Tag: Compilers
Making a Pratt Parser Generator Part 1
Defining the Wolfram Language Part 2: Operator Properties
In this third installment of our n part series, “Defining the Wolfram Language,” we begin to study the properties, namely the arity, affix, associativity, and precedence, of the Mathematica operators we found in Part 1. If we ended Part 1 proud of our accomplishment—perhaps even a little smug—then we will get reacquainted with our humility in this article.
Generalizing PEMDAS: What is an operator?
Defining the Wolfram Language Part 1: Finding Operators
Finding All Wolfram Language Operators
In this second article, Part 1 of an n part series on Defining the Wolfram Language, we start getting our hands dirty hunting down every single operator in Mathematica and each operator’s linguistic properties. To my knowledge, nobody outside of Wolfram has created such an exhaustive list before.
Defining the Wolfram Language Part 0: The Challenge
What is the definition of the Wolfram Language? This is the first in a series of articles attempting to answer this question.
The grammar of mathematical expressions
Using computers to do automatic translation has a long and rich history in computer science. A course in compiler construction is a veritable survey of topics in computer science running the gamut from formal languages to data structures and algorithms to Hopfcroft’s algorithm to minimize deterministic automata. One of the first things a student learns in a compiler construction course is how to formally describe the grammar of a language using (extended) Backus–Naur form (EBNF).
What is the IELR(1) Parsing Algorithm?
Tag: Software Engineering
Making a Pratt Parser Generator Part 1
Tag: COVID-19
Bayes' Theorem and the Deathly Hallows
Tag: Healthcare
Bayes' Theorem and the Deathly Hallows
Tag: Statistics
Bayes' Theorem and the Deathly Hallows
Tag: Mathematica
Defining the Wolfram Language Part 2: Operator Properties
In this third installment of our n part series, “Defining the Wolfram Language,” we begin to study the properties, namely the arity, affix, associativity, and precedence, of the Mathematica operators we found in Part 1. If we ended Part 1 proud of our accomplishment—perhaps even a little smug—then we will get reacquainted with our humility in this article.
Defining the Wolfram Language Part 1: Finding Operators
Finding All Wolfram Language Operators
In this second article, Part 1 of an n part series on Defining the Wolfram Language, we start getting our hands dirty hunting down every single operator in Mathematica and each operator’s linguistic properties. To my knowledge, nobody outside of Wolfram has created such an exhaustive list before.
Defining the Wolfram Language Part 0: The Challenge
What is the definition of the Wolfram Language? This is the first in a series of articles attempting to answer this question.
Using Mathematica From Python
In which I show you how to programmatically interface with a Mathematica kernel from Python.
Tag: Computer Science
Making a Pratt Parser Generator Part 1
Defining the Wolfram Language Part 2: Operator Properties
In this third installment of our n part series, “Defining the Wolfram Language,” we begin to study the properties, namely the arity, affix, associativity, and precedence, of the Mathematica operators we found in Part 1. If we ended Part 1 proud of our accomplishment—perhaps even a little smug—then we will get reacquainted with our humility in this article.
Generalizing PEMDAS: What is an operator?
Defining the Wolfram Language Part 1: Finding Operators
Finding All Wolfram Language Operators
In this second article, Part 1 of an n part series on Defining the Wolfram Language, we start getting our hands dirty hunting down every single operator in Mathematica and each operator’s linguistic properties. To my knowledge, nobody outside of Wolfram has created such an exhaustive list before.
Defining the Wolfram Language Part 0: The Challenge
What is the definition of the Wolfram Language? This is the first in a series of articles attempting to answer this question.
The grammar of mathematical expressions
Using computers to do automatic translation has a long and rich history in computer science. A course in compiler construction is a veritable survey of topics in computer science running the gamut from formal languages to data structures and algorithms to Hopfcroft’s algorithm to minimize deterministic automata. One of the first things a student learns in a compiler construction course is how to formally describe the grammar of a language using (extended) Backus–Naur form (EBNF).
Using Mathematica From Python
In which I show you how to programmatically interface with a Mathematica kernel from Python.
What is the IELR(1) Parsing Algorithm?
Tag: Education
How Springer sent me to collections for adopting their textbook.
The story begins with one of those little mundane activities that fill every professor’s day. Right before the spring semester began I was evaluating various textbook options for the next time I teach undergraduate real analysis. Stephen Abbott’s Understanding Analysis published by Springer seemed to be exactly the kind of book I was looking for.
How To Ask Your Professor For Something
Do you need to ask your professor for an extension on a due date or to reschedule a quiz? A little thought before you click send on that email can make a big difference. Here is some advice.
Sneaky Continuous Functions
While the target audience of this article is my fantastic calculus students, other math teachers might enjoy it as well.
Sneaky Continuous Functions
When students in first semester calculus first start learning about limits, they are often asked to determine limits using the graph of a function, which we will call the graphical method, and also by constructing a table of values of the function, which we will call the numerical method. Students should be warned that these methods, while perfectly legitimate and often quite useful, are really just fancy ways of guessing the value of the limit, that is, the graphical and numerical methods do not supply us with mathematical certainty regarding the value of the limit. After all, what if your function is very sneaky and merely looks like it’s approaching a value $L$ as $x$ approaches $c$ when in fact it ultimately approaches a different value $K$?
