Anki Deck Changes

Note 1: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: M,?u9cw(S%

modified

Before

Front

{{c1:: $\sum_{i = 1}^{n} i\log(i)$}} $\leq$ $O(n \log(n))$ (O-notation)

Back

{{c1:: $\sum_{i = 1}^{n} i\log(i)$}} $\leq$ $O(n \log(n))$ (O-notation)

After

Front

{{c1:: $\sum_{i = 1}^{n} i\log(i)$}} $\leq$ $O(n \log(n))$

Back

{{c1:: $\sum_{i = 1}^{n} i\log(i)$}} $\leq$ $O(n \log(n))$

Field-by-field Comparison

Field	Before	After
Text	{{c1:: $\sum_{i = 1}^{n} i\log(i)$}}  $\leq$ {{c2::$O(n \log(n))$ (O-notation)}}	{{c1:: $\sum_{i = 1}^{n} i\log(i)$}}  $\leq$ {{c2::$O(n \log(n))$:: (O-notation)}}

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation::Sums

Note 2: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: M11/nZaHIu

modified

Before

Front

	search	insert	delete
unsorted Array	$O(n)$	$O(1)$	$O(n)$
sorted Array	$O(\log n)$	$O(n)$	$O(n)$
DLL	$O(n)$ (no bin. search possible)	$O(1)$	$O(n)$

Back

	search	insert	delete
unsorted Array	$O(n)$	$O(1)$	$O(n)$
sorted Array	$O(\log n)$	$O(n)$	$O(n)$
DLL	$O(n)$ (no bin. search possible)	$O(1)$	$O(n)$

After

Front

ADT-Dictionary:

	search	insert	delete
unsorted Array	$O(n)$	$O(1)$	$O(n)$
sorted Array	$O(\log n)$	$O(n)$	$O(n)$
DLL	$O(n)$ (no bin. search possible)	$O(1)$	$O(n)$

Back

ADT-Dictionary:

	search	insert	delete
unsorted Array	$O(n)$	$O(1)$	$O(n)$
sorted Array	$O(\log n)$	$O(n)$	$O(n)$
DLL	$O(n)$ (no bin. search possible)	$O(1)$	$O(n)$

Field-by-field Comparison

Field	Before	After
Text	<b></b><b></b><b></b><b></b><table> <tbody><tr> <td></td> <td><b>search</b></td> <td><b>insert</b></td> <td><b>delete</b></td> </tr> <tr> <td>unsorted Array</td> <td>{{c1::$O(n)$}}</td> <td>{{c2::$O(1)$}}</td> <td>{{c3::$O(n)$}}</td> </tr> <tr> <td>sorted Array</td> <td>{{c4::$O(\log n)$}}</td> <td>{{c5::$O(n)$}}</td> <td>{{c6::$O(n)$}}</td> </tr> <tr> <td>DLL</td> <td>{{c7::$O(n)$ (no bin. search possible)}}</td> <td>{{c8::$O(1)$}}</td> <td>{{c9::$O(n)$}}</td> </tr> </tbody></table>	<b></b><b></b><b></b><b></b> ADT-Dictionary: <table> <tbody><tr> <td></td> <td><b>search</b></td> <td><b>insert</b></td> <td><b>delete</b></td> </tr> <tr> <td>unsorted Array</td> <td>{{c1::$O(n)$}}</td> <td>{{c2::$O(1)$}}</td> <td>{{c3::$O(n)$}}</td> </tr> <tr> <td>sorted Array</td> <td>{{c4::$O(\log n)$}}</td> <td>{{c5::$O(n)$}}</td> <td>{{c6::$O(n)$}}</td> </tr> <tr> <td>DLL</td> <td>{{c7::$O(n)$ (no bin. search possible)}}</td> <td>{{c8::$O(1)$}}</td> <td>{{c9::$O(n)$}}</td> </tr> </tbody></table>

