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Es ist möglich mithilfe von \texttt{bc\_type} beim Instanziieren der Klasse die Art des Splines zu ändern. 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all its partial derivatives are continuous. +$f$ is of class $C^k$ if it is differentiable and each of its partial derivatives are in $C^{k - 1}$. +If $f \in C^k(X; \R^m)$ for all $k \geq 1$, then $f \in C^\infty(X; \R^m)$\\ +% ──────────────────────────────────────────────────────────────────── +\setLabelNumber{all}{4} +\compactproposition{Mixed derivatives commute} $\partial_{x, y} f = \partial_{y, x}$, as well as $\partial_{x, y, z} = \partial_{x, z, y} = \ldots$, etc (all mixed derivatives commute) +Since we have symmetry, we can use the notation $\partial_{x_1^{m_1}, \ldots, x_n^{m_n}} f = \frac{\partial^k}{\partial x^m} f = D^m f = \partial^m f$, +where $m = (m_1, \ldots, m_n)$ and $m_1 + \ldots + m_n = k$. +There are ${n + k - 1 \choose k}$ possible values for $m$ and e.g. $(1, 1, 2)$ corresponds to the derivative $\frac{\partial^4 f}{\partial x \partial y \partial^2 z}$\\ +% ──────────────────────────────────────────────────────────────────── +\stepLabelNumber{all} +\shortremark Due to linearity of the partial derivative $\partial_x^m(a f_1 + b f_2) = a \partial_x^m f_1 + b \partial_x^m f_2$\\ +% ──────────────────────────────────────────────────────────────────── +\stepLabelNumber{all} +\compactex{Laplace operator} $f \in C^2(X)$, $\nabla f \in C_1(X; \R^n)$, so +$\displaystyle \text{div}(\nabla f) = \sum_{i = 1}^{n} \frac{\partial}{\partial_{x_i}} \left( \frac{\partial f}{\partial_{x_i}} \right) + = \sum_{i = 1}^{n} \frac{\partial^2 f}{\partial x^2_i}$ (called \bi{Laplacian}, $\Delta f$)\\ +% ──────────────────────────────────────────────────────────────────── +\compactdef{Hessian} $f : X \rightarrow \R$ in $C^2$. For $x \in X$, the \bi{Hessian matrix} of $f$ at $x$ is the symmetric square matrix +\vspace{-0.75pc} +\begin{align*} + \text{Hess}_f(x) = (\partial_{x_i, x_j} f)_{1 \leq i, j \leq n} = H_f(x) \mediumhspace (\text{$i$-th row, $j$-th column}) +\end{align*} + +\drmvspace diff --git a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/04_change_of_variable.tex b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/04_change_of_variable.tex index 68a07b7..080aa11 100644 --- a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/04_change_of_variable.tex +++ b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/04_change_of_variable.tex @@ -1,2 +1,5 @@ \newsectionNoPB \subsection{Change of variable} +The idea is to substitute variables for others that make the equation easier to solve. +A common example is to switch to polar coordinates from cartesian coordinates, as already demonstrated with continuity checks +% TODO: Add notes from TA notes diff --git a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex index d79479f..5fe339f 100644 --- a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex +++ b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex @@ -1,2 +1,24 @@ \newsectionNoPB \subsection{Taylor polynomials} +\compactdef{Taylor polynomials} +Let $f : X \rightarrow \R$ with $f \in C^k(X, \R)$ and $y \in X$. The Taylor-Polynomial of order $k$ of $f$ at $y$ is: +\vspace{-0.75pc} +\begin{align*} + T_k f(y; x - y) = \sum_{|i| \leq k} \frac{\partial_i f(y)(x - y)^i}{i!} +\end{align*} + +\drmvspace\rmvspace +% TODO: Find out what the \partial_1 notation means (likely TA notes 09) +where $i$ is a \textit{multi-index}, so: +\drmvspace +\begin{multicols}{2} + \begin{itemize}[noitemsep] + \item $i = (i_1, \ldots, i_n)$ (each $i_j \geq 0$) + \item $|i| = i_1 + \ldots + i_n$, $\partial_i = \partial_1^{i_1} \ldots \partial_n^{i_n}$ + \item $(x - y)^i = (x_1 - y_1)^{i_1} \cdot \ldots \cdot (x_n - y_n)^{i_n}$ + \item $i! = i_1! \cdot \ldots \cdot i_n!