Susan Meisenhelder's 'MOOC Mania'
When Students Die
Tag: Mathematics
Bayes' Theorem and the Deathly Hallows
Platonic Solids and the School of Athens
Euclid in The School of Athens
This is a very special fresco painting by Italian Renaissance artist Raphael in the Vatican Museum called The School of Athens. It depicts the great philosophers of ancient Greece, famously with Plato pointing up and Aristotle pointing down.
Hangout On Air - Math: A Love Story
The Mathematics Community on Google+ had our second ever Hangout On Air last week. I was joined by Luis Guzman, Jason Davison, and Amy Robinson in a conversation that ranged from fluid dynamics to applying the mathematics of networks to map our ideas to JPEG image compression.
Sneaky Continuous Functions
While the target audience of this article is my fantastic calculus students, other math teachers might enjoy it as well.
Sneaky Continuous Functions
When students in first semester calculus first start learning about limits, they are often asked to determine limits using the graph of a function, which we will call the graphical method, and also by constructing a table of values of the function, which we will call the numerical method. Students should be warned that these methods, while perfectly legitimate and often quite useful, are really just fancy ways of guessing the value of the limit, that is, the graphical and numerical methods do not supply us with mathematical certainty regarding the value of the limit. After all, what if your function is very sneaky and merely looks like it’s approaching a value $L$ as $x$ approaches $c$ when in fact it ultimately approaches a different value $K$?
Blogging the JMM: Saying Goodbye
It’s over. Getting my internet fix in the hotel lobby at midnight, walking 18 miles a day through the convention center, sitting in uncomfortable chairs for hours, getting dinner in a local restaurant and realizing halfway through the meal that every single person dining there is also a mathematician, randomly bumping into an old friend or mentor or student–it ended today at around lunchtime when I made the trek back to the hotel lobby one last time.
Blogging the JMM: Friday
I love the exhibit hall. I love books, and the exhibit hall is full of some of my favorite kinds of books. I spend hours picking through the texts, flipping through their pages. The AMS sold me on a great book directed at undergraduates on Fourier analysis and an advanced text on Riemannian manifolds. In fact, they managed to photograph me mid-purchase! I also learned they are selling their first ever children’s book this spring.
Blogging the JMM: Thursday
The best part of the Joint Meetings is networking with like-minded people. I ran into many old friends and colleagues. Today (Thursday) several math bloggers and Google+‘ers organized an impromptu meeting for lunch. I stuck a sign on the message board inviting other math bloggers to join us, and a cohort of tumblr bloggers discovered it and joined us. Such is the power of the JMM message board.
Blogging The JMM: Wednesday
Today I learned about connections between musical rhythm and knot theory, abstract algebra and dance, a Navy ship from the mid 1800s called the U.S.S. Constellation, and some great undergraduate real analysis pedagogy. In today’s post, I’ll share with you some of the most interesting mathematical ideas I heard today.
Blogging the largest math conference in the world
Tag: Programming
Using Mathematica From Python
In which I show you how to programmatically interface with a Mathematica kernel from Python.
Tag: Python
Using Mathematica From Python
In which I show you how to programmatically interface with a Mathematica kernel from Python.
Tag: Art
Platonic Solids and the School of Athens
Euclid in The School of Athens
This is a very special fresco painting by Italian Renaissance artist Raphael in the Vatican Museum called The School of Athens. It depicts the great philosophers of ancient Greece, famously with Plato pointing up and Aristotle pointing down.
Tag: Geometry
Platonic Solids and the School of Athens
Euclid in The School of Athens
This is a very special fresco painting by Italian Renaissance artist Raphael in the Vatican Museum called The School of Athens. It depicts the great philosophers of ancient Greece, famously with Plato pointing up and Aristotle pointing down.
Tag: Academia
How Springer sent me to collections for adopting their textbook.
The story begins with one of those little mundane activities that fill every professor’s day. Right before the spring semester began I was evaluating various textbook options for the next time I teach undergraduate real analysis. Stephen Abbott’s Understanding Analysis published by Springer seemed to be exactly the kind of book I was looking for.
Tag: Teaching
How To Ask Your Professor For Something
Do you need to ask your professor for an extension on a due date or to reschedule a quiz? A little thought before you click send on that email can make a big difference. Here is some advice.
Tag: Science Communication
Hangout On Air - Math: A Love Story
The Mathematics Community on Google+ had our second ever Hangout On Air last week. I was joined by Luis Guzman, Jason Davison, and Amy Robinson in a conversation that ranged from fluid dynamics to applying the mathematics of networks to map our ideas to JPEG image compression.
Tag: Data Science
Does a 1929 market chart predict a market crash?
No. No it does not. Not even a little bit.
Tag: Finance
Does a 1929 market chart predict a market crash?
No. No it does not. Not even a little bit.
Tag: Calculus
Sneaky Continuous Functions
While the target audience of this article is my fantastic calculus students, other math teachers might enjoy it as well.
Sneaky Continuous Functions
When students in first semester calculus first start learning about limits, they are often asked to determine limits using the graph of a function, which we will call the graphical method, and also by constructing a table of values of the function, which we will call the numerical method. Students should be warned that these methods, while perfectly legitimate and often quite useful, are really just fancy ways of guessing the value of the limit, that is, the graphical and numerical methods do not supply us with mathematical certainty regarding the value of the limit. After all, what if your function is very sneaky and merely looks like it’s approaching a value $L$ as $x$ approaches $c$ when in fact it ultimately approaches a different value $K$?