Math 3333---Intermediate Analysis---TESTS

<:html>Math 3333---Intermediate Analysis---TESTS

Math 3333 -- TESTS

There will be a 30 minute test after every chapter. The tests will have only four kinds of questions, and you will need to study for each of these four types separately. 1) State a definition (example: Define what it means for a set to be bounded); 2) State a theorem/proposition/corollary/lemma/Fact (example: State the nested intervals theorem. Or "Complete the sentence: The Heine-Borel theorem states that a set is compact iff _______); 3) Do an example identical or very similar to one done in class or on the homeworks. 4) Prove a theorem/proposition/corollary/lemma/Fact from a list of 6 or so that will be provided. So here is the recommended way to study for the tests: Read classnotes several times carefully, making sure that you understand everything (of course you will have already read through this once, as you were asked to do after each lecture), and understand how the concepts fit together; i.e. get the `big picture', but also have a tight hold of the details. Memorize definitions (again, you were asked to do this on a daily basis as we met them) and statements of the more important Facts, Theorems, Propositions, etc. Review all homework and quizzes, and their keys, learning from your mistakes. Understand and then memorize proofs of the list provided (you may need to write them out six or seven times without looking to ensure you really got them). Of course once you get into this, you will find that you are putting them in your own words, which is great so long as those words are correct. Do the mock exam after you have finished studying, as a reality check, then as a guide to what you should spend more time studying). The grading system on tests and exams is designed in part to benefit students who follow the instructions given to study for those tests (see the top of the `Tests' page on the website): thus many will get over 100% for tests, while others who do not follow the instructions (or who only follow part of the instructions) may well do very poorly.

Test 1 and 2 date on main course webpage. Tests 1 and 2 will cover up to the end of Chapter 3. Test 2 will cover the material from and including Section 3.4 on open and closed sets till the end of Chapter 3. Test 1 will cover the material before that section, plus the earlier material in the typed notes (negating statements, etc). Mock exams are provided, however they are a mix of Test 1 and Test 2 questions (Do the mock exam after you have finished studying, as a reality check, then as a guide to what you should spend more time studying). Read classnotes several times carefully, making sure that you understand everything. Follow the instructions above (on how to study for each of the 4 kinds of questions described above that will be asked.) Memorize proofs of the following list (numbers as in typed notes): Theorem 3.6, 3.7, 3.8, 3.9, 3.11, 3.12 (for Test 1), 3.14, 3.15, 3.19,3.20, 3.26, 3.27, 3.28 (for Test 2). More instructions will be given in class.

Mock exam for Test 1 and Test 2.

Another mock exam with Key for Test 1 and 2.

Key for Test 1

Key for Test 2

Test 3 is on Chapter 4 and Test 4 is on Chapter 5. The list of theorems whose proofs are examinable on Tests 3 (Chapter 4) and 4 (Chapter 5) are Facts 1, 6, 8, 9 on sequences (you may omit 9 (7)), then results 4.3a,c, 4.4, 4.10 (for Test 3), 5.1, 5.2, 5.3, 5.5, 5.6, 5.8, 5.11. These numbers are as in the typed notes. Other instructions for Tests 3 and 4 are exactly as above, and exactly as for Test 1.

Mock exam for Tests 3 and 4. There also may have been some proofs asked for here that were not on your list of proofs to study--such will not be on the real test).

Key to mock exam for Tests 3 and 4 (read only after you've tried the mock exam under test circumstances after you've finished studying).

Another mock exam with Key (again, a little long though).

Key for Test 3

Key for Test 4

Abbreviated notes version for Tests 3 and 4 attached: just the definitions, theorem statements, proofs on the list. I may possibly have made a mistake, so check it. Also, this is not intended as a REPLACEMENT for your classnotes; the classnotes have lots of other things that you may need for your understanding, like worked examples. Also, a couple of the proofs may be better in the classnotes than the version given here.

Tests 5 and 6 will include Chapters 6 and 7 respectively. The list of theorems whose proofs are examinable here are 6.1, 6.2, 6.4, 6.5, 6.6, 6.7, 6.8; and for Test 6: Chapter 7 Observations 1 and 4, 7.1, 7.3, and facts I4 , I9, I10. Other instructions for Tests 5 and 6 are exactly as above, and exactly as for the other tests above.

Tests 5 and 6 Mock Exam

Tests 5 and 6 Mock Exam Key

Abbreviated notes version for Tests 5 and 6 attached: just the definitions, theorem statements, proofs on the list. I may possibly have made a mistake, so check it. Also, this is not intended as a REPLACEMENT for your classnotes; the classnotes have lots of other things that you may need for your understanding, like worked examples. Also, a couple of the proofs may be better in the classnotes than the version given here, or may not even be on the list of proofs), and the proof of I9 is omitted here accidentally.

Tests 1, 5 and 6 material will not be tested on the final.

The list of theorems whose proofs are examinable on the final is the same lists for the tests, minus proofs that were on previous tests (however if for example you were asked to prove only part of a theorem on a previous test, then the remainder of that theorem is fair game). To make the list smaller still, remove 3.20, 3.27,3.28, (2, 5, 6, 7 of Fact 9 in Chapter 4), 4.3, 4.10, 5.8. The usual advice holds, like read the classnotes through again, clearing up any confusions, etc.

Mock exam for final (this is longer than the real final, and contains Test 5 and 6 material and series material that is not examinable this semester).

Key to most of mock exam for final.

After the semester is over, if you have any questions about regrades etc, or just want to review your grade email me to make an appointment at my office.