SP19:Syllabus

From CS2800 wiki

Topics

This course is different from many CS courses; especially beginning level courses. We do not require any programming (indeed, it is rarely discussed). Rather, this course has the flavor of a university-level mathematics course.

Skills

Throughout the course we will focus on

Definitions
clear descriptions of terms. For the most part, all of the words we use will have crisp definitions
Proofs
arguments; sequences of logical steps, starting from agreed upon facts or assumptions and leading to a desired conclusion.

These skills are critical in many areas of computer science. Clear definitions are very similar to specifications of functions, classes, or programs. Writing and working with definitions will help you write good specifications.

The ability to write proofs and reason logically is critical for writing code that works. It is also critical for reasoning about programs more generally. Reading and writing proofs will also make you communicate more clearly, and will help you evaluate evidence and come to solid conclusions.

Structures

The lecture schedule outlines the topics we will cover. In addition to providing lots of practice and examples for the skills listed above, they are all useful in various areas of computer science:

Basic toolssets, functions, and relations
These basic objects are useful for modeling a large variety of problems. Sets are simply collections of objects, be they the set of pages on a website, a set of users, or more abstract objects like the set of possible traces through a program. Functions model input/output relationships, and can be used to represent programs and data structures. Relations model more general kinds of relationships between objects, such as the "friend" relationship in a social network.
Number theory
We will study properties of the integers, as well as a new kind of number-like object called a modular number. modular numbers are useful for reasoning about remainders; we will see applications to hashing and cryptography. Modular numbers also have applications in digital circuits, for example to implement error correcting codes.
Automata
Automata are simple models of computers. After giving formal definitions, we will study the limits of computation, and will also show how the computational power of automata can be described with the high level language of regular expressions. Automata have applications in compilers, networks, and in the theoretical study of the limits of computation. Regular expressions are also useful for text processing.
Combinatorics
Combinatorics is the art of counting things without listing them. It is useful for the analysis of algorithms.
Probability
Probability allows reasoning about uncertain events, and assigning likelihoods to various outcomes. Probability has applications in artificial intelligence, systems, and the design of randomized algorithms.
Metalogic
We will apply the logical tools we've used all semester to study logic itself. Metalogic has applications in program verification and security, as well as in programming language design.

Grades

Your course grade will be based on:

  • two evening prelims (roughly 1/6 each),
  • a final exam (roughly 1/3),
  • weekly homework assignments (roughly 1/3)
    • We will drop your lowest homework score when computing your final grades.
  • "good citizenship" can help or hurt if you are right at a grade cutoff; this includes a small number of things like filling in the course evaluation. We will explicitly announce what is required for good citizenship.


We often grade individual problems on an A/B/C/D scale, with an A indicating mastery, a B indicating a flawed solution that demonstrates a good understanding of the problem, and a C indicating major misunderstanding or lack of clarity, and a D indicating that you drew a picture of your cat.

A/B/C/D problem scores do not translate linearly to final course grades. If you get all A's on the homework and exams, you may not get an A in the course (you'll probably get an A+). If you get all B's, that doesn't guarantee a B. There are many factors that go into my determination of final course grades.

In an ideal world, everybody would get an A+; of course this also means it's possible for everyone to get a C. In my experience, the median final course grade has usually been a B or B+. I will post grade estimates after each of the prelims.

Unless specified otherwise, assignments will be due Mondays at 5:00 PM. They should be submitted on Gradescope. We will accept late assignments until Tuesday at 5:00 PM. You may submit two late assignments with no penalty; subsequent late assignments will have a 50% penalty applied. In the case of unforseeable circumstances (e.g. a death in the family or a fire in your dorm), you should contact us; we may give additional extensions.

You may create the PDF files however you want (for example by scanning legible handwritten responses), but we encourage you to typeset them using LaTeX. Please check that you have handed in the right file by downloading it and comparing it to the original. Saying that you accidentally handed in the wrong homework does not count as an excuse!

