Why we organised the physics roadmap this way

I finished my integrated master’s in physics in 2022, but I have used the subject only occasionally since then. When I started thinking about returning to it, having the degree didn’t tell me where to begin. I had studied these ideas before; I couldn’t assume that I still understood them well enough to use them. I was prepared to revisit the basics, work through derivations, and solve problems. What I needed first was some way to see the extent of the work ahead.

There was no examination to define a syllabus and no deadline to decide how much I could cover. I wanted to learn physics for the sake of understanding it. That freedom left me with decisions a course would usually make for me: which topics belong together, how deeply to study them, and what I need to understand before moving on. Physica’s roadmap grew out of trying to make those decisions visible, both for myself and for someone approaching the subject independently.

Deciding how far to go

A book gives me a place to start, but its last chapter does not necessarily mark the end of a subject. An introductory mechanics book might build a strong understanding of forces and energy while leaving analytical mechanics for a later course. An advanced book can assume preparation that I have forgotten or never studied.

The roadmap begins with high-school and entry-level material, builds towards broad undergraduate coverage, and continues into selected postgraduate topics. We want that preparation to help readers develop their physical intuition and choose directions for independent study, including work beyond a master’s degree. A branch ending on the map means our coverage stops there, not that the subject does.

There is room to extend the route in either direction. We can add earlier foundations when a topic needs more preparation, or continue into a specialised subject when there is a reason to do so. For now, keeping those boundaries gives us a useful scope to develop without trying to account for someone’s entire education or every possible research direction.

Setting those boundaries came before deciding how many strands or segments we needed. Without them, every missing topic could become a reason to expand the project. We needed to distinguish material that belonged within our intended coverage from a direction we could leave for later.

Building a topic inventory before drawing the map

We compared topic lists from several books and university curricula to find gaps and reconsider the order. A single source reflects its audience and purpose: a course has limited teaching time, and a book may leave some preparation to another volume. Comparing them helped us separate recurring material from differences in emphasis.

We used those references to build and review the topic lists, then decided how to group them. Copying chapter boundaries would have inherited one author’s teaching sequence without explaining why it suited our roadmap. The useful questions were whether a topic belonged within our scope, what preparation it assumed, and which neighbouring ideas helped it make sense.

Coverage still needs review. When we postponed something, we kept a note of it so that a decision to address it later would not become an accidental omission. This gave us a way to keep working without pretending that every boundary was settled.

Subjects, segments and topics

We use a strand for a recognisable subject, such as classical mechanics or optics. Within it, segments group related material into learning units. Each segment contains a list of topics and subtopics in a suggested study order. These levels answer different questions: which subject we are following, which portion of it belongs together, and what someone needs to study within that portion.

The five broad theoretical branches give us a starting structure: classical mechanics, electromagnetism, thermodynamics and statistical mechanics, quantum mechanics, and relativity. They do not replace subjects such as acoustics, condensed matter physics or astrophysics. Those deserve their own paths when they have enough connected material to study in their own right. A subject can draw on several branches, so we cannot organise everything as a tidy tree with one shared starting point.

We chose strands for subjects that could support a continuing sequence of related learning units. A strand may begin with only one segment while the material is being developed; the reason for keeping it separate is the subject’s identity and room for progression. A new technique or example does not automatically need a strand of its own.

We also label segments Foundations or Advanced. These describe progression within a subject. Foundations in quantum field theory will still require substantial preparation elsewhere. The label does not mean that the segment is suitable for a beginner in physics.

Making each segment worth a stop

As the physics map grew past 150 segments, the size of each learning unit became important to how easily someone could follow it. We wanted to keep the breadth of the subject while giving readers fewer, more meaningful stops along the way.

We reviewed consecutive segments and merged those that formed a coherent learning unit. The topics stayed; some of the boundaries changed. Lagrangian mechanics and related mechanical systems, for example, can share a segment with an internal progression through their topics. Early material such as kinematics and Newton’s laws still has separate stops because those distinctions help someone beginning the subject.

A larger segment is easier to place on the map but takes longer to work through. We merge material when it belongs together, has a sensible internal order and does not create a circular dependency. If combining two segments means the new unit requires another unit that already depends on it, the proposed grouping needs to change. A smaller count alone cannot justify that merge.

