diff --git a/doc/Projects/ProjectWriting/projectwriting.ipynb b/doc/Projects/ProjectWriting/projectwriting.ipynb
index 92c215f4e..531e0ccde 100644
--- a/doc/Projects/ProjectWriting/projectwriting.ipynb
+++ b/doc/Projects/ProjectWriting/projectwriting.ipynb
@@ -3,9 +3,7 @@
   {
    "cell_type": "markdown",
    "id": "8b587bcb",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html projectwriting.do.txt  -->\n",
@@ -15,9 +13,7 @@
   {
    "cell_type": "markdown",
    "id": "ad025527",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "# How to write a scientific project\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
@@ -30,9 +26,7 @@
   {
    "cell_type": "markdown",
    "id": "28e54722",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report: how to write a good scienfitic/technical report\n",
     "**What should it contain? A typical structure.**\n",
@@ -59,9 +53,7 @@
   {
    "cell_type": "markdown",
    "id": "450156e7",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, the abstract\n",
     "The abstract gives the reader a quick overview of what has been done and the most important results. Here is a typical example\n",
@@ -75,9 +67,7 @@
   {
    "cell_type": "markdown",
    "id": "a5a7f13f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, the introduction\n",
     "**What should I focus on? Introduction.**\n",
@@ -93,9 +83,7 @@
   {
    "cell_type": "markdown",
    "id": "a80f8a9f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, discussion of methods and codes\n",
     "**What should I focus on? Methods sections.**\n",
@@ -112,9 +100,7 @@
   {
    "cell_type": "markdown",
    "id": "57974a1d",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, code part\n",
     "\n",
@@ -134,9 +120,7 @@
   {
    "cell_type": "markdown",
    "id": "448f9828",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, results part\n",
     "**What should I focus on? Results.**\n",
@@ -155,9 +139,7 @@
   {
    "cell_type": "markdown",
    "id": "fa3190a7",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, conclusions and perspectives\n",
     "**What should I focus on? Conclusions.**\n",
@@ -172,9 +154,7 @@
   {
    "cell_type": "markdown",
    "id": "4b15f2a0",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, appendices\n",
     "**What should I focus on? additional material.**\n",
@@ -191,9 +171,7 @@
   {
    "cell_type": "markdown",
    "id": "e982ec47",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The report, references\n",
     "**What should I focus on? References.**\n",
@@ -208,9 +186,7 @@
   {
    "cell_type": "markdown",
    "id": "ae212bd2",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Where do I find scientific articles, books etc and examples of reports\n",
     " * With a UiO IP number you can access freely all books and scientific journals available at our [University library](http://www.ub.uio.no/)\n",
@@ -221,9 +197,7 @@
   {
    "cell_type": "markdown",
    "id": "7d783b6f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Other resources\n",
     "\n",
@@ -234,9 +208,7 @@
   {
    "cell_type": "markdown",
    "id": "47b07b08",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Procrastination... the curse of all?\n",
     "<!-- dom:FIGURE: [fig-projectwriting/procrast.jpg, width=700 frac=0.9] -->\n",
@@ -251,7 +223,25 @@
    ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.10"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/pub/week39/html/week39-reveal.html b/doc/pub/week39/html/week39-reveal.html
index 3d840a792..41138aa98 100644
--- a/doc/pub/week39/html/week39-reveal.html
+++ b/doc/pub/week39/html/week39-reveal.html
@@ -244,6 +244,9 @@ MathJax.Hub.Config({
 <p>
 </ul>
 </div>
+
+
+<!-- rett opp tyrleif -->
 </section>
 
 <section>
@@ -587,9 +590,17 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <section>
 <h2 id="convex-function">Convex function </h2>
 
-<p><b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if <p>&nbsp;<br>
-$$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$
-<p>&nbsp;<br> for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \). If \( \leq \) is replaced with a strict inequaltiy in the definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the value of the function on the interval \( [x_1,x_2] \) is always below the line as illustrated below.</p>
+<p><b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex
+set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is
+continuous, then \( f \) is said to be convex if \( f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) \)
+for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \).
+If \( \leq \) is replaced with a strict inequaltiy in the
+definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said
+to be strictly convex. For a single variable function, convexity means
+that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the
+value of the function on the interval \( [x_1,x_2] \) is always below the
+line as illustrated below.
+</p>
 </section>
 
 <section>
@@ -598,7 +609,7 @@ $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$
 <p>In the following we state first and second-order conditions which
 ensures convexity of a function \( f \). We write \( D_f \) to denote the
 domain of \( f \), i.e the subset of \( R^n \) where \( f \) is defined. For more
-details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004" target="_blank">S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press</a>.
+details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/" target="_blank">S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press</a>.
 </p>
 
