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# Math 299 Syllabus – Spring 2023

• Course: Introduction to Mathematical Proof
• Term: Spring 2023
• Time: TR 6:00-7:40
• Location: LSC 329

Office Hours:  T-Th 5:15-6:00pm, 7:40-8:10pm and beyond (or following the end of Math 299, whichever comes last) and by appointment or email. Check both LSC 316 and LSC 329 (they are next door to one another).

Textbook: (optional) Vandervelde, Bridge to Higher Mathematics, 2nd edition, ISBN:9780557503377

Course Prerequisites: Math 221 or permission of the instructor

Course Objective: To provide the student with the ability to read and write mathematical proofs. This will be accomplished by covering the topics in the lecture notes for the course along with any supplementary material provided by the instructor.  Students should strive to obtain a mastery of the subject matter by 1) developing both the technical skill necessary to read, write, and typeset mathematical proofs, and 2) demonstrate a deeper understanding of the underlying theory. The assignments and exams will attempt to ascertain if each of these objectives have been met.

Attendance Policy: Class attendance is required and highly encouraged. Should you miss a class for any reason, you are still responsible for all announcements made and all material presented during that class.  Missed quizzes or exams due to absence cannot be made up.

Email and the Web: All students in this course are required to have a university email account and are expected to check their email frequently for announcements and other information I may send to you. I will use email and the internet quite extensively in the course. Each student is also expected to be able to access any information that I post on the web that is related to your course. Contact the Help Desk if you need assistance.

Homework: I will post your homework assignments on our course web page. Due to the large volume of homework I assign and the large number of students in all of my courses, I must insist that all homework satisfies the following criteria:

1. All homework must have the following information at the top of the document:
1. Name
2. Assignment number (this is the assignment number given on the homework assignment web page, not the number of assignments you handed in).
2. Place each assignment in a separate subfolder of your shared Dropbox folder named “Assignment nn” where nn is the Assignment number. File names should also contain your name and the assignment number.
3. All individual problems should be clearly labeled by writing the problem number and the problem itself at the start of the problem.
4. Formal and semi-formal proofs must have only one statement per line. Expository English proofs should be in word-wrapped paragraph form and follow the conventions for standard mathematical writing that we discuss in class.
5. Problems must occur in the assignment in the same order that they are assigned, e.g. problem #3 must appear before problem #4 which must appear before problem #7, etc.
6. Some assignments must be typeset. For those assignments, in addition to meeting the criteria above, you must also use some form of LaTeX to typeset your work. This can be done with raw LaTeX code, or by using a program such as LyX or Overleaf which produce LaTeX output. You cannot use Microsoft Word under any circumstance.

Most homework assignments are required to be done on Lurch or in $\LaTeX$.  In that case, please place a copy of your .lurch or .pdf file in our shared homework folder on Dropbox and name the file:

Assignment $n$ – $lastname$

where $n$ is the assignment number and $lastname$ is your last name.

Homework files that you hand in may be edited and marked up by me, so if you want to keep a copy for yourself you should make a backup copy of your original file. If you are handing in more than one Assignment number on a single day, each assignment must be handed in separately (i.e. in separate files).  Failure to follow these procedures may result in you not getting credit for all of your assignments.

Late Assignments: Don’t even think about it.  I have yet to accept one and don’t want to spoil my record.  You will receive no credit for late assignments.  I also will not pre-grade early assignments, although you can certainly ask me questions about any assignment you are working on.  Assignments must be handed in on the day they are due before the start of class.

Missed assignments: In order to allow for sickness, bad days, other exams, scheduling conflicts, etc. I will compute the average number of problems graded in each assignment and quiz at the end of the term and drop this number of points from the total possible points when computing your homework average (this is similar to “dropping” one homework assignment for everyone).

