Mat246 syllabus PDF

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MAT246 winter 2017 course outline...

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MAT246 Preliminary Course outline (as of Jan 6, 2017) Winter 2017

1. LECTURES: L0101: Mon. 3-4, HS610, Wed4-6 BA1160, Dietrich Burbulla, burbulla at math.utoronto.ca office hours: TBA L5101: Tues. 6-9, RW110, Soheil Homayouni, email: homayoun at math.toronto.edu Office hours: PG111, Tuesdays 9:30-11:30, Thursdays 10 - 11:45 2. TEXTBOOK AND READING MATERIAL: - ‘A Readable introduction to Real Mathematics’, by D& D & P. Rosenthal; publisher: Springer, available in the bookstore - Extra readings will be gradually posted on the course’s blackboard page. 3. PRE-REQUISITES: A full year course in Calculus: MAT133Y1/(MAT135H1, MAT136H1)/MAT137Y1, and MAT223H1. Students with pre-requisites of MAT133 or MAT135, or a low grade in MAT137 may be missing mathematical reasoning, and will find this course challenging. Note that we may set up problem sessions to help with necessary background and culture of mathematical reasoning (details to be announced when/if they are arranged.) 4. MARKING SCHEME: - Problem sets: (3 of them, due dates: see below) 12% - Webwork exercises (various deadlines) 5% - Quizzes: (6 quizzes, given in the tutorials) 9% - Midterms: two 15% each (Fridays, Feb 10 and Mar 17, 6-8 pm.) - Final exam: 44% (Note, even if the term mark is high, a minimum of 35% on the Final exam is required for passing the course.)

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5. Tutorials Tutorials are mandatory (and important) component of the course: - quizzes will be written in the tutorials, - the problem sets and quizzes will be returned in the tutorials, and the TAs will remain in possession of the papers till the end of the course. However if you do not collect the paper immediately on the day of return you may have to make special arrangement with the TA to bring your paper to the next tutorial. Your TAs are the first point of contact in dealing with the re-grading issues. And, re-grading is time sensitive (see details below.) - Tutorials act as unifying agents in the course. We make sure that important course material, ideas and examples and useful hints are discussed there. As much as the lectures focus on setting the language and elaborating on the theory, many examples will be presented in the tutorials which can clarify the theory. - Please do not use your TA’s time to dispute the grading issues; your TA may be different from the marker, and the precious tutorial time will be wasted. For regrading procedures please see the section on re-grading. TUT0101 TUT0201 TUT0202 TUT0301 TUT5101 TUT5102

Mon 1-2 Mon 4-5 Mon 4-5 Tues 3-4 Wed 5-6 Wed 5-6

BA 1200 MS2173 SS 1072 SS 2127 SS 1070 HS 106

Hannah Zack Debanjana Zack Debanjana George

6. Midterm Test: Please note that midterm tests will take place 6-8 in the evening on the test date. Please leave that time reserved for the test and do not plan to be away from campus at that time. There will be a make up for a missing midterm held within a couple of days of the term test. In case of missing the midterm due to medical reasons please immediately contact us to arrange for a make up (details to be posted.) Please note that doctor’s note without a UofT medical certificate will not be accepted. The incomplete and/or illegible medical certificates may be rejected. 7. QUIZZES: Scope of each quiz will be announced in advance. The quizzes will give you chance to prepare in small, weekly doses. Each quiz is like a mini Exam, condensed in one page; use the experience of a quiz for gaining experience in writing the midterm or the Final Exam. Marking schemes for the quizzes will be posted; these marking schemes demonstrate how the quiz should have been written and how it will be marked. Each tutorial will have their own individual quiz and as such by consulting all the quizzes from different tutorial you will find a good exposure to exam type questions. There will be no make up for a quiz, but there will be a few bonus marks built in to the marking scheme so that the mark of a missing quiz is easily recovered. However the experience of preparation for a quiz is valuable and should not be missed. 8. PROBLEM SETS: Problem sets are due Fridays 2pm. in the drop boxes located in PG math aid centre. The drop boxes are marked according to the tutorial sections. Problem sets that are deposited in the wrong tutorial section box may get lost in the system. So please be aware of your tutorial section. Problem sets are designed to complement the lecture material. They are based on the material presented in the textbook and the extra readings. Problem sets are used to extend the theory further in various directions and guarantee a depth of understanding of the course material. Even though students may be working together on a problem set, the final answers must be written independently of one another. Copying

