Programming in Mathematica

Name: Programming in Mathematica
Rating: 4.5 (611 reviews)

Learning Mathematica with Zero Programming Knowledge (but some Math Knowledge)

Created byShad Sharma, Sahand Hariri

Last updated 7/2020

English

What you'll learn

Visualize Mathematical Functions and Data
Solve Problems using Functional Programming and Procedural Programming Techniques

Course content

3 sections • 47 lectures • 6h 45m total length

Getting Started with Mathematica2:58
Hello and welcome. In this lesson, we are going to learn about the basics of Mathematica, including some general ideas about what it is and how it works. Before you start, you will need a copy of Mathematica. If you already have a copy of Mathematica, super, if not, we'll tell you how to go about getting a copy. The current version available is Mathematica 11. This is the version we will be using for the lessons. If you have an older version of Mathematica, don't fret; you should still be able to follow along with the lessons.

If you are a student, or an educator, first thing you should do is to check with your educational institution to see if they provide site licenses for your use. Most universities will have Mathematica available for students for free or at a discounted rate. If not, you will have to buy a license at www.wolfram.com/mathematica.

Another option is to create a wolfram account at www.wolframcloud.com and use the Wolfram Development Platform. Once you have created the account:
Click on "WOLFRAM DEVELOPMENT PLATFORM"
Log in
Click "Create a New Notebook"
You will be presented with the Notebook front end in browser.
If you have Mathematica installed, launch it and create a new Notebook.
You are now ready to follow along with our first evaluation presented in this video!
Notebook & Kernel11:26
Mathematica is a computing environment that consists of:
A front end, called the Notebook front end,
A back end, called the Kernel and,
A programming language, called the Wolfram Language.
In this lecture, we will introduce you to these three pieces of Mathematica.
Documentation Center5:41
In this lecture, we look at the self-help tools available in Mathematica, including the Definition function (?) and the Documentation Center.
Plotting Functions8:36
In this lecture we will learn how to plot functions that are defined in Mathematica. We will also explore ways to modify the visual representation of the plots.

Functions Covered:

Plot
GraphicsRow
Sin
Cos
Exp
Plotting Data9:31
One of the most powerful features of Mathematica is its facilities for visualizing data. In this lecture we will see how to plot data obtained form an experiments or other sources.

Functions Covered:

Range
Table
Thread
ListPlot
ListLinePlot
Random
Show
Parametric Plots15:50
In this lecture we look at parametric plots.
Functions Covered:
ParametricPlot
ListLinePlot
Creating Figures15:49
In this lecture, we'll learn the graphics commands necessary to draw figures. In particular, we'll look at how to draw a 2D model of a pendulum.

Functions Covered:

Line
Circle
Disk
Graphics
Text
Polygon
Rectangle
Triangle
RGBColor
EdgeForm
Opacity
Manipulate Part 110:57
In this lecture, we introduce the Manipulate function which enables us to animate functions over ranges of values.
Functions Covered:
Manipulate
Manipulate Part 212:13
In this lecture, we use Manipulate in conjunction with other functions to build a cool little app that shows how Sine and Cosine are used to build a circle.

Functions Covered:

Manipulate
GraphicsGrid
Rotate
Pendulum Project3:09
In this project, you will use some functions that we give you to animate the model of the pendulum that we drew in our Creating Figures lecture.
Pendulum Solution12:42
This lecture is the solution to the Pendulum Project. Please do the project before watching the solution!

