# Maths in IT #2: Venn diagrams

Hey everyone, welcome back to part two of the Maths in IT series. I got a lot of positive response, so I guess I should just keep doing what I was already doing. This post will continue where part one left off, so if you haven’t read it I suggest you do so now before continuing.

1. Maths in IT #1: Basic set theory
2. Maths in IT #2: Venn diagrams
3. Maths in IT #3: Algebra of sets
4. Coming soon…

Here’s a quick cheat sheet with symbols I’ll use in this article:
Explicit definition: $A = \{a, b, c\}$
Implicit definition: $A = \{x | \text{ x is a letter in the alphabet}\}$
a is an element of A: $a \in A$
a is not an element of A: $a \notin A$
A is a subset of B: $A \subset B$
Empty set: $\emptyset$

## Venn diagrams

As promised we’ll use this post to combine sets. Before we do that let’s take a look at how to visually represent collection. We can do this using a Venn diagram. A Venn diagram is about as simple as it gets (although they can be pretty complex too). Each set is represented by a circle. The diagram can illustrate relationships between the represented sets.

Let’s look at an example. We have two collections, $A = \{a, b, c\}$ and $B = \{d, e, f\}$. Let’s show them in a Venn diagram.

When two sets have no shared elements, or for every $x \in A$ goes that $x \notin B$, we say the sets are disjoint.

Now suppose $A \subset B$ (A is a subset of B). We can show this in a Venn diagram and you’ll recognize it immediately.

When A is a subset of B then B overlaps A completely.

In the next sections we’ll combine sets and use Venn diagrams to visualize what elements we’re interested in.

## Intersection

So suppose we have two collections, $A = \{a, b, c, d\}$ and $B = \{c, d, e, f\}$. If I asked you which elements are in both A and B you’d answer c and d.

This is called the intersection of A and B.
We can write this as $A \cap B$.
In this example we can say $A \cap B = \{c, d\}$
More formally we say that $A \cap B = \{x | x \in A \text{ and } x \in B\}$.
And the symbol for “and” is actually $\land$, so to formalize it completely:

$A \cap B = \{x | x \in A \land x \in B\}$

Phew, that looks a whole lot like maths! You should read that as “the intersection of A and B is the collection of every x where x is an element of A and x is an element of B.”
And here is the Venn diagram, which visualizes this nicely. The intersection is the part in the thick black line where A and B overlap.

With an intersection we can give a formal definition of disjoint sets. When $A \cap B = \emptyset$ then A and B are disjoint.

Furthermore we can say that for any collection A goes that $A \cap \emptyset = \emptyset$.
Also $A \cap A = A$.
And when $A \subset B$ then $A \cap B = A$ (check the subset Venn diagram).

## Union

The intersection of two sets is the set of elements x where x is in A and B. Likewise, the union of two sets is the set of elements that are in set A or B. So when we have $A = \{a, b, c, d\}$ and $B = \{c, d, e, f\}$ then the union of A and B is $\{a, b, c, d, e, f\}$ (no doubles).

We can write a union of A and B as $A \cup B$.
Like $\land$ is the symbol for “and” $\lor$ is the symbol for “or”. So the formal definition of union is as follows:

$A \cup B = \{x | x \in A \lor x \in B\}$

Read that as “the union of A and B is the collection of every x where x is an element of A or x is an element of B.”
In a Venn diagram the union is basically just both sets (the part in the thick black line).

Unlike an intersection, a union of disjoint sets is not an empty set (notice that both sets have a thick black line).

Now for any collection A goes that $A \cup \emptyset = A$.
And, again, $A \cup A = A$.
Also when $A \subset B$ then $A \cup B = B$ (check the subset Venn diagram).

## Universe and Complement

When we’re talking about sets we’re usually not talking about that set in isolation. When I tell you that non-smokers live longer you understand that they live longer compared to people that do smoke. And you also understand that non-smokers and smokers combined make up for the worlds population. In this case we’re saying that we have a set of non-smokers in a universe of all people. We denote a universe with the capital letter U.

