[00:00] Do you want to become a data scientist or machine learning engineer, but you feel intimidated by all the math involved? I get it, I've been there. I stepped out of high school after 10th grade, so I never learned any math beyond trigonometry in school. When I started my journey into machine
[00:13] learning, I didn't even know what a derivative was. Fast forward to today, and I'm an applied scientist at Amazon, and I feel pretty confident in my math skills. I've picked up the necessary math along the way using free resources and self-directed learning. Today I'm going to walk
[00:25] you through some of my favorite books, courses, and YouTube channels that helped me to get where I am today, and I'll also share some study tips on how to study effectively and not waste your time struggling and being bored. So, let's get through it. First, let's address a common question.
[00:38] Do you really need to know the math to work in machine learning? The short answer is, it depends on what you want to do. For research-heavy roles where you're creating new machine learning algorithms, then yes, you obviously need to know the math. But if you're asking yourself if you need to learn math, chances are that's not the
[00:52] kind of job you're looking for. For practitioners, most of us in the industry, you can be totally competent without knowing all the underlying details, especially as a beginner. At this point, libraries like NumPy, Scikit-Learn, and TensorFlow will handle most of the heavy lifting for you.
[01:05] You don't need to know the math behind gradient descent to deploy a model to production. If you're a beginner trying to get into machine learning, in my opinion, it's not strategic to spend a bunch of time memorizing formulas or studying linear algebra. You should be spending that time building things.
[01:18] Train a simple model, explore your data, build a pipeline that predicts something fun. That said, there are moments where knowing the math really helps. Here are a couple of examples. So imagine you're training a model, and it's just not converging. If you understand concepts like gradients and optimization functions, you'll know whether
[01:33] to adjust your learning rate, try a different optimizer, or tweak your data processing. Or, let's say you're running a linear regression, and you're interpreting the coefficients. Without math knowledge, you might miss problems like multi-colinearity, which makes the coefficients
[01:45] unreliable. Then you might make incorrect conclusions from the data, and cost the company millions and lose your job. Just kidding. Kind of. We do really need to be careful when making business decisions from the models that we build. can and should get started without deep math knowledge. It's definitely reasonable to build
[02:00] your comfort with math over time. Once your hands on, you'll start encountering problems that naturally push you to learn more. When you need to debug or explain your results, that's when the math is going to start to click because it's connected to something real. So seriously, don't let fear of math stop you from starting. You don't need to learn it all up front to make progress.
[02:16] Get your hands dirty with the tools, build your portfolio, and let math grow as a skill alongside your practical knowledge. All right, now let's talk about what to learn when you're building your foundation for machine learning jobs. First, linear algebra. Linear algebra is fundamental
[02:29] for machine learning, especially for deep learning. Many models rely on representing data and computations as matrices and vectors. Here's what to prioritize. First, matrices and vectors. Think of matrices as grids of numbers and vectors as lists of numbers. Data is often
[02:42] stored this way, and operations like addition, multiplication, and dot products are really essential to how models process that information. Determinants and inverses. Determinants tell you whether a matrix can be inverted, which is used in optimization problems and solving systems of
[02:54] linear equations Eigenvalues and eigenvectors These are key to understanding variance in data and are foundational of techniques like principal component analysis which can help to reduce the dimensionality in data sets Lastly matrix decomposition Methods like singular value decomposition are used in recommendation systems
[03:10] dimensionality reduction, and data compression. Now we're on to basic calculus. Calculus is called understanding how models learn from data. We don't need to worry about solving super complex problems. It's just about grasping a couple of key ideas. First, derivatives and gradients.
[03:23] Derivatives measure how things change and gradients, which are multidimensional derivatives, are what power optimization algorithms like gradient descent. These help models adjust their parameters to minimize error. The chain rule is central to neural networks.
[03:35] It's how backpropagation works, which is the process of figuring out how much each weight in the network contributes to the overall error so the model can learn effectively. Lastly, optimization basics. Concepts like local versus global minima, saddle points, and convexity
[03:47] are important to understand why some models get stuck and others manage to find the best solutions. Lastly, statistics and probability. Statistics and probability are the bread and butter of understanding data. While they're kind of more associated with data science, there's definitely a lot of value for machine learning as well.
