Topology ---Information on tests so far

Test 1 is on October 11 in person (face-to-face in classroom). Proofs that might be on the test are the items before Section 2.2 in this list.


Mock exam for semester midterm (some of the later questions are not relevant (not on the syllabus above for this test)). Also the actual test may not say in the instructions `Answer as many questions as you can', but may give more limited choice. Also, the actual exam may look quite different to this.
Instructions for studying for the first test. Read classnotes again carefully, making sure that you understand everything (this will be easy since you have already done it once in great detail (`main job'). Memorize definitions and statements of Facts, Theorems, Propositions, etc. Review all homework, and their keys, learning from your mistakes. Understand how the concepts fit together. Memorize proofs from the list of proofs above. 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.
Test 1 will have four kinds of questions. 1) State a definition (example: define a compact set and state several things equivalent to this); 2) State a theorem/proposition/corollary/lemma/Fact (example: State the Tychonoff theorem. Or "Complete the sentence: The Tychonoff theorem states that a product of _______); 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 the list above.
For memorizing proofs from the list given above, I suggest the following steps: 1) understand the proof fully, line by line. 2) Close the book and try write down the proof. 3) When you get stuck, reread the proof then do step 2 again. 4) Repeat step 3 many times, until you can write it out without errors. 5) Write it out twice more, quickly. 6) Congratulate yourself! The purpose of this is not to emphasize `parroting' or `rote learning', but mostly to hardwire certain thinking patterns, you are reconfiguring your brain to work and think in the kind of detailed logical way one needs to in pure mathematics.
Instructions for studying for the final exam are exactly as for Test 1 above but I will only test on the material after Test 1.
List of proofs that might be on the final: the items in Sections 2.2--3.1 in this list.


Mock exam for Final (some of the questions may not be relevant (not on the syllabus above)). Also the actual final may not say in the instructions `Answer as many questions as you can', but may give more limited choice. Also, the actual exam may look quite different to this. And there may be some extra questions on algebraic topology for those doing that project.