For every set $A_1, A_2, A_3... A_n$ goes that $A_n \subset U$.
That makes sense as U represents all elements we wish to consider for our case. No collection can ever contain an element that is not a part of all elements.

In a Venn diagram we draw a universe as a rectangle in which all our sets are drawn. In the following example N is the set of non-smokers and U is the universe containing all people.

Now with the notion of a universe we can say we want all elements that are not in any collection A. We call this the complement of A and we write it as $A^c$. In the following Venn diagram the white part represents $A^c$.

We can now formally define the complement:

$A^c = \{ x | x \in U \land x \notin A \}$

It goes without saying, but $\emptyset^c = U$ and $U^c = \emptyset$.
A little less obvious is that $(A^c)^c = A$. It makes sense though, as we first take everything that isn’t A (the complement of A) and then we take everything that isn’t in the resulting set, but that is A. Try drawing it in a Venn diagram and you’ll see what I mean.

A complement relative to a universe is called an absolute complement. A complement can also be relative to other sets. For example, when no universe is defined and we have sets A and B then the relative complement of A in B is the set of elements of B that are not in A. This takes the form of $B \cap A^c$ or $A \setminus B$.

$A \setminus B = \{ x | x \in B \land x \notin A \}$

In a Venn diagram $A \setminus B$ look as follows:

## Combining sets

We can now combine sets using intersection, union and complements. For example, let’s say our universe U is all living creatures on earth. Within U we have sets M, containing all mammals, B, containing all birds, and E, containing all animals that lay eggs. Formally:
$U = \{ x | \text{x is an animal} \}$
$M = \{ x | x \in U \land \text{x is a mammal} \}$
$B = \{ x | x \in U \land \text{x is a bird} \}$
$E = \{ x | x \in U \land \text{x lays eggs} \}$
Giving the following Venn diagram we can already draw some conclusions.

We can see that all birds lay eggs. Some mammals lay eggs too. No animal is both a bird and a mammal. As you see Venn diagrams can be really useful.
Now suppose we want the set of all mammals that lay eggs and also all birds. This is the collection $(M \cap E) \cup B$. That is, we take the intersection of M and E and union the result with B. In a Venn diagram we can see this collection (the red colored parts).

Now we can get every combination of sets using intersection, union and complement. It’s not always easy, but it’s possible.

## Some code

As promised I’m going to keep things practical. So what’s the practical use of all this? Well, most languages let you work with exactly these functions!

For example, take a look at this SQL expression.

(SELECT 1
UNION SELECT 2
UNION SELECT 3)
INTERSECT
(SELECT 3
UNION SELECT 4)

What will that return? It returns only 3 because 3 is an element of both collections. This example also shows the UNION operator. Basically this is the set $(\{1\} \cup \{2\} \cup \{3\}) \cap (\{3\} \cup \{4\})$.

And SQL knows complement too.

(SELECT 1
UNION SELECT 2
UNION SELECT 3)
EXCEPT
(SELECT 3
UNION SELECT 4)

What happens here is that we have (an implied) universe $U = \{1, 2, 3, 4\}$ and EXCEPT is the complement. So this query is basically the formula $\{3, 4\}^c$.
We could also say that U is not defined and this is the relative complement of $\{3, 4\}$ in $\{1, 2, 3\}$: $\{3, 4\} \setminus \{1, 2, 3\} = \{1, 2\}$.

But what about C#? In my previous post we’ve seen HashSet<T>, but I’m not going to use that now. Instead I’m just going with a List<T> as LINQ provides various extension methods for working with sets. Notice that HashSet<T> has its own methods in addition to the LINQ methods.

List<int> a = new List<int>();

List<int> b = new List<int>();

List<int> intersect = a.Intersect(b).ToList();
List<int> union = a.Union(b).ToList();
List<int> except = a.Except(b).ToList();

You may wonder what that looks like in Haskell (since I’ve shown you Haskell the last time too), but it’s not really that different.

