math

Example of Markdown features

# GitHub Markdown Example for Math Majors

This Markdown file demonstrates **basic GitHub Markdown features**, with examples tailored to math students. It also includes **LaTeX syntax** for equations and math formatting.

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## Table of Contents

1. [Headings](#headings)
2. [Text Formatting](#text-formatting)
3. [Lists](#lists)
4. [Links and Images](#links-and-images)
5. [Blockquotes](#blockquotes)
6. [Code and Syntax Highlighting](#code-and-syntax-highlighting)
7. [Tables](#tables)
8. [Horizontal Rules](#horizontal-rules)
9. [Task Lists](#task-lists)
10. [Math with LaTeX](#math-with-latex)

---

## Headings

```markdown
# H1
## H2
### H3
#### H4

H1

H2

H3

H4

---

Text Formatting

• Bold: **Bold** → Bold
• Italic: *Italic* → Italic
• Bold and Italic: ***Bold and Italic*** → Bold and Italic
• Strikethrough: ~~Strikethrough~~

---

Lists

Unordered List

- Item A
  - Subitem A1
    - Sub-subitem A1a

• Item A

  • Subitem A1

    • Sub-subitem A1a

Ordered List

1. First
2. Second
   1. Sub-second

1. First

2. Second

   1. Sub-second

---

Links and Images

Link

[GitHub](https://github.com)

Visit GitHub

Image

![Math image]([https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Integral_example.svg/300px-Integral_example.svg.png](https://placehold.co/600x400/000000/FFAAFF.png))

---

Blockquotes

> Mathematics is the queen of the sciences.

Mathematics is the queen of the sciences.

---

Code and Syntax Highlighting

Inline Code

Use the \lim_{x \to 0} \frac{\sin x}{x} limit rule.

Code Block

```python
def factorial(n):
    return 1 if n == 0 else n * factorial(n - 1)
```

def factorial(n):
    return 1 if n == 0 else n * factorial(n - 1)

---

Tables

| Symbol | Meaning       | Example         |
|--------|---------------|-----------------|
| ∑      | Summation     | $\sum_{i=1}^n i$ |
| ∫      | Integral      | $\int_0^1 x dx$  |
| ∂      | Partial Deriv | $\frac{\partial f}{\partial x}$ |

Symbol	Meaning	Example
∑	Summation	$\sum_{i=1}^n i$
∫	Integral	$\int_0^1 x dx$
∂	Partial Deriv	$\frac{\partial f}{\partial x}$

---

Horizontal Rules

---

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Task Lists

- [x] Review algebra
- [ ] Study calculus
- [ ] Learn topology

• Review algebra
• Study calculus
• Learn topology

---

Math with LaTeX

GitHub now supports inline and block math using LaTeX! Wrap with $...$ for inline, or $$...$$ for block.

Inline Math

Euler's identity is $e^{i\pi} + 1 = 0$.

Euler's identity is $e^{i\pi} + 1 = 0$.

Block Math

$$
\int_{a}^{b} f(x) dx = F(b) - F(a)
$$

$$ \int_{a}^{b} f(x) dx = F(b) - F(a) $$

Systems and Matrices

$$
\begin{bmatrix}
1 & 2 \\
3 & 4
\end{bmatrix}
$$

$$ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $$

$$
\begin{cases}
x + y = 1 \\
x - y = 3
\end{cases}
$$

$$ \begin{cases} x + y = 1 \\ x - y = 3 \end{cases} $$

---

Footnotes

Here is a statement with a footnote.[^1]

[^1]: This is the footnote.

Here is a statement with a footnote.¹

---

Final Thoughts

You can use GH Markdown and LaTeX, and you can write math-heavy documentation, or lecture notes, and even explanations that render in .md files on GitHub!

Footnotes

1. This is the footnote. ↩