Hi everyone,

In Is Math Real?, mathematician Eugenia Cheng wrote:

“Accepting a little intellectual discomfort (or sometimes a lot of it) is an important part of making progress in math.”

That captures my past couple of months pretty well. Baby steps, plenty of challenge, and those rare (but oh boy) satisfying moments of clarity.

Math progress

I finished a first pass through two of Seth Braver’s books:

• Full Frontal Calculus: An Infinitesimal Approach

• The Dark Art of Linear Algebra: An Intuitive Geometric Approach

I feel smarter now :)

Both books are terrific. I plan to do another pass, like a neural network making multiple passes through data to refine its understanding and detect patterns. Expect more chapter reviews soon.

I also discovered that Braver has videos on multivariable calculus. I watched a couple on partial derivatives and gradients, two fundamental math concepts for deep learning.

Seth, if you happen to see this (no pressure!), please consider writing a book on multivariable calculus and a second edition of the linear algebra one that covers SVD and PCA. Your material is outstanding.

More learning ahead

• Braver’s new trigonometry videos are excellent. Watching helps, but watching is not learning. Real learning happens through reading and doing exercises. I need to remind myself of that, otherwise it’s easy to spend hours on YouTube with zero retention.

• Next up: filling some serious gaps in probability and statistics. Probably a lot more discomfort is coming, but as they say, no pain, no gain.

Artificial neural networks and physics

I’ve been slowly working through Artificial Intelligence Engines by James Stone. It’s relatively short but dense with insight.

I revisited the chain rule for functions with several variables, and I’m currently going through the forward pass math in a simple 2-2-1 perceptron with a sigmoid activation in the hidden layer.

I’ve also been adding some conceptual physics into the mix. Math and physics feed each other, and to really understand how the world works, you need a bit (okay, maybe a lot) of both. I’m starting with classical mechanics for now.

A few other things

Work has a way of finding you. I’ve taken on a bit of consulting, helping a couple of teams run smoother and ship better software, faster. So far, so good.

A quote that’s been on my mind lately:

“The highest activity a human being can attain is learning for understanding, because to understand is to be free.” — Spinoza

If you’re celebrating, happy Halloween, and happy weekend wherever you are. Stay curious and keep climbing your own mountain.

— Ruslan

How many numbers are there from 5 to 18, including both ends?

Your first instinct might be to subtract:

18 - 5 = 13

Feels right.

But it’s wrong.

It’s a small thing, and kind of basic, but this mistake got me more times than I’d like to admit. Eventually I learned how to count ranges properly. :)

Basic counting

Let’s start with something simpler.

How many numbers are in this list?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

You’d probably say 13 without counting. And you’d be absolutely right.

That kind of range is easy. Our brain sees the pattern and knows what’s going on. We’ve been counting this way since we were little kids. But that instinct quietly fails in cases like 5 to 18.

So, how many numbers are there between 5 and 18 inclusive?

Let’s count manually

Here’s the full list from 5 to 18:

5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

That’s 14 numbers, not 13. So what went wrong with our subtraction?

Try a quick trick

Let’s take the above list from 5 to 18 and turn it into a list that we know how to count by subtracting 4 from every number (I first saw this approach in David Patrick’s book Introduction to Counting & Probability. A great resource if you enjoy these kinds of problems.):

Much easier to count! It has 14 items. Since we only shifted the numbers to start at 1 (without changing the count), the original list has 14 numbers too. Nice.

The formula

If you want to count how many numbers are in a list from a to b, inclusive, here’s the rule (given that both a and b are positive and b >= a):

That +1 is the key.

So for our original example:

18 - 5 + 1 = 14

For the curious: formula derivation

Using the same trick, we subtract a - 1 from each number in the range from a to b. This transforms it into a list we can count easily, starting from 1:

Our new list has b - a + 1 numbers, so the original list has the same count.

The +1 rule is simple, but surprisingly easy to overlook. Here’s where it often sneaks in.

Where this trips people up

This tiny +1 mistake shows up everywhere:

• Days between two calendar dates (inclusive)

• Characters in a string or line

• Steps in a workout plan

• Floors between 3 and 7 (did you forget to count the 3^rd floor?)

