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correcting typos

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This commit is contained in:
Morten Hjorth-Jensen
2023-09-27 10:49:57 +02:00
parent f9bb4a3803
commit 6de08dee25
7 changed files with 407 additions and 351 deletions
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doc/Projects/ProjectWriting/projectwriting.ipynb
+33 -43
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@@ -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
}
doc/pub/week39/html/week39-reveal.html
+20 -8
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@@ -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
doc/pub/week39/html/week39-solarized.html
+19 -4
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@@ -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
doc/pub/week39/html/week39.html
+19 -4
View File
@@ -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
doc/pub/week39/ipynb/ipynb-week39-src.tar.gz
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doc/pub/week39/ipynb/week39.ipynb
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doc/src/week39/week39.do.txt
+15 -4
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@@ -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