From bed3fcc809c4bea414d9dda90bf990f5c1dcc927 Mon Sep 17 00:00:00 2001
From: Michele Nottoli <michele.nottoli@gmail.com>
Date: Thu, 5 Oct 2023 11:46:37 +0200
Subject: [PATCH] Added a partial version of notebook 1.
---
1_Basics.ipynb | 630 +++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 630 insertions(+)
create mode 100644 1_Basics.ipynb
diff --git a/1_Basics.ipynb b/1_Basics.ipynb
new file mode 100644
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--- /dev/null
+++ b/1_Basics.ipynb
@@ -0,0 +1,630 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "7aad3586-d57e-4000-8688-aa5b53d48416",
+ "metadata": {},
+ "source": [
+ "# Basics"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bf904dbe-3197-4a91-bbb8-05e1c7f7dfee",
+ "metadata": {},
+ "source": [
+ "## Variables and elementary types\n",
+ "\n",
+ "Defining variables in Julia works like in most languages:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "3c44023b-06c9-4420-9af3-da2ec37b02da",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "int = 4 # An integer"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b2f9ba27-bf65-40d8-b0ac-e3d86c99dd40",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "str = \"Hi\" # A string"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "87a83355-5088-47d3-b698-2c6902aaa6a0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "float = 1.2 # A floating-point number"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "597523f1-4041-4fc6-9be2-2c94a93fd633",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "bool = true # A boolean (also false)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0c538bdb-f995-4589-bee7-0989c922090c",
+ "metadata": {},
+ "source": [
+ "The type is automatically inferred:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b80c6777-3dea-4f45-98b3-0a3eee196183",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "typeof(int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1fb6cbd2-871f-40a4-ae84-e7ee46e75a61",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "typeof(str)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a16a6f08-f19a-42e0-baac-aaa88ebba1af",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "typeof(float)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "09d035eb-22aa-49f5-9fd1-a5b16973f386",
+ "metadata": {},
+ "source": [
+ "Julia supports a large range of integer and floating-point types out of the box, for example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "88f24b01-f4a5-4030-af2c-a5d30223d047",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = UInt8(1) # 8-bit wide unsigned integer\n",
+ "y = Int32(-1) # 32-bit wide signed integer\n",
+ "z = Float32(0.2) # single precision\n",
+ "α = Float16(-1.0) # half precision\n",
+ "β = ComplexF64(2. + 8im) # Complex number (composed of two Float64)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a615bbc0-732e-461f-8c4c-a972fa2be731",
+ "metadata": {},
+ "source": [
+ "If you give a variable an illegal name, you get a syntax error:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1ca20515-6d66-40c3-84f1-2e24ece096cd",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "76trombones = \"big parade\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2c61f59e-2c2f-4049-8624-35e0712b2cf1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "more@ = 1000000"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "85040b19-b0a9-4baa-8748-5ea62f8b5633",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "struct = \"Advanced Theoretical Zymurgy\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cc36688b-c983-43f8-8bdf-9b82aae59909",
+ "metadata": {},
+ "source": [
+ "It turns out that struct is one of Julia’s keywords. The REPL uses keywords to recognize the structure of the program, and they cannot be used as variable names."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "de111dbe-f7ed-4e1a-8ec0-c5e65bd63bbf",
+ "metadata": {},
+ "source": [
+ "### Strings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1b3531e9-33db-4c51-b394-c1def6621519",
+ "metadata": {},
+ "source": [
+ "In general, you can’t perform mathematical operations on strings, even if the strings look like numbers, so the following are illegal:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "246f1db8-d734-413d-9237-b2434e071914",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"2\" - \"1\"\n",
+ "\"eggs\" / \"easy\"\n",
+ "\"third\" + \"a charm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c94f1187-67f8-473e-910c-2eb145ed59dd",
+ "metadata": {},
+ "source": [