The title provides another check. It should name what the segment actually covers in terms someone can recognise. If we can only describe the contents with a vague label or a string of unrelated subjects, the grouping probably needs another look. We settle the content first, then choose the title; we do not rearrange topics merely to make a name work.

The lists use topic names that readers can search for in a book, course or lecture. They are not lessons or a catalogue of every possible problem. Models such as projectiles, collisions and oscillators belong alongside the concepts they help us study. Working through those models matters, but we do not need a separate “applications” segment after every law.

Reading order and prerequisites are different

A sensible next topic does not always require everything in the previous one. Circular motion can follow a discussion of collisions without depending on collision theory. A map based only on prerequisites can split a subject into several paths without making its suggested reading order clear.

That led us to record two different relationships: suggested continuation and required preparation. “This is a useful next step” is a teaching decision. “This needs an idea introduced there” is a dependency. Keeping them separate lets us propose a continuous route without inventing requirements to make the drawing look tidy.

For each prerequisite, we ask what specific knowledge would be missing without it and where that knowledge is introduced. For the reading order, we ask which next step develops the subject sensibly. The order generally moves from foundations towards more advanced methods, but related models can appear where they help explain an idea.

Prerequisites point to segments containing the required material. You might need only part of a larger segment, and that is an accepted cost of grouping related topics. We also avoid repeating requirements already covered through an existing prerequisite. If integrals requires derivatives, a later segment that requires integrals does not need to list derivatives again.

This also explains why the structure is a graph. Several subjects can have different starting points. One segment can prepare someone for several directions, and a later segment can bring together ideas from different strands. A connection between strands does not mean that either subject ends there. Some continue independently; others support a new area that becomes worth studying as a subject of its own.

Accounting for preparation from another subject

Mathematics made the limits of a physics-only outline clear. Naming a physical topic was not enough if its treatment quietly assumed mathematical knowledge. We needed to account for that preparation without first attempting to map all of mathematics.

We chose to let the physics identify which mathematical segments to develop next. When a required idea has no suitable home, we can add a segment and, if necessary, a strand. Earlier preparation can be traced further back when it matters, while the entry boundary keeps that process from expanding indefinitely.

Within each mathematical segment, we still want a coherent treatment of its topic. Restricting it to the few operations immediately useful in physics could leave a fragmented account of the mathematics. This is a deliberate compromise: we select the segment because physics needs it, then give it enough substance to stand as a learning unit in its own right. That also makes it reusable if the mathematical roadmap grows later.

Keeping the structure readable as it grows

Even after grouping topics more carefully, the number of connections can make a map hard to read.

We separated the information we record from the amount we show at once. The underlying structure retains the prerequisites. A focused view can show one strand with its direct prerequisites, leaving earlier layers available to explore separately. Following every dependency backwards in the same view would often bring most of the map back into it.

That decision reduces visual clutter, but a focused view is only part of the graph. We should not mistake what is visible for everything that is required. The same principle applies to the suggested reading order: simplifying the presentation must not change the meaning of a connection.

Growth also needs to work within the route. A newly identified foundation might belong between existing segments, rather than at the end. Keeping topics, subject membership and relationships explicit lets us insert that material and review the affected connections. When we merge or split a segment, we need to check both its topic coverage and every reference to it. That work is what keeps expansion from becoming a collection of disconnected additions.

What carries over to another subject

The physics examples belong to this project, but the decisions are useful elsewhere. Someone building a roadmap for botany would need to choose the intended starting knowledge and depth before deciding what counts as sufficient coverage. Books and courses could help build a topic inventory; they would still need to judge which topics form coherent units and which subjects deserve continuing strands.

From there, the connections need the same care. What knowledge does a segment require? Where is that knowledge introduced? Which topic is a sensible continuation even when it is not a strict prerequisite? Answering those questions gives the graph a purpose before any lines are drawn.

What began as my search for somewhere to restart physics became a way to make these judgements explicit. The framework does not settle every curriculum decision for us. It gives us a consistent basis for making one, checking it against the material, and revising it when we find a gap. As the teaching content grows, those are the decisions I want to keep visible.