EulerFoldDiscrete Mathematics: From Logic to Proofs and Algorithms
“Master the core concepts of discrete mathematics, including logic, proofs, combinatorics, number theory, and probability, with rigorous techniques and practical applications.”
Logical Foundations and Set Theory
By the end of this module you will be able to construct rigorous logical arguments, manipulate sets, define functions and relations, and model discrete structures.
Proof Techniques and Induction
By the end of this module you will be able to prove statements using direct, indirect, and inductive methods, and apply recursion to define sequences.
Combinatorics and Counting
By the end of this module you will be able to count arrangements using permutations, combinations, inclusion‑exclusion, and generating functions.
Number Theory and Discrete Probability
By the end of this module you will be able to analyze divisibility, modular arithmetic, and apply discrete probability models, and correctly interpret p‑values in hypothesis testing.
References
Week 1: Logical Foundations and Set Theory
Week 2: Proof Techniques and Induction
Week 3: Combinatorics and Counting
Week 4: Number Theory and Discrete Probability
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