How to Ace Number Theory (and Other Proof-Based Classes)

  • divisibility
  • prime numbers
  • Diophantine equations
  • Pythagorean triplets
  • induction
  • linear and quadratic congruences
  • theorems of Euclid, Euler, Fermat, and Wilson
  • reciprocity
  • continued fractions
  • basic cryptography

The Four Stages of Competence

  • Unconscious Incompetence: you don’t know what you don’t know
  • Conscious Incompetence: you know what you don’t know
  • Conscious Competence: you somewhat know the material
  • Unconscious Competence: you effortlessly know the material

Note Taking

Strategy 0: Review Fundamentals In The First Week

Strategy 1: Daily Lecture-Note Worship



  • I can recall all definitions, theorems, axioms, and proofs covered from lecture
  • I can solve any example problem covered in class effortlessly
  • I can comfortably talk about the main ideas covered in the lecture

Strategy 2: Chunking

Strategy 3: Two-Pass Technique


  • I can solve any question from the assignment at lightning speed
  • I have a good understanding of each problem and how it relates to the topics covered in class
  • I can recall all of the definitions, theorems, and axioms the homework has covered

Strategy 4: Hard Questions Only (exam prep)

Strategy 5: Exam Performance




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