• Loop boundaries in code (<= vs <)

Miss it, and you might:

• Pack too few t-shirts for your vacation

• Underestimate your timeline

• Overrun an array and ship a bug

It’s such a common mistake, it even has a name: the off-by-one error. Software engineers run into it constantly, but it affects everyone.

Once you understand it, you’ll start spotting it everywhere. In code, in calendars, in life.

Dig deeper. And count carefully.

Talk soon.

P.S. If you feel extra adventurous, try the following exercises:

1. How many numbers are in the range from 42 to 58, inclusive?

2. Derive the formula b - a + 1 from scratch, no peeking

3. How many numbers are in the list 6, 8, 10, 12, …, 128, 130? (Hint: What do you need to do before applying the formula b - a + 1?)

If you enjoyed this post, share it with someone who loves small but important details.

If you’ve ever looked at a vector and thought, “Just a column of numbers, right?”, this chapter will change that. The Dark Art of Linear Algebra (aka DALA) by Seth Braver opens with one of the clearest intros I’ve read. Not every part clicks on the first pass, but the effort pays off. Paired with the author’s videos, this is a strong starting point whether you’re learning math for the first time or coming back to it with purpose.

As I wrote in Unlocking AI with Math and [Book Notes] Infinitesimals, Derivatives, and Beer – Full Frontal Calculus (Ch. 1), I’m not learning math to pass a test. I’m learning it to understand the machinery behind AI and robotics, and eventually build machines of my own. (That would be fun, right?)

That goal needs a solid grasp of linear algebra. And it starts with understanding what a vector really is. Not just how to work with vectors algebraically, but how they behave in space and fit into a larger structure.

This chapter helped me sharpen that understanding.

Chapter Notes

What’s a Vector?

The book makes it clear that the answer to this question will evolve as you go deeper into linear algebra. But Chapter 1 starts simple: a vector is an arrow. A geometric object. A displacement.

In the video that comes with the chapter, the author even says to forget everything you think you know about vectors. He introduces them geometrically, which makes them feel tangible and helps you see familiar algebraic ideas in a visual, spatial way.

Vector Addition

The book introduces vector addition visually. Once you see vectors as displacements or moves through space, the addition feels natural. Almost obvious.

The text doesn’t focus on vector subtraction, but there’s an exercise on it. The companion video shows two methods. One of them is subtraction by addition: flip the direction of the vector you want to subtract, then add. It reminded me of that Office scene where Andy says “addition by subtraction,” and Michael asks, “What does that even mean?” In that context, it’s just a throwaway phrase. But in vector math, subtraction by addition is a real method. Flip the vector, then add. If you’ve done engineering, you’ve likely seen this before.

Vector addition also follows familiar rules like commutativity and associativity. If those sound fuzzy, the book and video prove them using triangles and parallelograms. No heavy algebra, just geometry.

One nice bonus is that the commutative proof gives you another way to add vectors. Place both tails at the same point, draw a parallelogram, and the diagonal gives the sum. It’s clean and easy to visualize:

Stretching Vectors

Scalar multiplication is introduced as a way to stretch, shrink, or flip a vector, not just multiply its components.

The author even explains where the word scalar comes from. Numbers are called scalars because they scale vectors. I liked that he doesn’t assume you already know this.

To stretch a vector, multiply by 3.

To flip it, multiply by –1.

To collapse it, multiply by 0.

It’s easier to remember when you learn it by drawing instead of just computing.

Standard Basis Vectors

Only after you’ve built a solid geometric understanding does the author introduce the standard basis vectors: i, j, and k. By then, it’s clear that 2i + 3j + 5k is just a weighted sum of familiar directions.

The chapter shows how to express vectors in ℝ² and ℝ³ using these basis vectors, and how to rewrite them in column form.

Length of Vectors

Be sure to watch the videos that go with this chapter. They walk you through finding the length of a vector visually.

You’ll start with the Pythagorean theorem to calculate the length of a vector in ℝ³, then extend the idea to ℝⁿ. The chapter also proves the general length formula when a vector is written in Cartesian coordinates. Neat.

