Appendix B — Problem Sets
Structured practice for Chapters 0–2
These sets train you to recognize the mathematical structure of a chemical problem before choosing an operation. A numerical answer without units, reasoning, or interpretation is incomplete.
| Set | Problem set | Companion sections | Main mathematical object |
|---|---|---|---|
| 1 | Seeing the structure | Prologue | object, representation, constraint, scale |
| 2 | What kinds of numbers? | §1.1 | \mathbb N,\mathbb Z,\mathbb Q,\mathbb R,\mathbb C |
| 3 | COLLECTION: counting chemical possibilities | §1.2–1.3 | factorials, permutations, combinations, multiplicity |
| 4 | DIRECTION: vectors and bonds | §2.1–2.2 | components, magnitude, unit vectors, vector sums |
| 5 | DIRECTION: angles and projections | §2.3 | dot product, projection, cross product |
For extended vector practice there is also a printable supplement: Vector chemistry problem set (PDF).
When you are done, submit your answers here. Log in with the access code your instructor gave you. You can resubmit any time; the newest version replaces the old one.
Expectations
- State what mathematical object you are using.
- Show a symbolic setup before substituting numbers.
- Carry units through every physical calculation.
- Report sensible significant figures.
- End modeling problems with one sentence of chemical interpretation.