Mathematica/Elementary

These are draft notes from An Elementary Introduction to the Wolfram Language

1. Starting Out: Elementary Arithmetic (4:10)
   • Shift-Enter to perform a calculation
   • ^ for powers
   • asterisk for multiplication or space if it is clear
   • Keeps numbers as rational fractions if possible; converts to float with any floats involved
2. Introducing Functions (6:09)
   • Commands use CamelCase
   • Arguments in square brackets
   • Colors: Blue=unknown command, purple=bracket mismatch
   • Plus, Times, Power, Max, Min, RandomInteger
3. First Look at Lists (6:26)
   • Usually with { }
   • Edit->Extend Selection or CTRL-. will "grow" a selection to the next largest complete expression
   • ListLinePlot, ListPlot, Reverse, Range, Join
     • Range starts with 1
4. Displaying Lists (4:54)
   • CTRL-= for natural language input
   • Graphics can be part of a list
   • BarChart, PieChart, NumberLinePlot, Column,
5. Operations on Lists (6:17)
   • List math operations are element-wise
   • [[ ]] will index from list
   • Sort, Length, Total, First, Last, Part, Take, Drop, Count, IntegerDigits
     • Mathematica is 1-indexed
6. Making Tables (9:34)
   • Table
     • Table[item, number of items to generate]
     • Table[fcn[var], {var, start, end}]
     • Table[fcn[var], {var, start, end, step}]
     • Table[fcn[var], {var, {values}}]
   • The video has "ListPlot[Range[0, 1, 0.02]-Range[0, 1, 0.02]^2]" but "ListPlot[Table[x - x^2, {x, Range[0, 1, 0.02]}]]" seems more efficient
7. Colors and Styles (7:22)
   • Red, Green, Blue, ColorNegate, Blend, RGBColor, Hue, RandomColor
   • Style takes an item along with information about color, size, and face
8. Basic Graphics Options (7:54)
   • Graphics expression has graphics primitives that are changed by graphics directives
   • Graphics, Circle, Disk, RegularPolygon, Graphics3D, Sphere, Cone
   • Wrap graphics primitives with Style to change things
     • Thickness, Opacity
9. Interactive Manipulation (7:30)
   • Manipulate creates a selector; effectively picks items from a list but can continuously change if variable is continuous
   • Can manipulate multiple items
     • polyfit example?
   • ColorSetter
10. Images (5:22)
    • Importing the sample file did not work for me, nor did CurrentImage[] so I just imported another jpg I had
    • Import, Blur, Binarize, EdgeDetect, DominantColors, ImageAdd, ImageCollage, ExampleData
11. Strings and Text (7:55)
    • Double quotes
    • InputForm, StringLength, StringReverse, ToUpperCase, StringTake, StringJoin, Characters, TextWords, TextSentences, WikipediaData, WordCloud, WordList, RomanNumeral, IntegerName, AlphaBet, LetterNumber, FromLetterNumber, Transliterate, Rasterize
      • StringLength and others are mapped onto lists of strings
12. Sound (8:32)
    • Sound, SoundNote
      • Note 0 is middle C, integer values are keys (including black keys) away from middle C
      • To choose a style you also have to choose a duration
13. Arrays, or Lists of Lists (6:59)
    • Table with extra sizes
    • Grid, ArrayPlot, ImageData
    • ArrayPlot colorizes in reverse...ArrayPlot[ImageData[image]] is reversed
14. Coordinates and Graphics (7:57)
    • {{x1, y1}, {x2, y2}} etc
    • Graphics primitives take centers, sizes, other info
    • ListPlot, ListLinePlot, Point, Line, PointSize, Line, Polygon, Graphics3D, Sphere
15. Scope of the Wolfram Language (7:54)
    • Help->Documentation
    • Fast Introductions section
    • ?FunctionName, ?*LastPart, ?FirstPart*
    • Suggestions bar below result; code for result will be shown after using interactive suggestions
16. Real-World Data (8:05)
    • Plain English: CTRL-= then type statement
    • Can be indexed
    • Properties follow CamelCase even if EntityProperties return does not appear to
    • Entity, EntityClass, EntityList, EntityProperties
17. Units (8:38)
    • Units using plain English
    • InputForm to show how to enter using regular code
    • UnitConvert[thing, "Conventional"] will simplify
    • Quantity, InputForm, UnitConvert, CurrencyConvert, Rotate, esc-deg, AnglePath (turtle turns with step 1)
18. Geocomputation (6:23)
    • Natural language for locations
    • GeoListPlot, GeoGraphics, GeoPath, GeoDistance, GeoPosition, Here, GeoNearest
19. Dates and Times
20. Options (7:48)
    • kwarg -> value
    • Options[command, kwarg]
21. Graphs and Networks (9:43)
    • Vertices and edges, not plots
    • Rules in a list with -> to indicate relationships
    • Graph, FindShortestPath, UndirectedGraph, Flatten, Import, FilePrint, CommunityGraphPlot
22. Machine Learning
23. More about Numbers
24. More Forms of Visualization
25. Ways to Apply Functions
26. Pure Anonymous Functions
27. Applying Functions Repeatedly
28. Tests and Conditionals
29. More about Pure Functions
30. Rearranging Lists
31. Parts of Lists
32. Patterns
33. Expressions and Their Structure
34. Associations
35. Natural Language Understanding
36. Creating Websites and Apps
37. Layout and Display
38. Assigning Names to Things
39. Immediate and Delayed Values
40. Defining Your Own Functions
41. More About Patterns
42. String Patterns and Templates
43. Storing Things
44. Importing and Exporting (7:00)
    • Import web text, web links, web images
    • $ImportFormats, $ExportFormats
    • Import, LanguageIdentify, StringSplit, NestGraph, SocialMediaData, WebImageSearch, ResourceData, SendMail, Export
45. Datasets (9:22)
46. Writing Good Code
47. Debugging Your Code