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CS2130:Section 1.5

2024-02-29T01:07:30Z

Grant: WIP: matricies

== Matricies ==

=== Addition ===
Each matrix must be the same size (width & height must be the same)

<math>\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
+
\begin{bmatrix} 0 & -1 \\ 2 & -2 \end{bmatrix}
=
\begin{bmatrix} 1 & 1 \\ 5 & 2 \end{bmatrix}</math>

=== Multiplication ===
<math>M[a,b] \times N[c,d]</math>

<math>b = c</math> (M's height equals N's width)

Resulting dimensions will be <math>[a,d]</math>

<math>\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
\times
\begin{bmatrix} 0 & -1 \\ 2 & -2 \end{bmatrix}
=
\begin{bmatrix} (1*0)+(2*2) & (1*-1)+(2*-2) \\ (3*0)+(4*2) & (3*-1)+(4*-2) \end{bmatrix}
=
\begin{bmatrix} 4 & -5 \\ 8 & -11 \end{bmatrix}</math>

CS2130:Main Page

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__notoc__

== Sections ==

=== [[CS2130:Section 1.1 & 1.2|Section 1.1 & 1.2]] ===

=== [[CS2130:Section 5.1|Section 5.1]] ===

=== [[CS2130:Section 5.2|Section 5.2]] ===

=== [[CS2130:Section 1.3|Section 1.3]] ===

=== [[CS2130:Section 1.4|Section 1.4]] ===

=== [[CS2130:Section 2.1|Section 2.1]] ===

=== [[CS2130:Section 2.2|Section 2.2]] ===

=== [[CS2130:Section 6.5|Section 6.5]] ===

=== [[CS2130:Section 6.6|Section 6.6]] ===

=== [[CS2130:Section 3.1|Section 3.1]] ===

=== [[CS2130:Section 3.2|Section 3.2]] ===

=== [[CS2130:Section 3.3|Section 3.3]] ===

=== [[CS2130:Section 3.4|Section 3.4]] ===

=== [[CS2130:Section 1.5|Section 1.5]] ===

=== [[CS2130:Section 4.2|Section 4.2]] ===

=== [[CS2130:Section 4.3|Section 4.3]] ===

CS2130:Main Page

2024-02-29T00:53:44Z

Grant: + missing sections

== Sections ==

=== [[CS2130:Section 1.1 & 1.2|Section 1.1 & 1.2]] ===

=== [[CS2130:Section 5.1|Section 5.1]] ===

=== [[CS2130:Section 5.2|Section 5.2]] ===

=== [[CS2130:Section 1.3|Section 1.3]] ===

=== [[CS2130:Section 1.4|Section 1.4]] ===

=== [[CS2130:Section 2.1|Section 2.1]] ===

=== [[CS2130:Section 2.2|Section 2.2]] ===

=== [[CS2130:Section 6.5|Section 6.5]] ===

=== [[CS2130:Section 6.6|Section 6.6]] ===

=== [[CS2130:Section 3.1|Section 3.1]] ===

=== [[CS2130:Section 3.2|Section 3.2]] ===

=== [[CS2130:Section 3.3|Section 3.3]] ===

=== [[CS2130:Section 3.4|Section 3.4]] ===

=== [[CS2130:Section 1.5|Section 1.5]] ===

=== [[CS2130:Section 4.2|Section 4.2]] ===

=== [[CS2130:Section 4.3|Section 4.3]] ===

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CS2130:Section 5.2

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== Symbols ==
[[File:Floor-vs-ceiling.svg|thumb]]

=== Ceiling ===
<math>\lceil x \rceil</math>

Round up

==== Examples ====

# <math>\lceil 5.999 \rceil = 6 </math>
# <math>\lceil 3.001 \rceil = 4</math>

=== Floor ===
<math>\lfloor x \rfloor</math>

Round down

==== Examples ====

# <math>\lfloor 5.999 \rfloor = 5</math>
# <math>\lfloor 3.001 \rfloor = 3</math>
{{Clear}}

=== Modulus ===
<math>%</math>

Integer remainder from division

==== Example ====

# <math>7 % 3 = 1</math>

=== Min ===
<math>\min(x,y)</math>

Gives the lowest number out of the two given

==== Example ====

# <math>\min(1,2) = 1</math>

=== Max ===
<math>\max(1,2)</math>

Gives the highest number out of the two given

==== Example ====

# <math>\max(1,2) = 2</math>

== A Hash ==
For the purpose of this class, a hash is effectively a modulus

File:Floor-vs-ceiling.svg

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CS2130:Section 5.1

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== What is a function? ==
Unlike previous math classes, the '''Vertical Line Test''' is not used in this course

=== Terms ===

* Domain - Inputs of a function
* Range - Outputs of a function

=== Types of functions ===
''Todo: add graphics to go along with these functions''

==== Into ====
[[File:Into-set.svg|thumb|150x150px|A visual representation of the Into function]]
Everything in A is used, and goes to only one element in B
{{Clear}}

==== Onto ====
[[File:Onto-set.svg|thumb|150x150px|A visual representation of the Onto function]]
Everything in B is used
{{Clear}}

==== 1-to-1 ====
[[File:1-to-1-set.svg|thumb|150x150px|A visual representation to the 1-to-1 function]]
Any element in B can go to <u>at most</u> one element in A
{{Clear}}

==== Invertible ====
''Also known as a bijection''
[[File:Bijection-set.svg|thumb|150x150px|A visual representation of the Invertible/Bijection function]]
Both 1-to-1 & onto
{{Clear}}

== Symbols ==

=== Negation ===
<math>\overline{A}</math> = <math>U - A</math>

''Unsure if this is the correct name''

Everything in the Universe except what is inside A

=== Count Of ===
<math>|A|</math>

Count of elements inside A

=== Union ===
<math>A \bigcup B</math>

A combination of both sets

=== Intersection ===
<math>A \bigcap B</math>

A set containing what is in both sets

=== Element ===
<math>1 \in B</math>

<math>1</math> is an element of <math>B</math>

=== Subset ===
<math>\{1\} \subseteq B</math>

1 is a subset of <math>B</math>

==== Notes ====

# The total number of subsets a set can have is equivalent to <math>2^{|A|}</math>

=== Symmetric Difference ===
<math>A \oplus B</math>

Everything in <math>A</math> but not in <math>B</math>

Effectively a unique filter

===== Example =====
<math>A \oplus B = (A \bigcup B) - (A \bigcap B) </math>

=== Empty Set ===
<math>\varnothing</math>

An empty set

===== Notes =====

# An '''Empty Set''' is a '''Subset''' of any set, but not an element of every set
# An '''Empty Set''' is only an element of a set if explicitly a part of the set (you won't see this)

File:Bijection-set.svg

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File:Onto-set.svg

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File:Into-set.svg

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File:Into-set.svg

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Module:Yesno

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