From faecbc4dfd82fec7e933e2e228bad152f4950dfe Mon Sep 17 00:00:00 2001 From: Tom van Woudenberg Date: Thu, 12 Dec 2024 10:32:08 +0100 Subject: [PATCH 1/6] lesson 15.2 update --- book/course_information.md | 4 +-- book/week_15/session_2/intro.ipynb | 52 +++++++++++++++++++++++++++++- 2 files changed, 53 insertions(+), 3 deletions(-) diff --git a/book/course_information.md b/book/course_information.md index df91a58..2c79726 100644 --- a/book/course_information.md +++ b/book/course_information.md @@ -11,8 +11,8 @@ This aligns with the learning objectives of Structural Mechanics 3 of the regula As a prerequisite for the main objectives, you should be able to model, evaluate and reflect on forces, displacements and stresses in statically determinate structures. This is made specific in the following prerequisite learning objectives, you show to be able to:
    -
  1. Model, evaluate and reflect on validity of shape (only for cables), support reactions and section forces in statically determinate skeletal structures and cables using equilibrium relations and virtual work (only on beam structures), required for learning objective 2 and 2.
    2. -
  2. Model, evaluate and reflect on validity of displacements of truss- and skeletal bending structures using Williot, forget-me-nots and Moment-area theorems, required for learning objective 2 and 4
    3. +
  3. Model, evaluate and reflect on validity of shape (only for cables), support reactions and section forces in statically determinate skeletal structures and cables using equilibrium relations and virtual work (only on beam structures), required for learning objective 1, 2 and 3.
    4. +
  4. Model, evaluate and reflect on validity of displacements of truss- and skeletal bending structures using Williot and forget-me-nots, required for learning objective 1, 2 and 4
  5. Model, evaluate and reflect on validity of normal- and shear stresses in thick- and thin-walled cross-sections due to normal forces, bending moments and torsional moments, required for learning objective 3
diff --git a/book/week_15/session_2/intro.ipynb b/book/week_15/session_2/intro.ipynb index aba9cd1..9453984 100644 --- a/book/week_15/session_2/intro.ipynb +++ b/book/week_15/session_2/intro.ipynb @@ -13,7 +13,57 @@ "# Lesson December 12th\n", "\n", "Today we'll discuss the results of the first [exam assignment 2 on Statically indeterminate structures and exam assignment 1 on Continuum mechanics](exam2).\n", - "\n" + "\n", + "## Results second exam assignment on Statically indeterminate structures\n", + "\n", + "```{figure} ../session/intro_data/structure.svg\n", + ":align: center\n", + "```\n", + "\n", + "Approaches taken during the [exam assignment](../session/intro.ipynb):\n", + "- Hinge at $\\text{B}$ causes local mechanism $\\text{BE}$, could be dealt with by:\n", + " - For 'hoekveranderingsvergelijkingen', first all cantilever parts should be replaced by moments and/or forces\n", + " - If it's the only mechanism (only one degree of freedom), use hybrid method ('hoekveranderingsvergelijkingen' with movable nodes)\n", + "- Mistakes in sign moments around B\n", + "- $\\varphi_\\text{B}^{BE}$ set equal to rotation at tip of cantilever beam loaded by point load\n", + "- Displacement of $\\text{E}$ consists of:\n", + " - Bending $\\text{BE}$\n", + " - Rotation B\n", + " - Bending $\\texet{CD}$\n", + "- Mistakes in solving moment distribution\n", + "\n", + "\n", + "## Results first exam assignment on Continuum mechanics\n", + "\n", + "```{figure} ../session/intro_data/structure2.svg\n", + ":align: center\n", + "```\n", + "\n", + "Approaches taken during the [exam assignment](../session/intro.ipynb):\n", + "- \n", + "\n", + "## Creation knowledge graph\n", + "In the [third lesson of the first week](lesson3.3) you created a knowledge graph on the topics you've encountered in the prerequisite tests, and how they link to the learning objectives of this course. Let's try and extend today in a course graph. These course graphs will be incorporated in this book!