Prelude> import Data.List
Prelude Data.List> [1, 2, 3] intersect [3, 4]
[3]
Prelude Data.List> [1, 2, 3] union [3, 4]
[1,2,3,4]
Prelude Data.List> [1, 2, 3] \\ [3, 4]
[1,2]

I’ve actually needed this stuff in my day to day work. It’s not that hard and sometimes it’s an explicit business requirement. For example I needed all sales orders from The Netherlands, Belgium and Luxembourg (the BeNeLux). That’s really just a union! And I’ve needed intersect too, give me all Dutch customers that are not in some list of customers. And how about all non-Dutch customers? That’s just the complement!

Next time I’d like to continue with algebra and algebra of sets in specific. Does that sound like it will give you nightmares? Don’t worry, I’ll be gentle!

See you next time!

# Maths in IT #1: Basic set theory

Welcome back everyone. Today I have a little something different for you. No new language or framework, but something that’s been around for millennia: maths.
When asking programmers about maths you’ll find two kinds of people, those who say you don’t need maths to be a good programmer and those who say maths is essential. Personally I think both are true. For some applications and industries you really don’t need advanced maths, but go into robotics, machine learning, statistics, or that kind of thing and you’re going to need maths, lots of it. And whether you need it or not, computers, programming languages and databases all wouldn’t exist without maths.
For now, let’s put it this way: knowing a thing or two about maths gives you an edge as a programmer!

Maths is everywhere: physics, chemistry, biology, economy and, yes, even in the arts! For this series I’ll focus on the maths we need in IT. I don’t know how much entries it’s going to have or what I’ll be discussing (and what I won’t be discussing), but I’ll be sure to keep it somewhat practical. No prior maths knowledge is assumed. Don’t worry, I’ll still post about code once in a while too!

1. Maths in IT #1: Basic set theory
2. Maths in IT #2: Venn diagrams
3. Maths in IT #3: Algebra of sets
4. Coming soon…

## Collections

Do I need to tell you why we should study collections? You probably use them in your code every day in the form of arrays, database tables, lists or hash tables. What you probably didn’t know is that collections have a lot of mathematical theory! Since collections are very important in both maths as in programming I’m going to start this series here. More specifically we’re going to talk about sets.

A set is an unordered collection containing only distinct values.

Let’s look at an example of a set in real life. Do you collect anything? Maybe you collect old records, each record in your collection can be uniquely identified and doubles are for trading or selling. Also, no matter in which order you put the records on the shelf, it’s still the same collection of records. So a record collection is really a set.

Likewise we can have a collection of paintings or stamps. Another collection is an alphabet, for example the English, Russian or Greek alphabet. Using these alphabets we can construct a language. We have natural languages (like the ones I just mentioned) and formal languages. Programming languages like C#, Java, C or Haskell are examples of formal languages.

A collection in maths is usually indicated by a single suggestive capital letter, such as $R$ for records, $S$ for stamps or $A$ for alphabet. If we have more than one collection we can use index notations to uniquely identify them: $A_{1}, A_{2}, A_{3}$

The notation for a single collection containing elements $a$, $b$ and $c$ is $\{a, b, c\}$. This is called the explicit definition. We can now declare a collection $A$ as $A = \{a, b, c\}$.
And of course we can have a collection of collections: $C = \{\{a, b\}, \{c, d\}, \{a, c\}\}$. Notice that collection $\{a, c\}$ is unique even though $a$ and $c$ are already elements in other collections.
The following set of sets isn’t valid: $\{\{a, b\}, \{b, a\}\}$. Because the order of elements in sets is ignored this set contains the same set twice, but sets also must have distinct values.
Now let’s say we have English alphabet $E$, Russian alphabet $R$ and Greek alphabet $G$. The collection of alphabets is written as $\{E, R, G\}$.

Now we want to indicate that $a$ is an elements of $E$. We do this using the following syntax: $a \in E$.
To indicate that $\lambda$ (the Greek letter lambda) is not an element of $E$ we use notation: $\lambda \notin E$.

We can compare collections. Collections are considered to be equal when they contain exactly the same elements, no more and no less. $\{a, b, c\} = \{a, b, c\}$, $\{a, b, c\} = \{c, b, a\}$ (remember, order is ignored), $\{a, b, c\} \neq \{d, e, f\}$ and $\{a, b, c\} \neq \{a, \{b\}, c\}$ (the collection $\{b\}$ does not equal $b$).

