CmpE 220 Fall2015PS #1

Mehmet Kose

October 3, 2015

Contents

1 Example Formulas in LaTeX 1

2 Listing 32.1 Bulleted lists . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Numbered lists . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Figures 3

1 Example Formulas in LaTeX

1. Greek letters: α, β, γ, ε.

2. Prove A ⊆ B ⇐⇒ A ∪B = B

3. A logical expressiona ∧ b =⇒ c ∨ d

4. Assume a|b and b|c. Then∃k12 ∈ Z such that b = k1a, and∀k2 ∈ Z such that c = k2a⇒ c = k2(k1a) = (k2k1)a ⇒ a|c

5. Multi-char subscript and nested subscriptarray[nij] = numberab

1

6. Summation∞∑n=0

an (1)

7. A limit expression

limn→0+

x = 0 (2)

8. Suppose A and B are sets such that s(A) is infinite and s(B) is finite.f : A → B is a function. Prove that for at least one b ∈ B, the setf−1(b) = {x ∈ A|f(x) = b} is infinite.

9. Other formulas:

A∆B = (A−B) ∪ (B − A) (3)

W1(z) ≤∞∑

n=−∞

w1(n) · z−n (4)

EA ≥ EE +

√h[log(2N/h) + 1]− log(η/4)

n(5)

fA(x) = 1− fA(x) (6)

R(m) =−1∑

n=−m

h(n) · h(n+m)︸ ︷︷ ︸0

+R(m) (7)

∂L(w, b, α)

∂b=

N∑t=1

rtαt = 0 (8)

2

2 Listing

2.1 Bulleted lists

• List item

• Another list item

• Yet another list item

2.2 Numbered lists

1. First Item

2. Second Item

3. Third Item

3 Figures

1. An example for inserting a figure is given in Figure 1.

2. Figure environment can also be used for other purposes as in the Fig-ure 2.

3

Figure 1: Example Figure 1

Figure 2: Second Example Figure

This is a box. It can contain

• text

• mathematical formula

• figures

4