\n", + "\n", + "1. Login at https://prime-applets.ewi.tudelft.nl/login\n", + "2. In your sandbox, create a new graph\n", + "3. Add the topics of the learning objectives as domains:\n", + " - Solve structures using differential equations\n", + " - Statically indeterminate structures\n", + " - Continuum mechanics\n", + " - Buckling\n", + "4. Add the topics of the prerequisite learning objectives as domains:\n", + " - Statics\n", + " - Displacements\n", + " - Stresses\n", + "5. Add the relations between the topics as Domain relations as described in [](../../course_information)\n", + "6. Add at least one subject, ie. equilibrium\n", + "7. Click `Edit layout` - `Domains` - `Auto layout` - `Save`, you should get something like:\n", + "\n", + "\n", + "\n", + "8. Now the real part starts, add more subjects and links for subjects you encountered up untill now and arrange them in a way that makes sense for you.\n", + "9. Would you like to have you graph features in this book? Add Tom van Woudenberg as user to your sandbox as 'editor'" ] } ], From 31c0774b18e773f581d49e3848979de05f3f5c22 Mon Sep 17 00:00:00 2001 From: Tom van Woudenberg Date: Thu, 12 Dec 2024 10:40:13 +0100 Subject: [PATCH 2/6] added typothingies --- book/course_information.md | 4 ++-- book/week_15/session_2/intro.ipynb | 10 +++++----- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/book/course_information.md b/book/course_information.md index 2c79726..d86efe9 100644 --- a/book/course_information.md +++ b/book/course_information.md @@ -19,8 +19,8 @@ As a prerequisite for the main objectives, you should be able to model, evaluate The learning objectives a-c align almost entirely with the learning objectives of Structural Mechanics 1 and 2 of the regular BSc programme of Civil Engineering. The learning objectives are summarized in three subjects: - Statically indeterminate structures, including learning objective 1, 2, a and b -- Continuum mechanics, including learning objective 4, a and c -- Buckling, including learning objective 1, 3 and b +- Continuum mechanics, including learning objective 4, a, b and c +- Buckling, including learning objective 1, 4, a, b This course replaces Structural Mechanics 1, 2 and 3 of the regular Bachelor programme as a preparation for the MSc Civil Engineering. It is expecting some prior knowledge on learning objective a – c to be able to finish the course on time. diff --git a/book/week_15/session_2/intro.ipynb b/book/week_15/session_2/intro.ipynb index 9453984..3f70546 100644 --- a/book/week_15/session_2/intro.ipynb +++ b/book/week_15/session_2/intro.ipynb @@ -22,14 +22,14 @@ "\n", "Approaches taken during the [exam assignment](../session/intro.ipynb):\n", "- Hinge at $\\text{B}$ causes local mechanism $\\text{BE}$, could be dealt with by:\n", - " - For 'hoekveranderingsvergelijkingen', first all cantilever parts should be replaced by moments and/or forces\n", - " - If it's the only mechanism (only one degree of freedom), use hybrid method ('hoekveranderingsvergelijkingen' with movable nodes)\n", + " - For 'hoekveranderingsvergelijkingen', first all cantilever parts should be replaced by moments and/or forces\n", + " - If it's the only mechanism (only one degree of freedom), use hybrid method ('hoekveranderingsvergelijkingen' with movable nodes)\n", "- Mistakes in sign moments around B\n", "- $\\varphi_\\text{B}^{BE}$ set equal to rotation at tip of cantilever beam loaded by point load\n", "- Displacement of $\\text{E}$ consists of:\n", - " - Bending $\\text{BE}$\n", - " - Rotation B\n", - " - Bending $\\texet{CD}$\n", + " - Bending $\\text{BE}$\n", + " - Rotation B\n", + " - Bending $\\texet{CD}$\n", "- Mistakes in solving moment distribution\n", "\n", "\n", From d34ce58d34f26ae7c9abac7172d3a0dd4e52e417 Mon Sep 17 00:00:00 2001 From: Tom van Woudenberg Date: Thu, 12 Dec 2024 10:40:34 +0100 Subject: [PATCH 3/6] Update intro.ipynb --- book/week_15/session_2/intro.