3210 Foundations of Analysis I - Summer
2006
Date: Wednesday, June 28, 2005
Time: 8:45a.m.-10:00a.m.
Room: LCB 219
Textbook Coverage: Chapter
1 and Sections 2.1, 2.2 of Chapter 2, textbook
Format: 4-5 problems
Midterm # 1 will test your knowledge (and ability to use in your own proofs) of concepts covered in Chapter 1 and Sections 2.1 and 2.2 from Chapter 2 of the textbook, including (but not limited to): field axioms, order axioms, the absolute value of a real number, the well-ordering principle and the principle of mathematical induction, the binomial theorem, supremum and infimum of a set, the completeness axiom and the Archimedean principle, density of rationals, one-to-one (injective), onto (surjective) functions, bijections and inverses of functions, finite, countable and uncountable sets, sequences in R (convergent, bounded, divergent sequences, subsequences, limits, limit theorems).
The best preparation for the midterm would consist of a comprehensive
review of all relevant definitions, theorems, remarks and examples
covered in the textbook and lecture, as well as working through all
suggested homework problems (from Homework Assignments # 1 and # 2).
Notes:
1) I encourage you to seek help with the theoretical results and the exercises from the relevant homework assignments that you do not completely understand . Feel free to ask me any questions you might have during lecture or my office hours.
2) You are expected to recognize and be able to state and use all the definitions and the theoretical results that we discussed in lecture corresponding to the sections from the textbook covered on the Midterm # 1 (as announced above).
3) As a general rule, in order to receive full credit for your solutions you need to present a logically coherent justification of the facts that you claim as true. Make sure that you clearly indicate which theoretical results from the textbook or lecture you have used in your solutions to the midterm problems.