Start here: find your next question

You don’t need to read this archive from end to end. Start with a question you actually care about. Work through one example, check the arithmetic, then follow the series when you want the next piece.

I’m gdpark. These are the conversational notes I wrote while studying physics and finance, now edited into English. The drawings stay in the flow of the explanation, so you can see the calculation while we talk through it.

Physics: from vectors to motion

Start with: vectors, basic differentiation, and a willingness to draw the axes before doing the algebra. If vectors feel unfamiliar, use the linear algebra notes alongside this route.

1. Vectors and polar coordinates — see why the basis vectors themselves can change as a particle moves.
2. Work, energy, and conservative forces — follow the route from force to a useful energy equation.
3. Oscillations and damping — use that machinery on a system that moves, loses energy, and settles down.

After those, follow the mechanics series into driven motion and reference frames. Want a different puzzle? Try time dilation. For thermal physics, begin with counting states and Stirling’s formula before jumping into partition-function problems.

Finance: prices, returns, and risk

Start with: percentages and ordinary algebra. Probability becomes useful when we reach uncertainty; you can return to the math route below.

1. What stock market indices measure — calculate a small index yourself and see why the weighting rule matters.
2. Averaging portfolio returns — separate the different questions hidden inside the word “average.”
3. Risk and the risk premium — connect possible outcomes with expected return and dispersion.

The basic investing series keeps those pieces in order. If discounted cash flows are the part you want to unpack, take a detour through the time value of money. These examples are for understanding calculations, rather than choosing an investment for your own circumstances.

CFA: connect accounting with valuation

Start with: a patient look at what the statements describe. You do not need to know all the account names before opening the first note.

1. The balance sheet — identify what a company owns, owes, and leaves to its shareholders.
2. Income and cash flow statements — distinguish earning revenue from receiving cash.
3. Continue through the Level 1 notes in order as the accounts become more detailed.

Already comfortable with financial statements and discounting? The arbitrage-free valuation framework leads into the binomial bond model. Only then move to bonds with embedded options and their worked valuation. The dates on these study notes identify the original writing; use the curriculum for your own exam when checking current coverage.

Math: understand the step instead of memorizing it

Start with: algebra; differentiation and integration for the calculus derivations. A drawing can help, but pause and write a line yourself too.

• Vector spaces → linear dependence and independence: find out what it means for vectors to bring genuinely new directions.
• Moment generating functions → the Poisson distribution: connect a distribution to its moments and see a limiting argument at work.
• Gaussian integrals: follow parameter differentiation into integrals used in thermal physics.

If you already know binary logistic regression and Python, the one-vs-rest classification example shows how to extend a two-class model. It is a standalone worked note here, not a complete beginner’s AI course.

How to use a note

Read the question before the equations. Try the next algebra step before looking at the drawing, then compare the assumptions as well as the answer. Use Previous and Next to stay in series order. A Heads-up explains a known slip in an original drawing; the surrounding text gives the corrected calculation.

If a step still doesn’t make sense, send me the article and the line. You can also browse all notes or search a term. The editorial policy explains how English adaptation, AI assistance, and corrections are handled.