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/week_15/session_2/intro.ipynb b/book/week_15/session_2/intro.ipynb index 3f70546..82f3b10 100644 --- a/book/week_15/session_2/intro.ipynb +++ b/book/week_15/session_2/intro.ipynb @@ -42,7 +42,7 @@ "Approaches taken during the [exam assignment](../session/intro.ipynb):\n", "- \n", "\n", - "## Creation knowledge graph\n", + "## Create knowledge graph\n", "In the [third lesson of the first week](lesson3.3) you created a knowledge graph on the topics you've encountered in the prerequisite tests, and how they link to the learning objectives of this course. Let's try and extend today in a course graph. These course graphs will be incorporated in this book!\n", "\n", "1. Login at https://prime-applets.ewi.tudelft.nl/login\n", From 85d6bb57c3040c328ab67abe1b39107193bf8a8c Mon Sep 17 00:00:00 2001 From: Tom van Woudenberg Date: Thu, 12 Dec 2024 11:47:15 +0100 Subject: [PATCH 4/6] added course graphs --- book/_toc.yml | 5 ++++ book/week_15/session_2/intro.ipynb | 41 ++++++++++++++++-------------- book/week_15/session_2/louis.md | 3 +++ book/week_15/session_2/michael.md | 3 +++ book/week_15/session_2/patrick.md | 3 +++ book/week_15/session_2/quinten.md | 3 +++ 6 files changed, 39 insertions(+), 19 deletions(-) create mode 100644 book/week_15/session_2/louis.md create mode 100644 book/week_15/session_2/michael.md create mode 100644 book/week_15/session_2/patrick.md create mode 100644 book/week_15/session_2/quinten.md diff --git a/book/_toc.yml b/book/_toc.yml index 6d6bb18..09ca44d 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -301,6 +301,11 @@ parts: - file: week_15/homework/intro - file: week_15/session/intro - file: week_15/session_2/intro + sections: + - file: week_15/session_2/michael + - file: week_15/session_2/patrick + - file: week_15/session_2/louis + - file: week_15/session_2/quinten - caption: Miscellaneous chapters: diff --git a/book/week_15/session_2/intro.ipynb b/book/week_15/session_2/intro.ipynb index 82f3b10..30068a1 100644 --- a/book/week_15/session_2/intro.ipynb +++ b/book/week_15/session_2/intro.ipynb @@ -29,7 +29,7 @@ "- Displacement of $\\text{E}$ consists of:\n", " - Bending $\\text{BE}$\n", " - Rotation B\n", - " - Bending $\\texet{CD}$\n", + " - Bending $\\text{CD}$\n", "- Mistakes in solving moment distribution\n", "\n", "\n", @@ -40,30 +40,33 @@ "```\n", "\n", "Approaches taken during the [exam assignment](../session/intro.ipynb):\n", - "- \n", + "- Mistakes in calculating stresses\n", + "- Stresses in wrong direction acting on stress element\n", + "- Shear stresses on perpendicular faces not in equilibrium\n", + "- Normal stresses at both sides the $x$- and $y$-plane\n", + "- Incorrect direction of shear stresses after rotation\n", + "- Calculation of principal stresses inconsistent with stress element\n", "\n", "## Create knowledge graph\n", "In the [third lesson of the first week](lesson3.3) you created a knowledge graph on the topics you've encountered in the prerequisite tests, and how they link to the learning objectives of this course. Let's try and extend today in a course graph. These course graphs will be incorporated in this book!\n", "\n", - "1. Login at https://prime-applets.ewi.tudelft.nl/login\n", - "2. In your sandbox, create a new graph\n", - "3. Add the topics of the learning objectives as domains:\n", - " - Solve structures using differential equations\n", - " - Statically indeterminate structures\n", - " - Continuum mechanics\n", - " - Buckling\n", - "4. Add the topics of the prerequisite learning objectives as domains:\n", - " - Statics\n", - " - Displacements\n", - " - Stresses\n", - "5. Add the relations between the topics as Domain relations as described in [](../../course_information)\n", - "6. Add at least one subject, ie. equilibrium\n", - "7. Click `Edit layout` - `Domains` - `Auto layout` - `Save`, you should get something like:\n", + "You'll start with a template containing the (abbreviated) learning objectives and prerequisite learning objectives:\n", + "\n", + "\n", "\n", - "\n", + "Your task is to add subjects to the learning objectives and the links between those.