multiple Quantifiers More Quantifier Properties and Proofs (Optional) Sets Set Operations; Subset Proofs More Subset Proofs; Set Equality Proofs More Set Quality Proofs; Circle Proofs; Chain Proofs Small Sets; Power Sets; Contrasting ? and ⁶ Ordered Pairs; Product Sets General Unions and Intersections Axiomatic Set Theory (Optional) Integers Recursive Definitions; Proofs by Induction Induction Starting Anywhere: Backwards Induction Strong Induction Prime Numbers; Division with Remainder Greatest Common Divisors; Euclid's GCD Algorithm More on GCDs; Uniqueness of Prime Factorizations Consequences of Prime Factorization (Optional) Relations and Functions Relations; Images of Sets under Relations Inverses, Identity, and Composition of Relations Properties of Relations Definition of Functions Examples of Functions; Proving Equality of Functions Composition, Restriction, and Gluing Direct Images and Preimages Injective, Surjective, and Bijective Functions Inverse Functions Equivalence Relations and Partial Orders Reflexive, Symmetric, and Transitive Relations Equivalence Relations Equivalence Classes Set Partitions Partially Ordered Sets Equivalence Relations and Algebraic Structures (Optional) Cardinality Finite Sets Countably Infinite Sets Countable Sets Uncountable Sets Real Numbers (Optional) Axioms for R; Properties of Addition Algebraic Properties of Real Numbers Natural Numbers, Integers, and Rational Numbers Ordering, Absolute Value, and Distance Greatest Elements, Least Upper Bounds, and Completeness Suggestions f…
  note: Description based upon print version of record.
  subject:
    topic: Proof theory
  subject:
    topic: MATHEMATICS / Mathematical Analysis
  subject:
    topic: MATHEMATICS / Logic
  subject:
    topic: MATHEMATICS / Set Theory
  classification: QA39.2
  classification: 510
  identifier: 9781000709629
  identifier: 1000709620
  identifier: 9781000709803
  identifier: 1000709809
  identifier: 9781000709711
  identifier: 100070971X
  identifier: 9780429322587
  identifier: 0429322585
  identifier: 9780367338237 (hbk.)
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCoLC-P
    record creation date: 191123
    record change date: 20220613180032.6
    record identifier: in00004581957
    language of cataloging:
      language term: eng