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Ever since I finished reading Scott H. Young’s book titled “Ultralearning”, I wanted to try my hand at challenging myself to learn what I can call, “the project”. This project involves learning and developing the skills and processes involved in software engineering, data engineering, data science, and machine learning - and it is quite a big list. Fortunately, the skills build upon each other, and the processes follow a pipeline. During this learning project, I’ll be following Scott Young’s framework that he introduced in his book, with some slight adjustments due to the scope of the project and my end goal which is mostly self-enrichment. The framework itself can be easily defined, but the follow through is a different challenge in itself. I’ll start with the 9 principles of ultra-learning that Young laid out, followed by a brief explanation of what needs to be done, and how I will apply it on as I go through the challenge.
The first principle and possibly the one with a heavier impact in an Ultralearning project is to draw a map of what I will be tackling. He called this principle metalearning, or learning how to learn the subject. It entails looking for the best resources on how to learn the subject, identify the core skills that it relies on, and adopting the pathway that others followed to learn or even master the subject in question. Since my project can be done in a formal academic setting, I will base my curriculum on the course outline from a few Universities while omitting unnecessary elective if I choose to do so.
The following sub-headings list topics where computer science, software engineering, data science and machine learning converge. Please note that I used Qwen3 to help me map out these concepts.
Below is the list of foundational mathematics that I need to cover. I do think I don’t need to go past Optimization Theory in the current scope of the project.
| Domain | Core Topics | Relevance to CS/DS Convergence |
|---|---|---|
| Calculus | Single-variable, multivariable/vector calculus, partial derivatives, gradients | Essential for understanding optimization landscapes in machine learning; gradients drive backpropagation in neural networks |
| Linear Algebra | Vector spaces, matrix operations, eigenvalues/eigenvectors, SVD, PCA | The language of data representation; powers dimensionality reduction, neural networks, and recommendation systems |
| Probability Theory | Random variables, distributions, Bayes’ theorem, stochastic processes | Quantifies uncertainty in predictions; foundational for Bayesian methods and probabilistic graphical models |
| Mathematical Statistics | Hypothesis testing, confidence intervals, regression theory, experimental design | Enables inference from data; distinguishes signal from noise in model evaluation |
| Discrete Mathematics | Logic, set theory, combinatorics, graph theory, proof techniques | Provides formal reasoning tools for algorithms, database theory, and computational complexity |
| Optimization Theory | Convex/non-convex optimization, gradient descent variants, Lagrange multipliers | The engine of machine learning training; most ML algorithms reduce to optimization problems |
| Numerical Analysis | Numerical integration, interpolation, stability analysis, error propagation | Bridges continuous mathematics to finite-precision computation; critical for implementing algorithms reliably |
| Real Analysis | Limits, continuity, measure theory, function spaces | Provides rigorous foundations for convergence proofs in learning theory (advanced but increasingly relevant) |
| Abstract Algebra | Groups, rings, fields, finite fields | Underpins modern cryptography and secure computation; essential for privacy-preserving ML |
| Topology | Homotopy, persistent homology, manifold learning | Enables Topological Data Analysis (TDA) to extract shape-based features from complex datasets |
| Information Theory | Entropy, mutual information, channel capacity, coding theory | Quantifies information content; informs feature selection, model compression, and communication protocols |
| Area | Convergent Topics | Intersection Point |
|---|---|---|
| Algorithms & Data Structures | Hashing, trees, graphs, dynamic programming, amortized analysis | Efficient data manipulation at scale; algorithmic complexity directly impacts model training time |
| Computational Complexity Theory | P/NP classification, time/space complexity, approximation algorithms | Determines feasibility of learning problems; guides algorithm selection for large datasets |
| Database Systems | Relational algebra, query optimization, indexing, transaction processing | Data engineering pipeline foundation; bridges storage to analytics |
| Distributed Systems | Consensus protocols, fault tolerance, MapReduce, Spark RDDs | Enables processing of datasets beyond single-machine capacity; core to modern data platforms |
| Machine Learning | Supervised/unsupervised learning, reinforcement learning, deep learning architectures | The primary convergence zone where CS algorithms meet statistical modeling |
| Natural Language Processing | Tokenization, parsing, embeddings, transformer architectures | Applies linguistic theory + CS algorithms to extract meaning from unstructured text |
| Graph Theory / Network Science | Centrality measures, community detection, random walks, spectral graph theory | Models relational data (social networks, knowledge graphs); increasingly vital for recommendation systems |
The next principle is aimed towards the development of my ability to concentrate on learning these skills. He also identified three common hurdles that any learner would face. And these are hurdles on starting (procrastination), sustained concentration (distraction), and finding and staying in the “flow”. Young did suggest ways on how to tackle the three hurdles.