So far we’ve seen only explicitly defined collections. We can also implicitly define collections. This is especially useful when a collection contains too many elements to write down. For example a collection containing all countries on Earth. The notation for such a collection is as follows: $\{x | \text{x is a country on Earth}\}$. You should read that as “the collection consisting of all (objects) x for which x is a country on Earth”.
Generally we can say that an implicitly defined collection is in the form of $\{x | P(x)\}$ where, in this example, $P(x)$ is the statement that $x$ is a country on Earth. Actually $P(x)$ is a function taking parameter x and returning whether x is or isn’t a part of the set. We’ll look at functions in a later blog post.

To indicate how many elements are in any given (finite) collection we can use notation $|A|$. So $|\{a, b, c\}| = 3$ and $|E| = 26$ (where E is the English alphabet). Of course this is only possible when our collection is finite (we can count the elements).

If a collection is empty (it contains no elements) or some collection $A = \{\}$ we can use a special symbol $\emptyset$. And of course $|\emptyset| = 0$ (an empty set has $0$ elements).

When we allow the same element to appear in a collection more than once and we start taking the order of elements into consideration we’re speaking of a row. The syntax for a row is simply putting the elements next to each other. For example, using the set $\{a, b, c\}$ we can make the rows a, ababc, baac, caab, but not baad (because d is not in the set).

## Infinite collections

So far we’ve looked at finite collections.  Let’s look at some infinite collections now. Consider the collection of all numbers: 1, 2, 3, 4… In theory we can always add 1 to any number, so we can never stop counting. A few of these collections are so important that they got their own symbol.
First we have the natural numbers: $\mathbb{N} = \{0, 1, 2, 3, ...\}$.
If we add negatives to the collection we get all whole numbers, or integers: $\mathbb{Z} = \{..., -3, -2, -1, 0, 1, 2, 3, ...\}$.
If we also allow fractions, like $\frac{1}{2}$ (a half) or $\frac{1}{4}$ (a quarter) then we have the collection of rational numbers $\mathbb{Q}$.
Not all numbers can be expressed in fractions, for example pi ($\pi$, the surface of a circle with radius 1) or $\sqrt{2}$. When we want to include those numbers we get the collection of real numbers $\mathbb{R}$.

Now suppose we want all positive natural numbers, so 1, 2, 3… (excluding 0). We can indicate this with $\mathbb{N}^+$. Likewise, all negative numbers -1, -2, -3… can be indicated using $\mathbb{Z}^-$. And of course we can use $\mathbb{Q}^+$, $\mathbb{Q}^-$, $\mathbb{R}^+$ and $\mathbb{R}^-$ to indicate positive or negative fractions and real numbers too.

And we can now define new infinite collections using implicit definitions. The collection of all even numbers, for example, can be defined as follows: $E = \{ x | x \in \mathbb{Z} \text{ and x is even}\}$.
So here $E$ is a collection consisting of all x for which x is an element in $\mathbb{Z}$ (all integers) and x is even.

## Subsets

If a collection A contains elements that are all elements of another collection B we say that A is a subset of B. For example $A = \{a, b, c\}$ is a subset of $B = \{x | \text{x is a letter in the English alphabet}\}$ because a, b and c are all letters in the English alphabet.

More formally we can say that if A and B are both collections and for every $x \in A$ applies $x \in B$ then A is a subset of B.

We can write this as $A \subset B$. Since, in the previous example, A does not contain all letters in the English alphabet B we can also say that B is not a subset of A, this is written as $B \not\subset A$.

Given the above definition we can also say that $A \subset A$ or A is a subset of itself. The empty collection $\emptyset$ is a subset of all collections (including itself).

When a collection $A \subset B$, but $A \neq B$ then we say that A is a proper subset of B. We may write this as $A \nsubseteq B$.
Sometimes you may see the notation $A \subseteq B$ to indicate that A is a subset of B that may or may not be equal to B.
I’ll simply use $A \subset B$ throughout the series).

When $A \subset B$ and $B \subset A$ then $A = B$.

