Representation, analysis, techniques, and principles for manipulation of basic combinatoric data structures used in computer science. Rigorous reasoning is emphasized. (Counts as a CS Background Course for the concentration.)
Basic (high school level) calculus and algebra.
Tues-Thur 9:30-11:00 am, CAS 314.
I expect you to come to lectures (on time!) and I encourage you to participate. There is no perfect textbook for the class, and lectures are your important source of information. Be sure to take good notes.
Lab: MCS B31, Mon, 1:00pm-2:00pm
Lab: MCS B33, Mon, 2:00pm-3:00pm
Behzad Golshan, email@example.com
Office Hours: Thursday 12:00 (noon) - 1:30pm and Fri 3:00pm - 4:30pm.
Behzad’s office hours take place in the undergraduate lab
The Teaching Fellow will lead the discussion sessions. The objective is to reinforce the concepts covered in the lectures, and answer questions (or provide clarifications) regarding the homework assignments.
The purpose of the office hours of the Instructor and Teaching Fellow is to answer specific questions or clarify specific issues. Office hours are not to be used to fill you in on a class you skipped or to explain entire topics. Please come to class and to your discussion session.
There is no perfect textbook that covers all the material of this course from a CS perspective. We will mostly make use of the following online notes. Do not print anything yet! The notes are 339 pages long, so you might consider printing them out in chapters as we get to them rather than all at once. We won’t cover all chapters anyway.
Notes for MIT’s CS 6.042 course (PDF format), by Eric Lehman and Tom Leighton, 2004.
We will also cover some chapters from the following textbook: How To Prove It: A Structured Approach, by Daniel Velleman.
Together with your lecture notes, the above material should be quite sufficient. If for some reason you want to do additional reading, you might consider some discrete mathematics book, e.g., Discrete Mathematics and Its Applications, by Kenneth H. Rosen, McGraw Hill. However, be warned: each discrete math book has its cons and they can be quite expensive!
Problem sets (20%)
2 midterms (25% each)
1 final (30%)
Incompletes will not be given.
Late assignments will not be accepted. The assignment grade will be the average over all assignments (the two lowest-grade assignments will be ignored).
|Jan 22, 24||Logic||Chapter 1 from “How to prove it”|
|Jan 24||Homework I; due Jan 31||download, solution|
|Jan 29, 31||Logic and Proofs||Chapters 2 and 3|
|Jan 31||Homework II; due Feb 7||download,solution|
|Feb 5, 7||Proofs||Chapter 3|
|Feb 12, 14||Proofs||Chapter 3|
|Feb 14||Homework III; due Feb 21||download,solution|
|Feb 19 ,21||Induction||Leighton notes, and Chapter 6 from the book|
|Feb 26||Midterm I|
|Feb 28||Induction||Leighton notes and Chapter 6 from the book|
|Feb 28||Homework IV; due March 7||download,solution|
|Mar 5, 7||More induction|
|Mar 12 ,14||Spring break|
|Mar 18||Homework V; due March 26||download,solutions|
|Mar 19||Sums and Approximations||Chapter 10 from Leighton notes|
|Mar 21||Asymptotic Notation||Chapter 10 from Leighton notes|
|Mar 18||Homework VI; due April 2||download,solutions|
|Mar 26||Recurrences||Chapter 12 from Leighton notes|
|Mar 28||Recurrences||Chapter 12 from Leighton notes|
|Mar 29||Homework VII; due April 4||download, solutions|
|Apr 2||Recurrences||Chapter 13 from Leighton notes|
|Apr 9,11||Counting||Chapter 14 from Leighton notes|
|April 11||Homework VIII; due April 18||download solutions|
|Apr 16, 18||Counting||Chapter 14 from Leighton notes|
|Apr 23, 25||Probability||Chpaters 14 and 15 from Leighton notes|
|Apr 24||Homework IX; due May 1||download solutions|
|Apr 30, 2||Review|
Course participants must adhere to the CAS Academic Conduct Code. All instances of academic dishonesty will be reported to the academic conduct committee. Collaboration/Academic Honesty
I encourage you to discuss course material and even problem sets with other students in the class (esp. on the class mailing list), subject to the following rules:
You must write up your solutions completely on your own (and certainly without looking at other people’s write-ups).
In your solution to each problem, you must write the names of those with whom you discussed it.
You must include citations of all the materials you have used beyond the class notes and the textbook.
You may not consult solution manuals or other people’s solutions from similar courses or prior years of this course.
I expect you to follow these rules as well as the academic conduct code of CAS/GRS. If you have any questions or are not sure what is appropriate, consult me before taking steps that you are afraid may violate the rules.
If you violate the academic conduct code, you will be reported to the Academic Conduct Committee.