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MATH 2150: Higher Arithmetic

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MATH 2150: Higher Arithmetic

This course explores elementary number theory, numeration systems, operations on integers and rational numbers, and elementary combinatorics, using both inductive and deductive methods. Emphasis will be placed on the development of clarity and understanding of mathematical processes and ideas, the application of these ideas to problem-solving and the communication of these ideas to other people.

Mathematics
Author
Pamini Thangarajah
Publisher
Mount Royal University
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 55 sections
  1. 0: Preliminaries
  2. 0.1: Basics
  3. Contradiction
  4. 0.3: Proof Do's and Dont's
  5. 0.4: Egyptian Multiplication and Division (optional)
  6. 0.E: Exercises
  7. 1: Binary operations
  8. 1.1: Binary operations
  9. 1.2: Exponents and Cancellation
  10. 1.E: Exercises
  11. 2: Binary relations
  12. 2.1: Binary Relations
  13. 2.2: Equivalence Relations, and Partial order
  14. 2.3: Arithmetic of inequality
  15. 2.4: Arithmetic of divisibility
  16. 2.5: Divisibility Rules
  17. 2.6: Division Algorithm
  18. 2.E: Exercises
  19. 3: Modular Arithmetic
  20. 3.1: Modulo Operation
  21. 3.2: Modulo Arithmetic
  22. 3.3: Divisibility rules revisited
  23. 3.E: Exercises
  24. 4: Greatest Common Divisor least common multiple and Euclidean Algorithm
  25. 4.1: Greatest Common Divisor
  26. 4.2: Euclidean algorithm and Bézout's algorithm
  27. 4.3: Least Common Multiple
  28. 4.4: Relatively Prime numbers
  29. 4.5: Linear Congruences
  30. 4.E: Exercises
  31. 5: Diophantine Equations
  32. 5.1: Linear Diophantine Equations
  33. 5.2 : Linear Congruences Revisted
  34. 5.3: Non-Linear Diophantine Equations
  35. 5.E: Exercises
  36. 6: Prime numbers
  37. 6.1: Prime numbers
  38. 6.2: GCD, LCM and Prime factorization
  39. 6.3: Fermat Primes, Mersenne Primes and Primes of the form \(ax b\)
  40. 6.E: Prime Numbers (Exercises)
  41. 7: Numeration Systems
  42. 7.1: Historical numeral systems
  43. 7.2: Number Bases
  44. 7.3: Unusual Number systems
  45. 7.E: Exercises
  46. 8: Rational numbers, Irrational Numbers, and Continued fractions
  47. 8.1: Rational numbers
  48. 8.2: Irrational Numbers
  49. 8.3: Continued fractions
  50. 8.E: Exercises
  51. Mock exams
  52. Sample Final
  53. Sample term test
  54. Notations
  55. Notations