+ "But there are two exceptions, * and ^."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b3a0f6e1-e28b-4fb7-baa3-bb003de3dc24",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"Hello \" * \"world\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "0c963c3c-47c7-4805-8be6-621b72fdb62e",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"hello! \"^5"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "61ff8194-669c-4ece-ba31-44e88ed808ac",
+ "metadata": {},
+ "source": [
+ "## Exercises"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e0aecc9c-e77f-449e-8aff-e1ffcf5d7833",
+ "metadata": {},
+ "source": [
+ "Practice using Julia as a calculator:\n",
+ " - The volume of a sphere with radius r is 4/3πr^3. What is the volume of a sphere with radius 5?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "fc538246-418c-4ebe-b487-81feba4383c8",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "10f1604d-8e81-4f96-8b6f-95753f0b5c4f",
+ "metadata": {},
+ "source": [
+ " - Suppose the cover price of a book is € 24.95, but bookstores get a 40 % discount. Shipping costs € 3 for the first copy and 75 cents for each additional copy. What is the total wholesale cost for 60 copies?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5d99fb94-0d78-4812-abbb-b528bc8cbf73",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4f6858ae-316a-4102-b9d8-9a5e087af1ca",
+ "metadata": {},
+ "source": [
+ " - If I leave my house at 6:52 am and run 1 km at an easy pace (6:00 per km), then 3 km at tempo (5:00 per km) and 1 km at easy pace again, what time o I get home for breakfast?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "bd4150cf-005a-4087-aa92-5f4b18e4d197",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "dc9cddb9-717d-4ba0-b478-beb00afc46c8",
+ "metadata": {},
+ "source": [
+ "## Conditionals and Boolean Expressions\n",
+ "\n",
+ "A boolean expression is an expression that is either true or false. The following examples use the operator ==, which compares two operands and produces true if they are equal and false otherwise:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7de4ffe9-4730-47dd-b074-1525bf9937b1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "5 == 5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c02939dd-6f25-4916-8394-a5f95d0200df",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "5 == 6"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9a108e63-7d58-489d-b7ef-49629c879d29",
+ "metadata": {},
+ "source": [
+ "The == operator is one of the relational operators; the others are:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b59cd314-fd03-4609-ac1b-7329a2c3cc38",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = 3; y = 4\n",
+ "x != y # x is not equal to y\n",
+ "x ≠ y # (to get the ≠ symbol, type \\ne and then press TAB)\n",
+ "x > y # x is greater than y\n",
+ "x < y # x is less than y\n",
+ "x >= y # x is greater than or equal to y\n",
+ "x ≥ y # (to get the ≥ symbol, type \\ge and then press TAB)\n",
+ "x <= y # x is less than or equal to y\n",
+ "x ≤ y # (to get the ≤ symbol, type \\le and then press TAB)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15e20f55-1a43-4d0d-94bc-d2de0ee2fe8c",
+ "metadata": {},
+ "source": [
+ "There are three logical operators: && (and), || (or), and ! (not). The semantics (meaning) of these operators is similar to their meaning in English. For example, x > 0 && x < 10 is true only if x is greater than 0 and less than 10. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "d1e6e2ce-bb0c-4776-80b6-22ceb9c68397",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = 4\n",
+ "x > 0 && x < 10"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "da591654-6360-4f56-956b-07493d1d2247",
+ "metadata": {},
+ "source": [
+ "It is also worth mentioning that in combined logical expression not all conditions are necessarily executed."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e92abf7b-5414-4aee-abaf-a4e52b1c06d3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "true || println(\"The RHS of || is only run\")\n",
+ "false || println(\"if the LHS is false\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c8a9d8ac-5378-4ebb-810b-9ae3194d670c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "iseven(3) && println(\"The RHS of || is only run\")\n",
+ "isodd(3) && println(\"if the LHS is true\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "be0c63e0-35a9-43c7-9b30-d04072ee6904",
+ "metadata": {},
+ "source": [
+ "Finally, the ! operator negates a boolean expression, so !(x > y) is true if x > y is false, that is, if x is less than or equal to y."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e43ab736-03e2-4040-a15e-48305037ba23",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = 4\n",
+ "!(x > 0 && x < 10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7064ae20-6d63-40fc-85c5-080ace54e7b6",
+ "metadata": {},
+ "source": [