$ + \end{itemize} +\end{multicols} + +\drmvspace\rmvspace +The concept this formula uses is that we iterate through all possible partial derivatives of $f$ and assigns each a multi-index $i$ From 73412cfb08b65b460eb4dff0fa2c1456dc0a3978 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 10:32:00 +0100 Subject: [PATCH 03/16] [CI] Add automated upload of summaries to comsol --- .github/actions/upload-to-comsol/action.yml | 21 ++++++++++++++++++ .github/workflows/upload-ad.yml | 17 ++++++++++++++ .../analysis-ii-cheat-sheet.pdf | Bin 304950 -> 304979 bytes .../differentiation/05_taylor_polynomials.tex | 5 +++-- 4 files changed, 41 insertions(+), 2 deletions(-) create mode 100644 .github/actions/upload-to-comsol/action.yml create mode 100644 .github/workflows/upload-ad.yml diff --git a/.github/actions/upload-to-comsol/action.yml b/.github/actions/upload-to-comsol/action.yml new file mode 100644 index 0000000..9bf910b --- /dev/null +++ b/.github/actions/upload-to-comsol/action.yml @@ -0,0 +1,21 @@ +name: Upload to ComSol +description: Upload documents to VIS ComSol +author: Janis Hutz +inputs: + file: + description: File to upload + access_token: + description: Access token for the file on ComSol + url: + description: The upload URL as shown in the access token details page on ComSol +runs: + using: composite + steps: + - name: Upload file to ComSol + run: | + curl {{ inputs.url }} \ + -H "Authorization: {{ inputs.access_token }}" \ + -F "file=@{{ inputs.file }}" +branding: + icon: book + color: red diff --git a/.github/workflows/upload-ad.yml b/.github/workflows/upload-ad.yml new file mode 100644 index 0000000..f6bd1ce --- /dev/null +++ b/.github/workflows/upload-ad.yml @@ -0,0 +1,17 @@ +name: Upload Algorithms and Datastructures Summary +on: + push: + paths: + - 'semester1/algorithms-and-datastructures/**' +jobs: + build_docs: + runs_on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + access_token: {{ secrets.TOKEN_AD }} + file: ./semester1/algorithms-and-datastructures/ad-janishutz.pdf + url: https://exams.vis.ethz.ch/api/document/jahutz/summary-hs24_1/files/591/update/ diff --git a/semester3/analysis-ii/cheat-sheet-jh/analysis-ii-cheat-sheet.pdf 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of all algorithms discussed} \end{Large}\\[0.2cm] + \hlurl{https://github.com/janishutz/eth-summaries} \end{center} From 58711383dda546a4f89cbf318a0f0cac57754632 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 10:38:39 +0100 Subject: [PATCH 07/16] [CI] Actions fixes --- .github/actions/upload-to-comsol/action.yml | 1 + .github/workflows/upload-ad.yml | 2 +- 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/.github/actions/upload-to-comsol/action.yml b/.github/actions/upload-to-comsol/action.yml index 3793754..8e99dea 100644 --- a/.github/actions/upload-to-comsol/action.yml +++ b/.github/actions/upload-to-comsol/action.yml @@ -12,6 +12,7 @@ runs: using: composite steps: - name: Upload file to ComSol + shell: bash run: | curl ${{ inputs.url }} \ -H "Authorization: ${{ inputs.access_token }}" \ diff --git a/.github/workflows/upload-ad.yml b/.github/workflows/upload-ad.yml index 323cf55..16fc30c 100644 --- a/.github/workflows/upload-ad.yml +++ b/.github/workflows/upload-ad.yml @@ -4,7 +4,7 @@ on: paths: - 'semester1/algorithms-and-datastructures/**' jobs: - build_docs: + upload_summary: runs-on: ubuntu-latest steps: - name: Set up Git repository From 2e0b24982b415fa75c8ddaa1a425aa2b46fbff1a Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 10:39:54 +0100 Subject: [PATCH 08/16] [AD] Trigger CI --- .../ad-janishutz.pdf | Bin 449441 -> 449443 bytes .../ad-janishutz.