Professor A.J. de Jong, Columbia university, Department of Mathematics.

This is the webpage of the undergraduate course "Fall 2018 MATH 3025 UN sec: 001 MAKING, BREAKING CODES".

Day/Time: TR 2:40pm-3:55pm Location: 203 Mathematics Building.

** Grading. ** Grading will be based on
homework, 2 midterms, and final exam. The percentages will be roughly
25, 20, 20, and 35.

Exam policies: No electronic devices or study aids/notes of any kind are allowed on the exams. (Calculators are not allowed.) There are no make-up exams. If exceptional circumstances arise, let me know as soon as possible so an arrangement can be made. You will need to provide a letter from the dean.

Homework policies: * Late homework will not be accepted.*
To compensate, the lowest two grades of all your assignments will be dropped.
Note that since the exam questions will be similar to the homework,
you should complete all assignments whether the grade is dropped or not.

** TA. ** The TA will be Chung-Hang (Kevin) Kwan.
He will be in the help room Tuesdays 9:00-10:30 AM and
Wednesdays 9:00-10:30 AM in Room 406.

** Office hours. ** 9 - 10 AM Tuesday and Wednesday
in Room 523 in the mathematics building.

** Book. ** Introduction to Cryptography with Coding Theory, 2nd edition
by Wade Trappe and Lawrence C. Washington

** Lectures. **
The lectures will discuss material from the book. It is very
important to **attend the lectures**. You will not be able to
pick up the material by just reading this webpage and the book.

** Reading. **
Please keep up with the course by studying the material as listed
in the syllabus below
as we go through it. We will go through material at a rapid pace
and the assumption is that you'll spend a lot of time with the
theory by yourself in order to understand and keep up with the course.

** Syllabus and schedule. **
This is prelimenary and will change as we go along.
Perhaps the pace set by the schedule below may be too
optimistic and if so we will move things around.
However, the dates for the midterms will not be changed.

Date | Material | Textbook | Announcements |
---|---|---|---|

09/04 | Classical cryptography | 2.1-2.4, 2.9, 3.1 | |

09/06 | 2.1-2.4, 2.9, 3.1 | ||

09/11 | 3.2-3.8 | ||

09/13 | 3.2-3.8 | HW 1 is due 11:59 PM | |

09/18 | 6.1, 6.2 (esp. 6.2.2), 6.7 | ||

09/20 | 7.1, 3.7, 7.4, 7.5 | HW 2 is due 11:59 PM | |

09/25 | 6.4, 7.2 | ||

09/27 | 7.2 | HW 3 is due 11:59 PM (building closes at 11PM) | |

10/02 | Review for Midterm 1 | ||

10/04 | Midterm 1 | HW 4 is due 11:59 PM (building closes at 11PM) | |

10/09 | 3.9, 6.3, 6.4.1 | ||

10/11 | 7.2.3, 13.1, 14.1 | HW 5 is due 11:59 PM (building closes at 11PM) | |

10/16 | 14.1, 14.2, 16.1 | ||

10/18 | 16.1, 16.2 | HW 6 is due 11:59 PM (building closes at 11PM) | |

10/23 | 16.3, 16.5, 16.5.1, 16.5.2 | ||

10/25 | 16.5.2, 3.11 | HW 7 is due 11:59 PM (building closes at 11PM) | |

10/30 | 3.11, 3.11.1, 16.4 | ||

11/01 | 16.4 + Review | HW 8 is due 11:59 PM (building closes at 11PM) | |

11/06 | No lecture | ||

11/08 | Midterm 2 | HW 9 is due 11:59 PM (building closes at 11PM) | |

11/13 | 18, 18.1, 18.2 (start) | ||

11/15 | 18.2 | HW 10 is due 11:59 PM (building closes at 11PM) | |

11/20 | 18.3, 18.3.1, 18.3.2 | ||

11/22 | No lecture | ||

11/27 | 18.4, 18.4.1, 18.5 | ||

11/29 | 18.7 | HW 11 is due 11:59 PM (building closes at 11PM) | |

12/04 | Reed-Solomon codes | ||

12/06 | review | HW 12 is due 11:59 PM (building closes at 11PM) | |

Exam period | Final Exam |
You are responsible for checking the University exam schedule for time and location of the exam. |

** Final Exam. **
The final exam is cumulative, i.e., it will cover all the material
discussed in all the lectures. Thus the material consists of the
material listed in the first two review sessions (10/02 and 11/01)
plus the material on error correcting codes:
Sections 18.1, 18.2, 18.3, 18.3.1, 18.3.2, 18.4, 18.4.1, 18.5, and 18.7
of the book (the formulas in the bounds will be provided on the test
so you don't need to memorize them) and
the material on Reed-Solomon codes excluding
sections 9 and 10 of that pdf file.
You can expect there will be a little bit of an
emphasis on error correcting codes in the final.

** Homework. **
New: please read **feedback 1**,
**feedback 2**,
**feedback 3**, and
**feedback 6** from graders.
Hand in your work into the box outside Math 417.
All of the problems are taken from the book.
See the syllabus above for when these exercises are due.

- HW 1: Section 2.13 on page 55, problems 2, 3, 4, 5, 8, 10, 11.
- HW 2: Section 3.13 on page 104, problems 1, 2, 3, 5, 12, 13, 18, 19, 26.
- HW 3: Section 6.8 on page 192, problems 1, 7, 9, 11, 16, 27. Section 7.6 on page 214, problems 1, 2, 11.
- HW 4: Section 3.13 on page 104, problems 9, 10. CRT attack on RSA. Section 7.6 on page 214, problems 3, 4, 6, 10.
- HW 5: Section 3.13 on page 104, problems 25, 26, 27, Section 6.8 on page 192, problem 12, 13.
- HW 6: Section 13.3 on page 314, problems 2, 3 Section 14.3 on page 321, problems 1, 2, 3, 4, 5.
- HW 7: Section 16.7 on page 370, problems 1, 2, 3, 4, 5, 6, 7, 10
- HW 8: Section 16.7 on page 370, problems 11 (assume n is prime), 12 (assume n is prime), 16. Section 3.13 on page 104, problems 33, 34.
- HW 9: see hw9.pdf
- HW 10: Section 18.12 page 445, problems 1, 2. Also find a binary code of length 9 with minimum distance 5 and 6 codewords, i.e., a 2-ary (9, 6, 5) code.
- HW 11: Section 18.12 page 445, problems 3, 4, 5, 6, 7, 8, 9
- HW 12: Section 18.12 page 445, problems 10, 11, 12, 13 + give a generating matrix for a 5-ary [5, 2, 4]-code (hint: use a Reed-Solomon code as discussed in lectures).

** Midterms and finals. **
These are to give you an idea of what happend in previous years.
Of course my midterms and final will be different, and possibly
quite different.