Wednesday, January 22nd

1 + 1

2

1 + 4

5

Getting started with Jupyter notebook

• We can execute a cell using SHIFT + ENTER
• We can add a new cell using the plus symbol in the top-left corner
• We can delete a cell by selecting hit, then hitting D, D

Arithmetic operations

1 + 3

4

1 - 3

-2

4*5

20

4 / 5

0.8

3^4

7

To perform exponentiation, use ** or the pow function instead of ^:

3**4

81

pow(3,4)

81

Using the standard division / will return what is called a float.

5 / 2

2.5

4 / 2

2.0

2.0 ** 1000

1.0715086071862673e+301

2**1000

10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376

2.0**1500

---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
~\AppData\Local\Temp\ipykernel_23904\2939582728.py in <module>
----> 1 2.0**1500

OverflowError: (34, 'Result too large')

2**1500

35074662110434038747627587960280857993524015880330828824075798024790963850563322203657080886584969261653150406795437517399294548941469959754171038918004700847889956485329097264486802711583462946536682184340138629451355458264946342525383619389314960644665052551751442335509249173361130355796109709885580674313954210217657847432626760733004753275317192133674703563372783297041993227052663333668509952000175053355529058880434182538386715523683713208549376

Integers vs floats

• integers = numbers without any decimal point
• floats = numbers with a decimal point
• operations on integers are exact
• operations on floats are approximate
• integers can be arbitrarily large, but floats are represented only within a finite range.

Markdown

This is some text within a Markdown cell.

This is some text in a code cell, and will throw an error

  File "C:\Users\Luke\AppData\Local\Temp\ipykernel_23904\3831271697.py", line 1
    This is some text in a code cell, and will throw an error
                 ^
SyntaxError: invalid syntax

We can double-click on a markdown cell to edit it.

We can create headings using hashtags, #:

• # Heading gives a top-level heading
• ## Sub-heading gives a sub-heading
• ### Sub-sub-heading gives a sub-sub-heading

We can generate bulleted (un-numbered) using a space and hyphen:

• Item 1
• Item 2
• Item 3

• item 1
• item 2
• item 3

We can also nest lists:

• item 1
  • A
  • B
  • C
• item 2
  • X
  • Y
• item 3
• item 4

We can also create numbered lists using 1., 2., etc.

1. First item
2. Second item
3. Third item
4. Fourth item

Back to integers vs. floats

5 / 2

2.5

4 / 2

2.0

The normal division symbol / will always return a floating point number.

Sometimes, we would prefer to return an integer number. We can this using the // operation:

4 // 2

2

5 // 2

2

The integer division // will always return the quotient from performing long division.

We can get the remainder from integer division using %. This is called modular division.

5 % 2

1

123 % 7

4

123 // 7

17

The above calculation demonstrates that $123 = 7\cdot 17 + 4$.

(123/7 - 17) * 7

4.000000000000011

8 / 3

2.6666666666666665

Variable assignment in Python

Very often, we want to perform operations on some input that might change. We can define variables using the = symbol:

n = 130

We can recall the value of this variable with the variable name, n:

n

130

n // 7

18

n % 7

4

n

130