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/semester1/algorithms-and-datastructures/ad-janishutz.pdf b/semester1/algorithms-and-datastructures/ad-janishutz.pdf index 10fd28cc777ef20e2c883095e07e58b0f7cdf58d..d4fadb7542c25a4c62f26dd2051cf9669ac10b25 100644 GIT binary patch delta 3297 zcmaizX*3jk`^PcOSjJL`EMt!vRD+peq%32p?CWGu?ij|TY+1(A%#e_zCnRDTWbBh= zvSdm3UEKB=%h-}6*~XF)_l@}Lod1jG-Sgsm&gc4^>s-Hco$LGx8sv)_e{i6|Zgu<5r!<1*Gh9&>^wjX& zE6|MhpGvmT|9m``3$pi+8*#wFTe)4_l}B 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zhZYi^kTKNpi5`8Z2hxM%6<(g&Ydo-b;Wk2tWlYF4!b-V=dQ2k~d~m%LCIRkue(!?8 zu>fMvvE=Vj!qx7qt$Ki0W_q5`zJ+u(w^`QtWUF4eWIijitX8f*n~W?HCAy&1Z;}CQ zhxFO>U8P0n(Xw=Ci8BRUW)bn18&^`NS?d0+L1#9E^4>Yx;zI!$@d`9#y%O#C?DDbF zwbcTBGl|xS)>Ul%L5Auaq9>4=rPF;Z45$zWMxdl8_;*e$$nGR6`V4J$pfNuj--ZFc3+*gKb~l;1bXB$8@Thsxyc+w9&AFEMJc_(PrY!Q3rE1y#IFO~t z?2Q0&oyW4Hx5rp5d%%)h=ias^PtL0~`wLBCx!q)YlCNI++4U{7Ic%Q&C#lHo;F~u2 zs(ZlVW<=yi&6l)hgxk*_`EJ+AKc*IqyZj!j=>|9BL&o~fkk{Q~J8Q?1NZ5k06@u$D z{%h^-`yfc?z8m4Y)?N(&U|jgZ=Ta}l!tL!c=md6eI_Bzd%hyxVb+^Nr`M44<#kEy4sy zm5IV12mTZoY9WY%{@?u#wpKF+fG1)*87MxWM559?!WD2}9ZD5=LU8B@VHPRcj}ix- z6Fdof*n0%r!mpFpWRIDA*kpBRIEjEk* diff --git a/semester1/algorithms-and-datastructures/ad-janishutz.tex b/semester1/algorithms-and-datastructures/ad-janishutz.tex index b00def1..98f09a9 100755 --- a/semester1/algorithms-and-datastructures/ad-janishutz.tex +++ b/semester1/algorithms-and-datastructures/ad-janishutz.tex @@ -33,7 +33,7 @@ \begin{center} HS2024, ETHZ\\[0.2cm] \begin{Large} - \textsc{Summary of all algorithms discussed} + \textsc{Summary of the full course} \end{Large}\\[0.2cm] \hlurl{https://github.com/janishutz/eth-summaries} \end{center} From 341fd9ab6e0326b041fb7b2007b5a72c27ec2905 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 11:04:36 +0100 Subject: [PATCH 09/16] [CI] Add auto upload of all complete summaries --- .github/workflows/upload-ad.yml | 2 +- .github/workflows/upload-anaI-jh.yml | 23 +++++++++++++++++++++++ .github/workflows/upload-aw.yml | 17 +++++++++++++++++ .github/workflows/upload-eprog.yml | 17 +++++++++++++++++ .github/workflows/upload-la.yml | 17 +++++++++++++++++ .github/workflows/upload-pprog-jh.yml | 17 +++++++++++++++++ 6 files changed, 92 insertions(+), 1 deletion(-) create mode 100644 .github/workflows/upload-anaI-jh.yml create mode 100644 .github/workflows/upload-aw.yml create mode 100644 .github/workflows/upload-eprog.yml create mode 100644 .github/workflows/upload-la.yml create mode 100644 .github/workflows/upload-pprog-jh.yml diff --git a/.github/workflows/upload-ad.yml b/.github/workflows/upload-ad.yml index 16fc30c..2279601 100644 --- a/.github/workflows/upload-ad.yml +++ b/.github/workflows/upload-ad.yml @@ -4,7 +4,7 @@ on: paths: - 'semester1/algorithms-and-datastructures/**' jobs: - upload_summary: + upload_document: runs-on: ubuntu-latest steps: - name: Set up Git repository diff --git a/.github/workflows/upload-anaI-jh.yml b/.github/workflows/upload-anaI-jh.yml new file mode 100644 index 0000000..cbd625e --- /dev/null +++ b/.github/workflows/upload-anaI-jh.yml @@ -0,0 +1,23 @@ +name: Upload Analysis I (by janishutz) Cheat-Sheet +on: + push: + paths: + - 'semester2/analysis-i/cheat-sheet-jh/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload English version to ComSol + uses: ./.github/actions/upload-to-comsol + with: + access_token: ${{ secrets.TOKEN_ANA_I_JH }} + file: ./semester2/analysis-i/cheat-sheet-jh/cheat-sheet-en.pdf + url: https://exams.vis.ethz.ch/api/document/jahutz/analysis-i-cheatsheet-fs25/files/654/update/ + - name: Upload German version to ComSol + uses: ./.github/actions/upload-to-comsol + with: + access_token: ${{ secrets.TOKEN_ANA_I_JH }} + file: ./semester2/analysis-i/cheat-sheet-jh/cheat-sheet-de.pdf + url: https://exams.vis.ethz.ch/api/document/jahutz/analysis-i-cheatsheet-fs25/files/655/update/ diff --git a/.github/workflows/upload-aw.yml b/.github/workflows/upload-aw.yml new file mode 100644 index 0000000..21f4745 --- /dev/null +++ b/.github/workflows/upload-aw.yml @@ -0,0 +1,17 @@ +name: Upload Algorithms and Probability Summary +on: + push: + paths: + - 'semester2/algorithms-and-probability/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + access_token: ${{ secrets.TOKEN_AW }} + file: ./semester2/algorithms-and-probability/aw-summary.pdf + url: https://exams.vis.ethz.ch/api/document/jahutz/summary-fs25_0/files/653/update/ diff --git a/.github/workflows/upload-eprog.yml b/.github/workflows/upload-eprog.yml new file mode 100644 index 0000000..a35ce99 --- /dev/null +++ b/.github/workflows/upload-eprog.yml @@ -0,0 +1,17 @@ +name: Upload Introduction to Programming Short Summary +on: + push: + paths: + - 'semester1/eprog/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + access_token: ${{ secrets.TOKEN_EPROG }} + file: ./semester1/eprog/eprog-janishutz.pdf + url: https://exams.vis.ethz.ch/api/document/jahutz/short-summary-hs24/files/593/update/ diff --git a/.github/workflows/upload-la.yml b/.github/workflows/upload-la.yml new file mode 100644 index 0000000..e19d1c0 --- /dev/null +++ b/.github/workflows/upload-la.yml @@ -0,0 +1,17 @@ +name: Upload Linear Algebra Cheat-Sheet +on: + push: + paths: + - 'semester1/linear-algebra/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + access_token: ${{ secrets.TOKEN_LA }} + file: ./semester1/linear-algebra/linAlg-janishutz.pdf + url: https://exams.vis.ethz.ch/api/document/jahutz/cheatsheet-hs24_5/files/592/update/ diff --git a/.github/workflows/upload-pprog-jh.yml b/.github/workflows/upload-pprog-jh.yml new file mode 100644 index 0000000..96eab00 --- /dev/null +++ b/.github/workflows/upload-pprog-jh.yml @@ -0,0 +1,17 @@ +name: Upload Parallel Programming Compact Summary +on: + push: + paths: + - 'semester2/parallel-programming-compact/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + file: ./semester2/parallel-programming-compact/pprog-compact-summary.pdf + access_token: ${{ secrets.TOKEN_PPROG }} + url: https://exams.vis.ethz.ch/api/document/jahutz/summary-fs25_0/files/653/update/ From 866c91617e875c2a3a1799dd32cff69ea88c8df6 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 11:06:55 +0100 Subject: [PATCH 10/16] [CI] Update pprog file upload url --- .github/workflows/upload-pprog-jh.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/upload-pprog-jh.yml b/.github/workflows/upload-pprog-jh.yml index 96eab00..919e126 100644 --- a/.github/workflows/upload-pprog-jh.yml +++ b/.github/workflows/upload-pprog-jh.yml @@ -14,4 +14,4 @@ jobs: with: file: ./semester2/parallel-programming-compact/pprog-compact-summary.pdf access_token: ${{ secrets.TOKEN_PPROG }} - url: https://exams.vis.ethz.ch/api/document/jahutz/summary-fs25_0/files/653/update/ + url: https://exams.vis.ethz.ch/api/document/jahutz/compact-summary-fs25/files/656/update/ From 34712a04ce51aff9d9db8ba84548797edb67268e Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 11:17:51 +0100 Subject: [PATCH 11/16] [CI] Add upload for TI and NumCS --- .github/workflows/upload-numcs.yml | 17 +++++++++++++++++ .github/workflows/upload-ti-compact.yml | 17 +++++++++++++++++ .github/workflows/upload-ti-full.yml | 17 +++++++++++++++++ 3 files changed, 51 insertions(+) create mode 100644 .github/workflows/upload-numcs.yml create mode 100644 .github/workflows/upload-ti-compact.yml create mode 100644 .github/workflows/upload-ti-full.yml diff --git a/.github/workflows/upload-numcs.yml b/.github/workflows/upload-numcs.yml new file mode 100644 index 0000000..fb1cb3d --- /dev/null +++ b/.github/workflows/upload-numcs.yml @@ -0,0 +1,17 @@ +name: Upload NumCS Summary +on: + push: + paths: + - 'semester3/numcs/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + file: ./semester3/numcs/numcs-summary.pdf + access_token: ${{ secrets.TOKEN_NUMCS }} + url: https://exams.vis.ethz.ch/api/document/jahutz/summary-hs25/files/657/update/ diff --git a/.github/workflows/upload-ti-compact.yml b/.github/workflows/upload-ti-compact.yml new file mode 100644 index 0000000..8cecc5d --- /dev/null +++ b/.github/workflows/upload-ti-compact.yml @@ -0,0 +1,17 @@ +name: Upload Theoretical Computer Science Compact Summary +on: + push: + paths: + - 'semester3/ti/compact/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + file: ./semester3/ti/compact/ti-compact.pdf + access_token: ${{ secrets.TOKEN_TI }} + url: https://exams.vis.ethz.ch/api/document/jahutz/summary-hs25_0/files/659/update/ diff --git a/.github/workflows/upload-ti-full.yml b/.github/workflows/upload-ti-full.yml new file mode 100644 index 0000000..51757cd --- /dev/null +++ b/.github/workflows/upload-ti-full.yml @@ -0,0 +1,17 @@ +name: Upload Theoretical Computer Science Summary +on: + push: + paths: + - 'semester3/ti/main/**' +jobs: + upload_document: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v6 + - name: Upload to ComSol + uses: ./.github/actions/upload-to-comsol + with: + file: ./semester3/ti/main/ti-summary.pdf + access_token: ${{ secrets.TOKEN_TI }} + url: https://exams.vis.ethz.ch/api/document/jahutz/summary-hs25_0/files/658/update/ From a9805c198cdaf8cc8fb3367e91c09824cca22498 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 11:24:06 +0100 Subject: [PATCH 12/16] [AD] Add note --- .../algorithms-and-probability/aw-summary.pdf | Bin 1050319 -> 1054325 bytes .../parts/combinatorics.tex | 2 ++ 2 files changed, 2 insertions(+) diff --git 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a/semester2/algorithms-and-probability/parts/combinatorics.tex b/semester2/algorithms-and-probability/parts/combinatorics.tex index dc575f1..ec92487 100644 --- a/semester2/algorithms-and-probability/parts/combinatorics.tex +++ b/semester2/algorithms-and-probability/parts/combinatorics.tex @@ -1,6 +1,8 @@ \newsection \section{Combinatorics} \subsection{Introduction} +Please note: This section was not part of the book and is written in very simple terms (it is taken from a summary I wrote 4 years ago during Gymnasium) + Combinatorics was developed from the willingness of humans to gamble and the fact that everybody wanted to win as much money as possible. \subsection{Simple counting operations} From bb03c9597dffe3f2f6197f7e060fe93740a82974 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 11:24:16 +0100 Subject: [PATCH 13/16] [TI] Add title pages --- semester3/ti/compact/ti-compact.pdf | Bin 398639 -> 391564 bytes semester3/ti/compact/ti-compact.tex | 53 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zPW`tyr$G`O0@nVKbpfZ}vO3BG%AwtERN vWIfikQ)XS@&O4fxs};CV4S={Stealth[round]}] + \node[state, initial left, accepting] (q0p0) {$q_0, p_0$}; + \node[state] (q0p1) [right=of q0p0] {$q_0, p_1$}; + \node[state] (q0p2) [right=of q0p1] {$q_0, p_2$}; + \node[state, accepting] (q1p0) [below=of q0p0] {$q_1, p_0$}; + \node[state] (q1p1) [right=of q1p0] {$q_1, p_1$}; + \node[state] (q1p2) [right=of q1p1] {$q_1, p_2$}; + \node[state, accepting] (q2p0) [below=of q1p0] {$q_2, p_0$}; + \node[state, accepting] (q2p1) [right=of q2p0] {$q_2, p_1$}; + \node[state, accepting] (q2p2) [right=of