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15 Ways to Collect and Organize Ideas October 25, 2006

Posted by LearningNerd in English, Language, Wednesdays, Writing, Writing Basics.
7 comments

Like lightning, ideas tend to strike when least expected (and they can be quite shocking). But you never think of them when you need to! I hate nothing more than to get a good idea only to know that I’ll forget it before I can write it down. So, here are a few tips and tools to capture those bursts of creative energy:

Collecting Ideas

  • Get a PDA or Pocket PC.
  • Get a notebook or my personal favorite, the free PocketMod. As for a pen, you could buy one of those useful mini-pens made specifically to fit inside your wallet — or you could get a Swiss Army knife that includes a pen.
  • As commenter Brad Shorr suggested, keep your notebook next to your bed to keep track of those crazy, late-night ideas.
  • Keep a plain text file or other document on your computer just for listing those random ideas.
  • Get one of those mobile digital recorders.
  • Use your phone to leave yourself messages.
  • Use a service like Posticky or Evoca to save your recordings online.
  • Or, if you need to access your notes from any computer, use one of the many online note-taking services out there. See Fifty Ways to Take Notes for a great list of these.

Organizing Ideas

  • Keep all of your ideas in separate emails and use Gmail’s labeling feature to organize them. You might even want to create a separate email account just for ideas and notes.
  • If you like to list your ideas in a text document, just make one file for each project you have and organize them in folders.
  • If you prefer paper, use different colored sticky notes and stick them on larger pieces of paper to group your ideas together. To keep track of everything, keep all the paper in a 3-ring binder and use dividers to separate ideas for different projects.

I’m currently using an unorganized combination of several of the above methods until I decide which I like best. How do you keep track of your random ideas?

Discussing Numbers: The Number Line, Types of Numbers, Sets, Inequalities, and Intervals October 23, 2006

Posted by LearningNerd in Arithmetic, Math, Mondays, Number Theory, Pre-Algebra, Science.
1 comment so far

I said I’d start with the basics, so here they are!

Sections in this post: The Number Line and Absolute Value, Types of Numbers, Sets, Inequalities, and Intervals and a Final Review.

By the way, this post includes three videos. They’re a bit long and not particularly entertaining, but they’re useful if you’d like to take a break from reading.

The Number Line and Absolute Value

It all starts with the number line, which, as the name implies, is simply a line marked with numbers. Math teachers love to use number lines to teach everything from arithmetic to calculus, and though I remember the number line as it appeared on many repetitive worksheets, I realize that it can actually be useful. Like an outline, the number line is a great way to visualize the abstract ideas you’re working with: smaller numbers on the left, bigger numbers on the right. For an example, check out this nifty tool that compares two numbers using a number line.

Next, absolute value: the distance of a number from zero (the origin). This one’s pretty straightforward. See Absolute Value for a complete overview.

Types of Numbers

A set is a group of things (in this case, numbers) considered as a whole. Now, a lot can be said about sets (see set theory), but for now, that simple definition will do.

number system is a set of numbers that can be used in arithmetic operations (like addition and subtraction). As we all learned in school a long, long time ago, there are different types of numbers like positive numbers, negative numbers, even numbers and odd numbers. (Those types of numbers can be listed in sets, but they aren’t considered number systems. I looked for a formal explanation of this, but I’ve yet to find one.)

There are several types of numbers or number systems commonly taught in math classes:

See Number Types for a basic overview, and/or watch this video:

I’ll be learning more about irrational and complex numbers later; they aren’t important until you get to more advanced mathematics.  

Sets

Like I already mentioned, a set is just a group of things considered as a whole. When discussing numbers, mathematicians save time by using set notation. The whole thing’s pretty simple, but it uses some symbols that you don’t see too often. See Set Notation for a review, and be sure to bookmark the page for reference. The following video also explains set notation:

Just for fun, here’s an interesting math problem I came across: “Which is greater, the number of rational numbers between 0 and 1 or the number of rational numbers between 0 and 2?” See the answer and explanation here. (By the way, I got it wrong. :roll: )

Inequalities

The inequality signs (like < and >) are used to compare numbers. They’re pretty straightforward; 13 is less than 27 (13 < 27), two is greater than negative three (2 > -3), and so on. Rest assured, it does get more complicated.

