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"Exercises (lists, loops, if/else)\n",
"=================================\n",
"\n",
"**Exercise:**\n",
"- Construct the list of the 20th first terms of the sequence $x_n = cos(n)$ where $n \\geq 0$.\n",
"- In that list count how many terms are negative and how many are positive."
]
},
{
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{
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"cell_type": "markdown",
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"source": [
"**Exercise:** Write some code that displays the following multiplication table\n",
"```\n",
" 1 2 3 4 5 6 7 8 9 \n",
" 2 4 6 8 10 12 14 16 18 \n",
" 3 6 9 12 15 18 21 24 27 \n",
" 4 8 12 16 20 24 28 32 36 \n",
" 5 10 15 20 25 30 35 40 45 \n",
" 6 12 18 24 30 36 42 48 54 \n",
" 7 14 21 28 35 42 49 56 63 \n",
" 8 16 24 32 40 48 56 64 72 \n",
" 9 18 27 36 45 54 63 72 81 \n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
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"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exerecise:** Using a for loop (but no list) write some code that prints the first 20 terms of the sequence $x_n = sin(1/n)$ where $n \\geq 1$?."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
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"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:** Using a for loop (but no list) to print the first 20 terms of the sequence\n",
"$$x_0 = 0.5 \\qquad \\text{and} \\qquad x_{n+1} = 3.7 \\cos(x_n).$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
{
"cell_type": "code",
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:**\n",
"- Construct the list of the first 100th terms of the sequence\n",
"$$\n",
"z_0 = z_1 = 1 \\qquad \\text{and} \\qquad z_{n+2} = 3 z_{n+1} - z_n\n",
"$$\n",
"- How many terms among these are congruent to 1 mod 7?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise**:\n",
"- Write soe code that displays the following figure\n",
"```\n",
" *\n",
" **\n",
" ***\n",
" ****\n",
" *****\n",
" ******\n",
"```\n",
"- Write some code that displays the following figure\n",
"```\n",
" *\n",
" **\n",
" ***\n",
" ****\n",
" *****\n",
" ******\n",
" *****\n",
" ****\n",
" ***\n",
" **\n",
" *\n",
"```\n",
"\n",
"- Write some code that displays the following figure\n",
"```\n",
" *\n",
" ***\n",
" *****\n",
" *******\n",
" *****\n",
" ***\n",
" *\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:** Construct the list of even numbers between 0 and 100?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:** Write a small program that outputs the following\n",
"```\n",
" 1\n",
" 2 3\n",
" 4 5 6\n",
" 7 8 9 10\n",
" 11 12 13 14\n",
" 15 16 17 18 19\n",
" 20 21 22 23 24 25\n",
" 26 27 28 29 30 31 32\n",
" 33 34 35 36 37 38 39 40\n",
" 41 42 43 44 45 46 47 48 49\n",
" 50 51 52 53 54 55 56 57 58 59\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
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"outputs": [],
"source": []
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"execution_count": null,
"metadata": {
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"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:** Construst a list of lists `l` so that `l[n][k]` is the binomial number $\\binom{n}{k}$. For example, if we stop at $n=3$ the list should be\n",
"```python\n",
"[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]\n",
"```\n",
"Compute this list for $n=10$."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:** Given the two lists\n",
"```\n",
"m1 = [[1,2,3,4],[3,4,5,6],[5,6,7,8]]\n",
"m2 = [[1,2,1,2],[4,3,4,3],[6,5,6,5]]\n",
"```\n",
"- can you compute the sum of `m1` and `m2` seen as matrices?\n",
"- can you compute the product of `m1` and `m2` seen as matrices? and the product of `m2` by `m1`?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise:** Make the list of all positive integers smaller than 100 than can be written as the sum of two cubes. (For example $35$ can be written as $35 = 2^3 + 3^3$)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
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"outputs": [],
"source": []
},
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"metadata": {
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{
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"source": [
"Copyright (C) 2016 Vincent Delecroix <vincent.delecroix@u-bordeaux.fr>\n",
"\n",
"This work is licensed under a Creative Commons Attribution-NonCommercial 4.0\n",
"International License (CC BY-NC-SA 4.0). You can either read the\n",
"[Creative Commons Deed](https://creativecommons.org/licenses/by-nc-sa/4.0/)\n",
"(Summary) or the [Legal Code](https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode)\n",
"(Full licence)."
]
}
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