Math 342 Exams

Midterm, Tuesday 12th October 9.30-11.00, Location  BUCH B213

The topics covered are:  induction, greatest common divisors and least common multiples, Euclidean algorithm and Bezout, integer solutions to equations, FTA and unique factorization, exponential notation and its uses, congruences, solving congruences, affine ciphers, block ciphers, stream ciphers, equivalence relations.

Extra office hour: Thursday October 7th 3-4pm.

Practice questions: 3B19 i) iii); 3C 37; 3D 48; 4A 8 i) iii); 5B 12. Answers are in the back of the book.

Some study hints:

1. This is a Math Majors course, which means the exam will be about 50% proofs 50% calculation. You will be expected to prove results like on the homework.
   
2. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
   
3. Do the practice questions and old homeworks again without looking at the answers.
4. If you get stuck on a problem then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.

Final exam, Saturday 11th December 12.00-2.30, Location MATH 104

The topis covered are: induction, greatest common divisors and least common multiples, Euclidean algorithm and Bezout, integer solutions to equations, FTA and unique factorization, exponential notation and its uses, congruences, solving congruences, affine ciphers, block ciphers, stream ciphers, equivalence relations, well-defined, Z/mZ, abstract rings, units and 0-divisors, the order of an element of a finite ring, introduction to coding, repetition code,  ASCII, ISBN-10, UPC, Electronic Funds Transfer, SIN, Hamming distance and error correction/detection, sphere-packing bound and perfect codes, parity check, equivalence of codes, theorems of Fermat and Euler, RSA, groups and subgroups, including cyclic groups, cosets, index of a subgroup, Lagrange's theorem,  linear codes, generator and parity check matrices of a linear code, coset tables. 

Office hours: Thursday December 9th 2.30-4.30pm

Practice questions:

• here (Answer: included)
  
• 9C 42 (Answer: back of book)
  
• 11A 3 (Answer: here with answer to question below)
• CS 3.4 Q6 (Answer: here with answer to question above)
• Construct a coset table for the binary linear code C={0000, 1011, 0101, 1110} assuming errors only occur in the 1st, 2nd, 3rd position and decode 1111 (Answer: CS Example 3.28 without last column and 3.29)

Some study hints:

1. This is a Math Majors course, which means the exam will be about 50% proofs 50% calculation. You will be expected to prove results like on the homework.
   
2. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
   
3. Do the practice questions and old homeworks again without looking at the answers.
4. If you get stuck on a problem then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.