The Dot Product

The chapter defines the dot product using the same geometric approach as earlier sections, and it makes sense. But for me, it really clicked in the physics example where work is defined using the dot product. The author’s video made it even clearer.

In the screenshot above, I underlined “Thus we see that work, viewed in a more general setting, is simply a dot product” and scribbled “watch the video” in the margin. Just a reminder that the video is a great companion to the chapter.

The text then walks through key properties: commutativity, dotting a vector with itself, the distributive property, a test for perpendicularity, and how to compute the dot product in ℝ².

You could memorize the formula. But it’s much more satisfying to understand the parts and derive it from scratch. Like Einstein said, “Any fool can know. The point is to understand.” Here’s a step-by-step derivation from the chapter, written out in my notes:

Thoughts and Tips

Like Full Frontal Calculus did for derivatives, this chapter tears vectors down to the basics and builds them back up. It does that visually, intuitively, and from first principles. It starts with geometry, not formulas. By the end, it’s clear that coordinates are just a way to describe vectors. They are not the vectors themselves.

Verdict: Highly recommend if you want a clear, visual grasp of what vectors really are. Especially if linear algebra has ever felt abstract, dry, or overly symbolic.

If you plan to read the chapter, these tips helped me get the most out of it:

1. Read slowly. Then read slowly again. The material is clear, but it rewards focused attention. Grab a paperback if you can. Write in the margins. Make the book your own.

   

2. Watch the author’s YouTube videos. The book explains the idea. The video often makes it stick. If you’re reading any of Braver’s math books, don’t skip the videos. They’re short, clear, and worth it.

   1. Vectors (from a geometric perspective)

   2. The Dot Product (from a geometric perspective)

3. Don’t worry about the proofs. They’re explained in plain language, supported by visuals, and still rigorous. You don’t need a separate book on how to follow them. They just make sense.

4. Brush up on your trig. Knowing how cosine works pays off when finding angles between vectors. It’s a small part of the chapter, but if you’re rusty, check out the trig section in Precalculus Made Difficult by the same author.

5. Do the exercises. The book includes answers, which makes it great for self-study. But like in Full Frontal Calculus, the solutions are compact. Use ChatGPT or Grok (xAI) to expand on them when needed.

6. Use spaced repetition. For ideas that are hard to keep in memory, try active recall. I use Anki, but any similar tool should work.

7. Check out the book sample. The author offers a sample on his site. If you’re on the fence, it gives you a solid feel for the writing and style.

These pages and videos are exactly what I wish I had the first time I saw vectors. They make the concept click and give you a foundation you can build on, whether you’re starting fresh or coming back to review.

Dig deeper. I’ll be back with more soon.

— Ruslan

P.S. I’m not affiliated with the author. I just really enjoy his books and wanted to share that.

When I decided to return to math and rebuild my foundations for AI/ML, I didn’t expect to enjoy a calculus book this much. Shocking, I know. But that’s exactly what happened with Full Frontal Calculus.

Can calculus feel intuitive? Even fun? From the first few pages? Okay, from page 8 to be exact. For me, the answer is yes.

Why This Book Clicked for Me

As part of my self-study, I’m posting short, progressive reviews of the books I’m working through. On today’s menu: Chapter 1 of Full Frontal Calculus by Seth Braver.

Before I stumbled on Full Frontal Calculus, I tried a few limit-based calculus books and textbooks, but none of them spoke to me. Luckily, there’s no shortage of calculus material these days, so it’s easy to shop around and try different sources.

Braver’s book grabbed me right away. The early focus on infinitesimals, the tight writing, and the emphasis on intuition won me over. I even caught myself smiling more than once. Rare for a math book.

Chapter 1 Highlights

Chapter 1 starts with infinitesimals: “an infinitely small number, smaller than any positive real number, yet greater than zero.” One early example shows how a circle, imagined as a polygon with infinitely many infinitesimal sides, leads to the familiar area formula πr². If your geometry or trig is rusty, don’t worry - it still makes sense. Braver then uses the same idea to show how curves appear straight on a small enough (infinitesimal) scale, which is the heart of differential calculus.