q2p1] {$q_2, p_2$}; + + \path[->] + % Level 0 + (q0p0) edge node [above] {a} (q0p1) + (q0p1) edge node [above] {a} (q0p2) + (q0p2) edge [bend right] node [above] {a} (q0p0) + % Level 0 to level 1 + (q0p0) edge node [right] {b} (q1p0) + (q0p1) edge node [right] {b} (q1p1) + (q0p2) edge node [right] {b} (q1p2) + % Level 1 to level 2 + (q1p0) edge node [above] {a} (q2p1) + (q1p1) edge node [above] {a} (q2p2) + (q1p2) edge node [right, xshift=0.3cm] {a} (q2p0) + % Level 2 to level 1 + (q2p0) edge node [right] {b} (q1p0) + (q2p1) edge node [above left, yshift=0.1cm] {b} (q1p1) + (q2p2) edge node [right] {b} (q1p2) + % Level 2 + (q2p0) edge node [above] {a} (q2p1) + (q2p1) edge node [above] {a} (q2p2) + (q2p2) edge [bend left] node [below] {a} (q2p0) + % ──────────────────────────────────────────────────────────────────── + % Loops on level 1 + (q1p0) edge [loop left] node {b} () + (q1p1) edge [loop left] node {b} () + (q1p2) edge [loop left] node {b} (); + \end{tikzpicture} +\end{center} -\vspace{4cm} +\vspace{2.5cm} \begin{center} \begin{Large} - ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun. Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' + ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun? Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' \end{Large} \hspace{3cm} - Prof. Dr. Dennis Komm, 2025 \end{center} -\vspace{3cm} +\vspace{2cm} \begin{center} HS2025, ETHZ\\[0.2cm] \begin{Large} diff --git a/semester3/ti/main/parts/combinatorics.tex b/semester3/ti/main/parts/combinatorics.tex index 3b85d09..dfee9d0 100644 --- a/semester3/ti/main/parts/combinatorics.tex +++ b/semester3/ti/main/parts/combinatorics.tex @@ -2,6 +2,8 @@ \section{Combinatorics} \label{sec:combinatorics} \subsection{Introduction} +Please note: This section was not part of the book and is written in very simple terms (it is taken from a summary I wrote 4 years ago during Gymnasium) + Combinatorics was developed from the willingness of humans to gamble and the fact that everybody wanted to win as much money as possible. \subsection{Simple counting operations} diff --git a/semester3/ti/main/ti-summary.pdf b/semester3/ti/main/ti-summary.pdf index 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zq0%oiSTOx90u!M6Cg^la20399Bwd`Hv251=3$nt_ac?7zFE8U_{IssdTGeoa&~N`= g2VT)={Stealth[round]}] + \node[state, initial left, accepting] (q0p0) {$q_0, p_0$}; + \node[state] (q0p1) [right=of q0p0] {$q_0, p_1$}; + \node[state] (q0p2) [right=of q0p1] {$q_0, p_2$}; + \node[state, accepting] (q1p0) [below=of q0p0] {$q_1, p_0$}; + \node[state] (q1p1) [right=of q1p0] {$q_1, p_1$}; + \node[state] (q1p2) [right=of q1p1] {$q_1, p_2$}; + \node[state, accepting] (q2p0) [below=of q1p0] {$q_2, p_0$}; + \node[state, accepting] (q2p1) [right=of q2p0] {$q_2, p_1$}; + \node[state, accepting] (q2p2) [right=of q2p1] {$q_2, p_2$}; + \path[->] + % Level 0 + (q0p0) edge node [above] {a} (q0p1) + (q0p1) edge node [above] {a} (q0p2) + (q0p2) edge [bend right] node [above] {a} (q0p0) + % Level 0 to level 1 + (q0p0) edge node [right] {b} (q1p0) + (q0p1) edge node [right] {b} (q1p1) + (q0p2) edge node [right] {b} (q1p2) + % Level 1 to level 2 + (q1p0) edge node [above] {a} (q2p1) + (q1p1) edge node [above] {a} (q2p2) + (q1p2) edge node [right, xshift=0.3cm] {a} (q2p0) + % Level 2 to level 1 + (q2p0) edge node [right] {b} (q1p0) + (q2p1) edge node [above left, yshift=0.1cm] {b} (q1p1) + (q2p2) edge node [right] {b} (q1p2) + % Level 2 + (q2p0) edge node [above] {a} (q2p1) + (q2p1) edge node [above] {a} (q2p2) + (q2p2) edge [bend left] node [below] {a} (q2p0) + % ──────────────────────────────────────────────────────────────────── + % Loops on level 1 + (q1p0) edge [loop left] node {b} () + (q1p1) edge [loop left] node {b} () + (q1p2) edge [loop left] node {b} (); + \end{tikzpicture} +\end{center} -\vspace{4cm} +\vspace{3cm} \begin{center} \begin{Large} - ``\textit{Wenn Sie die Turing-Maschine als Touring-Maschine in der Prüfung schreiben, dann macht mich das sehr traurig. Ich seh das jeweils. Teilweise sind das sehr elaborierte Trolle, manchmal Leute die nie in die Vorlesungen kommen} (2025-10-14T08:51Z+02:00``) - - ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun. Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' + ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun? Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' \end{Large} \hspace{3cm} - Prof. Dr. Dennis Komm, 2025 @@ -52,7 +85,7 @@ \begin{scriptsize} \begin{itemize} \item \textit{Note: Definitions, Lemmas, etc are often 1:1 copies from the book or paraphrased (as I did not find an easier way of stating them)} - \item \textit{Note: In case I forgot to add the PDF page numbers, you can take the PDF page number is given by $P_{\text{PDF}} = P_{\text{Book}} + 15$} + \item \textit{Note: In case I forgot to add the PDF page numbers, the PDF page number is given by $P_{\text{PDF}} = P_{\text{Book}} + 15$} \end{itemize} \end{scriptsize} From 804ab6e80d35bfba7ba389385c545e594b442a82 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 11:42:33 +0100 Subject: [PATCH 14/16] [NumCS] Add title page --- semester3/numcs/numcs-summary.pdf | Bin 1445987 -> 1433966 bytes semester3/numcs/numcs-summary.tex | 48 ++++++++++++++++++++++++------ 2 files changed, 39 insertions(+), 9 deletions(-) diff 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give you a broad overview of the topics relevant for the exam. +While it aims to serve as a full on replacement for the script, please do not fully rely on it, as there may be mistakes, inaccuracies and missing details as compared to the script. +Furthermore, you will only have access to the script during the exam, so getting familiar with the script is a good idea. We have decided to write it in German, as is the new script and for some of the topics that are poorly explained in the script, we have added further explanations. -The numbering should match the script's numbering exactly (apart from the cases where two definitions were combined due to being closely related and short), making it easier for you to look up the relevant definitions, theorems, etc in context in the script. +The numbering should match the script's numbering exactly (apart from the cases where two definitions were combined due to being closely related and short), +making it easier for you to look up the relevant definitions, theorems, etc in context in the script. Many of the figures in this summary were taken directly from the Script or Lecture notes created by Professor Vasile Gradinaru. We have also taken some explanations and code examples from the slides of our TA, Nils Müller, whose slides can be found -\color{MidnightBlue}\fbox{\href{https://n.ethz.ch/~muellerni/courses/numcs25.php}{here}}\color{black} +\hlhref{https://n.ethz.ch/~muellerni/courses/numcs25.php}{here}. (Link will be updated if we are to get a new website link from him, as n.ethz.ch is down now) % TODO: Update this when n.ethz is taken offline completely % ──────────────────────────────────────────────────────────────────── From 0be60550c91a2fc32ed79c8ba590d742914ea396 Mon Sep 17 00:00:00 2001 From: Janis Hutz <98422316+janishutz@users.noreply.github.com> Date: Wed, 31 Dec 2025 17:28:01 +0000 Subject: [PATCH 16/16] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 77adaa8..416b878 100644 --- a/README.md +++ b/README.md @@ -3,7 +3,7 @@ The source code for summaries and cheat-sheets for the lectures of BSc Computer If you find mistakes, please open an issue or fix them yourself and open a PR. -## Credits +## Available Summaries & Credits ### Semester 1 - [Algorithms & Datastructures Summary (EN)](./semester1/algorithms-and-datastructures/ad-janishutz.pdf) Author: Janis Hutz - [Linear Algebra Cheat-Sheet (EN)](./semester1/linear-algebra/linAlg-janishutz.pdf) Author: Janis Hutz

