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Introduction to mathematical thinking

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Author(s): Alexandru Buium
Series: lecture notes
Edition: version 2019-09-13
Year: 2019

Language: English
Commentary: Downloaded from https://math.unm.edu/~buium/umath.pdf

Part 1. Logic 5
Chapter 1. Languages 7
Chapter 2. Metalanguage 15
Chapter 3. Syntax 21
Chapter 4. Tautologies 25
Chapter 5. Proofs 31
Chapter 6. Theories 39
Chapter 7. ZFC 49
Part 2. Set theory 53
Chapter 8. Sets 55
Chapter 9. Maps 59
Chapter 10. Relations 63
Chapter 11. Operations 69
Part 3. The discrete 75
Chapter 12. Integers 77
Chapter 13. Induction 81
Chapter 14. Rationals 85
Chapter 15. Combinatorics 87
Chapter 16. Sequences 89
Part 4. The continuum 93
Chapter 17. Reals 95
Chapter 18. Topology 97
Chapter 19. Imaginaries 101
Part 5. Algebra 103
Chapter 20. Arithmetic 105
Chapter 21. Groups 109
Chapter 22. Order 113
Chapter 23. Vectors 115
Chapter 24. Matrices 117
Chapter 25. Determinants 121
Chapter 26. Polynomials 125
Chapter 27. Congruences 129
Part 6. Geometry 133
Chapter 28. Lines 135
Chapter 29. Conics 139
Chapter 30. Cubics 141
Part 7. Analysis 145
Chapter 31. Limits 147
Chapter 32. Series 151
Chapter 33. Trigonometry 155
Chapter 34. Calculus 157