\n", + "\n", + "1. Login at https://prime-applets.ewi.tudelft.nl/login\n", + "2. Wait for Tom van Woudenberg to add you to the correct Course Graph course\n", + "3. Open the correct Course Graph Course: https://prime-applets.ewi.tudelft.nl/graph-editor/course-overview/CT1000\n", + "4. Click on [\"edit\" (edit)] for your own course graph\n", + "5. Click `Edit Layout` - `Domains` to check the layout and eventually change it a bit (remember to click `Save` when you're done)\n", + "6. Click `Edit Fields` - `Subjects` to add subjects. Try to keep the number of subjects per domain (which are the learning objectives) limited\n", + "7. Click `Subject relations` to show relations between subjects\n", + "8. Click `Edit Layout` - `Overview` to alter the layout (eventually use `Auto layout`) to a layout that makes sense to you\n", + "9. Repeat steps 6-9 until you're satisfied!\n", "\n", - "8. Now the real part starts, add more subjects and links for subjects you encountered up untill now and arrange them in a way that makes sense for you.\n", - "9. Would you like to have you graph features in this book? Add Tom van Woudenberg as user to your sandbox as 'editor'" + "You'll be able to view your graph in this book (see subpages)!" ] } ], diff --git a/book/week_15/session_2/louis.md b/book/week_15/session_2/louis.md new file mode 100644 index 0000000..6f0620b --- /dev/null +++ b/book/week_15/session_2/louis.md @@ -0,0 +1,3 @@ +# Course Graph Louis + + \ No newline at end of file diff --git a/book/week_15/session_2/michael.md b/book/week_15/session_2/michael.md new file mode 100644 index 0000000..b89bba6 --- /dev/null +++ b/book/week_15/session_2/michael.md @@ -0,0 +1,3 @@ +# Course Graph Michael + + \ No newline at end of file diff --git a/book/week_15/session_2/patrick.md b/book/week_15/session_2/patrick.md new file mode 100644 index 0000000..9dd976e --- /dev/null +++ b/book/week_15/session_2/patrick.md @@ -0,0 +1,3 @@ +# Course Graph Patrick + + \ No newline at end of file diff --git a/book/week_15/session_2/quinten.md b/book/week_15/session_2/quinten.md new file mode 100644 index 0000000..de90c17 --- /dev/null +++ b/book/week_15/session_2/quinten.md @@ -0,0 +1,3 @@ +# Course Graph Quinten + + \ No newline at end of file From 7dbb6f6f53b7714c89cd6cee0072aff4f49ab3ed Mon Sep 17 00:00:00 2001 From: Tom van Woudenberg Date: Thu, 12 Dec 2024 11:53:22 +0100 Subject: [PATCH 5/6] added one more --- book/_toc.yml | 1 + book/week_15/session_2/intro.ipynb | 8 ++++++-- book/week_15/session_2/louis.md | 2 +- book/week_15/session_2/michael.md | 2 +- book/week_15/session_2/patrick.md | 2 +- book/week_15/session_2/quinten.md | 2 +- book/week_15/session_2/thijs.md | 3 +++ 7 files changed, 14 insertions(+), 6 deletions(-) create mode 100644 book/week_15/session_2/thijs.md diff --git a/book/_toc.yml b/book/_toc.yml index 09ca44d..2ed2aad 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -306,6 +306,7 @@ parts: - file: week_15/session_2/patrick - file: week_15/session_2/louis - file: week_15/session_2/quinten + - file: week_15/session_2/thijs - caption: Miscellaneous chapters: diff --git a/book/week_15/session_2/intro.ipynb b/book/week_15/session_2/intro.ipynb index 30068a1..ca058d3 100644 --- a/book/week_15/session_2/intro.ipynb +++ b/book/week_15/session_2/intro.ipynb @@ -46,9 +46,13 @@ "- Normal stresses at both sides the $x$- and $y$-plane\n", "- Incorrect direction of shear stresses after rotation\n", "- Calculation of principal stresses inconsistent with stress element\n", + "- Rotation from rotation centre doesn't give correct new point\n", + "- Incorrect location of rotation centre\n", + "- A third nonzero principal stress\n", + "\n", "\n", "## Create knowledge graph\n", - "In the [third lesson of the first week](lesson3.3) you created a knowledge graph on the topics you've encountered in the prerequisite tests, and how they link to the learning objectives of this course. Let's try and extend today in a course graph. These course graphs will be incorporated in this book!