Core Language Overview4:52
In this lesson, we'll take account of what we've learned so far, and give you an overview of the core language ideas, which we'll expand upon in subsequent lessons.
Expressions4:42
In our Core Language Overview, we said that everything in Mathematica is an Expression. The goal of this lesson is to understand what this means and why it's important.
Functions Covered:
FullForm
Head
Part
Apply
Plus
Lists Part 114:43
Lists are Mathematica's workhorse data-structure. And you've probably noticed that they are used almost everywhere for almost everything. In this first part on Lists, we'll look at list generation, element access, property inspection.
Functions Covered:
Range
Table
Length
Depth
MatrixForm
Grid
Flatten
Partition
Part
Take
Span
Lists Part 210:38
In this lecture, we'll look at functions that modify and transform lists.
Functions Covered:
Append
Prepend
Insert
Delete
Drop
Join
DeleteDuplicates
Gather
Tally
RotateLeft
RotateRight
PadLeft
PadRight
A Note on Immutability0:06
Lists Part 312:42
In this lecture we'll look at how you can find elements in a list, sort lists, how to treat lists as sets and some basic list combinatorics.
Functions Covered:
Position
RandomInteger
Sort
Reverse
RandomSample
SortBy
Union
Intersection
ContainsAll
Complement
Tuples
Permutations
Subsets
Rules and Patterns Part 115:16
In this lecture, we introduce Rules and Patterns. A Rule is an ordered pair that creates a mapping from one Mathematica expression, to another. Patterns enable Mathematica to represent classes of expressions.
Functions Covered:
Rule
ReplaceAll
ReplaceRepeated
MatchQ
Pattern
Blank
BlankSequence
BlankNullSequence
Rules and Patterns Part 213:12
In this lecture, we dive deeper into Rules and Patterns. We look at Patterns that can perform arbitrarily complex tests on an expression. We also look at some of the various functions where Patterns can be used.
Functions Covered:
Framed
PatternTest
Negative
EvenQ
OddQ
PrimeQ
Condition
Count
Cases
DeleteCases
Position
Deck of Cards Project0:32
In this project, you will render a deck of cards using the tools that we've learned so far. The starter notebook is attached. Good luck!
Deck of Cards Solution6:00
This lecture is the solution to the Deck of Cards Project. Please do the project before watching the solution!
Delayed Evaluation4:27
In this lecture we look at Delayed Evaluation. Delayed Evaluation enables Mathematica to postpone the evaluation of an expression until the result is actually accessed.

Functions Covered:

SetDelayed (:=) – the delayed version of Set (=)
RuleDelayed (:>) – the delayed version of Rule (->)
Functions Part 112:45
In this lecture we will learn how to define functions.
Options6:43
Usage Docs1:33
In this lecture we'll take a quick look at how to add usage documentation to our functions.
Functions Covered:
:: Operator
? Operator
?? Operator
Map4:06
In this lecture, we introduce the Map function and use it to vectorize our Fibonacci function from the previous lecture.
Functions Covered:
Map
Functions Part 211:47
In this lecture, we introduce Pure Functions, also known as Anonymous Functions.
Functions Covered:
Function (&)
Slot (#)
Tally
Functional Programming Part 110:15
In this lecture, we introduce the tools you will need for functional programming.
Functions Covered:
Cases
Select
MapAt
MapAll
MapIndexed
Thread
MapThread
Functional Programming Part 212:40
In this lecture, we cover more tools used in functional programming.
Functions Covered:
Nest
NestList
NestWhile
NestWhileList
FixedPoint
FixedPointList
Fold
FoldList
NormalDistribution
RandomVariate
Cellular Automata Project3:40
In this lecture, we will build a Manipulate that shows the evolution of a cellular automaton system. The starter notebook is attached. Good luck!
Cellular Automata Solution9:40
This lecture is the solution to the Cellular Automata Project. Please do the project before watching the solution!
Procedural Programming Part 19:59
In this lecture, we introduce the tools you will need to do procedural programming in Mathematica.
Functions Covered:
CompoundExpression
Print
If
Which
Switch
Procedural Programming Part 24:14
In this lecture, we describe how to use loops in Mathematica.
Functions Covered:
Do
While
For
Variable Scoping10:02
In simple terms, the scope of a variable is the portion of code where a variable is defined. In this lecture, we'll learn about the tools Mathematica provides that enable us to effectively scope variables.
Functions Covered:
With
Module
Block
Sierpinski's Carpet Project1:01
In this project, you will apply what you've learned to use Mathematica's drawing system to generate Sierpinski's Carpet. Good luck!
Sierpinski's Carpet Solution9:28
In this lecture we present our solution to the Sierpinski's Carpet project. Please do the project before watching the solution!
Strings8:39
Strings are fundamental objects in just about every programming language, so it will be useful for us to go over how to create and manipulate strings in Mathematica.
Functions Covered:
String
Characters
StringJoin
StringLength
StringTake
StringPosition
StringSplit
StringRiffle
StringTrim
ToUpperCase
ToLowerCase
StringReplace
StringTemplate
String Expressions12:01
A super important feature of strings is the ability to match on patterns. In this lecture, we'll give a brief overview of string expressions and regular expressions.
Functions Covered:
StringExpression
RegularExpression
StringMatchQ
NumberString
StringCases
Associations8:30
In this lecture, we'll learn about Associations. Associations are a special type of data structure that represent a mapping between a unique key and a value. Due to their underlying implementation, pulling out a value from an Association by it's key can be done very quickly, independent of how large the Association is.
Functions Covered:
Association
Keys
Values
KeyExistsQ
Lookup
Import and Export15:31
In this lecture, we explore Mathematica's functions for reading and writing data from external sources, like files and URLs.
Functions Covered:
Import
Export
Directory
SetDirectory
NotebookDirectory
DirectoryStack
ResetDirectory
Longest Left Hand Word Project0:35
The other day, my brother told me that the longest word that you could type with your left hand is "stewardesses". I thought that was interesting, and I decided that it would be even more interesting to prove it. In this lecture, you will write a Mathematica program to determine if "stewardesses" is indeed the longest word that you can type with your left hand!
Longest Left Hand Word Solution3:20
In this lecture, we present our solution to the Longest Left Hand Word project. As always, please attempt the project before watching the solution!
Packages15:04
In this lecture, we describe how to create your very own packages!
Functions Covered:
Get
$Path
BeginPackage / EndPackage
Begin / End