 <div class="alert alert-block alert-block alert-text-normal">
@@ -606,10 +617,11 @@ details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004
 <p>
 <p>Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for
 all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \)
-is a convex set and <p>&nbsp;<br>
-$$f(y) \geq f(x) + \nabla f(x)^T (y-x) $$
-<p>&nbsp;<br> holds
-for all \( x,y \in D_f \). This condition means that for a convex function
+is a convex set and \( f(y) \geq f(x) + \nabla f(x)^T (y-x) \) holds
+for all \( x,y \in D_f \).
+</p>
+
+<p>This condition means that for a convex function
 the first order Taylor expansion (right hand side above) at any point
 a global under estimator of the function. To convince yourself you can
 make a drawing of \( f(x) = x^2+1 \) and draw the tangent line to \( f(x) \) and
diff --git a/doc/pub/week39/html/week39-solarized.html b/doc/pub/week39/html/week39-solarized.html
index aae5219af..3f1cce711 100644
--- a/doc/pub/week39/html/week39-solarized.html
+++ b/doc/pub/week39/html/week39-solarized.html
@@ -376,6 +376,8 @@ MathJax.Hub.Config({
 </div>
 
 
+<!-- rett opp tyrleif -->
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
 
@@ -673,7 +675,17 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="convex-function">Convex function </h2>
 
-<p><b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \). If \( \leq \) is replaced with a strict inequaltiy in the definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the value of the function on the interval \( [x_1,x_2] \) is always below the line as illustrated below.</p>
+<p><b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex
+set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is
+continuous, then \( f \) is said to be convex if \( f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) \)
+for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \).
+If \( \leq \) is replaced with a strict inequaltiy in the
+definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said
+to be strictly convex. For a single variable function, convexity means
+that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the
+value of the function on the interval \( [x_1,x_2] \) is always below the
+line as illustrated below.
+</p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="conditions-on-convex-functions">Conditions on convex functions </h2>
@@ -681,7 +693,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <p>In the following we state first and second-order conditions which
 ensures convexity of a function \( f \). We write \( D_f \) to denote the
 domain of \( f \), i.e the subset of \( R^n \) where \( f \) is defined. For more
-details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004" target="_blank">S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press</a>.
+details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/" target="_blank">S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press</a>.
 </p>
 
 <div class="alert alert-block alert-block alert-text-normal">
@@ -689,8 +701,11 @@ details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004
 <p>
 <p>Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for
 all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \)
-is a convex set and $$f(y) \geq f(x) + \nabla f(x)^T (y-x) $$ holds
-for all \( x,y \in D_f \). This condition means that for a convex function
+is a convex set and \( f(y) \geq f(x) + \nabla f(x)^T (y-x) \) holds
+for all \( x,y \in D_f \).
+</p>
+
+<p>This condition means that for a convex function
 the first order Taylor expansion (right hand side above) at any point
 a global under estimator of the function. To convince yourself you can
 make a drawing of \( f(x) = x^2+1 \) and draw the tangent line to \( f(x) \) and
diff --git a/doc/pub/week39/html/week39.html b/doc/pub/week39/html/week39.html
index 3623de81a..4fe12b2f9 100644
--- a/doc/pub/week39/html/week39.html
+++ b/doc/pub/week39/html/week39.html
@@ -453,6 +453,8 @@ MathJax.Hub.Config({
 </div>
 
 
+<!-- rett opp tyrleif -->
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
 
@@ -750,7 +752,17 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="convex-function">Convex function </h2>
 
-<p><b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \). If \( \leq \) is replaced with a strict inequaltiy in the definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the value of the function on the interval \( [x_1,x_2] \) is always below the line as illustrated below.</p>
+<p><b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex
+set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is
+continuous, then \( f \) is said to be convex if \( f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) \)
+for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \).
+If \( \leq \) is replaced with a strict inequaltiy in the
+definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said
+to be strictly convex. For a single variable function, convexity means
+that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the
+value of the function on the interval \( [x_1,x_2] \) is always below the
+line as illustrated below.
+</p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="conditions-on-convex-functions">Conditions on convex functions </h2>
@@ -758,7 +770,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <p>In the following we state first and second-order conditions which
 ensures convexity of a function \( f \). We write \( D_f \) to denote the
 domain of \( f \), i.e the subset of \( R^n \) where \( f \) is defined. For more
-details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004" target="_blank">S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press</a>.
+details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/" target="_blank">S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press</a>.
 </p>
 