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b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex index 5fe339f..23e5c56 100644 --- a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex +++ b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/05_taylor_polynomials.tex @@ -11,10 +11,11 @@ Let $f : X \rightarrow \R$ with $f \in C^k(X, \R)$ and $y \in X$. The Taylor-Pol % TODO: Find out what the \partial_1 notation means (likely TA notes 09) where $i$ is a \textit{multi-index}, so: \drmvspace -\begin{multicols}{2} +\begin{multicols}{3} \begin{itemize}[noitemsep] \item $i = (i_1, \ldots, i_n)$ (each $i_j \geq 0$) - \item $|i| = i_1 + \ldots + i_n$, $\partial_i = \partial_1^{i_1} \ldots \partial_n^{i_n}$ + \item $|i| = i_1 + \ldots + i_n$ + \item $\partial_i = \partial_1^{i_1} \ldots \partial_n^{i_n}$ \item $(x - y)^i = (x_1 - y_1)^{i_1} \cdot \ldots \cdot (x_n - y_n)^{i_n}$ \item $i! = i_1! \cdot \ldots \cdot i_n!$ \end{itemize} From 26aedca0852f48aed52e77db3491e6148b4d96d7 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 10:32:50 +0100 Subject: [PATCH 04/16] [CI] Fix actions --- .github/workflows/upload-ad.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/upload-ad.yml b/.github/workflows/upload-ad.yml index f6bd1ce..ad37b82 100644 --- a/.github/workflows/upload-ad.yml +++ b/.github/workflows/upload-ad.yml @@ -5,7 +5,7 @@ on: - 'semester1/algorithms-and-datastructures/**' jobs: build_docs: - runs_on: ubuntu-latest + runs-on: ubuntu-latest steps: - name: Set up Git repository uses: actions/checkout@v6 From 601a70584492b476461c52759d56d7a084a91d8f Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 10:33:52 +0100 Subject: [PATCH 05/16] [CI] Syntax fixes --- .github/actions/upload-to-comsol/action.yml | 6 +++--- .github/workflows/upload-ad.yml | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/.github/actions/upload-to-comsol/action.yml b/.github/actions/upload-to-comsol/action.yml index 9bf910b..3793754 100644 --- a/.github/actions/upload-to-comsol/action.yml +++ b/.github/actions/upload-to-comsol/action.yml @@ -13,9 +13,9 @@ runs: steps: - name: Upload file to ComSol run: | - curl {{ inputs.url }} \ - -H "Authorization: {{ inputs.access_token }}" \ - -F "file=@{{ inputs.file }}" + curl ${{ inputs.url }} \ + -H "Authorization: ${{ inputs.access_token }}" \ + -F "file=@${{ inputs.file }}" branding: icon: book color: red diff --git a/.github/workflows/upload-ad.yml b/.github/workflows/upload-ad.yml index ad37b82..323cf55 100644 --- a/.github/workflows/upload-ad.yml +++ b/.github/workflows/upload-ad.yml @@ -12,6 +12,6 @@ jobs: - name: Upload to ComSol uses: ./.github/actions/upload-to-comsol with: - access_token: {{ secrets.TOKEN_AD }} + access_token: ${{ secrets.TOKEN_AD }} file: ./semester1/algorithms-and-datastructures/ad-janishutz.pdf url: https://exams.vis.ethz.ch/api/document/jahutz/summary-hs24_1/files/591/update/ From 3761011649d185f383e1e616b8b40a62bf7e58ce Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 31 Dec 2025 10:35:57 +0100 Subject: [PATCH 06/16] [AD] Add link to repo --- .../ad-janishutz.pdf | Bin 449071 -> 449441 bytes .../ad-janishutz.tex | 1 + 2 files changed, 1 insertion(+) diff --git a/semester1/algorithms-and-datastructures/ad-janishutz.pdf 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