In a similar manner we can say that B is a superset of A if A is a subset of B. This is notated as $B \supset A$ (it’s the subset-symbol reversed). And of course we can say $B \supseteq A$ to indicate that B is a superset of A that may or may not be equal to A. For a proper superset we may use $A \nsupseteq B$ notation.

And when $A \supset B$ and $B \supset A$ then $A = B$.

## Some code

I promised I’d keep this series somewhat practical. So let’s look at some code. Consider the following C# sample using your favorite .NET collection class.

List<int> list = new List<int>();
int thirdItem = list[2]; // 0-based index.

The list now contains the items 1, 2, 3 and 1 again.  We can also get the item at the nth position, which is only useful when we know the order of the elements within the list. Based on that we can conclude that the List class in .NET is not a set. If we want a set in .NET we can use the HashSet class instead.

HashSet<int> set = new HashSet<int>();
{
}
//int secondItem = set[1]; // Doesn't compile.

Because a set only contains unique items a hash of each item can be generated which means that lookup time for sets is much faster than that of lists (especially when the size of the list grows). The HashSet<T> can be compared to the Dictionary<TKey, TValue> class, but without values.

Unfortunately C# doesn’t know list generators. Working with infinite collections isn’t very do-able in C# either. Let’s say you’d like to get all positive even numbers, $E^+ = \{ x | x \in \mathbb{N}^+ \text{ and x is even}\}$. We have a few problems. First $\mathbb{N}$ isn’t available in C#. We could take Int32.MaxValue (but that threw an OutOfMemoryException). So let’s just take all positive evens smaller than or equal to a million.

IEnumerable evens = from x in Enumerable.Range(1, 1000000)
where x % 2 == 0
select x;
List evaluatedEvens = evens.ToList();

Something like that is really the closest we can get in C# without going through a lot of trouble.

And at this point I stand corrected. Paulo Zemek pointed out that it’s actually pretty easy to work with infinite collections by utilizing the yield keyword. The next (Console Application) example illustrates this (although int will eventually overflow…).

static void Main(string[] args)
{
foreach (int i in Evens().Take(10))
{
Console.WriteLine(i);
}
}

static IEnumerable Evens()
{
return XToInfinity(1).Where(i => i % 2 == 0);
}

static IEnumerable XToInfinity(int start)
{
int current = start;
while (true)
{
yield return current;
current++;
}
}

That’s still a lot of typing though…

Let’s take another language that solves these kinds of problems a little better, a language that is a little closer to actual maths, Haskell.

evens = [ x | x <- [1..], x mod 2 == 0]

And there you have it. Notice that the code is actually pretty close to the mathematical notation. Take each x where x is an element of [1..] (one to infinity) and where x is even.
We can easily take the first 10 items of this infinite collection without crashing the program or encountering out of memory exceptions.

*Main> take 10 evens
[2,4,6,8,10,12,14,16,18,20]

This isn’t a blog on Haskell, so I can’t really expand on what it does, but I can say that Haskell is a “lazy” language, which means it doesn’t evaluate the items in the list until you actually need them. In this case it will only evaluate the first ten items of evens, keeping it from hogging our memory and CPU.

That’s it for now. We’ve had a very basic introduction to sets, but if you’re not familiar with this stuff it gets hard pretty quickly. So let’s take it nice and easy. Next time we’re going to combine collections and take a look at the Venn diagram.

Hope to see you next time!

# How to learn and polyglot vs. specialist

Welcome (back) to my blog. This weeks blog is going to be a little different than my other blogs. Unfortunately I’m a little short on time this week, too short to write up a small web page using some cool technology and write about it too. However, I still want to deliver you the blog you may have been waiting for.
If you read my blog every week, or at least regularly, please drop a line in the comments and let me know, I greatly appreciate it!
I also Twitter other articles that you might like @sanderrossel, so be sure to follow me if you haven’t done so already.

So what do I have in store for you this week? Well I recently got a question from someone who asked me what’s the best way to learn a new technology. I’ll answer that question at the end of this article, but first I’ll tell you why I think you need to learn new technologies from time to time.

