Math 213: Basic Discrete Mathematics
Spring 2006
Professor A.J. Hildebrand
http://www.math.uiuc.edu/~hildebr/213/

General Information

• Date/time/location: MWF 12:00 - 12:50, 149 Henry Administration Building

• Instructor: A.J. Hildebrand, office 241 Illini Hall (second floor, north end of hallway), phone 244-7721, email ajh@uiuc.edu. Office Hours: MW 1:30 - 2:30. In addition to these "official" office hours, I will hold a weekly "Open House", intended as an informal office hour, Wednesdays, 5 - 6 pm, in 147 Altgeld Hall.

Course Information

• Course description: From the Course Catalog: "Beginning course on discrete mathematics, including sets and relations, functions, basic counting techniques, recurrence relations, graphs and trees, and matrix algebra; emphasis throughout is on algorithms and their efficacy."
• Prerequisite: MATH 220 or equivalent.
• Text: "Discrete Mathematics and its Applications" by Kenneth H. Rosen, 5th edition. This text is an officially "required" text, so you definitely need to have a copy. There is an accompanying "Student Solutions Guide", which you may want to purchase (but are not required to do so - you have to decide yourself whether it is worth the money).
• Syllabus: Below is the official departmental syllabus for this course. I intend to follow this syllabus closely, but I may deviate from it slightly on occasion, and the list below should therefore be only regarded as a first approximation to what I intend to cover. I will make up the final syllabus as we move along; refer to the lecture summaries posted on the course website for a list of sections and topics covered each day.
  • Chapter 1 (Foundations): Sections 1.6-1.8
  • Chapter 2 (Algorithms): Sections 2.1-2.3
  • Chapter 3 (Sequences and Mathematical Induction): Sections 3.1-3.2
  • Chapter 4 (Counting): Sections 4.1-4.5
  • Chapter 5 (Discrete Probability): Sections 5.1-5.3
  • Chapter 6 (Recurrences and Inclusion-Exclusion): Sections 6.1, 6.2, 6.5, 6.6
  • Chapter 7 (Relations): Sections 7.1, 7.3, 7.5
  • Chapter 8 (Graphs): Sections 8.1-8.8
  • Chapter 9 (Trees): Sections 9.1-9.5
• About this course: As you can tell from the syllabus, this course covers a lot of territory. It is quite different from other math courses you may have had (such as calculus or matrix theory) in that the emphasis is on rigorous mathematical reasoning rather than rote applications of recipes and memorizations of formulas. It will be labor-intensive, probably more so than any other math course at the beginning undergraduate level.
• Related courses: A very similar course is CS 173, which uses the same text, with a slightly different syllabus, that emphasizes more the algorithmic aspects. You won't get credit for both Math 213 and CS 173. You can find out more about CS 173 from their website. I have never taught CS 173, and I don't know much beyond the information available on the course website.

Homework and Exams

• Non-graded homework and reading assignments: I will give out daily HW assignments, which will not be collected, as well as reading assignments from the text, intended to complement and reinforce what I did in the lecture.
• Graded homework: There will be weekly graded HW assignments, normally given out on Monday and due in class the following Friday. Assignments dropped off in mailboxes will not be accepted; however, you can turn in an assignment in my office, 241 Illini Hall, any time before the class hour in which it is due. Late assignments will not be accepted, but if you have a legitimate, documented, excuse for missing an assignment (e.g., illness), I will mark the assignment as excused (see the section "Missed/late homework policy" below). At the end of the semester, the lowest HW score will be dropped, and the remaining scores determine your HW grade.
  Note on group work: It is fine with me if you do the homework in groups (indeed, I encourage group work), provided you write up solutions yourself, using your own words. Simply copying answers from another student's solutions would defy the purpose of the HW assignments, and assignments that are near carbon copies of someone else's assignment will not be counted.
• Midterm exams: There will be three midterm Hour Exams, spread out evenly over the semester. I will poll the class before deciding on exact dates. Expect the first one to be in late February, the second in late March, and the third in late April.
• Final exam: The Final Exam will be cumulative and will be about twice as long as an Hour Exam. It will be given at the officially scheduled exam slot for MWF 12-12:50 classes: Tuesday, May 9, 7 pm - 10 pm. (See the Spring 2006 Final Exam Schedule.)

Grading Policy

• Course grade: The course grade will be based on homework, midterm exams, and the final exam, weighted as follows:
  • Homework: 1/6
  • Midterm Exams: 1/6 each (1/2 for all three midterms)
  • Final Exam: 1/3
• Missed exam policy: I do not give make-up exams. If you miss an exam and have a valid excuse, I will mark the exam as excused; the exam will then not be taken into account when computing the overall exam average. Valid excuses include illness, an out-of-town job interview, etc., and must be documented by a letter from the Dean or Emergency Dean; see the Emergency Dean's website for more information on this.
• Missed/late homework policy: I do not accept late homework. Since the lowest homework score will be dropped, you can afford to miss one homework and still get a perfect homework average. If you can't turn in an assignment due to illness or some other valid excuse, the same policy as for missed exams applies: With a Dean's letter as documentation, I will mark the assignment as excused; that is, it will not count towards the homework average (and you will still have the drop score).

Study Tips

• Attend the lectures. Reading the text is no substitute for attending the lectures; while I plan to follow the general outline of the text, I will put my own spin on the material, usually using different examples, and emphasizing topics that I feel are particularly important.
• Do the HW problems. The homework - both the graded weekly assignments, and the non-graded daily assignments - is an essential part of this course, and you should make sure to do the homework, including the non-graded homework.
• Read the text. The Rosen text is one of the best math text books I know, with a wealth of examples and problems, excellent end-of-chapter summaries, and an amazing variety of supplementary materials available, both in print and on the web. For each lecture, I will indicate (and post on the course webpage) the sections/topics in the Rosen text that you should read up on. These reading assignments are mainly intended to reinforce the material already covered in class, but they may also include topics that I have not had time to cover in class, but which I expect you to know. You should take these reading assignments seriously; don't expect to get by just doing the HW problems. The book and the lectures complement each other, and you cannot neglect one or the other.

Course Web Page