 <div class="alert alert-block alert-block alert-text-normal">
@@ -766,8 +778,11 @@ details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004
 <p>
 <p>Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for
 all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \)
-is a convex set and $$f(y) \geq f(x) + \nabla f(x)^T (y-x) $$ holds
-for all \( x,y \in D_f \). This condition means that for a convex function
+is a convex set and \( f(y) \geq f(x) + \nabla f(x)^T (y-x) \) holds
+for all \( x,y \in D_f \).
+</p>
+
+<p>This condition means that for a convex function
 the first order Taylor expansion (right hand side above) at any point
 a global under estimator of the function. To convince yourself you can
 make a drawing of \( f(x) = x^2+1 \) and draw the tangent line to \( f(x) \) and
diff --git a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz
index 0d317a1d8..1ab342b7b 100644
Binary files a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz and b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz differ
diff --git a/doc/pub/week39/ipynb/week39.ipynb b/doc/pub/week39/ipynb/week39.ipynb
index f8ed9613e..bd7a201f7 100644
--- a/doc/pub/week39/ipynb/week39.ipynb
+++ b/doc/pub/week39/ipynb/week39.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "97c9bb6c",
+   "id": "50bb2fae",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ade8d870",
+   "id": "28bece6e",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87cd74c3",
+   "id": "a96e7549",
    "metadata": {
     "editable": true
    },
@@ -65,12 +65,14 @@
     "\n",
     "    * [Video on gradient descent](https://www.youtube.com/watch?v=sDv4f4s2SB8)\n",
     "\n",
-    "    * [Video on stochastic gradient descent](https://www.youtube.com/watch?v=vMh0zPT0tLI)"
+    "    * [Video on stochastic gradient descent](https://www.youtube.com/watch?v=vMh0zPT0tLI)\n",
+    "\n",
+    "<!-- rett opp tyrleif -->"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "529184e5",
+   "id": "ad3725f3",
    "metadata": {
     "editable": true
    },
@@ -91,7 +93,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a65465a",
+   "id": "a750ab4f",
    "metadata": {
     "editable": true
    },
@@ -108,7 +110,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b67231b3",
+   "id": "237464b0",
    "metadata": {
     "editable": true
    },
@@ -123,7 +125,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f5e03db",
+   "id": "0d365922",
    "metadata": {
     "editable": true
    },
@@ -133,7 +135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e83141ae",
+   "id": "17dcc22b",
    "metadata": {
     "editable": true
    },
@@ -149,7 +151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cef5864b",
+   "id": "23a1111d",
    "metadata": {
     "editable": true
    },
@@ -161,7 +163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f59bbb1",
+   "id": "f69e6301",
    "metadata": {
     "editable": true
    },
@@ -172,7 +174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3869b3c6",
+   "id": "a98f91ae",
    "metadata": {
     "editable": true
    },
@@ -184,7 +186,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4656e92",
+   "id": "b4a058a7",
    "metadata": {
     "editable": true
    },
@@ -194,7 +196,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b73ae554",
+   "id": "4bef2a5f",
    "metadata": {
     "editable": true
    },
@@ -208,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70a2df05",
+   "id": "05001ecb",
    "metadata": {
     "editable": true
    },
@@ -220,7 +222,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e36f976",
+   "id": "82d01fbd",
    "metadata": {
     "editable": true
    },
@@ -230,7 +232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c4959c9",
+   "id": "36962ee1",
    "metadata": {
     "editable": true
    },
@@ -242,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c553379e",
+   "id": "c47c224b",
    "metadata": {
     "editable": true
    },
@@ -254,7 +256,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "145f9699",
+   "id": "ec3ede39",
    "metadata": {
     "editable": true
    },
@@ -274,7 +276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a68f686",
+   "id": "b869cb18",
    "metadata": {
     "editable": true
    },
@@ -290,7 +292,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d523ab61",
+   "id": "fd447d3e",
    "metadata": {
     "editable": true
    },
@@ -306,7 +308,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8205fd3a",
+   "id": "1d894c75",
    "metadata": {
     "editable": true
    },
@@ -317,7 +319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98d52e46",
+   "id": "0d508e5c",
    "metadata": {
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@@ -329,7 +331,7 @@
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-   "id": "203f65e8",
+   "id": "7ed0ad95",
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@@ -339,7 +341,7 @@
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-   "id": "dd40195b",
+   "id": "cd997af7",
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@@ -351,7 +353,7 @@
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+   "id": "7050afc6",
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@@ -361,7 +363,7 @@
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-   "id": "30c258c9",
+   "id": "a198702b",
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@@ -373,7 +375,7 @@
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-   "id": "84f880c9",
+   "id": "1514d0ff",
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@@ -395,7 +397,7 @@
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   {
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-   "id": "b237f214",
+   "id": "42154f58",
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@@ -408,7 +410,7 @@
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   {
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+   "id": "d1a8b99e",
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@@ -421,7 +423,7 @@
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   {
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+   "id": "34b84a08",
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@@ -431,7 +433,7 @@
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   {
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-   "id": "e9d217a4",
+   "id": "8ee3bd57",
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@@ -449,7 +451,7 @@
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   {
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+   "id": "f2fc5f78",
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@@ -459,7 +461,7 @@
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   {
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+   "id": "a5cd2cbc",
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@@ -474,7 +476,7 @@
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   {
    "cell_type": "markdown",
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+   "id": "c081ba3b",