Tags: ETH::1._Semester::A&D::05._Data_Structures::2._ADT_Dictionary

Note 3: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: Pf|C9|^n[w

modified

Before

Front

In a singly and doubly linked list, the operation:

Insert is $\Theta(1)$ as we know the memory address of the final element in the list and just have to set the null pointer to the new keys address. Without this pointer it's $\Theta(l)$.
Get is $\Theta(i)$ very slow as we need to traverse the entire list up to i
insertAfter is $O(1)$ if we get the memory address of the element to insert after.
delete is:
SLL: {{c4::$\Theta(l)$ as we need to find the previous element and change it's pointer}.}
DLL: $O(1)$ we know the address of the previous element and then just edit it's pointer.

Back

In a singly and doubly linked list, the operation:

Insert is $\Theta(1)$ as we know the memory address of the final element in the list and just have to set the null pointer to the new keys address. Without this pointer it's $\Theta(l)$.
Get is $\Theta(i)$ very slow as we need to traverse the entire list up to i
insertAfter is $O(1)$ if we get the memory address of the element to insert after.
delete is:
SLL: {{c4::$\Theta(l)$ as we need to find the previous element and change it's pointer}.}
DLL: $O(1)$ we know the address of the previous element and then just edit it's pointer.

After

Front

In a singly and doubly linked list, the operation:

Insert is $\Theta(1)$ as we know the memory address of the final element in the list and just have to set the null pointer to the new keys address. Without this pointer it's $\Theta(l)$.
Get is $\Theta(i)$ very slow as we need to traverse the entire list up to i
insertAfter is $O(1)$ if we get the memory address of the element to insert after.
delete is:
SLL: $\Theta(l)$ as we need to find the previous element and change it's pointer.
DLL: $O(1)$ we know the address of the previous element and then just edit it's pointer.

Back

In a singly and doubly linked list, the operation:

Insert is $\Theta(1)$ as we know the memory address of the final element in the list and just have to set the null pointer to the new keys address. Without this pointer it's $\Theta(l)$.
Get is $\Theta(i)$ very slow as we need to traverse the entire list up to i
insertAfter is $O(1)$ if we get the memory address of the element to insert after.
delete is:
SLL: $\Theta(l)$ as we need to find the previous element and change it's pointer.
DLL: $O(1)$ we know the address of the previous element and then just edit it's pointer.

Field-by-field Comparison

Field	Before	After
Text	In a <b>singly</b> and <b>doubly linked list</b>, the operation:<br><ul><li><b>Insert</b> is {{c1::$\Theta(1)$ as we know the memory address of the final element in the list and just have to set the null pointer to the new keys address. Without this pointer it's $\Theta(l)$. }}<br></li><li><b>Get</b> is {{c2::$\Theta(i)$ very slow as we need to traverse the entire list up to <b>i</b>}}<br></li><li><b>insertAfter</b> is {{c3:: $O(1)$ if we get the memory address of the element to insert after.}}<br></li><li><b>delete</b> is:<br>      SLL: {{c4::$\Theta(l)$ as we need to find the previous element and change it's pointer}.}<br>      DLL: {{c5:: $O(1)$ we know the address of the previous element and then just edit it's pointer.}}</li></ul>	In a <b>singly</b> and <b>doubly linked list</b>, the operation:<br><ul><li><b>Insert</b> is {{c1::$\Theta(1)$ as we know the memory address of the final element in the list and just have to set the null pointer to the new keys address. Without this pointer it's $\Theta(l)$. }}<br></li><li><b>Get</b> is {{c2::$\Theta(i)$ very slow as we need to traverse the entire list up to <b>i</b>}}<br></li><li><b>insertAfter</b> is {{c3:: $O(1)$ if we get the memory address of the element to insert after.}}<br></li><li><b>delete</b> is:<br>      SLL: {{c4::$\Theta(l)$ as we need to find the previous element and change it's pointer.}}<br>      DLL: {{c5:: $O(1)$ we know the address of the previous element and then just edit it's pointer.}}</li></ul>

Tags: ETH::1._Semester::A&D::05._Data_Structures::1._ADT_List::2._Linked_List

Note 4: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: nK{)v6I%zc

modified

Before

Front

The ADT stack can be efficiently implemented using a singly linked list:

push: $\Theta(1)$
pop: $\Theta(1)$ as this removes the first element. This means we just copy the pointer next from the first element to be the first pointer of the list.

