Broadening Horizons: From DBA to Data Science #2 Math Fundamentals
In the previous article in this blog series I told you my plans of expending my horizons towards the Data Science field. As I noted in that article my first steps towards Data Science consists of getting my math knowledge up-to-date again on math areas like linear algebra and matrices.
The first thing to note on (re)learning mathematics is that math is, largely, cumulative. What I mean is, you need to understand certain math formulas and rules before you can move on to more “advanced” topics since those advanced topics use the formulas you learned earlier. In one way this is great, reusing the knowledge you learned earlier makes it “stick” better in your brain. On the other hand it means you cannot just jump into certain areas of mathematics without going through the prerequisites first. Now keep in mind that my math knowledge was/is extremely rusty, this is the reason I choose to start at a very low level of math and work my way towards the subjects I am interested in. If you already have a good understanding of the different math subjects you can probably skip a lot of the areas I am currently going through and dive straight into linear algebra, or even skip the math fundamentals completely.
If we take a look at the “Road to Data Scientist” map by Swami Chandrasekaran, math is the first little bullet on the “Fundamentals” track.
Matrices & Linear Algebra are the starting point of our Data Science road trip
Like I said in the paragraph above, my math is in pretty bad shape, so learning linear algebra turned into a kind of sub-road for me. Thankfully, (basic) linear algebra doesn’t have very steep prerequisites and if you are familiar with the basic concepts of algebra you should be able to get the hang of it pretty quickly, or at least, that’s what I heard and read….
Since I wanted to refresh all my math knowledge, up until linear algebra, I made a plan to get there. What I basically did was research what skills are needed/advised before starting with linear algebra and build my own study guide. The list below shows the math subjects you should be familiar with before diving into linear algebra:
- Linear equations
- Quadratic equations
The list starts at the typical algebra subject, linear equations. For me this was a logical starting point since I was already pretty familiar with all the “pre-algebra” subjects like arithmetic’s, fractions, etc. If you aren’t on that level yet I can highly suggest going through Khan Academy’s Algebra Basics Foundations which you can find here https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations.
For all the three subjects I listed above I can recommend using Khan Academy as well if you prefer watching videos to reading a book. The Algebra I course contains all the three subjects mentioned above at https://www.khanacademy.org/math/algebra. If you want to go a bitter deeper into these topics the Algebra II course covers Polynomials and Quadratic equations as well and can be found here https://www.khanacademy.org/math/algebra2.
Next to using Khan Academy I also use a math book to learn from. One of the advantages of a traditional book (in my case) is that it has way more practice content than Khan Academy. Math requires a lot of practice so I definitely recommend you practice as much as possible. Still, I frequently visit Khan Academy when I can use some extra help because the book isn’t directly clear enough. That’s the main advantage of those videos, you can easily follow every step the instructor is doing and that makes learning easier when dealing with complex formulas for instance.
Right now I am working my way through the Polynomials topic and I spend the last couple of evenings on understanding the Binomial Theorem.
Binomial Theorem. It looks complicated but actually isn’t that bad
I think the main advantage of math is, the moment you truly understand the way a formula or calculation works, it isn’t very difficult anymore. Let me explain a bit more. When I am learning math it can take several hours until the pieces fall in place. For instance, the Binomial Theorem pictured above took me around 2 -3 hours to understand. When I first looked upon the formula it looked like magic and I had no idea what was happening. But after a lot of practice it suddenly “clicked” and I understood the reasoning and workings of the formula. I guess that’s the trick with math, keep practicing until you understand what you are doing.
Vectors, matrices and linear algebra
Vectors and matrices are very much a part of linear algebra, but as the paragraph heading suggests, they also deserve their own attention. Since I am getting closer and closer to linear algebra, I already examined some study resources. I noticed that the math community is a bit divided in the learning order for linear algebra. Some people say vectors and matrices will be discussed in enough detail as soon as you start work on linear algebra, others advice to start learning vectors and matrices before going into linear algebra. Either way, the list below shows some of the resources I have found to learn more about these topics:
- Vectors – Khan Academy: Vectors
- Matrices – Khan Academy: Intro to matrices https://www.khanacademy.org/math/precalculus/precalc-matrices
- Linear Algebra – Khan Academy Linear Algebra
As you can see these are all videos from Khan Academy. Another great resource, which is suggested frequently online, is the linear algebra video lectures by Prof. Gilbert Strang of MIT which can be found on the MIT website (http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/) or on YouTube (https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D).
One thing to keep in mind with the lectures of Prof. Strang is that he start with matrices while many of the other resources usually start with vectors.
Prof. Strang also wrote a book about linear algebra which is highly rated: “Introduction to linear algebra” (http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716). Just like Prof. Strang’s video lectures, the book also start with matrices instead of vectors.
An alternative to Prof. Strang’s book is David Poole’s “Linear Algebra: A Modern Introduction” (http://www.amazon.com/Linear-Algebra-Introduction-Available-Enhanced/dp/0538735457) but it has a much steeper price tag ($284 compared to Strang’s $65).
Hopefully this article gave you some pointers where to start with the math required for Data Science and I hope you can use some of the resources I have included in this article. I am still working through all this math myself, so if I run into additional resources I will include them in this article!