The Five-minute Rule - suggests that we only have to start working on our tasks for 5 minutes, as the mental resistance disappears within five minutes in to the activity. Recognize the “Urge” - By being mindful of our urges to stepping away from our task, we take away that urge once we recognize that its there. Scheduling - Set specific “low-intensity” time during the day.
Environmental Optimization - a clear workspace that is free of any possible distractions. This can be putting your phone on do not disturb mode, or blocking access to specific apps or even access to the internet if need be. Desirable Difficulty - sometimes our learning materials are the problem, try to find the goldilocks zone where difficulty and engagement are balanced. Keep your head in the game - there are times that our brains are the source of distraction. If a random task pop into our head, write it down so that you can handle it later and then go back to work.
There are similar techniques that Dr. Justin Sung and his team in ICandStudy.com teach to learners enrolled on their website, but if you can’t afford a subscription Dr. Sung has talked about distraction in his youtube channel. There are also other Youtube content creator that teaches skills related to distraction management.
Flow has been defined as a state of absorption and immersion on the current task. However people often struggle to reach it, or they wait for the flow state which then prevents them into doing relevant “deep work”. A steady and concentrated effort is more reliable, than forcing ourselves to get into this mental state (This never happens).
I have to admit that I made the mistake of assuming Directness is the same as Deliberate Practice. Young defined Directness as the path we take to learn the skill or subject in question while avoiding transfer issues caused by fake work. Transfer issues are usually caused by the assumption that studying automatically transfer the ability to do the skill or fully understanding the subject by doing buffer activities, like using a language learning app for an extended period of time without actively trying to have a conversation in that language. In my case, reading chapter by chapter of a Calculus textbook without working following the worked examples, or solving exercise problems.
Deliberate Practice on the other hand requires us to push beyond our current limits through repetition of task and increasing the desirable difficulty in order to refine our skills, or deepen our understanding of the concept. We should note that desirable difficulty can be affected by our own physical and/or mental states as well. For example, if we have a learning session yesterday where we’re fully rested, and ready to take on the session, and on the today we’re exhausted from our daily activities. We can experience a dip in our performance where the quality of our work isn’t the same as yesterday’s, and this is a totally normal thing to happen.
Bruce Lee once said, “I fear not the man who has practice 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.” This philosophy is a great example of how to practice with directness and with deliberate intensity. This is where Young’s 4th principle comes in.
Going back to what Bruce Lee once said, it is possible to master one thing by breaking down complex skills into smaller components, or breaking down a concept into its foundations. Young described this weakest point or knowledge-gap as the “rate-determining step”. By definition, a rate-determining step is the slowest part in a chemical reaction. To find out what these weak points are, we practice the direct skill first, and when we identify a bottleneck or knowledge-gap, we then drill that bottleneck down until we have understood it better, or the task has become second nature. Only then can we integrate it back into the main skill.
I’ll use Calculus again as an example. Let’s say in a session, I had a hard time applying the chain rule to a single-variable equation. So I go back to practice the direct derivative rules that build up to the chain rule, while deliberately increasing the difficulty and intensity (like changing the equation, adding, or removing a variable) until I can apply the chain rule intuitively. There is a chance that I might need to go down hierarchy of rules if I find myself stuck on a preceding rule.
This Direct-Then-Drill loop is one of the strongest catalyst of learning. But it doesn’t end on that point.