## Specialized vs. polyglot

One of the reasons I want to write about why you need to learn and how to learn effectively is because lately I’ve been in a few discussions with people about being a specialized programmer versus being a polyglot, or all-round programmer.

A few months ago I switched jobs. One of the reasons for me was that my previous employer wanted everyone to specialize. My specialization would be C# WinForms and Entity Framework, while other colleagues specialized in SQL Server. Sounds nice, right? Except that, next to a C# certificate, I also have a SQL Server certificate that wasn’t going to see any use in that setup… Besides, I had seen quite a bit in C# WinForms and I wanted to move on.
So I applied for another job at another company. Their motto is “we specialize in being all-round.” Put differently, everyone does everything. At one time you may be working with C# and SQL Server, while at another time you may be working with Java and Oracle. Now that’s something I could get into!

Let’s first define these terms, specialized and all-round, or polyglot, and see why you would want to be the one or the other.

I don’t think many people will disagree with me when I say a specialist is someone who has gathered a large amount of knowledge and experience in a specific field. The more specific this field the more specialized you are. Your expertise may be C#, which is a little broad, hardly an expertise actually. C# WinForms with Entity Framework, my specialization, is more specific. You could be as specific as specializing in a single Control, for example the C# WinForms DataGridView. Now that’s a specialization.
I recently read the book Soft Skills by John Sonmez from Simple Programmer. It’s a great book that I can really recommend. John talks in length about why you really need to specialize. In short, if someone has a very specific problem and you specialize in that specific field you’re worth a lot to that someone. The more you specialize the smaller the chances you’ll find someone with the exact problem you can solve, but that also means that the people who have such a specific problem will have trouble finding someone to fix it for them. Therefore, once these people find you (or you find them), and you are one of the few who can really solve their problem, they are going to want you, no matter the costs (to some degree).

So how about all-round, or polyglot. You may have heard about the polyglot programmer and how amazing they are. But what’s a polyglot anyway? The dictionary describes a polyglot as someone who speaks several languages. So a polyglot programmer is someone who knows his way around multiple programming languages. Let’s extend that a bit and say a polyglot programmer also knows multiple paradigms (Object Oriented Programming, Functional Programming,  Aspect Oriented Programming…) and probably lots of libraries too, because different languages require different libraries.
The good thing about being a polyglot is that each new language or technology is easier to learn. Is this a managed language? You’ve seen it before. Is it unmanaged? You’ve seen it before. C or BASIC syntax? You’ve seen it all before! So, in theory, you could work for just about anyone. Except that you’re probably not very good at all of these languages, so why would someone hire you over someone who has the exact knowledge they need? But when you think about it, how often do clients know exactly what they want or need.
On the other hand, once systems become real complex and need different languages, databases and paradigms in different parts of the system, well, you’re good to go.

It seems the world is pretty divided on which is best. As said, John Sonmez really urges you to take on a specialization, and it could really work out for you. But if you Google for “polyglot programmer” you’ll find websitesblogs and videos dedicated to that subject as well (both for and against)…

## Why not both?

So here’s my view on both specialized and polyglot programming. They’re both great and everyone’s right. I’m usually not that politically correct, so let me explain.

Expertise is great, right? When you’re doing any kind of serious development you’re going to run into issues that can only be properly solved if you really know your stuff. For example, in WinForms you may need to create your own user control. That’s really specialized work, you really need to know the design time implications associated with creating controls. As coincidence would have it just last week I inherited a Form with a DataGridView on it. Upon setting some property I populated the DataGridView with columns. What happened at design time? Everytime I did a build or I opened the WinForms designer it would re-populated the DataGridView, but didn’t actually throw away the old columns! Before I knew it I had over 100 columns on my Form! So apparently I’m no specialist in WinForms Control development. Luckily I was knowledgeable enough to recognize the problem and fix it right away. How did I get that knowledge? You may not like the answer, but I’ve been building non-trivial WinForms apps for over four years and I’ve been reading up on books and blogs dedicated to WinForms development. Could I have solved my problem without knowing what I know? Sure, just duplicate a lot of code in every Form I have so I don’t need Form inheritance. Or maybe make a fix for the bug, which then requires another fix, etc. etc… And I’ve seen these ‘solutions’ lots of time!

