Transcription of An Introduction to Higher Mathematics
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An Introduction to Higher Mathematics Patrick Keef David Guichard with modifications by Russ Gordon Whitman College c 2010. Contents 1. Logic 1. Logical Operations .. 1. George Boole .. 6. Quantifiers .. 8. De Morgan's Laws .. 11. Augustus De Morgan .. 13. Mixed Quantifiers .. 15. Logic and Sets .. 17. Ren e Descartes .. 20. Families of Sets .. 22. Equivalence Relations .. 24. 2. Proofs 29. Direct Proofs .. 32. Divisibility .. 35. Existence proofs .. 37. Mathematical Induction .. 40. Two Important Results .. 44. Strong Induction .. 49. Well-Ordering Property .. 53. Indirect Proof .. 58. Euclid of Alexandria .. 60.
Logic itself deserves study; the right tools and concepts can make logical arguments easier to discover and to discern. In fact, logic is a major and active area of mathematics; for our purposes, a brief introduction will give us the means to investigate …
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