Self-study Plan For Electrical Engineering

Why Now?

Brain-computer interfaces (BCIs) have been a fascination of mine for years, and with recent breakthroughs in non-invasive neural decoding, miniaturized implants, and AI-driven signal processing, 2025 feels like the right time to get serious. Last summer, I decided to stop passively reading about BCIs and start actively preparing to contribute to the field.

So far, I’ve deep-dived into foundational neuroscience through Fundamental Neuroscience, The Hippocampus, and various review papers. That gave me enough grounding to parse contemporary journal articles, which I now regularly read to stay current with the research.

Where I’m lacking is on the engineering side. I earned an applied math degree and then spent 13 years in industry—first as a quant at a hedge fund, then as a software developer and eventually a technical lead. In that time, I never touched electrical engineering, embedded systems, or hardware design. And now I want to fill that gap.

This personal curriculum is my roadmap for doing exactly that.

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The 2025 Approach

Over the next 12–24 months, I’m taking a hybrid approach:

1. Self-study through textbooks based on a modern Electrical and Computer Engineering (ECE) curriculum—loosely inspired by the University of Waterloo’s 2025 undergraduate track.

2. Hands-on projects that reinforce theory with real-world experimentation.

3. Community learning, ideally via a small, focused study group of people interested in BCIs, neurotech, or hardware for healthtech. If that sounds like you, please reach out—collaboration will make this more effective and more fun.

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Key Concerns

1. Missing Unknowns

I’m sure there are blind spots I’m not even aware of—especially in areas like biocompatibility, implantable power systems, or advanced signal acquisition. If you work on ultra-low-power, implantable medical devices, I’d love to talk.

2. Transitioning to Application

Once I’ve built this foundation, what’s next? I don’t yet have a concrete path into BCI work—whether academic, startup, or industry—but I'm hoping the network I build along the way helps guide that step.

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📘 Phase 1: Core Hardware Foundations (2025)

🔧 Projects

• Breadboard a digital clock (or a neuromorphic variant?)

• Explore simple signal amplification from a bioelectric source (e.g. EMG)

📚 Study Plan

• Electricity & Magnetism
  Textbook: Electricity and Magnetism by Purcell

• Digital Circuits & Systems
  Textbook: Digital Design and Computer Architecture – Harris & Harris 

• Linear Circuits
  Textbook: The Art of Electronics – Horowitz & Hill 

• Electronic Circuits
  Textbooks:

  • Microelectronic Circuits – Sedra & Smith

  • Microelectronics – B. Razavi 

• Materials Chemistry for Engineers
  Textbook: Chemistry: Molecular Nature of Matter and Change – Silberberg

• Signals & Systems
  Textbook options:

  • Signals and Systems – Oppenheim & Willsky

  • Linear Systems and Signals – B.P. Lathi

✅ Already Covered

• Math fundamentals (calculus, linear algebra, probability, transforms)

• Software development & system design (>10 years of experience)

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⚙️ Phase 2: Intermediate Systems & Applications

🔧 Projects

• Build a basic analog/digital radio

• FPGA-based signal processing prototype

• Real-time embedded system for biosignal acquisition (e.g. heart rate monitor)

📚 Study Plan

• Embedded Microprocessor Systems
  Textbook: TBD

• Digital Hardware Systems
  Textbook: TBD

• Communication Systems I
  Textbook: Intro to Analog & Digital Communications – Haykin & Moher

• Control Systems
  Textbooks:

  • Feedback Control of Dynamic Systems – Franklin et al.

  • Feedback Systems – Åström & Murray

• Information Theory
  Refresher only

• Digital Signal Processing (DSP)
  Textbook: Foundations of Signal Processing – Vetterli et al.

• Electronic Devices
  Textbook: Semiconductor Physics and Devices – Neamen

• Microwave & RF Circuits
  Textbook: Fundamentals of Microwave and RF Design – Michael Steer

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🚀 Phase 3: Advanced Topics & Electives

💬 Checkpoint

Before diving into this phase, I’ll be actively seeking advice from people working in neural interfaces and medical-grade electronics to validate whether I’m missing any vital topics or practical know-how.

🔧 Projects

• TBD (likely something in closed-loop neural stimulation or wireless data transfer from an implant)

📚 Study Plan

• Communication Systems II
  Textbook: Communication Systems – John Proakis

• Wireless Communications
  Textbook: Wireless Communications and Networking – Mark & Zhuang

• Micro/Nano Fabrication
  Textbook: Micro and Nano Fabrication Technology – Yan

• Integrated Analog Electronics
  Textbook: Analog CMOS Integrated Circuits – Razavi

• Integrated Digital Electronics
  Textbook: Digital Integrated Circuits – Rabaey et al.