So if you need four years to learn any language and/or framework to be able to build non-trivial applications with it there’s not much sense in being a polyglot, right? That’s just going to take ages and by the time you’ve mastered your second language your knowledge on the first will be outdated. Well, here’s the trick, you don’t have to be that sufficient in any language. I get my daily work done in either Visual Basic.NET or C# with WinForms, and more recently ASP.NET MVC, Entity Framework and SQL Server, and I’m pretty good at all of them. You could say that’s my specialization and it comes kind of natural as I’m working with them every day from 9 to 5. Once in a while I may need to read up on some stuff at home, and you need to keep challenging yourself, but overall, when you’re working with a technology that much you tend to get a little good at it.
To become truly specialized, an authority in your line of work, you’d need to put a lot of free time in it as well. But what if you spend that free time on learning other technologies? Well now we’re going a little polyglot while also being a little specialized! And here’s the good part, being a polyglot will make you a better specialist!

Wait, what? That sounded pretty contradicting. Let me put it this way. When all you’ve ever known is C# are you truly aware of its strengths and weaknesses?
I’m currently learning Haskell, a functional language, for my university study. When I saw the Haskell implementation of the quick sort algorithm that made me question all I ever knew about C# and object oriented programming. You may be familiar with the C# implementation, or you could maybe guess what it looks like. I can’t post it here, because it’s simply to big, but a quick Google search will give you lots of different implementations, like Iterative Quick Sort (haven’t checked if it’s actually the best out there). Beware that a lot of what you’ll find is recursive, which will give you a StackOverflowException in C# for large lists.
Now here is the Haskell implementation.

qsort []      = []
qsort (x: xs) = qsort smaller ++ [x] ++ qsort bigger
where
smaller = [a | a <- xs, a <= x]
bigger = [a | a <- xs, a > x]

You don’t actually have to understand it, but the takeaway is that this Haskell implementation is so much more concise, and ultimately readable, than any C# implementation you can come up with.
But there’s more. Are you using .NET LINQ? Well, where did you think that came from? Yes, the functional programming paradigm! Functional languages are also pretty good at multi-threading because values are immutable.
Does that make you want to throw C# out of the window and do everything in Haskell (or, since you’re a .NET dev, F#, or Scala if you’re a Java dev) from now on? No, and neither should you. But you should see what’s out there and if there’s some language or technology that solves your problem better than the technology you’re (ab)using now. Even if there isn’t you’ll have gained new insights that might help you on your current job. Just by taking a more functional approach in your object oriented language can help you in writing better and more readable code.

How about another example? So as said I do quite a lot of work in SQL Server. I have plenty of experience in developing databases (I even got certified) and some experience in maintaining them (I’m what they call an accidental DBA). SQL Server was just that one tool that could solve all my problems. And then I spend just a few evening with MongoDB (I wrote a blog about that, A first look at NoSQL and MongoDB in particular). NoSQL just blew my mind. All the troubles I had with SQL Server (and SQL in general), that I took for granted, had been solved by other databases. Those few evenings with NoSQL gave me another perspective on SQL and, I dare say, made me a better SQL programmer because I was now much more aware of SQL’s strong and weak spots.

One last example. I started out as a Visual Basic programmer. Many of you now shudder in disgust. I never understood what all the VB hate was about. Sure, a lot of bad VB has been written, especially pre-.NET VB. But I’ve seen equally bad code in C# as well. And nowadays VB does almost everything C# does and vice versa. It’s just a different syntax. Now this may come as a surprise to some, but not all languages use curly braces! VB is one such language, and because I know VB learning another such language may be easier. But there’s more. In VB there’s a thing called “Option Strict”, which is set to “Off” by default. This makes VB a lot more “forgiving” than C#. For example, the following code would run fine (except for the call to MethodThatDoesNotExist() which gives a runtime exception).

