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)