Solutions

These solutions show the reasoning, not only the final answer.

MATH-C01-C-001

Given:

x = 6

Compute:

3x - 2 = 3 \cdot 6 - 2 = 18 - 2 = 16

Answer: 16.

The function is:

g(t) = t^2 - t

Use 5 as the input:

g(5) = 5^2 - 5 = 25 - 5 = 20

Answer: 20.

The statement

\text{cat} \in Y

means cat is a member of the set $Y$ .

In the label example, it means cat is one of the allowed labels.

The tuple is:

z = (10, 20, 30, 40)

Using mathematical indexing:

z_1 = 10,\quad z_2 = 20,\quad z_3 = 30,\quad z_4 = 40

Answer: $z_3 = 30$ .

Expand the summation:

\sum_{i=1}^{3} a_i = a_1 + a_2 + a_3

Substitute the values:

2 + 5 + 8 = 15

Answer: 15.

The expression is:

\frac{1}{n}\sum_{i=1}^{n} \ell_i

Read it as:

add all n loss values
divide by n

This is the average loss over n examples.

The explanation mixes conventions.

In mathematical indexing, $x_1$ is the first item. So if

x = (4, 7, 9)

then:

x_1 = 4,\quad x_2 = 7,\quad x_3 = 9

In Python, the second item is x[1], not x[2].

Correct answer: $x_2 = 7$ in mathematical notation.

The set is:

V = \{\text{yes}, \text{no}, \text{maybe}\}

The token yes appears in the set. So:

\text{yes} \in V

is true.

Average loss means total loss divided by the number of examples:

\frac{4 + 6 + 8}{3} = \frac{18}{3} = 6

Answer: 6.

Enter 1.

A useful reading of a formula has more than symbol names. It should include:

For example, "sigma over i" is weaker than "add the loss for each example."

The deeper lesson is to name the operation and the meaning, not only the symbol.