For kids or anyone who wants some practice, here are a couple interactive games and quizzes:

Intervals and a Final Review

An interval is basically just a set of numbers containing every number between two numbers. As with sets, intervals have their own notation; see Interval Notation for a summary of the basics and remember to bookmark the page for reference.

The following video reviews inequalities, intervals, and set notation:

As a final review, check out this interactive example of Set and Interval Notation, where you can move an interval on a number line and see how the notation changes.

A Request for Your Suggestions and a Word on Roman Numerals October 22, 2006

Posted by LearningNerd in Personal.
1 comment so far

Thanks to Chris for his lovely suggestion — I’ll get to drawing that waffle conquering Denmark soon! See the end of my last post for details: What I (Don’t) Know About Art. So, I ask you, dear reader: give me any random object or idea, and I’ll draw it and upload it to my blog, where you will then be welcome to view and laugh at it. ;)

And this one’s for Brad Shorr (who had a great question the other day): Roman Numerals and Arithmetic. It’s interesting, but it might give you a headache!

I originally planned to write a post on Monday about the history of numbers and numerals, but I decided to leave that for later; I was overwhelmed by how much can be written just about numbers! The mathematical explanations were also a bit over my head, so I’m going to get back to that when I start learning about number theory (whatever that is). For now, I’ll just stick to arithmetic.

Oh, and the new RSS feeds are up! You can subscribe to them from the new Posting Schedule page. :)

What I (Don’t) Know About Art October 20, 2006

Posted by LearningNerd in Art, Fridays, Personal, Visual Art.
2 comments

Before I start learning about visual art, I thought I should evaluate how much I already (don’t) know about it. Years later, when I’m the next Picasso, I’ll look back at this post and marvel at my amateurishness. (And yes, that actually is a word.)

So, here we go:

  • I know that objects are smaller when further away.
  • I know that light affects color and creates shadows.
  • I know that the primary colors are red, yellow and blue, and the secondary and tertiary colors are mixtures of those.
  • I know that those all fit on a color wheel somehow.
  • I know what lines are, I know what shapes are, and I know what dots are.
  • I know that artistic works somehow involve balance, contrast, and other vague stuff like that.
  • I know that colors and images can somehow evoke certain emotions.
  • I know that painting usually involves paint and brushes.

But I don’t know exactly what perspective is, I don’t know the rules of composition (or what that term means), and I don’t even know how many artistic terms there are that I don’t know!

As for my drawing skills — well, I should just show an example! So, what should I draw? Suggest any object, creature, scene, abstract idea, or anything you can think of. I’ll (try to) draw it on a piece of paper, scan it, and then update this post with examples of my pathetic attempts at art.

This should be fun.

Overview of Mathematical Terms and Notation October 16, 2006

Posted by LearningNerd in Math, Mondays, Science.
5 comments

As Denning Miller explains in Miller’s Popular Mathematics,

…there is no vocabulary that is easier to acquire than the mathematical one. There are no tenses, no genders, no conjugations, no declensions, and only a minimum of grammar. Imagine how pleasant it would be, after you had learned a few words of Spanish, to begin talking and expressing yourself in the language. You can do that in mathematics… 

But mathematicians have a knack for avoiding plain English wherever possible. Instead of saying “Find the answer to this problem,” they’ll say, “Evaluate this expression.” So, before I start relearning math, I thought I should avoid future confusion by reviewing this mathematical gibberish.

Here I’ll keep an ongoing list of general math terms and useful websites. Sections in this post: General Terms, History, and Glossaries.

A List of General Mathematical Terms

It’s interesting to note how each math term relates to its plain English counterpart; for example, “to evaluate” means to judge the value of something (like appraising the value of a gold coin), and in math it means to find the numerical value of something. Value, another math term, is also a common word with overlapping definitions — see value. As you’ll notice, all the terms and concepts in math are just specific versions of abstract ideas that apply to every field.