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parts of the problem set answers will result in a receiving a mark of zero for all parties involved. , and all parties involved will be dealt with according the university regulations on plagiarism. Each problem set will be posted almost two weeks before the due date. However there will be a first draft of the problem set posted first and then the presentation draft will be posted. There are two main reasons for this: the first reason is that the class can start working on a partially complete version of the questions before we are certain about our coverage in the course. So please start working on the problems as early as you can. The second reason is that you will need the presentation draft only when you have worked out the answers. Please don’t use the presentation draft as a working draft, but use it rather to enter your final, polished work. It is expected that each student write numerous versions of a solution before they are satisfied with their polished answers. There is sufficient time for finishing a problem set, and therefore there is no need for extensions or make-up for a problem set. The solutions/marking scheme to the problem sets will be posted shortly after the submission deadline, to help with the remarking process, therefore any individual extension will interfere with the posting of the solutions, and therefore all requests for individual extensions will be rejected. NOTE: please be careful of the following: - please don’t allow anyone you know or you don’t know, to take a cell phone picture of a portion of your answer. Such pictures may be sent to others who may indiscriminately copy from your solutions while you are completely unaware of their actions. You will be responsible for this infraction. - please don’t give your problem set to anyone to drop it off for you; they may copy a portion of your solutions, and you will responsible. - if you wish to help someone with a question you must be able to distinguish between ‘the idea’ and ‘the details’; if you are not sure about the distinction, then you may become responsible for plagiarism. - if you commit the act of plagiarism, even if you drop the course, you will still be responsible for the act, and will still be dealt with according to the regulations. 9. PROBLEM SESSIONS: Starting the first week of classes there is a Fridays 4:30 - 6:00 problem session meeting in SS 2102, (except for Feb 17, which takes place in BA 1130), to discuss and study the necessary backgrounds for the course. These sessions also cover the extensions of the ideas discussed in the course, as well as the style of writing a proof. The topics and specific questions will be posted in advance. Please review these questions, write your own version of a solution, then attend the problem sessions and see how the solutions should be written. The nature of a course in mathematical proofs is that it not only requires the knowledge of mathematical concepts but also it also requires a strong understanding of the structure of a proof as well as a good intuition about the concept. Understanding the structure of a proof is not something that we can learn by memorizing and copying, but it is a sense that we must slowly and consciously develop. The problem sessions help with this process. 10. ADJUSTING GRADES: There is no adjusting of the grades in this course. However one can gain extra bonus marks (during the tests and exams and even problem sets.) Please note that this method allows for a group of motivated students to earn marks beyond 100% in each component of the evaluation, and as such we will have a larger than usual portion of A+ in the course. 11. RE-GRADING: Midterm tests, quizzes and the problem sets can be regraded. The procedure is as follows:

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- the solutions/marking schemes for all quizzes and problem sets will be posted prior to returning them in the tutorials. It is responsibility of the students to have access to these solutions/marking scheme at the time of pick up (in the tutorials.) Using this marking scheme one may catch the obvious marking mistakes. Some obvious issues will be corrected and returned to you by the TA, but for further, non trivial disputes please return your paper your TA with a note attached indicating the issues with marking. Please note that in general your entire paper may be looked at and remarked. - the remarking is done in your presence and it serves some educational purposes. Please come to the office hours of your professor to discuss the regrading of your paper, otherwise your paper may never get remarked. 12. HELP HOURS, MATH AID CENTER HOURS: There will be regular Math aid center hours (TBA) throughout the course. In addition, your professors will hold regular weekly office hours, and there are tutorials and a problem session. You are welcome to use all of these hours. In addition there will be extra MAC hours near the term tests. You may attend any of the office hours, your tutorial, and the problem session to ask your questions. Therefore at any given day you have access to one of the members of the teaching team to resolve your mathematical questions. Please refer to the schedule of our availability and don’t hesitate to approach us. 13. PLAGIARISM: This is an act which greatly impacts one’s personality and could have extremely damaging future consequences. Moreover there is the important and sensitive question of fairness across the course, and above all plagiarism is against university regulations. Therefore we shall be extremely vigilant to detect and to deal with such incidents. - In our course ’plagiarism’ can happen in the form of copying problem set solutions, or quiz answers. (In both cases our markers can easily detect such occurrences and as a first step the entire work will receive a mark of zero.)

- The act of plagiarism can take place between two individuals or a group of individuals. The later case is obviously easier to detect, and it surely has more serious consequences. Please note that an individual student may unknowingly become a member of a network of plagiarists by allowing lending their work to a “trusted friend”. - In any case, all the collaborators will all be treated similarly: they all receive the mark of zero on the plagiarized work, and they will be known to us, and for the rest of the term their work will be closely monitored. Therefore the marking of such papers may be delayed due to the need for special considerations. - Once plagiarism is detected in one piece of work then the previous work will be investigated for previous occurrences of the offense and the treatment will be retroactive. So in such situations one may be asked to provide us with their past work for further investigation. So please keep your collected work in good condition and ready to submit them for reviewing. - Should the weight of the plagiarized material exceed certain limit (10%) the offense will be forwarded to the the Faculty for investigation at a higher level. 14. COURSE OBJECTIVES: Please note that the focus of the course is on training the analytical ability and logical reasoning. There is special emphasis on what a ’mathematical proof’ is and how a theorem’s conditions fit together to produce a justification for its conclusions. Throughout the course we shall stress the value of Axiomatic thinking by practicing the journey from definitions and statements of theorems to proofs and justifications.

