Transitions, MTH 299-03
Instructor: | Tsvetanka Sendova |
Lectures Time and Place: | MWF 12:40 pm -- 13:30 pm, A118 Wells Hall |
E-mail: | tsendova@math.msu.edu |
Office: | C-137 WH |
Phone: | 517-884-1453 |
Office Hours: | TR 11:00 am - noon, MW 2:00 pm -- 3:00 pm and by appointment |
Teaching Assistant: | Jessica Stuart |
Recitations Time and Place: | R 12:40 pm -- 2:00 pm, 126 Chemistry |
E-mail: | stuartj8@msu.edu |
Course website for MTH299-03:
http://math.msu.edu/~tsendova/MTH299_F13.html
The course website is mandatory reading for the course. On it you will find the course schedule, syllabus, and supplementary reading. Homework assignments will be posted on the schedule page.
Textbook:
Required: Kevin Houston, How to Think Like a Mathematician: A Companion to Undergraduate Mathematics Cambridge University Press, 2009, ISBN 978-0521719780.
Supplementary: Matthias Beck, The Art of Proof, available free online.
Prerequisites:
Calculus I, either AP or MTH 132. The last few weeks of the course may require extra work if you haven't studied, or aren't currently studying, Calc II (MTH 133).
Writing:
In this course, you will learn to write mathematical proofs. This is a writing course. It is important that you take the time to present your solutions and proofs in clear, well written, English prose. Consequently solutions that are incompletely or poorly written will not be considered correct, even if it appears that the mathematical content is correct. You may be asked to revise and resubmit homework problems that are not well written.
Homework:
Homework will be due at every lecture. The assignments will be posted on the schedule page. Homework will usually be due on the second lecture after its assignment date, unless indicated otherwise.
This is the key to success in any mathematics class, as you cannot learn mathematics by watching - you need to do it yourself. After every class you are strongly advised to do on average an hour of reading and review, and at least two hours of homework. Daily assignments will be listed on the course web page.
Homework help is available in my office hours, during recitation, and at specified hours in the Math Learning Center.
Each homework assignment is due at the beginning of class on the assigned due date. If the assignment is turned in after the due date without a valid university excuse, it will be considered late. Late assignments will not be accepted. The lowest homework grade will be dropped at the end of the semester. Students may be called upon during class to share problem solutions.
You are encouraged to work with your peers on homework assignments and exercises in recitation. Math is a collaborative discipline and two or three minds are often better than one. However, you must follow two simple rules: 1) write your solutions in your own words and 2) cite your collaborators and sources. So let me know who you worked with and what sources (if any) you looked at. If you do work together, take the time to sit by yourself and write the homework up in your own words. You may be asked to revise and resubmit a proof that appears to be a near verbatim copy of another student's work.
Quizzes:
There will be a quiz in every recitation, except for exam days.
The quizzes will be a good indication of your standing in class. If you fail a quiz, seek help right away during my office hours, or during the specified hours at the MLC. No make up will be given for quizzes, however the lowest two quiz grades will be dropped at the end of the semester.
Exams:
There will be two midterm exams, tentatively scheduled for October 3 and November 7.
If you miss a midterm exam for any university excused absence, you need to notify me no later than the day after the exam to set up a time for a makeup. The makeup exam is to be taken within a week of the original test date. Any questions regarding grading/scoring must be addressed within two days of the return of the exams or no change in the grade will be made.
A detailed tentative list of lecture topics is listed on the schedule page.
Participation:
Please ask questions and make constructive comments during lecture. This course is for you: get the most out of it. In recitation you will be asked to work as a class and in groups on exercises central to the course. Attendance will be taken in recitation and your active participation in these activities will be part of your grade.
Grading:
Homework 25%, Quizzes 20%, Exams 15%x2, Final exam 25%
Use the following scale to convert each test score to a grade.
90--100 | 85--89 | 80--84 | 75--79 | 70--74 | 65--69 | 60--64 | 0--59 |
4.0 | 3.5 | 3.0 | 2.5 | 2.0 | 1.5 | 1.0 | 0.0 |
If the situation warrants, I retain the right of assigning grades higher than would otherwise result from the scale above.
Academic Integrity:
You are expected to complete quizzes and exams on your own, without collaboration or the use of outside resources. Any violation of this rule will be treated according to the MSU policies on academic integrity. Please familiarize yourself with these policies if you have not already.
Important dates:
See the schedule page.
Course Description
- Format
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Lecture Monday, Wednesday, Friday - 50 minutes, starting Wednesday 8/28, ending Friday 12/6.
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Recitation on Thursdays -- 80 minutes, taught by your assistant (Jessica Stuard - Advanced Track undergraduate)
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Two Midterm Exams in recitation hour (10/3 and 11/7).
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Common Final Exam Mon 12/9.
- Catalog: MTH 299 Transitions.
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Introduction to mathematical reasoning, basic logic, set theory.
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Integers, natural numbers and induction, basic number theory.
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Real numbers, limits, sequences, series.
- Audience:
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Second or beginning third year Math majors (including Actuarial majors), preparing for their first abstract math courses (Linear Algebra MTH 309, Abstract Algebra MTH 310, Real Analysis MTH 320).
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Students from other science and engineering majors have also enrolled, to get a taste of higher-level math.
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These students have learned mathematics in terms of computations and diagrams, with an occasional proof thrown in. Most have never examined a proof in detail and never attempted to write a proof. Most have never taken a geometry course with proofs.
- Goals
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Introduce the definition-theorem-proof paradigm. Teach how to state a clear definition or theorem, and what counts as a proof based on specified known facts or axioms.
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Learn the basic concepts around sets and functions, which they have never seriously used. Cover the most basic material of MTH 310 (divisibility of integers, field of rational numbers) and 320 (properties of real numbers and limits).