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@@ -484,7 +486,7 @@
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-   "id": "53651890",
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@@ -498,7 +500,7 @@
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   {
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@@ -508,7 +510,7 @@
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@@ -522,7 +524,7 @@
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@@ -537,7 +539,7 @@
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@@ -554,7 +556,7 @@
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@@ -566,7 +568,7 @@
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@@ -580,7 +582,7 @@
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@@ -595,7 +597,7 @@
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@@ -607,7 +609,7 @@
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@@ -618,7 +620,7 @@
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@@ -646,7 +648,7 @@
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@@ -668,7 +670,7 @@
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   {
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@@ -690,19 +692,28 @@
   },
   {
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-   "id": "076a32fa",
+   "id": "74adc3b0",
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    "source": [
     "## Convex function\n",
     "\n",
-    "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$. If $\\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below."
+    "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex\n",
+    "set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is\n",
+    "continuous, then $f$ is said to be convex if $f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2)$\n",
+    "for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$.\n",
+    "If $\\leq$ is replaced with a strict inequaltiy in the\n",
+    "definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said\n",
+    "to be strictly convex. For a single variable function, convexity means\n",
+    "that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the\n",
+    "value of the function on the interval $[x_1,x_2]$ is always below the\n",
+    "line as illustrated below."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "73adde3c",
+   "id": "e4b22b9e",
    "metadata": {
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@@ -712,14 +723,16 @@
     "In the following we state first and second-order conditions which\n",
     "ensures convexity of a function $f$. We write $D_f$ to denote the\n",
     "domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more\n",
-    "details and proofs we refer to: [S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press](http://stanford.edu/boyd/cvxbook/, 2004).\n",
+    "details and proofs we refer to: [S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press](http://stanford.edu/boyd/cvxbook/).\n",
     "\n",
     "**First order condition.**\n",
     "\n",
     "Suppose $f$ is differentiable (i.e $\\nabla f(x)$ is well defined for\n",
     "all $x$ in the domain of $f$). Then $f$ is convex if and only if $D_f$\n",
-    "is a convex set and $$f(y) \\geq f(x) + \\nabla f(x)^T (y-x) $$ holds\n",
-    "for all $x,y \\in D_f$. This condition means that for a convex function\n",
+    "is a convex set and $f(y) \\geq f(x) + \\nabla f(x)^T (y-x)$ holds\n",
+    "for all $x,y \\in D_f$.\n",
+    "\n",
+    "This condition means that for a convex function\n",
     "the first order Taylor expansion (right hand side above) at any point\n",
     "a global under estimator of the function. To convince yourself you can\n",
     "make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n",
@@ -739,7 +752,7 @@
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@@ -797,7 +810,7 @@
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@@ -817,7 +830,7 @@
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@@ -829,7 +842,7 @@
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@@ -839,7 +852,7 @@
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@@ -851,7 +864,7 @@
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@@ -863,7 +876,7 @@
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@@ -875,7 +888,7 @@
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@@ -887,7 +900,7 @@
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@@ -898,7 +911,7 @@
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@@ -911,7 +924,7 @@
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@@ -923,7 +936,7 @@
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@@ -933,7 +946,7 @@
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@@ -945,7 +958,7 @@
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@@ -955,7 +968,7 @@
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@@ -966,7 +979,7 @@
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@@ -978,7 +991,7 @@
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@@ -990,7 +1003,7 @@
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@@ -1002,7 +1015,7 @@
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@@ -1013,7 +1026,7 @@
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@@ -1024,7 +1037,7 @@
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@@ -1036,7 +1049,7 @@
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@@ -1046,7 +1059,7 @@
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@@ -1058,7 +1071,7 @@
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@@ -1068,7 +1081,7 @@
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@@ -1080,7 +1093,7 @@
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@@ -1090,7 +1103,7 @@
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@@ -1102,7 +1115,7 @@
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@@ -1112,7 +1125,7 @@
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@@ -1124,7 +1137,7 @@
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+   "id": "68749604",
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@@ -1135,7 +1148,7 @@
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    "cell_type": "code",
    "execution_count": 1,
-   "id": "a0e20ff7",
+   "id": "bf454b1d",
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@@ -1168,7 +1181,7 @@
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+   "id": "3569007f",
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@@ -1179,7 +1192,7 @@
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-   "id": "5b835c85",
+   "id": "0df89031",
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@@ -1193,7 +1206,7 @@
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   {
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+   "id": "d6ac010a",
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@@ -1204,7 +1217,7 @@
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-   "id": "19e1d73c",
+   "id": "d17a90d2",
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@@ -1217,7 +1230,7 @@