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Throughout the course students are asked to completely understand and memorize the exact details of definitions, and exact statements of theorems. Also a number of algorithms appear in the course; these algorithms also have to understood and memorized. The quizzes, midterm test and the final exam will all ask proof questions, and they are closed book exams. Therefore it is extremely important that the basic tools of proofs to be mastered. Also, in this course it is believed that we learn proofs by studying the classic proofs: these are the most polished versions of what mathematicians consider as clever arguments for proving certain facts. A successful student - reads these proofs over and over, - understands them, why they work, - understands how the details are relevant to one another, - is able to reproduce them and teach them to others, - keep them in her/his head as tools in a toolbox, - reviews them, reflects on them, to see how they can be modified and applied to new problems and situations. And this is how a mathematician is born. So, now that you are young and your brain has plasticity and can memorize, learn and adapt; please be prepared to absorb as many ideas as possible and as early in the course as possible. Allow these ideas to roam in your heads; it is then that the ideas begin integrating into a network of ideas, that soon become a flow, a process of thinking, and it is then that a rich network of mathematical thinking fills the brain. Please fight the temptation that claims: “mathematics is not about memorizing!” This policy perhaps creates a mathematician that does not remember the most polished classic proof techniques/ideas; one who, perhaps, spends lots of time in the library, checking the textbooks, or at best reinventing a badly shaped wheel. 15. EMAIL POLICY: In a large class and in the age of texting and smart phones and real time communication it may be a challenge for your instructors to respond to emails in real time. So please be advised that there will be a delay in responding to your emails. - Short answer, administrative emails are usually easy to answer and naturally they get answered faster, within a few hours or a day. - Emails regarding a typo or mistake in a posting are very much appreciated. They also get priority and they are responded within a few hours. - Your TAs have limited number of hours on their contracts with the course, so they are not required to answer any emails. Therefore we are not providing TA emails. - let’s say emails which refer to the information already covered in the course documents (posted on BB, and announcements mailed to the class) as well as the ideas discussed during the lectures may remain of low priority, and may never be answered. Your instructors also have to make sure their answers are consistent with the posted regulations and arrangements. Any mistake in email correspondences may become a liability on the part of the course administration. - Emails in which students propose an alternative arrangement in the course such as an alternative grading scheme, or an special consideration that may be unfair to other students, present your instructors with ethical and legal dilemma. Even though your instructors would be willing to respond to such emails it may take days or weeks or even months before they can resolve their ethical dilemmas and to compose a response. - Emails which refer to certain pages of the textbook or certain posting on BB may also take a couple of days to respond because your instructors may not be near their textbook nor they may have enough time to investigate your references. Therefore such email may be delayed.

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- Detailed mathematical answers may be difficult to communicate through email and they tend to become sketchy; possible confusions in these instances may also become liability for the course administration. Naturally such emails lose their priority, or the answer may simply be: ”please attend an office hour or help hour or a tutorial to ask your question.” Every day of the week there will be some help/contact hour in the form of office hours, math aid center hour, problem sessions or tutorials that are open to any student in the course. - Emails requesting a hint to a problem set question may be tricky: your instructor may want to be as sketchy as possible, and again there may be misunderstandings which in turn can be a source of liability on the part of the instructor. So the instructor may refrain from answering such emails all together. - we may set up a piazza account for the course, which can be taken as a forum for discussion about the course content. 16. COURSE COVERAGE: The plan is to cover almost all of the textbook. Any omissions will be coordinated between the lectures and the class will be notified. The best way to be aware of the exact coverage is to consult the weekly quiz coverage. Here is a tentative schedule: Week of Jan 8 Jan 15 Jan 22 Jan 29 Feb 5 Feb 12 Feb 26 Mar 5 Mar 12 Mar 19 Mar 26 Apr 2

coverage Chapter 1 Chapter 2 Chapters 3,4 Chapters 5,7 Chapters 6, 8 Chapter 9 Chapter 10 Chapter 10 Chapter 10 Chapter 12 Chapter 12 Chapter 12

event Tutorials and problem sessions begin Quiz 1 PS1 due Fri 17, 2 pm. Quiz 2 Test 1 Fri 10, 6-8 pm Quiz 3 PS2 due Fri 3 Quiz 4 Test 2 Fri 17 Quiz 5 Quiz 6 PS3 due Fri 7...