Things really clicked for me in the section titled A Gift From Leibniz: d-Notation. Braver’s explanation of dy/dx shows how it captures infinitesimal change in a way that just makes sense. It helped me understand why derivatives represent slopes and rates in a way I could explain to a 10-year-old. Working through the derivative of x² from first principles was also deeply satisfying.

Practically speaking, Chapter 1 covers:

• what infinitesimals are

• how they help us define rates of change

• the geometric meaning of derivatives

• the elegant dy/dx notation from Leibniz

• why we ignore higher-order infinitesimals like (dx)² or du * dv

• and a first-principles derivation of the derivative of x²

The chapter ends with two powerful tools: the power rule and linearity properties. These let you compute derivatives of polynomials using just basic mental math.

The writing is sharp and often funny, in a math kind of way. There’s even a cameo by the Sumerian beer goddess Ninkasi, who helps explain rate of change and derivatives using a vat of beer. It sounds quirky, but it works.

The book’s style, clarity, and focus on intuition made me want to keep going. That’s not something I’ve felt with many math books.

Final Thoughts and Tips

If you’re following along or just curious about studying calculus again, I recommend giving Chapter 1 a shot. It’s not always light reading, and the exercises are essential, but it might click for you like it did for me. Chapter 1 is available for free on the author’s site, so you can explore it before deciding whether to dive in.

If you do decide to dive into the book, here are a few tips to get the most out of it:

1. If you’re rusty on pre-calculus (I was), make sure you’ve got slope, rate of change, the point-slope formula, and the slope-intercept form down cold before the Rates of Change section on page 10. For that, Seth Braver’s other book Precalculus Made Difficult has excellent material on those topics. You can probably get through it in a day.

2. Read slowly, with a pen or pencil in hand. Write in the margins (get a paperback copy). It might feel painfully slow at times (pun intended), but it’s a recipe for deeper understanding.

3. The book includes answers to many exercises and is great for self-study. But the solutions are compact, so I recommend using Grok or ChatGPT to expand on them and deepen your understanding.

4. Once you’ve finished the chapter and exercises, check out the author’s YouTube videos that go along with the book. They’re criminally underrated and oddly hard to find. You might enjoy them as much as I do.

5. For topics that are hard to retain, try spaced repetition with active recall. Anki works great for that, or use whatever tool you prefer.

Chapter 1 sealed the deal. This is the calculus book I’m sticking with. Looking forward to seeing how Braver develops the ideas from here.

Dig deeper. More to come soon!

— Ruslan

P.S. I’m not affiliated with the author. I just really enjoy the book and wanted to share it.

As promised in my last email, I want to briefly cover some of the math topics I’ve been exploring over the past few months and share why I’m diving into math at this stage.

Being in my forties, I’m not approaching this to become a professional mathematician. My goal is more pragmatic: I want to see how things work under the hood, especially in AI. There’s a lot of hype and noise out there, and understanding the math helps cut through it. It will let me assess claims more critically and grasp what’s really going on in research papers. Plus, AI is a big part of robotics, so studying math tackles both fields at once.

Why focus on “pure” math? These days, many books mix math with Python code and real-world applications, and that’s where I started as well. But after a while, I felt I needed to step back and understand the core ideas on a deeper level. I also wanted a more intuitive, yet rigorous, introduction to these concepts.

That’s where the trio of books by Seth Braver came in:

• The Dark Art of Linear Algebra: An Intuitive Geometric Approach

• Full Frontal Calculus: An Infinitesimal Approach

• Precalculus Made Difficult

I was lucky to find these books because they were exactly what I needed at this point. Your experience may vary, of course, but if you’re self-studying and want an accessible introduction, I highly recommend them.

I started with linear algebra, then added calculus. Since calculus depends heavily on precalculus, especially trigonometry, I dove into precalc as well.