• Radio Wave Systems
  Textbook: TBD

• Digital Control Systems
  Textbook: TBD

• RF Integrated Devices and Circuits
  Textbook: TBD

• Geometrical & Physical Optics
  Textbook: TBD

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Final Thoughts

This is a living plan, subject to iteration as I learn more and talk to people in the field. If you're also exploring BCIs or neurotech in 2025—whether as a hobbyist, researcher, or entrepreneur—I’d genuinely love to hear from you. Let's build something together.

Self-Studying the MIT Applied Math Curriculum

A Deep Dive into Applied Math – The Self-Taught Way

This summer, I’ve committed to an intellectually ambitious (and deeply personal) project: independently completing the MIT Applied Math Curriculum. I’ll be auditing classes (in person and online), connecting with professors and mentors, and tackling the OpenCourseWare (OCW) assignments and exams wherever available.

In this post, I’ll outline the motivations behind this journey, share a bit about my academic and research background, and lay out the specific plan I’m following. If you're mainly interested in the course list, feel free to skip down to The Plan.

 

Why Take on the MIT Applied Math Curriculum in 2025?

Currently, I’m a dual Master’s student at Harvard and Georgia Tech, specializing in Machine Learning and Computational Biology. I also serve as a research assistant across several labs, where I work at the intersection of Applied Math, Theoretical Neuroscience, and Deep Learning. My previous experience includes co-founding an ML startup. This fall, I’m preparing to apply to PhD programs focused on AI and mathematical biology.

My journey here hasn’t been linear. I originally studied Biology and Cognitive Science at UC San Diego, and my early internships leaned toward Product Management. Along the way, I taught myself to code—initially for web and mobile development—and gradually became captivated by the parallels between information processing in computers and biology. That fascination, particularly with neural networks, led me into graduate programs in CS and Biology, where I began conducting ML research and independently learning the mathematical foundations necessary to interpret cutting-edge papers.

 

As I progressed, something unexpected happened—I fell in love with math itself. Although foundational topics like Linear Algebra, Probability, and Vector Calculus are often sufficient for ML, I’ve noticed that the most innovative thinkers around me draw upon a much broader and deeper mathematical toolkit. They’re able to tap into concepts from PDEs, Dynamical Systems, Numerical Methods, and Optimization Theory, and apply those ideas in novel ways.

After speaking with mentors, including professors and graduate students from Harvard and MIT, the consensus was clear: if I want to push the boundaries of my research and sharpen my mathematical intuition, pursuing a rigorous curriculum like MIT’s Applied Math track is an excellent foundation.

I've been fortunate to gain access to audit select courses, both online and in person, and this self-directed program is my way of organizing, committing to, and sharing that experience. Hopefully, others interested in ML, bioinformatics, or computational theory might find this roadmap helpful too.

The Plan: Courses I’ll Be Studying

MIT’s Applied Math curriculum is thoughtfully designed, blending mathematical theory with real-world applications. I’ve selected a sample path based on the 2024–2025 course listings, emphasizing courses available via MIT OCW, edX, and other open resources, supplemented with similar material at Harvard, Georgia Tech, and nearby institutions.

 

✅ Core Courses (Foundation Building)

• 18.03: Differential Equations

• 18.06: Linear Algebra

• 18.100B: Real Analysis

• 18.330: Introduction to Numerical Analysis

• 18.600: Probability and Random Variables

• 18.700: Linear Algebra (Theoretical)

🧠 Restricted Electives (Applied Focus)

• 18.303: Linear Partial Differential Equations

• 18.330: Numerical Methods for PDEs

• 18.404: Theory of Computation

• 6.041A/B: Probabilistic Systems Analysis

• 6.036: Introduction to Machine Learning (MIT AI curriculum)

• 18.650: Statistics for Applications

   

🔄 Electives and Supplementary Topics

• Optimization Theory (18.335 or equivalent)

• Stochastic Processes

• Information Theory

• Dynamical Systems

• Mathematical Biology (as applicable to my research)

What Comes Next?

I don’t plan to rigidly confine this journey to a summer timeline. While I’ll be actively involved in summer research and class auditing, this project will evolve organically throughout the year. My goal isn’t just to tick off course boxes, but to deeply internalize the material—to make the math intuitive, applicable, and generative for future work.

I’ll be posting updates, study notes, problem solutions, and reflections here periodically. Ideally, this process will lead to:

• More elegant and powerful approaches to ML modeling

• Cross-disciplinary research ideas

• New ways to think about problems in neuroscience and biology

And who knows—once I’ve finished Applied Math, maybe I’ll give the Pure Math curriculum a shot next!

 

Follow Along If you're curious, want to join the ride, or have resources to suggest—drop a comment or connect. I’m excited to see where this self-studying journey leads!