  • Number n. – An abstract entity representing a count or measurement.
  • Variable n. – A quantity that can be unknown and/or subject to change, usually represented by a letter like x.
  • Set n. – A collection of distinct things considered as a whole.
  • Equation n. – A statement that two things are the same, as in 2=2 or 2+2=4.
  • Operation n. – A process that combines two values to produce a third, like addition or division.
  • Expression n. – A group of numbers, variables, and operators (like + or -). I think of an expression as the mathematical version of a phrase in English, whereas an equation is like a complete sentence. (Compare the expression “two plus three” to the equation “Two plus three equals five.”)
  • Function n. –  An operation that creates a relationship in which one variable depends on another and each input can have only one output. (Don’t worry about this one until calculus.)
  • Value n. – A quantity; an output of an operation or a function.
  • Evaluate v. – To find the value of (an expression). (Evaluate 2+2 to get 4.)
  • Simplify v. – To reduce (an expression) to only the necessary parts. (Simplify 2x+3x to get 5x.)
  • Algorithm n. – A step-by-step set of rules used to solve a problem.
  • Axiom n. – A self-evident truth or a statement that is assumed to be true, which is used as a basis to prove other statements. Also called a postulate.
  • Proof n. – A logical demonstration that a statement is true; the process of establishing a theorem (see below).
  • Theorem n. – A statement that has been proven true, deduced from certain axioms using a proof.

History of Mathematical Terms and Notation

Glossaries of Mathematical Terms and Notation

  • Mathwords – a dictionary of math terms with lots of pictures and examples.

Monday and Wednesday Posts on Fridays? October 12, 2006

Posted by LearningNerd in Personal.
3 comments

I decided that I’d post about arts, crafts, and other miscellaneous subjects on Fridays, but I haven’t started learning about one of those yet. So, for now, I think I’ll just do more of my Monday and Wednesday posts on Fridays. That won’t be too confusing, will it?

In the meantime, I’ll be thinking about what to learn next. I’m leaning towards visual art — drawing, graphic design, photography. I’ve always found it interesting, but I don’t know the first thing about color, composition, or any of that artistic jargon!

NaNoWriMo and Taking My Own Advice October 10, 2006

Posted by LearningNerd in Personal, Writing, Writing Basics.
3 comments

I found a great list today (50 Strategies for Making Yourself Work), so I added it to my How to Write More Often post. And then it got me thinking: maybe I should listen to my own advice. (Now there’s an idea!) With NaNoWriMo soon approaching, I’ve been meaning to make some time to practice creative writing, but I’ve yet to actually start. I’d like to have some idea of a plot or at least a genre before November 1st. Is that too much to ask of myself?

“No,” says Myself, “That’s not too much to ask! I’ll do that right away — well, after this show. Actually, I have some other stuff to do, too. Maybe tomorrow.”

Then I get frustrated and angry at Myself for procrastinating so much and I wonder why I chose such a lazy person to do my work. Grrr! Looks like I’ll have to do it.

That’s what actually happens, though: I plan to do something, but somehow I act as if I had delegated it to someone else. Why would I let myself get caught up in playing a new video game when I had decided just the other day that I’d set aside more time for writing?

Well, it’s time to take my own advice. I need to designate a certain time of day for creative writing. 9:32? 4:45? Right now?

Eh, maybe later.

How to Enjoy Learning Math October 9, 2006

Posted by LearningNerd in Math, Mondays, Science.
4 comments

I don’t need to explain why people should know math. You know why. But how can we convince ourselves that math is actually interesting? Since I’m going to relearn mathematics on my own, I thought I should start by examining the reasons why I and so many others don’t love math, in order to get some ideas about how to make it more interesting. I asked a few questions on the sci.math Usenet group and on 43 Things. A few mathematicians responded, one of whom has been studying math since the year I was born!

This introduction to mathematics has two parts: Why Don’t People Like Math? and Making Math Interesting.

Why Don’t People Like Math?

Unfortunately, the more common question is “Why do people like math?” As explained by these responders, math simply isn’t taught in an interesting way — and our cultural stigma against it certainly doesn’t help, either.