Background5:16
In this lecture, we present the inspiration for the final project. The next lecture will describe precisely what we want you to do.
We used the following resources when making this video:
By Kulac - Self-published work by Kulac, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2298427
By Forest & Kim Starr, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=6178248
By Evan-Amos - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=16918371
By Coyau / Wikimedia Commons, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=31365778
By Coyau / Wikimedia Commons, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=31366420
By Eric Hunt - Own work, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=1318818
By in Alcide Dessalines d'Orbigny - Voyage dans l'Amérique méridionale, Public Domain, https://commons.wikimedia.org/w/index.php?curid=20036892
By Didier Descouens - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=15719115
By Madprime - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2063426
By Robert Louis Stevenson (died before 1900) - Frontpiece of memoir of FJ by RLS edition of 1912 available at: http://archive.org/details/memoiroffleeming00stevuoft Stated out of Copyright, Public Domain, https://commons.wikimedia.org/w/index.php?curid=26438629
By Leonard Darwin - Woodall 1884, Public Domain, https://commons.wikimedia.org/w/index.php?curid=16959735
Intro and Project Starter Files5:52
In this lecture we will describe what we want you to accomplish in the final project.
Functions Covered:

SeedRandom
Blending Model Solution14:20
This lecture is the solution to the Blending Model. As always, please try to solve the project yourself before watching this video.
Mandellian Model Solution12:26
This lecture is the solution to the Mendelian Model. As always, please try to solve the project yourself before watching this video.

Requirements

Buy Mathematica from Wolfram or your school's software portal

Description

In this course, we're going to teach you how to use the powerful graphics and animation tools available in Mathematica for prototyping ideas and visualizing data.

While Mathematica has many built in functions for doing really amazing things, we feel that a good understanding of how to code frees you to be able to make just about anything. And so our focus in this course is programming using the Wolfram Language. To get you started off quickly, we will jump right in with plotting and animating, data and mathematical functions. After that, we will get into the nitty gritty details of programming with the Wolfram Language.

In each lecture, we will introduce new concepts, and demonstrate use cases with interesting examples. You can download the lecture notebook and follow along with us, as the best way to learn to program is to get as much practice as possible. Each lecture is also accompanied by an exercise notebook. These notebooks provide a bunch of problems for you to work on and will really help to internalize the new material. You will get the most out of this course if you do all of the exercises.

Periodically, we’ll have projects for you to work on. These project are often challenging and will test your ingenuity, but will also teach you how to program and solve real problems with Mathematica. Our projects include:

Programming and visualizing the oscillations of a simple pendulum
The evolution of cellular automata
Sierpinski’s carpet
Simple simulation of an evolution model

We feel that this course will best serve college level students, graduate students, and maybe even professors, since Mathematica is great for producing publication quality graphics. However, even if you are not an academic, you will benefit from taking this course.

We look forward to teaching this course and we hope you enjoy it. See you at the next lecture!

Who this course is for:

College level students in engineering

Programming in Mathematica

What you'll learn

Explore related topics

Course content

Introduction – Crash Course11 lectures • 1hr 49min

Programming32 lectures • 4hr 19min

Final Project4 lectures • 38min

Requirements

Description

Who this course is for: