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Introduction to Mathematical Thinking
- Introductory material
- Analysis of language – the logical combinators
- Analysis of language – implication
- Analysis of language – equivalence
- Analysis of language – quantifiers
- Working with quantifiers
- Proofs
- Proofs involving quantifiers
- Elements of number theory
- Beginning real analysis
Calculus
- Functions and limits
- Infinity and continuity
- The derivative
- Techniques of differentiation
- Chain rule
- Derivatives of transcendental functions
- Applications
- Optimization
- Linear approximation
- Antidifferentiation
- Integration
- Fundamental theorem of calculus
- Substitution rule
- Techniques of integration
- Applications of integration
Introduction to Logic
- The main ideas of logic
- Proofs
- Propositional logic
- Relational logic
- Relational Logic proofs – Fitch and Resolution
- Resolution theorem proving
- Induction
- First-order logic
- General Game Playing