Same reason a lot of people hate spinach or broccoli. They’ve been forced to have it because, they are told, “it’s good for you”, but they can neither see nor perceive those benefits, and it is being served by mostly uninspired cooks who don’t much care for its taste either. — See full post.

I learned much better on my own than in high school which was a detriment to my learning. — See full post.

Some have had a math teacher in the past who was either incompetent or who hated math…. However, I think the biggest reason why a lot of people hate math is because of a prevailing culture in which it’s “cool” not to know any math. — See full post.

I don’t think math is really the problem most people have, I think how it’s TAUGHT is what people have a problem with! — See full post.

But no-one ever mentioned anything interesting about maths at school. I never learnt about sacred geometry, I learnt to ‘use a compass’; I never learnt aout the concept of ‘relativity’, I learnt greater-than and lesser-than signs. It didn’t work for me. I don’t think the teachers were very inspired or the syllabus was holding them back or something. — See full post.

Making Math Interesting

Like many of the responders, I didn’t like math because of school. Memorization, repetitive worksheets, stressing about grades, cramming for finals — no wonder so many people hate math! But you have to take responsibility for your own education; only you can make yourself interested in a subject. Here are a few ways to help yourself enjoy learning math:

Know what math really is. Math isn’t about arithmetic or memorizing formulas. It’s about problem-solving, deducing truth, and exploring the concepts of change, quantity and structure. Take a glance at Wikipedia’s entry on Mathematics for more details — it’s actually an interesting read.

Learn to apply math. Like I said, math is all about problem-solving; so, use it to solve your problems! This is what makes math a creative subject as well as a logical one. Sure, applied mathematics is quite advanced, but identifying a use for it will motivate you to work your way up. Math classes generally teach students the formulas before giving any examples of how they can be applied, but perhaps it’d be more interesting if you started with a real-world problem that requires math and worked backwards, finding the formulas that you would need. I might try this myself.

Explore the history of math. This won’t help everyone, of course. “Ew, math and history? Are you trying to kill me?” I don’t like history much, either, but it adds another dimension to the study of mathematics. Take a break from math problems and do some reading. Try learning the origin of a formula before you learn how to use it. Who discovered it? How? Why? What I hated most about math class was not having time to answer those kinds of questions. The teacher had to finish the lesson plan every day, and I had to spend my time on homework every night. That’s why I highly recommend learning math (or any other subject) on your own; you can leave room for yourself to stray off topic.

Relate math to other subjects. Math relates to music, art, architecture, business, science, and even philosophy. If you’re interested in any of those, then learn about them while you learn about math. I’m hoping to write posts about all of those subjects in the future, and I plan to find out for myself just how well math can help with them. In the meantime, here are a couple interesting websites: Wolfram Tones: An Experiment in a New Kind of Music (interactive) and A Logarithmic Image Transformation (at least scroll through to see the cool images).

Surround yourself with math enthusiasts. Sure, you sit with a bunch of other students in math class, but the students rarely talk to each other about math. Most of them don’t want to be there, and it shows. Get inspired by joining a group of people that are passionate about math — people who truly want to learn and discuss it. If you want a study partner, feel free to email me!

Hang in for the long haul. I was surprised at how many math enthusiasts said that learning math shouldn’t be fun. They brought up a good point, though: it can’t all be fun. As one responder said here, enjoying math is like enjoying chess; it becomes more interesting over time. Like learning a new language or learning to play an instrument, mathematics doesn’t become truly rewarding until you’ve made a long-term commitment to it.

So, tell me: what do you think of math? Love it? Hate it? How do you think we could make it more interesting?

New Topic and New Posting Schedule October 8, 2006

Posted by LearningNerd in Personal.
5 comments

I’ll be interrupting my series on prewriting techniques to make a few changes around here. I started this blog a couple months ago, and since then I’ve been writing nothing but how-to posts every other day! I haven’t burned out yet, but I’m worried I will — especially with everything else I’ll be doing soon, like getting my driver’s license and then getting my first job (hopefully).