Regrade requests for homework assignments and exams should be submitted on Gradescope, within a week of when grades are released. We will regrade the entire exam or problem set; your score may go up or down.

Websites and information

  • Lecture summaries and office hours are on the course website
  • We will be using Piazza for all course announcements. Piazza is also a good place to ask questions about the course. Please enroll yourself.
  • We will be using Gradescope for assignment submissions and grades.

References

We do not follow any single textbook particularly closely. The best resource are the lecture notes posted on the course website.

We will use the textbook "Mathematics for Computer Science" (MCS) by Lehman, Leighton, and Meyer. It is freely available.

The textbooks "Lecture Notes in Discrete Structures" by Pass and Tseng. and "Discrete Mathematics and Its Applications" by Rosen have been used in past semesters, and may serve as helpful additional references.

The textbook "Introduction to Automata Theory, Languages, and Computation" by Hopcroft and Ullman is an excellent reference on automata theory.

Exams and Assignments

Your course grade will be based on:

  • two evening prelims (roughly 1/6 each),
  • a final exam (roughly 1/3),
  • weekly homework assignments (roughly 1/3)
    • We will drop your lowest homework score when computing your final grades.
  • "good citizenship" can help or hurt if you are right at a grade cutoff; this includes a small number of things like filling in the course evaluation. We will explicitly announce what is required for good citizenship.


We often grade individual problems on an A/B/C/D scale, with an A indicating mastery, a B indicating a flawed solution that demonstrates a good understanding of the problem, and a C indicating major misunderstanding or lack of clarity, and a D indicating that you drew a picture of your cat.

A/B/C/D problem scores do not translate linearly to final course grades. If you get all A's on the homework and exams, you may not get an A in the course (you'll probably get an A+). If you get all B's, that doesn't guarantee a B. There are many factors that go into my determination of final course grades.

In an ideal world, everybody would get an A+; of course this also means it's possible for everyone to get a C. In my experience, the median final course grade has usually been a B or B+. I will post grade estimates after each of the prelims.

Unless specified otherwise, assignments will be due Mondays at 5:00 PM. They should be submitted on Gradescope. We will accept late assignments until Tuesday at 5:00 PM. You may submit two late assignments with no penalty; subsequent late assignments will have a 50% penalty applied. In the case of unforseeable circumstances (e.g. a death in the family or a fire in your dorm), you should contact us; we may give additional extensions.

You may create the PDF files however you want (for example by scanning legible handwritten responses), but we encourage you to typeset them using LaTeX. Please check that you have handed in the right file by downloading it and comparing it to the original. Saying that you accidentally handed in the wrong homework does not count as an excuse!

Regrade requests for homework assignments and exams should be submitted on Gradescope, within a week of when grades are released. We will regrade the entire exam or problem set; your score may go up or down.

Collaboration Policy

The types of problems assigned in this class lend themselves naturally to a two-step approach. First, you have to understand the question and devise a solution. Second, you have to clearly describe your solution.

During the first phase, you are encouraged to work together and consult outside references. However, you should do the second phase completely on your own.

While writing your solutions, you must not consult any notes.. Do not sit next to the whiteboard that contains the formula that you and a friend devised. Do not look at anything on the web. Do not consult the notes you took during office hours. Don't do anything you wouldn't do in an exam situation. If you find you are stuck, set your submission aside, consult your notes, and then restart the question you were working on.

You may not copy any part of someone else's solution. To do so is a violation of the academic integrity code. This includes solutions downloaded from the Internet.

It is also against the academic integrity policy of the course to upload any course materials (problem sets, handouts, lecture notes, etc) to a public service. All material is copyrighted by Michael George.

Special Needs

We provide appropriate academic accommodations for students with special needs and/or disabilities. Requests for academic accommodations are to be made during the first three weeks of the semester and must be accompanied by official documentation. Please register with Student Disability Services in 420 CCC to document your eligibility.

All accommodation forms should be submitted to Professor George and to Amy Elser (ahf42, Gates 401).