Math 414: Analysis I
Exam 1 Topics
1. Sets involving Unions and Intersections, Set Minus Operation, and DeMorgan’s
Laws (See in book: 0.3.1, 0.3.6, 0.3.8, HW 1 #1)
2. Functions (Injections, Bijections, Surjections, Composition of Two Functions), Direct Images and Inverse Images (See in book: 0.3.10, 0.3.3, 0.3.4, HW 1 #2,3,6)
3. Principle of Induction (See in book: 0.3.13, 0.3.15, 0.3.16, 0.3.17, HW 1 #4)
4. Properties of Ordered Fields (See in book: 1.1.1, 1.1.3, HW 2 #2, HW 2 #3)
5. The Completeness Property (Existence of a sup/inf) (See in book: 1.2.9, 1.2.10,
1.1.2, 1.1.4, 1.1.5, 1.1.6, 1.1.9, HW 2 #4-6)
6. The Archimedean Property/ The Density Theorem (See in book: 1.2.1, 1.2.2, 1.2.8)
7. Problems involving Absolute Value (See in book: 1.3.1, 1.3.2, 1.3.3, 1.3.4, 1.3.5,
1.3.7, HW 3 #4-5)
8. Intervals/The Characterization Theorem (See HW 3, #2)
Additional Details
• Exam 1 will occur in class on Monday, February 17 in our usual classroom.
• In addition to going over the homework, please refer to the examples done in class,
as parts of the exam may resemble these examples.
• Although you have 50 minutes to complete the exam, I will be in the classroom at
10:55 AM for those who would like extra time. The exam will conclude at 11:05
AM.
• No notes or electronic devices may be used on the exam.
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