74SHW - Math 74 Homework Assignments. Adam Booth. Spring...

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Math 74 – Homework Assignments. Adam Booth. Spring 2008. 1 Due 2/1. From the book do: (1.1) 3, 4, 6, (1.2) 2, 4, 6, 8, 10, 12, 15, (1.3) 2, 4, 6, 8. Also: Find two substantially different proofs of Pythagorus’ theorem and present them (acknowledging your sources). Each of these will probably use some other theorems from High School Geometry; you should state these clearly, but need not prove them. 2 Due 2/8. From the book do: (1.4) 2, 6, 7, 9, 14, (1.5) 3, 5, 7(b), (2.1) 2, 3, 5, 6, 8 Also: Read the handout 1 on axioms for the real numbers and use it to prove the following facts directly from the axioms: 1. If ab = ac and a 6 = 0, then b = c ; 2. If ab = 0 then a = 0 or b = 0. [There are ways of proving both these things which are ‘structurally’ 2 very simple and should remind you of proving algebraic or trigonometric identities, or doing the logic proofs using the laws from last week. This style of proof is, in a way, the bread and butter – we’ll add more sophisticated structures to it as we go through this course.] 3 Due 2/15. From the book do: (2.2) 2, 3, 7, 9, 10 (2.3) 2, 3, 5, 6, 10, 14. No reading assignment this week, to give you time to start preparing for the midterm. 4 Due 2/23. From the book do: (3.1) 2, 3, 7, 8, 12, 15. Also: Referring to p. 84 of M. E. Munroe, Introduction to Measure and Integration , Reading, MA: Addison-Wesley (1953), answer the following questions. 1
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74SHW - Math 74 Homework Assignments. Adam Booth. Spring...

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