[04:00] Here's what you need to know. Distributions. Get familiar with common distributions like the normal, binomial, and uniform. The normal distribution in particular pops up everywhere in data science and machine learning. Variants and covariants.
[04:12] Variants tells you how spread out your data is, while covariants shows you how two variables relate. These concepts are really important for feature selection and understanding your data structure. Phase theorem. While it has kind of a silly, maybe intimidating name, Bayes Serum is a pretty simple but powerful tool for probabilistic reasoning.
[04:27] It's foundational for algorithms like naive Bayes, Big Surprise, which is used for things like stand detection, as well as for Bayesian optimization for hyperparameter tuning. You'll also want to understand maximum likelihood estimation, which helps to estimate model parameters by finding values that maximize the likelihood of your data.
[04:42] It's a really fundamental concept, especially in algorithms like logistic regression. Finally, sampling and conditional probability. Sampling lets you work with subsets of data efficiently, and conditional probability is essential for understanding the relationship between events,
[04:54] especially in Bayesian models. Now, this is definitely not an exhaustive list, but I think it's a good overview of the common concepts you'll need to know to do a good job as a data scientist who's focused on machine learning or as a machine learning engineer. Next up, I'll share the best resources to learn these concepts
[05:07] without it being stressful or overwhelming, and hopefully also not too boring. Personally, I would highly recommend starting with a visual and intuitive understanding of the key concepts before you start reading really difficult textbooks and trying to solve equations.
[05:19] For linear algebra and calculus, I cannot speak highly enough about 3Blue1Brown's Essence of Linear Algebra and Essence of Calculus series. These videos give a really solid introduction to what is actually being measured and manipulated when we use these mathematical approaches.
[05:32] More importantly, they kind of show the beauty in it. It's kind of strange to say that math videos could be inspirational in a way, but these ones are. For statistics and probability, I am a huge fan of StatQuest. The videos are clear, engaging, and just a joy to watch.
[05:45] StatQuest has playlists with overviews on course stats and machine learning concepts. So, I'd recommend starting there. Once you have a visual intuition, you can start working through more structured books and courses. There are a lot of great options here as well.
[05:57] Let's go through a few that I personally used to learn. I completed the Mathematics for Machine Learning Specialization from Imperial College London on Coursera when I was just starting out The specialization is divided into three courses linear algebra multivariate calculus and a last one on principal component analysis
[06:11] The courses are well-structured and include a mix of video lectures, quizzes, and programming assignments in Python. I found the course to be a little bit challenging as a beginner, but it was a really good overview, and I did manage to pass everything with a little bit of effort.
[06:23] DeepLearning.ai also recently released a master machine learning specialization on Coursera. This specialization has courses on linear algebra and calculus, but instead of PCA, the final course focuses on stats and probability. I'm personally working through this specialization right now, and overall, I'm finding it to be another really great option.
[06:38] Each module starts with a nice motivation for how the math connects to an applied machine learning concept. It has coding exercises in Python, and some neat 3D tools to mess around with to get a good kind of visual understanding of the concepts as well. If you prefer learning from books, I have some suggestions there too.
[06:52] First up, if you like anime or nerdy stuff, boy oh boy do I have a recommendation for you. Did you know that they have manga math books? So I've read the Manga Guide to Calculus, Manga Guide to Linear Algebra, and Manga Guide to Statistics.
[07:05] They also have a ton more. They have some on like physics, I think, and some other engineering concepts. So they're super, super fun. I can't say the instructional quality is like world class or anything, but they're cute and engaging, and they made me not dread reading a math book.