So, three things:

Thing #1: I’m going to start relearning math, since I’ve gotten pretty rusty. (If you know long division, I’d like to hear from you!)

Thing #2: I’ll be posting smaller, more personal posts as well as my comprehensive how-to guides. I don’t know about you, but I need a little variety. And now that I’ll be learning math, I need to let myself learn in smaller chunks, rather than trying to learn everything at once and put it together at the same time.

Thing #3: From now on, I’ll be posting about different subjects on different days of the week, instead of focusing on one subject for weeks at a time and then switching to a new one. My current plan is this: math, science, and technological stuff on Mondays; language, humanities, and social stuff on Wednesdays; and later, art and miscellaneous stuff on Fridays. This may very well change in the future, of course. I’m still not sure if or how I’ll offer a separate RSS feed for each of those days, but I’ll figure that out. (Your feedback would be greatly appreciated!) Depending on how much time I have, I’ll post my smaller, more personal posts on the other days of the week — or, if I’m really busy, I might have to downgrade a major post to a minor one sometimes. We’ll see how it goes.

So, check back on Monday (tomorrow) for my first math-related post, and on Wednesday for Prewriting Techniques: Brainstorming (Listing). See you then!

How to Write More Often September 30, 2006

Posted by LearningNerd in English, Language, Writing, Writing Basics.
3 comments

If an infinite number of monkeys are typing on an infinite number of typewriters (or keyboards) for an infinite amount of time, they’ll eventually reproduce the entirety of Shakespeare’s work. This is known as the Infinite Monkey Theorem.

Similarly, the Write More Often Theorem states that if you spend enough time writing, you’ll eventually end up with something good. Aim for quantity, and quality will follow.

Step 1: Commit to Your Goal

If you haven’t already, see Nine Ways to Commit to Any Goal. You’ll need to be seriously committed to writing more often, since it’s one of those personal goals that are often superseded by other priorities. Don’t let yourself say, “I’ll get to it later.” You need to hammer it into your routine; once you get over that first hurdle, writing more often will be much easier.

Step 2: Join or Start a Writing Group

Getting involved in a community will make writing practice more fun. So, either join a group or get a writing buddy for one-on-one motivation. I’m one of almost 2,000 people on 43 Things trying to Write More.

If you’ve always wanted to write a novel, be sure to join NaNoWriMo (National Novel Writing Month) or the new BlogYoNoMo (Blog Your Novel Month). You might also want to check out Writing.com, one of the largest online writing communities.

Step 3: Make Time for Writing

I read somewhere that there’s no such thing as free time. That’s an excellent piece of advice for those of us who complain about not having enough of it. Instead of looking for nonexistent “free time”, make time. Evaluate and prioritize. Instead of watching TV or browsing through news sites, save a few minutes for writing.

Set a quota, like 30 minutes of writing or two typed pages a day. If writing practice is important to you, you’ll find a way to squeeze it into your schedule. Even if you can only set aside five minutes a day or ten minutes a week, it’s better than not writing at all just because you think you don’t have the time.

Step 4: Incorporate Writing Into Your Routine

Here are a few ideas to make writing a habit:

  • Write as soon as you wake up. Work it into your morning routine, along with brushing your teeth and having breakfast.
  • Write just before you go to sleep. Wind down and clear your mind by getting your thoughts on paper — this is a great time to do some freewriting!
  • Write in small chunks throughout the day, in between your other activities (like before or after meals).
  • Always keep a notebook (or PDA or PocketMod) handy so you can write in your free time. If you don’t mind getting stares, you could even write while you’re waiting in line somewhere.
  • When writing for an extended period of time, take breaks at regular intervals. The rhythm will help you stay focused and keep track of your progress.

Step 5: Try Different Writing Activities

Writing practice should be enjoyable — or at least tolerable. Try starting a blog, keeping a personal journal, freewriting, or just exploring different genres and types of writing like poetry, short stories, news articles, and how-to guides. Contribute to wikis like Wikipedia and wikiHow. Get involved in a collaborative story or start your own. Even writing me an email counts for something!

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