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+   "id": "d6ccbd2b",
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@@ -1228,7 +1241,7 @@
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-   "id": "7d8247e6",
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@@ -1246,7 +1259,7 @@
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@@ -1257,7 +1270,7 @@
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-   "id": "bb8a0fd8",
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@@ -1272,7 +1285,7 @@
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+   "id": "1a84e70d",
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@@ -1282,7 +1295,7 @@
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@@ -1296,7 +1309,7 @@
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@@ -1308,7 +1321,7 @@
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+   "id": "2462039a",
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@@ -1319,7 +1332,7 @@
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@@ -1331,7 +1344,7 @@
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@@ -1342,7 +1355,7 @@
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+   "id": "cda299f2",
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@@ -1353,7 +1366,7 @@
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@@ -1365,7 +1378,7 @@
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@@ -1375,7 +1388,7 @@
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@@ -1387,7 +1400,7 @@
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@@ -1399,7 +1412,7 @@
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@@ -1411,7 +1424,7 @@
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@@ -1423,7 +1436,7 @@
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@@ -1434,7 +1447,7 @@
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@@ -1446,7 +1459,7 @@
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@@ -1456,7 +1469,7 @@
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@@ -1468,7 +1481,7 @@
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@@ -1478,7 +1491,7 @@
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@@ -1490,7 +1503,7 @@
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@@ -1510,7 +1523,7 @@
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@@ -1522,7 +1535,7 @@
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@@ -1532,7 +1545,7 @@
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@@ -1544,7 +1557,7 @@
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@@ -1554,7 +1567,7 @@
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@@ -1565,7 +1578,7 @@
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@@ -1577,7 +1590,7 @@
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@@ -1589,7 +1602,7 @@
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@@ -1601,7 +1614,7 @@
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@@ -1614,7 +1627,7 @@
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@@ -1625,7 +1638,7 @@
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@@ -1637,7 +1650,7 @@
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@@ -1653,7 +1666,7 @@
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@@ -1665,7 +1678,7 @@
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@@ -1676,7 +1689,7 @@
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@@ -1688,7 +1701,7 @@
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@@ -1698,7 +1711,7 @@
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@@ -1710,7 +1723,7 @@
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@@ -1720,7 +1733,7 @@
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@@ -1732,7 +1745,7 @@
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@@ -1742,7 +1755,7 @@
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@@ -1754,7 +1767,7 @@
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@@ -1778,7 +1791,7 @@
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@@ -1791,7 +1804,7 @@
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@@ -1802,7 +1815,7 @@
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@@ -1814,7 +1827,7 @@
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@@ -1824,7 +1837,7 @@
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@@ -1836,7 +1849,7 @@
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@@ -1850,7 +1863,7 @@
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@@ -1866,7 +1879,7 @@
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@@ -1876,7 +1889,7 @@
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@@ -1888,7 +1901,7 @@
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@@ -1898,7 +1911,7 @@
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@@ -1910,7 +1923,7 @@
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@@ -1924,7 +1937,7 @@
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@@ -1934,7 +1947,7 @@
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@@ -1945,7 +1958,7 @@
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@@ -1960,7 +1973,7 @@
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@@ -1970,7 +1983,7 @@
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@@ -1982,7 +1995,7 @@
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@@ -1994,7 +2007,7 @@
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@@ -2009,7 +2022,7 @@
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@@ -2022,7 +2035,7 @@
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@@ -2079,7 +2092,7 @@
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@@ -2090,7 +2103,7 @@
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@@ -2117,7 +2130,7 @@
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@@ -2129,7 +2142,7 @@
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@@ -2141,7 +2154,7 @@
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@@ -2151,7 +2164,7 @@
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@@ -2165,7 +2178,7 @@
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@@ -2175,7 +2188,7 @@
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@@ -2187,7 +2200,7 @@
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@@ -2198,7 +2211,7 @@
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@@ -2213,7 +2226,7 @@
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@@ -2227,7 +2240,7 @@
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@@ -2238,7 +2251,7 @@
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@@ -2299,7 +2312,7 @@
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@@ -2321,7 +2334,7 @@
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@@ -2334,7 +2347,7 @@
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@@ -2400,7 +2413,7 @@
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@@ -2411,7 +2424,7 @@
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@@ -2485,7 +2498,7 @@
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@@ -2497,7 +2510,7 @@
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@@ -2518,7 +2531,7 @@
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@@ -2550,7 +2563,7 @@