Back

The ADT stack can be efficiently implemented using a singly linked list:

push: $\Theta(1)$
pop: $\Theta(1)$ as this removes the first element. This means we just copy the pointer next from the first element to be the first pointer of the list.

After

Front

The ADT stack can be efficiently implemented using a singly linked list:

push: $\Theta(1)$
pop: $\Theta(1)$ as this removes the first element. This means we just copy the pointer next from the first element to be the first pointer of the list.

Back

The ADT stack can be efficiently implemented using a singly linked list:

push: $\Theta(1)$
pop: $\Theta(1)$ as this removes the first element. This means we just copy the pointer next from the first element to be the first pointer of the list.

Field-by-field Comparison

Field	Before	After
Text	The ADT <b>stack</b> can be efficiently implemented using a {{c1::~~ ~~<b>singly linked list</b>}}:<br><ul><li><b>push</b>: {{c2:: $\Theta(1)$}}<br></li><li><b>pop</b>: {{c3:: $\Theta(1)$ as this removes the first element. This means we just copy the pointer next from the first element to be the first pointer of the list.}}<br></li></ul>	The ADT <b>stack</b> can be efficiently implemented using a {{c1::<b>singly linked list</b>}}:<br><ul><li><b>push</b>: {{c2:: $\Theta(1)$}}<br></li><li><b>pop</b>: {{c3:: $\Theta(1)$ as this removes the first element. This means we just copy the pointer next from the first element to be the first pointer of the list.}}<br></li></ul>

Tags: ETH::1._Semester::A&D::05._Data_Structures::1._ADT_List::4._Stack

Note 5: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: C18gm]huq&

modified

Before

Front

In a Group:
{{c1:: $\widehat{a * b}$ }} = {{c2:: $\widehat{b} * \widehat{a}$}} This is a property from a Lemma.

Back

In a Group:
{{c1:: $\widehat{a * b}$ }} = {{c2:: $\widehat{b} * \widehat{a}$}} This is a property from a Lemma.

After

Front

In a Group:

{{c1:: $\widehat{a * b}$ }} = {{c2:: $\widehat{b} * \widehat{a}$}}

Back

In a Group:

{{c1:: $\widehat{a * b}$ }} = {{c2:: $\widehat{b} * \widehat{a}$}}

Field-by-field Comparison

Field	Before	After
Text	~~<p>~~In a Group:<br> {{c1:: $\widehat{a * b}$ }} = {{c2:: $\widehat{b} * \widehat{a}$}} ~~This is a property from a Lemma.</p>~~	In a Group: <br><br>{{c1:: $\widehat{a * b}$ }} = {{c2:: $\widehat{b} * \widehat{a}$}}

Tags: ETH::1._Semester::DiskMat::5._Algebra::2._Monoids_and_Groups::3._Inverses_and_Groups

Note 6: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: GE_=q.pKz`

modified

Before

Front

Group axiom G1 states that the operation $*$ is associative: $a * (b * c) = (a * b) * c$ for all $a, b, c$ in $G$.

Back

Group axiom G1 states that the operation $*$ is associative: $a * (b * c) = (a * b) * c$ for all $a, b, c$ in $G$.

After

Front

Group axiom G1 states that the operation $*$ is associative: .

Back

Group axiom G1 states that the operation $*$ is associative: .