[07:18] The next level up would be real math books. These are some of the best. The Mathematics for Machine Learning e-book by Dyson Ross and colleagues is a great comprehensive resource and it's available for free for personal reasons. It covers key topics we've already
[07:30] discussed like linear algebra, calculus, probability, and optimization with a focus on how these concepts apply to machine learning algorithms. It's relatively beginner friendly and is generally regarded as one of the best books for learning this material. Next, Practical Statistics for
[07:44] Data Scientists is another well-loved resource that includes code examples in Python and R. Now before we actually start studying, I think it's important to spend a little bit of time thinking really deeply about why you even want to do this. Personally, I find that if I'm studying
[07:56] just because I feel like I should or because it's some arbitrary assignment, I get distracted easily and I don't actually end up retaining that much of the information. Instead, I try to connect to some kind of a deeper motivation if possible. Personally, right now, I have a really basic
[08:10] motivation. I want to do well in my job because I want to earn a lot of money so that I can take care of everyone I love. I have these great resources to learn from that weren't even available a couple of years ago, and I have this opportunity to push myself and make sure that
[08:22] everyone I love is safe and cared for now and in the future. So this isn't to put extra pressure on myself, but actually just a way that works for me to kind of get excited that I have this opportunity to learn and grow and hopefully help others along the way. Your motivation might be totally different,
[08:37] but whatever it is, try to tie this work to a larger goal. In terms of optimizing your study time, I found that one of the most effective methods is writing notes in my own words. Don't just copy definitions or formulas, take time to summarize concepts as if you were explaining
[08:50] them to someone else, or really to a future you. For example, if you're learning about derivatives, you might write, a derivative measures how a function changes given a tiny nudge to its input This forces you to actively process the material Delatedly when it comes to math formulas don just stare at them I know it easy to do It really helpful to translate them into plain English or whatever spoken language you prefer For instance take the equation y equals mx plus b
[09:13] You might describe m as the slope that shows how steep the line is, and b as the point where the line crosses the y-axis. So the final formula might be the value of y, the output, is determined by taking the slope, m,
[09:25] multiplying it by x, the input, and then adding b, the starting point where the line intersects the y-axis. You can even use your notes as like a personal blog, kind of. Writing short posts about what you've learned is a really solid way to clarify your understanding,
[09:38] and teaching others, even if nobody reads it, solidifies the material in your own mind. Plus, sharing your posts on Medium or LinkedIn not only potentially helps others, but also allows you to build kind of a portfolio showcasing your learning journey.
[09:51] Also, trust me, when it's interview time, you're going to be really happy that you have these notes. I use my own study notes all the time. The next piece of advice I have might not be super duper fun, but I also recommend not using just one resource.
[10:03] Personally, I've had a lot of success from taking many different courses and kind of just throwing all my notes together at first. Then I'll write a blog like I was just talking about that summarizes all of my learnings. There are a couple of advantages to this approach. First, repetition helps you retain things.
[10:16] If I see a concept multiple times explained from multiple angles, I'm much more likely to actually get what's going on and remember it for longer than a day. Plus, not only do I see the information presented to me multiple times, I'm writing the concepts out in my own words multiple times,
[10:30] including that final time where I synthesize it all and get ready to share with others. So I have to be really confident that I actually got it by the end if I'm going to be putting it out publicly. Let me show you an example. Here are three different explanations for the concept of Rank and Rainier Algebra.
[10:43] Starting with 3Blue1Brown, you can see this visual intuition, which is a great starting point, but, you know, it lacks a little detail. Then we can look at how Rank was presented in deeplearning.ai, which has some more detail, but is still presented in a really simple way.
[10:56] Finally, we can go to the Mathematics for Machine Learning ebook to get an even more formalized definition with additional detail. Each one of these builds on the other and adds to my store of knowledge. Finally, once you've built that foundation and get to the level of math where you can
[11:08] actually use it for stuff, I really recommend coding concepts from scratch. If you can code gradient descent or logistic regression using just NumPy, you have to get a really strong start. While I know at this point you are super excited to start learning math, I do want to just
[11:20] circle back to the important fact that if you're a beginner trying to get your first In my opinion, math should not be the first thing you prioritize. It's really unlikely that your math skills are going to be the same that gets you a job as a data scientist and machine learning engineer.
[11:33] Instead, prioritize gaining hands-on experience by working on projects and actually building stuff. Employers are far more interested in seeing what you can do with the tools and knowledge you already have and how many formulas you've memorized. As you encounter challenges in your work, you'll naturally be motivated to learn the math behind the algorithms.
[11:49] Remember, math is a tool to help you succeed and shouldn't be a barrier to getting started. If you're curious about what else you need to know to become a data scientist, I have a really comprehensive video that lays out the entire roadmap from absolute beginner to your first job, including skills to learn, project examples, how to get experience, preparing
[12:05] for interviews, and more. Definitely check that out next.