Collaboration: All questions on each assignment can be done either individually or collaboratively as teams of two or more students in our class (no outside help). If you discuss a problem with another student, that student becomes your collaborator on that question and you must write their name at the top of your question like this:

#5 (Team: John Doe, Mary Smith)

This indicates that you spoke to John Doe, and Mary Smith about problem #5 (do not include your own name in the team list, since your name is on the top of the assignment).  Similarly, John and Mary would list you, and each other, on their problem #5 as team members.  Note that it does not matter how much or how little you discuss on a particular problem.  Whether you work out the solution entirely together and read each other’s write ups, or simply ask for a small hint from another student, each of you must list the other as a collaborator on that problem.  When working on a problem as a team, each member of the team must still write up their own solution, even if the solutions of all team members are identical.  Credit for a correct problem that is selected to be graded will be shared equally among all team members (see grading policy below).

Thus, it is in your best interested to follow the following guidelines regarding doing your homework.  If you can get a question entirely correct on your own, you should do so without talking to anyone else, otherwise your credit for that question will be divided by the number of members on your team. However, if two or more students are really stuck on a question and are not going to be able to get it by themselves and want to team up to try to answer it together, then it would be in their best interest to do so since they would receive at least some partial credit instead of no credit at all.  So if you can get it by yourself, you should, and if you can’t, find someone else who can’t and work together.

The solutions to all homework problems should be your own in your own words and symbols. You should not google solutions although you can certainly read about definitions and proofs online to learn the material.

No two students should submit the same homework file.  Just like paper assignments, you should each do your own write-ups even if you collaborate. Any acts of cheating on assignments or exams which come to my attention will be dealt with in the most severe manner possible under University guidelines. Plus, I will be really upset!

Quizzes:  There will be quizzes, both announced and unannounced, in some classes. These quizzes will be graded the same way as the homework assignments, except that you cannot collaborate with other team members on the quizzes.

Grading:  There will be a midterm exam and a final exam unless I determine that it is in the best interests of your education to not have them. There will be a lot of homework which may be graded at random, and a lot of quizzes. Quizzes will consist of zero or more problems selected randomly by Maple or intentionally by me from the homework assignments that you hand in, or a problem or two that I give you in class to work on, or a memorization quiz where I ask you to state definitions in our lecture notes. When selected at random, the selection process will be as follows: a random sequence of problem numbers will be selected (this sequence can contain duplicates) and graded in the order they appear on the list. If a problem has more than one part the part will then be selected by a second random sequence of part letters.  Which problems are are on the quiz will not be announced before you hand in the homework assignment, thus you should strive to get all of the homework problems correct. There will also be some bonus problems assigned which you can solve for extra credit. I will keep a tally of the number of these optional problems that you solve during the semester and take that into account when determining your final course grade. Each part of each quiz problem will be worth 100 points, with points awarded as follows:

 Points awarded Awarded if: $100/n$ Your response is complete and correct and there are n members on your team. 10 You made a significant attempt at the problem which is either incomplete or incorrect, and you clearly write (or type) “NOT CORRECT” at the very top of your solution. 0 Your response is either incomplete or incorrect.

There will be no partial credit for any solution, especially on proofs. Thus, you should strive to get as many problems entirely correct as possible rather than wasting your time trying to get partial credit on a lot of problems but have them all be wrong.

At the end of the term I will compute your grade as follows:

Let $x$ be a student.

Let $p(x)$ be the total number of points earned by $x$ on all exams, quizzes, and graded homework problems.

Let $T$ be the total number of points possible.

Let $D$ be the number of points I drop for everyone in order to account for sickness and excused absence.

Let $K$ be a constant (the curve) to be determined by me at the end of the semester.

Let $G(x)$ be the student’s final grade.

Then $G(x)$ is computed by:  $$G(x) = \frac{p(x)}{T-D}+K$$ and this number is converted to a letter grade in accordance with the following table:

Conversion between numeric
is greater than
or equal to …
will be at least …
93A
89A-
85B+
82B
78B-
74C+
70C
67C-
63D+
60D
0F

Remember that the best way to learn mathematics by doing it yourself.

I hear and I forget.

I see and I remember.

I do and I understand

– Ancient Proverb

Adaptability: I retain the right to modify or change any of the policies stated in this syllabus during the term if I feel it is in the best interests of the students and the course. That includes the right to give letter grades which are not consistent with the numerical grades computed above.