Introduction to Mathematical Thinking Course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
Overview (80-120 words) describing structure and time commitment.
Module 1: Welcome and Introduction
Estimated time: 3 hours
- Course objectives and structure
- What is mathematical thinking?
- Differences between school math and mathematical thinking
- Introduction to logical reasoning
Module 2: Logical Combinators
Estimated time: 4 hours
- Introduction to logical operators (AND, OR, NOT)
- Truth tables and logical equivalence
- Implication and contrapositive
- Applications in mathematical statements
Module 3: Quantifiers
Estimated time: 4 hours
- Universal and existential quantifiers
- Negating statements with quantifiers
- Order of quantifiers in logical expressions
- Interpreting complex quantified statements
Module 4: Proof Techniques
Estimated time: 4 hours
- Direct proof methods
- Proof by contradiction
- Proof by contrapositive
- Structure and style of mathematical proofs
Module 5: Set Theory
Estimated time: 4 hours
- Basic definitions: sets, elements, subsets
- Set operations: union, intersection, complement
- Venn diagrams and set identities
- Cartesian products and power sets
Module 6: Functions and Relations
Estimated time: 4 hours
- Definition and properties of functions
- Injections, surjections, and bijections
- Equivalence relations and partitions
- Order relations and their applications
Module 7: Number Theory
Estimated time: 4 hours
- Integers and divisibility
- Prime numbers and factorization
- Modular arithmetic basics
- Applications in cryptography and computing
Module 8: Induction and Recursion
Estimated time: 4 hours
- Principle of mathematical induction
- Strong induction
- Recursive definitions and sequences
- Inductive reasoning in problem solving
Module 9: Final Project
Estimated time: 4 hours
- Construct a mathematical proof using learned techniques
- Analyze a real-world problem using logical reasoning
- Submit written report with peer feedback
Prerequisites
- Familiarity with basic high school mathematics
- Willingness to engage in abstract thinking
- Basic computer literacy for online learning platform
What You'll Be Able to Do After
- Develop logical reasoning and problem-solving skills
- Understand mathematical proofs and their applications
- Think abstractly and critically about mathematical concepts
- Apply mathematical thinking to real-world problems
- Prepare for advanced studies in mathematics and related fields