[posted March 30 2011] Solutions for Homework Sets H6 and H7 are up. See the end of this web page.
Textbook: A Transition to Advanced Mathematics, 6th or 7th edition by Smith, Eggen, and St.Andre. published by Brooks/Cole
This course is specifically intended to prepare Mathematics majors for Math 311 and Math 351.
Catalog copy for this course: 01:640:300 Introduction to Mathematical Reasoning
Fundamental abstract concepts common to all branches of mathematics. Special emphasis placed on ability to understand and construct rigorous proofs. Prerequisite: CALC2 or permission of department.
Format: Two 80-minute classes each week.
Learning goals: strengthening a student's
understanding of the reasons for deductive reasoning,
understanding of the results of calculus and the basis for their validity
ability to understand definitions and proofs,
ability to analyze conjectures, to find counter-examples to false statements, and to construct proofs of true statements
ability to use mathematical reasoning to analyze problems, to find solutions, and to verify their correctness,
mathematical communication skills
Lecturer: Amy Cohen
Contact Information:
Office: Hill 530 on Busch Altenate SERC235
E-mail: acc@math.rutgers.edu
Web-page: math.rutgers.edu/~acc
Phone: 732-445-2390 ext 3098 Alternate 445-8260
Course Meetings:
Tuesdays and Fridays, period 3, noo n to 1:20pm, in SEC 202 on Busch
Office Hours:
tentatively Thursdays 4-5pm in SERC 235, unless otherwise announced. permanent hours to be announced later.
also by appointment (Send me email. We'll work out time and place)
Usual Format: lectures, discussion of homework, and workshops. two midterm exams and a final exam.
Content: naive set theory, the language of mathematical reasoning, common methods of proof applied to a reasonable (but not minimal) set of axioms for the rational numbers, some comments on extensions to the real number system.
[posted 31Jan2011] Sample solutions are now available for Homework Set #1.
[posted 8Feb2011] Solutions to Homework Set 2 are available. The link is at the end of this page.
[posted 2Feb2011] I have corrected the previous corrupted version of this web-page. Please re-read carefully, especially about grading.
GENERAL ISSUES
A tentative course schedule and homework list will be available soon. Beware of frequent adjustments. Watch this website regularly for announcements.
Read the assigned sections once before each lecture. Read them again after each lecture before starting on the homework. Re-read them as often as necessary! Additional material may be posted on this web page.
Attendance is crucial. I will accept late homework only in special cases and even then only if I have not yet returned the graded set.
Make-up exams will be offered only if there is adequate reason to do so. A student's lack of preparation or lack of confidence is not an adequate reason. In most cases, if you must miss an exam you will know in time to discuss the matter with me (in person, by phone, or by email) IN ADVANCE. If we have not discussed the matter in advance, then I will need evidence of an emergency.
EXAMS: There will be two midterm exams and a final exam.
HOMEWORK: There will be weekly homework. I will assign lots of problems "to do". Do all those and as many more as you need to acquire fluency and mastery. I will assign fewer "to turn in". We will discuss some of these in class. My grader will grade four problems per homework set. Each problem is worth 10 point: 6 for content and 4 for exposition. See the directions below for write-ups.
WORKSHOPS: We may have occasional workshop sessions in which students will work on specially constructed problem sets. Most problems will deepen understanding of recently presented material. Some problems will connect recent material to earlier material in the course. Some problems will provide motivation for upcoming material.
The lecturer will circulate among the groups coaching, but not demonstrating solutions. The goal at first is to offer ideas for analyzing the problem. Later in the term the goal is to ensure that groups can make use of the ideas offered repeatedly earlier.
At the end of each workshop session, one problem will be assigned to be written up and submitted at the next workshop. While students are encouraged to work together outside of class, the write-ups should be individual work. These write-ups will be graded on two scales: 0-6 for content and 0-4 for exposition. Good reasoning and good mathematical exposition may be more valuable in the long run than any particular piece of mathematical technique.
If a student has made an honest effort but not achieved much success, I may permit the student to revise and resubmit with the original attached for regrading. In such a case the original score will be replaced by the average of the two scores if that average is higher than the original.
HOMEWORK:
I will assign about 5 to 10 textbook exercises a week for you to work on. There is link to the homework assignments below. I will assign about 3 to 5 of these to be turned in. These will be due one week after they are assigned. Of these, some (usually not all) will be graded. Other homework (whether turned in to not) may be discussed in class.
Homework will be due one week after it is assigned, usually on Thursdays.
Each homework problem will be graded on a scale of 0-10. Remember, the grader cannot grade your mathematics unless its exposition makes it clear what is going on.
I have been known to put homework problems on exams. Obviously, it is to your benefit to learn from doing the homework and to learn more from the reader's comments and from the class discussions.
DIRECTIONS FOR WRITING UP HOMEWORK AND WORKSHOP REPORTS
Each write-up is a short technical report. It should be a well-considered professional document; not a first draft.
Write on one side only. Put your name on each page. Number pages. Maintain at least a one-inch margin on all four sides.
Edit carefully. Use correct spelling and grammar.
Begin each problem, or major part of a problem, with the caption "Task" and a statement of the task. This statement should be self-contained.
Next, using the caption "Result", state the result of the task. Do not use any notation in the result that is not defined in the statement of the task. This step is omitted if the task asks for a proof.
Finally, using the caption "Work" or "Proof" justify the result. Include diagrams or graphs if these will help the reader follow the work. Include special cases if that will help. Use correct mathematical reasoning and cite reasons for your assertions.
A proof of an assertion should explain why that assertion is valid.
TERM GRADES:
Each midterm exam counts for 100 points. The final exam counts for 200 points. Any workshop problems will be included in the homework computation. The homework sum will be rescaled to count for 50 points.
Homework is intended to help you learn the material. Poor performance on homework will not necessarily lower your term grade. However, I have rarely seen students do well on exams who have not worked diligently on homework.
An extremely weak final exam may lower a term grade below that suggested by the point-total taken altogether.
Be alert for modifications in this schedule.
Be alert for modifications!
In general solutions to each problem set will be posted after that set has been graded and returned, possibly not immediately after! Once I have posted solutions for a homework set, I will not accept late solutions for that set.