Here’s what I’ve covered so far by reading those three books:

Linear Algebra

• Vector addition and scalar multiplication

• Standard basis vectors

• Vector length

• Dot product

• Vector basis and subspace

• Parametric representations of subspaces and affine spaces

• Linear maps, matrices, and matrix algebra

• Gaussian elimination for solving linear systems, matrix inversion, image and kernel

Calculus

• Basic ideas of differential calculus (infinitesimals, rates of change, the derivative, derivatives of polynomials)

• Product, quotient, and chain rules

• Concavity

Precalculus

• Various topics to support calculus, like slope formulas and trigonometry

Seth Braver says these books are meant to be read slowly and carefully. I’ve definitely taken that to heart, maybe too much. I’m doing most of the exercises that have answers in the book. Understanding math, like programming, requires getting your hands dirty. It’s a “contact sport,” and working through exercises is the only way to truly understand it.

Recently, I discovered that the author has video lectures to accompany the books. I’m now revisiting the topics through his YouTube channel, which I also highly recommend after you’ve spent some time with the text and exercises.

Some key ideas that have stuck with me: in linear algebra, matrix-vector multiplication can be understood as mapping one vector to another via a linear transformation. In calculus, the idea that on an infinitesimal scale, curves become straight lines is both paradoxical and illuminating.

So far, it’s been a slow climb, but each step forward is a step closer to the freedom of understanding Spinoza spoke of.

Dig deeper. Until next time!

— Ruslan

It’s been a while. Nine months, to be exact. Life took a few unexpected turns, and my plans for tech deep dives got sidelined. But I’m back, and this time I’m diving into math.

Why math? Because if you really want to understand AI, machine learning, or any modern tech, you need to get the math behind it. Not just memorize formulas, but actually grasp the ideas. So for the past few months I’ve been quietly rebuilding my math foundation from scratch. It’s been quite a ride - surprisingly fun in your 40s :)

Right now I’m working through three challenging but fascinating books:

• Precalculus Made Difficult

• Full Frontal Calculus: An Infinitesimal Approach

• The Dark Art of Linear Algebra: An Intuitive Geometric Approach

I’m not a math expert. Just sharing my journey. What trips me up, what clicks, and everything in between. If you’re into tech, AI, or curious about someone learning it out loud, you might enjoy this.

So, what’s coming up?

• Posts on what I’m learning every couple of weeks, or whenever there’s something worth sharing

• Occasional lessons from my time as a director and engineer

• A few tech book reviews

• More frequent, shorter updates on X (@rspivak)

If this sounds like your thing, stick around. Otherwise, feel free to unsubscribe anytime. No hard feelings.

Excited to reconnect,

Ruslan

P.S. First post drops in about two weeks. I’ll break down what I’ve learned so far from precalculus, calculus, and linear algebra.

Like any skill, if you don’t practice it, you lose it. And this applies to both individual contributors and managers. Sometimes, staying technical means sharpening your existing tools. Other times, it means picking up entirely new tools — or even an entirely new toolbox.

With that in mind, I’m kicking off a new series called Technical Deep Dive (TDD) Tuesday where I’ll explore various technical topics. The first sub-series will focus on a specific Leetcode problem: Basic Calculator (Hard level).

I’ve implemented two solutions that were accepted on Leetcode: one using a modified version of Dijkstra’s two-stack algorithm and the other using syntax-directed interpretation (who knew some compiler and interpreter knowledge could come in handy? :)

In this Basic Calculator sub-series, I’ll walk you through these solutions. My hope is that you’ll enjoy the ride — and who knows, you might even find it useful if you’re prepping for interviews or practicing on Leetcode.

Just a heads-up: I’m not claiming my solutions are the most optimal. Consider this an exploration. I’ll be using Python 3, and each post will include exercises to help you dig a little deeper if you’re up for the challenge.

Stay curious, and I look forward to diving into this with you in the next post of the TDD Tuesday series.

Ruslan

Growth as a software engineer is an ongoing journey. Looking back, a few key principles helped me progress during the early days of my career. These lessons shaped my path, and many of them continue to guide me today, even though I’m no longer an individual contributor:

1. Drive

Ambition isn’t a skill — it’s a will. You either have it or you don’t. To grow, you need that inner drive pushing you forward. Sometimes it’s a conscious choice, and other times, you just can’t help it — something inside you refuses to stand still, driving you to keep learning and moving forward. I remember diving into Python and CI/CD back in the day, teaching it even when I was still learning myself.