\n", + "In the [third lesson of the first week](lesson1.3) you created a knowledge graph on the topics you've encountered in the prerequisite tests, and how they link to the learning objectives of this course. Let's try and extend today in a course graph. These course graphs will be incorporated in this book!\n", "\n", "You'll start with a template containing the (abbreviated) learning objectives and prerequisite learning objectives:\n", "\n", @@ -59,7 +63,7 @@ "1. Login at https://prime-applets.ewi.tudelft.nl/login\n", "2. Wait for Tom van Woudenberg to add you to the correct Course Graph course\n", "3. Open the correct Course Graph Course: https://prime-applets.ewi.tudelft.nl/graph-editor/course-overview/CT1000\n", - "4. Click on [\"edit\" (edit)] for your own course graph\n", + "4. Click on \"edit\" (edit) for your own course graph\n", "5. Click `Edit Layout` - `Domains` to check the layout and eventually change it a bit (remember to click `Save` when you're done)\n", "6. Click `Edit Fields` - `Subjects` to add subjects. Try to keep the number of subjects per domain (which are the learning objectives) limited\n", "7. Click `Subject relations` to show relations between subjects\n", diff --git a/book/week_15/session_2/louis.md b/book/week_15/session_2/louis.md index 6f0620b..884297c 100644 --- a/book/week_15/session_2/louis.md +++ b/book/week_15/session_2/louis.md @@ -1,3 +1,3 @@ # Course Graph Louis - \ No newline at end of file + \ No newline at end of file diff --git a/book/week_15/session_2/michael.md b/book/week_15/session_2/michael.md index b89bba6..f7f6ba0 100644 --- a/book/week_15/session_2/michael.md +++ b/book/week_15/session_2/michael.md @@ -1,3 +1,3 @@ # Course Graph Michael - \ No newline at end of file + \ No newline at end of file diff --git a/book/week_15/session_2/patrick.md b/book/week_15/session_2/patrick.md index 9dd976e..4491c1a 100644 --- a/book/week_15/session_2/patrick.md +++ b/book/week_15/session_2/patrick.md @@ -1,3 +1,3 @@ # Course Graph Patrick - \ No newline at end of file + \ No newline at end of file diff --git a/book/week_15/session_2/quinten.md b/book/week_15/session_2/quinten.md index de90c17..72fe4b0 100644 --- a/book/week_15/session_2/quinten.md +++ b/book/week_15/session_2/quinten.md @@ -1,3 +1,3 @@ # Course Graph Quinten - \ No newline at end of file + \ No newline at end of file diff --git a/book/week_15/session_2/thijs.md b/book/week_15/session_2/thijs.md new file mode 100644 index 0000000..4100735 --- /dev/null +++ b/book/week_15/session_2/thijs.md @@ -0,0 +1,3 @@ +# Course Graph Thijs + + \ No newline at end of file From 793ba0593774001c4a290bc7d5653c1a3290a580 Mon Sep 17 00:00:00 2001 From: Tom van Woudenberg Date: Thu, 12 Dec 2024 11:58:39 +0100 Subject: [PATCH 6/6] added all --- book/_toc.yml | 11 +++++++++++ book/week_15/session_2/amir.md | 3 +++ book/week_15/session_2/chayenne.md | 3 +++ book/week_15/session_2/danyal.md | 3 +++ book/week_15/session_2/dino.md | 3 +++ book/week_15/session_2/eren.md | 3 +++ book/week_15/session_2/julian.md | 3 +++ book/week_15/session_2/maarten.md | 3 +++ book/week_15/session_2/mats.md | 3 +++ book/week_15/session_2/mees.md | 3 +++ book/week_15/session_2/robert.md | 3 +++ book/week_15/session_2/ties.md | 3 +++ 12 files changed, 44 insertions(+) create mode 100644 