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@@ -2567,7 +2580,7 @@
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@@ -2580,7 +2593,7 @@
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@@ -2593,7 +2606,7 @@
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@@ -2606,7 +2619,7 @@
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@@ -2620,7 +2633,7 @@
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@@ -2642,7 +2655,7 @@
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@@ -2657,7 +2670,7 @@
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@@ -2669,7 +2682,7 @@
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@@ -2682,7 +2695,7 @@
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@@ -2696,7 +2709,7 @@
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@@ -2707,7 +2720,7 @@
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@@ -2732,7 +2745,7 @@
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@@ -2748,7 +2761,7 @@
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@@ -2769,7 +2782,7 @@
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@@ -2789,7 +2802,7 @@
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@@ -2808,7 +2821,7 @@
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@@ -2843,7 +2856,7 @@
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@@ -2856,7 +2869,7 @@
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@@ -2933,7 +2946,7 @@
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@@ -2948,7 +2961,7 @@
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@@ -2963,7 +2976,7 @@
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@@ -2975,7 +2988,7 @@
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@@ -2993,7 +3006,7 @@
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@@ -3012,7 +3025,7 @@
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@@ -3024,7 +3037,7 @@
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@@ -3034,7 +3047,7 @@
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@@ -3050,7 +3063,7 @@
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@@ -3062,7 +3075,7 @@
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@@ -3072,7 +3085,7 @@
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@@ -3084,7 +3097,7 @@
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@@ -3094,7 +3107,7 @@
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@@ -3106,7 +3119,7 @@
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@@ -3122,7 +3135,7 @@
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@@ -3134,7 +3147,7 @@
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@@ -3167,7 +3180,7 @@
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@@ -3179,7 +3192,7 @@
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@@ -3197,7 +3210,7 @@
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@@ -3207,7 +3220,7 @@
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@@ -3238,7 +3251,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "218edcf1",
+   "id": "1696cb1c",
    "metadata": {
     "editable": true
    },
@@ -3253,7 +3266,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18dbc91c",
+   "id": "41db75b1",
    "metadata": {
     "editable": true
    },
@@ -3271,7 +3284,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0bfcf74a",
+   "id": "5d71f114",
    "metadata": {
     "editable": true
    },
@@ -3283,7 +3296,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5fedd6f0",
+   "id": "adf7201e",
    "metadata": {
     "editable": true
    },
@@ -3295,7 +3308,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b210b2a4",
+   "id": "266384e4",
    "metadata": {
     "editable": true
    },
@@ -3313,7 +3326,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34ffacbb",
+   "id": "9f0d4429",
    "metadata": {
     "editable": true
    },
@@ -3342,7 +3355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd03375d",
+   "id": "eac0bb77",
    "metadata": {
     "editable": true
    },
@@ -3360,7 +3373,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0db5d6e0",
+   "id": "ffa6229f",
    "metadata": {
     "editable": true
    },
@@ -3372,7 +3385,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "84c709d9",
+   "id": "35df09ae",
    "metadata": {
     "editable": true
    },
@@ -3384,7 +3397,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4e47496",
+   "id": "c2b911fd",
    "metadata": {
     "editable": true
    },
@@ -3396,7 +3409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "164f27df",
+   "id": "761d3704",
    "metadata": {
     "editable": true
    },
@@ -3408,7 +3421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "591f4833",
+   "id": "49a8bed5",
    "metadata": {
     "editable": true
    },
@@ -3420,7 +3433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2127e8a",
+   "id": "445813d3",
    "metadata": {
     "editable": true
    },
@@ -3437,7 +3450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5cef8b84",
+   "id": "0419e1d5",
    "metadata": {
     "editable": true
    },
@@ -3456,7 +3469,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "505c8905",
+   "id": "3e3d0a9f",
    "metadata": {
     "editable": true
    },
@@ -3468,7 +3481,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca96ddec",
+   "id": "e8caeab7",
    "metadata": {
     "editable": true
    },
@@ -3482,7 +3495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa011176",
+   "id": "51df4797",
    "metadata": {
     "editable": true
    },
@@ -3502,7 +3515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b91c4543",
+   "id": "ffbf4496",
    "metadata": {
     "editable": true
    },
@@ -3540,7 +3553,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f13065e5",
+   "id": "2d87427e",
    "metadata": {
     "editable": true
    },
@@ -3552,7 +3565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22937f5e",
+   "id": "f5424c8f",
    "metadata": {
     "editable": true
    },
@@ -3562,7 +3575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1459fe1",
+   "id": "47f14695",
    "metadata": {
     "editable": true
    },
@@ -3574,7 +3587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "441a109a",
+   "id": "e2c6cff7",
    "metadata": {
     "editable": true
    },
@@ -3585,7 +3598,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "9043abae",
+   "id": "28e44462",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3630,7 +3643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "787d5d78",
+   "id": "09458bca",
    "metadata": {
     "editable": true
    },
@@ -3647,7 +3660,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "6a677479",
+   "id": "ef273753",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3675,7 +3688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f94a1d32",
+   "id": "ae06dfcf",
    "metadata": {
     "editable": true
    },
@@ -3690,7 +3703,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "c0eb89fd",
+   "id": "7d050e00",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3734,7 +3747,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05d7497d",