2. Delivering results

You might have gaps in your technical or soft skills, but if you consistently deliver, that goes a long way.  I always gave extra effort (probably leaning a bit on the workaholic side), especially on projects that excited me. Delivering results also helps you build your reputation and credibility — a win-win.

3. Choosing the right projects

Whenever possible, work on projects that have the highest impact for the company and that interest you personally. There are two benefits: high impact projects give you the visibility and future opportunities you need, and personal interest helps you push forward when the going gets tough, and the going will get tough at some point — pretty much guaranteed.

4. Craft

Delivering high impact with speed and quality requires deep expertise in your field. Which, in turn, requires understanding what’s going on under the hood. Expanding the breadth of your knowledge while diving deep into specific technologies (the so-called T-shaped expertise) served me well.

5. Teaching

Teaching is a great way to solidify your knowledge and identify gaps in your understanding. Teaching also boosts your visibility and can establish you as a go-to person. Sharing what you know helps others and also helps you deepen your understanding. Personally, I view well-done code reviews as a form of teaching too.

6. Tolerance for conflict

Criticism comes with the territory. Sometimes it’s called feedback, and other times it’s just plain criticism. I took many classes at the University of Hard Knocks on this one: I missed deadlines, over-engineered technical solutions, cut corners, and delivered feedback in a less-than-perfect way at that stage of my career. My advice: start building a thick skin sooner, but be smart about it. Know when to stand your ground and when to let things slide. Above all, don’t be a jerk.

7. Learning how business works

This one’s underrated, and it took me a long, long time to learn. I wish I’d figured it out sooner, but better late than never.  While you can succeed at a certain level without focusing on this, understanding how the business works helps you identify high-impact projects and stand out as a valued partner — not just another tech person from a cost center.

As the saying goes, “The only way to do great work is to love what you do.” I’d add — love the challenges, love the process, and love the growth that comes with them.

Stay curious,

Ruslan

Hey there!

Let’s be real, avoiding dumb decisions would make any manager’s life a lot easier. But doing this consistently? Easier said than done.

• Don’t make dumb decisions when hiring

• Don’t make dumb decisions when firing or letting people go

• Don’t make dumb decisions during re-orgs

• Don’t make dumb decisions about your high performers and “sleeping stars”

• Don’t make dumb decisions when creating and communicating your strategy

• Don’t make dumb decisions when prioritizing

• Don’t make dumb decisions when choosing your tech stack

And the list goes on.

Mastering the fundamentals won’t completely prevent dumb decisions, but it will help reduce their likelihood. No matter where you are in your journey, getting the essentials right can make all the difference.

Here is my opinionated list of the top 5 essential fundamentals for engineering managers:

1. Technical expertise

2. Soft skills in general, and communication specifically

3. Project management

4. Team management and development

5. Strategic thinking and yes, decision making

Now, let’s unpack these a bit.

1. Technical expertise: when interviewing at many big tech companies, managers have to pass the same (or a similar) technical bar as software engineers, taking both coding and system design rounds. In my opinion, this is a good thing. Having technical proficiency as an engineering manager can lead to greater respect from the software engineers you work with (I’ll discuss the specifics in a separate post in the future).

2. Soft skills in general, and communication specifically: soft skills are crucial for any engineering manager, with communication standing out as particularly important. Presenting to stakeholders, conducting 1-1s, and facilitating team discussions (just to name a few) all require strong communication skills, which are essential for your effectiveness as a leader.

   1. I remember when I was an individual contributor (shortly before becoming a team lead), I knew I wanted to improve my communication skills. I even put that into my performance review as an explicit area for improvement. The reality was, I knew little about what it would mean practically. It took me many years and attending multiple classes in the UHK (University of Hard Knocks) to find out what good communication means and looks like in the real life of an engineering manager. It’s one of those skills that takes a lifetime to master.

3. Project management: we’re all project managers now, and it’s a crucial skill for building highly productive engineering teams that deliver consistently and with focus. I have a separate post that describes more benefits of project management here.