The next two principles goes together and builds upon the Direct-Then-Drill loop turning an already powerful method into a supercharged activity.
First, we’ll look into what retrieval and feedback is. Retrieval is the action where we pull the knowledge from our heads, and try to reproduce it from scratch. While feedback is the input we get from colleagues, mentors, or from the public or audience. While there is not a single best method for retrieval, the best results come from a mixture of drills or challenging activities, and the quality or “helpfulness” of the feedback.
I’ll leave out the example for now because the next principles will show us the importance of effective retrieval and the quality of a feedback. And how the other principles above builds up towards an end goal.
Even if we practice the Direct-then-drill method, and our retrieval and feedback loop is impeccable, if we don’t implement a retention strategy to address information decay and interference, we are practically wasting our time. Cognitive Scientist calls this information decay as the forgetting curve. To help mitigate or “flatten the curve”, we can add more components in our study-practice-feedback loop by implementing Spaced repetition, overlearning, and practising a skill until it becomes a habit or a procedure.
Spaced repetition is the act of spreading out the time for practice and free recall throughout the week, instead of doing it on a single day for an arbitrarily large amount of time.
Overlearning is the act of continuous, deliberate practice even when we are able to do a skill correctly a single time. This flattens the forgetting curve by pushing the level of proficiency to a certain point that it feels automatic. This then opens up the door to “procedualization”.
Procedualization is when we practice our skills until it becomes second nature through constant application. By continuously drilling the core components of a skill, it flattens the forgetting curve by reinforcing neural connection until we develop “muscle-memory”.
We can then look at the importance of intuition in any learning activity. Intuition is the by-product of frequent retrieval and reflection and application of quality feedback which can only be reached through deep engagement with the subject matter. It is an ability to convey a concept without using fancy jargon. Or the ability to solve a new problem using the knowledge we have.
According to Young, the best method to gauge our intuition is through using the Feynman Technique. It is an activity where we identify a concept, explain it using our own words, and if we are unable to describe the concept in that manner, we don’t fully understand the concept and we must go back until we can explain this concept better. On the other hand, if we managed to explain the concept in such a way, the next step is to simplify the explanation by using analogies.
This is the end goal of my learning project. Building a strong foundation of the concepts, techniques and procedures involved in Data Science and Machine Learning.
I have never tried to push myself to learn more advanced mathematical concepts during my time as a university student. And I was happy that I passed the required classes even if the final grade was low. This was the time where I stayed in my comfort zone because I didn’t had the drive or the motive to do break through my box.
But as I mature, I developed this appreciation for maths beyond elementary calculus, and first year courses in linear algebra, statistics and probability. This is learning project is both a challenge and an experiment, and one that I know will be one of the activities that I will pursue to keep myself sharp.
I will add a single point to Young’s principles of ultralearning. While it wasn’t explicitly mentioned in the book, it lays hidden through the pages.
Encoding is the invisible thread that ties the 9 principles together, and it is defined as the process of transferring new knowledge in our working memory into the long term memory. There are three places where encoding happens during the lifetime of a learning project, namely:
Deep Encoding happens while we develop intuition using various practices and techniques. It is done by forming relationships with what we know, to what we are learning. The use of analogies and visualizations are a good way to encode abstract data into concrete mental pictures.
Contextual Encoding happens when we think about how we think, and learn about how we learn which helps us recognize the structure of a subject and enables us to observe and reflect on our study sessions.
Situational Encoding happens when we learn a skill within an environment that facilitates the actual use of the skill.
Young argues that we don’t just want to encode new concepts, we also need to understand the reasoning behind the concept so that our ability to encode drives better intuition.
After the exposition on the 9 principles of Ultralearning, it actually armed me with better understanding of the process, what those entail, and how I should apply the principles throughout the lifetime of the project. This then enabled me to practice reading a book analytically, and it taught me how to write properly.
While I develop the skills laid out in the table in Principle 1, I will also be writing my progress through the learning journey, and if possible, share my insights about the books I have in my back log.
And thank you for staying this far.
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