Structure of Mathematical Proof: Direct Deduction and Exhaustion

7 lessons

Goal

Construct direct algebraic proofs, deductions from axioms, and proofs by exhaustion for finite cases and number-theoretic properties.

Propositions, Logical Connectives, and Quantifiers in Mathematical Proof

7 lessons

0 of 7 done

Propositions, Logical Connectives, and Quantifiers in Mathematical ProofUp next
Constructing Direct Deductive Proofs for Algebraic IdentitiesPremiumNot started yet
Direct Proofs of Divisibility and Integer Parity PropertiesNot started yet
The Fundamental Theorem of Arithmetic: Every Number Has a Unique FactorisationNot started yet
Proof by Exhaustion: Case Analysis for Finite DomainsNot started yet
Proof by Cases Using Modular Arithmetic ResiduesNot started yet
Verifying Geometric and Algebraic Properties via Deductive ChainsNot started yet

Standards Covered

Curriculum Framework

7 lessons

Construct direct algebraic proofs, deductions from axioms, and proofs by exhaustion for finite cases and number-theoretic properties.

7 lessons

Master indirect proof methods including contradiction, contraposition, and finding minimal counterexamples to refute conjectures.

6 lessons

Analyze the topological structure of the real line, including Archimedean property, density of rationals, and the completeness axiom.

6 lessons

Manipulate complex surd expressions, apply index laws across all rational exponents, and rationalize multi-term radical denominators.

8 lessons

Perform arithmetic on complex numbers in Cartesian form, compute modulus and conjugates, and graph loci in the Argand diagram.

7 lessons

Convert between Cartesian, polar, and Euler's exponential forms, compute products and quotients, and evaluate powers via De Moivre's Theorem.

8 lessons

Apply the Fundamental Theorem of Algebra, factor polynomials completely over the complex numbers, and solve higher-degree equations.