Field-by-field Comparison

Field	Before	After
Text	<p>Group axiom <strong>G1</strong> states that the operation $$ is {{c1::associative}}: {{c2::$a (b * c) = (a * b) * c$}} for all $a, b, c$ in $G$.</p>	<p>Group axiom <strong>G1</strong> states that the operation $$ is {{c1::associative: {{c2::$a (b * c) = (a * b) * c$}} for all $a, b, c$ in $G$}}.</p>

Tags: ETH::1._Semester::DiskMat::5._Algebra::2._Monoids_and_Groups::3._Inverses_and_Groups

Note 7: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: l];xKGd{%I

modified

Before

Front

A function $ f: A \rightarrow B$ is surjective (or onto) if $ \forall b \ \exists a \ , b = f(a)$, i.e. every value is taken

Back

A function $ f: A \rightarrow B$ is surjective (or onto) if $ \forall b \ \exists a \ , b = f(a)$, i.e. every value is taken

After

Front

A function $ f: A \rightarrow B$ is surjective (or onto) if $ \forall b \ \exists a \ , b = f(a)$, i.e. every value is taken.

Back

A function $ f: A \rightarrow B$ is surjective (or onto) if $ \forall b \ \exists a \ , b = f(a)$, i.e. every value is taken.

Field-by-field Comparison

Field	Before	After
Text	A function $ f: A \rightarrow B$ is {{c1::surjective (or onto)}} if {{c2::$ \forall b \ \exists a \ , b = f(a)$, i.e. every value is taken}}	A function $ f: A \rightarrow B$ is {{c1::surjective (or onto)}} if {{c2::$ \forall b \ \exists a \ , b = f(a)$, i.e. every value is taken}}.

Tags: ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::6._Functions

Note 8: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: xH`d$W-97_

modified

Before

Front

In a Group:
$\widehat{(\widehat{a})} =$ $a$ (inverse of inverse is the original element). This is a property from Lemma 5.3.

Back

In a Group:
$\widehat{(\widehat{a})} =$ $a$ (inverse of inverse is the original element). This is a property from Lemma 5.3.

After

Front

In a group:

$\widehat{(\widehat{a})} =$ $a$

Back

In a group:

$\widehat{(\widehat{a})} =$ $a$

Inverse of inverse is the original element.

This is a property from Lemma 5.3.

Field-by-field Comparison

Field	Before	After
Text	~~<p>~~In a Group:<br> $\widehat{(\widehat{a})} =${{c1:: $a$ }} ~~{{c1:: (inverse of inverse is the original element)}}. This is a property from Lemma 5.3.</p>~~	In a group: <br><br>$\widehat{(\widehat{a})} =${{c1:: $a$ }}
Extra		Inverse of inverse is the original element.<br><br>This is a property from Lemma 5.3.

Tags: ETH::1._Semester::DiskMat::5._Algebra::2._Monoids_and_Groups::3._Inverses_and_Groups

Note 9: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: yAP=DE#~t<

added

New Note

Front

An abelian group has the following properties:

Closure
Associativity
Identity
Inverse
Commutative

Back

An abelian group has the following properties:

Closure
Associativity
Identity
Inverse
Commutative

Field-by-field Comparison

Field	Before	After
Text		An <b>abelian group</b> has the following properties:<br><ol><li>{{c1::Closure}}</li><li>{{c2::Associativity}}</li><li>{{c3::Identity}}</li><li>{{c4::Inverse}}</li><li>{{c5::Commutative}}</li></ol>

Tags: ETH::1._Semester::DiskMat::5._Algebra::2._Monoids_and_Groups

Note 10: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: Dd-0>Kd049

modified

Before

Front

The columns of $A$ are independent if and only if $x = 0$ is the only vector for which $Ax = 0$ (Linear combination view).

Back

The columns of $A$ are independent if and only if $x = 0$ is the only vector for which $Ax = 0$ (Linear combination view).

After

Front

The columns of $A$ are independent if and only if $x = 0$ is the only vector for which $Ax = 0$.

