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(based on MATH0450, Spring 2010 notes, courtesy of Piotr Hajlasz). Written Projects: It is required that the projects be typed on a computer. Refer to the discussion in the class on Monday Feb. You should prove all the properties of such a field. Here is a list of suggested topics , but you are not limited to that list.
Grading: Your final grade depends on your performance on the final exam as well as on your total grade calculated as follows: Homework (10%), Written projects (10%), Class midterms (40%), Final (40%). Using Te X or La Te X is preferred, but you can also use Word or other systems. Assuming the premises and basic facts of the axiomatic set theory, write the definitions of the notions of equivalence relations on a set and partition of a set. Assuming the existence of real numbers, construct an ordered field which includes them but is not complete. If necessary, I could give you some further personal advice on the choice of your topic.” Not a pleasant situation, but not a hopeless one.After all, solving such problems is what our service was created for!If you are active on social media, you might have noticed your friends and other people desperately seeking help with their written assignments, leaving tweets or comments like “Can anyone do my homework for money? Unlike many people who could respond to these requests, our writing service guarantees that your work will be done by a professional who has at least a few years of experience in academic writing and is proficient in several fields of knowledge.Due to the variety of skills our employees have, they can deal with pretty much any written assignment you need to get done.You may work with other students or use library resources, but each student must write up his or her solutions independently. A bonus point will be accorded to the most elegant and original expository examples. It is not necessarily required that all minor proofs are presented.Copying solutions from other students will be considered cheating, and handled accordingly. If you miss the midterm exam for a *documented* medical reason, your grade on it will be the prorated grade of your final exam. It must be typed/word-processed, and should be approximately eight pages in length, double spaced. Papers that include passages lifted verbatim from other sources without appropriate citations will receive a grade of F. Clarity and tidiness of presentation, completeness and correctness are necessary to obtain full grade. To encourage using Te X or La Te X, 1 bonus point for each project typed in that system will be accorded. State and write the proof of the fundamental theorem of equivalence relations and provide an illustrating example. Refer to the discussion in the class on Monday Feb. You should prove all the properties of such a field and show that it cannot be complete. Your paper should be interesting and comprehensible to a reader who does not already know your topic.In particular untidy presentations of correct proofs will be severely penalized. Your paper must be written in such a form that your proof could possibly be included in a hypothetical textbook. It must include some technical detail or proofs and some expository examples and explanations.Attending office hours is greatly encouraged, in particular at the beginning of semester.Recitation: Tu PM-PM at Thack 524, Instructor: Mark Tronzo Objectives: This is an advanced course for highly motivated students. Homeworks are due on Tuesdays and have to be handed in to the TA.