Tag Archives: answer

User Generated Flash Cards

When I originally started LEARNINGlover.com, I had the idea in my mind that I would utilize my skills in programming and mathematics to help others. While this remains an important goal of mine, I remain curious about how I can use this site in other ways. One thought that has occurred to me for a while is how do I expect to handle users who want to learn things that are not currently offered by the site? I do plan to regularly add sections, data and programs to the site, but what about people who don’t want to wait, or who don’t want to learn the things that I have been studying? My thought process on this is that I’d like to provide users with tools that I believe can be used to help learn, in particular to help teach yourself, just about anything – as long as you have a good source. We live in an age where information is everywhere. With just the click of a mouse we have the power to download an online textbook, read journal articles, learn a new language and a host of other things – if we know how to use this information correctly.

The concept of flash cards has been around much longer than I have. That said, I don’t see flash cards used outside the realm of vocabulary often. When I began studying theoretical mathematics, I found the number of vocabulary words offered in each class intimidating. So by instinct, I just used flash cards to learn these words. The class, though, also consisted of theorems, lemmas, proofs, corollaries, etc that do not fit into the vocabulary ‘box’ that I had seen flash cards used for. Nonetheless, I needed to study these concepts if I was going to do well in my classes.

What I found is that in my notes, not only are the notes themselves important, but there is also a question – ‘Why is this line that I just underlined important?’ Or phrased differently, ‘What question was this line written to answer?’ Take for example the following note which may come up in a class on Graph Theory:

The complexity of Kruskal’s algorithm is O(E log V).

This is certainly an important fact, as we are interested in how well algorithms perform and would like to compare these complexities. But once I have underlined it in my notes, I want a way to remember it. I know the question that will come to me during an exam or in real life practice is:

What is the complexity of Kruskal’s algorithm?

So I create a flash card with this question and answer pair.

I don’t have any ‘rules’ for creating these questions, but here are some things that come to mind:

  1. In general I try to make my questions open-ended (not yes/no questions).
  2. For definitions, I generally ask “What is the definition of <insert word>”.
  3. Many times, things such as theorems, lemmas, or corollaries will connect two things together (either in one direction or two), so I ask questions like “What is the relationship between <insert concept 1> and <insert concept 2>?” for these.
  4. Other times, theorems simply state facts (like the example above), or link a well known function (complexity) to a particular object (Kruskal’s algorithm). For these I form questions like “What is the value of <insert function> on <insert object>?”
Of course I don’t live by these rules and feel free to change or add to them as you like. I have used similar concepts on reading and understanding journal papers as well as some philosophy books. I hope this helps you as much as it has helped me. 

Flash Cards Page

One of the most effective ways I remember studying for vocabulary quizzes in high school was through flash cards. During my time in college, I wondered why a similar method was not used to help study for other things, particularly in math and math-like classes where new definitions and concepts are introduced everyday. As a result of this, I wrote an initial flash cards script to help me with my advanced calculus class. Because of my success in this class, I continued developing flash cards to help study many other concepts. Here,  I have decided to share some of those concepts with you.

The general concept behind how I develop the flash cards is simple. Each flash card consists of a question on one side and the answer to that question on the other. For definitions, the question is generally of the form “What is the definition of _____” and the answer will generally go “The definition of _____ is _____”. This may vary a bit, but I try to keep it in this context to allow for searching easier. The other things I generally put onto flash cards are Lemmas/Theorems/Corollaries. These are a bit more difficult to put on flash cards though. The flash cards are still in a question and answer format, but I tried to make the question center around what the question being asked that led to the development of the Lemma/Theorem/Corollary was. Sometimes I may be off-base with these questions, and I’ve had to go back and re-do these questions a number of times. However, I hope they can be helpful.

For algorithms, which are a large part of this site, I generally asked to include the pseudocode for the given algorithm. However since pseudocode is far from formal, this can lead to a bit of a debate among whether you feel that your answer is the same as mine.

The AMS Graduate Student Blog lists some other sites where you can get math generated flash cards.