1. Mathematics in CS

• 1. Mathematics in CS
  • 1.1. content
    • 1.1.1. Discrete Mathematics
    • 1.1.2. Discrete Mathematical Structures
    • 1.1.3. Discrete Probability Theory
    • 1.1.4. What dose Discrete means
  • 1.2. Proofs
  • 1.3. Proof by contradiction
    • 1.3.1. make a suppose eg
    • 1.3.2. If an assertion implies something false then the
    • 1.3.3. $\sqrt2$ is irrational

1.1. content

1.1.1. Discrete Mathematics

• sets relations proof methods

1.1.2. Discrete Mathematical Structures

• numbers graphs trees counting

1.1.3. Discrete Probability Theory

1.1.4. What dose Discrete means

• the ability to discreting

1.2. Proofs

• $a^2 + b^2 = c^2$ in a triangle
• the interesting thing between Graph and Caculate. Elegant and correct
• but something lack of the infomations

Roots of $ax^2 + bx + c => [-b +-\sqrt{(b^2-4ac)}]/2a$
"$a !== 0 D !==0$"

1.3. Proof by contradiction

1.3.1. make a suppose eg

• Is $\sqrt[3]{1332} <= 11$?
• if so $1332<=1231$ this is not true
• so $\sqrt[3]{1332} > 11$

1.3.2. If an assertion implies something false then the

assertion itself must be false

1.3.3. $\sqrt2$ is irrational

• suppose$\sqrt2$ was rational
• so have n d intergers without common prime fators such that $\sqrt2 = n/d$
• so n and d are even
• $\sqrt2 = n/d$
• $2d^2 = n^2$
• so $n$ is even