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Mathematical Reasoning - Writing and Proof

Nguồn ngoài

Mathematical Reasoning - Writing and Proof

Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.

Mathematical Logic and ProofMathematics
Tác giả
Ted Sundstrom
Nhà xuất bản
Grand Valley State University
Nguồn
LibreTexts
Giấy phép
CC BY-NC-SA
Ngôn ngữ
EN
Danh mục
Tiếng Anh
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 54 mục
  1. 01: Introduction to Writing Proofs in Mathematics
  2. 1.01: Statements and Conditional Statements
  3. 1.02: Constructing Direct Proofs
  4. 1.S: Introduction to Writing Proofs in Mathematics (Summary)
  5. 02: Logical Reasoning
  6. 2.01: Statements and Logical Operators
  7. 2.02: Logically Equivalent Statements
  8. 2.03: Open Sentences and Sets
  9. 2.04: Quantifiers and Negations
  10. 2.S: Logical Reasoning (Summary)
  11. 03: Constructing and Writing Proofs in Mathematics
  12. 3.01: Direct Proofs
  13. 3.02: More Methods of Proof
  14. 3.03: Proof by Contradiction
  15. 3.04: Using Cases in Proofs
  16. 3.05: The Division Algorithm and Congruence
  17. 3.06: Review of Proof Methods
  18. 3.S: Constructing and Writing Proofs in Mathematics (Summary)
  19. 04: Mathematical Induction
  20. 4.01: The Principle of Mathematical Induction
  21. 4.02: Other Forms of Mathematical Induction
  22. 4.03: Induction and Recursion
  23. 4.S: Mathematical Induction (Summary)
  24. 05: Set Theory
  25. 5.01: Sets and Operations on Sets
  26. 5.02: Proving Set Relationships
  27. 5.03: Properties of Set Operations
  28. 5.04: Cartesian Products
  29. 5.05: Indexed Families of Sets
  30. 5.S: Set Theory (Summary)
  31. 06: Functions
  32. 6.01: Introduction to Functions
  33. 6.02: More about Functions
  34. 6.03: Injections Surjections and Bijections
  35. 6.04: Composition of Functions
  36. 6.05: Inverse Functions
  37. 6.06: Functions Acting on Sets
  38. 6.S: Functions (Summary)
  39. 07: Equivalence Relations
  40. 7.01: Relations
  41. 7.02: Equivalence Relations
  42. 7.03: Equivalence Classes
  43. 7.04: Modular Arithmetic
  44. 7.S: Equivalence Relations (Summary)
  45. 08: Topics in Number Theory
  46. 8.01: The Greatest Common Divisor
  47. 8.02: Prime Numbers and Prime Factorizations
  48. 8.03: Linear Diophantine Equations
  49. 8.S: Topics in Number Theory (Summary)
  50. 09: Finite and Infinite Sets
  51. 9.01: Finite Sets
  52. 9.02: Countable Sets
  53. 9.03: Uncountable Sets
  54. 9.S: Finite and Infinite Sets (Summary)