Dim s As String = 42
Dim i As Integer = "42"
Dim o As New Object()
o.MethodThatDoesNotExist()

You may not like it, but this taught me a lot about implicit and explicit casting and late and early binding (which helped me get into JavaScript later). And on the subject of late binding, there’s times when it’s pretty handy. In fact, C# introduced the dynamic keyword for it in .NET4.0. Well guess what, as a VB programmer I was way ahead of you! Optional and named parameters, introduced in C# in 2010, came straight from VB. And what about those new cool Exception filters in C# 6.0? VB has had them for years.
Of course the same can be said for C# features that were introduced in VB, like Iterators (yield), but the takeaway is, that even these two very closely related siblings take stuff from each others, and knowing one can make you better at, or more prepared for, the other.

So why not spend a few hours with some new language once in a while? Just get something up and running in a language you’ve heard about, but don’t know yet, use a framework you haven’t used before, or get a taste of some NoSQL database. Make sure you pick one that’s popular as you’ll be able to find lots of documentation.

## How to learn

So I may have convinced you that learning new languages, paradigms or frameworks can be fun and that it can actually help you get an edge as a programmer. But how do you learn a new language or framework? I mentioned Soft Skills before, but I am going to do so again. In this book John Sonmez has a ten step plan for learning just about anything as quickly as possible. I know it works, because John’s approach to learning closely resembles my own method. So here’s what to do.

Read up on the topic you’re interested in. Get a feel of what’s important and what you need at the very least to get started. Also get a feel of how big this thing is you’re learning. Is it a few days of work, or will years of study go into this? Don’t spent to long on this though.
Once you have a picture of what it takes to become proficient at whatever it is you’re trying to learn determine what parts you want to do. Set some bigger goal you want to reach and some smaller goals that will take you there.
After that find resources, books, blogs, videos, whatever it takes to get your started. And then filter them so you can get started with reaching your first goal.
For most languages and frameworks my first goal is to set up the environment. Once I’ve done that I need some “Hello, world!” kind of application, so I know I can actually write and run code with it. Usually that’s not too difficult with all the pre-reading I’ve done.
After that just play around a bit, get familiar with the syntax, the libraries, the tools, etc. After that you can do whatever you want. I’d repeat those last few steps, keep setting new, small goals, and just get there.
Don’t spend to much on any tool you won’t be using though. Just get a feel for it and see how you can use certain elements from it in your day to day programming.

That’s my approach to learning. John does a much better job at explaining it than I do, so I suggest you buy his book, or order his course 10 Steps to Learn Anything Quickly.
Now John’s 10th step, one I didn’t have, is rather interesting. Teach! Of course I’ve been doing that by writing my articles, but I’ve never thought about it as a part of the learning process. So how can you teach? Well, start a blog! And, as you might’ve guessed, John has a (free) course on that as well. If you’re interested in learning and teaching I suggest you sign up for his three week email course on blogging.

I’ve successfully used this approach (including teaching) while learning web development. Try learning that, “web development”. No way you can pull that off! Web development is such a broad topic you’ll be overwhelmed, discouraged, and, ultimately, you’ll probably fail. Unless you start by learning HTML, then learning CSS, etc. Just take it one step at a time.
And you can see how I did this by reading up on my series on web development. In eight easy lessons you’ll have learned the ‘impossible’ task of “learning web development” and it wasn’t even hard.

I did the same with NoSQL. First I needed to know what NoSQL is. So apparently there’s different ‘flavours’. Then I needed to pick one, so I picked the one that’s closest to SQL (easy starting point!). Then I picked a database, MongoDB was listed as most popular, so that means I can find a lot of stuff about it. Then I needed to know how I can install it, after that run it, then try to insert some data, read it, edit it, read it again, delete, etc. And finally try doing that from C#, first connect, then read, then edit. Step by step. I’ve blogged about the result, A first look at NoSQL and MongoDB in particular.

There you have it. Get started now. Pick up that language you’ve been interested in, but that you never got around to doing. It might benefit you in more ways than you know. Now is as good a time as any. And on that subject, John’s book Soft Skills also talks about how to stop procrastinating and just do what you should be doing (actually the book talks about a lot).
Next week I’ll be back with hopefully a ‘normal’ technical article again. So stay tuned!

Happy coding!