Back

The columns of $A$ are independent if and only if $x = 0$ is the only vector for which $Ax = 0$.

Field-by-field Comparison

Field	Before	After
Text	The columns of $A$ are independent if and only if {{c1::$x = 0$ is the  only vector for which $Ax = 0$}} (Linear combination view).	The columns of $A$ are independent if and only if {{c1::$x = 0$ is the  only vector for which $Ax = 0$::(Linear combination view)}}.

Tags: ETH::1._Semester::LinAlg::2._Matrices::1._Matrices_and_linear_combinations::1._Matrix-Vector_multiplication

Note 11: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: col^b$YzMt

modified

Before

Front

$v^\top v = $ $||v||^2$ (in terms of norm)

Back

$v^\top v = $ $||v||^2$ (in terms of norm)

as $||v|| = \sqrt{v^\top v}$.

After

Front

$v^\top v = $ $||v||^2$

Back

$v^\top v = $ $||v||^2$

as $||v|| = \sqrt{v^\top v}$.

Field-by-field Comparison

Field	Before	After
Text	$v^\top v = ${{c1:: $\|\|v\|\|^2$}} (in terms of norm)	$v^\top v = ${{c1:: $\|\|v\|\|^2$::(in terms of norm)}}

Tags: ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::2._Euclidean_norm

Note 12: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: gU%jisb2z3

modified

Before

Front

Scalar product properties: $u, v, w \in \mathbb{R}^m$ be vectors and $\lambda \in \mathbb{R}$ a scalar.

$v \cdot w = w \cdot v$ (symmetry / commutatitivity
$(\lambda v) \cdot w = \lambda (v \cdot w)$ (scalars move freely)
$u \cdot (v + w) = u \cdot v + u \cdot w$ and $(u + v) \cdot w = u\cdot w + v \cdot w$ (distributivity)
$v \cdot v \geq 0$ with equality if and only if $v = 0$ (positive definiteness

Back

Scalar product properties: $u, v, w \in \mathbb{R}^m$ be vectors and $\lambda \in \mathbb{R}$ a scalar.

$v \cdot w = w \cdot v$ (symmetry / commutatitivity
$(\lambda v) \cdot w = \lambda (v \cdot w)$ (scalars move freely)
$u \cdot (v + w) = u \cdot v + u \cdot w$ and $(u + v) \cdot w = u\cdot w + v \cdot w$ (distributivity)
$v \cdot v \geq 0$ with equality if and only if $v = 0$ (positive definiteness

After

Front

Scalar product properties

Let $u, v, w \in \mathbb{R}^m$ be vectors and $\lambda \in \mathbb{R}$ a scalar:

$v \cdot w = w \cdot v$ (symmetry / commutativity)
$(\lambda v) \cdot w = \lambda (v \cdot w)$ (scalars move freely)
$u \cdot (v + w) = u \cdot v + u \cdot w$ and $(u + v) \cdot w = u\cdot w + v \cdot w$ (distributivity)
$v \cdot v \geq 0$ with equality if and only if $v = 0$ (positive definedness)

Back

Scalar product properties

Let $u, v, w \in \mathbb{R}^m$ be vectors and $\lambda \in \mathbb{R}$ a scalar:

$v \cdot w = w \cdot v$ (symmetry / commutativity)
$(\lambda v) \cdot w = \lambda (v \cdot w)$ (scalars move freely)
$u \cdot (v + w) = u \cdot v + u \cdot w$ and $(u + v) \cdot w = u\cdot w + v \cdot w$ (distributivity)
$v \cdot v \geq 0$ with equality if and only if $v = 0$ (positive definedness)