4. Team management and development: a key responsibility of engineering managers is to build high-performing teams that deliver results. This includes mentoring, coaching, giving feedback, and developing the skills and careers of team members. This is Engineering Management 101, if you will.

5. Strategic thinking and yes, decision making: oh boy, this one might either excite you or make you feel like it’s all “corporate BS.” But here’s the deal: strategic thinking is critical, and the higher you climb the career ladder, the more important it becomes. If you are in the “non-believer” camp, my advice is to reframe the importance of strategic thinking and make it interesting for yourself. It’s that important.

Mastering these fundamentals - technical expertise, communication, project management, team development, and strategic thinking - can significantly improve your effectiveness as an engineering manager. While it might seem overwhelming, remember that continuous learning and improvement are key.

Happy managing, and cheers to making fewer dumb decisions! :)

P.S: For a related opinionated list of software engineering fundamentals, read here.

Stay curious,

Ruslan

Hey there!

Let’s talk fundamentals today. Why are they important? John Wooden’s quote sums it up nicely, but let’s unpack it a bit more:

1. Strong foundation:

   • A solid grasp of fundamental concepts provides a strong foundation for building advanced skills. Just like a house needs a sturdy base, your knowledge in software engineering needs a solid groundwork. It may sound cliché, but it’s still true.

   • Continuous learning: fundamentals serve as a launchpad for continuous learning. Once you have a solid base, you can explore more advanced topics and specializations, keeping your skills sharp and relevant.

2. Confidence: mastering the fundamentals boosts your confidence.  Remember, competence breeds confidence.

3. Shelf-life: technology evolves at a breakneck pace. Remember when new JavaScript frameworks seemed to pop up before your morning coffee? Or just look at how quickly the AI space is advancing these days. While frameworks come and go, fundamentals like data structures, algorithms, math, software design, OS internals, and soft skills have enduring value. Investing in these fundamentals offers a much better return on investment compared to the often fleeting value of the latest frameworks.

Understanding the fundamentals is essential for software engineers at all levels; they’re not just for beginners.

Which specific fundamentals are important for software engineers?

Well, everyone loves a good list, so here you go - an opinionated list of essential fundamentals for software engineers at all levels, from entry-level to senior IC, staff, and beyond:

1. Programming languages: this one’s super obvious. The main question is which languages? Python, JavaScript, Go, and some C are the usual suspects. Bonus points if you dive into how interpreters and compilers work.

2. Software design and architecture

3. Data structures and algorithms (DSA)

4. Operating systems: this also includes basic computer architecture and networking.

5. Databases: design and internals

6. Distributed systems: nowadays, systems run on multiple machines and instances, so understanding the basics of distributed systems is important.

7. Math: this might be controversial, but it can also be the secret sauce, especially statistics and math for AI.

8. Soft skills: fundamental to any engineer’s career unless you’re living in a cave alone. The truth is, soft skills are actually hard to master.

Consider this a teaser! I’ll be doing deep dives into these fundamentals in upcoming posts, along with other key essentials for software engineers.

Spotlight

In today’s spotlight: “The Pragmatic Programmer: Your Journey to Mastery”

Andy Hunt and Dave Thomas offer a wealth of practical advice, timeless tips, and real-world examples. Every software engineer needs “The Pragmatic Programmer” on their shelf. Now in its second (20th anniversary) edition, this book is a must-read. I fondly remember the original edition titled “From Journeyman to Master.” My copy is well-worn from many reads - truly good books are worth revisiting.

Sneak Peak

In the next post, I’ll talk about essential fundamentals for engineering managers.

Stay curious,

Ruslan

At the beginning of my career, I thought project management was just a fancy term for unnecessary bureaucracy. But when I first became a team lead and was tasked with building a fund management system from the ground up, my perspective changed. My project was a year behind schedule, and I quickly (well, relatively quickly) learned the value of project management. People often talk about the school of hard knocks, and let me tell you, I graduated from the University of Hard Knocks with that project (the whole story is for another day).

