MA284: Discrete Mathematics (2017/2018)

Tutorials will begin in Week 3 (the week starting 18 September), except for the one on Tuesdays at 15.00, which starts in Week 4.

• Kenneth Rosen, Discrete Mathematics and Its Applications, McGraw-Hill. Located at 511 ROS
• Normal L Biggs, Discrete Mathematics, Oxford Science Publications. There are about 10 copies in the library at 510 BIG.

• Q2: try to avoid doing calculations with large factorials by simplifying the expression by hand as much as possible. Examples:
  • $$\frac{220!}{5! 115!} = \frac{116 \times 117 \times 118 \times 119 \times 200}{5\times 3 \times 2 \times 1}=190578024 $$
  • Some number are too large or small to represent all digits. In that case, using scientific notation where, for example, 123456789 is written as 1.23456789E+08. Also give at least 7 digits after the decimal place. E.g. $$\frac{430!}{420! 30!} = \frac{430 \times 429 \times \dots \times 421}{30 \times 29 \times \cdots \times 1}=7.3322390E-07 $$
• Q3: simplify the expressions involving factorials as much as possible. For example, you can simplify $\frac{(n+1)!}{(n-1)!}$ as $$ \frac{(n+1)!}{(n-1)!} = \frac{(n+1)(n)(n-1)(n-2)(n-3)(n-4)\cdots (2)(1)}{(n-1)(n-2)(n-3)(n-4)\cdots (2)(1)}=(n+1)(n)$$.