Many aspiring Data Scientists, especially when self-learning, fail to learn the necessary math foundations. These recommendations for learning approaches along with references to valuable resources can help you overcome a personal sense of not being “the math type” or belief that you “always failed in math.”
There is one thing you need to focus on first: how much math for data science. Use these posts as a reference on what you need to learn:
- A good blog post by Josh Ebner of Sharp Sight Labs. He explains the difference between Junior and Senior data scientists, the math you need for data science foundational skills, the difference between data science theory and practice, etc.
- A blog post by Tim Hopper. He was a math major and was also a Ph.D. math student for a year before he became a data scientist. Here is his YouTube talk on how much math you need for data science.
- Rebecca Vickery has a list of math topics you need to learn for data science. This is what I use for reference.
Based on the above as a guide, here is how I learned math:
Step 1: A New Approach To Learning
Learning Statistics was very confusing. I could not connect different parts of the topics. I took a STAT100 from Penn State online (a week), and I still could not remember anything.
Then there is Probability. I have spent days and nights and my weekends trying to get a grip on Bayes’ Theorem, but it was like a mystery I could never solve. I asked myself:
In my personal life, how did I entertain myself in the last few months? Where did I find joy?
I loved watching House of Cards, SUITS, Ghost in the Shell, Billions, and Star Wars. I binge-watched many seasons/volumes of these. I decided to binge-watch, binge-read, and binge-practice Probability for one whole week: Monday to Sunday. I came up with a new plan:
I will not read a mathematics textbook. I will not do any MOOC either. The reason is: both of these come from academic standards designed for graduate studies (3+ years). People in academics are already experts in their subjects, they had been teaching those for years, and hence the MOOCs/books written on the same are one or two semester-long at minimum. What about a guy who does not know anything about those subjects and does not have a semester or two to learn?
How I Learned
- If I didn’t understand something from one place, I quit and went to a second place. Rather than working hard on the same article, blog-post, or video for hours, I focused on working hard for the topic at hand, and that made me flexible. I used another resource and then another till I understood the concept.
- I practiced problems. We can’t learn math by reading and understanding. We need to apply it to the problems. mathsisfun.com has a list of problems with answers.
Step 2: Binge-*
I ended up binge-watching, binge-reading, and binge-practicing many concepts:
- Eddie Woo’s discrete random variable. Total 3 videos (this includes expected value)
- Permutations and combinations from Eddie Woo
- Permutations and combinations from Mario’s Math Tutoring
- Bayes’ Theorem from Math is fun
- Conditional probability, Bayes’ Theorem and others from Investopedia
- Probability distributions from zedstatistics (it explains in terms of the gradient)
- Probability density function (PDF) from Explained by Michael (explains the same in terms of algebra and graphs)
- Cumulative Distribution Function (CDF) from Explained by Michael
- Discrete probability distributions from Jason Gibson of mathtutordvd.com (the best video on what is a discrete probability distribution)
- An excellent StackExchange post on PDF vs PMF
- Math insight link on the idea of PDF from StackExchange post I mentioned above
- MIT OCW lecture on PDF (it is mentioned in the StackExchange post)
Now I can explain all about PDF with the Feynman technique 🙂
I am not the only one who understood this principle of learning. Ken Jee has come up with a similar plan in his YouTube video:
Ken Jee on YouTube.
Step 3: Statistics and Linear Regression
His Linear Regression and Linear Models playlist is what I am watching right now. The guy is great at explaining stuff. He does not waste any time, he keeps things to-the-point and makes sure he reviews before moving ahead, and all that with hardly any code. He strives for clarity and fundamentals, which is the whole point of learning anything anyway. Josh has the best introduction to logarithms and linear regression I have come across so far. And you will love his BAMs and tiny bam and triple BAMs 🙂
Step 4: Linear Algebra
Rather than using traditional learning methods (picking up a book and spending months on it), I recommend you learn from these places, and you can do it in a week. They have all the Linear Algebra you need for data science:
- Linear Algebra from Ritchie Ng
- Linear Algebra from Dive Into Deep Learning
- Linear Algebra from Pablo Caceres (most comprehensive. I did 70% of it because I wanted to learn certain topics. It has a lot of theory, and I think it contains more than enough of whatever you need to know for even for deep learning)
- Linear Algebra from Deep Learning Book
Step 5: Combating The Fear Of Math
There are a lot of learners who fear math. This fear of math does not let us understand and grasp whatever topics we need to learn. We think we don’t have a mathematical mind. Being a genius like Georg Cantor and creating mathematical entities and being able to understand and use math as a tool or as a model for solving problems are two very different things. The former is a gift from the Universe (or God), while the latter is a skill-set. Also, neither of us is a genius and nor we are excellent Harvard or Oxford graduates. We can’t do anything about this limitation. We can do something about attitude and capacity to acquire math as a skill-set. Check these videos out to change your beliefs about math:
Any video you like from The Math Sorcerer (I have watched 30+). Start with these:
- Three Tips For Learning Math on Your Own
- 6 Little Known Reasons Why Self Study is the Key to Success in Math
- Why Do Some People Learn Math So Fast
- How to Overcome Failure in Math
- What does it take to learn math? To live a life? | Miroslav Lovric
- Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh
- How you can be good at math, and other surprising facts about learning | Jo Boaler
- The interesting story of our educational system | Adhitya Iyer
The Last video is about how the Indian education system works. That is where I studied, so I have a bit of bias to include it here. It is an interesting video, by the way.
Pick up a math topic you always wanted to learn, go to math is fun and read it, work through all the exercises. You will lose half of the fear right away by doing this. The explanations have been made so simple and basic that you see through math, no matter what is your age or background.
Step 6: How Not To Forget What You Learn
While you learn all the above by reading and watching and solving problems, you will soon forget 80–90% of it in a week or so. The only way to make learning permanent is: use it daily in your work.
The curse of self-study to become a data scientist is that you can’t use everything you have learned. So, here is a different method:
- Once you learn a topic. Use the Feynman technique next
- Put the heading/title of the topic on a list
- At the end of the week, check your list and use the Feynman technique to explain all topics on the list
Benefits Of This Approach
This approach of Binge-* + Feynman technique has several benefits:
- You save a lot of time because you are not reading an entire book or doing a MOOC, both of which require months.
- You learn only what you need to. Data science is not mathematics. Don’t forget the business value, portfolio preparation, stakeholders, and storytelling using data. They are more important than “learning mathematics comprehensively”.
- Your focus remains on the real-work.
- You learn how to explain. A very useful skill in being able to put your point across in your workplace while respecting everyone around you. It is beneficial in interviews too.
- Since you got the fundamental idea behind certain math topics, you can explore and learn in detail later when you are employed.