book/week_15/session_2/amir.md create mode 100644 book/week_15/session_2/chayenne.md create mode 100644 book/week_15/session_2/danyal.md create mode 100644 book/week_15/session_2/dino.md create mode 100644 book/week_15/session_2/eren.md create mode 100644 book/week_15/session_2/julian.md create mode 100644 book/week_15/session_2/maarten.md create mode 100644 book/week_15/session_2/mats.md create mode 100644 book/week_15/session_2/mees.md create mode 100644 book/week_15/session_2/robert.md create mode 100644 book/week_15/session_2/ties.md diff --git a/book/_toc.yml b/book/_toc.yml index 2ed2aad..4b28d89 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -307,6 +307,17 @@ parts: - file: week_15/session_2/louis - file: week_15/session_2/quinten - file: week_15/session_2/thijs + - file: week_15/session_2/julian + - file: week_15/session_2/eren + - file: week_15/session_2/dino + - file: week_15/session_2/ties + - file: week_15/session_2/danyal + - file: week_15/session_2/amir + - file: week_15/session_2/mees + - file: week_15/session_2/maarten + - file: week_15/session_2/robert + - file: week_15/session_2/chayenne + - file: week_15/session_2/mats - caption: Miscellaneous chapters: diff --git a/book/week_15/session_2/amir.md b/book/week_15/session_2/amir.md new file mode 100644 index 0000000..677e00e --- /dev/null +++ b/book/week_15/session_2/amir.md @@ -0,0 +1,3 @@ +# Course Graph Amir + + \ No newline at end of file diff --git a/book/week_15/session_2/chayenne.md b/book/week_15/session_2/chayenne.md new file mode 100644 index 0000000..0aaa854 --- /dev/null +++ b/book/week_15/session_2/chayenne.md @@ -0,0 +1,3 @@ +# Course Graph Chayenne + + \ No newline at end of file diff --git a/book/week_15/session_2/danyal.md b/book/week_15/session_2/danyal.md new file mode 100644 index 0000000..0cd6a4f --- /dev/null +++ b/book/week_15/session_2/danyal.md @@ -0,0 +1,3 @@ +# Course Graph Danyal + + \ No newline at end of file diff --git a/book/week_15/session_2/dino.md b/book/week_15/session_2/dino.md new file mode 100644 index 0000000..1c70811 --- /dev/null +++ b/book/week_15/session_2/dino.md @@ -0,0 +1,3 @@ +# Course Graph Dino + + \ No newline at end of file diff --git a/book/week_15/session_2/eren.md b/book/week_15/session_2/eren.md new file mode 100644 index 0000000..5b5ba88 --- /dev/null +++ b/book/week_15/session_2/eren.md @@ -0,0 +1,3 @@ +# Course Graph Eren + + \ No newline at end of file diff --git a/book/week_15/session_2/julian.md b/book/week_15/session_2/julian.md new file mode 100644 index 0000000..6ae5a23 --- /dev/null +++ b/book/week_15/session_2/julian.md @@ -0,0 +1,3 @@ +# Course Graph Julian + + \ No newline at end of file diff --git a/book/week_15/session_2/maarten.md b/book/week_15/session_2/maarten.md new file mode 100644 index 0000000..04b4f23 --- /dev/null +++ b/book/week_15/session_2/maarten.md @@ -0,0 +1,3 @@ +# Course Graph Maarten + + \ No newline at end of file diff --git a/book/week_15/session_2/mats.md b/book/week_15/session_2/mats.md new file mode 100644 index 0000000..c877eaf --- /dev/null +++ b/book/week_15/session_2/mats.md @@ -0,0 +1,3 @@ +# Course Graph Mats + + \ No newline at end of file diff --git a/book/week_15/session_2/mees.md b/book/week_15/session_2/mees.md new file mode 100644 index 0000000..9c6c3a1 --- /dev/null +++ b/book/week_15/session_2/mees.md @@ -0,0 +1,3 @@ +# Course Graph Mees + + \ No newline at end of file diff --git a/book/week_15/session_2/robert.md b/book/week_15/session_2/robert.md new file mode 100644 index 0000000..ec0a1ef --- /dev/null +++ b/book/week_15/session_2/robert.md @@ -0,0 +1,3 @@ +# Course Graph Robert-Jan + + \ No newline at end of file diff --git a/book/week_15/session_2/ties.md b/book/week_15/session_2/ties.md new file mode 100644 index 0000000..5bbc067 --- /dev/null +++ b/book/week_15/session_2/ties.md @@ -0,0 +1,3 @@ +# Course Graph Ties + + \ No newline at end of file