The reality is, we’re all project managers now. Whether you’re an individual contributor or an engineering manager, project management skills can be incredibly beneficial. Here are a few reasons why:

Benefits of Having Project Management Skills

For Engineers:

1. Get things done: manage your time like a pro so you can actually finish your tasks and projects on time. There’s nothing like the feeling of shipping something impactful to production quickly and reliably (bonus points if you address tech debt in a smart way).

2. Work smarter: streamline your workflow, keeping your projects organized and on track without the chaos. Who knows, maybe even Marie Kondo would be proud of you.

3. Boost your career: stand out with a skill set that can lead to promotions and new opportunities. No, seriously, if you’re using these skills to help your team and manager, you’ll put yourself in the limelight, and that’s a good thing.

For Engineering Managers:

1. Deliver value consistently: meet deadlines and build trust with stakeholders. If you’ve ever lost trust with customers and stakeholders due to missed deadlines, you know how much this sucks. Avoid re-enrolling in the University of Hard Knocks.

2. Juggle multiple projects and stay organized: keep all your projects aligned with company goals, keep track of all the moving parts and make sure nothing falls through the cracks. Plus, your team will thank you for the harmony where everyone knows what they are working on and their role.

3. Risk management: look around the corner to see what kind of “monsters” are lurking, spot potential problems early, and deal with them before they escalate. Obvious? Maybe. But consistency is key here, especially making sure the whole team applies a risk-up-front approach.

In “97 Things Every Engineering Manager Should Know,” Camille Fournier, author of “The Manager’s Path: A Guide for Tech Leaders Navigating Growth and Change,” talks about a common question she gets: What makes a great engineering manager? While many qualities are important, she says (and I totally agree) that the ability to build highly productive engineering teams is non-negotiable.

And what do highly productive engineering teams do? They deliver, consistently and with focus, understanding why they’re doing what they’re doing and feeling good about their work. Fournier lists several skills necessary to achieve this, and the first is - you guessed it - project management. 

Identifying stakeholders, clarifying scope and requirements, breaking work into smaller tasks, sequencing them, identifying the minimum viable product (MVP), keeping stakeholders in the loop, creating launch and release plans, and proactively identifying risks. Yep, all of this is project management.

Spotlight

I’ll be diving deeper into various project management topics in future posts.

In the meantime, if you want to start digging into project management without feeling overwhelmed, I highly recommend checking out “Project Management for the Unofficial Project Manager.” It’s a great little book.

Sneak Peek

In the next few posts, I’ll cover essential fundamentals for engineers and managers.

What’s your experience with project management? Share your thoughts, battle scars, and stories in the comments below.

Stay curious,

Ruslan

Welcome to the very first post of Beyond Basics! I’m Ruslan Spivak, and I’m thrilled to have you here as we embark on this journey together.

Why Beyond Basics?

Having worked my way up from a software engineer to a director of engineering at a Fortune 500 company, I’ve accumulated a wealth knowledge and experience that I’m eager to share. My goal with this newsletter is to provide you with valuable insights, actionable advice, and a clear roadmap to help you navigate your career in the tech industry, whether you’re just starting out or looking to move into leadership roles.

What Can You Expect?

Here’s a glimpse of what you can look forward to in Beyond Basics:

1. Actionable Advice: Practical tips and strategies that you can implement in your career immediately.

2. Personal Insights: Stories from my own career journey, including challenges, triumphs, and the lessons I’ve learned.

3. Industry Trends: Insights into the latest trends and technologies shaping the tech industry.

4. Leadership Strategies: Best practices for managing teams, leading projects, and driving success in start-up and corporate environments.

5. Growth Mindset: Resources and tips for continuous personal and professional development.

Explore My Technical Posts

In addition to this newsletter, feel free to explore some of my past technical posts focused on writing an interpreter and web server from scratch at ruslanspivak.com. These posts dive into the technical nitty-gritty and may be good for those looking to deepen their tech skills.

Engage and Share Your Thoughts

I want this to be a collaborative space where we can learn and grow together. Please feel free to share your thoughts, ask questions, and let me know what topics or challenges you’re most interested in. To get started, I’d love to know: What topics or challenges are you most interested in or facing right now?

Thank you for reading Beyond Basics and I’m excited to share this journey with you.

Cheers,
Ruslan