Field-by-field Comparison

Field	Before	After
Text	Scalar product properties: $u, v, w \in \mathbb{R}^m$ be vectors and $\lambda \in \mathbb{R}$ a scalar.<br><ol><li>{{c1::$v \cdot w = w \cdot v$ (symmetry / commutatitivity}}</li><li>{{c2:: $(\lambda v) \cdot w = \lambda (v \cdot w)$ (scalars move freely)}}</li><li>{{c3:: $u \cdot (v + w) = u \cdot v + u \cdot w$ and $(u + v) \cdot w = u\cdot w + v \cdot w$ (distributivity)}}</li><li>{{c4:: $v \cdot v \geq 0$ with equality if and only if $v = 0$ (positive definiteness}}</li></ol>	Scalar product properties<br><br>Let $u, v, w \in \mathbb{R}^m$ be vectors and $\lambda \in \mathbb{R}$ a scalar:<br><ol><li>{{c1::$v \cdot w = w \cdot v$ (symmetry / commutativity)}}</li><li>{{c2:: $(\lambda v) \cdot w = \lambda (v \cdot w)$ (scalars move freely)}}</li><li>{{c3:: $u \cdot (v + w) = u \cdot v + u \cdot w$ and $(u + v) \cdot w = u\cdot w + v \cdot w$ (distributivity)}}</li><li>{{c4:: $v \cdot v \geq 0$ with equality if and only if $v = 0$ (positive definedness)}}</li></ol>

Tags: ETH::1._Semester::LinAlg::1._Vectors::1._Vectors_and_linear_combinations::2._Scalar_multiplication

	search	insert	delete
unsorted Array	\(O(n)\)	\(O(1)\)	\(O(n)\)
sorted Array	\(O(\log n)\)	\(O(n)\)	\(O(n)\)
DLL	\(O(n)\) (no bin. search possible)	\(O(1)\)	\(O(n)\)

	search	insert	delete
unsorted Array	\(O(n)\)	\(O(1)\)	\(O(n)\)
sorted Array	\(O(\log n)\)	\(O(n)\)	\(O(n)\)
DLL	\(O(n)\) (no bin. search possible)	\(O(1)\)	\(O(n)\)

	search	insert	delete
unsorted Array	\(O(n)\)	\(O(1)\)	\(O(n)\)
sorted Array	\(O(\log n)\)	\(O(n)\)	\(O(n)\)
DLL	\(O(n)\) (no bin. search possible)	\(O(1)\)	\(O(n)\)

	search	insert	delete
unsorted Array	\(O(n)\)	\(O(1)\)	\(O(n)\)
sorted Array	\(O(\log n)\)	\(O(n)\)	\(O(n)\)
DLL	\(O(n)\) (no bin. search possible)	\(O(1)\)	\(O(n)\)

Field	Before	After
Text	~~<p>~~In a Group:<br> \(\widehat{(\widehat{a})} =\){{c1:: \(a\) }} ~~{{c1:: (inverse of inverse is the original element)}}. This is a property from Lemma 5.3.</p>~~	In a group: <br><br>\(\widehat{(\widehat{a})} =\){{c1:: \(a\) }}
Extra		Inverse of inverse is the original element.<br><br>This is a property from Lemma 5.3.

Note 1: ETH::A&D

Before

Front

Back

After

Front

Back

Note 2: ETH::A&D

Before

Front

Back

After

Front

Back

Note 3: ETH::A&D

Before

Front

Back

After

Front

Back

Note 4: ETH::A&D

Before

Front

Back

After

Front

Back

Note 5: ETH::DiskMat

Before

Front

Back

After

Front

Back

Note 6: ETH::DiskMat

Before

Front

Back

After

Front

Back

Note 7: ETH::DiskMat

Before

Front

Back

After

Front

Back

Note 8: ETH::DiskMat

Before

Front

Back

After

Front

Back

Note 9: ETH::DiskMat

Previous

New Note

Front

Back

Note 10: ETH::LinAlg

Before

Front

Back

After

Front

Back

Note 11: ETH::LinAlg

Before

Front

Back

After

Front

Back

Note 12: ETH::LinAlg

Before

Front

Back

After