How to study maths for CS

Updated

July 30, 2025

How to study maths for CS

How to study maths for CS

Before Day 1. This volume is not a lab course and not a video binge. You understand a concept when you can define it from memory, work an example cold, prove a short claim, and solve exercises without peeking. Everything else is optional decoration.

Important

No programming labs. No VM. No repo requirement. Pen and paper (or a notes app) is the primary tool. Calculator/Python only after a hand solution, and only to check arithmetic.

What each day contains

Section Purpose
Goal One-sentence contract for the day
Why this matters CS motivation — not fluff
Theory Definitions, theorems, short proofs
Worked examples Full steps — cover, then redo
Exercises Lock the idea; graded easy → challenge
CS connection Vocabulary bridge to algorithms/systems
Pitfalls Typical mistakes
Checkpoint “Can I explain this without the page?”
Tomorrow Forward link

Gates (Days 10, 22, 34, 46, 58, 70, 80) are mixed dossiers for retention, not grades. Capstone (88–90) is a written portfolio you can defend.

Daily loop (~2–3 hours)

  1. Skim the Goal and Why (2 min).
  2. Read theory once; highlight every definition and theorem.
  3. Close the book; write each new definition on a card from memory.
  4. Cover each worked example; redo on blank paper; uncover only to check.
  5. Exercises without notes. Mark unknowns with ¿? — do not stall forever.
  6. Check solutions / re-derive; log every error.
  7. Write one CS sentence in your own words.
  8. Tick the checkpoint honestly (re-open theory only for failed ticks).

If a day overruns 3h: finish theory + half the exercises; schedule the rest next morning before new material.

Definition card (every new term)

Name:
Symbols / notation:
In words (one sentence):
One example:
One non-example:
Related to (earlier term):

Proof card (from Stage III onward)

Claim (quantifiers explicit):
Given / Assume:
Want:
Method (direct / contra / cases / induction / …):
Steps (each line justified by def, IH, or algebra):
Therefore:
Sanity check (n=2 or numeric instance):

Counting card (Stage V)

What is an outcome?
Are order / repetition allowed?
Product, sum, complement, or IE?
Did I overcount? Under-count?
Check tiny n by listing.

Graph card (Stage VI)

V = ?
E = ? (undirected / directed / weighted?)
Question type: path / cycle / tree / color / match / topo / distance?
Which theorem applies?

Error log (non-negotiable)

Keep a running list (paper or file):

Date Day What I wrote Why wrong Correct idea in one line

Weekly: re-solve only the error-log items, cold.

Weekly review (≈ 1–1.5h)

  1. One exercise from each finished gate, cold.
  2. Re-prove one induction or divisibility claim.
  3. Re-count one combinatorics problem with full justification.
  4. Skim pitfalls tables for the week’s days.

How to use gates

Approach Use
First attempt Timed-ish, closed notes
Score Honest self-rubric in the gate file
Fail a section Revisit listed days; retest that section only
Pass Archive; schedule a 2-week delayed retest

Gates beat calendars: if Gate III fails, do not rush into Stage IV counting.

Active techniques that work for this volume

Technique When
Feynman: explain aloud without notes After theory
Dual solution Counting and modular problems
Adversarial check Assume your proof is wrong; find the gap
Tiny instances Always list \(n=2,3\) before general formula
Symbol inventory Before a proof, list free vs bound variables

What “fluent” means (by stage)

Stage Fluency signal
I Evaluate mixed expressions; convert bases; state div algorithm
II Solve linear/quadratic; manipulate \(\sum\); \(2\times2\) systems
III Truth tables; negate quantifiers; 3 proof styles + induction
IV Set identities; check RST; inj/surj; pigeonhole
V Justify counts; binomial/Catalan awareness; simple recurrences
VI Model \(G=(V,E)\); trees/DAGs; BFS levels; bipartite/Hall stmt
VII Euclid + inverse; Fermat reduce; CRT; RSA story literacy
VIII \(O/\Theta\) proofs; Master cases; expectation + indicators

Tools policy

Allowed Forbidden as the lesson
Pen, paper, whiteboard “Learning by writing a program first”
Calculator to check CAS that does the algebra for you on first pass
Optional Python after hand work Notebook as primary solution method
Companion textbooks (Rosen, MCS) Skipping proofs because a video “felt clear”

When you are stuck

  1. Re-read the definition of every symbol in the claim.
  2. Try a smaller instance.
  3. Name the method (which Day taught it?).
  4. Write what you know and what you want — gap becomes the next step.
  5. If still stuck after 15 min, mark ¿?, finish other exercises, return later.

Capstone mindset (Days 88–90)

Start collecting candidate proofs and counts from Day 28 onward. The capstone is assembly and polish, not three days of new learning. Keep a “dossier candidates” page in your notebook.

Checkpoint

  • Definitions-before-exercises habit accepted
  • Error log created
  • Proof / counting / graph cards understood
  • Gate retest idea accepted
  • Tools policy clear (no labs)

Next

→ Day 1 — Integers & order of operations