Syllabus for MTH U170: Math, Discovery, and the Computer

Fall, 2004




Instructor: Professor Mark Bridger (Office 527NI, e-mail bridger@neu.edu)

Class Web Site: http://www.math.neu.edu/~bridger/U170/U170.html

Text: MATLAB: An Introduction with Applications by Amos Gilat (Wiley)

Computer Labs: Math Dept EXCEL Lab: 553 LA; INFOCOMMONS: Snell library; other labs around campus.

Office Hours: Mon, Wed, Thurs, 10:30 - 11:30 and after class; also, by appointment.




Introduction: This course is about learning and doing mathematics. The mathematics one finds in a textbook or technical paper is merely the last step in a process that may include formal introductory study, questioning, experimentation, guesswork, inspiration, collaboration, frustration, exhilaration, proof and exposition. Some of this is done verbally, some in imagination, some in longhand, and some on a computer. We will experience a bit of it all.

Skills: Here are some of the skills that you will learn in this course:

  1. Listening, observing and note-taking. Since there is no formal mathematics textbook, all necessary mathematics will be presented verbally, on the board, in handouts, or through references (often on the Web). You will be expected to write this up on a daily basis.

  2. Working out examples and finding patterns. This is the heart of mathematical discovery. Some of this will be done with pencil and paper and some of it will be done using powerful computer programs such as MATLAB and Excel.

  3. Using mathematical logic and constructing careful proofs.

  4. Writing computer programs.

  5. Writing good mathematical prose.

Topics: We have a lot of flexibility, but tentatively here are some of the topics we may examine.

  1. The whole numbers, mathematical induction, divisibility, Euclidean algorithm, prime numbers, the rational numbers, irrational numbers.

  2. Lattices and lines passing --- and not passing --- through lattice points.

  3. MATLAB: simple commands, function graphing, programing using script files ("m-files")

  4. Parametric curves.

  5. "String Art" and envelopes

  6. Mapping Diagrams

  7. More on lattice points: theorems of Gauss, Minkowski, Pick and Blitchfeldt.




Class organization: For working in the computer lab you will choose or be assigned a lab partner. For certain other work the class will be divided into (voluntary) teams. This is also a way of meeting other students and having a source of information in case you have to miss a class due to illness etc.




Notes/journals: You are expected to take careful class notes and write them up periodically. From time to time I will collect these rewrites, but I will always give you notice no later than the class before they are collected. I expect you to include in these write-ups questions and/or comments on the material. These provide useful feedback about how the class is going and problems that you have encountered. These notes/journals will not be graded (other than acceptible/unacceptible).




Written assignments (including computer labs): These must be neat and readable. Unless otherwise specified, they need not be typed, but they should be checked for grammar and spelling. Mathematicians and other technical people should be able to communicate their ideas effectively!




Joint work and plagiarism: For most assignments you will are encouraged to consult with other students. You may use any kind of standard reference materials, including the Internet, for assignments done outside of class. However, please note the following:

  1. ALL WRITTEN ASSIGNMENTS MUST BE WRITTEN INDIVIDUALLY, IN YOUR OWN WORDS. Two or more students whose work contains significant identical overlap will be in danger of receiving failing grades.

  2. FOR EACH ASSIGNMENT, YOU MUST LIST THE NAMES OF ALL STUDENTS YOU WORKED WITH.

  3. FOR EACH ASSIGNMENT, YOU MUST LIST ALL REFERENCES YOU USED. ALL DIRECT QUOTES, INCLUDING "CUT-AND-PASTE" MUST BE PUT IN QUOTES AND REFERENCED. This is especially true for material downloaded from the Net.

If you have any questions about these matters, please consult with me before you hand in your assignment.




Grading: There will be periodic quizzes based on class work, various written assignments and computer labs, and a final exam. You will be able to select and assemble final (polished) versions of written assignments, including labs, to include in your portfolio, which will represent the best of your work. This will count as 45% of your grade. Quizzes will count as another 30%, the final 20% and class participation the final 5%. These percentages are subject to small adjustments determined by possible changes in the course and individual circumstances.




Attendance: Attendance will be taken and you are expected to be present for every class. If you miss more than 2 classes you will be on probation and a further absence may result in a failing grade. If you must miss a class, the best thing is to let me know in advance. "Excused" absences must be discussed during my office hours. You are responsible for making up any work you missed in any case, and you should get classnotes and assignments from fellow students.




Some IMPORTANT resources:

  1. I will always be in my office during the hours to be announced. Please come to see me! I will be more than happy to help you with work related to this course, or help you cope with the Northeastern bureaucracy, or be useful in any other way I can. Even if you want to talk about non-academic things (baseball, bicycling, politics, etc.), I'm interested in what you have to say.

  2. I check my e-mail periodically during the day (till about 10 PM, sometimes later) and will be happy to respond to (reasonable) messages as soon as I possibly can. Try me!

  3. I will post useful information on the class Web site fairly frequently. This includes announcements, hints, assignment information, corrections of mistakes I made (it happens!), and other useful items. So check out the page frequently.