+ "Unsurprisingly Julia has the standard conditionals."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4f140e2c-a240-496d-904c-c60778397bcf",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = 3; y = 5\n",
+ "\n",
+ "if x < y\n",
+ " println(\"x is less than y\")\n",
+ "elseif x > y\n",
+ " println(\"x is greater than y\")\n",
+ "else\n",
+ " println(\"x is equal to y\")\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4c57139e-da0c-48ef-a86f-4de80e1d7ca4",
+ "metadata": {},
+ "source": [
+ "There is also an inline conditional."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9d0801fd-b0d3-41e0-8b54-19a6b4539231",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = 3\n",
+ "x < 5 ? \"smaller than 5\" : \"larger or equal 5\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e4510840-0890-4217-8a8c-c24aa5d3405b",
+ "metadata": {},
+ "source": [
+ "## Iterations\n",
+ "\n",
+ "Julia implements the standard for and while constructs."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9632f210-c713-4829-8187-cf5554adad87",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for i in 1:5\n",
+ " println(\"Hello from number $i\")\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f00caf15-4992-4c0a-8324-9d2be966346d",
+ "metadata": {},
+ "source": [
+ "Where the `1:5` is a `Range`-object, but it could be any iterable. There are a few syntax variations, including:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "70a9f620-e4ce-4367-b0f5-de37db3f48b5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sum = 0\n",
+ "# To get ∈ write \\in and then press TAB\n",
+ "for j ∈ 1:0.5:3 # Note the step parameter\n",
+ " sum += j\n",
+ "end\n",
+ "println(sum)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e83b2d88-b0f2-43f1-9187-65fbc75f0d3b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 10\n",
+ "while n > 0\n",
+ " print(n, \" \")\n",
+ " n = n - 1\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f19d5051-ce82-49cc-80aa-2434a6adc9d0",
+ "metadata": {},
+ "source": [
+ "The loops can be further controlled with the break and continue keywords."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d0ebce97-3054-4eba-821d-92f27793d752",
+ "metadata": {},
+ "source": [
+ "Sometimes you don’t know it’s time to end a loop until you get half way through the body. In that case you can use the break statement to jump out of the loop."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9bb642e3-e3b1-488d-939f-6932feb62479",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "while true\n",
+ " print(\"> \")\n",
+ " line = readline()\n",
+ " if line == \"done\"\n",
+ " break\n",
+ " end\n",
+ " println(line)\n",
+ "end\n",
+ "println(\"Done!\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "98eee547-21fe-4022-bde5-b02ababa26dd",
+ "metadata": {},
+ "source": [
+ "The break statement exits the loop. When a continue statement is encountered inside a loop, control jumps to the beginning of the loop for the next iteration, skipping the execution of statements inside the body of the loop for the current iteration. For example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7f1c2595-8836-4308-9769-f4140d402582",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for i in 1:10\n",
+ " if i % 3 == 0\n",
+ " continue\n",
+ " end\n",
+ " print(i, \" \")\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "990cefae-abfe-4649-8d68-3fac1b1e268b",
+ "metadata": {},
+ "source": [
+ "### Exercises"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bdb2eef9-bdee-4cf3-8bab-d6c1d46ecc2f",
+ "metadata": {},
+ "source": [
+ "The mathematician Srinivasa Ramanujan found an infinite series that can be used to generate a numerical approximation of 1/π"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "feeb613b-544b-4a01-8817-9db86b8775e3",
+ "metadata": {},
+ "source": [
+ " 1 2 √2 ∞ (4k)! (1103 + 26390 k)\n",
+ " - = ------ ∑ ------------------------\n",
+ " π 9801 k=0 (k!)^4 396^(4 k)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8a8ae5ef-f9ec-480e-9927-8d21ecdf1915",
+ "metadata": {},
+ "source": [
+ "Use this formula to compute an estimate of π. It should use a while loop ot compute terms of the summation untile the last term is smaller than 1e-15. Afterwards, you can check the result by comparing it to π (to get π in Julia, write \\pi and then press TAB)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "cd1a716d-ddaf-4167-a83f-129dc3163ea1",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4ff56e28-969e-4a2d-b33c-21b4a4ecc4de",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Julia 1.9.3",
+ "language": "julia",
+ "name": "julia-1.9"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
--
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