+   "id": "7d19a1a4",
    "metadata": {
     "editable": true
    },
@@ -3744,7 +3757,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24e3ca02",
+   "id": "e22e77ea",
    "metadata": {
     "editable": true
    },
@@ -3755,7 +3768,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "a616e696",
+   "id": "340b92f2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3783,7 +3796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f695da56",
+   "id": "9114dbaa",
    "metadata": {
     "editable": true
    },
@@ -3798,7 +3811,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ac073ee",
+   "id": "8bfebd09",
    "metadata": {
     "editable": true
    },
@@ -3809,7 +3822,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "efc8906e",
+   "id": "e0ac03cb",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3837,7 +3850,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c587e8f",
+   "id": "3eb22ded",
    "metadata": {
     "editable": true
    },
@@ -3848,7 +3861,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "6428be1f",
+   "id": "22977dd4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3873,7 +3886,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8e1de777",
+   "id": "21eb7d2b",
    "metadata": {
     "editable": true
    },
@@ -3884,7 +3897,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "770ff6aa",
+   "id": "52e57a88",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3920,7 +3933,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "b924cc5d",
+   "id": "cbd8dcdc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3940,7 +3953,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0b0e1e9",
+   "id": "039e394f",
    "metadata": {
     "editable": true
    },
@@ -3951,7 +3964,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "1585ab28",
+   "id": "ee0186c2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3989,7 +4002,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2718df1a",
+   "id": "73478ba8",
    "metadata": {
     "editable": true
    },
@@ -3999,7 +4012,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8fa5235",
+   "id": "d9b9f60a",
    "metadata": {
     "editable": true
    },
@@ -4013,7 +4026,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "196a52d6",
+   "id": "64f20453",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4035,7 +4048,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9127a2c5",
+   "id": "dfa62def",
    "metadata": {
     "editable": true
    },
@@ -4045,7 +4058,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b12ed61",
+   "id": "9b5930f8",
    "metadata": {
     "editable": true
    },
@@ -4056,7 +4069,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "8ced55c8",
+   "id": "5a6e27d7",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4078,7 +4091,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92ebdc2b",
+   "id": "2c15d379",
    "metadata": {
     "editable": true
    },
@@ -4091,7 +4104,7 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "276f763e",
+   "id": "4e8bbe52",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4116,7 +4129,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7841ad0b",
+   "id": "4815cbb5",
    "metadata": {
     "editable": true
    },
@@ -4128,7 +4141,7 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "10107989",
+   "id": "48a68d92",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4143,7 +4156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c1139c0",
+   "id": "6b9621b8",
    "metadata": {
     "editable": true
    },
@@ -4158,7 +4171,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "3022af88",
+   "id": "7031c5bf",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4218,7 +4231,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04d09021",
+   "id": "151dbb95",
    "metadata": {
     "editable": true
    },
@@ -4229,7 +4242,7 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "71bf4b6d",
+   "id": "55da74a7",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4293,7 +4306,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad417bba",
+   "id": "6a59ec6f",
    "metadata": {
     "editable": true
    },
@@ -4304,7 +4317,7 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "c394bcef",
+   "id": "ecd93c24",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4353,7 +4366,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e4cf4b5",
+   "id": "5c094787",
    "metadata": {
     "editable": true
    },
@@ -4365,7 +4378,7 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "id": "47411bcf",
+   "id": "8209bb0a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4449,7 +4462,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8e30af2",
+   "id": "c8761b25",
    "metadata": {
     "editable": true
    },
@@ -4460,7 +4473,7 @@
   {
    "cell_type": "code",
    "execution_count": 32,
-   "id": "dd594924",
+   "id": "88782543",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4538,7 +4551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75c4c29d",
+   "id": "2c44e1d1",
    "metadata": {
     "editable": true
    },
@@ -4549,7 +4562,7 @@
   {
    "cell_type": "code",
    "execution_count": 33,
-   "id": "4dd14fc5",
+   "id": "4f6a2867",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4608,7 +4621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be4ce0cd",
+   "id": "639027f1",
    "metadata": {
     "editable": true
    },
@@ -4618,7 +4631,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b739495",
+   "id": "2c2e20f4",
    "metadata": {
     "editable": true
    },
@@ -4629,7 +4642,7 @@
   {
    "cell_type": "code",
    "execution_count": 34,
-   "id": "ae87789c",
+   "id": "21f48a1f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4694,7 +4707,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76c8872b",
+   "id": "bc8cc44b",
    "metadata": {
     "editable": true
    },
@@ -4705,7 +4718,7 @@
   {
    "cell_type": "code",
    "execution_count": 35,
-   "id": "e99dbaa4",
+   "id": "84b02c51",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4775,7 +4788,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "596df570",
+   "id": "0bb635d0",
    "metadata": {
     "editable": true
    },
@@ -4786,7 +4799,7 @@
   {
    "cell_type": "code",
    "execution_count": 36,
-   "id": "6693f042",
+   "id": "af9f10b1",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4830,7 +4843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a40ed853",
+   "id": "f8a20f65",
    "metadata": {
     "editable": true
    },
@@ -4849,7 +4862,7 @@
   {
    "cell_type": "code",
    "execution_count": 37,
-   "id": "02f88360",
+   "id": "f02783dc",
    "metadata": {
     "collapsed": false,
     "editable": true
diff --git a/doc/src/week39/week39.do.txt b/doc/src/week39/week39.do.txt
index 57722437e..008a97359 100644
--- a/doc/src/week39/week39.do.txt
+++ b/doc/src/week39/week39.do.txt
@@ -338,7 +338,16 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 !split
 ===== Convex function =====
 
