Class Syllabus

Course Web Page

Course Description

Text:

Prereqs

Assignments:

• Assignments are due at the beginning of class on the due date. Assignment deadlines are strict: late homeworks will automatically receive a grade of zero, without prior approval. Prior approval is generally given only in the case of a medical problem or family emergency.
• Group collaboration is encouraged on the homeworks, provided that you write at the top of your homework the names of all the other students that you collaborated with. Note that although collaboration is encouraged, the solutions must always be written up individually. You should not look at or copy another student's solution and should not copy solutions from the Internet. A rough rule of thumb here is the ``American Idol`` Rule. After working with your group, go watch a half hour of American Idol on TV (or your favorite mindless but fun TV show) before you write up the solutions. You may consult other textbooks or the Internet as you would another student (i.e. cite your source and use the ``American Idol'' rule). Remember Copying solutions from another student or from the Internet is cheating. In case a student presents a solution that is essentially identical in whole or in part to solutions from another student or other source, that student will receive a 0 on the assignment, may be reported to the University Administration and may not be permitted to continue in the class.
• Put pages of hw in order. We don't care what order you solve the hw in, but before you turn it in, you must put the problems in order (this makes grading much easier)
• Staple hws, do not use paper clips, folding, tape, putty, gum, etc. Prof Saia and the TA do not bring staplers to class, so make sure you staple the hw before class (stapling helps us keep together all pages of your hw)
• Regrades: if you feel a mistake was made grading your hw, please let the TA know about it (if you still feel there is a problem, then please talk to Prof. Saia). Please ask for a regrade within one week of receiving the graded assignment.

Notes on Grading Hws

• Clarity: Make sure all of your work and answers are clearly legible and well separated from other problems. If we can't read it, then we can't grade it. Likewise, if we can't immediately find all of the relevant work for a problem, then we will be more likely to grade only what we see at first.
• Completeness: Full credit for all problems is based on both sufficient intermediate work (the lack of which often produces a 'justify' comment) and the final answer. There are many ways of doing most problems, and we need to understand exactly how YOU chose to solve each problem. Here is a good rule of thumb for deciding how much detail is sufficient: if you were to present your solution to the class and everyone understood the steps, then you can assume it is sufficient.
• Succinctness: The work and solutions which you hand-in should be long enough to convey exactly why the answer you get is correct, yet short enough to be easily digestible by someone with a basic knowledge of this material. If you find yourself doing more than half a page of dense algebra, generating more than a dozen numeric values or using more than a page or two of paper per problem for your solution, you're probably doing too much work. Don't turn in pages with scratch work or multiple answers - if you need to do scratch work, do it on separate scratch paper. Clearly indicate your final answer (circle, box, underline, etc.). Note: It's usually best to rewrite your solution to a problem before you hand it in. If you do this, you'll find you can usually make the solution much more succinct.

Topics

• The Foundations: Propositional Logic, Predicates, Quantifiers, Rules of Inference, Proofs (roughly 2 weeks, all of Chapter 1)
• Sets, Functions, Sequences, Sums, Functions (roughly 2 weeks, Chapter 2)
• Basic Algorithms and Number Theory: Growth of Functions, Complexity of Algorithms, Modulo Arithmetic, Euclid's Algorithm, Chinese Remainder Theorem (2 weeks, Chapter 3.1-3.5)
• Applications of Number Theory: RSA Encryption, Residue Number Systems, Secret Sharing Based on the Chinese Remainder Theorem (2 weeks, Chapter 3.6-3.7)
• Induction and Recursion: Strong Induction, Recursive Algorithms and Recurrences (2 weeks, Chapter 4)
• Graphs: Terminology and Graph Types, Isomorphism, Connectivity, Paths and Cycles, Coloring (2 weeks, Chapter 9)
• Basics of Modeling Computation: Finite State Machines and Turing Machings (2 weeks, Chapter 12)
• Time Permitting: Probability, Randomized Algorithms and Expectation (1 week Chapter 6)

Course Assessment

• Homeworks, 20%
• Midterm 30%
• Final 40%
• Class Participation, 10%. I expect about 90% attendance in class, and will frequently ask questions to the class. The participation grade will based on attendance and class participation. It will be a very coarse grade: students who attend the lectures regularly and speak up will likely receive full marks for participation.

Grading Policies