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Advanced Methods of Proof and Mathematical Reasoning

12th Grade · Math · Open Global Math

11 lessons

Goal

Construct, analyze, and evaluate formal mathematical arguments using deduction, exhaustion, contradiction, contrapositive, and induction across number theory and algebra.

11 lessons
0 of 11 done
  1. Direct Proof and Deductive Reasoning in AlgebraUp next
  2. Proof by Exhaustion and Finite Case AnalysisNot started yet
  3. Formulating Counterexamples to Disprove ConjecturesNot started yet
  4. Logical Structure of Proof by ContradictionNot started yet
  5. Proving the Irrationality of Square Root of 2 and SurdsNot started yet
  6. Proving the Infinitude of PrimesNot started yet
  7. Proof by Contrapositive in Number TheoryYou are here
  8. Divisibility and Modular Arithmetic ProofsNot started yet
  9. Principle of Mathematical Induction for Sums and SequencesNot started yet
  10. Mathematical Induction for Inequalities and DivisibilityNot started yet
  11. Critiquing and Correcting Flawed Mathematical ProofsNot started yet
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Learning standards covered

GlobalOGM.13.PRF.1Open Global Math Standards 2026™ · 12th Grade

Construct rigorous mathematical arguments and formal proofs using deduction, exhaustion, disproof by counterexample, and proof by contradiction (including the irrationality of √2 and the infinity of primes); apply number-theoretic principles to justify relations involving natural numbers.