-_Convex function_: Let $X \subset \mathbb{R}^n$ be a convex set. Assume that the function $f: X \rightarrow \mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \in X$ and for all $t \in [0,1]$. If $\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \neq x_2$ and $t\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below.
+_Convex function_: Let $X \subset \mathbb{R}^n$ be a convex
+set. Assume that the function $f: X \rightarrow \mathbb{R}$ is
+continuous, then $f$ is said to be convex if $f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2)$
+for all $x_1, x_2 \in X$ and for all $t \in [0,1]$.
+If $\leq$ is replaced with a strict inequaltiy in the
+definition, we demand $x_1 \neq x_2$ and $t\in(0,1)$ then $f$ is said
+to be strictly convex. For a single variable function, convexity means
+that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the
+value of the function on the interval $[x_1,x_2]$ is always below the
+line as illustrated below.
 
 !split
 ===== Conditions on convex functions =====
@@ -346,13 +355,15 @@ _Convex function_: Let $X \subset \mathbb{R}^n$ be a convex set. Assume that the
 In the following we state first and second-order conditions which
 ensures convexity of a function $f$. We write $D_f$ to denote the
 domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more
-details and proofs we refer to: "S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press":"http://stanford.edu/boyd/cvxbook/, 2004".
+details and proofs we refer to: "S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press":"http://stanford.edu/boyd/cvxbook/".
 
 !bblock First order condition
 Suppose $f$ is differentiable (i.e $\nabla f(x)$ is well defined for
 all $x$ in the domain of $f$). Then $f$ is convex if and only if $D_f$
-is a convex set and $$f(y) \geq f(x) + \nabla f(x)^T (y-x) $$ holds
-for all $x,y \in D_f$. This condition means that for a convex function
+is a convex set and $f(y) \geq f(x) + \nabla f(x)^T (y-x)$ holds
+for all $x,y \in D_f$.
+
+This condition means that for a convex function
 the first order Taylor expansion (right hand side above) at any point
 a global under estimator of the function. To convince yourself you can
 make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and